On the Elements of Ontology: Attribute Instances and Structure 9783110455212, 9783110454208

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D. W. Mertz On the Elements of Ontology

Philosophische Analyse/ Philosophical Analysis

Herausgegeben von/Edited by Herbert Hochberg, Rafael Hüntelmann, Christian Kanzian, Richard Schantz, Erwin Tegtmeier

Band/Volume 68

D.W. Mertz

On the Elements of Ontology Attribute Instances and Structure

ISBN 978-3-11-045420-8 e-ISBN (PDF) 978-3-11-045521-2 e-ISBN (EPUB) 978-3-11-045451-2 ISSN 2198-2066 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2016 Walter de Gruyter GmbH, Berlin/Boston Printing: CPI books GmbH, Leck ♾ Printed on acid-free paper Printed in Germany www.degruyter.com

| To Polly, Emily, and Ryan

Contents Preface | IX 1 1.1 1.2 1.3 1.4 1.5 1.6

2 2.1 2.2 2.3 2.4 2.5 2.6

Overview: Attribution, Structure, and the Five Forms of Composition | 1 The Overarching Thesis: Ubiquity of Structure and Ontic Primacy of Attribution | 1 Previewing Attributes as Structuring IntensionedCombinators | 28 Intension Universals and the Five Types of Unification | 34 On the Emergence of Attributes and Wholes | 44 On the Fictive Nature of Unifier-less Wholes: Formalized Sums and Sets | 53 The Proposed Holism via Attribute Instances as the ‘Primary Beings’ | 66 Instance vs. Classic Ontology: Individuation and Adherence | 72 Classic Aristotelian/Common-Sense Assumptions | 72 The Classic Assumptions in Aristotle’s Metaphysics | 76 The Dependence Contradiction and Individuation Regress | 93 The Alternative of Absolutely Bare Particulars and Their Incoherence | 97 The Alternative of Near-Bare Particulars and Their Error | 109 The Specious Inherence Model of Attribution and Property-Reduction of Relations | 112

3.3 3.4

Instance vs. Classic Ontology: Intensions and Unification | 126 Further Problems Via the Classic Assumptions, E.g., Bradley’s Regress | 126 Implying the Alternatives of Relation Elimination or Substance Monism | 130 Denying Attribute Dependence: Bundle Theories | 137 Hume and the Denial of the ‘Inseparability’ of Attributes | 143

4 4.1 4.2 4.3

Atomic Structures: Facts and Their Natures | 167 Structural Unity via Attribution; Facts as Atomic Structures | 167 On Intensions and Their Prescribed Foundations | 173 Assaying Attributes as Intensioned Combinators | 187

3 3.1 3.2

VIII | Contents 4.4 4.5 4.6 4.7 5 5.1 5.2 5.3 5.4 5.5 5.6

The Individuation of Attributes | 200 Attribute Intensions as Universals | 206 The Simple ‘Continuous Composition’ of Attribute Instances | 220 Summary | 228 Complex Structures and Ontic Atoms | 231 Complex Structures by Inter-Attribute and Emergent Composition | 231 Attribute Instances as ‘Primary Beings’ | 241 The Identity and Indiscernibility of Structured Entities | 250 Answering the Problem of Composition | 257 Some Implications: On Dispositions, Causation, and Change | 266 Conclusion: The Route to Realist Instance Structuralism | 279

References | 291 Index | 301

Preface This work is a study in analytic ontology. It has as an initiating thesis what is fundamental in the genesis of any ontology: the truism generalized from ordinary experience that all that exists divides exhaustively, though not dichotomously, into subjects and their attributes (qualities, characteristics, modes, descriptors). All entities, including attributes, are subjects of characterizing/ descriptive attributes—properties and relations. E.g. and in standard symbolism, for certain planet b and moon c, we have the attributions (and so the facts that) Has-Mass(b), Gravitationally-Attracts(b,c), Is-a-Basic-Force(GravitationalAttraction). Included are conceptual entities, e.g., grammatical subjects and predicates that are themselves subjects for specific but tacit syntactical and semantical relations and whose unions (e.g., those of propositions) allow us to think and communicate about all entities and their attributes. Among an ontology’s central claims are necessarily those that derive from its critique of further expansions of the subject-attribute distinction. Intuitively and classically, these ostensible refinements include the following. It is an apparent fact that reality consists of a plurality of entities, some ‘unrepeatable’ individuals or particulars (objects, ‘substances’, e.g., sun a and planet b), where each exists in non-arbitrary unions with specific attributes (some of single subjects, e.g., Is-Hot(a), some of multiple subjects jointly, e.g., Revolves-about(b, a)), and, essentially, where each attributional union obtains because the attribute is somehow what its subject(s) is(are jointly). An attribute is a ‘way’ its subject(s) is(are). More refined, attribution is a type of asymmetric union involving a property or relation and its subject(s) whereby the attribute is both formative and informative of the reality that composes or subsumes its subject(s). Attributional unions are formative of resultant wholes that are the tradition’s facts or states of affairs. And they are informative because, prima facie, an attribute is or has in some sense a ‘shareable’ or ‘repeatable’, and so classificatory, intension (qualitative aspect or content, quiddity (Latin: ‘whatness’), connotation, sense, meaning, e.g., the senses of the terms ‘mass’ or ‘revolution’) that sets prerequisite conditions on potential subjects. More specifically, an intension is a determinate kind or sort, what as such is intrinsically an ‘other-entity descriptor’ in that it specifies (as laid out in its definition) conditions that other entities must satisfy in order for it or its attribute to qualify them (e.g., the criteria for having mass or to revolve about something). When a subject (or subjects) do so satisfy these descriptions, there is then a non-arbitrary attributional union of the thus relevant attribute with it (or among them). Further, an intension has as its identity condition that of synonymy, and it is the intension that in some

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sense is ‘the same’ in conditioning the attributional union of itself or its attribute with different (sets of) subjects—its ‘extension’ (e.g., as the property of HasMass can be had by distinct objects a and b). In sum, it would seem that every entity has its being in various ways, kinds, or sorts, these being ‘repeatable’ intensions that are, or are parts of, attributes— properties or relations—that either give, or are founded in and so are descriptive of, part of the reality that either composes or subsumes their subjects. Every ontology is in fundamental ways a critique—as either integrative affirmations, eliminative reductions, or reasoned denials—of these theses and their elaborations. In ways displayed herein, a developed theory will provide further specifics, principally in its mutually related accounts of unification/composition and of the nature and role of the intensional, and, utilizing these, its accounts of complex being and ontic dependence. Crucial, then, to ontology, as it is derivatively so for epistemology and logic, is a correct understanding of the nexus of qualitative relevance that is the ‘having’ of attributes by their subjects. My intent is to make this clear first with a preliminary analysis of the historically prominent but much criticized (in some ways to be detailed) and reacted-to Aristotelian/‘common-sense’ ontology. There the primary complementary categorization is proposed to be between ‘substances’ and their ‘properties’ (‘qualities’, ‘accidents’, ‘modes of being’), their defining specifics determined in the context of certain classic assumptions (key ones below) regarding the attributional union and the role of an intension in it, assumptions often tacit in the debate and that, I will detail, are mostly false. I will argue that the principal failure here, and indeed remarkably across and retarding of the entire tradition, is the absence of a penetrating analysis and so a proper and implicationally rich understanding of composition generally, and of attribution in particular. To this point, a central project of this work will be an extended analysis of attribution—the intension-determined unions properties and relations have with subjects they thus characterize. Founding what I will detail are its profound implications for a comprehensive ontology, one corrective of many classic and persistent errors, will be an assay of the nature of an attribute’s defining union with its subject(s) whereby they jointly form a single structured whole—a fact (or state of affairs). In particular, the following will display how attributes proper, and as distinct from linguistic/grammatical predicates for which some are referents, are constituent structurally-unifying causes of factual wholes, the latter being truth-makers for certain propositions containing the corresponding predicates. An example is the structuring unity determined by the spatial relation Is-Between among entities a, b, and c whereby they jointly form the complex existent that is the fact

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that b is between a and c. This fact-structure is the reality grounding the truth of the proposition that ‘b is between a and c’ and the falsities of other propositions such as ‘a is between b and c’ and that ‘b is not between a and c.’ (Propositions are themselves facts but of cognitive origin and dependence, wholes generated by implicit semantic relations, and, together with certain corresponding facts (extra-conceptual or conceptual) they are descriptive of, are joined together to form next-level facts under the relation Has-as-a-Truth-Maker.) Intuitive in our example, it will be argued that all attributionally generated unification results in wholes that are ‘more than the sum of their parts’, each itself being internally organized by its attribute according to its intension and thus externally the subject of emergent attributes not had by its parts arbitrarily collected in mereological sums or sets, e.g., in the example what is a specific ordering. More specifically, it will be argued how all attributes correctly assayed, both monadic properties and polyadic relations, and existing both extraconceptually (e.g., spatial, temporal, efficient-causal) and conceptually (e.g., semantic, logical, psychological), are ontically primary and ineliminable as fact-generating unifiers. And it will be shown how derivative of attributes so understood all Reality is a dynamic hierarchical system of facts and their emergent wholes networked via what are the only ontic atoms of composing and inter-connecting attributes. Among its benefits the analysis will display how attributional unification can give an integrative explication of the concepts involved in the central ontological dichotomies of independence|dependence, particular|universal, and (equally primary I will argue) structured|unstructured unities. A particular implication will be how attributional unification founds epistemology in giving a specific account of the bridge between knower and known, e.g., of the isomorphisms between structured phenomenon and structures known. The primary ontological status of attribution has been recognized from the beginning of Western philosophy, but its nature as fact-generating unification has remained obscure and disputed. Construals of attribution found in the tradition include: a) ‘participation’ in Platonic Forms, b) the structuring agency of Aristotelian substantial and accidental form-attributes, with some, if not all, attribution taken to be in some manner inherence in the resultant whole, c) in every case an external union of either a relation or a ‘non-relational tie’ with supporting and collecting substrata; or as derivative of more fundamental kinds of unifiers such as d) Humean association, e) bundle theory ‘compresence’, or f) those implicit in mereological ‘sums’ (‘fusions’) or in sets (classes). Across these proposals are represented the possible forms of oneness among the nonidentical: internal inherence as unity by the container on and among the con-

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tained, or external adherence by either a mediating relation or an immediate non-relational tie. And with the latter, when the tie is held uncontrolled by any qualitative/intensional relevance between the attribute and its subject(s), this is the arbitrary union explicitly intended by Humean association, and is necessarily the nature of the compresence unifier of bundle theories, as well as the implicit essential unifier for the sums of mereology and the sets of set theory (I shall argue). As either inherence or adherence, proffered assays have remained impotently problematic, this exhibited in the dialectic between the two now prominent theories of attribution—substratum and bundle theories—a dialectic that, as I assess it, persists in unprogressing stalemate. It is in response to this persisting state of frustrating obscurity that I offer this work as a clarification of the nature of attribution, one that will have broad synthesizing implications for ontology, including and giving warrant to the analysis, the solutions to a number of fundamental and classic problems. Principal among these implications, and hitherto crucially absent from the tradition, are advancing insights into what is the required nature of any union among the non-identical (importantly: this including but not the same as unification among the discrete) and, with this as a guide, the identification of what are the five modes of all composition. And seen will be how attribution is essential, directly or indirectly, to all other types of composition. The analysis will proceed in the context of a correlative project of developing an ontology of structure. The importance of the latter is the neglected fact that structure (system, organization, gestalt), in its most general sense intuited as any ‘ordered inter-connectedness’ (not just spatial-temporal and/or causal), is a ubiquitous feature across the content of all of which we are aware, and therefore demands a serious ontological account. And it is, I will argue, both within structures that the nature of attribution is ‘writ large’, and that reciprocally the latter properly expanded explicates the nature of structure. The synthesizing result of this mutual clarification will be a refined ontology of attributes where their natures as fact-generating unifiers will be made precise under what I intend by the descriptor ‘intension-determined agent-combinators’. So understood it will be seen how attributes are necessarily individuated as ‘instances’, and then how as such they can as a single category serve to found the existences of all other entities as or derivative from structures. I.e., attribute instances are ontologically primary in the sense of Aristotle’s prōtē ousia (‘primary being’). I will detail how, on the theses warranted by the analysis, attributes as instances can generate all other entities and forms of unification, and in this way found all forms of ontic dependence. Brought into sharp relief will be five necessary and sufficient forms of ontic unification: four deriving directly

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from attribute instances—what is either the ‘continuous composition’ among the non-discrete parts of each instance or the ‘articulated composition’ of instances externally on their subjects and so forming structures, i.e., facts and their compounds—and a fifth form, emerging upon the specific structures that are minds, of articulated but subject-indifferent cognitive associations. In these ways all composition is ‘restricted’ by the prerequisite ‘selecting and collecting’ natures of either attribute instances or individual associations. In particular, we will have under the developed assays of attribution and association a refined and integrated account of the prima facie given of both ‘necessary’ and ‘arbitrary’ (Humean) ‘connections among distinct existences’, and how attribution is a, if not the, source of all ontological/metaphysical necessity, this in a way that likewise accounts for real contingency. Crucial insights will be the manner in which agency (power/efficacy) is essential equally to attributions and to associations (the latter contrary to a primary Humean assumption), this as both are necessarily states of, in Aristotelian-like terms, outwardly-achieving unification, and how the intension-controlled unifying agency of attribution is ontically fundamental and the source of nomic necessity. The developed theory of individuated properties and relations proprietary to their subject-sets is a realist version of a perennial ontology now popularly termed ‘trope theory’. The term, however, is widely associated with the nominalist version that denies universals in addition to their instances, and so I shall avoid its usage. I will argue to the contrary that intensions are universals—are numerically common qualitative content across all exactly resembling instances—and, far from the charge that universals in addition to their instances are redundant, I will lay out how universals are both necessary and, when recognized as the combinatorially-inert intensional components of their combinatorial instances, are explanatorily potent. This work will refine the realist ontology of attribute instances I proposed in Moderate Realism and Its Logic (Yale, 1996) and in papers collected as Essays on Realist Instance Ontology and its Logic: Predication, Structure, and Identity (Ontos Verlag, 2006). A survey of the long and persistent history of individuated attributes, going back to Plato and Aristotle, is given in Moderate Realism, a history I propose to be inductive evidence for the explanatory importance and so supporting the veracity of the theory. In this work I will provide more direct arguments for the realist theory of unit attributes—particularly as to the necessity for, and the details of what is implied by, their natures as intension controlled agents—magnifying what is their power to solve ontological problems and literally provide the unifying synthesis of a comprehensive ontology.

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As a preparatory context for generating our positive theses I will detail how in Western philosophy the concepts of attribution and structure have been distorted. Symptoms of the latter are the persisting radically differing assays of attribution (e.g., inherence, adherence, the subject-irrelevant unities of sums or sets) and the, at best, peripheral attention given to and even there the lack of analytic progress concerning the nature of structure. Underlying this obscurity are distortions that are rooted in, I will argue, a set of classic and common-sense plausible, but mostly false, assumptions, theses going back to Aristotle and what in the subsequent tradition various subsets have been adopted, often implicitly. It is the falsity of most of these assumptions, or the denials of the few that are true, that are the source of the persistent distortions of attribution and structure. Central to establishing this claim will be the demonstration of how various combinations of these assumptions imply contradictions, vicious infinite regresses, or counter-factual and questionable results. These assumptions, with supporting references in Aristotle’s works, are listed as follows, an ‘(F)’ preceding the number indicating that on my analysis the assertion is false. Classic Aristotelian/Common-Sense Assumptions: A1. (Attributes as Dependent) It is of the nature of attributes to characterize/ qualify—be ontic predicates of—other ‘subject’ entities, and so to exist only in unions with, and thus be dependent for their existences upon, these subjects. In this ontic dependence, attributes are in themselves inherently ‘incomplete’ as inseparable from their subject-others, this notwithstanding the possibility of a cognitive isolation via the selective attention of abstraction. (E.g., De Inter. 16b10-11; Physics 185a30-32; Gen. & Cor. 327b23; Meta. 1017b13-14, 1028a10-30, 1069a22-25) (F) A2. (Attributes as Universals) Attributes are repeatable universals, i.e., are numerically the same for all subjects or sets of subjects they qualify/characterize. (E.g., De Inter. 17a37-b1; Meta. 999a28, 999b35, 1001b30-32, 1003a5-16, 1038b10-16, 1040a35) (F) A3. (Per se Subjects) All attributes have their beings in qualifying other entities—their correlative subjects—and in this way are intrinsically ontically dependent entities. In general, ontic/existential dependence is asymmetric and transitive, and so in order to avoid a vicious regress of prior ontic dependence (cf. Meta. 994a1ff) there must be a substratum class of per se

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subjects (the tradition’s ‘through-themselves subsistents’) that are ontically independent and support the existence of dependent entities. According to Aristotle, “If these last did not exist, it would be impossible for anything else to exist.” (Cat. 2b5) In particular, per se subjects are subjects of attribution but are not themselves attributes (they are non-attribute objects), nor are they dependent for their existences upon further attributions. (E.g., Cat. 2b4-6, 2b37; Prior Analy. 43a25-43; Physics 185a29-31, 189a30-34; Meta. 1003b5-29, 1028a10-30, 1029a21-24, 1030a10, 1037b2-3, 1038b15-28, 1049a2336) A4. (Required Essences) Every entity x has a composing positive, qualitatively delimited being and unity whereby it is a determinate and definite something and not something else, what contrasts with undifferentiated nothingness. This composing being of x—‘that by which x is what it is’—and what in its absence x would not exist, is, in the most general senses of the terms, x’s ‘essence’ or ‘nature’. This essence has components that are the foundations for certain ‘essential’ (per se) attributes, F, G, H,…., that x has necessarily (as opposed to those per accidens) and whereby this essence is intelligible, what, according to Aristotle, are included in x’s definition. (E.g., Post. Analy. 96a23-96b14; Topics 103b20-39; Meta. 1029b11-1032b14, 1041a27-b30) (F) A5. (Inherent Essential Attributes) The attributes that qualify/characterize a subject x essentially—those that go to define it—are constituents of the composing essence/being of x, this then founding their attribution to x. (E.g., Post. Analy. 73a34-35, 73b23-24, 84a13&25, 96b1-14; Meta. 1023b24, 1034b20-1038a35) (F) A6. (Non-Attribute Individuals) All non-attributes, i.e., objects, including primary subjects, are unrepeatable individuals/particulars. (E.g., Cate. 3b10; Meta. 1003a5-9, 1017b25, 1029a28-29) A7. (Attribute Agent-Organizers) There exist organized wholes, or structures, where the internal ‘ordering’ of each has as its cause one or more constituent attributes (e.g., ‘forms’) functioning as qualitatively determined agent organizing-unifiers, these attributes being jointly essential to the nature of each resultant structure as a specific kind. (E.g., De Anima 412a29-412b9;

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Parts of Animals 645a26-36; Meta. 1016b7-14, 1041a6-1041b32, 1045a71045b24) (F) A8. (Unity by the Constituent One) Every composite whole as a unification of non-identical entities has as the cause (principle, source) of its unity, and so what is essential to its existence, a shared one, what is a single (‘indivisible’) constituent entity linking all the other elements—‘Oneness is by the constituent one’. (E.g., Physics 227a13-17; Meta. 1015b16-1016b17, 1052a15b8, 1061a15-18 & 1061b12-14, 1075a12-19) Working through the errors implied by various subsets of the above classic assumptions will provide a clarity and motivation for an assay of attribution in the perspicuous context of structure where it is fundamental (what Aristotle glimpsed with A7). Specifically, to be defended are the ten theses given below, the first, T1, being a summary declaration of both the grounds and promised results of our assay. The remaining substantiating propositions divide into two groups. Theses T2-T6 jointly clarify the natures of attribution and structure in the context of the latter’s simplest form, viz., single facts. I.e., displayed in a fact, an attribute has the dual aspects of an externally connecting agent controlled as to its subjects by a specific intension, the former rendering it an unrepeatable individual—an instance, the latter requiring a descriptive fit with its subjects, and the two aspects together being non-identical but non-discrete parts of the instance. Then utilizing attributes so understood, theses T7-T10 detail how compound structures are generated hierarchically from single facts, i.e., how the single category of dependent attribute instances is sufficient to found all independent structures (no per se subjects required), and based upon this provide criteria for the identity and indiscernibility of all structures. Jointly theses T1-T10 provide a complete and precise explication of all simple and compound forms of the ‘ordered inter-connectedness’ that is structure. Note on notation: Below and in the body of the work I will use a colon locution ‘:Rni(a1,a2,…,an)’ to designate the fact (or state of affairs) composed of an attribute instance Rni as it is an ontic predicate of all the entities jointly in the ntuple , the latter Rni’s subjects. E.g., the fact that b is spatially between a and c would be designated by ‘:Is-Between3i(b,a,c)’. The expression without the colon, ‘Rni(a1,a2,…,an)’, will designate a proposition, what would have the corresponding fact as its ‘truth-maker’. On an instance term ‘Rni’ the subscript ‘i’ indicates that the instance is an individual, and without this subscript the term ‘Rn’ designates an intension that is common across and by which exactly resemble non-identical instances, Rni, Rnj, Rnk,… The superscript ‘n’

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indicates the adicity, or number of subjects, that the intension Rn requires in order to characterize them. (Super- and/or subscripts may be omitted at places in the text when no confusion will result.) The ten key theses to be argued herein can now be stated as: The Ten Primary Theses: T1. Structure (system, organization, gestalt) is a ubiquitous feature of reality, and as such not only requires an ontological account, but this account is foundational to all ontology. Specifically, an analysis of structural unity and its implications warrants an ontology with a single atomic ontic category of individuated attributes—property and relation instances, where all forms of ontic dependence and composition, and so all other existents, are those of, or derive hierarchically from, attribute instances. T2. Structure as qualitatively conditioned unification has as its simplest form single facts or states of affairs, i.e., :Rni(a1,a2,…,an), n ≥ 1, where an n-adic attribute, Rni, qualifies jointly an n-tuple of subjects. Included here are monadic properties as the limiting 1-adic case with general form :P1i(a1). The unification of a fact involves a descriptive ‘fit’ or relevance of the constituent attribute’s intension Rn with corresponding ‘foundations’ had by each subject, these foundations being either aspects of the subjects’ internal composing natures, and/or some external contextual unions had by the subjects. In this way unity of a fact contrasts with the nature- and context-indifferent unifications composing mere sets, mereological sums, random lists, or ‘heaps’. T3. In a fact :Rni(a1,a2,…,an), the characterizing attribute (instance) Rni functions as an intension-determined agent-combinator, i.e., by means of a constituent externally-directed agency, Rni is the cause of a sustained union of itself with and among its intensionally relevant subjects/relata, a1, a2, …, an. The attributional unity that Rni effects preserves itself and its subjects as each discrete, and is such that Rni is completely external to each subject—Rni is not a component of the beings of any of its subjects. As intrinsically an outward-directed unifier, an attribute Rni is ontically dependent upon concomitant subjects as recipients of its unifying agency. Hence, the Principle of Instance Instantiation: Attributes proper do not exist inde-

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pendently of their subject n-tuples, and hence do not exist independently of the subsuming facts whose unities and so existences they effect. T4. In a fact :Rni(a1,a2,…,an) the attribute/ontic-predicate Rni, in effecting an act of unification of itself with and among the elements of the subject n-tuple , is both unrepeatable, i.e., is an individual (an ‘instance’), and is existentially dependent uniquely upon this subject n-tuple. From this follows the Principle of Subject Uniqueness: If Rni(a1,a2,…,an) and Rni(b1,b2, …,bn), then a1 = b1, a2 = b2, …, an = bn. T5. An attribute instance Rni has two non-identical components: its outwardlycombinatorial agency and the latter’s controlling intension. For exactly resembling instances, Rni, Rnj, Rnk, ..., they share numerically the same qualitative content or intension: the universal Rn. Intensions/universals exist primarily as components of instances, separate from which they exit only conceptually as either derivative abstractions, or subjective creations prior to any instantiation. Intensions in themselves are non-agents/non-combinatorial, i.e., are not attributes/ontic-predicates. T6. In composing the being of an attribute instance Rni, the aspects of combinatorial agency and its controlling intension Rn are a unified whole not by attribution or association, and so though these aspects are non-identical, they are in Rni undifferentiated/non-discrete and form a seamless ‘continuous composite’. The differentiation of these aspects is posterior and external to Rni in the tradition’s ‘formal’ abstraction. In a continuous composite at least some of the parts, e.g., the combinatorial agency of an instance Rni, are reciprocally ontically dependent with the subsuming whole, e.g., instance Rni—neither prior to the other, and the unity of all the parts is by the whole, what stands in contrast to a plural ‘articulated composite’, e.g., a fact, that is ontically dependent upon prior and remaining discrete parts, and requiring as such one or more of these parts be agent-unifiers among the others. T7. All complex structures (organizations, systems, gestalten) are composed, some hierarchically, from atomic structures, i.e., facts (T2), :Rni(a1,a2,…, an), combined as follows: a) If x and y are two structured wholes (e.g., facts :Rni(a1,a2,…,an) and :Smk(b1,b2,…,bm)) having at least one constituent in common (e.g., a1 =

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b2), then there is a structured whole that contains as constituents all and only the constituents of both x and y (Inter-Attribute (‘Horizontal’) Composition). b) For any fact :Rni(a1,a2,...,an), if for 1 ≤ j ≤ n, aj is a structured whole, then Rni as emergent upon aj is part of a hierarchically structured whole whose constituents are all and only the constituents of the fact and constituents of aj (Emergent (‘Vertical’) Composition). T8. Attribute instances, Rni, Smj, Tok,…, as a category of inherently ontically dependent entities, do not require further categories of inherently independent per se entities in order to avoid a vicious regress of dependence. In particular, it is possible that there is at some base ontic level atomic attribute instances that have their dependence satisfied by only other atomiclevel instances as subjects, and this via shared instances forming closed chains of atomic facts; :Rni(..,Smj,..,Tok,..), :Smj(..,Tok,..,Rni,..), :Tok(..,Rni, ..,Smj,..), … I.e., there can be an ontic atomic level of mutually sustaining dependent instances. T9. For any structures x and y, x = y if and only if, for every intension Rn and every instance Rni of Rn, Rni is a constituent of x if and only if Rni is a constituent of y. T10. Entities x and y are (absolutely) indiscernible if and only if a) x = Rni and y = Rnj, where Rni and Rnj are instances of the same intension Rn, or b) x = :Rni(a1,a2,...,an) and y = :Rnj(b1,b2,...,bn) and ak and bk are indiscernible for 1 ≤ k ≤ n, or c) x and y are fact complexes with a one-to-one correspondence φ between their constituents, i.e., between the instances, resultant facts, and emergent wholes that compose each, such that φ(:Rni(a1,a2,...,an)) = :φ(Rni)(φ(a1),φ(a2),...,φ(an)), where :Rni(a1,a2,...,an) and :φ(Rni)(φ(a1), φ(a2),...,φ(an)) are indiscernible and respective constituents of x and y. (The readier may wish to ‘dog-ear’ these pages for purposes of convenient reminder or joint comparison of the above assumptions and theses.) Theses T1-T10 are founding ‘elements’ of a single-category ontology of attribute instances, one that I will term ‘Realist Instance Structuralism’, or simply ‘Instance Ontology’. In line with fact-ontologies, the global implication will be

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that Reality is indeed (with D. M. Armstrong) a ‘world of states of affairs’ but this understood in the much-refined sense of being derivative of an all-encompassing stratified network of inter-connecting attribute instances, with minds and their products (e.g., associations) emerging within it. In its details Instance Ontology represents a ‘Copernican reversal’ on fundamental features of both classic substance-attribute and standard trope-bundle ontologies. These reversals include: dependent attribute instances have an ontic primacy over independent ‘substances’ (including substance-like tropes); attributes (as instances) are not components of their subjects (i.e., not their own foundations) but components along with their subjects of subsuming facts they serve to unify; polyadic relations are paradigm intensioned unifiers, monadic properties being the limiting case easily misunderstood as such, neither properties nor relations being reducible to the other; unity among the discrete is not necessarily by a shared one or by one kind of unifier (e.g., ‘Compresence’), but can and most often is by the joint agencies of multiple unifiers, and for structures these of various intensions/kinds and adicities; contrary to it being restricted to just certain complexes (e.g., living creatures) or in fact absent (e.g., as with Compresent wholes), hierarchical structure is ubiquitous; and there is no ‘unrestricted composition’, i.e., there is not a whole for every diversity of entities (as posited sums or sets), rather, all unity is by the delimited agency of attribute instances or individual associations. The analyses leading to these and other results will be seen to resolve a number of traditional and contemporary errors, in part generated by at least tacit adherence to false, or the denials of true, propositions from among classic assumptions A1-A8. Also indicated will be how Instance Ontology might serve as the missing theoretical underpinning for the research field of General Systems Theory, and how it might give expansive content to the contemporary proto-ontology of Ontic Structural Realism recently proposed as best suited for Quantum Mechanics and General Relativity. The ontology defended in this work has evolved over thirty years and has been influenced by the analyses and insights, including the beneficial details of what I have come to assess as errors, of many philosophers, classic and contemporary. I acknowledge them and their specific contributions in the text and footnotes. Of unique importance, I, like all philosophers, benefit from the legacy that is the metaphysics of Aristotle and the long cumulative history of reactions to it. The persistence of the latter reactions evidences Aristotle’s penetrating genius, but their diversity, in part, stems from the opaqueness of his relevant texts. I confess to long frustration in attempting to ascertain Aristotle’s underlying ontological assumptions and their entailments. My best efforts in

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regard to attribution are A1-A8 above and what I will make explicit are some of their implications. Concerning its ‘mode of exposition’, my intent in this work has been a heuristic economy that achieves maximum perspicuity with relative succinctness. Part of this is the avoidance of a less precise ‘conversational style’, and yet part of it is also the use of strategic repetition, the latter in service of clarity of analysis and the avoidance of misunderstanding. Second-nature due to years of teaching, I have herein deliberately utilized the device of ‘conceptual parallax’ where subsets of the same fundamental concepts and theses are clarified and reinforced by their explanatory power across a number of different problem nexuses and their displayed superiority over historically proffered solutions. In exhibiting the epistemic reality and value of structure, this itself supports the ontology of structure advanced in this work. Finally, I wish to express my gratitude to the University of Missouri – St. Louis, and especially Provost Glen Cope, for material support during the early stages of this work. In this regard also I thank Prof. Ronald Munson and the Dept. of Philosophy for allowing me an interim teaching and research position. I express my gratitude to David Linzee for his assistance in preparing the manuscript concerning matters of form and grammar. Most especially, I thank my loving spouse Polly for her unwavering support and encouragement—sine qua non.

1 Overview: Attribution, Structure, and the Five Forms of Composition 1.1 The Overarching Thesis: Ubiquity of Structure and Ontic Primacy of Attribution This work is a study in analytic ontology. Succinctly and in traditional terms, an ontology is a theory of the ultimate kinds or ‘categories’ of things. What this expands to and the lines along which I will propose advancements herein: an ontology is a comprehensive theory of both the most general modes in which entities have their beings, including the characteristics differentiating them into these kinds, and, correlatively, of the general types of inter-connections and dependencies between entities within and across these kinds. Central here are the identification and accounts of all types of unification and resultant composition, i.e., of all forms of ‘oneness’ among the yet non-identical. In what follows I will detail and defend a single-category ontology of individuated attributes, or attribute instances. It will be argued that all other categories of entities, all general forms of unification and composition, and all types of ontic dependence, are derivative of attribute instances. An attribute instance of adicity n is a property or relation that is unique to its subject n-tuple, though it is of ‘the same kind’—‘shares’ the same descriptive content, i.e., intension—as that of any other exactly resembling instances. And by ‘intension’ I mean what in the tradition has been intended variously by the terms ‘kind’, ‘quiddity’ (Latin: whatness), ‘sense’, ‘connotation’ or ‘comprehension’, viz., either an objective/extra-conceptual or, as known or created, a conceptual locus of descriptive specifications or conditions whereby an n-tuple of entities in satisfying them is non-arbitrarily included in the extension of the attribute having this intension. So, for example, on the ontology to be argued the dyadic attribute Evenly-Dividesi in the fact that 2 evenly divides 4, and the attribute Evenly-Dividesj in the fact that 3 evenly divides 6, though they both ‘share the same’ subject-prescription that is intension Even-Division, the attributes are numerically distinct. I.e., since with these subject 2-tuples, ≠ , it will follow straightforwardly on the assay of attribution to be given that instance Evenly-Dividesi ≠ instance Evenly-Dividesj. Further and in distinction from individuated attributes nominalistically construed under now prominent versions of trope theory, herein instances are of ‘the same kind’ because they share numerically the same, and hence universal, intension, a realist thesis found historically but unrefined and for which our

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analysis will provide rare direct arguments. The latter will be but one implication of a potent (but, remarkably and as I shall indicate, historically absent) sustained and discerning analysis of what, in general, is essential to the generating nexus of any unification, or ‘heterogeneous oneness’. Central will be attribution and the details of the role of an intension in conditioning the transentity union that is an attribute qualifying its subject(s). These gains will provide the means for demonstrating how the single category of attribute instances is necessary and sufficient to generate all entities and forms of composition. A crucial insight giving the proposed ontology much of its explanatory power is the intension-conditioned unifying nature of attribute instances. This will be seen to be the immediate generative principle of all atomic structures, viz., facts (or states of affairs), and mediately, through the then possible lateral and hierarchical networking of facts, to be the principle of all physical and abstract entities and structures of our experience and theory, e.g., from quantum entities up through the cosmos. Removing a source of much distortion, nonstructured wholes of discrete parts, e.g., ‘heaps’, sums, sets, lists, are argued to be derivative of cognitive fact-structures that are minds. The developed theory will correct and refine the fundamental Aristotelian and global attribute|nonattribute dichotomy, its advance beyond Aristotle and the tradition (where the dichotomy was taken to be, e.g., that of ‘accident’|‘substance’) being an account of how all non-attributional entities and forms of unification are derivative, directly or indirectly, from attribute instances and their jointly composing intensions and unifying acts. Among the gains are clarifying corrections as to why and what fall on the sides of the other classic Aristotelian ontological dichotomies of universal|particular (repeatable|unrepeatable) and dependent|independent. The refinement in the analysis to be given lies in its answers to certain questions fundamental to fact ontologies, and indeed to ontologies generally, answers that in their explanatory and synthesizing implications far exceed those of the tradition. The crucial questions are: What is it to be the subject of an attribute (how do subjects found their attributes and how is this related to the subjects’ composing ‘essences’)? What is the nature of the union of an attribute with its subject(s) (inherence, adherence, ‘non-relational tie’, combinatorial agency)? In general, what is the nature required of any unification among the non-identical (sharing in the being of a subsuming whole, linking by an external single shared thing, linking via multiple unifiers)? What distinguishes attributional from other kinds of unities (factual unions from those of sums, sets, lists and heaps, and both from wholes whose parts are only ‘formally distinct’)? How do facts compound with other facts, and this hierarchically (how do facts

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join into stratified unities that are given structured wholes, e.g., complex machines and living bodies)? And, what are the kinds and relationships of ontic dependencies thus generated (stratified whole to part, or lateral agent on subject(s), or ‘patient(s)’)? Now, though answers to these questions are crucial to ontology, as I propose to show they are in comprehensive and inter-related ways, part of the latter will be the observation that historically, if the questions were considered at all, the proffered answers are either erroneous and in cases far-reaching in their distortions, or too unrefined and implicationally weak to be of explanatory value. And this, as will be detailed, is so because in part the tradition’s relevant analyses regarding attribution and unity among the nonidentical have occurred within contexts of classic ontological assumptions of which a number are false. With the identification of these assumptions and their errors as a guiding corrective I will then argue for what I claim is an exhaustive account of all forms of composition, and with each an understanding of the correlative natures of the subjects unified, the resultant wholes, and, essential to the latter and a primary topic herein, the natures of effecting unifiers. In particular, it will be a principal advance of this work to have demonstrated how the single category of intensioned unifiers—attributes—is ontically primary, i.e., how attributes proper as individuated/unrepeatable instances are the ultimate metaphysical atoms containing or generating, directly or indirectly, everything else, (e.g., intension universals, non-attribute ‘objects’, and arbitrarily conjunctive associations) via the internal and external types of unifications they effect. I would expand upon these anticipatory points in the following ways. Important to our analysis will be the neglected details underlying the classic distinction of wholes as either intensional, e.g., the qualitative relevance of an attribute with its subject(s), or extensional, e.g., the qualitative mutual irrelevance of the elements or parts of the same set or mereological sum. Starting with intensional unions which I will argue are ontologically fundamental, attribution is an apparently universally instanced form of composition, one seemingly sine qua non to all existents and our knowledge of them. As an ontological thesis: No entity, whether physical, abstract, phenomenal, conceptual, etc., exists without attributes or ‘qualities’—i.e., properties and relations—that each give it or are descriptive of it as having some real differentiating specificity— ‘characterizes’ it—singly or jointly with others (e.g., the attributes of being Physical, Abstract, Phenomenal, Conceptual). Or in expanded form: every entity both a) has a composing being where necessary to its identity is it having certain monadic properties (e.g., Has-Mass, Is-Prime, Reflects-Purple-Light, IsSentient), and b) exists in a subsuming network of polyadic relations (e.g., Gravitationally-Attracts, Is-Proportional-to, Is-a-Citizen-of, Is-Darker-in-Color-than,

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Is-Implied-by) where it and its relations are essential to the identities of what are resultant and subsuming organized wholes or structures—from single facts to complexes of facts, e.g., planetary systems, living bodies, perceptions, arguments. Our intuitive understanding of attributes is that they make a qualitative difference to the ‘wholes of which they are parts’. This is witnessed in the alternative construals of attributes as either constituents of (‘inherent in’) their subjects (what is plausible only for monadic properties and rules out the accidental), or as separate from but entering into structure-forming unions with their subjects, these subsuming wholes being facts (this assay applicable to both properties and relations, essential and accidental). In either case, the subsuming whole— subject or fact—has its identity in part not by the mere conjunction or ‘juxtaposition’ (the sum or set) of the attribute and its subject(s), but because of the characterizing or attributional union of the attribute with (or among) its subject(s). Or, to reinforce the point, attribution is a union of relevance, i.e., a union involving essentially an intension, e.g., Red, Mass, Love, Prime-Divisor, Gravitational-Attraction, Betweenness, and one or multiple subjects (i.e., those of some n-tuple, n ≥ 1), and that obtains in ‘selecting and connecting’ these subjects because they jointly satisfy the conditions prescribed by (the qualitative content or ‘meaning’ that is) the intension. By their specific intensions attributes are of more or less generality and are for their subject n-tuples objectively classifying kinds or sorts. Further, attributes themselves have attributes, i.e., divide according to various classificatory kinds, e.g., Essential or Accidental, Necessary or Contingent. E.g., entity a is characterized as being of the kind ‘chair’, has the essential properties of Is-an-Artifact and Is-Composed-of-Atoms, and the accidental one of being Is-Wobbly, stands in what is for it the accidental relation to Bill of Is-Sat-Upon-by, and for it the essential relation to the floor of SupportsAbove. Intuitively, then, attributes are real and specific ways or modes that entities have their beings. Attributes contribute qualitative definiteness and differentiation to the subsuming realities that are the unions of each of them with or among some n subjects. They are as such distinct from, though the referents of, some linguistic predicates. To have knowledge of the attribute’s union with some subject(s) is to know it (them-jointly) in this determined/specific way, i.e., attributes are ‘carriers of information’ about their subject n-tuples. Indeed, attribution is fundamental to epistemology. Knowledge in its paradigm ‘propositional’ form (‘knowing that’ in contrast to the ‘knowing how’ of skill) is the having of warranted belief that a proposition asserting an attribution corresponds to a fact of this actual attribution—the latter fact then the proposition’s

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corresponding ‘truth-maker’. And, it is a common maxim that we have no cognitive access to extra-cognitive entities except through their properties and relations, the latter founding or being causal epistemic relations between their subjects and us as relata knowers, what are essential to warranting our beliefs that the putative facts obtain. This primary ontological and epistemological status of attribution has been recognized from the beginning of Western philosophy, in detail starting with the works of Aristotle and through which the topic became canonical. It was Aristotle’s particular thesis that all that is—all that has being—falls into ten categories (Cate. 1b25-2a4; cf. Post. Analy. 83a19-24), what are, with the exception of ‘primary substances’, descriptive attributes of and ontically dependent upon these substances. And in regard to knowledge Aristotle observed that, “all things that we come to know, we come to know insofar as they have some unity and identity, and insofar as some attribute belongs to them universally.” (Meta. 999a28) In this way ‘inquiry’, i.e., seeking after knowledge, has as its goal answering “why something is predicable of something” (Meta. 1041a23), or alternately, “why does one thing attach to some other?” (Meta. 1041a11). Concerning unification and fundamental to ontology as assayed and exploited herein, Aristotle argued in the context of taking some attributes to be necessarily organizing forms that the ‘attachment’ of attribution is more than just a conjunctive ‘being-together’. That is, a fact, e.g., that a man is musical, is more than just a ‘heap’ of otherwise mutually irrelevant and unordered subject(s) and an attribute, just as a complex object, e.g., a house, is more than bricks and boards just collected together. Rather and to anticipate, what he in effect implies as foundational to all ontology is that attribution is an intensioncontrolled unifying act effecting an emergent structure (e.g., Meta. 1041a7-b33, 1045a6-b25). And as such, attribution is the principle of all organized wholes, e.g., Socrates, a house a, or a fact b. Reinforcing this but going further, I will argue that ‘unorganized’ wholes, viz., mereological sums and sets/classes, e.g., the set {Socrates,house a,fact b}, to the extent that they are not fictionalized projections, are constructions out of cognitive associations, and so are derivative of structures, and thus of attributions, that compose the producing minds. The global thesis is then that all unification among the discrete has, directly or indirectly, attribution as its source. And so, contrary to the common tack of assigning the role of primary unifiers to one or more specific attributes, e.g., properties that are substantial forms, or relations whose intensions are those of Exemplification, Co-location, Part-of, or Compresence, the argument here is that attributes as such and of any intension or adicity are the ultimate sources of all ontic nexuses. Stated otherwise, our analysis will be that attributes properly

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understood are kind- or intension-determined unifiers, what implies they are individuated as ‘instances’, and that attributes as instances are the only primary ontic category, all other entities (i.e., all non-attribute subjects, e.g., ‘substances’), their unifications, stratifications, and dependencies being ultimately derivative of attribute instances. Included here are the resultant complexes that are minds and the informative attributional unions—instances of epistemic relations—between them and things known. Despite, however, its apparent fundamental position within ontology, the nature of attribution has remained obscure and contentious across the philosophical tradition. Displaying the poor understanding historically of the attributional union are the facts that the facile metaphorical accounts of it as either ‘inherence’—some sort of containment, or as a specific connecting relation of Exemplification or Instantiation, have well-known serious problems (rehearsed herein), as does, I will argue, the reaction re-construal of it as a ‘non-relational tie’. Relevant also to the long-prevailing obscurity concerning attributional unions are broader historical and persisting controversies, e.g., of substratum versus bundle theories, the various interpretations of Bradley’s Regress, and relatedly the question of the reducibility of polyadic relations to monadic properties. And evidencing the concomitant obscurity of intensions are such perennial problems as: whether attributes are universals or particulars (attribute instances, tropes), or somehow incorporate both aspects; the related problem of providing a viable account of individuation—a principium individuationis; the persistent controversies over essential versus accidental, and necessary versus contingent attributions; and the grounds for the implausibility of replacing subject-relevant attribution with Humean arbitrary association. Commenting upon this explanatory vacuum historically, Robert Pasnau observes: “The impressively Latinate ‘inherence’ is just another word for talking about the completely familiar but metaphysically opaque relationship that a thing stands in to its properties, and the scholastics no more shared a theory of how that happens than do philosophers today.”1 Speaking of the current understanding, Patrick Monaghan observes that “If one scours the relevant contemporary literature (such as it its) for a clear and precise answer to the question of what it even means to claim that a property inheres in an entity, or that an entity exemplifies or instantiates a property, one’s search is in vain.”2 The problem of property possession, starting with Aristotle, “really never has been settled, but has re-

|| 1 Robert Pasnau, Metaphysical Themes: 1274-1671 (Oxford: Clarendon Press, 2011), p. 204. 2 Patrick Monaghan, Property Possession as Identity: An Essay in Metaphysics (Frankfurt: Ontos Verlag, 2011), p. 15.

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mained open down to the present day.”3 And D. M. Armstrong assesses Western philosophy’s failure to properly understand the union of instantiation as leading to pronouncements of its incomprehensibility and such skeptical positions as the unknowability of substances, the existence of only non-attributional things, the rejection of universals misconstrued as separated entities, the mental status of relations or their reduction to sets of sets, and the neglect of facts or states of affairs. And even with his own assay of the attributional union as a non-mereological dependent “way” its subject(s) are, Armstrong says that it remains “the most puzzling unity of all.”4 (A particular worry for Armstrong is how contingent states of affairs can exist despite apparent necessary unions between the involved attributes and their subjects. A different assay of the problem and an answer to it will be given in Sect. 4.2.) In response, then, to these symptoms of a crucial explanatory vacuum, I will in the following offer an extended analysis of attribution. Intended by the descriptor ‘analytic’, this will include the identification and detailed critique of a set of relevant classic ontological assumptions found in Aristotle and common thereafter, but what have remained mostly implicit in their joint implications, and that when the latter are made explicit they force the recognition that many of these assumptions are false. The details of this analysis will provide warrant for a number of correcting and refining theses regarding the nature of attribution, and of facts and their combinations. The veracity of these theses will be further supported by the clarifying and synthesizing implications they will be seen to have across all of ontology. I propose as a heuristically potent starting point for our analysis a related but more obvious and practically recognized generality than that of abstract attribution, viz., that of structure. To be laid out in the sequel, it is through the examination of structure and its pervasiveness that we can gain insights into the nature and primary ontological status of attribution, most general among them being that structure and attribution are correlatives and have extensions approaching, but yet with an ontic priority to even, the Aristotelian correlatives of being and unity (e.g., Meta. 1003b24, 1053b20). Toward these insights we observe first that structured wholes are manifest across all of which we are aware—wholes, static and dynamic, that are ontically dependent upon both the existences of their constituents as well as the qualitatively determined inter-

|| 3 Ibid. 4 D. M. Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997), pp. 30–31, 113ff, 267–68; Sketch for a Systematic Metaphysics (Oxford: Clarendon Press, 2010), pp. 26–33.

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connections by some constituents among the others. Compositionally richer and causally efficacious beyond their abstracted skeletons as just wholes-composedof-parts, the latter the generic and coarser subject-matter of the formalisms of mereology and set theory, structures have specific natures and so emergent attributes determined by particular organizations—‘configurations’, ‘arrangements’, or ‘assemblages’—of their parts. Understood as such are material objects of our experience and theory, e.g., plants, machines, molecules, and atoms, as well as less- or non-localized systems whose obvious ‘arranging’ relations are variously spatial-temporal, causal, logical, mathematical, semantic, psychological, social/political, economic, etc., e.g., electrical circuits, weather, the Natural Number System, and nations. Wholes like the latter ‘looser’ or ‘more scattered’ kinds are equally real as structures in that they each have a composing unity sufficient to make it as a single thing the subject for attributes emerging upon foundations beyond generic part-whole arrangements, e.g. and respectively, the emergent properties of lighting a city, spawning a hurricane, being a commutative semiring, or having a national debt. All these structures are ‘real’ in that their composing unities—the kinds and combinations of their inter-connections—are actual (on my assay literally ‘acts’) in effecting what is sine qua non to the defining being of the whole, whether they are in part cognitively generated (e.g., as with social or political structures) and so are ontically dependent upon minds, or are completely extra-cognitive and ‘out there in the world’ as with common physical structures (e.g., crystals or buildings). Put succinctly and as an application of Plato’s Eleatic Principle5, structures are real because each has unique real effects, viz., emergent attributes (Sect. 1.4), and, because the latter are absent when a structure’s parts are not so specifically organized, then by the same principle whatever constitutes the structuring intra-connections among the latter parts must themselves be real parts of the resultant whole. Recognition and then analysis of what is the pervasive given of complex structured wholes will provide context and data for our assay of ontically prior attribution, this in turn providing the basis for a critical ontology of all structure, including its simplest form of single facts. It is their ‘configurational’ roles within complex structures that amplify the fundamental nature and reality (cognitive and extra-cognitive) of attributes, this particularly of polyadic relations, and with the latter a clarifying of the less obvious limiting case of monadic properties. Conversely and explaining how, remarkably, so little attention || 5 Plato, Sophist 248c, “We proposed as a sufficient mark of real things the presence in a thing of the power of being acted upon or of acting in relation to however insignificant a thing.”

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has been given to structure by ontologists, are the specious and impotent misconstruals of attribution in ways congenial to the limiting case of properties but distorting of relations (e.g., as inherence or as specially endowed relations of Exemplification or Compresence). The historical focus on monadic properties has diverted attention from the otherwise evident nature of relations as interrelata linkings, or combinators, the latter being ‘writ-large’ in complex structures. A principal argument herein is that differences in adicities (though not the having of adicities) are accidental to the defining nature of attributes qua attributes, but rather what is essential is that they are all intensioned-combinators (with each intension specifying its own particular adicity). In particular and contra a perennial error, there is no categorical difference between monadic properties and polyadic relations. Profound will be the consequences of these insights. In general, on the premise to be argued that structure is a pervasive and irreducible feature within and across all strata of reality, subjective and objective, spatial-temporal and not, then not only does it demand an ontological analysis, but this analysis holds out the promise of clarifying and ratifying, or correcting, classical ontological theses in persuasive ways. Indeed, the following work will display precisely the latter: how structure as a qualitatively-determined unification among the discrete, in some cases in subsuming stratification, brings into sharp relief and contrast the natures of a set of related concepts fundamental to ontology: attribution, universal, intension, individual, agency, relation, association, ontic dependence, per se subject, modality, discrete and continuous unification, hierarchical composition, emergence, disposition, identity and indiscernibility, change, etc. In this way the topic of structure provides a rich coherence-nexus within which to develop and test ontological theses. The above, then, is a condensed overview of what we shall be about in this work. With this as contextual outline, let me now add some precision to these claims, especially those asserting the pervasive given and obvious characteristics of structured wholes, and the role of attribution within them. First and a matter of simple recognition, it is the specific and usually various ‘ways’ that the parts of a structure are inter-connected (the medieval ‘ordered’) that contribute essentially to its defining being and so determine—‘make a difference in’—the attributes of the structure as a whole. Or alternately, some attributes, e.g., dispositions and causal relations, externally ‘emerge’ on organized wholes as thus single subjects because among these attributes’ necessary foundations are the specific internal ways some of the wholes’ constituents organize/‘arrange’ other constituents. Now by ‘ways’ here we must mean more precisely intensionally-specific inter-connections, and this is the definition of relations—

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polyadic attributes. And because they make a real difference to their resulting wholes, marked by the wholes’ emergent attributes, these networking relations are then as real and essential constituents of the structure as are the parts thus variously linked. One need only think of possible effects in re-arranging (‘rerelating’), say, circuits in a computer, or lines of responsibility among a corporation’s personnel. Indeed, much of human effort is devoted to building, maintaining, and negotiating artifact and social structures precisely because, due to the constructed kinds and configurations of their composing relationships, they as wholes have attributes that better satisfy human needs (biological-psychological needs that are themselves structured in a Maslowian hierarchy). Some of these constructions are in support of and benefit from the physical sciences that increasing reveal a reality of complex hierarchies, where each stratum emerges with its own powers and dispositions due to the manners in which its parts are spatial-temporally and causally related. As a simple example often referenced, many beneficial properties of sodium chloride (salt) emerge upon an electro-static structure via an ionic bond between sodium and chloride atoms, properties not had by either the highly active sodium or the poisonous gas chlorine. Yet even prior to theoretical scientific knowledge, attentive unaided observation is of a world where, as Aristotle describes, “All things are ordered together somehow, but not all alike—both fishes and fouls and plants; and the world is not such that one thing has nothing to do with another, but they are connected.” (Meta. 1075a16-19)6 But likewise in regard to systematic science Aristotle observed that “The principal object of natural philosophy is not the material elements, but their composition, and the totality of the form, independently of which they have no existence,” where this composition is “the relation of such parts to the total form”. (Parts of Animals 645a30-37) Concerning the ubiquity of structures as wholes in the paradigm form of parts inter-relating other parts, not only does attuned awareness warrant this thesis for the ordinary things and systems of daily concern, but our sciences and technologies extend it to what is a spectacularly intricate underlying and subsuming physical and cognitive reality. Reinforcing and adding specificity to the above examples, consider the organized systems of stratified and interacting subsystems that are: physical objects, e.g., molecules, DNA, living bodies, or computers and power grids; ecological systems, local and global; the total intraconnected space-time and energy-force system that is the cosmos (from the Greek kosmos = ‘an ordered system’) and every sub-region of it; the phenomenal || 6 Unless otherwise cited, all quotes from Aristotle in this work are taken from translations in The Basic Works of Aristotle, Richard McKeon (ed.), (New York: Random House, 1941).

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contents of our perceptional fields and of consciousness generally; the physiological and psychological systems involved in our cognitive and emotive functioning; and our consequential familial, social, economic, and political systems. Phenomenally, the given of perception, e.g., visual, auditory, or tactile fields, are informative to a large extent via the structuring of their contents7, and knowledge insofar as it is propositional exists in the context of logical, linguistic, and dynamic cognitive structures. A particularly obvious example of a dynamic phenomenal structure is an auditory experience of a musical piece—more than noise as a sequence of co-experienced random sounds, music at standard complexity is a diachronic structure of inter-related substructures involving tones and relations among them founded upon pitch, loudness, duration, and timbre, and upon temporal orderings, and these organized into substructures of melody, rhythm, texture, etc.8 Change the substructures in certain limited ways and you get an ‘interpretation’ of the piece; change them radically and you get a different piece of music. And relevant to our knowledge of these and all types of structure are the abstract and hierarchical cognitive structures of logic and mathematics, e.g., deductive systems, number systems, algebras, geometries, topologies, what particularly with mathematical systems and by means of partial isomorphisms (isomorphisms themselves being structures of structures) between their formal substructures and the substructures of other domains (e.g., the experimental observations of physics, logistical networks, the compositions that are music) we have contributions to scientific theories of the latter.9

|| 7 That things-as-related are given in experience is important to emphasize, as it contradicts the ‘granular’/atomistic views of classical British empiricists, e.g., Hume. Against the latter William James observed: “The statement of fact is that the relations between things, conjunctive as well as disjunctive, are just as much matters of direct experience, neither more so nor less so, than the things themselves. The generalized conclusion is that therefore the parts of experience hold together from next to next by relations that are themselves parts of experience. The directly apprehended universe needs, in short, not extraneous trans-empirical connective support, but possesses in its own right a concatenated or continuous structure.” The Meaning of Truth (New York: Longman Green, 1911), pp. xvi–xvii. See Sing-Nan Fen, ‘Has James answered Hume?’, The Journal of Philosophy 49 (1952): 159–67. 8 For an ontological assay of music as phenomenal structures of attribute instances see John Lango, ‘Relation Instances and Musical Sounds’, Australasian Journal of Philosophy 78 (2000): 176–88, and his ‘Why Can Sounds Be Structured As Music?’, Teorema XXXI (2012): 49–62. 9 Kathrin Koslicki in arguing for the ontological importance of structure provides case studies from mathematics, logic, linguistics, chemistry, and music, from which she observes that there cannot be genuine doubt that structures are “central explanatory principles in their respective disciplines”. (p. 262) The Structure of Objects (Oxford: Oxford University Press, 2008), pp. 240– 52. My analyses can be seen as extending Koslicki’s expansive assay of complex wholes by

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Living bodies are spectacular examples of highly complex hierarchical and distinct but inter-acting systems, what in their self-sustaining complex unities impressed Aristotle as paradigm examples of ‘substances’. Detailed in textbooks on molecular biology are intricate process structures of molecular interactions involved in cell morphology, metabolism, and reproduction, what then effect emergent structures, e.g., of tissue, organs, and bones, and these integrated into mutually supporting systems—circulatory, nervous, skeletal, etc. Each level, subsystem, and integrated whole has a specific nature, i.e., what because of its internal organization and/or its role in external subsuming systems, is a single subject for certain emergent characteristics and dispositions, some definitional of the whole (cf. Aristotle, Parts of Animals 640b16-29). (The latter attributes are ‘emergent’ in a broad sense to be developed herein (Sect. 1.4), viz., these attributes as unrepeatable instances exist only in having the resultant whole as a subject, and so cannot exist as parts of the whole. Further and in the narrower sense often given to ‘emergence’, some of these attributes can have intensions that no instance composing their subject complex whole has and so are sui generis.) And, a living system develops dynamically over time by its various substructures evolving through successive stages (e.g., infancy, childhood, adolescence, etc.), the whole at each stage having attributes specific to the then net underlying structure, attributes that cumulatively over a lifetime define a repeatable ‘nature’, e.g., Human. With an evolving system where each configuration determines the changes that morph the system into a new configuration we have the motivation for Aristotle’s claim that the total enduring chain exhibits a telos or ‘end’, what for Aristotle was the relatively stable physical and behavior structure of a mature adult of its biological kind. Less but still immensely complex structures are static and dynamic artifacts (e.g., a house, an automobile, a computer, the interacting algorithms of a computer operating system, the micro-artifacts of nanotechnology), each having attributes serving its intended end—to mesh in specific ways with other structures—due to the parts being organized and stratified in deliberately specific ways. Social structures, e.g., economic systems, have both designed and unanticipated emergent attributes, what fall under such terms as ‘synergies’, ‘econ-

|| detailing the mechanism of how within structures the essential formal components (my attribute instances as analyzed in Chapter 4) ‘constrain’ (in ways specified in Chapters 4 and 5) objects into defining configurations. In this way is answered a question Koslicki leaves open: Whether structures are attributes or objects? Specified herein will be how structures are individual independent objects consisting ultimately of only attributes as individuated dependent intension-determined combinators.

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omies of scale’, and ‘unintended consequences’. Bridging artifact and social structures are the current vastly complex telecommunication systems, a substructure being the Internet. The pervasive given of structure or system and the resulting emergent causation is the starting motivation for the active research field of General Systems Theory.10 The theory in part is a reaction to the sterility of classical explanations of complex dynamic systems in terms of otherwise isolated individuals (e.g., classic ‘corpuscles’) entering into simple one-way causal chains and whose results are the production in the effect of attributes of the same category as those had by the cause qua cause. For example, in a collision, the directed motion of one billiard ball causes directed motion in another. Here there is nothing new in type across the causal structure. But the complex structures of particular interest to system theory are diachronically evolving lattices of multiple interconnected causal chains, hierarchically arranged and in some cases cyclical and with ‘downward causation’ (e.g., feed-back mechanisms), with emergent properties and relations at or across various levels, some of which are sui generis. For living systems these include directedness and control of internal differentiation and external augmentation, self-replacement, self-maintenance, adaptiveness, and goal-seeking. Among the desiderata of General Systems Theory has been for an underlying ontology of system/structure, one that can support an account of these latter emergent dispositions. This work is, in part, intended to make some advance toward this long-persisting goal.11 Important because of its status as physically fundamental, structure is central to a proto-ontology termed ‘Ontic Structural Realism’ (OSR) which is argued as best suited to account for the entities of Quantum Mechanics and General || 10 General Systems Theory has its roots in Ludwig von Bertalanffy’s General Systems Theory (New York: George Braziller, 1969). Also see Ervin Laszlo, Introduction to Systems Philosophy (New York: Gordon & Breach, 1972). A number of journals are dedicated to systems theory (and relatedly to Complexity Theory). E.g., International Journal of General Systems published by Taylor & Francis. 11 J. H. Marchal asserted in 1975, almost twenty years after the Society for General Systems Theory started publishing its yearbook, that the nature of a system was “still an open problem”. To my knowledge it has remained so up to now. Marchal’s offered approximation was that a system is a set of elements together with a set of relations holding among these elements. He noted that what remained unsatisfactory was “A general account of when a relation or set of relations holds among the members of a set”, what would “distinguish, in more detail, between systems and other denizens of the world of sets.” This I claim to achieve herein in a clarifying and generalizing way: systems are attribute instances, of both properties and relations, interconnecting themselves in ways specified in Chapters 4 and 5. See Marchal, ‘On the Concept of a System’, Philosophy of Science 42 (1975): 448–68.

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Relativity.12 It is said that, on our current understanding of the identity and individuation of space-time points and of elementary particles, and of certain properties of the latter (by quantum entanglement), these characteristics can be had only in the contexts of ontically prior structures. Prominent in advocating OSR, James Ladyman summarizes its motivating thesis as the fact that our warranted science describes a micro-level where “Relational structure is ontologically more fundamental than individual objects.”13 And specifically for entangled compound systems, Vassilios Karakostas describes the physical facts as implying that “the nature and properties of component parts may only be determined from their ‘role’—the forming pattern of the inseparable web of relations—within the whole.”14 What is required then for these primary entities is a paradigm shift in ontology from classic object-oriented atomism where some ultimate independent substances support dependent attributes (often restricted to just ‘intrinsic’ properties and external spatial-temporal relations, e.g., as with Lewis’ ‘Humean Supervenience’) to an attribute-oriented one where the fundamental entities are ‘networks of pure relatedness’. Clarified and generalized in the instance ontology to be developed herein will be how, in fact, there can and must be an atomic ontic level where dependent but mutually supporting attributes, as individuated instances, are more fundamental than non-dependent non-attribute entities (Sect. 5.2). What will be seen and contrary to the claims of some15, a stratum of ‘pure relatedness’ does not require relations without relata, nor relata as essenceless ‘place holders’ (a cousin to ‘bare particulars’), but can exist as closed chains of attribute instances having other fully-essenced instances as relata. Given, then, the fundamental concepts involved with structure, its ubiquity and causal significance (including sui generis emergence), and its status as both practical and theoretical tool and goal of most human effort, one might expect it to have been, or at least in contemporary times to be, an explicit standard and

|| 12 James Ladyman, ‘On the Identity and Diversity of Objects in a Structure’, Proceedings of the Aristotelian Society, Supplementary Volume LXXXI (2007): 23–43. Also see Ladyman, ‘Structural Realism’, The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/sum2009/entries/structural-realism/; Steven French, ‘The Interdependence of Structure, Objects and Dependence’, Synthese, Issue 1 Supplement (2010): 89–109; and his The Structure of the World: Metaphysics and Representation (Oxford: Oxford University Press, 2014). 13 Ladyman, ‘Identity and Diversity of Objects in a Structure’. 14 Vassilios Karakostas, ‘Humean Supervenience in the Light of Contemporary Science’, Metaphysica 10 (2009): 1–26. 15 Ladyman, ‘Structural Realism’.

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integrating focus of ontological analysis. This is not the case. At best and due to related but erroneous prior assumptions concerning the nature of attribution as its essential component, the notion of structure has been historically and, I urge, even today remains distorted and opaque, what continues to render it ontologically peripheral and explanatorily impotent. Early on, structure so distorted was prominent in Aristotelian/scholastic philosophy where it motivated the signature posit of ‘substantial forms’: predicable agents that, top-down, create from prime matter, and impose organization among, proper parts so as to generate organized substances, e.g., souls as organizing principles of then living bodies. These stood in contrast to some ‘accidental forms’ that were each the unifier of a structured whole that presupposed, bottom up, certain types of internal compositions among what are already substances, e.g., the ‘orderings’ required among the bricks, boards, etc. that then has the single accidental form whereby it is a house. For both types, but particularly for primary substantial forms, they are tied to a nexus of classic ontological assumptions, often appealed to tacitly, concerning attribution and unification, the latter essential to any assay of structure. These are theses A1-A8 announced in the Preface and that will be identified in context and critiqued in Chapters 2 and 3. It is these assumptions, the majority erroneous, that I will argue are jointly the source of the tradition’s distorted conception of organized wholes, and of the suspicion of emergent attributes that identify any whole to be such (Sect. 1.4). In particular, it will be made explicit how subsets of these theses imply contradictions, vicious regresses, or other problems. These negative consequences are among the tradition’s classic ontological problems, yet despite a long history of proffered solutions, the latter persist in stalemated dispute because, I propose to show, they fail to identify the exact premises and their combinations that give rise to the problems. The identification of these errors will point to their source and correction—presuppositions regarding the nature of attribution as the principle of structuring unification, including the confusion of subject-relevant attribution with subject-irrelevant cognitive association (Sects. 1.3, 1.5, 3.4). It will be seen how attribution properly understood, viz., under theses T1-T10 as stated in the Preface and argued for across Chapters 4 and 5, can provide perspicuous solutions to a number of key ontological problems, and how when joined with associations properly distinguished from attribution there are grounds for an explanatorily comprehensive or ‘total’ ontology (Sects. 1.6, 5.4). The misconstrual of structure under Aristotelian/scholastic assumptions, and yet its continuing fundamental ontological status, is evidenced in the broad rejection by natural philosophers of the seventeenth-century and thereafter of explanations in terms of Aristotelian forms and yet their replacement with ac-

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counts in terms of mechanical-mathematical structures. Forms as posited principles of internal organization and causes of characteristic internal and external functioning were rejected as obscure and occult, and in considerable part because of their impotence in explaining increasingly detailed static and dynamic systems of non- or pre-biological matter.16 Forms were abandoned for the greater explanatory and predictive power of corpuscular/mechanistic physics whose explanations were in terms of composing efficient and material structures (Aristotelian ‘accidental’ compositions). These explanations consist essentially of systems of polyadic relations concerning position, motion, size, shape, and forces (of impact and later ‘at a distance’ (e.g., gravity and micro-attraction and -repulsion)) among small particles of matter and their aggregates, what together form physical structures that are perspicuously described with intrinsically relational structures of (‘form-al’) mathematics. The emphasis was reductionist and minimally hierarchical, with the attributes recognized as emerging on such organized wholes being limited to the mechanistic and mathematical. But even then, though the role of bottom-up structure was explicitly recognized to be essential, it and the nature of structure generally remained distorted due to an error persisting historically from at least Aristotle and on all sides up to the present, viz., the ontological neglect, or indeed hostile reductive elimination, of polyadic relations in favor of the limiting case of monadic properties. To anticipate with a here-relevant illustration of the error, on the reduction, structure in the most obvious case of entities-inter-related becomes these entities each having non-relational properties that at most, and as Aristotelians would have it, ‘point-toward’ some of the others (a relation being an ens ad aliud = ‘a being toward something else’). Now, to avoid regress, the latter multi-subject ‘pointings’ cannot be further relations, and so they can be but intensionless associations (details given below and in Sect. 2.6). But merely associated entities are just collected but unorganized Aristotelian ‘heaps’ (Meta. 1040b9) and not as such structured.17 So on this construal what is then required for these parts to have their given organized unity is some further intension-determined but nonrelational unifier; hence the necessity of positing a monadic attribute or ‘form’,

|| 16 For an overview of scholastic suspicions on the knowability of substantial forms and the rejection of these forms by seventeen century natural philosophers, see Robert Pasnau, ‘Forms, Substance, and Mechanism’, The Philosophical Review 113 (2004): 31–88. 17 Real ‘heaps’ or ‘random piles’ do have spatial and causal structure among their parts, this though being unintended. I take Aristotle to use ‘heap’ as metaphor for wholes that are completely without structure, and unless otherwise indicated this is how I shall use the term herein.

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e.g., Is-a-House, to do the job. Thus, contradictory of a monadic property as an ontic predicate of a single subject, the property-form as a single unifier must simultaneously organize multiple subjects, what can be achieved in fact only by one or more multi-subject relations. A monadic property, e.g., Is-Human, can in the definitional expansion of its intension be descriptive of a complex structure and so be an attribute of it as an already constituted single subject, but it cannot be a constituent cause of the structure’s composing multiple-part/subject unification. The distorted assay of relations, and so that of structure and its importance, was and is, I will argue, part of the larger failure to understand the proper nature of attribution or ontic predication.18 The errors here are, secondarily, the taking of monadic properties as paradigm, what is reinforced by the classic inherence model of attribution, the latter impossible for relations as polyadic or ‘between’ multiple subjects. But primarily and abetting the former is the failure to recognize that all attributes of any adicities are principles of structuring unification of themselves with the subjects they thereby qualify/characterize, their effected structures being the corresponding facts. This insight of the structuring agency of all attributes and its implications are the heart of our analysis and will be fully developed in Chapter 4. In contrast and historically, with regard to not only Aristotelianism and the reactions directly to it, but across the entire Western tradition, there have persisted conflicting and undeveloped conceptions of attribution: specifically, as to what is the nature and source of the union between subjects and their attributes. To understand the range of proffered and defective assays of attribution consider the following possibilities. Assume there exists a fact that subject a has property F. Since, prima facie, the attributional union between a and F is both itself real and not identical in being to either a or F, yet is ontically located somewhere in the resultant fact, then it must be a subpart of either 1) F, 2) a, 3) F and a both, or 4) be, or be a subpart of, some implicit third and mediating entity M that provides the union between a and F. One can find in Aristotelianism both types 1) and 2): Conforming to 1), some properties are other-directed combinators of themselves with their subjects (part of the presumed meaning behind Aristotle’s descriptor ‘being-said-of-another’), this the assigned natures of those attributes that are substantial and accidental ‘forms’. As observed above, forms were and are widely rejected, and we will give specific reasons justifying

|| 18 For a brief historical overview of theories of attribution or ontic predication see Uwe Meixner, ‘From Plato to Frege: Paradigms of Predication in the History of Ideas’, Metaphysica 10 (2009): 199–214.

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this rejection in the next chapter. The form-theory glimpses, however, a fundamental truth to be exploited herein: that structure is derivative of attributes and of the latters’ natures as intension-directed unifiers. Equally present but less developed in Aristotle and subsequently is type 2) attribution, where subjects are the unifier of themselves with their attributes, and what abets the facile and long-persistent inherence model where subjects are said to have their attributes as components. For, on Aristotle’s (and our) anti-Platonist thesis that attributes are not distinct from their unions with their subjects (what is implied in classic assumption A1 (Sect. 2.1)), joined with the current assumption that attributional unions are composing parts of their subjects, then the attributes themselves are placed within their subjects. Aristotle is explicit in certain texts that accidental properties are inherent in the entities they qualify (Sect. 2.2). And likewise with substantial forms—a substantial form F is a descriptive and necessary ontic predicate of a substance a of which it is a constituent along with prime matter. Yet and a sign of obscurity here, the same ontic predicate F effects the structure definitional of resultant a and is the grounds for it being F by also being an ontic predicate of F’s prime matter, of which it cannot be a part and is a contingent attribute. We will detail the problems with inherence in Sections 2.2 and 2.6. Suffice it here to observe that if a subject a has its properties by their entering into its composing being then a has all its properties necessarily—it cannot persist through change of properties. A few philosophers have theorized attribution to be of type 3)—an attribute F characterizes a subject a by each sharing part of its being with—overlapping with—the other. But on an extension of an argument given in Section 3.2, this alternative degenerates into distinction-obliterating homogeneous monism. The last option, 4), construes the attributional union between F and a to be or be part of some implicit third and actually linking entity M. This facile but specious view of unity-by-a-third is articulated by Plato in the Timaeus: “But two things cannot be rightly put together without a third; there must be some bond of union between them.” (31c) And here there are two sub-options: a) M is either itself an attribute—has an intension that makes it relevant to its subjects— and what has been widely adopted under the terms ‘Exemplification’ or ‘Instantiation’, or b) M is not an attribute and so as the only alternative is a union of ungrounded intensionless association, the minimal and subject-irrelevant form of plural unification. This is in fact the meaning of the sometimes characterization of attribution as a ‘non-relational nexus’ or ‘tie’, what is posited as an an-

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swer to Bradley’s Regress (Sect. 3.1).19 The problem with a) is that M as an attribute, specifically a dyadic relation, is as much in need of an account of its attributional union with each of F and a as it is posited to give to the same kind of union directly between F and a in the original fact. Moreover, if one were to adopt an elimination strategy that reduced relation M to properties each of F and a, this would simply push back and double the problem without an account for the attributional unity among F and a. To the contrary and key to our analysis, there is no need for a third thing to effect a ‘bond of union’ between two other entities as long as one of the two, e.g., attribute F, is self-effecting of its own unity with the other, e.g., F’s subject a. In regard to sub-option b), of historical figures it was first David Hume who most explicitly and stridently drew out the consequences of the associationist conception of attribution, implications I will argue at length in Section 3.4 are reductio’s of the position. I also note that the Compresence ‘relation’ of bundle theory as often construed is, in effect, association. In any case, association cannot go proxy for attribution, for otherwise, because of the indifference association has to the natures of the things associated (Sect. 1.3), it would be possible for the same subject to be simultaneously characterized by contrary attributes, e.g., be both round and square, which is absurd. This and other problems with bundle-theory will be detailed in Section. 3.3. The above possibilities assume that given the fact that a is F, both a and F are their own beings, neither reducible to entities defined in terms of the other. Such reductions are, however, commonplace in contemporary ontologies, often involving modelings within set theory or mereology. The underlying assumption in these accounts, and a fundamental ontological error on the analysis herein, is that the unity and ontic dependence inherent in attribution is the same as that of whole upon parts. On this assumption the unity and dependence within the monadic fact that a is F is modeled as either: 1) attribute F = {a,b,c,…} (or = the sum [a,b,c,…]), the set (sum) being the extension of F and where the unity of the fact :F(a) is that of the set (sum) and the ontic dependence is that of F upon a as a component, or 2) subject a = {F,G,H,…} (or = the sum of, or ‘bundle of’, F, G, H, …), the elements of the set (sum, bundle) being monadic properties of a, and where the unity of the fact that a is F is that of the set (sum, bun-

|| 19 Gustav Bergmann, Realism (Madison: University of Wisconsin Press, 1967), pp. 9, 42ff. Herbert Hochberg, ‘A Refutation of Moderate Nominalism’, Australasian Journal of Philosophy 66 (1988): 188–207. P. F. Strawson, Individuals (London: Methuen, 1971), pp. 168ff. D. M. Armstrong, A World of States of Affairs, pp. 30, 38, 99, and Universals: An Opinionated Introduction (Boulder: Westview Press, 1989), pp. 96–97, 110.

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dle) and the ontic dependence is that of a upon F as a component. Mode 1) is the tack of class (or mereological) nominalism and against which there are wellknown arguments I propose are decisive (e.g., given by Armstrong20). Mode 2) underlies various types of bundle theories, also with observed problems, some of which I will extend herein. As anticipated above, the overall argument will be that both types of reduction fail because the unities of the wholes involved, i.e., sets, sums, bundles, like that of all composition among discrete parts, exist only by the agency of outward-achieving unifiers, but with these kinds of wholes the required but implicit unifiers are only subject-indifferent/irrelevant and non-ordering associations (Sect. 1.3 & .5). What are required to explain the unifications that are facts, especially evident in facts with polyadic relations, are agent unifiers controlled by intensions as to their subjects and the subjects’ orderings. This being the nature of attribution, the above subject-irrelevant reductions cannot go proxy for subject-prescriptive/subject-descriptive attributions. A crucial insight for ontology will be that, contrary to a widely held, if tacit, assumption that all unity and ontic dependence is that of whole upon parts, more fundamental and from which all forms of composition and dependence are derivative, is the unity and ontic dependence of agent upon subject(s)/ ‘patient(s)’, what in its primary form is the combinatorial acts of attributes with their subjects (Chaps. 4 & 5). Prominent among contemporary modelings of plural unification, including that of attribution, is the proposal to construe all composition as ‘sums’ or ‘fusions’ of formally precise but, to be argued, ontologically spurious classical extensional mereology (CEM).21 Its axioms are: 1) Unrestricted Composition: Whenever there exist some things, there exists a unified composite of those things, their sum (or fusion); 2) Uniqueness of Composition: It never happens that the same things have different sums, and 3) Transitivity (of Parthood): If x is a part of a part of y, then x is a part of y. Importantly, because by 1) sums are posited to exist for any diversity of entities whatsoever, what is implied is that each such composite has its unity and so existence in a way irrelevant to both the qualitative natures of any entities, constituents or not (and so irrelevant to any specific relations among the parts), and to the existences of any other entities than its constituents. Here and crucially, any internal cause(s) of selective, limited (‘restricted’) unification among certain entities and not others, whether

|| 20 D. M. Armstrong, Nominalism and Realism (Cambridge: Cambridge University Press, 1978), pp. 28–43. 21 See Koslicki, The Structure of Objects, p. 17. Koslicki provides in some detail the formalities of standard mereology: its concepts, definitions, and alternative axioms.

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intension-determined attributions or arbitrary/random associations, is ignored as irrelevant.22 In these ways sums are structureless and, more fundamentally, none of their parts account for their delimited and differentiating unities. Now and a crucial point to be elaborated below, without operating unifiers among entities there are no thereby circumscribed wholes. And to hold otherwise is to posit sums as wholes that are each certain entities jointly or together, and thus entities related to their whole as all and only its parts, but where this selective ‘gathering’ or unification has no being in addition to the beings of the selfcontained entities gathered. I.e., a sum is then ‘nothing over and above’ its parts independent of any delimiting unifications among them. This is the content of David Lewis’ Composition-as-Identity Thesis (CI), what is the basis for his claims that CEM is “ontologically innocent” and so is added support for adopting mereology as a general theory of all composition.23 To the contrary, it will be argued that despite the formal perspicuity and modeling utility of axiomatic mereology, in abstracting away what is essential to composition—unifiers and their resultant (‘additions to being’) wholes—it is ontologically falsifying. Such wholes being like, in Alice in Wonderland, the smile described as remaining while its supporting cat evaporates away. The resulting fictive models of composition are crucially disanalogous to real plural wholes because they abstract away what are essential composing and selecting inter-connections. Symptomatic of the error, in the absence of these delimiting constituent unifiers there is no middle option, nor principled way to decide between the extremes one finds advocated in the literature, viz., Mereological Universalism (e.g., David Lewis, Theodore Sider)24: under Unrestricted Composition, any entities whatsoever, however mutually irrelevant and gerrymandered, form a composite, and Mereo-

|| 22 This ‘loosest possible kind of comprising unity’ of mereological wholes under Unrestricted Composition is recognized by Roberta De Monticelli, what she describes as being of degree zero, it being a “unity quite indifferent to the kinds C1,..,Cn of the united contents.” She argues that there are wholes of higher degrees, ones whose comprising unities are not so indifferent. The argument herein is that the latter are facts and their compounds, all of whose unities are effected by the combinatorial agency of attribute instances, what are conditioned on (restricted by) the qualitative relevance of their intensions to the natures of their subjects. See Monticelli, ‘Constitution and Unity: Lynne Baker and the Unitarian Tradition’, The Monist 96 (2013): 3–36. 23 David Lewis, Parts of Classes (Oxford: Basil Blackwell, 1991). 24 Lewis, On the Plurality of Worlds (Oxford: Basil Blackwell, 1986), and Parts of Classes. Theodore Sider, Four-Dimensionalism: An Ontology of Persistence and Time (Oxford: Clarendon Press, 2001).

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logical Nihilism (e.g., Cian Dorr and Gideon Rosen)25: no plurality of entities form a composite. Trenton Merricks has argued that both extremes follow from the Composition-as-Identity Thesis, where the latter is a correlative of the Unrestricted Composition assumption.26 More on these issues in Sections 1.3 and 1.5. Reacting to these extremes and to the reductive dismissal of structure by advocates of CEM as an ontology of composition, some contemporary philosophers have reiterated the ubiquity, ontological importance, and irreducibility of structured wholes. The reaction is exemplified in a quote from Kathrin Koslicki. Commenting upon the work of Kit Fine in recognizing and analyzing structure, she writes: “Once Fine brings to our attention just how blatantly ordinary material objects diverge from standard mereological sums with respect to their conditions of existence, location and part-whole structure, one wonders how the standard conception could ever have had such powerful hold on the minds of so many philosophers.”27 I intend that the examples and observations of this chapter evoke a similar reaction in the reader. To be amplified, a central problem with formal mereology, or its cousin set theory, made the ontology of composition is that there is thereby overlooked the ontic role of constituent discriminating unifiers, and, fundamentally, those controlled by intensions. To get a sense of the problem in regard to intensions, consider that for real structures—from single facts to compounds of them forming complex systems—their obtaining precludes the existences of some facts and contributes to effecting the existences of thus emergent others. E.g., the fact that a is the father of b obtains precludes the would-be fact that a is a sibling of b from obtaining, and, along with a fact that b is the father of c, makes for a two-fact structure prerequisite to and upon which emerges the fact that a is the grandfather of c. It is the intensions of the attributes that determine the exclusions and emergences here, and this is the very nature of attribution and the role of intensions in it; attributional unions in this way are ‘more than the sum or set of their parts’. This intension-conditioned unification, however, is what Lewis and others deny as ‘unmereological composition’.28 The then ersatz modeling of attribution within mereology or set theory (respectively, ‘mereolog|| 25 Cian Dorr, ‘What We Disagree About When We Disagree About Ontology’ in Mark Kalderon (ed.), Fictionalism in Metaphysics (Oxford: Oxford University Press, 2005), and Gideon Rosen and Cian Dorr, ‘Composition as Fiction’ in Richard Gale (ed.), The Blackwell Companion to Metaphysics (Oxford: Blackwell, 2002). 26 Trenton Merricks, ‘Composition and Vagueness’, Mind 114 (2005): 615–37. 27 Koslicki, Structure of Objects, p. 72. 28 David Lewis, ‘Against Structural Universals’, Australasian Journal of Philosophy 64 (1986): 25–46, and Parts of Classes, pp. 56–7.

The Overarching Thesis: Ubiquity of Structure and Ontic Primacy of Attribution | 23

ical nominalism’ and ‘class nominalism’29) is intended to eliminate such roles for intensions, i.e., intensions are to be eschewed and so to have no descriptive relevance to the unifications that compose the modeling wholes—certain sums or sets.30 A point to be made much of in our analysis, the unity of a sum or set is indifferent to any qualitative aspects of the parts or elements unified, and thus intensions play no role in their existences as unified wholes. Now, within these modelings an intension, e.g., the relational one of Fatherhood, is treated extensionally as a certain sum or set, F, and particular facts having that intension, say, our fact that a is the father of b, is identified with a sum or set S composed ultimately of a and b (as with the Wiener-Kuratowski device for modeling ordered pairs as sets of sets31) and which is a part or element of F (the technicalities are irrelevant here). All these sums or sets are available because under their theories all possible sums or sets on the given domain are posited to exist, and this without the intension Fatherhood having any role relative to their existences—without any role in their composing and delimiting unifications. Nor is the intension descriptive of these sums or sets as resultant wholes (sums or sets cannot be relata for the relation of Fatherhood). That is and a crucial fact, what this means is that officially nothing about an attributional role involving the intension Fatherhood determines the nature of its modeling, but, and as the alternative, the intension is simply arbitrarily assigned—associated with—the modeling sum or set F. To amplify this point consider that not excluded by the existence of the sum or set S is the existence of one Sʹ that would be the modeling corresponding to a would-be fact that b is the father of a, what as a fact cannot exist if the fact a is the father of b does, given the asymmetry of the intension Fatherhood. Yet, both of the sums or sets S and Sʹ exist within their respective theories. Further, what would also exist under these theories is a sum or set Fʹ consisting of the sums or sets composing F, including S, and that of Sʹ. And because the intension Fatherhood is arbitrarily assigned to F, it could alternately and equally be arbitrarily assigned to Fʹ, a modeling that would allow simultaneously for the facts that a is the father of b and b is the father of a. Inclinations contrary to such an assignment stem from the fact that we ‘unofficially’ intuitively understand the role of the intension Fatherhood in conditioning the unities that are its facts and this is used to guide the extensional

|| 29 See Armstrong, Nominalism and Realism, pp. 28–43. 30 E.g., modelings in terms of sets proposed by Lewis in Plurality of Worlds, most sets then for him modeled in terms of mereological sums in Parts of Classes. 31 Here the ordered pair is modeled with the set {{a},{a,b}}.

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modelings, and particularly its association with set F, but on these intended intension-decoupling modelings this is officially denied. The use of arbitrary or ad hoc association is more obvious in what these formal theories allow for complex structures. There is, for example, Lewis’ notorious ‘trout-turkey’32—an entity consisting of half of a trout ‘joined with’ half of a turkey. The claim is that trout-turkeys are equally as real in being no different in the kind of unifications that make them wholes as are complete trout or turkeys and the kind of unifications that make them each a whole. Yet, only construed as complex sums or set can such wholes be considered partitioned and halves of each forming sub-sums or sub-sets of an existing sum or set to which is associated the term ‘trout-turkey’. Living trout and turkeys are each in their defining realities complex and hierarchically integrated dynamic physiological structures such that halving them in any manner destroys the functioning systems and so the wholes so defined. Only parts of corpses would remain, what, of course, can be freely associated, e.g., juxtaposed on a butcher’s block, but none of these halves now have the same structural unifications—functioning physiological systems—that they had when integrated into their respective living trout or turkey.33 To retain the kind of ‘unmereological composition’ that is the structural unity had by trout and turkey halves as they exist in their wholes is to separate them only in conceptual abstraction and then to unite them by what can only be conceptual associations. Below I shall argue for a much more intimate relationship between arbitrary associations and sums and sets, viz., that subject-indifferent associations are the required discriminating unifiers for the existences of wholes that, fictionalized via abstractive elimination of these constituent associations, are theoretical sums or sets (Sect. 1.5). In regard to this last point, the formal perspicuity and utility of mereology and set theory serves, I suggest, as a pacifying distraction from what is the telling fact that the posits of these theories are themselves wholes each of just some and not other entities, and that this presupposes the reality of a differentiating selection or partitioning among existents that cannot be accounted for by these theories. The analysis below will fill this explanatory lacuna, and in a way that || 32 Lewis, Parts of Classes, pp. 7–8, 80. 33 The situation with the term ‘trout-turkey’ is similar to what Aristotle noted in regard to the term ‘finger’ used to describe a severed ‘finger’ at Meta. 1035b24-5, or for ‘hand’ when referring to a severed ‘hand’ or the ‘hand’ on a dead body at Parts of Animals 640b34-641a4. A finger (and similarly for a hand) in its proper defining sense is a living appendage to a life-supporting body of a certain sort, and if the finger is severed and so the material that remains is no longer living, this material is a ‘finger’ not in the same sense or intension—in Aristotle’s words “a dead finger is a finger only in name.”

The Overarching Thesis: Ubiquity of Structure and Ontic Primacy of Attribution | 25

dissolves the grounds for any claims of explanatory parsimony and ontic primitiveness for sums and sets. In terms from the current literature, what Koslicki and like philosophers see as necessary is a theory of ‘restricted composition’, what would be a middle ground between nihilism and universal/unrestricted composition. Proposed in this regard are various causes of internally-constrained structural unification, e.g., Koslicki’s structuring via formal elements themselves organized by instantiation of ‘kinds’34; Lynne Baker’s ‘constitution relations’ whereby entities of new ‘primary kinds’ emerge with their own distinct properties35; Fine’s structuring via ‘rigid’ and ‘variable embodiments’ of relations or systems of relations36; or Peter Simons’ structuring of trope bundles via Husserlian ‘foundationalism’, causal chains, and Gestalt qualities37. Each of these is an attempt to answer what Peter van Inwagen has made prominent as the General Composition Question: What is composition?, or alternately, How can we account for composition in non-mereological terms? Van Inwagen’s proposal is that limited composition is found only in the dynamic structures of living things38. Yet with all these proposals an ontological account of hierarchical structuring is wanting (Simons providing the most relevant detail), as is a more fundamental analysis of attribution as a cause of structured unity. What van Inwagen intends is what I would term the Problem of Composition: What are the nature and kinds of selective unities where, to the exclusion of others, some non-identical entities are unified, ‘made one’, but in such a way that each retains its differentiating identity? Or in short: How are we to understand wholes as each a delimited plural oneness? Towards the solution I propose that what is missing throughout the above weak and flawed accounts of plural unity, structural or not, is what Aristotle discerned as essential to organized wholes and what will be key in the following. It is the recognition that all inter-entity unification among what are yet discrete entities requires one or more

|| 34 Koslicki, The Structure of Objects, Chapters VII–IX. 35 Lynne Rudder Baker, The Metaphysics of Everyday Life: An Essay in Practical Realism (Cambridge: Cambridge University Press, 2007). 36 Kit Fine, ‘Things and Their Parts’, Midwest Studies in Philosophy XXIII (1999): 61–74. Also see Koslicki, The Structure of Objects, pp. 72–90. 37 Peter Simons, ‘The Ties that Bind: What Holds Individuals Together’, in Substanz: Neue Überlegungen zu einer klassischen Kategorie des Seienden, Käthe Trettin (ed.), (Frankfurt am Main: Klostermann, 2005). And Simons, ‘Particulars in Particular Clothing: Three Trope Theories of Substance’, Philosophy and Phenomenological Research LIV (1994): 553–75. 38 Peter van Inwagen, Material Beings (Ithaca: Cornell University Press, 1990). For arguments against van Inwagen’s thesis on his own assumptions, see Ned Markosian, ‘Brutal Composition’, Philosophical Studies 92 (1998): 211–49.

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of them be agent-combinators among the others. Particularly for the more fundamental form of structural unity, the crucial insight is that in each such delimited whole—what are facts or complexes thereof—the linkings among its elements are attributes as intension-controlled unifying acts. This fact will be seen to have potent clarifying and synthesizing consequences for ontology generally, and for understanding structure in particular. Chief among these are, first and primarily, that attributes in their defining roles of characterizing/qualifying subjects are unrepeatable particulars—‘instances’—e.g., in the facts that 3 is prime and 5 is prime, there are two numerically distinct instances of the same intension Prime, each unique to its subject. Further, building upon this and explanatory of the fact that structured unions are pervasive, attribute instances will be seen to be sufficient, through their agency and the modes of composition identified, for the generation of all compound entities. Established will be how, outside of what is derivative of cognitive abstraction or invention, every existent is compound, and how attribute instances as both ontologically fundamental and compound can and must at some ultimate stratum be ontic atoms, i.e., how their components have a mode of composition that precludes an infinite regress of decomposing instances. Otherwise stated, it is an overarching thesis of this work, in part an assertion of motivating fact, and in part a hypothesis to be warranted by the analysis to follow, that: T1. Structure (system, organization, gestalt) is a ubiquitous feature of reality, and as such not only requires an ontological account, but this account is foundational to all ontology. Specifically, an analysis of structural unity and its implications warrants an ontology with a single atomic ontic category of individuated attributes—property and relation instances, where all forms of ontic dependence and composition, and so all other existents, are those of, or derive hierarchically from, attribute instances. A central focus herein are the various types of unifications constituent of structured wholes, and the other types of unifications they presuppose and/or stand in contrast with. The account given will yield an ontology I shall term Realist Instance Structuralism, or more simply Instance Ontology.39 Instance ontology is

|| 39 Previously I have referred to this ontology as ‘Network Instance Realism’, but this misses the mark in not emphasizing the fundamental role of structure as a ‘network’ of variously relating attribute instances.

The Overarching Thesis: Ubiquity of Structure and Ontic Primacy of Attribution | 27

characterized by proposition T1 and nine further and amplifying theses, T2-T10. Primary theses T2-T6 delineate the nature of attributes as they display themselves in their defining ontic roles as structural unifiers. An overview of these theses will be given in this introductory chapter, with detailed arguments provided in Chapter 4 in contexts that display their power to solve problems arising from the structure-relevant but mostly erroneous classic/Aristotelian ontological assumptions A1-A8. The remaining four theses, T7-T10, develop the nature of complex structures that derive from composing attribute instances so assayed. Arguments for the latter theses and the explanatory power of the resultant complexes will be developed in Chapter 5. Among the clarifications and solutions to be advanced are: the long-absent account of attribution, i.e., what it means for an attribute (relations and properties (as the limiting case of relations)) to characterize/qualify its subject(s); insights into de re modality; clarification of the specious nature of ‘bare particulars’ (posits that challenge the universality-of-attribution thesis); an expanded and exhaustive account of plural unity yielding five types of unification/composition and so of ontic dependence; the elimination of the traditional concept of ‘substance’ and the providing of a coherent account of an ontic substratum; the providing of a non-posited principium individuationis (i.e., a solution to the Problem of Individuation) and a context for developing convincing direct arguments for universals (i.e., a solution to the Problem of Universals)40; an explanation and disarming of the classic Bradley’s Regress argument; and the providing of a ‘pure relatedness’ ontology for mirco-physics. The remainder of this introductory chapter will preview some of the arguments for and relationships between these and other claims that will be detailed in latter chapters. The exception is Section 1.5 which will be my full argument for the fictive nature of mereological sums and sets.

|| 40 I have stated elsewhere the Problem of Individuation as: What explanation can be given of the fact that, though absolutely every characteristic of an individual is a repeatable intension, that entity can nevertheless be unrepeatable qua individual?, and the Problem of Universals as: What explanation can be given of the apparent fact that numerically one and the same intension can be predicably ‘in’ diverse subjects—unum in multus? These in Mertz, ‘Combinatorial Predication and the Ontology of Unit Attributes’, in Essays on Realist Instance Ontology and its Logic: Predication, Structure, and Identity (Frankfurt: Ontos Verlag, 2006).

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1.2 Previewing Attributes as Structuring IntensionedCombinators The prevailing definition of structure is that of its most obvious form, viz., a plurality of entities inter-linked via a specific arrangement of polyatic relations, and these of one or more kinds/intensions. Consider such examples as: 1) a complex argument as a branched system or network of implications, each implication a dyadic relation between a conjunction of premise propositions and a conclusion proposition, the latter, if not the final conclusion, itself part of a further conjunction of premises in the network, and so on (an analogy being a tree-diagram in the direction of branches to trunk); 2) multiple circuits so arranged as to make up a particular electrical grid; or 3) an automobile’s drivetrain consisting of a particular sequence of part-pairs—engine-trans-mission, transmission-driveshaft, driveshaft-differential, etc.—each designed to interface with the next at a compatible mechanism and in such a way so to pass on controlled motion. In the first example the relations forming the structuring ‘pathways’ are logical relations among propositions, including Implies, whereas in the second example there is the single Is-Wired-to relation. The third example is complex, involving structures composed of various spatial-mechanical relations between segment-pairs in a drivetrain. Illustrated with such examples is the fact that a structure’s composing relations in their specific intensions are as essential to the existence and the emergent attributes of the whole as are their relata. Alter the relational ‘arrangements’ and the wholes may no longer be the single subjects of, respectively, Is-Valid, Lights-a-City, or Moves. These structures are each ‘more than the sum of its parts’ due to the types and arrangements of intra-connecting relations that are parts of it, and in this stands in crucial contrast with a sum or ‘heap’ of just the relata, e.g., as in a mere list of propositions, or a pile of automobile parts. Organized wholes being ‘more than the sum of their parts’ is intended by the common observation that such wholes have ‘persistence conditions’ different from those of their parts. What is wanting here is a precise sense of ‘sum’, what I shall offer in Section 1.5. A heuristic analog for simple non-hierarchical structures like the electrical grid would be a networked ‘rods-and-nodes’ model (e.g., the physical models used in chemistry to depict molecular structure), where, like the connecting rods, relations ‘bridge ontological space’, and in this have an ontic role, relative to the whole, different from their subject nodes. And, depending upon how various nodes are shared by the rods there result different structures (‘configurations’). A close naturally occurring example is the lattice structure within a unit cell composing a crystal, where atoms are related by ionic bonds and deriv-

Previewing Attributes as Structuring Intensioned-Combinators | 29

ative geometrical relations. Importantly, for the rods-and-nodes model to also represent hierarchical structure, nodes themselves must be allowed to be complex structures treated as each a single endpoint for further rods, the latter rods representing attributes that their subject structures have in their singular totalities. In the first example above, it is a conjunctive chain of premise propositions that jointly as one composite entity is a subject (one node) for (an instance of) the Implication relation (rod) whose other subject (node) is a conclusion proposition. Details on hierarchical structure and their diagrams will be given in Chapter 5. These observations, then, point to a more refined definition of commonly recognized structure: each is a plurality of entities unified via a combination of relational facts or states of affairs—for n > 1, n-adic relations relating n-tuples of these entities—and where these facts are chained together via either their relations sharing subjects, or by some facts jointly composing what are single relata for other composing relations. In these ways each entity is ‘path-connected’ with every other. Now what will be amplified below is that relational facts as the elemental segments in these inter-connecting paths are each itself an atomic structured connection via its relation being attributional of its subjects. Specifically, in an attribution a relation is the cause of an outward-directed and intension-conditioned unification—‘cohesion’—of itself with each relata respectively satisfying its intension, and thus is a single linking among all and just these entities. Further and founding a completely general specification of structure, it will be argued that this is the case with all attribution, whether by monadic properties or polyadic relations, i.e., for all n-adic attributes, n ≥ 1. Using the rods-and-nodes model, a rod with only one end-node is analogous to a monadic property and its subject. The model, then, captures two of our central claims about all attribution: that as rods are not composing parts of their nodes, attributes are not composing parts of their subjects, what is intuitive for relations but runs counter to the common inherence conception of property attributions, and, like rods, attributes are as particular/unrepeatable as any individual node. In further detail, among the specific theses advanced in this work are that, proper to their nature and prior to diluting abstraction, all attributes—properties and relations: 1) do not enter into the composition of, but exist necessarily in union with—are intrinsically ontically dependent upon—other extrinsic entities, their subjects (‘attribute’ from the Latin: attribuere = ‘to bestow upon [something else]’); 2) are agents of unification with other entities, their subjects—they are ‘ontoglial’, and this agency is the cause of their being individuals/unrepeatables; and 3) via their intensions (‘senses’ or qualitative contents whose identity condition is synonymy), attributes are informative/descriptive of what are either

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the internal composing natures of their subjects and/or what are external contextual unions had by their subjects. Concerning the latter, for example, in the fact that Philip is the father of Alexander, the intension Fatherhood requires of Philip and Alexander that each be internally a certain kind of biological entity (not, say, a rock or a proposition), and that externally they be jointly part of a specific kind of causal relation from Philip to Alexander.41 We shall expand upon these points in Section 4.2. The overall point is that an intension, e.g., Fatherhood, Square, Prime, determines how an attribute is descriptive of—‘fits’ or is kind-relevant to—its subject(s), i.e., an intension specifies conditions, internal and/or external, a subject or subjects jointly must satisfy in order for the intension’s subsuming property or relation (instance) to characterize it or them. Otherwise stated, an intension prescribes certain necessary and sufficient requirements that an entity or entities jointly must fulfill—the ‘foundations’ or ‘grounds’ they must have—in order for an attribute instance with that intension to characterize it or them. Here, if each of an n-tuple of subjects (e.g., ) satisfies the respective requirements (e.g., that 2 be in the same ratio to 3 as is 4 to 6) set by a specific attribute intension (e.g., Proportionality), then an instance of this attribute will necessarily obtain among and thus be jointly informative of the n subjects as all constituents of an emergent fact (e.g., the fact that 2, 3, 4, and 6, in that order, are proportional). It is in their unique ontological role of setting necessary and sufficient conditions on would-be subjects whereby attribute intensions are the principles of all ‘intrinsic connectedness’ or ‘necessary connections among the distinct’ (this point expanded in Sect. 4.2). If it were otherwise then attribution would be but the alternative of arbitrary association, and so reduced to this Humean subject-indifferent ‘extrinsic connectedness’ attributes would have no descriptive relevance to the subjects they are attached to—all connectedness could be otherwise and in the indifference things could have contrary properties, e.g., be both square and round. Even ‘external’ spatial and temporal (or spatial-temporal) relations specify foundations of their subjects, contrary to some Humean construals, and neces-

|| 41 The point here might be made in another way: if it is reported that my dog was observed eating an unknown something, the intension Ate2 specifies certain conditions that had to be satisfied for this to be a fact, e.g., what the eaten something could be, viz., it must be material and ingestible by the dog, and not, say, an act of heroism or an automobile. If, in contrast, it is reported simply that someone has associated my dog with something, there are no constraints on what this unknown object of association could be—it could be literally anything, including an act of heroism or an automobile. Associations are undetermined and irrelevant to any aspects of their subjects (other than their existences), whereas attributions are constrained and relevant to these aspects.

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sary but not sufficient among them is the internal natures of these subjects. The latter is seen from the fact that some kinds of subjects cannot possibly have these relations, i.e., do not satisfy the prerequisite conditions, e.g., intensions, concepts, numbers, sums/sets, propositions, arguments. As observed by E. J. Lowe, these entities are such (i.e., ‘abstract’) “because time and place do not enter into their existence- and identity-conditions.”42 (I would urge here the irony in the fact that for some philosophers being a relatum for spatial or temporal relations is a necessary criterion for something to exist, yet insofar as they argue for such a position their argument, by their criterion, has no reality and so no force.) But also required as foundations by spatial and temporal relations are other external connections had by their relata, viz., other spatial or temporal relations. For example, for objects a, b, and c to enter into a spatial relation of b being between a and c, it is necessary not only that each be the kind of things that can be relata for spatial relations, but also that other spatial relations obtain among the three, such as that b lie on a straight line joining a and c, that b be in the direction of c relative to a and b be in the direction of a relative to c. Or for a and b to enter into the relation of being 5 meters apart they must lie on a straight line divisible into five equal segments each equal to a standard distance of one meter. And if asked: How long is a meter?, one can only appeal to some other spatial distance and ultimately to that of some standard. In general, there are no definitional specifications of spatial (and temporal) attributes without appeal to other such attributes. This is consistent with the Relational (as opposed to the ‘Substantival’) Theory of space and time, what is said to be warranted by contemporary physics, and is made increasingly plausible by the details of the structural ontology developed herein.43 That common attributes require as foundations aspects of the beings of their subjects is the motivation for the classic and erroneous inherence model of attribution, what violates theses 1) and 2) above. On this model attributes are simplistically identified with their foundations and these taken to be parts of their subjects, what is plausible for monadic properties but requires the impossible reduction of polyadic relations that are ‘between’ multiple subjects to properties wholly contained within single subjects.

|| 42 E. J. Lowe, ‘Metaphysical Nihilism and the Subtraction Argument’, Analysis 62 (2002): 62– 73. 43 See, e.g., Mauro Dorato, ‘Substantivalism, Relationism, and Structural Spacetime Realism’, Foundations of Physics 30 (2000): 1605–1627. For a discussion in the context of the technicalities of current physics see the papers in The Structural Foundations of Quantum Gravity, D. Rickles, S. French, and J. Saatsi (eds.), (Oxford: Clarendon Press, 2006).

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Of the above three theses, 2) and 3) are primary, with 2) implying 1), and thus the claim to be argued is that the nature of attributes can be accurately synopsized as intension-determined agent-combinators (Sect. 4.3). That is, an attribute with intension Rn (e.g., Spin1, Betweeness2, Proportionality4) in qualifying an n-tuple of subjects , for any n ≥ 1, is the causal agent of a qualitatively conditioned unity of itself with and among these subjects, with the resultant being the primary structured whole of a fact (or state of affairs). Now, fundamental and potent among the implications of the intensioned-combinator assay of attribution is that an attribute in qualifying an n-tuple of subjects is a unifying act, and hence is individual and unique to that n-tuple (Sect. 4.4), i.e., attributes exist properly in facts and there as unrepeatable ‘instances’, ‘Rni’ (e.g., Has-Spin1i, Is-Between3j, Is-Proportional-to4k), the subscript indicating that it is a particular/unrepeatable. (Restating my notational conventions (given in the Preface), a colon locution ‘:Rni(a1,a2,…,an)’ will be used in this work to designate the fact composed of instance Rni and its being the ontic predicate of all the entities jointly in the n-tuple , the latter as such Rni’s ‘subjects’. The expression without the colon, ‘Rni(a1,a2,…,an)’, will be used to designate a proposition, what would have the corresponding fact as its ‘truthmaker’. I alert the reader, however, that in the following I will at places omit super- or sub-scripts when not germane to the topic at issue.) In their composition, then, it will be argued that an instance Rni, e.g., Gravitationally-Attracts2i, has two constituent aspects: an unrepeatable unifying agency unique to its ntuple of subjects, e.g., , and an intension Rn, e.g., Gravitation2, that conditions this agency as to prerequisite foundational aspects had by each of its subjects, and the number (n), and order (if any) among them. Our analysis in support of attribution as thus individuated acts of intension-conditioned and thereby necessary unifications will remove the explanatory vacuum abetting the counter-factual Humean theses that motivate the mereological surrogates for attribution, viz., Hume’s claims that “nothing is more evident, than that the human mind cannot form such an idea of two objects, as to conceive any connexion betwixt them, or comprehend distinctly that power or efficacy, by which they are united.”44 To the contrary, we do ‘conceive’ of intensions as prescribing conditions whereby they are descriptors of possibly other entities, and insofar as there are entities so described, we ‘conceive’ in this way that the intension and these entities are necessarily ‘connexted’ (though it may be that the circumstances satisfying these conditions do not obtain necessarily and thus the re|| 44 David Hume, A Treatise of Human Nature, David Norton and Mary Norton (eds.), (Oxford: Oxford University Press, 2005), 1.3.14.13, p. 109.

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sulting fact would be contingent (more in Sect. 4.2)). And with proper analysis it can be seen that all unification among the discrete, even that of Humean association, requires outward-achieving agency (Sect. 4.3), and so understood we do ‘comprehend’ the ‘power or efficacy’ required for such a union, as we do as well the implication that these acts and so their subsuming attributes are unrepeatable individuals (Sect. 4.4). Highlighting the counter-factual status of these Humean theses is their self-nullifying implications, e.g., these theses are expressed in complex English sentences whose grammatical and semantical structures—systems of specific linguistic relations—effect wholes that are their corresponding ‘meanings’, i.e., the asserted propositions. If we did not ‘conceive’— understand as such—these particular structures, and hence the specific relational connections involved, we could not understand the claims being made, and these ‘sentences’ would be as much nonsense as other random rearrangements that can be made of these same words. Supporting the proposed analysis, the doctrine of individuated attributes understood as ontically predicable and so dependent entities is perennial in Western philosophy, evidence for the thesis found in the works of Plato and Aristotle, with it being explicitly adopted variously thereafter.45 What has been wanting is a direct and compelling argument for them; what the recognition of the combinatorial nature of attributes supplies. In turn, the latter leads to the insight that outwardly-directed combinatorial agency generally is for ontology its principium individuationis—a cogent contextual account of individuation that stands in contrast to the troubled posits of primitive self-individuated ‘haecceitas’ (Latin: thisness) or ‘bare particulars’ (Sects. 2.4 and 2.7). An account of ‘contextual individuation’ (individuation via outward connections) is a desideratum of Ontic Structural Realism in explaining the individuation and the thus completed and differentiating identities of elementary particles that share all of their identity-contributing (‘intrinsic’) attributes and so violate the Identity of Indiscernibles.46 To be argued in our analysis, what constitutes the identity of

|| 45 A survey of the history of unit attributes can be found in Mertz, Moderate Realism and Its Logic (New Haven: Yale University Press, 1996). For a detailed overview and some analysis of the views of more contemporary advocates of the theory—D. C. Williams, Anna-Sofia Maurin, Ivan Segelberg, and myself—see Christer Svennerlind, Moderate Nominalism and Moderate Realism, (Götenborg: Acta Universitatis Gothoburgensis, 2008). Arguments for individuated attributes as part of the best semantics to account for certain constructions in natural language are given by Friederike Moltmann in Abstract Objects and the Semantics of Natural Language (Oxford: Oxford University Press, 2013). 46 E.g., French, ‘Interdependence of Structure, Objects and Dependence’; Steven French and Michael Redhead, ‘Quantum Physics and the Identity of Indiscernible’, British Journal for the

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any pre-abstraction entity, quantum or otherwise, are the property and relation instances that are solely what compose and internally structure it (these are an entity’s true ‘identity-contributing attributes’, with those essential attributes that have it as a subject (those pertinent to the Identity of Indiscernibles) being derivative in emerging upon the former). It is the ‘predicable’ agencies of each of the entity’s composing attributes that individuate them as instances and from which the entity as the resultant whole inherits its individuation. Moreover, all attribute instances, regardless of their intensions, are by their agencies, and so individuations, real and irreducible, even those that have their origins and sustained existences in the intellect, e.g., Is-Truei, Impliesj. No instances, even those that emerge on wholes as single subjects, just ‘supervene’ on their subjects in the reductionist sense that the term is often used. In any inventory of what there is, every instance of every intension, and every ‘arrangement’— structure—they jointly form, would have to be included or the inventory would be incomplete. Indeed, on what will be argued herein, attribute instances of every kind and adicity, and their joint ‘arrangements’, are not only each an ‘addition to being’, they and what compose them or emerge upon them are all that is, and this according to the five types of unification, with attribution as primary, that we will introduce next.

1.3 Intension Universals and the Five Types of Unification Central to our analyses will be the identification of five general types of unification, these, it will be argued, being exhaustive of all the ways non-identical entities can be ‘one’. First and as a preliminary, the individuation of attributes will provide a context for arguments (Sect. 4.5) that, for an instance Rni, its contained intension Rn is a repeatable universal, numerically identical in each of (and the cause of their being) exactly resembling instances. More specifically, by characterizing a universal as ‘repeatable’ I mean the possibility of it making as a constituent what is numerically the same contribution to the composing beings of numerically distinct entities. The arguments’ refined and amplified details laying out the necessary dual composition of attribute instances gives them greater force than other standard arguments for universals (e.g., their

|| Philosophy of Science 39 (1988): 233–46; and Ladyman, ‘Identity and Diversity of Objects in a Structure’.

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necessity in explaining natural laws47, or their warrant by ‘inference to the best explanation’). Universals as intensions means their defining identity criterion is synonymy, or, as argued for recently by Douglas Ehring, ‘exact inherent similarity’48. This differentiates universals from particulars/individuals: for universals, exact inherent similarity implies numerical identity, whereas for particulars it does not. Or alternately, intensions/universals cannot have exact qualitative duplicates, but particulars can. It is a point of this work that the simplest illustration of the latter are two attribute instances of the same intension, e.g., IsPrime1i ≠ Is-Prime1j. Ehring rightly argues for what we would establish more directly—that it is identity by exact inherent similarity, rather than by the having of adicity, dependence (‘incompleteness’ or ‘gappyness’), simultaneous distinct spatial locations, or being a subject in asymmetric Exemplification, that distinguishes universals from particulars.49 Further and correlative with the existence of intrinsic universals, an instance’s two aspects of unrepeatable agency and repeatable intension are necessarily joined in what is an internally undifferentiated ‘continuous composite’, their separation possible only externally in cognitive abstraction (Sect. 4.6). The necessity of such a union is seen in the implications of a classic error. The effect of what is the agent-combinator aspect of each instance, though not recognized as such, has been, as noted, referred to in the literature as a ‘nonrelational tie’50, or ‘nexus’51, what provides ‘a unity closer than relation’52. The error has been the assumption that, for example, in the fact :Is-Redi(a), the attribute’s unifier aspect, U, has as the object of its linking agency not just subject a, but also the intension Red. But the effect is either 1) a further fact, :U(Red,a) with U a relation, what iterates to vicious regress, or 2) U is simply arbitrary association which cannot account for the kind of unity required for the original fact. I.e., the ‘continuous’ unity of the dual aspects of an attribute instance

|| 47 E.g., Armstrong, A World of States of Affairs, pp. 23–24, 223ff.; E. J. Lowe, The Four-Category Ontology: A Metaphysical Foundation for Natural Science (Oxford: Clarendon Press, 2006), pp. 28–30. 48 Douglas Ehring in Tropes: Properties, Objects, and Mental Causation (Oxford: Oxford University Press, 2011), pp. 19ff. 49 On our assay both intensions/universals and their subsuming instances, the latter attributes proper, have adicity, instances are other-dependent entities but intensions are not, some intensions, e.g., Frictionless-Surface, are not relata for Exemplification, and no intensions are subjects for spatial-temporal relations. 50 Strawson, Individuals, pp. 167ff. 51 Bergmann, Realism, pp. 9, 42ff. 52 Armstrong, Universals: An Opinionated Introduction, pp. 96–97, 110.

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cannot be the ‘articulated’ unity effected by characterizing instances or even looser arbitrary association—the unity must be ‘closer than attribution’. This point was made by some scholastic philosophers who observed that for each occurrence of an attribute, e.g., on our analysis as individuated, Redi, the differentiation between its outwardly-directed combinatorial mode and ‘the attribute’—more accurately: the intension of the attribute, e.g., Red—is not between two ‘things’ distinct in the ontic predicate, but between two conceptually distinguishable aspects both of a single unarticulated reality. Francisco Suarez referred to this distinction as “modal” and one sense of the distinctio rationis ratiocinatae, and John Duns Scotus termed it a distinctio formalis a parte rei.53 Here then we have the subtle distinction that an attribute instance as a continuous composite is ontically simultaneous with its combinatorial aspect, the unity of the latter and its delimiting intension dependent upon the whole, and their differentiation posterior to the whole; whereas derivative from an instance and its subject(s), a fact is an articulated composite ontically dependent upon these prior parts, but not vice versa, and with a unity effected by the constituent attribute instance. Observing within an attribute instance Rni a composition of both unrepeatable combinatorial and repeatable intension aspects dissolves distortions that arise from the otherwise common assumption that identifies the contained intension universal Rn with the subsuming attribute proper. It clarifies, for example, the ‘moderate realism’ of the scholastics as summarized in the apparently contradictory slogan: ‘Attributes are individuated in things, but universal in the intellect.’54 On our assay this is refined to: An attribute as an intensioned unifier is individuated as such, but the intension separated in abstraction from any unifying agency is universal, and so separated is conceptual only. It is not, it will be argued, that intension-universals exist only in the intellect—for they exist as numerically the same constituents across all exactly resembling instances, conceptual or extra-conceptual—but that in isolation from any instance they exist only in the intellect. Anticipating support for these theses (what will

|| 53 Francisco Suarez, On the Various Kinds of Distinctions (Disputationes Metaphysicae, Disputatio VII, de variis distinctionum generibus), trans. Cyril Vollert, S.J. (Milwaukee: Marquette University Press, 1947), I, pp. 17–29, 28–38. For Scotus’ views see his Ordinato II, d.3, part 1, qq. 1–6, in Paul Spade, Five Texts on the Medieval Problem of Universals (Indianapolis: Hackett Publishing Co., 1994), pp. 57–113. For a detailed analysis of this type of union see my ‘The Nature and Necessity of Composite Simples, E.g., Ontic Predicates’ in Mertz, Essays on Realist Instance Ontology and its Logic. 54 For a detailed description of moderate realism, especially as epitomized in Thomas Aquinas, see Peter Coffey, Epistemology, Vol. I (Gloucester, MA: Peter Smith, 1958), pp. 268–83.

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be argued for in detail in Sect. 4.5), we routinely and without notice conceptually abstract from attribute instances as actually characterizing—i.e., as outwardly combinatorial on and so ontically incomplete and dependent upon—given subjects, e.g., , Is-Roundi, Has-Spinj, Is-in-Love-withk, Propelsl, what are their contained intensions and the referents of abstract singular nouns, e.g., Roundness, Spin, Love, Propulsion. In contrast to their subsuming instances, the latter abstracted intensions or ‘senses’ are intrinsically complete and independent— substance-like—entities, what when confused with their actual attributional instances makes plausible such specious doctrines as that of Platonic Forms and nominalistic tropes. In particular, though not so for polyadic relations, it is an easy mistake to identify a subject-dependent monadic property, e.g., Is-Justi, with its abstracted intension, e.g., Justice, and to make the latter’s concomitant unifying agency with a subject they jointly characterize a further and interposing relation—and so attribute—specifically intensioned to do the job, traditionally that of ‘Exemplification’ or ‘Instantiation’ (‘Compresence’ being the analog in trope theory55). Yet, to be consistent, polyadic relations would have to get the same analysis. And, evidence of the error here is the fact that the relation of Exemplification (Instantiation, Compresence) must itself be an exception to this analysis. For, to analyze an instance of the Exemplification relation in the same way is to require an instance of Exemplification in the analysans, and this iterates into a vicious regress, i.e., Bradley’s Regress—the attribute posited at step n to account for the trans-entity unity of itself with its subjects is denied this combinatorial nature in step n + 1. So, on this assay of attributes, properties and/or relations, we must, in order to avoid a fruitless chase after necessary unifiers, appeal to a special kind of attribute that is an exception to and contradictory of the proposed analysis—a kind of ‘required hypocritical exemption’ and a sure sign of an error.56 Exemplification is in fact a real intension with real instances, but all are derivative and conceptual (like Truth and its instances (cf. Aristotle, Meta. 1027b24-27)), an instance of Exemplification, e.g., as in the fact :Is-Exemplified-

|| 55 The problem here in regard to Compresence is discussed by Ehring in Tropes: Properties, Objects, and Mental Causation, pp. 13, 119ff. 56 E.g., in Tropes, Ehring proposes that to stop the regress and achieve the unity required of Compresence among tropes as its subjects (an analog applying to Exemplification), we can construe it as a special kind of ‘self-relating’ relation, i.e., one whose instances each “can take itself as a relatum” (p. 13). But to posit an instance of Compresence among subject tropes t1 and t2 to have itself as one more implicit relatum does not solve the problem of its unification with and among t1 and t2, but simply increases the number of subjects requiring an account of their unification.

38 | 1 Overview: Attribution, Structure, and the Five Forms of Composition by2i(Human,Socrates), being descriptive of a prior unity effected by an instance of the intension that is its first relatum on (or among) the entity (or entities) that is (or are as an n-tuple) its second relatum, e.g., descriptive of the attributional unity effected by Is-Human1j on its subject Socrates in the fact :Is-Human1j(Socrates). Building upon what will be identified as the two primary types of unity and so composition—the continuous unity internal to attribute instances and the external articulated unity instances effect in facts—we will detail in Chapter 5 two further and derivative types of ‘transitive’ articulated unity via multiple instances. These are essential to complex structured wholes and their hierarchies, e.g., the ordinary objects of our experience. Here we have ‘chains’ or ‘lattices’ of inter-connected facts, these via either 1) facts having attribute instances that share subjects—‘inter-attribute composition’, or 2) by entire complexes being themselves single subjects for further attribute instances—‘emergent composition’. The latter attributes are ‘novel’ in at least one of two senses (Sect. 1.4), and their resulting complexes can be iterated into hierarchical complexes. Contra Wittgenstein’s Tractarian thesis57, reality is not just a flat plane of first-order facts, but a stratified lattice of ‘facts about which there are facts about which there are facts…’ Inter-attribute and emergent composition are two different ways that subjects are path-connected via attributes. And, both types of unity contradict the classic assumption that ‘All unity is by the one’ (A8), an assumption whose implications are discussed in Chapter 3. There is finally as the fifth and ‘loosest’ form of unification the above referenced arbitrary associations, i.e., non-structuring linkings, each limited in its extent and independent of and irrelevant to anything about the entities unified, with the exception of their existences. That is, there are here unifications each of a fixed and non-global—‘restricted’—range that is ‘free’, ‘arbitrary’, or ‘random’ in being unconditioned by either the internal natures of, and/or the external unions had by the constituents. With such unions, no matter what, if any, psychological motives there are for selecting associated entities, a union of association itself obtains, or not, completely irrelevant to anything qualitatively specific/descriptive, internally or externally, about these subjects; only their existences matter. In this, associations—‘extensional combinators’—stand in contrast to both attributions—‘intensional combinators’—and continuous composites. Or, in Humean terms, associations are ‘non-necessary connections’, whereas attributions and continuous compositions are (contra Hume) ‘neces|| 57 Ludwig Wittgenstein, Tractatus Logico-Philosophicus, trans. by D. F. Pears and B. F. McGuinness (London: Routledge & Kegan Paul, 1961), Props. 1.1–1.2, 2.04, 2.011, 2.061, and 2.062.

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sary connections’. I propose a cause of much ontological error and misdirection, what will be detailed in the sequel, has been the failure to properly understand the nature, source, and roles of associations, and thus their differentiation from attributions. It is this obscurity that has abetted the hold that mereology—CEM—has had on the ontology of composition. Fundamental to a correct understanding is attention to the fact that we are familiar with associations as the subjective products of minds, either as willed consciously (e.g., as with random lists or ‘sets by enumeration’) or as generated subconsciously (a standard topic in psychology). Associations so given have played a primary role in the ontology of British empiricism, and there in their immediate and defining natures as cognitive arbitrary unifications. John Locke, for example, observes: “’Tis evident then, that the Mind, by its free choice, gives a connexion to a certain number of Ideas; which in Nature have no more union with one another, than others that it leaves out.”58 This is repeated by Hume who states that “nothing is more free” than the imagination in forming associations as ‘bonds of union’ among ideas “in what form it pleases.”59 The point relevant herein is that regardless of whatever external psychological mechanisms there are that motivate the creation of associations, e.g., Hume’s “principles of union or cohesion among our simple ideas”, i.e., “RESEMBLANCE, CONTIGUITY in time and place, and CAUSE and EFFECT”, and that function, in Hume’s words, as ‘gentle forces’ for the creation of associations, each association is itself “not to be consider’d as an inseparable connexion.”60 I.e., nothing about, internally or externally, associated entities necessitates their being thus connected. Expanded ontologically, these theses point to the fact that an association is a combinatorial act by a sustaining intellect, one that selects-and-links just certain subjects independent of any relevance to or conditions on them, and what as such neither necessitates nor precludes any other unions (associations or attributions) among any entities. It is to be noted that, though private to and ontically dependent solely upon the mind whose agency produces and retains them, the replication of such wholes in other minds—the production of isomorphic networks of associations—is possible through the motivating medium of language.61 Now the further clarifying and synthesizing thesis I would advocate

|| 58 John Locke, An Essay Concerning Human Understanding, P. Nidditch (ed.), (Oxford: Clarendon Press, 1975), III, V, 6, p. 431. 59 Hume, A Treatise of Human Nature, 1.1.4.1, p. 12. 60 Ibid., 1.1.4.1–7, pp. 12–14. 61 E.g., in the minds of each student as a teacher says “Let us consider the set consisting of 3, 5, 7, and 9.”

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herein is that all wholes whose unifications are arbitrary and unconditioned by any mutual qualitative relevance among the constituents (e.g., what I will argue are the wholes fictionalized as theoretical sums and sets) are effected by acts of cognitive association, with the resulting wholes thus subject to the finite and discursive limitations of the minds that effect them. Warrant for this thesis is that, first, to otherwise posit extra-conceptual arbitrary unifications is to hypostatize the conceptual, analogous to the projection of abstracted or invented intensions into Platonic Forms existing in a transcendent realm. Second and relatedly, the thesis is supported by an application of Ockham’s Razor: with the existence of unifying intension-conditioned attributions, conceptual and extraconceptual, we simply do not have the explanatory need to posit extra-conceptual random unifications. The remainder of this work will be offered as warrant for this ‘shave’. In net, the contention is that all extra-conceptual and some conceptual plural unifications are intension-determined (i.e., are facts or their complexes), whereas all arbitrary connections, i.e., associations, are conceptual only (what I will argue form the real wholes behind the fictions that are theoretical sums or sets). In particular, I will in this work (mainly here and in Sects. 1.5 and 3.4) give a brief and tangential analysis of associations, but one sufficient both, first, to avoid two consequential types of errors concerning plural unities one finds in the tradition, and second, to understand how associations can be integrated into and so reinforce the ontology of attribute instances that is our primary focus. In regard to errors, there is first the easy error of misidentifying associations with the linking aspects of attributes, what is correlative with and abets the error of misidentifying an attribute instance, e.g., Is-Redi, with either its subsumed intension, e.g., Red, a common construal of realism, or with this intension somehow individuated, e.g., Redi, as with trope theory. An attribute as either of the latter is combinatorially inert—substance-like—and so in need of something further to link it to the subject(s) it characterizes. And so again, this link cannot be a further attribute on pain of vicious regress, and thus one is left with the only other alternative for inter-entity connectivity—associations. This is, for example, Hume’s error and lies behind his tenet that “the mind never perceives any real connexion among distinct existences.”62 What for Hume is being denied as ‘real’ are intension-determined connections, i.e., attributions, requiring then that he account for given ‘connexions among the discrete’ with associations. Correctly, Hume recognizes associations are private cognitive

|| 62 Hume, A Treatise of Human Nature, Appendix, 21, p. 400.

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acts. And, because Hume has denied real relations, eliminated is the epistemic bridge between the conceptual and extra-conceptual and thus the only subjects available for his associations are private sensa, e.g., the association of Redi, Sweetj, Crispk, etc., under the term ‘Apple a’. The issues here will be detailed in Section 3.4. Relatedly and of import, though Hume recognizes associations as cognitive acts of unification among the discrete (the ‘separate’), he does not appreciate that such acts are, like all acts, expressions of agency (power/efficacy), what Hume denies in any form and especially as the nature of efficient causation. I will argue in Section 4.3 how all unity among the yet discrete, whether by attribution or association, requires in its atomic form a state of outwardlyachieving trans-entity unifying act—a sustained exercise of combinatorial agency—by one entity of itself with and among other entities thus unified. A second type of error related to associations concerns substitution of formal constructions out of mereological sums or of sets, as posited by their respective formal systems, for objective aspects of reality. In regard to sets this has been the recent complaint of, for example, Peter Simons63, and independently by Lowe64, Simons arguing also for the explanatory vacuity of formal mereology with regard to structured wholes65. Despite whatever advantages such constructions have, such as scope (trading width for depth) and logical precision (often at the cost of perspicuity) reinforced perhaps by aesthetic elegance and ingenuity, it is an error to identify these models with the systems modeled. Underlying all such errors is the failure to understand the nature and source of associations and, I argue, their essential though often implicit roles in wholes that are fictionalized as theoretical sums and sets. First, because the production of associations is psychologically facile, including subconsciously, and this because they are not tied to anything descriptive of their subjects, they and their subjective dependence are easily ignored or abstracted away. Abstracting away their source and ontic dependence upon minds but retaining explicitly the unity effected by arbitrary associations, we have, for example, the posited Platonized ‘mappings’ or ‘functions’ assumed in theoretical mathematics. Going further and sliding in easy inattention to both the cognitive dependence of and the ‘subject-irrelevant’ connections that are associations, the specious illusion is that the results are objective unities—‘composites’—without constituent unifi-

|| 63 Peter Simons, ‘Against Set Theory’, in J. Marek and M. Reicher (eds.), Experience and Analysis. Proceedings of the 2004 Wittgenstein Symposium (Vienna: öbv & hpt, 2005): 143–52. 64 Lowe, The Four-Category Ontology, pp. 5–6. 65 Peter Simons, ‘Real Wholes, Real Parts: Mereology without Algebra’, The Journal of Philosophy 103 (2006): 597–613.

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ers. This is the conceptual a priori source of the understanding of sets found in set theory and of the sums of mereology (CEM). For both, the resultant wholes are retained but the necessary effecting unifiers are absent from their official formalizations. In regard to CEM the evidential residue of ignored subjectirrelevant associations, whereby any things are freely united or not, is the Humean ‘principle of recombination’: in Lewis’ words, “Apart from that [the “proviso: ‘size and shape permitting’”], anything can coexist with anything, and anything can fail to coexist with anything.”66 Finally, if in this abstractive process the wholes themselves, as numerically distinct entities with their own beings, are denied, but somehow differentiated groups or ‘blocks’ of different elements are retained, the latter groups are mereological sums (or fusions) as intended under the Composition-as-Identity Thesis (CI): a sum is nothing more than its parts. In regard to sets (or ‘classes’) the absence-of-unifiers point is made by the early Bertrand Russell who observes that their “parts have no direct connection inter se”67, what is likewise true of mereological sums. But, what I urge is that with such wholes so construed we have the unobserved contradiction of ‘isolated (unconnected) elements taken jointly’ (connected), and where at least in set theory the ‘jointly’ implies an emergent whole distinct from its elements, but where this is denied of sums under Composition-as-Identity (CI). With all such wholes and constructions we have logical fictions, and in being inherently fictitious—ignoring what is essential—they are ontological distortions. At their core these mereological and set-theoretic construals of composition sin against a fundamental ontological principle, one that will be central to this work. Viz., All unity and so composition requires agent-unifiers both to ‘hold-together’ and to ‘select’/delimit just the entities that jointly with the unifiers give differ-

|| 66 Lewis, Plurality of Worlds, pp. 87–90. For a critique of Lewis’s adoption of a principle of recombination see Frank Hofmann, ‘Truthmaking, Recombination, and Facts Ontology’, Philosophical Studies 128 (2006): 409–40. As evidence that Lewis thinks of all unity among the discrete as arbitrary, and what I am arguing can only be by associations, is his statement regarding attribution that there may be among “alien individuals” a particle that is “both positively and negatively charged” (ibid. pp. 91, 114); what is my point that attribution as association (e.g., as under Compresence) allows for an entity to be characterized, absurdly, as both, say, round and square. 67 Bertrand Russell, The Principles of Mathematics, 2d ed. (1903; reprt. ed., New York: Norton, 1938), p. 140.

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entiating identity to necessarily emergent wholes and their emergent attributes. For, a plural whole of whatever kind is not just any entities singly and in isolation, but precisely certain-ones-together and in this excluding all others. Even Armstrong in advocating the reductive advantage of ‘permissive mereology’ asserts that “mereological wholes are identical [his emphasis] with all their parts taken together [my emphasis]”68, though for his reductionism the ‘taken together’ can be nothing in itself and in addition. To the contrary, such a particular ‘togetherness’ of just certain entities cannot be identical to any of these entities joined, but yet it is essential to the being of their collective whole, and so it must likewise enter into the composition of this whole. Because of this a whole is essentially something more than (i.e., emerges upon) its parts, and this because it has one or more inter-connectors—‘gatherers’—as its parts. Both are Aristotelian theses, my emphasis here being Aristotle’s insight that all unity among the non-identical requires ‘principles of unity’.69 Aquinas later reiterates the point: “Every composite has a cause, for things in themselves different cannot unite unless something causes them to unite.”70 Importantly however, assumed by Aristotle, Aquinas, and at least implicitly by many subsequently, is the intuitively plausible but erroneous assumption that each whole has its unity by a single shared principle—unity as a oneness is by the constituent one (A8). The correction is that oneness among the non-identical describes the singularity of a resultant of, not the causes of, what can be the combined effect of multiple agent unifiers. Or in short: To be one describes the effect, not necessarily the cause(s), of a unified complex whole. We will emphasize an important case of this mistake in Aristotle’s assumption that a monadic form, e.g., Is-Human, both attributionally describes a whole and is the single internal unifier/organizer that gives it the completed nature that can be so described. Our powerful refinement on all of this is that the generating ‘togetherness’ of a plural whole (i.e., a whole in which the parts remain discrete) is by the unifying-selecting agencies of either 1) one or more subject-relevant/descriptive attribute instances and their derivative fact-structures (a structure being more than the ‘sum’ of its parts), or 2) by one or more arbitrarily constructed cognitive associations (each

|| 68 Armstrong, A World of States of Affairs, pp. 12–13. 69 For a detailed exposition of Aristotle’s analysis of parts and wholes see Koslicki, The Structure of Objects, pp. 122–64. 70 Thomas Aquinas, Summa Theologica, 3 Vols., trans. Fathers of the English Dominican Province (New York: Benziger Brothers, Inc., 1947), Pt. I, Q. 3, Art. 7.

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such whole being precisely the ‘sum’—as unities via associations—of their parts). This distinction then supports the caution that artificial constructions out of the latter are not to be confused with the objective structures that derive from the former. And in particular, associations as subject-indifferent linkings cannot, singly or jointly, provide any order among, or differentiate different wholes from among the same plurality of, associated subjects, the opposite being essential to structures and effected by relations. Associations cannot go proxy for relations, nor indeed, in the absence of controlling intensions, can they go proxy for monadic properties in their defining attributional natures. Our summarizing and global theses are then that all composition whatsoever is ‘restricted’ in being by means of one or more of the above five types of unification, and, in these constituent ways, composition is identity. Included here is a correction of the above and explanatorily impotent ‘Composition-as-Identity Thesis’ and its assertion that wholes as sums are nothing derivative and distinct from just their parts, what a fortiori requires the denial of their having emergent attributes that presuppose such wholes as singular subjects, e.g., as the second relata of mereology’s own Is-a-Part-of relation.

1.4 On the Emergence of Attributes and Wholes We can restate the above theses in terms of the recently prominent analytic concept of emergence (= ‘to arise out of’ (from the Latin emergere: ‘out of an immersion’)). Viz., all wholes emerge upon their parts, and an external mark of this is their being each one subject for emergent attributes (the immediate such attribute being Is-a-Whole (or the synonymous Is-a-Plural-Unity, Is-a-Heterogeneous-One, etc.)). And internally, wholes of discrete parts are emergent single entities because among their multiple parts are inter-connections that are either attribute instances or associations, both themselves emergent: instances upon relevant foundations had by their subjects and associations upon the minds that create them. Principally, attributes and their resultant wholes— facts—emerge correlatively, and hence emergence is as ontically fundamental and pervasive as attribution. Thus, analyses of each can serve to inform that of the other. It is said that within contemporary philosophy, particularly in the philosophy of science, there has been an ‘emergence of emergence’. As preparatory context for considering emergence as currently analyzed, let us observe how the concept behind the modern term is situated in the tradition. Underlying what motivates its attention is the founding problem of ontology’s classic topic of wholes and parts, a topic central to this work. The problem is succinctly: Is a

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delimited diversity of entities, as such differentiated from other such pluralities, i) an addition in being—something distinct from and ‘over and above’—the beings of each of these entities, and ii) if so, is the then emergent whole or composite something in its being beyond the beings of all these parts taken jointly? Only the extreme mereological nihilists answer no to i), and our analysis will explain the intuitive yes in arguing that no unity among the non-identical exists without a unifying connectedness among them, and this oneness makes for a being in its own right distinct from each of its proper parts—an ontic addition beyond the parts that are unified and their unifiers which are also parts. Further and in regard to ii) is a relevant and crucial clarification of what is to be meant by ‘parts taken jointly’. On our assay the ‘jointness’ or ‘togetherness’ of the entities that are then parts of a composite is necessarily by some parts that have the ontic role of connectors, i.e., agent unifiers, of themselves with the other parts, the then transitive unification across all the composing connections making for a whole whose being is just these ‘parts taken jointly’ in this sense. I.e., here and necessarily the ‘taken jointly’ is an inter-part oneness achieved by some parts being selective unifying causes among the others. If, however, we mean by a composite’s ‘parts taken jointly’ all and only these parts but construed as absent any causes of their circumscribed togetherness, then the composite, which requires such constituent causes in order to exist as its own particular and differentiated entity, would be more than the abstraction of ‘parts taken jointly’ in this sense. Unless ‘entities jointly’ means ‘oneness among entities as inter-connected’, and so where the inter-connectedness brings with it an addition to being beyond that of each and all of the entities prior to this connectedness, then there is no resultant—emergent—whole and so nothing for these entities to be ‘parts’ relative to. Thus, composition as ‘parts taken jointly’ conceived in this second sense involves contradiction: entities ‘jointly’ without joining inter-connections are no unified one or whole, and so there is no single subject for them to be related to by the attribute Has-as-a-Part. This understanding, however, is what is implicit in Lewis’ Composition-as-Identity Thesis (CI) and by which he can hold: “Mereology is innocent in a different way [from plural quantification]: we have many things, we do mention one thing that is the many taken together, but this one thing is nothing different from the many.”71 (my insert) Here a mereological sum or fusion, and hence all composition according to Lewis, is such that the sum is nothing over and above—is just—its parts, where this means ‘parts taken jointly’ in our second sense, i.e.,

|| 71 David Lewis, Parts of Classes, p. 87. Also see his ‘Against Structural Universals’, p. 34.

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nothing beyond just the accumulated beings of its parts each construed as selfcontained and, in Humean terms, without ‘real connexion’. More on these issues in Section 1.5. A traditional if usually implicit criterion for the existence of composites or wholes being emergent in the sense of having beings beyond that of each as well as all of their prior-to-being-unified parts is what could be termed the Emergent Attribute Principle (EAP), Viz.: If a diversity of entities, x, y,…, is the subject of an attribute F not characterizing any of x, y,…, then the diversity is, as one subject/relatum for F, its own singular entity w—a whole—with a being distinct from each of its parts, i.e., w ≠ x, w ≠ y,…, and if F is a structural attribute, i.e., one whose prerequisite foundation(s) are both x, y,…, and these having a certain ‘arrangement’ or ‘organization’, then the whole w = x-y-,…,-arranged, and in this w is an increase in being over just the unarranged parts, i.e., w ≠ x, y,… The attribute F is emergent and its characterization of the plurality presupposes the latter to be a single subject-whole that itself is emergent upon— distinct but derivative from—its many parts. Appeal to the Emergent Attribute Principle (EAP) as a test for emergence is evident, for example, in Aristotle. In the Topics he observes that “among the ways of showing that the whole is not the same as the sum of its parts” are “cases where the process of putting the parts together is obvious, as in a house and other things of that sort: for there, clearly, you may have the parts and yet not have the whole, so that parts and whole cannot be the same.” (Topics 150a1520)72 The difference is that a house is its parts “compounded in such and such a way”, i.e., structured in a certain ‘manner of composition’ (Topics 150b20-25). And among texts important to our analysis herein (Sect. 4.3), Aristotle observes at Metaphysics 1041a33-b32 that a syllable or flesh are not the same as their parts absent respective types of structurings. Absent the latter, the parts of syllables or flesh are just his “heaps” and do not have the additional beings and oneness that founds them having the emergent attributes, respectively, of Is-aSyllable or Is-Flesh. Also, I point out in passing that Richard Cross has observed appeal to what I have elaborated as the EAP in the scholastics Scotus and William of Ockham.73 According to Cross, the principle is assumed by both in their

|| 72 Aristotle, Topics, trans. W. A. Pichard, at http://classics.mit.edu/Aristotle/topics.html. This text was brought to my attention in reading Koslicki who cites it as evidence that Aristotle, along with Plato, rejects the Composition-as-Identity Thesis (CI). Koslicki, The Structure of Objects, pp. 125–26. I take Plato at Parmenides 129c-d to be assuming the EAP. 73 Richard Cross, ‘Ockham on Part and Whole’, Vivarium 37 (1999): 143–67. Also see Calvin Normore, ‘Ockham’s Metaphysics of Parts’, The Journal of Philosophy 103 (2006): 737–54.

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debate on whether a material substance is an entity over and above its parts. According to Scotus a material substance consists of matter, form, and a real relation not reducible to its foundations and that is an actual union between them. As such the substance is something numerically distinct from each part and what is simply an aggregate of these parts, and a proof is that the parts each or their aggregate do not have attributes such as generation, corruption, and certain passions, actions, or accidents that the substance has. Ockham denies real ‘between’ and inter-connecting, and thus organizing, relations74 and holds that a material substance is numerically the same as just its matter and form, though the union is not that of aggregation.75 He holds that at least some of the emergent attributes Scotus cites are properly attributes of the parts and derivatively of the whole. For substantial and accidental wholes, e.g., artifacts, the “whole is nothing other than its parts joined together and united” but where this unity is “no new thing”.76 Ockham holds, as does apparently Lewis and explicitly John Heil (below) as contemporaries, that at least for some wholes “The whole is nothing other than all of its parts—not always, but only when they are collected, arranged, or united in the right way”, and yet this structuring or ‘arrangement’ is nothing beyond the things arranged—“no new res is generated anew in its own right as a whole.”77 Key and telling here is that for all three philosophers polyadic relations are not in themselves conceived as real interconnecting or ‘bridging’ entities that would be generative of an emergent oneness beyond the things joined, but rather relations are reduced to their relata, monadic properties of their relata, or to sets of ordered pairs (also construed as sets) of their relata. With each strategy, relations (and indeed monadic properties for the same reason) are ‘retracted’ back into their then mutually ontically isolated subjects, and thus there is no new and resultant whole. This focuses us on the crucial assumption behind the EAP as a criterion for emergence: structure or organization is one mark of emergent wholes because the composing attributes, most obviously relations, that are essential to the structuring are as real as the subjects they externally unify themselves with, and the latter unifications cooperatively generate a oneness and so a whole distinct from the otherwise isolated parts. However, if attribution as external adherence is denied and replaced with its historically prominent misconstrual as internal inherence then

|| 74 William Ockham, Summula philosophiae naturalis, I, 20, 1078–9, trans. by Robert Pasnau, and available at http://spot.colorado.edu/~pasnau/research/ockham.summula1.pdf. 75 Ibid., Preamble, 25–40. 76 Ibid., 19, 985 and 20, 1074 77 Ibid., 19, 1050–1, 1063–4.

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any real inter-entity connectedness disappears and with it any new entity that is ‘more than just its parts’. Most forceful in establishing the error in attribution conceived as inherence is the impossible monadic reduction of relations argued in Section 2.6. We can summarize, then, the position of Ockham and his ontological kin metaphorically as their contracting to own a house but thinking this only requires them to pay for the materials and not the construction necessary to properly organize them. To avoid confusion regarding the EAP relative to my theses, note first that I argue that any diversity of entities which is one subject for an attribute, whether each entity singly is characterized by it or not, e.g., Is-Many, Is-One, Is-Complex, Has-as-a-Proper-Part, Has-a-Conceptual-Existence, is necessarily its own single entity, this by an ineliminable lattice of constituent unifiers, and so a whole with a reality distinct from just the nodes linked. And second, the agentunifiers essential to effecting an emergent whole can be other than intensioncontrolled n-adic attributes for any n—they can also be arbitrary cognitive associations, and so the resultant additions to being need not be just structured wholes, but can be as well the conceptual complexes, the latter the cognitive realities from which theoretical sums or sets are fictional abstractions. In regard to more recent views, advocates argue that emergence exemplified as structured wholes is pervasive: it being “extremely common—the rule, rather than the exception,” technical examples being offered from the physical, biological, and psychological sciences.78 These and the more intuitive and simple examples of the previous sections all point to it being an essential characteristic of structures that, determined by the defining specific ‘arrangements’ of their parts, they have emergent attributes, these attributes then being as pervasive as are structures. Mentioned previously is the classic chemical example of table salt with it and its beneficial properties emerging upon reaction structures among highly reactive sodium and poisonous chlorine atoms. A similar exam-

|| 78 William Wimsatt, ‘Aggregativity: Reductive Heuristics for Finding Emergence’, Philosophy of Science 64 (Proceedings) (1997): S372–S384. The literature on emergence is extensive, my studies having included Michael Silbertsein and John McGeever, ‘The Search for Ontological Emergence’, The Philosophical Quarterly 49 (1999): 182–200; Paul Humphreys, ‘Emergence, Not Supervenience’, Philosophy of Science 64 (Proceedings) (1997): S337–S345; F. Boogerd, et al, ‘Emergence and its Place in Nature: A Case Study of Biochemical Networks’, Synthese 145 (2005): 131–64; William Hasker, The Emergent Self (Ithaca: Cornell University Press, 1999); The Re-Emergence of Emergence, Philip Clayton and Paul Davies (eds.), (Oxford: Oxford University Press, 2006). Concerning the emergence of the animate from the inanimate see Jeremy Sherman and Terrence Deacon, ‘Teleology for the Perplexed: How Matter Began to Matter’, Zygon 42 (2007): 873–901.

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ple is that of water, it and its properties (e.g., related to fluidity, adhesion and cohesion, density) emerging upon reaction structures among hydrogen and oxygen atoms that in their separated states are gases. To reinforce these points and as a heuristic for the following, consider the even simpler example of a geometric square, an example given in the literature as an obvious counter to those who would deny emergence.79 A square, □, consists of four equal straight line segments joined in pairs at their endpoints and arranged so that among certain pairs there are four right-angles that together make a closed figure. Restructure these right-angles (substructures) differently and you can get, for example, a cross, . The square is a single entity determined by but distinct from its parts (what are these right-angles, their line segments, and the specific relations among them), this marked according with the EAP by the fact that it is itself a single subject for attributes, and especially when these attributes are had neither by its parts, nor by other possible re-arrangements of them (e.g., the cross). Some of these emergent attributes are, for example, the properties IsSquare, Is-Closed, Has-Equal-Diagonals, Has-Parallel-Sides, and certain relations with other geometric figures. The first three attributes listed are ‘novel’, ‘new’, or sui generis in the sense that they are not instanced by the parts of the square, novelty being often cited as an essential characteristic of emergence. Reinforced by the example of the square is the important fact that, though emergence is usually studied as characterizing properties of structures, it is also wholes qua wholes of whatever kind (e.g., structures or random ‘heaps’) that each exists and only so as emerging from—as ‘something more than’—its parts. And, it is a central thesis of this work that there are ontically fundamental and mutual relationships between the emergence of attributes and the emergence of any wholes. Toward these insights let us add some precision to the concept of emergence. From among the suggested criteria found in the literature for emergent properties I propose a generalization of ones given by Paul Humphreys80: X is emergent upon S, T, U,… if: 1) X is in some sense novel with respect to S, T,

+

|| 79 Reinhardt Grossmann, The Categorical Structure of the World (Bloomington: Indiana University Press, 1983), p. 249. A similar example of geometric emergence extended to a three dimensional cube is found in Pier Luigi Luisi, ‘Emergence in Chemistry: Chemistry as the Embodiment of Emergence’, Foundations of Chemistry 4 (2002): 183–200. 80 Humphreys, ‘Emergence, Not Supervenience’. I consolidate into 1) what Humphreys separates as the criteria that emergent properties are novel and that they are qualitatively different from the properties from which they emerge. He states that he is not suggesting that any emergent phenomenon must satisfy all of these criteria. My claim is that in what are the two categories of emergent entities—attributes and wholes—there are senses in which all of the above criteria apply.

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U,…, 2) X could not exist at a lower level of each of S, T, U,…, 3) different laws apply to X and to each of S, T, U,…, 4) X derives from an essential interconnection among and only S, T, U,…, and 5) X is holistic in being existentially dependent upon S, T, U,… only in their togetherness as a unified one. Humphreys intends that X, S, T, U,… be properties, but these criteria apply equally to X as any whole, e.g., a structure, where S, T, U,… are its parts. Details on this below. What I suggest here as underlying these criteria and the core sense of the phrase ‘to emerge’ is: ‘to have an existence and nature distinct from (‘new’) but determined by the existences and natures of (‘arising out of’) other entities’. In this broad sense and with regard to attributes as ontically primary, on our assay every n-adic attribute proper is an instance, Rni (e.g., Is-Square1i), emergent upon some n subjects jointly (e.g., the square □, where n = 1). Citing the above relevant and more specific criteria in brackets, this is so because of the defining nature (the ‘laws’ (our T2-T10)) of attribute instances relative to the subjects they join into facts [3]: when the necessary and sufficient foundational conditions prescribed by an intension Rn (e.g., Square1) are satisfied by some n subjects, then there exists, distinct from all of these, an instance Rni attributionally combinatorial of itself to and among the n subjects [4,5]. Instance Rni, being unique in its unifying act among the n subjects it presupposes, can exist on no other subjects, and a fortiori not at the level of its parts [1,2]. Significantly, attribute instances can be novel or ‘new’ in two ways, a distinction corresponding to and making precise one found in the literature.81 Each individuated instance is numerically new in being unique to its subject n-tuple, though its intension may be repeated in instances at the level of its subjects. For example, a property instance Is-Complex1i may have a whole w as a subject, while the parts of w may also be or have other instances of the intension Complex1 as their attributes. In a contrasting narrower sense usually associated with emergence, an instance Rni may exist among an n-tuple of subjects but where no other instance of the intension Rn exists on or among parts of these subjects, Rni then being qualitatively as well as numerically sui generis relative to its subjects. E.g., it may be the case that a certain neural structure (e.g., a brain) is the subject of an instance Is-Conscious1i, but that no part or substructure (e.g., a neuron) is characterized by an instance of this intension. An n-adic attribute instance all

|| 81 The distinction is discussed by Jaegwon Kim, who attributes it to Robert Van Gulick under the terms, respectively, of ‘specific value emergence’ and ‘modest kind emergence’. See Kim, ‘Emergence: Core Ideas and Issues’, Synthese 151 (2006): 547–59, and Van Gulick, ‘Reduction, Emergence and Other Recent Options on the Mind-Body Problem: A Philosophic Overview’, Journal of Consciousness Studies 8 (2001): 1–34.

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of whose n subjects are simple would be emergent in this narrower sense. Among examples here would be the obvious Is-Simple1i, and, on the assay of instances in Chapter 4, an instance Is-a-Correlative-Aspect-of-an-Instance-with2j, since a relata-pair for such an instance is a combinatorial act and an intension controlling the act, both simple on our assay. Further and also in the above broad sense of emergence, every whole qua whole (e.g., a structure or a random ‘heap’) is an entity that emerges from (is ‘over and above’) its constituents/parts. To reinforce the point, consider a diversity of Humean entities a, b, c, …, each of whose identity is independent from any of others, and let s be a grouping of any two or more of them. If the whole s is not something in addition to these constituents, it can have no attributes not had by these constituents singly. But s precisely as a whole having these constituents has the attribute of being dependent upon each (and all) of them, an attribute none of its constituents have. A whole is not just diverse entities singly, but certain entities and not others collected in a unity—a delimited and differentiated one. As previously observed, Aristotle makes this point in his Topics, VI, 13, against those “who seem to assert that the parts are the same as the whole,” for “you may have the parts and yet not have the whole, so the parts and whole cannot be the same”, as in the clear case of a house. In terms of emergence, a whole exists only as itself a unified and single entity [4,5], distinct then in its being and identity from its parts (sui generis; [1,2]), what in the compositional details making up its unity there are foundations for unique (‘new’) instances of attributes of it [3], some of these then possibly intensionally novel relative to its parts. With all of this we give detail to the Aristotelian maxim that ‘Being and unity are convertible’ (e.g., Meta. 1061a15). Now, a principal argument herein is that all plural (‘articulated’) wholes have their existential unity only by constituent agent inter-connectors, viz., attribute instances or associations. Specifically, derivative of (‘arising out of’) composing unities effected by attribute instances are the emergences of wholes that are facts, and their compounds of more complex structures. These wholes are each ‘more than the sum of its parts’ in being a structure via inter-connecting attribute instances among other parts. And further but in contrast to attributions, it will be argued that associations also emerge, though not from their subjects to which they have no intrinsic relevance, but from the agencies of minds and their structures that create and sustain them, and with the thereby cognitively associated subjects there emerge arbitrary conceptual wholes, e.g., sets properly understood. These wholes are each ‘precisely the sum of its parts’ when ‘sum’ is understood properly as ‘a unity via inter-connecting associations’ (Sect. 1.5). Succinctly, whether by attribution (things-‘arranged’) or association (things-‘heaped’), the con-

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stituent unifying agency prerequisite for things-unified makes the latter an ontic gain over just the things. Both emergent attributes and wholes have been denied, at least for certain classes of entities, e.g., the reductive elimination of ‘internal relations’ (Sect. 2.6), the denial of mereological sums or fusions as anythings more than their parts (Sects. 1.3 and 1.5), or of any composites whatsoever (Sect. 1.1). Indicative, the denial directed at structured wholes is held to be that “Structures simply do not have properties, only their parts do!”82 (The assumed further but correct principle here is: To have no attributes is to have no being (a principle crucial to the debate over substrata of ‘prime matter’ or ‘bare particulars’; Sects. 2.4-2.5).) John Heil, for example, has recently urged that what truly exist are atomic simple substances and their monadic properties, everything else being ‘organizations’ or ‘arrangements’ of these and the latter complexes and their ‘properties’ and as such are “no addition to being”.83 Heil holds that, though “organization is important”, genuine properties cannot be ascribed to an organization as a whole (e.g., a tomato, what is a substance only ‘by courtesy’), a claim to the contrary having “the aura of a category mistake.”84 Though not clear from the text, it would seem that by ‘category mistake’ he means that monadic properties require each a single subject—something that is a ‘one’—but an ‘arrangement’ (i.e., a structured whole) is a plural ‘many’ that, I surmise, he thinks lacks sufficient unity (cf. Russell’s ‘bewilderment’ concerning classes as each both a one and a non-identical many, Sect. 1.5).85 At any rate, what for Heil has properties in the true sense are only atomic substances and these are without discrete parts—his substances being per se subjects (classic assumption A3).86 For Heil and others, abetting their specific denials has been a general criticism of emergence: that there is with it an explanatory gap—an ontological ‘missing link’—between an emergent entity and the base from which it is said to derive. Or in Heil’s words, “Any conception of emergence is incomplete without an account of the bearers of emergent proper-

|| 82 Grossmann, Categorical Structure of the World, p. 249. Grossmann rejects the thesis as counterfactual, ibid, pp. 238ff. 83 John Heil, The Universe as We Find It (Oxford: Clarendon Press, 2012), pp. 24, 46, 52, 54, 141, 274–88. 84 Ibid., pp. 8, 21–22. 85 E.g., ibid., pp. 21–22, 28, 141, 286–87. 86 Ibid., pp. 4, 18–19, 28–29, 38, 51, 99, 277–78. Heil holds that “We use predicates to express truths, truthmakers for which are rarely properties of substances. Only when you get to fundamental physics, do predicates begin to line up with properties.” (p. 287)

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ties”87 (his emphasis), and he is skeptical that this is possible. I take the question to be: What is the composing nature of a complex whole whereby it is a single subject for attributes that are intensionally relevant to this composition? Our analysis will answer this question and show how there is no explanatory gap between emergent attributes and their bases. Viz., every attribute instance in characterizing one or more subjects effects a real (‘addition to being’) external connection of itself with them, and this real unity can be compounded transitively across multiple instances via shared subjects resulting in lattice-like complexes. The resultant heterogeneous unities are each a real oneness, each complex then a single subject ‘bearer’ for further attribute instances emergent upon it. And these emergent attribute instances Rni are bound with a necessity to their subjects (Sect. 4.2) because the foundations/grounds their intensions Rn prescribe as prerequisite for and that are satisfied by their subjects include some of the intra-linkings—specific properties and relations—that make up the structures of their subject wholes. Detailed here will be a demonstration of how real (‘addition to being’) unity is not the reserve of the simple or of the numerically one (contra classic assumption A8), but equally and more commonly achieved by the collective agencies of multiple attribute instances articulated in certain, including hierarchical, ways (Sect. 5.1). In all this it will be seen how programs of attribute-to-foundations and whole-to-parts reductionism are bogus and derive from fundamental and related ontological errors.

1.5 On the Fictive Nature of Unifier-less Wholes: Formalized Sums and Sets Contrary to our thesis of Section 1.3 asserting that all unity among the discrete requires constituent selecting and collecting agent-unifiers, sums (fusions) and sets (classes) are within their various formalizations taken to exist independently of any such internal connectors. And relatedly, they are held to exist independent of any mind that might provide the requisite intra-connectedness (an interesting exception, and one relevant to my analysis, would be the apparent view of Georg Cantor (the ‘father’ of set theory) that the unity among elements forming a set is provided by the Divine Intellect (below)). That is, given the existences of any entities, their and just their unification as a sum or a set is

|| 87 Ibid., p. 28.

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held to exist (with exceptions required by the classic set theoretical paradoxes88) and to be independent of any unifying connections, cognitive or extra-cognitive, among them.89 If one takes this ‘Platonist’ view that sums and sets are real and not fictitious posits, then we would have, contrary to the above thesis, categories of wholes for which there is no cause of the being-bestowing and differentiating unity of each beyond just the independent and isolated existence of each of its parts/elements. Focusing first on sets, a set is then somehow just certain entities and not others, i.e., the former jointly/collectively—hence an emergent whole—and so to the exclusion of the latter non-elements, and yet where there is no cause or principle of this selective unity among and just what are then related to the set as elements. The point can be amplified as follows. Made canonical by the Axiom of Extensionality, the only contributors to the being of a set are its elements, and implicit here is the understanding that set unification is such that an entity makes numerically the same contribution, viz., itself, to each set in which it is an element. But then no entity, say a, can as itself and as part of its identity be a cause of the collecting unity of a set of which it is an element, e.g., {a,b,c}, i.e., an element a cannot as part of its composing being be the set-forming unifier of itself with and so join together the other elements, e.g., b and c. For otherwise, a in making numerically the same contribution—its identical self—to every set it is a member of would have to make numerically the same contribution to the unity of every set in which it is a member—this being part of its identity. But, to make numerically the same contribution to the unification of two sets is to effect numerically the same connections and so be linked to the same connected things, i.e., given that a is the principle of unity of itself with b and c in {a,b,c}, then b and c would have to be elements in every set in which a occurs, e.g., there could be no sets like {a,e}, or {a,b,e} for e ≠ c. Since no element of a set is a unifying cause of the set, and the only entities composing the being of the set are its elements, then a set has no unifying cause. But reinforcing our thesis and as noted above, this observation smacks of contradiction: a set is a whole distinct from and emerging upon its

|| 88 I have argued elsewhere that the logic inherent in the instance ontology developed herein, what I have termed Particularized Predicate Logic, or ‘PPL’, can diagnose and avoid in non-ad hoc ways the classic self-referential paradoxes, including Russell’s Set Paradox. See ‘The Logic of Instance Ontology’, Journal of Philosophical Logic 28 (1999): 81–111, with minor corrections reprinted in Mertz, Essays on Realist Instance Ontology and its Logic, pp. 183–214. 89 An intended intuitive difference between sums and sets is that the same parts cannot make up distinct sums, but the same elements can compose distinct sets, e.g., {a,b,c} ≠ {a,{a,b}, {b,c}}, i.e., the last set has elements that occur more than once, something not possible for sums.

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elements ‘together’ which requires for them a unifying connectedness (i.e., a combination (= an act and resultant of entities being combined)), and yet without a composing cause of this connectedness the elements must remain isolated (i.e., not combined/linked together) things. Max Black once described in a humorous way this conflict with regard to sets: it is supposedly the case “that a set having three members is a single thing, wholly constituted by its members but distinct from them [i.e., emergent upon just the existences of each of the elements and not upon their being connected by further constituents]. After this, the theological doctrine of the Trinity as ‘three in one’ should be child’s play.”90 (my insert) The difficulty here is symptomatic of the failure to recognize that all plural wholes require constituent unifiers. Instructive in this regard and anticipating a scheme we shall generalize (Sect. 5.2), medieval philosophers/theologians (e.g., Aquinas91) offered as an explication of Trinitarian unity a construal of each Person as a relatedness among the other two. Here the intent is that the things connected are themselves the connectors,92 what I will argue is to be generalized as both the possible and necessary nature of foundational entities making up any primary ontic stratum. But the latter are attributes, as intended in the Trinity theory (e.g., IsFather-of), and all attributes (as instances) are intension-determined and subject-relevant connectors, as such structuring of their resultant fact-wholes. Hence, they cannot be the unifiers of unstructured sums or sets whose unities are independent of any mutual relevance among the elements. Directly relevant here is Russell’s “bewilderment” in the earlier Principles of Mathematics over the nature of classes/sets as each both a ‘many’ and a unified single entity. According to the then Russell, a class as many is not identical to the class as one. His assessment was that: “In a class as many, the component terms, though they have some kind of unity, have less than is required for a whole. They have, in fact, just so much unity as is required to make them many, and not enough to prevent them from remaining many.” 93 One explicit source of the confusion here is the combination of Russell’s recognition that for elements to be a class they must have a unification that involves something more than

|| 90 Max Black, ‘The Elusiveness of Sets’ in Caveats and Critiques: Philosophical Essays in Language, Logic, and Art (Ithaca: Cornell University Press, 1975), p. 86. 91 Aquinas, Summa Theologica, Pt. I, Q’s. 28–40. 92 Aquinas asserts that “Thus it is clear that in God relation and essence do not differ from each other, but are one and the same.” Summa Theologica., Pt. I, Q. 28, Art. 2. And, “The persons are the subsisting relations themselves.” (Ibid., Pt. I, Q. 40, Art. 2) 93 Russell, Principles of Mathematics, p. 69.

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just their otherwise isolated selves, together with his crucial assumption that only attributes, and in particular relations, are trans-entity connectors. But concerning the latter, attribution is not the kind of unity found in a class. Russell argues in effect and rightly that unity via an attribute and the foundational conditions it sets on its subject(s) is selective and effects a structured fact (Russell’s ‘propositions’94), whereas the natures of the elements of a set are mutually irrelevant or random—any entities whatsoever forming a set—and a set is an internally unstructured entity. Hence for Russell, the unification that is a set is not via any constituent unifiers—the elements of a class “have no direct connection inter se.”95 And yet this, he asserts, is required to make the elements one—a whole.96 Coming close to our analysis in terms of association, Russell’s discussion is in a context where he proposes that the kind of connection required among elements of a class is the referent of one sense of the term ‘and’, as in the class ‘A and B and C’. Focusing on the simplest case of a ‘many’, he observes that “Every pair of terms, without exception, can be combined in the manner indicated by A and B”, where he implies that ‘and’ in this sense provides the needed kind of unity, viz., one unconditioned by anything other than the existences of the elements. But then Russell asks: Is ‘and’ in the set ‘A and B’ anything beyond just A or B? He answers that “if it were, it would have to be some kind of relation between A and B; A and B would then be a proposition [i.e., a fact], or at least a propositional concept [perhaps (?) a fact with a conceptual existence only], and would be one, not two.”97 (my inserts) Russell is of course correct in observing that ‘and’ in the sense intended here is not an attribute in that it prescribes no conditions that subjects must satisfy in order to be conjoined by it, it being in this sense synonymous with association. But he errs in not recognizing association as distinct from but in its unifying efficacy on a par with attribution. Indeed, it would seem that if anything could provide the kind of loose unity that Russell apparently requires of a class as ‘many’ it would be a chain of arbitrary associations, what would be an articulated unity by the cooperative agencies of multiple constituents, the resultant unity—oneness—not effected by one attribute of or any one thing common to all the elements. For, Russell seems to think that if, contrary to the latter, a unity is by one thing then it is ‘one’ in a sense that precludes it from being ‘many’.

|| 94 Ibid., pp. 47, 71, 140. 95 Ibid., pp. 140–41. 96 Ibid., p. 71. 97 Ibid.

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This last point is central to what may be a second and implicit source of Russell’s confusion over wholes as one and as many. One gets the impression from the texts, I suggest, that Russell is committed to the classic but erroneous thesis that a plural unity is ‘one’ in his sense only as effected by a single shared entity, what is intended by the classic assumption I have termed Unity by the Constituent One (A8). That is and what was the explicit ancient and medieval conception, insofar as something is one it is undivided, so that, in particular and in order to avoid vicious regress, a cause qua cause of such a unity must itself be without division, i.e., a single entity identical across all it serves to unify. Supporting my contention that this is Russell’s view is his assertion in a later summary of his considered views that “What gives unity to a class is solely the intension which is common and peculiar to its members.”98 A whole having no such common unifier—no single collecting thread—is perhaps what Russell intends by a ‘many’. But to the contrary, as broached above and to be detailed in Section 5.1, there can be plural unities where each has a oneness via a transitivity across multiply distinct but articulated unifiers, the latter combinators being either attribute instances or associations. My point here is that it is heterogeneous wholes via associations, fictionalized in abstracting away these associations, that are classes/sets. And, these observations point to the means of removing confusion over how a whole can be both ‘one’ and ‘many’. Namely, the same complex entity can provide what are different foundations for the attributes Is-Many and Is-One: a) for Is-One the required foundation for its attributional union with a subject is ‘being undivided or if, having proper constituents, there are constituent combinators that in sharing elements provide a transitive unity (‘a oneness’) across all of them’, and b) for Is-Many the required foundation would be ‘there exist a diversity within a subject with the attribute

|| 98 Bertrand Russell, My Philosophical Development (London: Allen & Unwin, 1959), p. 67. Russell sees confusedly the role of intensions in plural unification where he would have it do double-duty: in or as a property have it be essential to providing the factual unity of the attribute with its subject(s), and, mistakenly, as something shared across all such subjects (or subject n-tuples) have it be the unifier of the whole that is its extension set. There is an analogous error with regard to monadic substantial forms (Sect. 2.2): each, e.g., Human, is posited both to be a unifier of itself with prime matter in being predicable of it as a single subject, and to be the organizing unifier of multiple parts that jointly compose its substance, e.g., a human being, i.e., to be polyadic as predicable of multiple subjects. In regard to sets, the error of having shared intensions be their unifiers is that sets (and sums) are posited as having their unities independent of any mutual relevance of parts (elements), be it by a shared intension or otherwise.

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Is-One (as given in a))’. Both grounds can be had by the same wholes. (How attributes are related to their foundations is developed in Sect. 4.2). Going further in the direction of eliminative abstraction are mereological sums or fusions under the axioms of classical extensional mereology, CEM. The ontologically substantive theses are Unrestricted Composition (Whenever there are some things, there exists a sum of those things) and Uniqueness of Composition (It never happens that the same things have two different sums). I argue that both of these theses are false. Symptomatic of this is the fact that under these axioms CEM makes reference to groupings—sums/fusions—that are required to exist each as a singular thing—a whole in addition to its parts—and yet without what are necessary causes that ‘wrap up into one’99, or group (the term intended as a verb), its parts into a resultant further whole, and so as a result and in contradiction eliminates the whole as something in addition to the parts. I.e., mereologists posit ‘manys’ that are not ‘ones’, and this is like positing color absent extension, or a one-sided coin. As previously emphasized, wholes construed as ‘nothing over and above the parts’ is the intent of the Composition-asIdentity Thesis (CI). Theodore Sider has shown how for CI in the form: For any X’s and any y, y is composed of the X’s if and only if y = the X’s, the axioms of CEM can be derived.100 Sider observes that CI underwrites mereology analogously to how the intuitive iterative conception of sets is the constraining motivation for the axioms of Zermelo-Frankel set theory.101 That CI is ‘built-into’ CEM can be illustrated in a simple way. It follows from the axioms that for any two admitted things, a and b, there is a sum [[a,b],a,b], and that this sum is identical to the sum [a,b], i.e., [[a,b],a,b] = [a,b]. This characteristic of mereology is what Fine calls ‘leveling’.102 Now what this says is that the sum [a,b] subsumed in [[a,b],a,b] contributes nothing to the latter’s identity distinct from just that of a and b. I.e., sum [a,b] has no being distinct from—‘is nothing over and above’— just a and b, and this is the claim of CI. Now, it is my point that CI is implied by mereology’s implicit assumption that its ‘wholes’—sums or fusions—do not have among their parts trans-part unifiers, for if they did these would give the resulting wholes each a beingconstituting oneness of its own distinct from its parts. Or stated in a different

|| 99 This is Theodore Sider’s characterization, his view being that in a sum the ‘wrapping into one’ is a function of identity. ‘Parthood’, Philosophical Review, 116 (2007): 51–91. 100 Sider, ‘Parthood’. 101 Theodore Sider, ‘Nothing over and above’, Grazer Philosophische Studien 91 (2015): 191– 216. 102 Kit Fine, ‘Towards a Theory of Part’, The Journal of Philosophy CVII (2010): 559–89.

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way, a sum of CEM mereology is either ‘nothing over and above its parts’ (CI) or is a real whole with a being and identity distinct from any of its parts. But the latter is possible only by constituent unifiers, what for sums would (because of the Unrestricted Composition axiom) have to be subject-indifferent associations. But, associations can be hierarchically iterated just as sets can (indeed, it is my point that the former is the source of the latter), e.g., a can be associated with b, a+b, and the latter as a single entity can be associated with c, (a+b)+c, which is different from the chain of association a+b+c, and so a violation of Uniqueness of Composition. Hence, because sums are devoid of the only appropriate unifiers—associations—they just are their (unconnected) parts and nothing more; CI. Yet, constituent unifiers are prerequisite to the beings of all plural wholes, and what for mereological sums are subject-irrelevant associations are not global and independent existents but the local and dependent creations of minds (contra Unrestricted Composition), and wholes by association can in their own right and via the same minds be single subjects for further associations and so nonreducible parts of next-level wholes (contra Uniqueness of Composition). Eliminate the local inter-connecting associations (what because of the subjectirrelevance of association is an easy error) and the wholes they effect collapse like houses-of-cards, and then in the explanatory vacuum global unrestricted and uniqueness of composition and CI become plausible. I would emphasize some of these points in another way: To generate a whole it takes things-that-are-unified and agent-(and thus individuated)-unifiers, the resultant whole necessarily ‘restricted’ in extension and differentiated from other wholes by the ‘selecting and collecting’ of the unifiers—by intensionconditioned attributions or cognitively-generated arbitrary associations. If one abstracts away the role of agent-unifiers in generating wholes then what must account for the given of such differentiated groupings are just the things-thatare-unified independent of their whole-delimiting inter-connec-tions. But here we have entities just whose separate existences taken independent of and prior to such outward-connections are sufficient grounds for them being parts of groupings—their non-separation—with others—the latter as such being sums. I.e., mereology as CEM allows only for basic entities that each just by its existence and independent of any links whatsoever with others is sufficient for it to be in groups with any other such entities. This implies Unrestricted Composition. And because sums require no constituents whose natures are inherently dependent trans-constituent unifiers—‘holding themselves together with’ other constituents and so jointly ‘wrapping up into one’ the other parts—there is posited with each such group a kind of oneness without equally composing chains of inter-connectedness transitively linking all and just its constituents. The

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existence of the latter would make for a real unity with its own reality not identical to any of the entities linked, and so would effect an emergent whole with a being distinct from its constituents. In the absence of constituent unifiers, however, a mereological sum can have no being of its own distinct from its constituents. Hence, CI. And because there are in CEM no emergent wholes with beings distinct from that of the composing basic entities, then it never happens that from among the latter the same things can have two different sums, i.e., Uniqueness of Composition. In ontological strictness, however, a mereological sum is impossible, its euphemistic description as “strictly a multitude and loosely a single thing”103 being similar to saying a whole as necessarily many things together to the exclusion of all others is ‘strictly a many and only loosely things together to the exclusion of all others.’ Things not parts of a whole are in the Exclusion relation, not with each part of the whole, but with the whole as a singular entity, the resultant of a unity among the parts—their ‘togetherness’. The difficulty would seem apparent in David Lewis’ assertion that: “A whole [i.e., a mereological sum] is an extra item in our ontology only in the minimal sense that it is not identical to any of its proper parts; but it is not distinct from them either, so when we believe in the parts it is no extra burden to believe in the whole.”104 (my insert) So described, a sum is required to be distinct from each but to be all and only some entities jointly, and yet to be nothing distinct from each of them but just these entities independent of any additional selective unification among them—these and just these entities not joined. Contra philosophers like Lewis who hold mereology is a general theory of composition105, it is in fact no theory of composition—from the Latin: ‘to put together’—since it denies the existence of constituent agent unifiers necessary ‘to put the (other) parts and just them together.’ In advocating CI, Lewis claims that with a sum “we do mention one thing that is the many taken together, but this one thing is nothing different from the many.”106 Though despite the fact that we can apparently make successful singular reference to sums as each a collection, to their differentiations and comparisons, yet each sum is held to have no being beyond that of each of its parts, what would require at best they be the plural referents of terms taken distribu-

|| 103 This apt characterization of sums given by Achille Varzi in his detailed overview ‘Mereology’, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = . 104 Lewis, ‘Against Structural Universals’. 105 Lewis, Parts of Classes, p. 17. 106 Ibid., p. 87.

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tively.107 Yet even the latter require the range of distributive reference be delimited—that a sum have a collective unity differentiating it from things not so referenced. In regard to plural reference this point has been made by Henry Laycock: “In referring to several objects all at once, such reference circumscribes certain particular objects collectively, demarcating just these objects from the rest of what is. And if we group or single out these objects and distinguish them collectively from those, do we not thereby single out two unique and distinct groupings or collections?”108 (his italics) As I read Laycock, he goes on to imply that the unity involved in plural reference is a ‘grouping work’ of our own construction based upon “something other than a feature of the objects of that reference.”109 But this is precisely the work of cognitive associations, and with it we have wholes that as such consist of more than just their unconnected parts. In contrast, in mereology under CI a sum is less than the ‘sum’ (i.e., ‘combination’ understood as either noun or verb) of its parts. But like sets, it is held that just the existences of any entities whatsoever are sufficient for them to be somehow ‘together’ as a sum. The problem here, as with sets, is that the ‘togetherness’ essential to a sum must be sufficient as a cause to discriminate between entities it collects and those that it does not, and so be a reality distinct from its collected entities but joint with and just them in constituting the sum. A sum is its-elements-discriminately-collected, and this is more than just its

|| 107 Plural reference divides according to whether it is collective, e.g., as in ‘Tom, Dick, and Harry painted the house’, or distributive, e.g., as in ‘Tom, Dick, and Harry were sunburned while painting the house.’ In the collective example the attribute of painting the house is asserted of three men jointly, and thus we could not infer that, say, ‘Tom painted the house.’ In the distributive case the attribute of being sunburnt is not asserted of the three men jointly— it being nonsense that they can jointly share a sunburn—but rather it is each man in the collection of the three that is said to have the attribute. Relevant to this work and supportive of the ontological significance of structure, I note that a prominent way of treating collective reference has been to have the referent be a set, e.g., in our example the set of Tom, Dick, and Harry. Yet correctly, it has been objected that this would make for such absurdities as in our example that the set of Tom, Dick, and Harry painted the house. Rather and pointed to here is the proper structural assay: it is an event structure involving the three men that can be properly characterized as a painting of the house. For the beginnings of such an analysis see J. R. Cameron, ‘Plural Reference’, Ratio XII (1999): 128–47. Cameron’s proposal is that an object of plural reference is a “structured aggregate or a plurality”, i.e., where an aggregate is under some principle composed “in a unique and precise way”. 108 Henry Laycock, ‘Variables, Generality and Existence: Considerations on the Notion of a Concept-Script’, p. 43, in Topics on General and Formal Ontology, Paolo Vlore (ed.), (Milan: Polimetrica, 2006), pp. 27–52. 109 Ibid., pp. 43–45.

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elements—contra Lewis, the ‘taken together’ of many counts as an ontic addition and is prerequisite to the emergent ‘many’. Lewis and others promote CI on the virtue of its economy: “Mereology is ontologically innocent.” Using the example of all cats, Lewis asserts: “The fusion [of all cats] is nothing over and above the cats that compose it. It just is them.”110 (my insert) As with the proverbial cake, CI mereologists want their cake—a sum as such a delimited collection, i.e., a particular whole—and yet require it be digested too—reduced without remainder to just its parts, i.e., independent of any consolidating links (whether associations or attributions) among them. The thesis has been adopted by Armstrong who advocates for sums as an ontological ‘free lunch’ in having no beings beyond that of the beings of just their parts.111 Of course, the would-be advantage here is that sums can then be used for certain ontological constructions without thereby ‘multiplying entities’ beyond the already admitted parts (more marvelous ‘cake’ for the ontological dieter!). But as Armstrong himself came to assert, the unity of a sum is in fact “a ‘unity’ that does not unify”,112 and this is the heart of the problem with construing sums as anything other than logical fictions. To amplify this point consider a universe of distinct entities a, b, and c, and the sums [a,b,c] and [a,b]. A sum taken to be identical with its parts would be so independent of any connectedness or disconnectedness any part has with any other entity, part or not. So in particular, c is part of [a,b,c] because c exists, this simply/tout-court, and not because c is connected or disconnected in any way with anything else, including with a and b. Yet, observe that c satisfies precisely these same conditions relative to sum [a,b]. Hence, c could be as much a part of [a.b] as it is of [a,b,c], in which case the two sums would be identical, which is absurd. Generalizing this argument on any universe, there could be but one sum, that of everything that exists. The argument can be stated otherwise: the existence of a whole must be conditioned on more than just the existences of each of its elements, for existence is had by everything, and on this criterion for unification there would be only one global whole—the universal sum or set (I take this to be Merricks’ argument; note 26). What is needed for the delimited unity of any non-global whole is then not just the existences of each of the elements, but something that ‘selects and collects’ just these elements and not others. As emphasized, an agent for the type of subject-irrelevant unity composing wholes from which are abstracted sums and sets is given as cognitive

|| 110 Lewis, Parts of Classes, p. 81. 111 Armstrong, A World of States of Affairs, pp. 12–13, 120, 185. 112 Ibid. p. 185.

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association, real parsimony dictating that no objective correlate be posited. I note that the beginnings of something like my account has been proposed and formalized by M. Carrara and E. Martino. They argue that both sums and sets can be seen as each having its members selectively collected “by means of an act of an arbitrary plural choice.”113 Involved in both kinds of wholes is arbitrary reference, and Carrara and Martino propose that the best way to formalize it is to “invoke an ideal agent who is supposed to be able, by an arbitrary act of choice, to isolate any individual”, or more than one with “plural choices”. They propose that the resulting formal set theory and mereology are ontologically innocent—or “virtual”—because “acts of choice are not objects”. Translated into my proffered assay, the ‘arbitrary plural choices’ are cognitive acts of ungrounded association and are as real and essential to the resulting wholes as the minds that create and sustain them. The formal theories are fictive or ‘ideal’ in abstracting away the combining associations and the effecting minds along with their limitations. And with unifiers absent, it is easy for CEM to go further and abstract away the resultant wholes in favor of just their circumscribed parts. These proposals are supported by a naturalist view advanced by Philip Kitcher concerning set theory.114 Viz., set theory is a formalized theory of posited possibilia that would result from idealizing cognitive operations, these extrapolated beyond human limitations. Kitcher says that fundamental here are the operations of collecting and correlation, and I propose these are easily seen as operations of cognitive association viewed from the two emphasis-perspectives: respectively, of entities-linked and of linkings-among-entities. Something like Kitcher’s constructivist view was apparently held by the mathematician Richard Dedekind who is explicit is asserting that “Different things… can be associated in the mind, and we say that they form a system [i.e., a set] S” (my insert), and with these among the foundations we build up our concepts of numbers as thus “free creations of the human mind.”115 Georg Cantor, the father of set theory, was notoriously non-explicit concerning the cause of the unity of sets. Yet, indicative of his few remarks in this regard is: “By an ‘aggregate’ [i.e., set] we are to understand any collection into a whole M of definite and separate

|| 113 Massimiliano Carrara and Enrico Martino, ‘On the Ontological Commitment of Mereology’, The Review of Symbolic Logic 2 (2009): 164–74. 114 Philip Kitcher, The Nature of Mathematical Knowledge (Oxford: Oxford University Press, 1984), pp. 108ff, 133. 115 Richard Dedekind, Essays on the Theory of Numbers (New York: Dover, 1963), pp. 45, 31.

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objects m of our intuition or our thought.”116 (my insert) At another place he says: “When… the totality of elements of a multiplicity can be thought without contradiction as ‘being together’, so that their collection into ‘one thing’ is possible, I call it a consistent multiplicity or a set.”117 Since any things can form a set, not just those ‘of our intuition or our thought’, it is plausible what Cantor intends is that it is the unifying cause of sets that resides within an intellect. This point is observed by Michael Hallett who also notes the evidence for Cantor holding that the unity and objective existence of sets, and especially that for transfinite sets, is guaranteed by their existence in the Divine Intellect.118 Apparently then, Cantor is warranting the objective existence of sets by idealizing human set-forming operations and their results, especially their projected completeness in ‘collecting’ infinite things, and making them those of the Divine Intellect. Remove appeal to the latter, and we have something like Kitcher’s naturalist view. Indeed, the iterative conception of sets, what motivates the standard axiomatizations of set theory119, is easily seen as an idealization of the cognitive processes of linking things through chains of iterated associations, the transitive unity across subject-sharing links making for the collective ‘oneness’ of single sets, associations that can likewise be iterated among the latter to form sets of sets, and so on. The theories are idealizations in that they abstract away the role of minds and their association-chains, and so do away with finite constraints on the latter. It is interesting that Cantor held cardinal numbers to be double abstractions from sets, and as such subjective: “Is not an aggregate an object outside us, whereas its cardinal number is an abstract picture of it in our mind?”, where a cardinal number is “the general concept which, by means of our active faculty of thought, arises from the aggregate M when we make abstraction of the nature of its various elements m and of the order in which they are given.”120 Giving support to my analysis, Cantor’s conception is confused but with grains of truth: it is the prior set M that is doubly abstract, or ‘in us’: first, as a resultant of conceptual associations that as such are irrelevant to ‘the

|| 116 Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers (New York: Dover, 1955), p. 85. 117 Georg Cantor, ‘Letter to Dedekind’ (1899) in From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931, Jean van Heijenoort (ed.), (Cambridge: Harvard University Press, 1967), p. 114. 118 Michael Hallett, Cantorian Set Theory and Limitation of Size (Oxford: Clarendon Press, 1984), pp. 32ff. 119 See Hao Wang, ‘The Concept of Set’, in Philosophy of Mathematics, 2d. ed., P. Benacerraf and H. Putnam (eds.), (Cambridge: Cambridge University Press, 1983): 530–70. 120 Cantor, Transfinite Numbers, pp. 80, 86.

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nature of their subjects and the latters’ order’, and, second, with these linking associations then abstracted away. Insofar as sums and sets are real and underlie their theoretical fictionalizations, the latter designated for example as ‘[a,b, c]’ and ‘{a,b,c}’, they are ontologically more accurately designated as, respectively, ‘[a+b+c]’ and ‘{a+b+c}’ where the ‘+’ indicates the necessary ontic element of unifying association. It is instructive to observe an analogy between what I propose is the difference between actual and projected arbitrary collections via associations (fictionalized as sums and sets and their theoretical projections), and a distinction Armstrong has posited between actual and possible sets/classes.121 Worried particularly about the ontological status of infinite sets and their hierarchies, Armstrong would give them the status of possibilities based upon the realities of certain set-theoretical constructs (he refers to as ‘structures’) that they could possibly instantiate, this on the analogy of his uninstantiated universals which could possibly be instantiated. What I take to be implied here is that these constructs/‘structures’ are real in having a conceptual existence, just as is the implied ontic status of uninstantiated universals. Yet Armstrong adopts David Lewis’ strategy of identifying a set with the mereological sum of the unit sets of its elements, and, on their theory, as long as the elements exist, and so each their unit sets, then the sum exists and so the set. I am arguing that sets and sums are both alike as each and all fictions, but that the arbitrary collections they are abstractions from can be actual as relatively few and ephemeral subjective constructs. It is from the latter that when their composing associations are abstracted away but the wholes presupposing them are retained we have theoretical sets and sums, sums here taken intuitively and innocent of the Composition-as-Identity assumption, CI. But when both the associations are conceptually ignored and their effected wholes are officially denied we have the sums of CI mereology. In both cases the results are fictional possibilia. Contrary to Lewis in thinking that “mereology already describes composition in full generality,”122 by abstracting away the essential internal combinators (or ‘operators’) of cognitive associations we do not have an account of composition of any kind. And the five types of unification we shall detail herein together answer Lewis’ question: “What is the general notion of composition, of which the mereological form is supposed to be only a special case?”123 (his italics) Specifically, it will be

|| 121 Armstrong, Sketch for a Systematic Metaphysics, pp. 89–90, 99–100. Also see his A World of States of Affairs, pp. 185–95. 122 Lewis, ‘Against Structural Universals’. 123 Ibid.

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seen that all composition is, in opposition to Lewis, 1) not ‘unrestricted’—all unity is by one or more individual attributes or associations, each existing only on the obtaining of certain conditions and for certain fixed and finite numbers of subjects; 2) not ‘unique’—in the sense that certain entities can both form a fact and a distinct whole by association, and in the sense that two facts can have the same subjects and attribute universal (though not attribute instances, e.g., a loves b, and b loves a); 3) not ‘ontologically innocent’—all wholes have beings over and above their parts; and 4), with the breadth and depth of the account herein, composition in all its forms is rendered ‘unmysterious’, the analysis removing the basis for the mystery Lewis finds with all non-mereological composition.124 In subtotal, the above observations support the proposed thesis that theoretical sets and sums are simplifying (de-)constructs, similar to ideal gases and frictionless planes, and under their various axiom schemas are theorized to exist in accordance with further idealizations of the human cognitive operations of association formation. Here sets and sums find an account in ontology, and not vice versa. It is my point that, given the above, such an account is completed with the integration of cognitive associations into what, I will finish this introduction by outlining, is a total theory of types of unification, derivative wholes, and ontic dependencies all derived from the single category of attribute instances. Indirect warrant for what I have argued in this section is the global synthesis and ontological savings achieved. But I emphasize that even if the cognitive-associationist account of sums and sets must be abandoned, the direct and indirect arguments for the core instance ontology remain in force.

1.6 The Proposed Holism via Attribute Instances as the ‘Primary Beings’ If one adopts a non-reductive physicalism which I will take to be the most plausible explanation of mind and its operations (viz., the naturalist thesis that they emerge upon but are distinct from what are evolved neuro-physiological structures, principally the brain), then, derivatively, cognitive associations and their resulting wholes—what are fictionalized as sums and sets—are likewise emer-

|| 124 Lewis, Parts of Classes, p. 17. For an overview of Lewis’ advocacy of the contradictory theses see Karen Bennett, ‘“Perfectly Understood, Unproblematic, and Certain”: Lewis on Mereology’ in Blackwell’s Companion to David Lewis, Barry Loewer and Jonathan Schaffer (eds.), (West Sussex: John Wiley & Sons, 2015).

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gent and so ontically dependent upon these physical structures. And so in the ways above mentioned, the latter themselves will be explained as deriving hierarchically from—but not reductively eliminated to—lower-level physical structures, and these down ultimately to a quantum level. Further and a cardinal advantage of our assay of attribution in terms of individuated instances, it will be demonstrated how there can exist a lowest and supporting ontic level consisting of only mutually dependent attribute instances, these then composing the simplest non-attribute entities, perhaps quantum particles (Sect. 5.2). The crucial insight here is that, avoiding a vicious regress of dependence, it is possible for multiple attribute instances to form closed systems where each composing instance has its subject(s)-dependence satisfied by taking other instances in the system as subjects. Because attribute instances are dependent upon subjects as objects of their defining outward combinatorial agencies but not because they share in the composing beings of their subjects (as they might be construed under the inherence model of attribution), then circular chains of instances are possible without themselves involving vicious dependence. I shall indicate briefly how this assay fits well with the above mentioned current understanding of quantum level reality as one of ‘pure relatedness’. But to be noted, the demonstration of the possibility of a bottom-most ontic level consisting only of attribute instances will be independent of the instances being of any specific intensions—types or kinds—leaving open the further possibility that the ultimate ontic foundations for all reality are physical and non-physical attribute instances. What all of this will then evidence is how attribute instances can be the ontic atoms upon which all other entities are dependent for their existences and from which all complex entities are built-up or emerge (e.g., associations). Attribute instances will prove to be what Aristotle sought as ‘primary being’ (Greek: prōtē ousia): that which gives each entity its differentiating essence— what makes it to be the very thing that it is, including for most entities their beings as structured wholes (i.e., makes them more than just random ‘heaps’ of their parts). But also, atomic-level instances will be what Aristotle sought as ultimate subjects of ontic predication: ‘substances’ (Latin: substare = ‘to stand under’; for the Greek: hupokeisthai = ‘to lie under’). As displayed in the difficult central books of the Metaphysics, Aristotle could not, on his background assumptions, reconcile in a single category entities that are both primary beings and ultimate subjects, this due, I will detail, to his requiring ultimate subjects of dependent attributes be non-dependent non-attribute entities—per se subjects (classical assumption A3). The larger point is that, standard in the tradition derived from Aristotle, the latter ‘substances’ are theoretical posits, supposedly

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needed both as subjects persisting through change of attributes, or ‘accidents’, (a point we will challenge in Sect. 5.5), and relevant here, as independent, per se subjects that stop an otherwise infinite regress of intrinsically other-dependent, per aliud attributes.125 The latter argument is found explicit, for example, in the synoptic work of the late scholastic Suarez: “Although one accident can befall another accident… it must necessarily be stopped in some being that is a substance and that is first, and, as it were, the root subject and foundation of the accidents.”126 What was historically the posited status of such non-dependent entities as presupposed supports for dependent accidents was later emphasized by Hume and rejected by him, referring to such theorized entities as “fictions of ancient philosophy”.127 Hume removed the need for such posits, and so the controversial difficulties that go along with them, by simply denying that attributes are in their very natures dependent upon subject-others. Rather, “Every quality… may exist apart, not only from every other quality, but from that unintelligible chimera of a substance.”128 In effect for Hume attributes are themselves independent ‘little substances’: nothing of their composing beings are or require connections with other entities, what otherwise would make them inherently ontically dependent. It is my argument that this denial is Hume’s great ontological error, what will be expanded upon in Section 3.4. Rather, Aristotle, the scholastics, and some modern philosophers (e.g., Armstrong, Lowe)129 are correct in emphasizing that attributes are entities intrinsically outwardly-dependent upon subjects, though crucially they fail to grasp the reason/cause for this, an explanatory vacuum that abets alternative Humean-type theories (e.g., standard trope theory). Our assay will identify this cause, viz., the intension-controlled outwardly-combinatorial agency of attributes on or among their subjects, what in turn will imply the individuation of attributes as instances, and these two re-

|| 125 For some scholastic and post-scholastic history in this regard see Pasnau, Metaphysical Themes: 1274-1671, pp. 102ff. 126 Francisco Suarez, Disputationes Metaphysicae, Disputatio XXXII, trans. Sydney Penner, 2013, found at http://www.sydneypenner.ca/su/DM_32_1.pdf, 1, 4, 15–20. I think the posited nature of independent substance in response to the intuitive given of dependent attributes is found, e.g., in Aquinas: “Substance is understood as that which has a quiddity to which it belongs to be not in [i.e., not an attribute dependent upon] another.” (my insert) From Thomas Aquinas, On the Truth of the Catholic Faith (Summa Contra Gentiles), Book One: God, trans. by Anton Pegis (Garden City: Doubleday & Co., Inc., 1955), I, 25, 10, p. 128. 127 Hume, Treatise of Human Understanding, 1.4.3.1, p. 145. 128 Ibid., 1.4.3.7, p. 147. 129 E.g., Armstrong, A World of States of Affairs, and Lowe, The Four-Category Ontology.

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sults will allow for the possibility of having a lowest ontic level of only mutually dependent attribute instances. Hence, foundational per se subjects or ‘substances’ need not be posited: every entity, from the least to the most complex, is a dependent entity—dependent upon either attribute instances as ultimate constituents, or as emerging upon wholes composed of instances. Indeed, crucial in solving a host of ontological problems is the recognition that attribute instances can have the role of primary beings precisely because of their doubledependent natures: outward dependence due to their combinatorial agencies, and inward dependence upon their non-identical but non-discrete components of intension universals and the individuating acts of unification the intensions control. In particular, it is this nature whereby attribution is the primary and explanatory principle of all non-arbitrary unification, objective causation, and necessity. And, with all reality being or emerging from intension-conditioned inter-connecting attribute instances we have an account of given global and stratified unity among and within qualitatively differentiated structures, what goes unaccounted for in a Humean world composed of only isolated and inert attributes treated as individuals and linked by arbitrary associations, or worse, taken to exist in wholes without any composing connectors, i.e., as theoretical sums or sets. In summary, this work will display how all entities whatsoever derive their existences and internal and external unities, and thus their qualitative essences, directly or indirectly from properly assayed attribute instances. The analysis will be a response to errors in classic Aristotelian/common-sense assumptions A1-A8 identified in Chapters 2 and 3, and that concern principally composition and intensional/qualitative characterization. It will follow from ontological theses T1-T10 developed and defended in Chapters 4 and 5 that the single category of attribute instances provides the five forms of composition ontologically necessary and sufficient for both the support and generation of all other entities. Here we have the basis for the Aristotelian claim that being and unity are convertible, i.e., to have being is to either be, to be an aspect of, or be derivative of one or more agent-unifiers, and conversely. These forms of unification are: 1) internal to each attribute instance, the continuous unity of a repeatable intension and its controlled unrepeatable outwardly-linking agency, and, by the latter external linkings the articulated unities of instances with their subjects as 2) single facts or in combinations as 3) inter-attribute or 4) emergent compositions (e.g., ordinary objects, and minds and their operations), and, emergent upon the latter, 5) conceptual associations and their articulated chains that are arbitrary and random wholes, i.e., actual sets, sums, lists, etc. We can summarize these claims in the Figure 1.1.

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Fig. 1.1: The Five Kinds of Unification/Composition (arrows indicating direction of dependence)

These results solve the Problem of Composition (van Inwagen’s General Composition Question, Sect. 1.1; and Lewis’ question about the general notion of composition of which mereology is but one case) and more: there is here a complete account of all composition, structured (‘non-mereological’) and non-structured (‘mereological’). I.e., answered is Aristotle’s most general question: “Why does one thing attach to some other?”, and to which he gave the overly restrictive answer: because of “the predication of one thing of another.” (Meta. 1041a11-25; Sect. 1.1) The identified five forms of unification represent an implicationally potent ‘precising’ of the general definition of mereology as ‘a theory of the relations of part to whole and the relations of part to part within a whole’, what fictional abstract systems (e.g., CEM or set theories) cannot provide. In short, it will be argued that the five forms of unification are ontology’s crucial and fundamental principles of composition—principia compositionem, what historically have been almost entirely undifferentiated and in this is a source of explanatory impasse, a failure correlative with the superficial treatment of attribution and abetted by neglect or denial of relations and structure. A principal thesis is that the primary form of composition is attribution and this as it occurs in facts; facts, though derivative entities, being the least things that can have independent existences. And it will be the acquired insights into the nature of attribution, specifically as to how the external-achieving attributional bond is conditioned/determined by its concomitant intension, that will be seen to offer solutions to core ontological problems that turn on qualitative specificity and differentiation by non-synonymy. Included here are problems

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concerning essences/natures, universals, monadic vs. polyadic attributes, intrinsic vs. extrinsic attributes, necessary vs. contingent facts, identity and indiscernibility, causation, dispositions, and change. Our analysis will support in its details a holism where all existents form a totally inter-connected and emergently stratified lattice of static and dynamic inter-connections and their resultant wholes. I.e., Reality is an integrated system composed mostly and at its core of attribute instances of various intensions and the structures they effect, existing in re and in mente. Only at the two extremes of structured composition do we have non-structured unification: at its simplest are the structuring ontic atoms of attribute instances each of whose unities is that of non-structuring continuous composition, and at the other extreme, emerging from certain highly complex physical-cognitive structures that are minds, there are subjective arbitrary associations and their conceptual wholes existing only in mente. Implied here is a refinement on the Eleatic Principle130: To exist is to exercise combinatorial agency on or among other entities, primarily as attribute instances and derivatively as associations, or to be wholes that emerge from these unions, all according to the above five ways. This integrated and complete theory of composition fills a crucial ontological void and is in its synthesizing power inductive warrant for the underlying assay of attribution and related concepts we shall argue for in subsequent chapters. The result is a comprehensive or ‘total’ ontology founded by ontic dependence upon a single category of attribute instances.

|| 130 See note 5.

2 Instance vs. Classic Ontology: Individuation and Adherence 2.1 Classic Aristotelian/Common-Sense Assumptions In Western philosophy, among the ontological assumptions with the most pervasive influence, direct and indirect, are those that underlie the ‘common sense’ substance-attribute and hylomorphic ontology of Aristotle. The appeal of Aristotle’s ontology derives from both the breadth of ontologically-relevant concepts he utilizes, and with them his formulation of primary theses that are global generalizations of intuitive common features given in ordinary experience (this displayed below). Central among the latter are his hylomorphic theses regarding the causal role of attributional ‘forms’ in structuring or organizing a subject or subjects as then correlative ‘matter’. Subsequent and vying ontologies up to the present often dispute in fact over fundamental issues having Aristotelian theses as logically prior, yet in many contexts, including in Aristotle, these assumptions and their joint implicational roles remain unnoticed or obscure. As clarifying groundwork for the following, then, it will be instructive to make explicit and examine the implications of various subsets of these Aristotelian assumptions. Specifically, in this chapter and the next I will give and critique eight assumptions that I propose are: common-sense plausible, have support in Aristotle’s texts, persist historically as often unrecognized points of contention, are directly relevant to structure via attribution, and the majority of which, it will be argued, are false. As will be indicated, adoption of or reactions to what in effect are the implications of various combinations of these propositions shape significant portions of the past and current debate. Though not intended as a complete list of key Aristotelian assumptions, what is important about these is their assertion of a fundamental and unifying relevance of attribution to key ontological and analytic concepts: the dichotomies of repeatability|unrepeatability and dependence|independence, and the concepts of essence, unity, and structure. It is these assumptions jointly with his criteria for ‘primary being’ that effect Aristotle’s conflicted dialectic of the central books of the Metaphysics, and out of which he adopts the compromised conclusion that attributions from the class of ‘substantial forms’ provide the defining essences and highly structured unities that are ‘substances’, e.g., living animals. Substantial forms are the primary beings. Lesser structures, e.g., artifacts such as houses, have their unity via other types of attributes, ‘accidental forms’, on or among entities whose exist-

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ences they do not effect, e.g., boards, bricks, etc. Yet, despite the fact that the identified assumptions are pre-critically plausible, it will be seen below that various combinations of them are either mutually inconsistent, lead to vicious infinite regresses, or they or their various denials yield counter-factual and indefensible implications. These negative consequences explain the conflicts within the Metaphysics and, more far-reaching, are among the tradition’s classic and perennial ontological problems. From our analyses of their implications it will be concluded that five of these assumptions are specious. It is these errors that block the recognition that structure is a significant, and indeed ubiquitous feature of the real, and that in composing structures attributes generally are the primary ontic category (our thesis T1). Making these errors and their implications explicit will contribute to arguments for the contrary correct analysis to follow. With all the assumptions brought to explicit critique we will avoid the mistake of other reform ontologists who proffer alternatives that either assume some of the same false theses, e.g., that dependent entities presuppose independent entities, this with substratum theories, or reject theses that are true, e.g., deny ontic predicates are dependent entities, as with much contemporary trope theory. These example errors have contributed to the current stalemate between the dominant rival genera of classic substance/attribute ontologies and modern trope bundle theories. Substance theories must contend with the necessity of positing supporting ‘prime matter’ or ‘bare particulars’, and classic trope theories with the subtler problem of how there can be non-arbitrary unions among any things. Aristotelian ontology takes as its working core, as must every ontology initially, the recognition of the following general and exhaustive types of entities: 1. Attributes, i.e., properties and relations that qualify/characterize other entities as subjects, singularly for properties (e.g., Is-Red, Is-Rational), jointly for relations (e.g., Is-a-Father-of, Is-a-Unifier-of). Attributes have an intensional relevance to their subjects, what epistemically ‘tell’ us something about their subjects. (E.g., Cat.; Topics 103b20-40; Meta. 1003b6-10, 1029a6-26) 2. Objects, i.e., the non-attribute subjects of attributes. These further divide as: a. Non-composite (e.g., supposed ‘prime matter’ or ‘bare particulars’, and on the assay to follow, all intension universals) b. Composite: i. Structured, i.e., objects that are plural wholes with elements organized—‘ordered’—in various ways, each as structured having a nature and emergent attributes due to its specific organization (e.g., a living

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body, a house). (E.g., Parts of Animals 640b17-29, 645a31-37; Meta. 1041b12-34, 1043b4-14, 1045a8-24) ii. Non-structured, i.e., plural wholes with no internal organization or ordering (e.g., random and arbitrary collections—Aristotle’s ‘heaps’, sets and mereological sums). Ontologies are variously developed and differentiated on how they explicate the natures of and the relationships between attributes and objects. Crucial here are necessarily related accounts of attribution/qualification, unification (including structural unity), and how and why entities are divided according to each of the dependence|independence and repeatability|unrepeatability dichotomies.1 Specifically for Aristotelian ontology, its analyses of these topics include at their core the following theses: A1. (Attributes as Dependent) It is of the nature of attributes to characterize/ qualify—be ontic predicates of—other ‘subject’ entities, and so to exist only in unions with, and thus be dependent for their existences upon, these subjects. In this ontic dependence, attributes are in themselves inherently ‘incomplete’ as inseparable from their subject-others, this notwithstanding the possibility of a cognitive isolation via the selective attention of abstraction. (E.g., De Inter. 16b10-11; Physics 185a30-32; Gen. & Cor. 327b23; Meta. 1017b13-14, 1028a10-30, 1069a22-25) A2. (Attributes as Universals) Attributes are repeatable universals, i.e., are numerically the same for all subjects or sets of subjects they qualify/characterize. (E.g., De Inter. 17a37-b1; Meta. 999a28, 999b35, 1001b30-32, 1003a5-16, 1038b10-16, 1040a35) A3. (Per se Subjects) All attributes have their beings in qualifying other entities—their correlative subjects—and in this way are intrinsically ontically dependent entities. In general, ontic/existential dependence is asymmetric and transitive, and so in order to avoid a vicious regress of prior ontic dependence (cf. Meta. 994a1ff) there must be a substratum class of per se sub-

|| 1 As I read Categories 1a20-b9, these dichotomies are central to what Aristotle intends in his four-fold division according to the dichotomies of, respectively, in-a-subject|not-in-a-subject and said-of-a-subject|not-said-of-a-subject.

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jects (the tradition’s ‘through-themselves subsistents’) that are ontically independent and support the existence of dependent entities. According to Aristotle, “If these last did not exist, it would be impossible for anything else to exist.” (Cat. 2b5) In particular, per se subjects are subjects of attribution but are not themselves attributes (they are non-attribute objects), nor are they dependent for their existences upon further attributions. (E.g., Cat. 2b4-6, 2b37; Prior Analy. 43a25-43; Physics 185a29-31, 189a30-34; Meta. 1003b5-29, 1028a10-30, 1029a21-24, 1030a10, 1037b2-3, 1038b15-28, 1049a2336) A4. (Required Essences) Every entity x has a composing positive, qualitatively delimited being and unity whereby it is a determinate and definite something and not something else, what contrasts with undifferentiated nothingness. This composing being of x—‘that by which x is what it is’—and what in its absence x would not exist, is, in the most general senses of the terms, x’s ‘essence’ or ‘nature’. This essence has components that are the foundations for certain ‘essential’ (per se) attributes, F, G, H,…., that x has necessarily (as opposed to those per accidens) and whereby this essence is intelligible, what, according to Aristotle, are included in x’s definition. (E.g., Post. Analy. 96a23-96b14; Topics 103b20-39; Meta. 1029b11-1032b14, 1041a27-b30) A5. (Inherent Essential Attributes) The attributes that qualify/characterize a subject x essentially—those that go to define it—are constituents of the composing essence/being of x, this then founding their attribution to x. (E.g., Post. Analy. 73a34-35, 73b23-24, 84a13&25, 96b1-14; Meta. 1023b24, 1034b20-1038a35) A6. (Non-Attribute Individuals) All non-attributes, i.e., objects, including primary subjects, are unrepeatable individuals/particulars. (E.g., Cat. 3b-10; Meta. 1003a5-9, 1017b25, 1029a28-29) A7. (Attribute Agent-Organizers) There exist organized wholes, or structures, where the internal ‘ordering’ of each has as its cause one or more constituent attributes (e.g., ‘forms’) functioning as qualitatively determined agent organizing-unifiers, these attributes being jointly essential to the nature of each resultant structure as a specific kind. (E.g., De Anima 412a29-412b9;

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Parts of Animals 645a26-36; Meta. 1016b7-14, 1041a6-1041b32, 1045a7-1045b24) A8. (Unity by the Constituent One) Every composite whole as a unification of non-identical entities has as the cause (principle, source) of its unity, and so what is essential to its existence, a shared one, what is a single (‘indivisible’) constituent entity linking all the other elements—‘Oneness is by the constituent one’. (E.g., Physics 227a13-17; Meta. 1015b16-1016b17, 1052a15b8, 1061a15-18 & 1061b12-14, 1075a12-19) These Aristotelian assumptions have been and continue to be central to the tradition, involving and inter-relating as they do concepts that are analytically fundamental to any ontology. A critique of these assumptions will be a richly suggestive and salutary starting point for the positive instance ontology developed herein.

2.2 The Classic Assumptions in Aristotle’s Metaphysics As a preface to their detailed critique in this and the next chapter, let us consider in summary fashion key points where the above assumptions play a role in Aristotle’s ontology, and particularly in his tellingly difficult and conflicted attempts in the Metaphysics to identify ‘primary being’ (= Greek: prōtē ousia), i.e., the category of entities that are ontologically basic. In the process we will anticipate some of the key problems and proposed solutions that will be detailed latter. In his early Categories Aristotle describes these fundamental things to be such that, if they did not exist, nothing else would exist (Cat. 2b5). Among the criteria there for primary beings are that they be non-attribute individuals (A6) (my ‘objects’) that admit no contraries or degrees, and persist through change of accidental attributes. In addition and more importantly as criteria, what I take to be prescribed both in the Categories and initially in the Metaphysics, are the following (the above assumptions indicated where relevant): Primary beings must be 1) ontically independent and ultimate substrata, this in order to support dependent entities, including, fundamentally, attributes (A3), and they must each have a self-sufficient completeness, both 2) intension-

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ally, as not further determinable, i.e., instantiating an infima species (A4, A5)2, and 3) extensionally, as both a unified whole—a unit/one—(A8), and an unrepeatable individual (A6). It is perhaps conditions 2) and 3) that Aristotle intends when requiring of a primary being that it be a tode ti = ‘a this-somewhat’3. Criterion 1) requires primary being to be an ultimate supporting substratum, i.e., a per se subject (A3), Aristotle’s term being hupokeimenon = ‘that which lies under’. As a possible source of confusion4, Aristotle’s term ousia is standardly translated as ‘substance’, from the Latin substare = ‘to stand under’, ‘support’. For, in the dogged analysis of the mature Metaphysics Aristotle argues that the ultimate substratum—prime matter—of criterion 1) cannot satisfy criteria 2) and 3) (details below), and so 1) must be abandoned, i.e., substance as primary being cannot be identified with ‘substance’ literally as an ultimate substratum or per se subject. In the Categories primary beings or substances are taken as primitive and unanalyzed, given examples being individual men, horses, and oxen. In the later works these and other kinds of objects, e.g., artifacts, are recognized to be internally complex and in such a way as to require both ‘metaphysical parts’ in addition to the given material parts, and an account of the types of unities among all of them. Specifically, Aristotle observed these objects to be, in effect, structured wholes, each as such having parts organized (e.g., Parts of Animals 645a27-35)—in some cases hierarchically (e.g., Parts of Animals 640b17-29, 646a13-24; Gen. of Animals 715a6-11; Meta. 1070a10-15)—in kinds of (i.e., qualitatively specific) ways, what accounts for the whole being more than a sum or “heap” of its parts (e.g., Meta. 641a10-16; cf. Topics VI, 13).5 We would now say that such structures consist of networks of variously intensioned types and combinations of inter-connections among multiple parts, the specific details of the arrangement giving/founding essential attributes of the whole, e.g., ration-

|| 2 Aristotle in the Categories implies that determinateness varies inversely with generality in the line of substance—infima species—genus, e.g., at 2b1–14. 3 E.g., see J. A. Smith, ‘ΤΟΔΕ ΤΙ in Aristotle’, The Classical Review 35 (1921): 19; Rogers Albritton, ‘Forms of Particular Substances in Aristotle’s Metaphysics’, The Journal of Philosophy 54 (1957): 699–708. For an overview of the controversy concerning interpreting Aristotle’s use of tode ti see Jiyuan Yu, The Structure of Being in Aristotle’s Metaphysics (Dordrecht: Kluwer, 2003), pp. 122–26. 4 The warning of possible confusion here is made, e.g., by Vasilis Politis, Aristotle and the Metaphysics (London: Routledge, 2004), p. 12. 5 Aristotle asserts: “In the case of all things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something besides the parts, there is a cause.” He then asserts that this cause is a form. Meta. 1045a9–25.

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ality, metabolism, locomotion. I.e., definitional of paradigmatic structure is one or more constituent polyadic relations among other parts, what renders the resultant structured whole such as to have its own emergent attributes. In contrast, Aristotle assayed many organized wholes, including all that are ontically fundamental, i.e., complex substances, to be each the effect of the agent unification by a single (A8) monadic attribute—a form—acting on correlative subjects— matter—with the passive potency for receiving it (A7) (e.g., Meta. 1041b3-30, 1045a6-b20). The term ‘matter’ (from the Greek hyle = wood) carries with it the sense of ‘that of which something is made’, and particularly as the correlative of productive action. Further, on the assumptions that the whole-into-unifiedparts analysis cannot iterate downward indefinitely, and that a whole has only one unifier (A8), there must be some structures that are primary and consist each of what is held to be a monadic form predicable of a thus single and ultimate per se subject (A3)—the latter in the Aristotelian tradition being termed ‘prime matter’. For Aristotle the concept of ‘prime matter’ serves two apparent ontological needs: 1) to be the ultimate non-attribute non-dependent subject of dependent attributes, and this immediately for substantial forms (A3; references there), and 2), on the assumption that all change requires a persisting substratum (Physics I, 6-9), prime matter is the substratum for the mutual transformations of the ultimate material elements of earth, air, fire, and water (prime matter being what persists across exchange of the elemental contraries: hot, cold, wet, and dry) (Gen. & Cor. II.1 & 7). In both cases and reinforcing each other, a historically long-standing view has been that Aristotle requires of prime matter that it be pure potentiality, devoid of all specificity itself but capable of being determined by certain attributes (e.g., for 1) see Meta. 1028b34-29a26, and for 2) see Gen. & Cor. 329a24-5 & 33, 335a32-b6). In contemporary times, however, there has been a debate in the literature, centering around 2), over whether Aristotle did intend prime matter to be totally without determination.6 We need not enter into this debate here, but I note, first, that in Chapter 5 it will be seen how, in the instance ontology developed, a single entity as a dynamic structure can persist across a radical change where no initial and ultimate components, i.e., attribute instances, survive—there need be no persisting substratum. And

|| 6 For debate references and a defense of Aristotle’s adoption of the ‘pure potentiality’ understanding of prime matter see Frank Lewis, ‘What’s the Matter with Prime Matter?’ in Oxford Studies in Ancient Philosophy, Vol. XXXIV, David Sedley (ed.), (Oxford: Oxford University Press, 2008), pp. 123–46. For an argument that Aristotle did not hold such a view see Mary Louise Gill, Aristotle on Substance: The Paradox of Unity (Princeton: Princeton University Press, 1989).

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second and concerning 1) which is directly relevant to the analysis herein, it will be argued in Section 2.4 (anticipated in part below) that in fact Aristotelian assumptions A1-A5 do imply what is an incoherent essenceless substratum. The offered alternative instance ontology will correct, among other Aristotelian assumptions, A2 (Attributes as Universals), A3 (Per se Subjects), and A5 (Inherent Essential Attributes), and eliminate the need to posit ultimate supporting (and individuating) non-attribute entities—and so the need to posit ultimate but totally indeterminate entities. The organizing forms whose subjects are prime matter are ‘substantial forms’ and the resulting wholes are complex substances. Organizing forms that have as their subjects already existing substances and not prime matter are termed ‘accidental’, as are the resulting unities, e.g., those of artifacts. Crucially, Aristotle recognized these organizing forms to be a subclass of ontic predicates, i.e., of attributes generally—properties and relations. And, he held there to be a fundamental ontological dichotomy between attributes whose nature is to qualify or characterize other entities and in this way are ontically dependent upon them (A1), e.g., Is-an-Animal, Is-White, Is-Three-Cubits-Long, and nonattribute entities that are the presupposed ontic support for attributes. The latter are either the per se subject (A3) prime matter or wholes derivative of substantial forms in attributional unions with prime matter, i.e., ‘substances’ in the sense of form-matter composites (e.g., Physics 185a29-32). The assumption that all forms, organizing or not, are ontic-predicates/attributes is what is implied by ‘universal hylomorphism’: the thesis that no attribute-form exists independently of subject(s)-matter. I note there is disagreement over whether Aristotle held consistently to this view, viz., whether he allowed for subjectless ‘pure forms’ in the cases of God, the intelligences moving the spheres, and the active intellects of humans.7 However this may be, insofar as entities are attributes they are for Aristotle either essential, i.e., what are defining species of substances, or the latters’ genus and differentia, or the attributes that define these, or they are accidental as not had necessarily by, or not implied by the definitions of (propria), their subject substances. Concerning their ontic dependence, the scholastics were consistent with Aristotle in describing accidents that are monadic properties as each an ens in alio (a ‘being-in-another’), and polyadic relations as each an ens ad aliud (a ‘being-toward-something-else’). For them the general principle was: Accidentis esse est inesse (‘The being of an accident is

|| 7 Eugene Ryan, ‘Pure Form in Aristotle’, Phronesis 18 (1973): 209–24.

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to-be-in [something else]’).8 The medievals disagreed over whether all forms must be ontic-predicates/attributes of some matter—God and angels held by some to be counter-examples.9 At places Aristotle is explicit that attributes are repeatable universals (A2), and that “the universal is predicable of [and so dependent on] some subject always” (Meta. 1038b15; my insert), but it is a matter of scholarly debate whether certain texts imply he also admitted individuated attributes or instances, the latter serving to remedy, as we shall rehearse, an otherwise inconsistent theory of forms.10 However this may be, it is a principal argument below that the individuation of attributes is an immediate implication of their natures as linking-agents, what Aristotle correctly assessed to be the natures of attributes in the class of ‘forms’ (A7); forms are ‘actuality’ (energeia), their corresponding subjects ‘potentiality’ to them, and for each pair their “totality is not, as it were, a mere heap, but the whole is something besides the parts [i.e., an organized whole].” (Meta. 1045a29; my insert) Also I note that insofar as Aristotle allowed for attribute-forms independent of subjects, contra A1, they would be individuated under A6. Now importantly but with an import blocked to the tradition by other distorting assumptions,11 for Aristotle all structured wholes are taken to have their unities both through a single constituent entity x (A8) and, derivative of x, a transitivity across composing and articulated inter-connections. For x as a substantial or accidental attribute-form (A7), the derivative inter-connections are qualitative specific “relation[s] of such parts to the total form” (my insert) or the “orderings” (i.e., relations) among the parts, ‘orderings’ also possible under certain x’s that are object-substances, e.g., a general that provides the leadership organization in a functioning army (e.g., Parts of Animals 645a26-35, b2934; Meta. 1075a11-16). In each case the single unifier x is understood as the cause of a subordinate but essential system of specific structuring relationships, in this way x being the “the primary cause” of the resultant whole (Meta. 1041 b25-30). Among these wholes with subordinate unifiers there is held to be a ranking of degrees of unity, what I propose can be relevantly understood as

|| 8 E.g., Thomas Aquinas, Summa Theologica, 3 vols., trans. Fathers of the English Dominican Province (New York: Benziger Brothers, Inc., 1947), Pt. I, Q. 77, Art. 1, and Pt. I.II, Q. 110, Art 2. 9 A Companion to Philosophy in the Middle Ages, Jorge Gracia and Timothy Noone (eds.), (Oxford: Blackwell, 2002), passim. 10 Albritton, ‘Forms of Particular Substances’, and Charlotte Witt, Substance and Essence in Aristotle (Ithaca: Cornell University Press, 1989). 11 Central to these distorting assumptions is the monadic reduction of polyadic relations, this implied by the inherence conception of attribution, the latter abetted by A5 (Inherent Essential Attributes) and its generalizations (see below and Sect. 2.6).

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follows. In increasing order, degrees of complex unity are understood as: with no unifying agent x, diverse entities are just a ‘heap’; if the entities subordinately unified by x are not by their defining essences required to be so mutually arranged (and so survive independently of it) then the unity is per accidens (e.g., for the boards of a house or men in an army it is not of their essences to be, respectively, among the parts of a house or an army, these states being accidental to them); and if otherwise the entities unified by x are required by their essences to be so inter-related then the unity is per se or substantial. That is for the latter, if for the parts subordinately inter-related by x , e.g., x a human soul, it is essential to the existence of any one of the parts, e.g., a living human heart, that it be so connected to other parts, e.g., to other living human organs, then the unity is per se and the highest form of compound unity (e.g., Meta. 1023b34, 1035b10-25, 1045a6-25). In contrast to organizing attributes, non-organizing attributes, e.g., Is-White, Is-Simple, have each as the cause x of its unity with its subject the single subject itself, and the unities are ranked according to whether or not the attribute is included in the defining essence of subject x, being included in the essence considered a higher form of unity than the alternative or accidental unity. The two scales can be meshed, as was explicit with later Aristotelians12, on the criteria that substantial unity is greater than accidental, and that within each of these scales a unity by an x without subordinate multiple orderings ranks higher than that with them. On the latter, less parts combined corresponds to greater unity. A simple being having no need for compositional unification has the greatest unity of all, e.g., as with God. Now central to these theses, I will argue, is Aristotle’s profound error of causal reversal in regard to organizing forms, viz., the taking of what are attributes upwardly emerging on— as the effects of—ontically prior parts and their structuring attributes, to be, rather, the downward causes of these then ontically posterior or ‘subordinate’ inter-relations, and, with substantial forms, generators of the connected parts as well. It is because of the latter that under a substantial form the generated parts cannot exist without the concomitantly generated inter-connections. It is in the context of his subject-attribute/matter-form analysis that Aristotle in the Metaphysics seeks to answer the question: What is primary being? He first argues that prime matter, what is an ultimate per se subject under A3, cannot be primary being. To be a primary being under the criteria above, matter would have to be a non-dependent and intensionally determined individual. Yet using the heuristic device of successive abstraction—‘stripping off’—of the || 12 Robert Pasnau, Metaphysical Themes: 1274-1671 (Oxford: Clarendon Press, 2011), p. 556.

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attributes of a particular, e.g., Socrates, Aristotle argues that these attributes’ posited and supporting per se subject would, as the ultimate residuum of this process, be itself other than and so devoid of any attributes, i.e., completely indeterminate/essenceless (Meta. 1028b33-1029a34). The implication turns on the assumptions that, if a per se subject x could not itself survive the removal of an attribute F, then F is essential to x, but, under A5, F would have to be a constituent of x, making x dependent upon F and so contradicting x’s independence under A3. So x survives as something not characterized by any essential attributes, and so not by any accidental attributes as well—to exist and so have accidental attributes an entity must as ontically prior have a differentiating essence and so essential attributes (cf. Meta. 1007a20-b18). But, as Aristotle now asserts and contrary to the above criteria, matter as completely qualitatively indeterminate is furthest from what is thought to characterize a primary being (criterion 2), and moreover such a thing cannot even be ‘separable’ (i.e., have the attribute Is-Independent; criterion 1) or be ‘a this’ (i.e., have the attribute Is-Individual; criterion 3) (Ibid.). Aristotle responds by asserting that the alternative definitional essence as predicational form is to be primary being, abandoning thereby the criterion 1) requirement that primary beings be ultimate substrata, i.e., per se subjects under A3. Plausibly, form is primary being since it is an agent cause (as an attribute/ontic-predicate) of a structured unity that ‘makes something to be what it is’ (i.e., gives it its defining essence and essential attributes). But this, then, conflicts with his criterion 3) above in that forms as structure-giving ontic predicates are apparently universals (A2), whereas primary beings are to be individuals (A6). Aristotle himself points out this inconsistency in the general context of considering universals as candidates for primary beings (Meta. 1038b1-35). The universals(A2)-individuals(A6) inconsistency would be removed if Aristotle adopted the view that forms are attribute instances (i.e., revise A2). Indeed, key arguments of this work are that historically persistent assumptions A2 (Attributes as Universals) and A3 (Per se Subjects) are insidious errors: contra A2, attributes are individuated as instances, and, contra A3 ontically dependent entities do not require a base of ontically independent entities to support their existences. We will see herein how a proper assay of attributes as intensioned-combinators implies their individuation, and, building upon this, how ontically dependent and individuated attribute instances are sufficient to be at some atomic level mutually supporting in attribute-only structures, and to generate hierarchically from these all other entities. I.e., instances are the ‘primary beings’. In this way is reconciled Aristotle’s view in the Categories that primary beings are ultimate bearers of attributes and his view in the Metaphysics that primary beings are unifying-organizing agents (A7).

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Amplifying key points, for Aristotle, as for us in this work, the related realities of attribution and structured wholes are fundamental to ontology. Aristotle recognized rightly that artifacts, living organisms, and indeed the whole universe (Meta. 1075a16-19), are structured, “ordered”, wholes. Living bodies are spectacularly so, what as obviously more than random ‘heaps’ of parts, they have their specific natures due to the “mode of composition” of the parts (Parts of Animals 640b25). That is, a living creature has its nature by the intensionspecific linkings that together are the “combination” of its parts. And Aristotle is explicit that for living things these relational combinations form an emergent hierarchy, viz. and in subsuming succession: primary qualities (hot, cool, dry, moist), the ‘elements’ (earth, air, fire, water), homoeomerous13 materials (e.g., homogeneous ‘tissues’, metals, stones, wood), organs and limbs, and ultimately living substances, e.g., Socrates (Gen. of Animals 715a1-11; Meta. 1070a10-11).14 The theses implied are that entities of each level are structured/inter-related in certain ways to form wholes, each whole itself a single subject for attributes, including whole-forming relations of the next level, and where some of the attributes are not found at lower levels. A reasonable account of these thus multiorgan, multi-system creatures would have been the positing of a ‘plurality of (each specifically organizing) forms’, what was the position of a number of scholastic philosophers, a notable exception being Aquinas who sided with Aristotle in advocating a single structuring form for each substance (A8).15 Artifacts, e.g., a house or a couch, are also structured wholes analogously but less complex than biological creatures—they are absent the internal and dynamic complexities that make for self-motion or -change, including, e.g., metabolism and self-replication. Aristotle’s ontological analysis of what specifically is structural unity is given primarily in the Metaphysics (1040b5-1045b25). There he observes the requirement that for every system/structure, in order to account for what he glimpsed are in fact each a qualitatively manifold inter-related unification, static and/or functionally dynamic, among yet differentiated parts, there must be constituents that have a distinct ontic role and status relative to the rest. That || 13 ‘Homoeomerous’ materials are those that divide into parts that are qualitatively identical to each other and to the whole. Even homoeomerous materials, e.g., wood, have ultimate substructures of certain arrangements involving their ‘pores’, e.g., ‘cohering lengthwise and not crosswise’, that give them certain emergent properties, e.g., being fissile (i.e., cracking beyond the place of being struck). See Aristotle’s Meteorology, Book 4, Chaps. 9 and 10. 14 Paul Bogaard, ‘Heaps or Wholes: Aristotle’s Explanation of Compound Bodies’, Isis 70 (1979): 11–29. 15 Pasnau, Metaphysical Themes: 1274-1671, pp. 574ff, 630–32.

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is, in order to avoid infinite regress (Meta. 1041b1126; what later became known as ‘Bradley’s Regress’), entities that account for the diverse connectedness that is a structured whole must function as trans-constituent unifiers of themselves with the other elements, what otherwise would be but further and ‘inert’ (my term) elements in need of unifiers with and along with the initial elements. Each such structuring constituent “is not an element but a principle [of organized unity]” (Meta. 1041b30; my insert). Of fundamental significance, Aristotle realizes that this trans-subject unification requires a cause that is an “actuality”—“In substance that which is predicated of matter is the actuality itself” (Meta. 1043a6), it being the case that “the essence certainly attaches to the form and the actuality [energeia]” (Meta. 1043b1; my insert). Specifically, Aristotle is arguing that the constituents needed to account for the organization of structured wholes—what makes them ‘principles’ in this regard—must be, in effect, intension-determined agent-combinators (A7). Stated otherwise, there must be one or more constituents that act in the crucial defining sense of going-beyondthemselves to link themselves with, and so provide connections among, the other constituents, and this in qualitatively specific ways, i.e., each being correlative with a passive potency—foundations—in the nature(s) of it subject(s). Aristotle would have for any structured whole there be but one intensioned-combinator (A8). The latter is a consequential error, but with the potential to correct it is Aristotle’s profound insight that for a structured whole there is required an agent unifier exercising a qualitatively determined combinatorial ‘energeia’ (Greek for ‘at-work-ness’) with or among its subjects, and this via attribution. The potency of these insights is central to this work and will be developed in Chapter 4. What I will argue for is the generalization to all attributes of what Aristotle recognized as the nature of attribute-forms, viz., that which gives resultant wholes their structure or organization (A7) and in this way makes attributes necessary components in their wholes’ determinate beings, or ‘essences’ (A4). It is the ‘at-workness’ of ontic predicates that “makes this thing flesh and that a syllable. And similarly in all other cases. And this is the substance [primary being] of each thing (for this is the primary cause of its being).” (Meta. 1041b2627; my insert in brackets) Yet, a primary impetus for this generalization of the structuring nature of forms to all attributes and its explanatory potential, including the correction of A8, was lost to Aristotle and many philosophers up until the present by their adoption of a reductive elimination program for polyadic attributes—relations. Inter-subject combinatorial ‘at-workness’ is most obvious with relations full and unreduced, especially as they occur multiply in intra-connected networks. In the absence of fully polyadic relations, the work

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of structuring parts must be done by monadic properties, and this by only one per whole on assumption A8, e.g., by substantial forms. The same thesis for accidental forms is explicit in Aquinas.16 An immediate difficulty here is that now a monadic form, e.g., Is-Human, as such what must be predicable of—be an agent of unification of itself with—a single non-attribute subject—prime matter (A3), is required magically to both act to bring into existence from this matter, which is nothing definite in itself, many qualitatively differentiated parts— secondary matter, e.g., limbs and organs—as well as be an inter-ordering agent effecting and orchestrating various kinds of static and/or dynamic links within and between these parts so as to yield an organized functioning whole, e.g., Socrates. But in fact, the latter multi-subject links cannot be the effects of monadic properties, but only of polyadic relations, either by several relations of various intensions and connected by shared relata, or, as some would admit, by some single ‘multigrade’ relation.17 What is the error here is that Aristotle takes an essential attribute F construed as a substantial form18 with a monadic inten-

|| 16 According to Aquinas, “Among all the things that are ordered to one another [i.e., structured], furthermore, their order to one another [i.e., their inter-relations] is for the sake of their order to something one, just as the order of the parts of an army among themselves is for the sake of the order of the whole army to its general. For that some diverse things should be united by some relationship cannot come about from their own natures as diverse things, since on this basis they would rather be distinguished from one another. Nor can this unity come from diverse ordering causes, because they could not possibly intend one order in so far as among themselves they are diverse. Thus, either the order of many to one another is accidental [i.e., random and so not structured], or we must reduce it to some one first ordering cause that orders all other things to the end it intends.” (my inserts) Thomas Aquinas, On the Truths of the Catholic Faith (Summa Contra Gentiles),Book One: God, trans. Anton Pegis (Garden City: Doubleday, 1955), I, 42, 7, pp. 159–60. 17 Purported ‘multigrade’ relations, e.g., Is-Surrounded-by, are said to have no fixed adicity. I doubt there are such relations and will assume herein that there are none—all supposed examples being reducible to ones with fixed adicity. In the example ‘a is surrounded by b, c, d, …’. The supposed multiple relata b, c, d, … is really a single relatum of an unspecified structure containing b, c, d, … . Supporting this view D. M. Armstrong gives as an argument against multigrade relations that they would violate the Indiscernibility of Identicals. His point is “that the number of terms a universal has is part of what that universal is. And a universal requires strict identity in its different instantiations.” Sketch for a Systematic Metaphysics (Oxford: Clarendon Press, 2010), pp. 23–24. Also see Armstrong, ‘How Do Particulars Stand to Universals?’ in Oxford Studies in Metaphysics, Vol. 1, Dean Zimmerman (ed.), (Oxford: Oxford University Press, 2004), p. 147. 18 Informed by contemporary Aristotelian scholarship, my reading of the central books of the Metaphysics is that they imply as a consistent assay of substantial forms: substantial form (substance; a ‘this-somewhat’ (tode ti) = essence = [infima species (definition or ‘formula for the

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sion (viz., a species, e.g., Human) and sub-merges it into an object x , e.g., Socrates, as a part (A5) where it is the prior single (A8) source/principle of x’s defining and essence-bestowing internal organizing unity (A7), and yet only such an organized unity in its completeness, not any part or substructure, and as a resultant single entity is the sufficient foundation for x having the then essential monadic attribute F (A4), e.g., Is-Human. Stated otherwise and crucially, an Aristotelian form is required to do two contradictory things: 1) be a constituent provider of the defining organization of a resultant whole, and so be prior to the whole, and yet 2) be descriptive of the whole only in its completed organization, and so be posterior to the resultant whole. Whereas properly and in ways to be specified in Chapter 5, an attribute F of x descriptive of its composing structure e-merges externally on x due to x’s composition by prior and internal structuring attributes, usually of varying intensions and adicities, and different in intensions from F and its defining attributes. The source of these problems and militating against Aristotle’s insights concerning attribution and structure is his assumption, explicit for essential attributes, that the union between an attribute and its subject(s) is one of containment or ‘inherence’ taken literally (A5). The thesis is intuitively appealing for essential attributes as descriptive of what makes something to be what it is, and is easily extended pre-critically and tacitly to all monadic properties. The latter extension is found in contemporary ontology, sometimes under the term ‘constituent ontology’19, in both realist (admitting universals) and nominalist (denying universals) forms. On the realist-substratum side are, for example, the theories of J. P. Moreland (who also admits instances of accidents)20 and D. M.

|| essence’ (Meta. 1031a12), a universal ‘somewhat’ (ti)) + a creating agency (energeia) effecting composing secondary matter and a characteristic organization among these parts (Meta. 1042b9ff); a particular ‘this’ (tode)]. If so, this parallels my proposed analysis of attribute instances: instance Fni = [universal intension Fn in continuous composition with an individuating combinatorial agency, designated by ‘i’, on/among a particular n-tuple of subjects]. For an overview of recent Aristotelian scholarship and references see Mary Gill, ‘Aristotle’s Metaphysics Reconsidered’, Journal of the History of Philosophy 43 (2005): 223–41. 19 The alternative is termed ‘relational ontology’ and would include the instance ontology argued herein. The terminology is found in Nicholas Wolterstorff, ‘Divine Simplicity’, Philosophical Perspectives 5 (1991): 531–52. For a discussion of Aristotle’s constituent ontology see Michael Loux, ‘Aristotle’s Constituent Ontology’, Oxford Studies in Metaphysics, Vol. 2, Dean Zimmerman (ed.), (Oxford: Clarendon Press, 2006) pp. 207–50. 20 James Moreland, ‘Exemplification and Constituent Realism: A Clarification and Modest Defense’, Axiomathes 23 (2013): 247–59.

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Armstrong (who eschews attribute instances)21. Inherence is also intrinsic to current nominalist bundle theories, what, I shall argue, are mistaken responses to problems arising from what is the erroneous assumption of substratum theories: that dependent-attributes (A1) presuppose independent substrata (A3). Common to all, inherence means that a fact :F(a) obtains because attribute F is a constituent of a and so is its own foundation or grounds for the non-arbitrary characterizing union it has with a. I.e., under self-grounding inherence, an attribute by being a constituent of its subject makes or causes the subject to be what the attribute describes. In Aristotle, the substantial form (e.g., Is-Human) of a substance a is its composing essence, and he is explicit that the essence of a contains its definition and that the parts of the definition, e.g., genus (e.g., Isan-Animal) and differentia (e.g., Is-Rational), which as attributes of a are parts of its essence-form (A5) (e.g., Post. Anal. 73a34, 96b12; Meta. 1031b32, 1034b20, 1045a12-15)22. Yet literal inherence, though plausible for essential properties, is less so for accidental properties, and impossible for polyadic relations. For a relational fact, say of the form :R(a,b), inherence would require intrinsically dyadic R, as its own foundation, to be numerically the same in each of its relata, a and b, what for asymmetric or non-symmetric R is not possible, and, independent of this, would require R to be a monadic attribute of each subject. This is motivation for Aristotle’s and the thereafter persistent error of reductively eliminating polyadic relations in favor of monadic properties of each relatum. We will detail the nature of this error in Section 2.6. Relevant here is the observation that an acceptance of inherence-inspired self-founding attribution would make apparently plausible the otherwise much mocked vacuous explanations attributed to later Aristotelians, e.g., that a compound induces sleep because it has inherent in it the property of Is-Soporific (a ‘virtus dormitiva’). Evidence of Aristotle’s commitment to generalized inherence and displaying its error is his apparent treatment of accidental properties, e.g., Is-White, IsSitting, Is-Healthy. A long-observed obscurity in Aristotle’s ontology concerns the distinctness of the beings of accidents from that of their subjects, a topic of

|| 21 See D. M. Armstrong, ‘Particulars Have Their Properties of Necessity’, 2004 Pufendorf Lecture, Lund University, Sweden. Available at http://www.pufendorf.se/2004_lecture_4.html. Also, Armstrong, ‘How do Particulars stand to Universals?’. He adapts the ‘partial identity’ thesis of Donald Baxter where then, as Armstrong sees it, “property-universals are actually parts of the particular.” For Baxter, see ‘Instantiation as Partial Identity’, Australasian Journal of Philosophy 79 (2001): 449–64. 22 Also see Meta. 1013a27, 1017b22, 1024a24, and 1035b35.

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intense attention and various conflicting determinations in scholastic ontology.23 On the one hand, Aristotle asserts that subjects ‘have’ accidents in the same manner of containment as a statue has its form (Meta. 1023a11), and that it is not dependent accidents but subjects-having-accidents that are true existents (Meta. 1028a20-30, 1071a2). The implication would seem to be that accidents share in the beings of—inhere as ‘modes’ of—their subjects (A5 is then generalized to all attributes, essential and accidental). But then contradictorily, accidents would be essential attributes of their subjects. So, the alternative would seem more plausible: Accidents must be distinct from the composing being of their subjects since they can come and go while the (ostensible) subjects remain the same. These are what the scholastics after the fourteenth century accepted as ‘real accidents’, i.e., accidents external to the beings of their subjects and connected to them in a way other than compositional inherence.24 In regard to the prior deflationary view, a contemporary analysis of Aristotle’s text argues that he, in effect, attempts to save inherence for accidents by positing the ‘kooky’ entities of each a subject-having-accidents, what is distinct from but coincides with the subject taken as distinct from its accidents. For example, the subject-having-an-accident whole that is Socrates-sitting has the accident IsSitting inherent in it and so an essential attribute of this whole, and the latter whole temporarily and so accidentally coincides with subject Socrates.25 What is then accidental here is the relation between the entity that is the subjecthaving-an-accident and the subject independent of the accident. Thus on this proposal the accidental attribution of monadic properties reduces to dyadic relations, but since the latter in the full inter-subject reality required of them here is not possible on the inherence model of attribution, neither is accidental monadic attribution. What all of this implies is at the least a bifurcated assay of the union of attribution: one for essential and another for accidental and relational attribution. A related inherence-induced bifurcation is found in contemporary trope bundle theories where the monadic properties of a subject a are such because they are in/compose a, each in itself a non-combinatorial/inert ‘little-substance’, what then requires the posit of unifying (Is-Compresent-with) and kind-differentiating (Resembles) relations whose attributional natures are

|| 23 E.g., Fabrizio Amerini, ‘Utrum inhaerentia sit de essential accidentis. Francis of Marchia and the Debate on the Nature of Accidents’, Vivarium 44 (2006): 96–150. Also see Chapter 10, ‘Real Accidents’, in Pasnau, Metaphysical Themes: 1274-1671, pp. 179–99. 24 See Chap. 11, ‘Inherence’, in Pasnau, Metaphysical Themes: 1274-1671, pp. 200ff. 25 For a defense of the view and references see S. Marc Cohen, ‘Kooky Objects Revisited: Aristotle’s Ontology’, Metaphilosophy 39 (2008): 3–19.

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necessarily actively combinatorial/predicative among the thus selected and unified tropes. I.e., monadic tropes passively inhere in wholes existing only by the active adherence of polyadic relations. And here all monadic attributes as trope constituents of their subjects are essential to them. We will expand upon these issues in Section 3.3. A further problem for Aristotelians and the inherence model concerns the predication of monadic substantial forms as considered above. Inherence is an attempt to account for why attribution is more that arbitrary association. There must be some qualitatively specific basis—some foundation or ground—had by a subject x for why it is characterized/qualified by an attribute F, otherwise the attributional union between x and F is that of a mere ‘bare linking’—one irrelevant to anything about (and so uninformative of) x and F other than that they exist. Inherence solves the problem by making an attribute F a constituent of its subject and so its own qualitatively specific foundation: x is F, i.e., the proposition F(x) is true, if and only if F is a component of x. We have seen that prime matter as a per se subject cannot have inhering essential attributes (A5) for this would violate its independence (A3). So, if prime matter has any attribute F— and recall that every substantial form, insofar as it has a subject, has prime matter as a subject—then F must be accidental to it. This was the position of some of the scholastics. Yet what could this mean? Even for an accidental attribute, such as Is-White, there must be something specific and determinate about the subject, e.g., a specific surface molecular composition, that is the condition why it exists in an attributional union with the subject, and not a union of just random juxtaposition—as in a ‘heap’. But as completely indeterminate, prime matter is devoid of any grounds for having attributes, including accidental ones. Hence substantial form attribution is not attribution, but indeed just arbitrary and non-structuring association. This argument will be developed in Sections. 2.4 and 2.5. In addition, we have with inherence the following more general problem. An inherent property F of a subject x is self-founding in that the intension F both sets the necessary and sufficient condition required for it to characterize a subject x, and, by being a constituent of x, F is held to satisfy these conditions. Now, there would seem to be nothing other than ad hoc reasons for restricting ‘constituent of’ here to ‘proper constituent of’, and hence because F is a (improper) constituent of F it follows that F(F), i.e., that F characterizes itself— inherence implies self-attribution. But, if at least essential attributes are inherent and self-founding (under A5) and so self-attributional, then we would have such absurdities as ‘The substantial form Is-Human is human’ (or as Aristotle

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would put it: ‘Man is man’), and, if attributes are universals, ‘The universal Individual is individual’. Relevant here is the observation that, under the term ‘Self-Predication Thesis’ (SP), universal self-attribution—for every property F, F(F)—has been identified as one of two premises proposed as central to the classic but obscure Third Man Argument (TMA). TMA is a regress argument that Aristotle claimed, but in the extant texts he does not detail, is an unacceptable consequence of Plato’s theory of Forms. Proposed as the other key premise for the TMA is that of ‘NonIdentity’ (NI): An attribute is always something different from its subject. There is an extensive and contentious literature on what constitutes the TMA, and how Aristotle could himself avoid it, and, in particular, whether or not he accepted or rejected SP or NI and in what texts.26 I would offer here as a clarifying suggestion what I take to be, in representing Plato’s views, a more refined version of NI. Viz., NI*: If F(x), then F is the required grounds for this non-arbitrary union between itself and x, but F is something distinct from what composes x. From SP and NI*, however, there is implied the immediate contradiction that F is distinct from what composes F. But if we ignore this contradiction we can nevertheless draw out the problem here in the alternate form of a vicious regress. To see this consider that, consistent with NI*, Plato held that the fact that several entities, e.g., Socrates, Zeno, Parmenides, …, have an attribute in common, e.g., Is-Human, or simply ‘Man’, requires that the grounds for this be something distinct from each subject. Plato then identified this ground and so the attribute Man with a posited separate transcendent Form Man, each individual man’s ‘participation’ in this Form accounting for it having the attribute Man. But now, under SP the Form Man as an attribute is also a subject of itself, i.e., Man(Man). And under NI* the grounds for this attribution must be something distinct from the subject Man, what to be consistent with his first move requires the posit of a further attribute Form Manʹ (a ‘third man’). This, of course, is the beginning of a vicious regress—an infinite progression of unsuccessful attempts at locating the grounds for the initial attribution of Man to Socrates, Zeno, Parmenides, … (In a related way, Bradley’s Regress also spreads out an initial contradiction into a vicious regress.27) So construed, Aristotle

|| 26 E.g., Frank Lewis, Substance and Predication in Aristotle (Cambridge: Cambridge University Press, 1991); Gail Fine, ‘Owen, Aristotle, and the Third Man’, Phronesis 27 (1982):13–33; James Dybikowski, ‘Professor Owen, Aristotle, and the Third Man Argument’, Mind 81 (1972): 445–47. 27 Bradley’s Regress ‘spreads out’ the initial contradiction that an attribute is both 1) the unifying agent among its subjects effecting a fact, and 2) not such an agent. Starting with a given fact :R(a,b) and its unity, by 2) R cannot be the agent unifier for this fact. But by 1) there

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avoids the TMA regress and the prior contradiction by holding to the inherence assay of attribution which replaces NI* with: for F(x), F is the required grounds for this non-arbitrary union between itself and x, and F is a component of x. Our analysis of attribution implies the falsity of the latter as well as of both NI* and SP. Returning to previous points from another perspective, by the majority of his explicit statements Aristotle maintained that substantial forms are universals (A2), but then, as much noted, this is inconsistent with his theses in the Metaphysics that substantial forms are primary beings and that primary beings are not universals (each required to be rather an unrepeatable ‘this’). Abetting this inconsistency is his joint commitment to A7 (Attribute Agent-Organizers), A8 (Unity by the Constituent One), and the reductive elimination of polyadic relations (I will argue in Sect. 3.1 that this reduction follows for A2 and A8). A7 and A8 require that the unifying cause of a structural whole, e.g., a substantial form, be a single constituent attribute ‘shared by’ the other parts, a, b, c,… In regard to A8, Aristotle apparently thinks of the cause of a plural unification on the analogy of a vessel holding its contents (Cat. 15b17-26; Meta. 1023a7-17) or as a band tying together a bundle of things (Meta. 1016a1). Indeed, polyadic relations conform to A8 where for each a single relation R jointly characterizes its multiple relata a, b, c,…, as they occur in a single fact :R(a,b c,…), this on the analogy, say, of a common string providing the unity among the beads of a necklace. But with Aristotle eliminating relations, the shared unifier required by A8 of a plural whole can only be a monadic property F, and, because the only way a monadic property can be shared as common to distinct subjects is by being a repeatable intension, F must be a universal (A2). I.e., substantial forms must be universals. Yet as we have seen, Aristotle recognizes that in order to avoid vicious regress, an organizing attribute-form must as such be in a state of outward-unity-achieving act relative to the parts it organizes as matter. But relevant now is the crucial and common maxim that all acts are individuated events and particular to the subjects acted upon. From these premises it would follow immediately that all structuring attributes are unrepeatable instances (contra A2). That is, ontic predicates, e.g., forms, are, or are analogous to, individuated events in their combinatorial agency among their subjects. Indeed, Aristotle himself states succinctly that principles of ‘actuality and potency” are “different for different things” (Meta. 1071a6), and he does this in one of the few

|| must be a further attribute Rʹ such than Rʹ provides the necessary unity, and so :R(a,b) = :Rʹ(R, a,b). And so on to a vicious regress where the unity essential to the initial fact, and so the existence of the fact itself, is never established.

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contexts where there is apparent reference to individuated forms: “And those of things in the same species are different, not in species, but in the sense that the causes of different individuals are different, your matter and form and moving cause being different from mine, while in their universal definition they are the same.” (Meta. 1071a26-29) What is missing in the extant texts is then the simple syllogism proving individuated forms (and so the contradiction of assumption A2) from the two premises: forms as ontic predicates are agent organizers (A7), and the organizing agency (‘being-at-workness’) of ontic predicates is necessarily unrepeatable/individual. This argument will be expanded upon and exploited for its rich implications in Chapter 4. I note here its immediate consequence of doing away with the need to posit bare particulars or ‘haecceitas’ as principles of individuation. We have, then, with the above overview a sense of the roles assumptions A1-A8 play in Aristotle’s metaphysics and some of the problems they generate there. Western ontology is in fundamental ways a history of refinements on these and other problems and reactions to them, but with both having among their mostly tacit premises either false assumptions from among A1-A8, or contradictions of those that are true. Grounds for this claim will be detailed below, there with the advantage of starting explicitly with subsets of Aristotle’s assumptions and observing the variously implied contradictions, regresses, and other problems, these and their proposed avoidance being then observed in the tradition. The insights gained will lay the groundwork for an ontology of attribute instances that I shall develop. To anticipate, it will be argued that all attributes of any adicity occur as dependent (A1) and unrepeatable (contra A2) instances, each having as its essence (A4) a repeatable intension and an outwardly-directed unrepeatable combinatorial act whereby it externally links itself to its subject(s) (contra A5). The attributional link is conditioned by a relevance or ‘fit’ between the attribute’s intension and aspects of (possibly including the essences(s) of (A4)) its subject(s), and whereby it is descriptive of them. Instances are organizing ‘forms’ (A7), each structuring its resultant fact, and in multiple facts jointly structuring resultant complex systems (contra A8). And it will be seen how all entities and forms of unity whatsoever are or derive (e.g., conceptual associations and non-attribute universals (contra A6)) from attribute instances exclusively (contra A3), making instances what Aristotle sought as ‘primary beings’.

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2.3 The Dependence Contradiction and Individuation Regress Despite whatever intuitive plausibility each of assumptions A1-A8 may have, their joint roles in the above problems within Aristotle’s hylomorphism and in his attempts at characterizing and identifying primary being are symptomatic of at least some of them being false. Indeed, below and upon detailed examination of various subsets of A1-A8 we will see implied a number of serious problems, starting with what is demonstrative of error: mutual inconsistency and vicious infinite regress. The lesson will be that the majority of the classic assumptions are false, what historically have been far-reaching in their distorting consequences. Examined also will be the inadequacies of proffered responses to some of what are the vaguely perceived problems here, a lack of clarity due to a failure to identify explicitly the roles of the above background assumptions. Within this clarifying context we will initiate arguments intended to show that, as indicated above, five of the eight assumptions are false, viz., A2 (Attributes as Universals), A3 (Per se Subjects), A5 (Inherent Essential Attributes), A6 (NonAttribute Individuals), and A8 (Unity by the Constituent One). In advancing through the analysis of this chapter and the next I will take advantage of certain pregnant contexts and the points or problems they raise to indicate how theses from the realist instance structuralism developed in Chapters 4 and 5 are relevant to them. First, let us make precise the argument skimmed above of how classic assumptions A3 (Per se Subjects), A4 (Required Essences), and A5 (Inherent Essential Attributes) are jointly inconsistent, a contradiction that turns on ontic dependence. By A3, let x be a non-dependent per se subject—what is supposed necessary to support its dependent attributes. By A4, x has a specific nature that determines certain essential attributes of it, F, G, H,…., (e.g., the attribute Is-Independent as an essential attribute for x under A3), and by A5 these attributes are constituents of x. But then x is dependent for its existence upon these attributes as proper parts, and this contradicts the non-dependent nature of x under A3. Indeed, it is an immediate implication of A3 that per se subjects are simple—have no proper parts, attributes or objects—since otherwise they would then be ontically dependent upon these parts (cf. Meta. 1087a3-4) which contradicts their definition.28 Hence, one or more of theses A3, A4, or A5 is false. In

|| 28 John Heil, for example, argues in this way for the simplicity of substances: “I merely note that the idea that substances are non-dependent entities, in concert with the idea that wholes depend on their parts, provides independent support for the thesis … that substances must be simple.” The Universe as We Find It (Oxford: Clarendon Press, 2012), p. 34.

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what follows I shall refer to this argument as the ‘Dependence Contradiction’. Aristotle comes close to the argument at Metaphysics 1038b24-28 where he asserts that if attributes of a per se subject are prior to it as constituents of it (what would be implied under A4 and A5), then these attributes would have to have the essential characteristic of the per se subject, viz., “separability”, i.e., independence (violating the dependent nature of attributes under A1 (Attributes as Dependent) and presupposed in A3 (Per se Subjects)). The apparent reductio argument is that if something is a part of an independent entity then it must also be independent; or the contrapositive: if something is a dependent entity, then if it is part of another entity the latter is also dependent. Regardless of what Aristotle intended, what the Dependence Contradiction does demonstrate is that under assumptions A3, A4, and A5 the per se subject that is the prime matter of a substance a must have, but cannot have, an essential attribute. What has perhaps preempted efforts that would lead to the recognition of this contradiction is a further erroneous assumption broached in the previous section: that a substantial form F (e.g., Is-Human), what in the contradictionproducing context is an attribute of prime matter (e.g., Socrates’ prime matter), is the same attribute and the same unproblematic attribution that is F charactering the subsuming substance (e.g., Socrates having the attribute Is-Human). In contrast and to anticipate, it will be argued herein that ontic dependence involving discrete things (cf. Sect. 4.6) is of two asymmetric modes: internal whole-upon-parts and external agent-upon-patients, and that all attributes are externally dependent (A1) as agent unifiers on or among their subjects, with no subject being internally dependent upon its attributes otherwise misconstrued as constituents (contra A5). And more subtly, it will be seen that though attributes proper as individuated instances (contra A2), e.g., Is-Squarei or Is-Contrarytoj, are not constituents of their subjects (i.e., not their own foundations), each instance contains as a proper part a non-combinatorial non-attribute intension universal (so contra A6), e.g., Squareness or Contrariety. The intension part is easily confused with the subsuming instance, this abetting the error that attributes are parts of their subjects—assumption A5 or its generalizations. Of fundamental importance, it will be seen how attributes proper as instances, though both externally and internally dependent entities, can and must necessarily have the role of Aristotelian ‘primary beings’: all other entities, including structured and unstructured wholes, being derivative from and so ontically dependent upon them (contra A3). In addition to the Dependence Contradiction implied by classic assumptions A3, A4, and A5, there is also the problem of the vicious infinite regress that follows from the slightly different set of A2 (Attributes as Universals), A4,

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and A5, and turns on the issue of individuation.29 Let x be an ordinary thick particular, e.g., an apple. Then x has by A4 (Required Essences) and A5 (Inherent Essential Attributes) constituents that are attributes, F, G, H,…, what by A2 are repeatable universals. (To reiterate, by ‘repeatable’ is meant the possibility of making as a constituent what is numerically the same contribution to the beings of numerically distinct entities.) Yet, for subsuming x to be an unrepeatable individual, it must also have, in addition to these constituent repeatable universals, at least one proper constituent individual, xʹ, to account for the unrepeatability of x. For, a collection of universals the elements of which each qualify the same entity is itself repeatable in that all its elements can be possibly shared by another subject, and so this collection is not an unrepeatable particular. However now, by A4, individuator xʹ itself must have a positive essence, what by A5 is composed at least in part by some attributes, M, N, O,…, these by A2 being universals. Then by the same reasoning, xʹ itself must have as a proper constituent at least one further individuator, an unrepeatable individual xʺ, and so on to vicious infinite regress. This argument is found, for example, in the work of Michael Loux30, and in the following I will refer to it as the ‘Individuation Regress’. In general, what this regress shows is that nothing that is an individuating principle/source can have a universal, any more than another individual, as a proper constituent—primary individuators are simple. This will be true of our assay of principles of individuation as the combinatorial-agency aspects of attribute instances, where intension universals form continuous wholes with, but are not constituents of, their concomitant outwardly-connecting and individuated acts of attribution. Focusing first on the Individuation Regress, in order to stop it and ensure a needed supply of basic individuals, and yet retain as much as possible of the Aristotelian assumptions, a simple tack would be to posit the needed individuals as exemptions, and the only ones, to either A4 or A5. Here the choices are: 1) to modify A4 (Required Essences) and allow for some individuals that are devoid of positive essences/natures, and so have no universal attributes that otherwise by A5 would be required to be constituents of them, or 2) to retain A4

|| 29 It is to be noted that the root issues involved in the Dependence Contradiction and the Individuation Regress, respectively, ontic dependence and individuation, are central to the cross-classificatory criteria that Aristotle makes his first concern in the Categories (1a20-b9), respectively, in-a-subject|not-in-a-subject and said-of-a-subject|not-said-of-a-subject. 30 Michael Loux, Metaphysics: A Contemporary Introduction (New York: Routledge, 1998), pp.116–17. It is also found in Richard Davis and David Brown, ‘A Puzzle for Particulars’, Axiomathes 18 (2008): 49–65.

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allowing every entity to have a determinant essence but requiring as exceptions to A5 (Inherent Essential Attributes) individuals that have no universal attributes as proper constituents, whether essential (i.e., as founded on the individuals’ essences) or not. On either assumption the posited individuals can then serve as per se subjects required under A3. And as such both alternatives are found in the tradition: Under 1) is the completely undetermined—‘pure potentiality’—Aristotelian ‘prime matter’, or the same notion pluralized and referred to by modern authors as ‘bare particulars’. Under 2), and as a response to problems with the posit under 1) of things empty of any attribute-founding content and so specificity, are the posit by some contemporary authors of barelyessenced individuals, i.e., per se subjects that found the attribute Is-Individual and possibly a few other formal ones, all other attributes being simply ‘tied-to’, i.e., arbitrarily associated, with them. These latter posits are in the literature also termed ‘bare particulars’, but in order to avoid confusion I shall refer to them as ‘near-bare particulars’. The impossibility of either alternative will be the work of the following two sections. Historically, the broader context here is that, first, in Aristotelian hylomorphism a structured whole, like Socrates, is a function of the organizing agency of a constituent definitional attribute F (A7), and only one (A8), what would be a monadic ontic predicate—the substantial form—of the single underlying per se subject—prime matter. The form-matter whole is the subject of further accidental attributes (Meta. 1049a24-36). Whether Aristotle himself held that prime matter is the individuator of substances is controversial31, however, if he did hold the classic assumptions I have identified then the only plausible candidate for individuators is prime matter (by A3 and A6 per se prime matter is individual, whereas the form as the only other component of a substance is universal by A2). In more modern substratum theories Socrates is construed as the whole composed of his property universals, or at least most of them, arbitrarily associated with an individuating and unifying (absolute or near-) bare particular. Besides issues with prime-matter/bare-particulars to be observed presently, there is with such a theory, as with Aristotelian hylomorphism, the problem that most entities, e.g., Socrates or an apple, are each essentially structured by constituent polyadic relations among parts and this prior to—as prerequisite foundations for—then emergent monadic properties had by the resultant whole, and yet both theories would have these emergent properties be constituents of and so prior to the whole, and would have all the constituent

|| 31 E.g., see Edward Regis, ‘Aristotle’s Principle of Individuation’, Phronesis 21 (1976): 157–66.

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attributes be only monadic properties. In contrast to substratum theories, the standard rival is trope bundle theory that retains both A4 (Required Essences) and A5 (Inherent Essential Attributes), the latter generalized to all tropes. Properties as tropes are constituents of their subjects, and the Dependence Contradiction is avoided by declaring tropes to be non-dependent, contra A1, what then removes the need for per se subjects, contra A3. The Individuation Regress is avoided by denying A2 (Attributes as Universals) of tropes: tropes are independent particulars, not dependent universals. Among the troubles here are that, first and following from arguments to be given in Section 4.5, standard tropes would have to each assay internally into a repeatable quality and an individuator, the latter under trope theory being an agencyless bare particular, and both kinds of entities the theory eschews. And secondly, trope bundles cannot go proxy for ordinary objects in that the former are completely devoid of the complex and hierarchical structures essential to the latter. Distinct from both the substratum and bundle views, our analysis will be that there are necessarily simple particulars, but there are no ‘per se subjects’ in the sense of A3, i.e., no atomic non-dependent (non-attribute) individuals thought otherwise to be required ultimate subjects for dependent attribute universals. Rather, the argument will be that the atomic principles of individuation are the subjectlinking/combinatorial aspects of thus individuated attribute instances (contra A2 (Attributes as Universals)). And with all attributes as instances characterizing their subjects by external adherence there is a denial of A5 and so in this way also an avoidance of both the Dependence Contradiction and Individuation Regress.

2.4 The Alternative of Absolutely Bare Particulars and Their Incoherence A means by which the ‘substratum’ tradition has avoided both the Individuation Regress (implied by A2, A4, and A5) and the Dependence Contradiction (implied by A3, A4, and A5) is its retaining all the premises except for the selective denial of A4 (Required Essences) for one or more posited individuals, these serving as per se subjects for A3. By this tack the first step for both the regress and the contradiction is avoided, i.e., an entity without an essence has no essential attributes that A5 would then require to be constituents of it and upon which it would otherwise be further dependent or require additional individuators. This denial of essence restricted to a single entity is what we have in fact with Aristotelian ‘prime matter’. It is to be noted, however, that with the posit

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of prime matter the question of a principle of individuation remains open. It is the case that by A6 prime matter is a non-attribute object and so itself an unrepeatable individual. But this does not make it a principle of individuation— prime matter could be analogous to a particular thread to which bundles of universals that characterize each ordinary particular attach. I.e., different bundles of universals would have the same individuator and so be numerically the same. A number of scholastics did hold prime matter to be numerically one across all particulars and assigned the task of individuation to some entity or entities, e.g., the accident of quantity. Simplifying this, some contemporary substratum theorists pluralize essenceless posits as ‘bare particulars’, one each as an individualizing substratum for each thick particular. In either form, however, essenceless entities suffer from the same self-nullifying incoherence to be observed presently. The denial of essences (contra A4) for certain entities may seem plausible on the following considerations. An ordinary individual a, e.g., an apple, has an essence—a composing being—that founds certain essential attributes descriptive of it (A4) and these attributes as universals (A2) are on assumption A5 constituents of a. Indeed, any attribute that entered into the composition of a would contribute to its qualitative ‘the-what-it-is-to-be-that-thing’ (Aristotle’s phrase for what is translated as ‘essence’). As components of a these properties are necessary for a to exist and so are each its own foundation for what is its necessary attribution to a. Essence construed as these property universals has in the literature been termed a’s ‘specific’ or ‘general essence’. But now ordinary object a must have as a component something in addition to all of the repeatable properties forming its specific essence, viz., an individuator. So expanded and completed, and thus containing necessarily a’s specific essence, is what is termed a’s ‘individual essence’. Now, consider the remainder when a’s specific essence is abstracted (‘subtracted’) from its individual essence. The residuum will be a’s individuator which a must necessarily have, but it will be without a specific essence and so without an individual essence. For if it had a specific essence it would be composed of essential attribute universals, which would also be constituents of a—what is essential to a’s individuator is essential to a. But no such property universals, not even the universal Is-Individual, can be constituents of the residuum for these are all constituents of a’s specific essence assumed to have been set aside in abstraction. Without any essential attributes this individuator is essenceless in being of no ‘such’ or kind, and whether singular or multiple as ‘bare particulars’, each is taken to be solely an unqualified ‘this’—an uncharacterized atom of pure particularity. In regard to the latter and as thus theoretically constructed, proponent Gustav Bergmann

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asserts that “Bare particulars neither are nor have natures.”32 And D. M. Armstrong as an opponent concurs: “A bare particular would not instantiate any universals, and thus would have no nature, be no kind or sort.”33 Or stated alternately, if the individuator of an entity a is prime matter or a bare particular, pa, then for every property F, F does not characterize pa. Whether as Aristotelian prime matter or contemporary bare particulars34, it has struck many that the notion of such essenceless individuators/independentsubstrata is incoherent, and, I would argue, rightly so.35 The argument can be put succinctly: Prime matter or a bare particular, pa, is posited as a required constituent individuator and ultimate subject (A3) for the dependent attributes (A1) of an individual a on the further assumptions that all other components making up the being/essence of a (A4) are attributes of a (A5) and are repeatable universals (A2). Now pa itself can have no constituent attributes, for if it did then, first, these constituents would be universals (A2) and so require pa itself to have a further constituent individuator to account for its unrepeatability, and this would be the beginning of the Individuation Regress above. And second, if pa had an attribute as a proper constituent then it would be ontically dependent upon this attribute, but as a per se subject pa is to be an ultimate independent entity posited as necessary to support the existence of dependent entities, including attributes, and so pa cannot be dependent upon anything else, including proper parts—it must be simple. This is the crux of the Dependence Contradiction above. But now, being without any constituent attributes, this in effect

|| 32 Gustav Bergmann, Realism (Madison: University of Wisconsin Press, 1967), p. 24. 33 D. M. Armstrong, Universals: An Opinionated Introduction (Boulder: Westview Press, 1989), p. 94. 34 E.g., Arguments for bare particulars are found in J. P. Moreland, ‘Theories of Individuation: A Reconsideration of Bare Particulars’, Pacific Philosophical Quarterly 79 (1998): 251–63, and J. P. Moreland and Timothy Pickavance, ‘Bare Particulars and Individuation: A Reply to Mertz’, Australasian Journal of Philosophy 81 (2003): 1–13; Theodore Sider, “Bare Particulars”, Philosophical Perspectives 20 (2006): 387–97. References for other advocates are found in Andrew Bailey, ‘No Bare Particulars’, Philosophical Studies 158 (2012): 31–41. 35 E.g., Michael Loux has argued that it is impossible there exist entities that have no properties essentially. See Loux, Metaphysics: A Contemporary Introduction, pp. 115–16. Other arguments against bare particulars are found at pp. 92ff. Also see Loux, Substance and Attribute (Dordrecht: Reidel, 1978), pp. 140–52; D. W. Mertz, ‘Individuation and Instance Ontology’, Australasian Journal of Philosophy 79 (2001): 45–61, and ‘Against Bare Particulars: Response to Moreland and Pickavance’, Australasian Journal of Philosophy 81 (2003): 14–20; Richard Brian Davis, ‘‘Partially Clad’ Bare Particulars Exposed’, Australasian Journal of Philosophy 81 (2003): 534–48, and ‘Are Bare Particulars Constituents?’, Acta Analytica 28 (2013): 395–410; and Bailey, ‘No Bare Particulars’.

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must make pa an ‘essenceless entity’, i.e., devoid of all positive being. For, to have any composing non-zero being (‘ontic mass’) whatsoever—to be other than homogeneous nothingness—is to have some differentiating determinateness, and this would be the specific foundation for a concomitant property and for relations of contrariety or complementarity descriptive of it. I.e., to exist is always to be of some definite character or other, or alternately: positive being is always a differentiated kind (‘such’ or ‘what’).36 But then the founded property would be an essential property and so, on assumption A5, a constituent of pa, contradicting our above conclusion. In sum and more precisely, the descriptor for the term ‘pa’ would require a referent to exist—have positive being—that is devoid of positive being. Hence, the notion of prime matter or bare particular is incoherent. This is the incoherence in attempts by some to salvage such entities by characterizing them as ‘pure potentiality’, i.e., to claim for them the specific being of being something but not specifically anything.37 But it is precisely the fundamental ontological point here that to be is to be specifically differentiated, to be ‘some-such-a-thing’—complete qualitative undifferentiation is homogenous nothingness. We will return to the pure potentiality characterization below. The obscurity concerning prime matter led many scholastic philosophers to describe it as ‘unintelligible’, but taking it to be theoretically necessary they could not accept its non-existence.38 Indeed Plato, in initiating within the tradition the per se subject thesis (A3) with the posit of the ‘Receptacle’ as the necessary subject of all properties (Forms), had argued that it must itself be “formless and free from the impress” of any properties, and yet that as such it is “incomprehensible” (Timaeus 50b-51b; also see 52b). The impossibility of essenceless individuators/substrata is evidenced also in less generic ways. Consider first that advocates take ‘Is-a-Bare-Particular’, abbreviated here as ‘Par’, to be a real and positive attribute universal characterizing certain subjects, e.g., pa, and not others, e.g., an apple a. For Par to characterize—be in an attribution union with—pa and not be just arbitrarily associated with it, pa must have a specific foundation f within its composing being || 36 In the words of John Heil, the “ontological precept” here is: “For there to be something rather than nothing, there must be something that is some way or other.” The Universe as We Find It, p. 176. 37 This argument is made against Aristotle’s prime matter as the substratum for substantial change by Daniel Graham, ‘The Paradox of Prime Matter’, Journal of the History of Philosophy 25 (1987): 475–90. 38 Pasnau, Metaphysical Themes: 1274-1671, pp. 119ff. It is interesting that Aquinas is willing to assert that “matter in itself can neither exist, nor be known.” Summa Theologica, Pt. I, Q. 15, Art. 3.

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that grounds the attribution, what is distinct from the foundations for and so preventing pa’s attributional union with attributes like Is-Universal or IsDependent. But for advocates who adopt inherence under A5, universal Par is identical to its foundation f, Par = f, and so individual pa has universal Par as a proper constituent. And, this contradicts pa’s required simplicity. As a further critique let us look closer at what I take to be Aristotle’s argument implying the complete vacuity of prime matter. It is not clear from the text whether or not Aristotle himself considered this a reductio ad absurdum of the notion of per se subjects under his then assumptions.39 At Metaphysics 1029a630 he observes that if we “strip away” (Greek: aphairesis), i.e., abstract away, all the attributes from what is their supposed distinct and supporting per se subject we end up with what is in the limit and at best an absolutely indeterminate entity, one that does not even have what are its defining properties of independence (by A3 (Per se Subjects)) and individuality (by A3 and A6 (NonAttribute Individuals)). In detail, for an ordinary or ‘thick’ particular composed of at least its essential/defining properties (A4 and A5), if we iteratively ‘remove’ via abstraction these properties, one by one, each from the remainder of the previous separation, we will eventually reach the level of a ‘thin’ particular. And if too the latter is at all a non-null entity, thus with a defining essence and so defining composing properties, it will not be an independent per se subject and the removal analysis will apply to it. This would proceed until in the limit the remainder, which must be a per se subject, will shrink to complete indeterminateness. Any ontic content that would found defining/determining properties will have been removed. But then, this remainder cannot even be the subject of the attributes necessary to define it as the needed per se subject, viz., “separability” (independence) and “thisness” (individuality). Aristotle leaves his analysis at this but it would ground his subsequent identification of substantial form with “the essence of each thing and is primary substance” (Meta. 1032b1). If in a hylomorphic compound that is an ordinary substance a the matter reduces to zero qualitative specificity, i.e., is devoid of all ‘whatness’ (or ‘suchness’), then it must be the form of a that supplies a’s total essence/‘whatness’—that-by-which-a-is-what-it-is. At any rate, what we have here is a reductio of the concept of an essenceless entity, what is an ontic void left when all internal qualitatively-relevant and differentiating content, i.e., any grounds/ foundations for an attribute, has been theoretically removed from an entity and made an attribute of what under A3 is a hypothesized common remainder. In || 39 For a discussion and references see Theodore Scaltsas, Substances and Universals in Aristotle’s Metaphysics (Ithaca: Cornell University Press, 1994), pp. 222–28.

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effect, an essenceless per se subject is an assumption-mandated ‘peg’ on which to consolidate and hang attributes, but of which there is no content left that could found their attribution of it. This intended substratum and individuator, whether as prime matter or one of pluralized bare particulars, is an impossible fiction. In contrasting coherence, in the ontology of attribute instances argued herein every entity, including the ultimate individuators, viz., the unifying agency of each instance, has a composing essence that is a content that founds but is not composed of its properties nor necessarily of universals/intensions. Here instances in attribution externally adhere to, not internally inhere in, their subjects whose positive beings are presupposed in founding them, and so in abstraction attribute instances can be separated from their subjects without these subjects reducing to nothing. An additional problem for an essenceless individuator/substratum multiplied as bare particulars turns on the fact that the only union each can have with any other entities is that of arbitrary and subject-indifferent association, and not that of attribution/ontic-predication. The arbitrariness of association stems from the fact that it requires no foundational conditions be satisfied by its subjects in order to connect them. On this point, in a recent attempt to save bare particulars by James Moreland and Timothy Pickavance40 they have distinguished between the ‘rooted-in’ relation of founded attribution and the ‘tied-to’ relation between an attribute and a bare particular. In this regard Moreland observes that bare particulars have their “properties tied to them in a primitive way ungrounded in capacities or properties within those bare particulars.”41 He also observes rightly, but fails to appreciate the consequences of its source, that “it seems inexplicable as to why bare particulars always come tied to certain properties (e.g., Particularity).” 42 For here, an ordinary individual a is held to have as ‘rooted-in’ it a property F if and only if F is ‘tied-to’ a’s constituent bare particular pa. But now and in particular, since the ‘tied-to’ connection is simply unconditioned association, it is possible that contrary properties, e.g., IsSpherical and Is-Cubical, can be freely associated with pa. Yet in this case the biconditional would require an ordinary particular a, our apple, to have contrary properties, e.g., be both spherical and cubical. And this is absurd. Now it might be responded that it is the intensions of contrary properties that prevent them from being simultaneous attributes of the same subject, but this misses

|| 40 Moreland and Pickavance, ‘Bare Particulars and Individuation’. 41 J. P. Moreland, Universals (Montreal: McGill-Queen’s University Press, 2001), pp. 155–56; Moreland, ‘Theories of Individuation’. 42 Moreland, Universals, pp. 155–56.

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the point. Contrary intensions prevent their properties from simultaneously entering into an attributional union with a common subject, but not from a simultaneous union of association with some common entity, e.g., as in the associations resulting in the mereological sum [a,Is-Spherical,Is-Cubical]. Arbitrary association cannot go proxy for ontic predication. We will return to this point below. Advocates who, to bolster their case, further posit that bare particulars have attributes, because rightly every entity must have them, necessarily equivocate on ‘attribution’. This is the flaw in Armstrong’s thinking that states of affairs, or facts, assayed as ‘thin particulars’ instantiating universals, along with the claim that every entity must instantiate at least one property, dissolves the problem of his thin particulars being, in fact, bare particulars. He holds that the thin particular exists only in abstraction from what is the real and ontically primary states of affairs. Yet his thin particulars remain bare particulars with their attendant problems as above. Specifically, Armstrong asserts that “The fact that an object instantiates a certain property does not flow from the nature of the object and the nature of the universal that are involved.”43 I.e., what he here, and correctly, is asserting is that his nexus of ‘instantiation’ is but arbitrary association, what any union with a natureless bare particular must be. Yet, ‘instantiation’ as association makes states of affairs mereological sums, what on Armstrong’s view would be no addition to being over that of their parts of thin (now bare) particulars and universals—states of affairs are no longer primary. But Armstrong needs and wants ‘instantiation’ to be attribution in order to account for the non-arbitrary non-mereological unity of states of affairs, what makes them more than their constituents, and is writ large in the ordering within states of affairs having asymmetric and non-symmetric relations.44 In defense of bare particulars it has been objected, e.g., by Moreland and Pickavance45, that apparent attributes such as Is-Individual (or Is-Unrepeatable) and Is-Simple, and what would have to be the same for Is-Independent, are not genuine properties, but rather are negative linguistic predicates that describe the absences of properties with the correlative positive intensions. As such they constitute no challenge to bare particulars. If to the contrary, these linguistic predicates reference corresponding properties, and one adopts the inherence model of ontic predication, as does Moreland and Pickavance, then a bare par-

|| 43 Armstrong, Universals, p. 109. 44 Ibid., p. 90, and A World of States of Affairs (Cambridge: Cambridge University Press, 1997), pp. 118ff. 45 Moreland and Pickavance, ‘Bare Particulars and Individuation’.

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ticular would have to be a complex entity, since the then composing attributes Is-Individual and Is-Simple are non-identical, and this would contradict the fact that a bare particular is to have the attribute Is-Simple. In response to the claim here I would make in passing the counter-claim that if an entity has of itself the necessary and sufficient foundations for a predicate ‘to be true of it’, then the predicate references a real property. Some properties, like the ones above, are dependent upon minds to sustain their existences, but this does not make them unreal or mere arbitrary associations, for the properties specify foundations had completely by their subjects, and so necessitate their union with their subjects. Inclinations to the contrary may be motivated by the inherence assumption that properties must be constituents of their subjects. Aside from all of this, however, I would emphasize a different point. It is an often stated criterion that for an entity to exist—to be other that no-thing—it must have at least one genuine property. The principle is held by Moreland and Pickavance where, specifically in support of bare particulars, they claim that each has necessarily the attribute I will term ‘Is-Propertied’, i.e., the having of some property or other but no specific one.46 Now against this, first and simply, is the observation that the property of Is-Propertied would itself be a specific essential attribute of a bare particular, and so would violate its own definition. The contradiction is seen in another way: bare particulars qua bare particulars would have the Is-Propertied attribute necessarily, though it is asserted that “bare particulars actually have no necessary properties.”47 On the one hand, Moreland and Pickavance intend the property Is-Propertied to be descriptive of a subject bare particular’s intrinsic being, what in this way would be ‘rooted-in’ and had necessarily by the bare particular, and yet, on the other hand, they would require of Is-Propertied, like any property of a bare particular, to be only ‘tied-to’—just arbitrarily associated with—a bare particular and so not had necessarily by it. In addition, if one holds with Moreland and Pickavance an inherence assay, minimally A5, and that attributes are universals, A2, then the attribute Is-Propertied would have to be a proper constituent of its subject bare particular. But then every bare particular would have the necessary and genuine properties of Is-Complex and IsDependent, what they cannot have as bare, or as simple. In short, Is-Propertied is not a genuine property and bare particulars are no-things. Further and despite the intent to satisfy what is the manifest need for a plurality of such individuators, each bare particular, in having no constituting positive essence and so no true attributes (neither part of it internally nor at|| 46 Ibid. 47 Ibid.

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tached to it externally), has nothing to differentiate it from any other bare particular (or, in fact, anything else). Or in a slogan: no essence, then no grounds for being other-than. But then, there can be but one bare particular 48, and so plurality becomes an illusion.49 The analogous argument for the absence of division within prime matter is found among medieval philosophers.50 For example, the scholastic Tommaso Cajetan argued that “prime matter is itself one in number” because it “includes within itself nothing distinctive, since it is stripped of all act, whose function it is to distinguish.”51 Leibniz made the point in another way with the direct analog of geometric points, the would-be limits of diminishing extension. I note that more recently Theodore Sider has proposed that space-time points are best taken as each a “truly bare particular that stands in a network of spatiotemporal relations.”52 But then as Leibniz observes, in themselves “One point of space does not absolutely differ in any respect whatsoever from another point of space. …One would be the same thing as the other, they being absolutely indiscernible…”53 For these reasons the prime matter of Aristotelian/scholastic ontology is always and properly referred to in the singular. It is ironic but no accident that in the Aristotelian tradition prime matter is sometimes taken to be a principle of individuation for each of a plurality of objects, though Aristotle himself motivates the thesis only indirectly (e.g., Meta. 1034a5-8).54 For, if every object/particular has as its ultimate metaphysical parts

|| 48 Aristotle himself may be making this point in another context when at Meta. 991b21–27 he asserts it to be absurd that numbers can be composed of homogenous units because there could be no plurality of such entities, “for in what will they differ, as they are without quality?”, i.e., each is a characterless other. Theodore Scaltsas cites this text as evidence that Aristotle at Meta. 1029a6-30 is rejecting characterless prime matter. See Scaltsas, Substances and Universals in Aristotle’s Metaphysics, pp. 222–28. 49 This point was made by Keith Campbell in his Abstract Particulars (Oxford: Basil Blackwell, 1990), p. 7. For this reason he argues that his individuated attributes as nominalistic tropes must be simple though with two aspects differentiable in reason. In tropes themselves there is no distinctness of otherwise individuating bare particular and quality-bestowing intension universal. 50 Pasnau, Metaphysical Themes 1274-1671, p. 55. 51 Tommaso Cajetan, Commentary on St. Thomas Aquinas’ On Being and Essence, trans. L. Kendzierski and F. Wade (Milwaukee: Marquette University Press, 1964), Chap. 3, Para. 50, p. 126. 52 Sider, “Bare Particulars”. 53 Gottfried W. Leibniz, Philosophical Papers and Letters, 2d. ed., ed. by L. Loemker (Dordrecht: Reidel, 1969), p. 682. 54 Note, tellingly, that Aquinas saw that prime matter as pure potentiality had to be given a minimal positive determination of some three-dimensional quantity in order to individuate.

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only universal attributes and individual per se subjects, then on Aristotle’s assumptions the latter prime ‘subject-matters’ are the ultimate individuators though they are required to be both essenceless particulars and an undifferentiated singular entity. In the Aristotelian traditional a counter to the charge of complete ontic evaporation has been the construal of prime matter in its ‘pure-potentiality’ as yet being a something, i.e., an entity that is nothing definite or differentiated in itself but potentially anything as can and must be determined by a ‘substantial form’ attributed of it. The assumption is that prime matter as potentially anything has some minimal positive being that differentiates it from nothingness— nothingness is not potentially anything (what is intended by the Eleatic slogan: From nothing nothing comes (ex nihilo nihil fit)). This is the view attributed to Aristotle and held famously by Aquinas55. It is at the center of what Robert Pasnau terms the ‘paradox of pure potentiality’ and reports was the source of much debate by scholastic philosophers centered around the charge of incoherence.56 The issue was whether what is potentially characterizable as anything can exist, given that to exist is to be actually and specifically characterized. Pasnau observes that one response was to describe prime matter as something half-way between non-being and being. But this is hardly possible: things either exist or they don’t—no entity quasi-exists any more than a fact ‘sort-of’ or partially obtains. An entity has full and complete existence or no existence. A second response was that being potentially characterizable as anything is itself a characteristic that prime matter has, and as so characterized it can exist if necessitated by the theory. But this claim involves a contradiction seen in its expansion as: prime matter is completely indeterminate (i.e., its composing being is such as not to found any attributes), but yet is minimally determined in being something that can be determined (i.e., has a composing being that founds the attribute ‘Can-be-Determined’57). An analogy here would be that because a bank account has the potential for being non-empty this is sufficient for it to be non-empty—imagine offering this to your bank as a defense against insufficient funds.

|| See, e.g., Kevin White, ‘Individuation in Aquinas’s Super Boetium de Trinitate, Q.4’, American Catholic Philosophical Quarterly LXIX (1995): 543–56. 55 Aquinas, Summa Theologica, Pt. I, Q. 4, Art.1. 56 Pasnau, Metaphysical Themes 1274-1671, pp. 35–52. 57 Can-be-Determined is a second-order attribute only descriptive of a subject because the subject has first-order attributes with more specific intensions or determinations, and these prime matter cannot have.

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The remaining option is just to assign prime matter a being with a determinant essence, and therewith we return to the nexus of assumptions implying the Dependence Contradiction. Assigning some essence to prime matter was the position taken, for example, by the late-scholastic Francisco Suarez against the pure-potentiality position of Aquinas. Suarez argued that matter to be anything at all cannot be devoid of all act (actus)—prime matter having to have “in itself the entity or actuality of existence distinct from the existence of form.”58 But now, prime matter in having some actuality has “true reality and a partial essence”59, in this way having some essential attributes (A4 (Required Essences)). For Suarez these essential properties include Has-Act, Is-a-Subject-for-Substantial-Form, Is-Dependent-Upon-Substantial-Form, Is-a-Proper-Subject-of-Quantity, and Persists-through-Substantial-Change. Now on an inherence construal of at least essential attribution (A5), these attributes would be constituents of prime matter, making it thereby dependent and non-simple60 and so contradicting the conditions placed on it as a per se subject under A3, and in particular Suarez’s claim that prime matter is simple61. Even if Suarez would deny the inherence of the above essential attributes in prime matter and would have only their necessary and sufficient foundations be parts of it62, a contradiction would follow. Take, say, Has-Act and Is-a-Subject-for-Substantial-Form, since all of the foundations for each are inherent in prime matter and prime matter is simple, then these foundations are identical. So because they have identically the same foundations, any subject for one is a subject for the other, but then every

|| 58 Trans. by Jorge Gracia from Suarez’s Diputationes Metaphysicae XIII (The Material Cause of Substance), Sect. 4, 13, and given in Gracia’s Glossary section ‘materia’ to his Suarez on Individuation (Milwaukee: Marquette University Press, 1982), pp. 229–30. Also see the section ‘Actus’, pp. 178–79. Arguments by Suarez for the entitative actus of prime matter are given in Sect. 5 of Disputatio Metaphysica XIII, translated by Sydney Penner, at www.sydneypenner.ca/ su/dm_13_5.pdf. For an analysis of Suarez’s arguments against Aquinas’ view see J. Kronen, S. Menssen, and T. Sullivan, ‘The Problem of the Continuant: Aquinas and Suarez on Prime Matter and Substantial Generation’, The Review of Metaphysics 53 (2000): 863–885. 59 Francis Suarez, On the Formal Cause of Substance: Metaphysical Disputation XV (Disputationes Metaphysicae, XV), trans. J. Kronen and J. Reedy (Milwaukee: Marquette University Press, 2000), Sect. 7, 7, p. 93. Also see Sect. 8, 7, pp. 101–2. 60 The first three of these intensions are non-identical since their extensions are not identical. 61 Suarez, On the Formal Cause of Substance, Disputationes Metaphysicae XV, Sect. 5, 1 and 2, p. 77, and Sect. 9, 3, p. 117. 62 These foundations in prime matter for its attributes would be similar to what Suarez claims are in substantial forms as ‘roots’ for the “whole variety of powers and accidents” that characterize resultant substances. On the Formal Cause of Substance, Disputationes Metaphysicae XV, Sect. 1, 7, p. 21.

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entity, e.g., an accident, since it has the property Has-Act will also have the property Is-a-Subject-for-Substantial-Form which is not the case, e.g., no accident has this property. It is to be noted that though both Aquinas and Suarez hold, in agreement with one of the assertions of A3, that prime matter is the ultimate non-attribute subject of attribution, contra another assertion of A3 they both deny that it is ontically independent: matter is as dependent upon form as form is upon matter. Suarez asserts that it is because it “is so imperfect that [prime] matter cannot exist naturally without form.”63 The dependence here of prime matter upon substantial form is not that of agent-upon-patient, i.e., attribution, or whole-upon-part, but is rather due to a kind of weakness by deficit of being, and this would seem to return to the bogus notion of quasi-being. We can summarize this section as showing that classic assumption A4 (Required Essences) has no exceptions. I.e., every entity as an existent has a composing positive, qualitatively delimited being—a specificity-bestowing ‘ontic mass’—that differentiates it from other existents and from nothingness, and what as such would be the ground/foundation for it having certain essential attributes. This positive content is what Aristotle intended by an essence as ‘that by which something is what it is’. Here we have the basis for the common maxim: An entity exists if and only if it has at least one (essential) attribute.64

2.5 The Alternative of Near-Bare Particulars and Their Error In the previous section it was argued how, in an attempt to parry the Dependence Contradiction and the Individuation Regress of Section 2.3, the tack of limiting the range of A4 (Required Essences) from including certain posits necessary to serve as individuators and per se subjects—‘prime matter’ or ‘bare particulars’—yields absurdities. As noted then, an alternative and one broached in the contemporary debate is rather to hypothesize a class of individuating

|| 63 Trans. by Jorge Gracia from Suarez’s Disputationes Metahysicae XIII (The Material Cause of Substance), Sect. 4, 14, and given in Gracia’s Glossary section ‘materia’ to his Suarez on Individuation, referenced in note 58. The position is restated at Disputationes Metaphysicae XV, Sect. 8, 9, pp. 102–3. Also see John Kronen, ‘The Importance of the Concept of Substantial Unity in Suarez’s Argument for Hylomorphism’, American Catholic Philosophical Quarterly LXV (1991): 335–60. 64 E.g., Reinhardt Grossmann, The Categorical Structure of the World (Bloomington: Indiana University Press, 1983), p. 391; and D. M. Armstrong refers to the maxim as ‘The Strong Principle of the Rejection of Bare Particulars’ in Nominalism and Realism (Cambridge: Cambridge University Press, 1978), p. 113.

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substrata as individuals that are not composed of their attributes, these then being exempted from the range of assumption A5 (Inherent Essential Attributes). These simple independent particulars are exceptions to the inherence model of attribution in having all their attributes externally attach to them. All other non-per-se entities are held to contain their attributes, or at least essential ones, as constituents. Going furthest in this direction, I will in the next section argue for a global rejection of inherence as a model for the attributional union, a position taken, for example, by both E. J. Lowe and Michael Loux as removing the need to posit bare particulars.65 There are philosophers, however, who are reluctant to give up the inherence model, and so in the face of the above problems with bare particulars, they propose in effect to allow as exceptions to it, and in particular to A5, only the single class of posited individuators/per-sesubjects. Unlike (absolutely) bare particulars, these posits each has a qualitatively determined essence (as required by A4) founding essential attributes descriptive of it, but as exceptions to attribute inherence its properties, essential or accidental, are not constituents of it, i.e., none of its attributes are their own foundations. I shall refer to these posits as ‘near-bare particulars’. We will see that, though they are coherent as simple particulars, they cannot serve as the supporting per se subjects required by A3 (indeed, it is my point that nothing can). It may be this fact and the conflation of absolute with near-bare particulars that give some advocates of the former their dogged conviction. At any rate, just as with absolute bare particulars, we shall see that the above assumptions require of near-bare particulars that they be the subjects of a special kind of ‘attribution’, what is an unfounded union and so not attribution at all but merely ‘tied-to’ association, this then reduplicating problems we have already seen. In contrast, the instance ontology argued for herein retains only the single and intuitive notion of non-arbitrary foundation-relevant attribution. In the literature it is near-bare particulars which I take Theodore Sider to intend when in an attempt to save bare particulars he asserts: “Thick particulars contain their universals as parts, thin particulars do not”, but nevertheless thin (bare) particulars do “have intrinsic natures.”66 Yet within the subtleties here Sider backslides when he says that nevertheless such natures/essences are

|| 65 E. J. Lowe, The Four-Category Ontology: A Metaphysical Foundation for Natural Science (Oxford: Clarendon Press, 2006), pp. 14–15, 27, 97. Loux, Metaphysics: A Contemporary Introduction, pp. 117ff., and ‘Beyond Substrata and Bundles: A Prolegomenon to a Substance Ontology’ in Contemporary Readings in the Foundations of Metaphysics, S. Laurence and C. Macdonald (eds.), (Oxford: Blackwell Publishers, 1998). 66 Sider, “Bare Particulars”.

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“exhausted by the fact that they instantiate no monadic universals.” Difficulties of the last section then reappear: if an entity has any non-vacuous being at all it would be sufficiently determined so as to found one or more monadic attributes, and thus without the latter the nature that Sider desires must evaporate into nothing—a natureless nature. With consistency but without development, Matteo Morganti has argued that to save something like bare particulars then Is-Particular, Is-Simple, and perhaps other characteristics, must be genuine ‘aspects’ or ‘ways of being’ of them.67 But this can be so only in a way where the “truthmakers”—the foundations—for their attributional unions with these particulars are just the particulars themselves and not specific components “endowed with autonomous existence.” These are the near-bare particulars as characterized above. Let us now make these issues precise. The assumptions at work here are that a thick particular a, e.g., our example apple, is composed in part of its attributes that as universals (A2) require a further constituent simple particular, pa, to be both an individuator of a, and a unifying and supporting per se subject for the attributes of a (A3). Then on the exception-to-A5 analysis, it is theorized that pa has a non-vacuous positive essence (conforming to A4 and so avoiding the absurdity of being an absolutely bare particular), but an essence restricted to being necessarily and essentially characterized by—founding—just those ‘formal’ attribute universals that are required by the classic assumptions adopted, e.g., Is-Independent and Is-Simple by A3, Has-Essential-Attributes by A4, IsIndividual by A3 and A6. Second, these formal attributes are held not to be constituents of their then ‘very thin’ individuating per se subject pa (contra A5), but rather to be attached externally to it. I.e., on this analysis and only for these individuals, their attributes and the foundations for them are not identical: these attributes are external while their foundations are internal and composing of the essence of these individuals, essences that are nevertheless simple. Each as such individuating primary subject is not quite ‘bare’ in the sense that it has the above mentioned and only these essential formal properties, hence the term ‘near-bare particulars’. With the denial of A5 the foundation here for the ontic union between an attribute universal, e.g., Individual, and the near-bare particular it qualifies is not that of identity with a part, i.e., not ‘inherence’, but an external adherence based upon a qualitative compatibility or appropriateness— ‘a fit’ or ‘mesh’—between the intension Individual and the distinct essence of

|| 67 Matteo Morganti, ‘Substrata and Properties: From Bare Particulars to Supersubstantivalism’, Metaphysica 12 (2011): 183–95.

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the near-bare particular. The attributes proper then to such a near-bare particular adhere to it because they are ‘rooted-in’ its minimal but positive essence. A primary issue here, as it was for the absolute variety, is how near-bare particulars must stand in regard to attributes that do not characterize them but that characterize the thick particulars that the near-bare particulars are posited to individuate, support, and unify. That is, for a thick particular a, e.g., Socrates, (intrinsic) attributes of a such as Has-Mass, Is-Rational, Has-CirculatorySystem, Is-Biped, Is-White, that are other than the formal attributes that the adopted assumptions require of its near-bare particular pa, cannot be ‘rooted-in’ the nature of pa. For, though Socrates does, his near-bare particular pa does not itself have characterizing ontic predicates like the example attributes. Nor does a proposed ‘core’ consisting of pa together with its formal ontic predicates itself have any of these other attributes: this minimal core cannot be biped, white, or have a circulatory system. Hence the non-formal attributes must be merely ‘tied-to’ pa, these attachments being irrelevant to and non-descriptive of the now narrowly posited nature of indivduator pa. So like above, for any such nonformal attribute F, F(a) ≡ Tied-to(F,pa), where conditions described in the rightside, Tied-to(F,pa), are the truth-conditions/grounds for the truth of the leftside, F(a). The adherence of the non-founded ‘tied-to’ operation is not the union of ontic predication, e.g., a ‘rooted-in’ union, but can only be the unity of unconditioned association. So, to make near-bare (or absolutely bare) particulars work as individuators and per se subjects for ordinary thick particulars one must make use of ‘bare linkings’ whose existences are arbitrary and indifferent to the internal natures, or the presence or absence of external unions, of the entities linked. But as observed with absolutely bare particulars, the prior and telling problem here is that there is nothing that prevents certain property pairs, viz., contraries, e.g., Is-White and Is-Red, or Is-Positively-Charged and Is-Negatively-Charged, from both being simultaneously arbitrarily ‘tied-to’ the same subject. Specifically, there is no constraint on either side—neither by the intensions of the attributes nor by the nature of the subject—limiting the arbitrary linking by the ‘tied-to’ operation. And again as previously, the fact that such properties are contraries does not preclude them from being ‘tied-to’ the same near-bare particular any more than does it preclude them from being arbitrarily associated with one another to form a set, e.g., {pa,White,Red}. If then it is ontically possible on the meaning of the tied-to operation that Tied-to(White,pa) and Tied-to(Red,pa), then by the biconditional F(a) ≡ Tied-to(F,pa) it is so possible that White(a) and Red(a), i.e., that a is qualified both as white and red. But this, of course, is absurd.

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A response made to the having-of-contraries argument is that one can simply add to the tied-to operation the restriction that when, say now, Round is tiedto near-bare particular pa, the contraries of Round are not tied-to pa.68 Yet this does not avoid the problem, but misses the fundamental point which is the necessarily arbitrary unions of most properties (intensions) with near-bare particulars. For what is introduced on the proposed tack is a new but still arbitrary operation relative to a near-bare particular pa, Restrictedly-Tied-to, so that Round is restrictedly-tied-to pa if and only if Round is tied-to, i.e., arbitrarily associated with, pa, and contraries of Round, e.g., Square, are not tied-to in the sense of arbitrarily not associated with pa. Then for all F that are not pa’s formal properties, F(a) ≡ Restrictedly-Tied-to(F,pa), the right-side providing the truthconditions for the left. So that now though the propositions Restrictedly-Tiedto(Round,pa) and Restrictedly-Tied-to(Square,pa) cannot both be true, one or the other, or neither, of their truths is equally possible as not constrained/conditioned by anything to do specifically with subject pa. This translates over to the arbitrariness of the truth of Round(a) or Square(a), or neither, yet certainly for intensions like Round and Square their characterizations of subjects are not arbitrary but determined by the intrinsic beings of—their being ‘rooted-in’— their subjects.

2.6 The Specious Inherence Model of Attribution and Property-Reduction of Relations We saw in Section 2.4 how the inherence model of attribution made speciously plausible what upon analysis is the incoherent notion of a (absolutely) bare particular. And in the previous section it was observed how a proposed fix of the latter by selectively exempting only per se subjects from the inherence thesis made for near-bare particulars that require replacing most attributions with arbitrary associations. These results evidence what I shall argue more directly here is the falsity of the inherence/containment construal of the attributional union. Rather, it is the case that no attributes, of any intension or adicity, characterize their subjects by being constituents of them (hence contra A5)—no attribute is its own foundation(s). Principal among the inherence model’s distorting consequences are the property-reduction of relations and an obscuring of the unifying-agent nature of attribution, both fundamental to an ontological

|| 68 I understand this to be the response of Morganti in ‘Substrata and Properties’. Morganti presents what I take to be a further argument against bare particulars.

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account of ubiquitous structure. Central below will be showing the impossibility of the property-reduction of relations, what then is a reductio of the inherence model. Freed from this distortion, the alternative that all attributes externally adhere to their subjects forces the insight—‘writ large’ with polyadic relarelations—that it is their natures to be intension-determined agent-combinators, a recognition with profound consequences for ontology to be observed in Chapters 4 and 5. Consider first an argument against the inherence model of ontic predication in the limited form of assumption A5 (Inherent Essential Attributes)—requiring only the inherence of their essential attributes. The argument is simply that the monadic property of Is-Individual, one had essentially by every particular, cannot be the constituent foundation in a particular for its attribution to the particular. Contradictory to this, A4 (Required Essences) and A5 jointly assert that the foundation that is part of the composition of a subject a for it having an essential attribute, F, is the attribute F itself. I.e., an attribute F, e.g., NegativeCharge, as part of the composing being of a, e.g., an electron, is what makes subsuming a characterizable as an F, e.g., the attribute Has-Negative-Charge as a part of a is the truth-maker for the proposition Has-Negative-Charge(a). Now consider the fact that an individual a as such has the attribute Is-Individual (or synonymously: Is-Particular, or Is-Unrepeatable), this attribute being essential to a as a particular/unrepeatable. There are two possibilities: the attribute IsIndividual as characterizing subject a is either an intension universal (as asserted by A2) or an individuated attribute, i.e., a trope or an instance (the latter as understood and advocated herein), Is-Individuali. Now, on the first alternative, it cannot be the intension Individual, what is in itself a repeatable universal, that as a constituent of a founds—is the basis/cause for—a having the attribute Is-Individual, for what makes a an individual/particular must be precisely that part of the being of a that is unrepeatable and in this way necessarily unique to a—not possibly sharable with anything else. Or in short: what makes a an individual cannot be something possibly common to many things, so the universal Individual cannot make a an individual and so found its descriptive attribution to a. On the other alternative, assume the attribute expressing a’s particularity is itself an individual, a trope or an instance, so that the proposition Is-Individuali(a) is true, and that, by A5, instance Is-Individuali is a constituent cause of both a being unrepeatable and the foundation for it being an attribute of a. But now, attribute instance Is-Indviduali itself has necessary and essential attributes that are then also individuals, at least two of which are Is-Individualj and Is-Monadicn. But, under A5 the latter attribute instances are part of the composition of initial instance Is-Individuali. Specificially, it is the case that Is-Indiv-

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iduali ≠ Is-Individualj and Is-Individualj is the proper constituent cause of the unrepeatability of initial instance Is-Individuali. But this is the beginning of a vicious infinite regress, analogous to the Individuation Regress, of constituent causes of the unrepeatability of initial instance Is-Individuali. For, instance IsIndividualj would likewise have as a proper constituent a further instance IsIndividualk that would both found its attribution to Is-Individualj and be the source/cause of the latter’s unrepeatability, and so on. Hence on either construal of attributes, whether universals or particulars, A5 in requiring essential attributes be constituents of their subjects is false. As a simpler example of an essential attribute that cannot be its own foundation consider Is-an-Object (equivalent to what some would mean by ‘Is-aSubstance’), where objects and attributes are taken to be complimentary classes (Sect. 2.1). Let a be an object, so that on the assumption here the attribute Is-anObject thus characterizing a would be a constituent of a and sufficient to be its own foundation, i.e., sufficient to make a an object. But this cannot be, for Isan-Object is an attribute and not an object and so in itself is not sufficient to make or cause a to be an object. Something in addition to the attribute Is-anObject would have be a constituent of a so that in itself or jointly with the attribute we would have a sufficient grounds in a for it being an object. I observe in passing that the fact that even some essential monadic properties are distinct from their foundations and adhere externally to their subjects (as necessitated by the existence of these foundations) removes what historically has been a conceptual barrier to accepting polyadic relations full and unreduced—as entities existing ‘between’ their relata. For, if some properties, as distinct from their foundations, do not make their subjects to be what these properties in their external attachment describe these subjects to be, then there is no reason why relations could not likewise exist as external to but grounded in (intrinsic and/or extrinsic (Sect. 4.2)) aspects of their subjects, the only difference between such properties and relations being the number of subjects each unifies itself with in one attribution. I.e., just as such properties, though dependent upon subjects (A1) do not share in the beings of their subjects, having realities distinct from them, so relations and as they are given intuitively are each dependent upon a relata n-tuple, but as ‘between’ these relata the relation does not share in their beings but has a reality distinct from them. As an additional argument against A5 (Inherent Essential Attributes), and one equally relevant to traditional ontology’s neglect of structure, is the fact that the property instance Is-a-Unityi or Is-a-Onej, as essential to its subject, implies under A5 assumption A8 (Unity by the Constituent One), but A8 is counter-factual. By A5 the attribute Is-a-Unityi, as essential to its subject x, is a

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constituent of x and there serves as the internal foundation and so inherent cause of x being a unity. I.e., this attribute as a single thing is the constituent cause of the unitary being of x, and this implies A8. But in fact and contra A8, there are myriad wholes, indeed every complex structure, e.g., a chain, each of whose total unity is a function of the cooperative agencies of multiple unifiers. Metaphorically, the unification of a complex structure is not via a single rope threading through all the parts, but via a transitivity across multiple links in a unifying chain or lattice. A central thesis of this work is that every complex structure as a whole and externally has a monadic property Is-a-Onej posterior to foundations that are the multiple and composing attribute instances that make the structure one. In Chapter 5 we will detail the two modes of composition among instances that give unity to complex structures. Let us now turn to the common, if mostly tacit, assumption that is the generalization of A5 to include all attributes. This is the general inherence (or containment) model of ontic predication which asserts that for every entity, all its attributes, essential or accidental, are constituents of it. We noted in Section 2.2 evidence in Aristotle for general inherence. The doctrine as explicit is perhaps most strongly associated with Leibniz in his resolute advocacy of the praedicatum-inest-subjecto thesis.69 And, it is in his work that we have an overt drawingout of its consequences: principally, the necessary reductive elimination of polyadic relations to monadic properties. As a preliminary to taking up the reduction-of-relations implication, it is worth using Leibniz’s work to make certain clarifications. The praedicatum-inest-subjecto thesis—that a (ontic- as referent of a linguistic-) predicate is in its subject—can be construed in two ways. First, it can be taken as asserting that, for any attribute, it ‘is in’ its subject in the sense of entering into the composition of the subject’s being—one of its material components, e.g., as a pebble forms part of the composing wall of a vessel (cf. Post. Anal. 73a34-37). This is the inherence doctrine. Under it an attribute is ontically prior to its subject, and it implies A5. Alternately, on the second understanding of the praedicatum-inest-subjecto thesis it can be construed as asserting that, for any attribute, it ‘is in’ its subject in the sense that the subject is the cause/source of the attribute’s union with it, but the attribute does not enter into the composition of its subject, e.g., as a pebble is caused by a vessel to be contained/constrained within it as part of its contents (cf. Cat. 15b17-31; Meta. 1023a7-24). So understood the attribute is not ontically prior to its subject, and the thesis would, for essential attributes, contradict A5. Leibniz uses the thesis

|| 69 Leibniz, Philosophical Papers, pp. 264, 267, 334, 337, 365, 503–4, 643ff.

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in both senses: In the first sense, he claims, for example, that the Identity of Indiscernibles follows from it70, but the only way entities can be identical due to the sharing of all of their attributes is that the latter compose, without remainder, the beings of these entities, i.e., by literal compositional inherence. Any remainder, e.g., an individuating component of each, opens the possibility that they can be numerically distinct by it. Leibniz uses the thesis in the second sense in his claim that each monad (his per se subjects), though an individual simple in nature, has ‘in’ it a “complete concept” consisting of all of the attributes it will ever have: past, present, and future, all of which are essential to it.71 These attributes are ontic predicates of the monad, but because the monad is simple the attributes cannot compose it. Rather and consistent here, Leibniz has these attributes contained in their monad as “perceptions” of it, analogous to the contents of a vessel. In this way Leibniz implies the denial of compositional inherence. Now in regard specifically to the implied reduction of relations, Leibniz recognized that a relation is, as the medievals described, an intervallum (Latin for ‘interval’)72; what I propose is captured in a slogan: a relation ‘bridges ontological space’. Leibniz describes this inter-subject ‘betweeness’ as a relation requiring “one leg in one [subject] and the other in the other [subject].”73 (my inserts) Yet, on the inherence model it is “impossible that the same individual accident should be in two subjects or pass from one subject to another.”74 I.e., attribution construed as containment is necessarily restricted to one subject per attribution—to monadic properties. To amplify this point, the inherence construal of attribution both collapses the distinction between an attribute and the foundations that subjects must have in order for it to qualify them, and makes, for every attribute, all of its foundations constituents of their respective subjects—both errors on my analysis. But many polyadic relations, e.g., those that are asymmetric or non-symmetric, each requires two or more sets of non-identical foundations, one set per relatum, and so a relation as one thing cannot be numerically the same as its multiple sets of foundations. Hence under the inherence model, if there is to be any attempt to save the defining characteristic of a rela-

|| 70 Ibid., p. 268. 71 Ibid., pp. 264, 268–9, 310, 365, 390, 524–5. 72 See Jeffrey Brower, ‘Medieval Theories of Relations’, The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = . 73 Leibniz, Philosophical Papers, p. 704. 74 Ibid.

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tion as an intension-determined inter-connection among the yet discrete, and in this way provide an account of the ubiquitous fact of structure/system (a first approximation being A7 (Attribute Agent-Organizers)), then at best polyadic relations must somehow reduce to monadic properties, but properties that each, while qualifying only its single subject, somehow ‘points’ toward one or more other subjects and in this establishes a kind of virtual linking without any actual intervening reality. This was in fact the analysis of the medievals who referred to these as, respectively, the esse-in (‘being-in’) and the esse-ad (‘beingtoward) aspects of a relation. Returning to a previous example, an assay of the relational fact that Philip is the father of Alexander is that Philip has the monadic property of Is-a-Father, the latter as such being ‘toward’ its ‘terminus’ Alexander, Alexander concomitantly having the property Is-a-Son, the latter being ‘toward’ its terminus Philip. With variations, the classic esse-in/esse-ad property-reduction strategy for polyadic relations goes back to at least Aristotle75, but Leibniz, who has his own version of the reduction76, is the most resolute in drawing out the extreme consequences of the inherence model that motivates it. Required by the model, he rightly concludes to a granulated world of absolutely isolated ‘monads’, entities that, though without equally real and external linking relations (i.e., without a real trans-subject lattice of inter-action/‘mutualinfluence’), each “mirrors from its perspective”—‘points toward’—every other monad via what are constituent reducta properties for these would-be relations. These reducta along with every other monadic property a monad will ever have form part of what for Leibniz is the monad’s “complete concept”. Leibniz, as did the scholastics before him, recognized that our pervasively systematized world requires an account of various qualitatively-determined connectedness (physical, mathematical, psychological, logical, social, etc.), but constrained by their ontological assumptions they were forced to conclude to what in fact is the contradictory situation of things structurally connected absent the reality of the appropriate connections. For, as Bertrand Russell rightly pointed out the esse-ad (‘being-toward’) aspect of a would-be monadic reconstruction of relations is delusion—there is no ‘pointing’ without there being ‘something pointed to’ and so an esse-ad metaphor itself implies a completed linking, and as relevant to relations the linking cannot be just arbitrary associa-

|| 75 See Mertz, Moderate Realism and Its Logic (New Haven: Yale University Press, 1996), and Mark Henninger, Relations: Medieval Theories 1250-1325 (Oxford: Clarendon Press, 1989). 76 Mertz, Moderate Realism, pp. 136–53.

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tion, but must be a full polyadic attribute.77 And on a property-reduction of relations that denies the latter, there is no attributional/structural connectedness. Apparently offered as a dodge to this nagging fact was the standard claim that relations are conceptual—in mente.78 But, even if relations are existentially dependent upon a mind, e.g., as are the ‘formal’ attributes of Exemplification, Element-of, and Implication, and perhaps all ‘internal’ relations, they, like the monadic property True (or Truth), are both entities in addition to their relata, and their intensions are a necessary condition for their union with their relata, a union that would otherwise be subject-indifferent association. Even as existentially dependent upon particular minds, (instances of) relations are fully ‘between’ and in addition to their relata. More on this when we consider Hume’s view of relations in Section 3.4. This is the answer to the sometimes claim79 that one can have relational truths expressible only in relational vocabulary without having relations as real intermediating entities essential to the truth-makers for these truths. For, the semantics presupposed by relational expressions will itself be necessarily a complex cognitive structure composed of non-random intension-specific inter-connections—relations—of syntax, sense, reference, and predication, and yielding as substructures emergent propositions (the ‘relational truths’). And we cannot explain away the semantic relations forming these structures by appealing to super-relational-truths asserted via a super-semantics, and so on. The proposed reductive elimination of polyadic relations persists into contemporary ontology. It was, for example, the initial ‘foundationalist’ strategy of Keith Campbell in advocating trope theory, and more recently is advocated by Armstrong in terms of mereological sums, and by John Heil in outlining how all relations can, on the standard reductionist tack, be construed as ‘internal’ and so reducible to intrinsic non-relational features of their relata.80 Trope theory conforms to the inherence doctrine, assaying an ordinary particular as a whole composed of its monadic attributes theorized as individuals (contra A2) and as non-dependent entities (contra A1 and A3) (hence avoiding the Dependence Contradiction and Individuation Regress (Sect. 2.3)). The unification of tropes

|| 77 Bertrand Russell, The Principles of Mathematics, 2d. ed. (1903: reprt. ed., New York: Norton, 1938), pp. 221ff. 78 For the view in Leibniz see Philosophical Papers, pp. 609, 704. 79 The early Campbell, Abstract Particulars, p. 100, and Heil, The Universe as We Find It, pp. 135–50. 80 Campbell, Abstract Particulars, pp. 97ff.; Armstrong, ‘Particulars Have Their Properties of Necessity’, Pufendorf Lecture; Heil, The Universe as We Find It, pp. 135–50.

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into a single entity/object, including highly structured ones, is held to be somehow provided by what is the non-structuring Compresence ‘relation’ (contra A7). Importantly, any ontology that would have all attributes be non-dependent must in some way eliminate polyadic relations, for relations by definition presuppose and are therefore dependent (A1) upon multiple relata.81 Consistent with this, Campbell sought to extend to all relations (including Compresence) a strategy proposed by some for the reductive elimination of the subclass of ‘internal relations’. Following Armstrong82, the reduction strategy so limited can be put succinctly as: If, if given properties F and G ‘intrinsic’ to subjects a and b, respectively, then a relation R necessarily holds between a and b, then R is an ‘internal relation’ that as such is ‘supervenient’, i.e., R is “no addition to being” over and above the being involved in a having F jointly with b having G. F and G are ‘intrinsic’ properties of their subjects if the respective foundations they prescribe of their subjects in order to be attributes of them do not involve anything extrinsic and in addition to components of their subjects (more on this in Sect. 4.2). For example, if a has a height of 6 ft. and b has a height of 5 ft., then necessarily the relation Is-Taller-than holds from a to b. Under the reduction thesis, the relation Is-Taller-than has no being beyond or in addition to that of its intrinsic foundational properties taken jointly—it is an “ontological free lunch.”83 The assumption here is that internal relations are ontologically idle— their foundational properties (‘esse-in’s) being sufficient to do all the ontic work—and so economic virtue requires these relations as distinct entities to be shaved away under Ockham’s Razor. Or in short: internal relations are ‘retracted’ within the beings of their relata. For some philosophers the remaining ‘external relations’ are considered beings in additional to (beyond as distinct from) their relata and the relata’s properties. Armstrong originally held this view, with most spatial-temporal and causal relations considered external and irreducible84, though more recently he has proposed that external relations are like-

|| 81 Campbell, Abstract Particulars, p. 90. At one place (p. 98) Campbell proposes that it is impossible to have a world of only relations but devoid of substances (subjects for attributes) and monadic properties. How theoretically this need not be the case is shown in Sect. 5.2. 82 Armstrong, A World of States of Affairs, pp. 11–13, 87–89. Also Armstrong, Universals: An Opinionated Introduction, pp. 43, 56. 83 Armstrong, A World of States of Affairs, p. 13. 84 Ibid., p. 88, and Universals: An Opinionated Introduction, p. 43.

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wise reducible, though in a different way, to monadic properties85. Armstrong’s strategy is different from Campbell’s who originally sought to show that all relations are internal and in this way reductively eliminable.86 Now, let us look closely at this reductive strategy and how it is specious. The most plausible reading of what is being asserted is: if, given facts :F(a) and :G(b), for intrinsic F and G, and dyadic intension(-concept) R, it follows that the (conceptual-linguistic) proposition R(a,b) is necessarily true, then this means that R is an ‘internal relation’ and as such the truth-maker for proposition R(a,b) is just the whole that is facts :F(a) and :G(b) taken jointly, i.e., the association of :F(a) and :G(b), or symbolically, :F(a) + :G(b). I.e., no facts other than :F(a) and :G(b)—and so no facts involving R—are necessary for the truth-maker of proposition R(a,b). The ‘taken jointly’ unity could not be via a further attribute, say S, for then we would have the fact :S(:F(a),:G(b)) as the truth-maker for proposition R(a,b) and the ontic reduction intended by this strategy would be defeated. Reductionists like Armstrong would have the whole :F(a) + :G(b) be a mereological sum which supposedly is nothing beyond fact :F(a) and fact :G(b)—in particular, without a mediating connector. But, reinforced by the analyses of Sections 1.3-1.5, the ‘and’ here belies the fact that sums are just-their-parts-together, this selective togetherness being an additional and necessary part of the whole, what I argued is cognitive association. This reduction retains, for ‘internal’ R and apparent fact :R(a,b), the analogs of the Aristotelian/medieval assay’s essein’s, i.e., :F(a) and :G(b), but denies any attributional connection between them, including the tradition’s ersatz esse-ad’s. What the elimination strategy for ‘internal relations’ thus described fails to recognize is the role intension R, e.g., Taller, must have in a fact essential to the truth-maker for proposition R(a,b), e.g., ‘a is taller than b’. As in our example, let R be asymmetric and so through it there being an order among its subjects.87 Facts :F(a) and :G(b), e.g., respectively that a is 6 ft. high, and b is 5 ft. high, are relevant to the truth of proposition R(a,b) because is among the ordered pairs of foundation conditions, e.g., , , , …, prescribed by intension R as necessary for corresponding ordered pairs of subjects, e.g., , to be characterized by R. But this requires that the elements of each ordered pair be selected, linked, and mutually ordered by their relevance as foundations for intension R. And so since this un-

|| 85 Armstrong, ‘Particulars Have Their Properties of Necessity’, Pufendorf Lecture. 86 Campbell, Abstract Particulars, pp. 100 ff. 87 Relevant here is Russell’s famous argument against the reduction of relations to sums of monadic properties. Russell, The Principles of Mathematics, pp. 221ff.

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ion-by-relevance cannot be an arbitrary association of R and, say, ordered pair , the union must be via an attribute in a fact, i.e., :Has-as-Foundations(R, ). Thus, on the current reduction strategy the necessary and complete truth-maker for a proposition R(a,b) for ‘internal’ R, e.g., our ‘a is taller than b’, is both fact :Has-as-Foundations(R,) and association :F(a) + :G(b), e.g., fact :Has-as-Foundations(Taller,) and association :Is-6-ftHigh(a) + :Is-5-ft-High(b). But with this is contradicted the proposed reduction’s claim that there are no facts beyond monadic :F(a) and :G(b), and certainly none involving internal R, necessary for the truth-maker of a fact R(a,b). And if a fact must be introduced as part of a truth-maker for proposition R(a,b), intuitively this would be simply fact :R(a,b) with the here complex fact-plus-association being seen as a confused assay of it, relation R then being as real and ineliminable as a and b. As a second point against the reduction strategy, consider how a relational fact :R(a,b) with ‘internal’ R can itself enter into causal relations that the corresponding association or ‘sum’ :F(a) + :G(b) cannot. As an example, assume a horse owner is to choose from among a pool of candidates a jockey to ride his horse in a race. Assume the first presented candidate a is 6 foot high, and for this reason is rejected as undesirably tall to be a jockey, and that a second presented candidate b is 5 foot high, and for this reason is also rejected. So now we can have the association of facts :Is-6-ft-High(a) + :Is-5-ft-High(b) and no chosen jockey. If the owner now finds that a and b are the only candidates, something else becomes relevant, viz., the fact :Is-Taller-than(a,b). It is this fact as a comparison under the intension Taller and on the same foundations effecting the monadic facts, and not just the mutual indifferent juxtaposition of these monadic facts, that is a cause for the owner to choose b as the better candidate. (A related argument against Armstrong’s reduction thesis for internal relations is given in Section 4.2.) The relational fact is a reality distinct from, and with causal consequences not had by, the corresponding association (or sum or set). Thirdly, there is against the reduction of ‘internal’ relations the critique of the kind: ‘What is good for the polyadic goose is good for the monadic gander.’ If the current reduction strategy is more than simply an expression of bias against the polyadic, then its analog should apply equally to monadic properties. This point has been made by Simon Bostock in arguing to extend Armstrong’s ‘ontological free lunch’ status for ‘internal relations’ to include ‘internal properties’.88 The point is that on an analogy to Armstrong’s reductive

|| 88 Simon Bostock, ‘Internal Properties and Property Realism’, Metaphysica 5 (2004): 73–83.

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strategy for ‘internal relations’, if the existence of a single subject a implies the necessary truth of proposition F(a) for monadic intension F, i.e., if F is an ‘internal property’ of a, then analogous to the above there exists no corresponding truth-making fact, including no fact :F(a), over and above just a. Here, such an F, which is any quality essential or definitional of a, would have no existence as an attribute of a. Or alternately, for it to make sense that the proposition F(a) is true, F must be a semantic/cognitive intension that is linked to a but not because a has some foundation or ground for F being descriptively relevant to it, for otherwise F would be an attribute of a and yet distinct from a, what is being denied. Hence, the union between F and a is but arbitrary association, what is essential to a ‘sum’ and antithetical to a fact. We have then the result that F which started as a necessary and essential predicate of a is now a non-descriptive contingent and accidental associate of a. All of this is contrary to what Armstrong asserts of his states-of-affairs ontology. A version of this critique applies as well to John Heil’s thesis that ordinary objects are ‘arrangements’, i.e., structures, of simple substances and their monadic properties, but where the relations definitional of the arrangements, and so the arrangements themselves, are said not to be real.89 A single relational fact would be the minimal such arrangement, and Heil would have it reduce to just substance relata and the monadic properties of each. However, for Heil the attributional union between a property and a substance is external and so is itself an ‘arrangement’ in the same sense as a relation orders its relata, i.e., a property F is linked with its subject in a way whereby it characterizes (qualifies, is descriptive of) its subject, and not vice versa. Thus, if arrangements via relations, and so relations, are not real, then neither are arrangements via properties, and so properties. But for Heil, properties (as had by substances) are real and fundamental to his ontology. The problem here and throughout, I propose, is the absence of a proper assay of plural unification—composition—and, particularly and fundamentally, attributional composition. With the correct analysis (Chap. 4) it is evident that there is no categorical difference between monadic and polyadic attributes. As a final critique here, though I shall return to it in Section 4.2, of the Campbell-Armstrong reduction strategy for internal relations consider the following. Given the four numbers, 2, 4, 6, and 12, there is necessarily among them a tetradic relation of proportionality, say ‘Pro’, with the resultant fact that proportionally 2 is to 4 as 6 is to 12, or :Pro(2,4,6,12). So according to the reduction

|| 89 Heil, The Universe as We Find It, pp. 18–25, 51–2, 139–50, 167, 279, 286–87.

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strategy, Pro is an internal relation and thus is no addition to being beyond that of the four numbers: 2, 4, 6, and 12. But now there is also by the same ‘internal’ relation the fact that proportionally 12 is to 4 as 6 is to 2, or :Pro(12,4,6,2), and which would likewise reduce to the four subject numbers. Yet these facts are not identical since the first is founded on the involved ratios being 1/2, whereas the second is founded on the involved ratios being 3/1. So on the reduction strategy we have the absurdity of two distinct things each numerically identical to a third thing—the four numbers, 2, 4, 6, and 12. It might be responded that the facts should be considered as each reducing to the four numbers plus an ordering among them. But this order cannot be arbitrary, or we could have, e.g., :Pro(2,12,4,6), which is impossible—the compared ratios being 1/6 and 2/3. The order would then have to be controlled by the relation’s intension Pro, and hence the Pro relation, though ‘internal’, cannot be reductively eliminated from these facts. Returning to Campbell, in advocating trope theory he eventually came to recognize the necessity of exceptions to the property reduction of relations.90 These are the Is-At relation between a trope and its spatial location, the Refersto relation between a term and the entity it names, and, indeed, the latter generalized to any relation linking the content of a mental state and what the content represents. But as considered previously, overlapping Campbell’s specific relations, as well as the class of ‘internal’ relations as defined above, are large classes of relations for which there are different and powerful arguments for their non-reducibility to monadic properties, viz., ordering asymmetric (e.g., the above ‘internal’ relation of Is-Taller-than) and non-symmetric relations. The locus classicus for these arguments is Bertrand Russell’s The Principles of Mathematics.91 I have sought to reinforce and extend Russell’s arguments elsewhere, what includes responses to Campbell’s attempts to parry them.92 I refer the reader there. The last-referenced arguments are also destructive of Armstrong’s recent attempt to “reduce all instantiation of universals to the monadic case.”93 His motivation is once again the inherence construal of attribution. Armstrong pro|| 90 Keith Campbell, ‘The Place of Relations in a Trope Philosophy’, Proceedings of the Colloque International de Philosophie de Grenoble: La Structure du Monde; Objets, Propriétés, États de Choses, in Recherches sur la Philosophie et le Langage, Universite Pierre Mendes France, Grenoble, 2003. And in his ‘Unit Properties, Relations, and Spatio-Temporal Naturalism’, The Modern Schoolman 79 (2001): 151–62. 91 Russell, The Principles of Mathematics, pp. 221ff. 92 Mertz, Moderate Realism, pp. 163–71. 93 Armstrong, ‘Particulars Have Their Properties of Necessity’, Pufendorf Lecture.

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poses that the best account for the instantiation union between a particular and its monadic properties is that of ‘partial identity’, i.e., that properties are “actual parts of the particulars.”94 He says that “it will be natural” to give an account of the instantiation of polyadic relations as likewise lying within their relata. (It is my point that underlying this ‘naturalness’ is the consequential fact that properties and relations are categorically the same in their natures as attributes, differing only in the number of subjects simultaneously characterized. The difference is that Armstrong wants all attributes to be in their subjects, whereas I argue that no attribute shares its being with its subjects.) We saw above his account for an internal relation R, viz., :R(a,b) = :F(a) + :G(b), where on his mereological ‘free lunch’ thesis the sum is nothing over and above its two monadic facts. Now Armstrong proposes to extend the monadic reduction to external relations, e.g., Is-Two-Miles-Apart or Is-Left-of, by a slightly modified device. For external relation R, he suggests that :R(a,b) = :S(a + b), where S is a “structural” monadic property of sum a + b. Yet, like its counterpart for internal relations, this strategy also fails. First, S is to be a monadic property, requiring that its subject, sum a + b, be a single entity. But, on Armstrong’s ‘free lunch’ thesis sum a + b is not a single whole with its own being over and above just a and b. And, to be an attribute on what are multiple things—a, b—is to be a polyadic relation, not a monadic property. That Armstrong wants both external relations to be polyadic, and the sums involved to be exceptions to the ‘free lunch’ reduction (inconsistently and ad hoc?), comes out in the statement: “External relations become, as it were, the cross-bracings [polyadic linkings] of certain non-simple objects [i.e., sums as single entities with their own beings].”95 (my inserts) This internal ‘cross-bracing’ seems plausible to Armstrong who has S be a constituent of sum a + b, what he is explicit to assert and is required by his inherence thesis. But then because the sum a + b has only the constituents a and b this requires that S = a or S = b, which cannot be the case. Further, even if sum a + b is taken as a single entity with its own differentiating being, which it is, as we argued above the associations effecting a mereological sum do not order its constituents, e.g., sum a + b = sum b + a. So this assay cannot account for ordered (e.g., asymmetric) external relations, e.g., Is-Left-of or Is-Between (what would require sums like a + b + c). Armstrong’s intent is that a “structural property” S itself internally both inter-connects and structures/orders the constituents of its sums, analogously to how Aristotelian monadic substantial forms, e.g., Is-Human, are to do

|| 94 Armstrong credits Donald Baxter for influencing him to adopt a version of the ‘partial identity’ view. See Baxter, ‘Instantiation as Partial Identity’. 95 Armstrong, ‘Particulars Have Their Properties of Necessity’, Pufendorf Lecture.

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the same for structured substances, e.g., Socrates. But then the same critique applies: a ‘structuring property’ S in its intension describes a structured whole, i.e., multiple things inter-connected, the latter prescribed by S and required as foundations for its attribution of a subject, but S as a monadic attribute applies to only a single subject per attribution, and in this way cannot itself be a cause of a unity (i.e., be a combinatorial agent) among multiple things required to effect a structure. The problem here, as in the tradition, is confusing what a property describes with what it effects. In sum, reinforced in this section have been the theses that polyadic relations do not reduce to monadic properties of their relata, and that the general inherence (containment) model of ontic predication (a generalization of A5 (Inherent Essential Attributes)), what requires the reduction, is false. For the chapter as a whole it has provided evidence that classic assumptions A5 and A8 (Unity by the Constituent One) are false, and that A4 (Required Essences) is true. Particularly in regard to A5 and its generalization, the potent truth lies with the opposite: no attribute is a constituent of its subject(s), a point recently emphasized by Lowe as a counter to the “indefensible doctrine of ‘bare particularity’”96, and for which we can give a detailed rationale. We shall see that it is the non-attributional union between an intension and an outwardly combinatorial and individuating act jointly composing a truly attributional attribute instance which eliminates the need to posit bare particulars. The replacement of passive inherence with acts of adherence will dispose of A5 (Inherent Essential Attributes); eliminate the need for the per se subjects (contra A3); provide an otherwise absent account of the direction of dependence of attributes upon their subjects (A1 (Attributes as Dependent)); and supply the basis for extending and clarifying the nature of attributes as structuring agents (A7 (Attribute AgentOrganizers)), and as multiple unifiers for a single whole, (contra A8 (Unity by the Constituent One)). With all of this is eliminated both the Dependence Contradiction and Individuation Regress of this chapter and the problems arising from other combinations of the classic assumptions we shall identify in the next chapter.

|| 96 Lowe, The Four-Category Ontology, pp. 14–15, 27, 97.

3 Instance vs. Classic Ontology: Intensions and Unification 3.1 Further Problems Via the Classic Assumptions, E.g., Bradley’s Regress In the previous chapter we detailed how a number of problems follow from combinations of classic ontological assumptions A2 (Attributes as Universals), A3 (Per se Subjects), A4 (Required Essences), and A5 (Inherent Essential Attributes). In this chapter we will observe further errors implied, first, by combinations of assumptions A2, A7 (Attribute Agent-Organizers), and A8 (Unity by the Constituent One), and then those resulting from the denial of A1 (Attributes as Dependent) (a denial that eliminates the need for A3 (Per se Subjects)). Regarding assumptions A2, A7, and A8, it will be shown how the three jointly imply a contradiction. And taken in pairs, it will be seen how A2 and A7 yield Bradley’s Regress, and how A2 and A8 lead to either 1) the forced elimination of polyadic relations in a yet retained plural universe, and with it a crippling loss of explanatory power for complex unity and the ubiquitous reality of structured entities (e.g., Leibniz’s monadism), or 2) an implied counter-intuitive substance monism where attributes and subjects alike are eliminated in the evaporation of all plurality (e.g., the implications of Bradley’s monism). Regarding the denial of A1, the assumed non-dependence of attributes is characteristic of various theories that assay complex entities as bundles of attributes. In addition to other problems commonly observed against such theories, especially the trope version, it will be argued that they require of attribution a conflicting duality. Because the denial of attribute dependence is central to popular trope theories that take their inspiration from David Hume’s influential attribute-sensa-plus-associations ontology, I shall devote the last section to Hume’s theses, Hume’s motivation for them, and the nature of their errors. Consider first the contradiction implied by A2, A7, and A8. Let :F(a) be a contingent fact consisting of the union of property F with individual a, e.g., that the moon is spherical. By A8 this union has a single constituent cause, what must either be attribute F or subject a. The cause, however, cannot be the attribute F for the following reason. Assume attribute F, e.g., Is-Spherical, is the cause of the unification of fact :F(a). Let :F(b) be any other contingent fact, e.g., that ball b is spherical, so that :F(a) ≠ :F(b), for a ≠ b. Now, by A2 attributes are universals, and so it is numerically one and the same F that occurs in both facts,

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:F(a) and :F(b). Hence, universal F would, on the present assumptions, be numerically one and the same cause/means of the unification in both facts. This being the case, assume b ceases to have the attribute F, i.e., that the contingent fact-composite :F(b) goes out of existence due to F no longer having a characterizing union with b, e.g., that ball b is no longer spherical. Then, distinct fact :F(a) would likewise cease to exist since F is numerically/identically the same in both facts and so is numerically/identically the same as its ‘act’ of unification of itself with its subject in both. For, by A2 the attribute F just is the universal and not the universal-plus-a-further-unifying-aspect-unique-to-each-distinct-subject (such an aspect being what some scholastics termed a ‘mode’1 and what I contend must indeed be the case—what is an agent-combinator aspect and a simple particular). But, that a contingent fact :F(a), e.g., that the moon is spherical, necessarily ceases to exist when any other contingent fact :F(b) does so, e.g., when ball b is no longer spherical, is absurdly counter-factual. (Note: this argument is generalizable to contingent attributes of any adicity.) The same would hold for necessary facts. Returning to the arithmetic attribute of proportionality, consider the two necessary facts: that proportionally 2 is to 4 as 6 is to 12, and that proportionally 4 is to 2 as 12 is to 6. For both facts the relata for the proportionality relation are the same. Now, if the proportionality relation is the cause of the unity among them and is itself numerically identical across both facts, then having all the same constituents, including the same unifier, the facts would have to be identical, which obviously they are not. Therefore, under assumptions A2 and A8, in a fact-composite it must be the subject(s) that is (are) the cause(s) of the union of itself (themselves) with the concomitant attribute. It would then follow by A3 that per se subjects are the ultimate source of all attribute attachment. Aristotle comes close at places to being explicit in holding the subjects-as-unifier thesis, saying: “For the cause of an attribute’s inherence in a subject always itself inheres in the subject more firmly than that attribute” (Post. Analy. 72a27-29)2, and elsewhere he would seem to imply that any subject, in being ‘something receptive of’ its attributes, ‘holds’ its attributes analogous to a vessel holding its content (Meta. 1023a7-24). Yet, this implication that subjects are the cause/source of their unification with their attributes contradicts

|| 1 Francisco Suarez, On the Various Kinds of Distinctions (Disputationes Metaphysicae, Disputatio VII, de variis distinctionum generibus), trans. Cyril Voller, S.J. (Milwaukee: Marquette University Press, 1947), Sect. I, 17–29, pp. 28–38. 2 The thesis is repeated later, e.g., by John Duns Scotus, Ordinatio II. d.3, part 1, q. 6, in Spade, Five Texts on the Mediaeval Problem of Universals (Indianapolis: Hackett Publishing Co., 1994), p. 113.

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A7 (Attribute Agent-Organizers). For observed previously, like the more obvious polyadic facts :R(a,b), monadic facts :F(a) are structured wholes—F characterizes/qualifies its subject a, and not vice versa—and A7 asserts that this structured ‘ordering’ is a unification that is a function of the constituent attribute F, not its subject a. The tension exists for Aristotle who is explicit in adopting A7 for those monadic attributes that are substantial forms—these attribute forms, e.g., Is-Human, are ‘actualities’ that differentiate and structurally unify the parts of complex substances, e.g., Socrates, in their being ontic predicates of prime matter as ‘potentiality’ (Meta. 1041a7-1045b24). Retaining A7, we shall in Section 4.4 use the above distinction-of-unifying-acts argument to show that attributes of any adicities (as distinct from their contained intensions) are agentcombinators (T3) and thus, contra A2, individuated uniquely to their subject ntuples (T4). Even more minimally and with classic consequences, if we attempt to avoid the last contradiction by retaining, say, only A2 (Attributes as Universals) and A7 (Attribute Agent-Organizers), these assumptions yield an assay of a fact that as a whole, when contrasted with the corresponding set of just the fact’s elements, leads to Bradley’s Regress. And, if alternately we assume just A2 and A8 (Unity by the Constituent One), there results either the reductive elimination of all inter-subject relatedness, or a plurality-obliterating homogeneous monism. Take first the implication of A2 and A7. Let :R(a,b) be any contingent dyadic fact. As noted previously, :R(a,b) is a structured whole, and by A7 there is a constituent attribute that is the cause of this organization, what is prima facie attribute R. But, on the assumption that R is a universal, this is not the case, and indeed implied is a vicious regress of needed organizing combinators. To see this, compare fact :R(a,b) with the corresponding class or aggregate {R,a,b}. Clearly the two wholes are not identical: First, the fact :R(a,b), e.g., the fact that Antony loves Cleopatra, is contingent and can come into and go out of existence, but the set {R,a,b}, e.g., {Loves,Antony,Cleopatra}, is necessary (per set theory) and independent of whether or not the corresponding fact obtains. Second, the fact is the truth-maker for the proposition that a is R to b, whereas the set is not. And third, though the fact, but not the set, has an internal ordering/structure due to R jointly qualifying—being an ontic predicate of—a and b, and not vice versa, a further more obvious ordering of the fact occurs when R is asymmetric or non-symmetric, a structuring the set does not have. Indeed, the set has no internal ordering, organization, or structure—it is by theoretical posit an Aristotelian ‘heap’. A structured whole has a unity that involves a mutual relevance of aspects of the parts, whereas the unity of a set is completely inde-

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pendent/indifferent to the natures of the elements, only their existences being relevant (Sections 1.3 and 1.5). Now consider that the fact :R(a,b) has at least the constituents that the set {R,a,b} has, where in particular for relation R, it is guaranteed by A2 to be numerically the same in both wholes—attribute R asserted to be a universal. But, if the fact :R(a,b) had as its only constituents, R, a, and b, then it would be identical to the same whole that is the set, which it is not. Hence, because the set is by definition just these elements, it must be the fact :R(a,b) that has an additional, albeit implicit, constituent that differentiates the two. Now, thesis A7 specifies what this additional constituent must be, viz., the fact :R(a,b) must contain an attribute-organizer, Rʹ, where Rʹ ≠ R and such that :R(a,b) = :Rʹ(R,a, b). This, of course, is the beginning of a vicious infinite regress of attributes, Rʹ, Rʹʹ, Rʹʹʹ,…, one posited in the n-th step to be, under A7, an agent-organizer of its fact, but inferred with the help of A2 not to be such in the n+1-th step. This argument in contemporary times is known as Bradley’s Regress, but it is historically perennial. For example, Pasnau reports that the argument was omnipresent among scholastic philosophers and there intended to show that the cause of the union (‘inherence’) of an accident with its subject(s) is essential/intrinsic to the attribute and not something in addition to it.3 In other words, the argument was to force a distinction between an attribute proper as a source/principle of its union with its subject(s) and its misconstrual as absent this agency and so having the same status relative to the unity of the would-be fact as its subject(s). Contrary to this intent, Bradley was explicit in adopting the above conclusion that there is no difference between a relation as it relates in a fact (Russell’s ‘actually relating relations’) and one that does not so relate as but one more element in an aggregate of itself and its terms.4 Yet, in conformity to A7, Bradley asserts that “Relations are nothing if not conjunctive,”5 where a relation is of its nature a way to “hold a diversity in unity”6, it being not only something “between” its terms but also a “together”, i.e., a cause of the unity, of its terms.7 Bradley’s conclusion was that relations, indeed all attributes, ‘commit suicide’ as self-contradictory. On the analysis herein both Russell and Bradley err in not || 3 Robert Pasnau, Metaphysical Themes: 1274-1671 (Oxford: Clarendon Press, 2011), pp. 211–12. Some history for the argument is found also in Mertz, Moderate Realism and its Logic (New Haven: Yale University press, 1996). 4 F. H. Bradley, ‘Reply to Mr. Russell’s Explanation’, Mind 20 (1911): 74–76. 5 F. H. Bradley, ‘Relations’, in Collected Essays, Vol. 2 (Westport: Greenwood Press, 1970), p. 655. 6 Ibid., p. 634. 7 Ibid., p. 644.

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differentiating relations proper as intensioned-combinators (i.e., as ‘actually relating’ or being ‘conjunctive’ and so individuated (contra A2)) among their relata, e.g., Is-in-Love-withi or simply Lovesi, from what are their component intensions, e.g., Love, each in itself an inert/non-unifying abstraction.8 As with any object, an intension Rn taken independent of any attributional agency it might control can enter into a fact, not by its association with other things (this the unity of sets and sums, and what Bradley intended by the term ‘between’), but only as a subject of the attributional agency (Bradley’s ‘conjunctiveness’) of a further attribute proper, Smi, as such acting to unify an m-tuple of relata that include intension Rn and as they jointly satisfy the intension Sm.

3.2 Implying the Alternatives of Relation Elimination or Substance Monism We have just seen that Bradley’s Regress is a consequence of assuming both A2 (Attributes as Universals) and A7 (Attribute Agent-Organizers). Consider now the likewise untoward implications of A2 and A8 (Unity by the Constituent One). Jointly, the latter theses require us to either declare unreal our intuitive understanding of polyadic/mutli-subject relations as entities ‘external’ and in addition to but linking their relata, or, to the contrary, construe them as ‘internal’ in the sense of Bradley, i.e., as constituting part of the essences of their relata, this implying in the end a homogeneous substance monism, what apparently Bradley did not intend. Assume, for example, that R is a dyadic attribute in a fact :R(a,b), a ≠ b (though our argument would follow analogously for relations of any adicity). If there is such a fact-complex it is because there is a union || 8 Russell in the 1899–1900 manuscript ‘Do Differences Differ?’ held that relations as “actually relating”, i.e., as unifying their relata, occur as individuals unique to their relata n-tuples (my instances), though what are exactly resembling instances instantiate the same abstract nonunifying intension/universal. His argument there is for instances that are simple, and so precluded is an assay like mine where the abstract intension can be seen as a constituent of and so distinct from each instance. This may be an underlying factor in Russell’s rejection of the ‘Differences’ view in the Principles of Mathematics (1903) and thereafter, holding that relations occur only as universals but where each has a “two-fold nature” of being “a relation in itself and a relation actually relating”. ‘Do Differences Differ?’ in The Collected Papers of Bertrand Russell, Vol. 3, G. H. Moore (ed.), (New York: Routledge, 1993), and The Principles of Mathematics, 2d. ed. (1903: reprt. ed., New York: Norton, 1938), pp. 47–52. For details regarding texts and the then relevant debate between Russell and his contemporaries, including Bradley, see James Levine, ‘Russell, Particularized Relations and Bradley’s Dilemma’, Dialectica 68 (2014): 231–61.

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of R with subjects a and b jointly, a union which, we have seen above, would under A2 and A8 have to have as its cause the two subjects a and b. Now to the first alternative, let R be ‘external’ to both a and b in the sense that R is distinct from and does not share in the beings of either a or b. Here we would have a fact-complex :R(a,b) consisting of three distinct things and with two subject unifiers under the present assumptions, the latter a violation of A8 which requires a single unifying cause for each plural whole. The only way to avoid this and retain these assumptions is to construe polyadic R as reduced to monadic properties, i.e., where fact :R(a,b) is eliminated in favor of the mereological sum of facts :F(a) and :G(b). Here each monadic fact can have its subject as its single unifier. This, of course, is the classic property-reduction of relations which we argued in Sect. 2.6 is erroneous. The second alternative under the implication from A2 and A8 that subjects are the cause of their unions with their attributes is, in a relational fact, say :R(a.b), to retain R as unreduced—as a single shared thing—but to construe the unities that subjects a and b cause themselves to have with R as being numerically one and the same ‘tie’ or ‘nexus’. Now this single instance of unification cannot be via something outside the beings/essences of each of a and b, for otherwise it would have to be an external relation and this would bring us back to the issues of the first alternative. So, on this second alternative we must construe the relation R in a fact :R(a,b) as not something distinct from each subject a and b, but as simultaneously a common/shared part identical in contributing materially to the constituting beings of each—R is a coinciding element, or ‘intersection’, of the composing essences of each of its subjects. I.e., the beings of a and b are partially identical at relation R—R a shared proper part of both a and b. In this way R simultaneously ‘inheres’ in both subjects, what would extend to relations the inherence thesis of essential attributes under thesis A5. Unlike the first construal of relatedness as an external linking between relata, here relatedness is modeled as an internal and at least partial mutual melding of the relata into one another. As Bradley held, to form a unity with its terms “a relation must at both ends affect, and pass into, the being of its terms”9, and that “the terms and the relation must ‘enter’ one into the other”.10 In this way, “A relation is unmeaning, unless both itself and the related are the adjectives of a

|| 9 F. H. Bradley, Appearance and Reality (Oxford: Clarendon Press, 1978; reprint of 2d ed., 1897), p. 322. 10 Bradley, ‘Relations’, p. 638. Also Appearance and Reality, p. 201.

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whole.”11 Stated alternately by Brand Blanshard in also advocating monism, “A relation is internal to a term when in its absence the term would be different…”,12 i.e., the term’s composing being/essence would be materially altered. On this construal of relations, thesis A8—that unity is by one unifier—is not violated since the whole that is the fact :R(a,b) has collapsed into one composed of just a and b, and though both of the latter are causes of their mutual union, it is via what is one and identically the same component of the beings of each, i.e., unity by R as an overlapping part of both a and b. Succinctly, with the absorption of R into the beings of both subjects a and b, we have the mutual consistency of A2 (Attributes as Universals) and A8 (Unity by the Constituent One) with A7 (Attribute Agent-Organizers). For, Bradley’s Regress follows from A2 and A7, and the contradiction of A7 follows from A2 and A8, a premise for both being the assumption that a relation R or a property F is distinct from the beings of its subjects. But this absorption-assay of relata-relation connectedness is a pyrrhic victory, one destroying the presupposed distinction between relata and relation. In this line Bradley rightly observed, on the supposition that a relation is absorbed into the beings of its relata, both relation and relata “are ruined if they do so”13. To see this consider that, via their common part R whereby their beings overlap as identical, a and b jointly form the continuous being of a subsuming whole. Bradley asserts that for a diversity containing A and B to exist “this means that A and B are united, each from its own nature, in a whole which is the nature of both alike. And hence, it follows that in the end there is nothing real but the whole of this kind.”14 And, on the assumption that any two entities whatsoever are related in some way (e.g., Meta. 1075a12-20), then, via these relations so construed, any two entities have coinciding parts—where in this mutual ‘sharing’ of their constituting beings, everything contributes to the being of everything else—and in this forms an intra-connected, all-encompassing whole—the One of substance monism (Bradley’s ‘Absolute’). This is why, epistemically, advocates of this assay hold, in the words of Blanshard, that “no knowledge will reveal completely the nature of any term until it has exhausted the term’s rela-

|| 11 Bradley, Appearance and Reality, p. 394. Earlier at p. 121 he asserts: “Difference forced together by an underlying identity, and a compromise between the plurality and the unity—this is the essence of relation.” 12 Brand Blanshard, The Nature of Thought, Vol. 2 (New York: Humanities Press, 1964), p. 451. 13 Bradley, ‘Relations’, p. 638. 14 Bradley, Appearance and Reality, p. 510.

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tions to everything else.”15 Moreover and yielding explicitly the monism here, what is implied of the One is an all-encompassing whole with no internal differentiation. For, assume the One has differentiated proper parts c and d, as such with composing beings exclusive of one another. Now, c and d would be related by the triadic relation C of being co-parts of the One—indeed, given the One, c and d would necessarily be so related. Yet, this makes relation C on the here inherence assay a shared coinciding part of c, d, and the One, what in particular contradicts the posited mutually distinct beings of c and d. In sum, on these assumptions the resulting One as total reality lacks all differentiation and composition—it is a uniformly amorphous, homogeneous simple; the ‘night in which everything dissolves into the black’—and anything not exactly identical with the One has no reality. Here we have a complete melding of essences to the exclusion of any differentiated plurality. Bradley himself stopped short of this conclusion, asserting that somehow in his Absolute there is a reconciliation of the reality of both unity and plurality, what is a “super-relational unity of the One and the Many”, despite this being an apparent violation of Bradley’s non-contradiction criterion for the real.16 Bradley’s intent notwithstanding, the inescapable conclusion of an absolutely distinctionless One, following as it does from the ‘ruin’ of all attribution taken as the attribute being something distinct from its subject(s), renders the ubiquitous given of a plurality of entities having myriads of attributes—and with them structure—as total illusion. Wiped away is not only the reality of facts as each a unified-but-complex truth-maker for propositions, but, equally as cognitive attributional structures, eliminated are propositions themselves as well as all discursive reasonings that involve them. Delusional then is the reasoning whereby we have concluded to this undifferentiated One, it being euphemistic to describe it even as ineffable and inscrutable. This, I propose, is a further reductio of the inherence construal of ontic predication. Let us approach some of these points from a different angle. We have seen above that theses A2 (Attributes as Universals) and A8 (Unity by the Constituent One) imply that objects are the causes of the union of themselves with their attributes. But in conforming to A8, an object cannot unify to itself its many attributes by some outward agency—‘a reaching beyond itself’—that collects them externally to it. For, since the external unification here is non-arbitrary

|| 15 Blanshard, The Nature of Thought, Vol. 2, p. 452. 16 Bradley, ‘Relations’, p. 650. Also see Appearance and Reality, pp. 180, 334, 403ff, 432. At ‘Relations’, p. 635, Bradley seems explicit in asserting the contradiction: “Contradiction everywhere is the attempt to take what is plural and diverse as being one and the same…”

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and so not that of association, it must be that of attribution, and this, absurdly, makes an object an attribute, viz., a relation. Hence to the contrary, on assumptions A2 and A8 an object would have to unify its attributes inwardly by subsuming them as constituents, what is the generalization to all attributes of the inherence model for essential attributes under A5 (Inherent Essential Attributes). Now, this would make the resultant being of an object derivative of and so ontically dependent upon, at least in part, the composing beings of its constituent attributes—a ‘bottom-up’ emergence where the parts are ontically prior to the resultant whole. But then this contradicts thesis A1—that attributes are dependent upon their subjects, and not vice versa—and, when these objects are per se subjects, we likewise have a violation of A3. If assumptions A2 and A8 are to be retained, then one must give up A1 and A3 and reverse the order of dependence of subject whole and attribute parts, i.e., adopt a ‘top-down’ differentiation where the whole is ontically simultaneous with its attribute parts, and, in particular and importantly, the unification among the parts is the prior unity of the whole. Here the beings and unity of the parts are not prior to that of the whole. This view extrapolated to the cosmos and its parts is a basic tenant of the priority monism argued, for example, by Jonathan Schaffer.17 I will argue that this type of top-down ontic dependence and unity is found only at the atomic level of attribute instances—an instance gives both being to its component outwardly combinatorial aspect, and internal unity to its two components of the latter agency and a concomitant intension (Sect. 4.6). Specifically in regard to classic assumption A8 (Unity by the Constituent One), despite its common exemplification and the aesthetic appeal of simplicity and symmetry in the notion of ‘oneness by the one’, there are also common counter-examples to it. I.e., not all structures have their unity in a way analogous to a jar as a single container holding its contents or to a necklace as beads on a unifying string. There are, for example, chains composed of links, and, more complex, automobile drivetrains composed of specifically sequenced parts, where in neither type are there single constituent parts running through and so connecting all the others. As emphasized in Chapter 1, these examples can be multiplied endlessly as networks of any kind: the jointly functioning organs of living bodies, neural systems, machines and factories, artifacts generally, mathematical and logical systems, etc. Consider a chain as a paradigm example: it does not need a single cable strung through all the links to give it its unity and structure, rather it is the transitive unities effected by local relations || 17 Jonathan Schaffer, ‘Monism: The Priority of the Whole’, Philosophical Review 119 (2010): 31– 76.

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among pairwise shared parts that collectively make it one and specifically organized thing. The contradictory unitarian thesis A8 was championed among medieval scholastics by Aquinas and the Thomists in regard to substantial forms, viz., that all structuring within a complex substance, e.g., a living body, is via a single form.18 This became Church doctrine in the case of the human soul. Yet also found among the scholastics was the view that a ‘plurality of partial forms’ is necessary, even if humans had to be excepted, in order to account for the facts that substructures can have distinct emergent attributes, and that a common form can go out of existence or be separated from the parts, e.g., a soul upon death, but substructures can remain for some periods of time with their emergent and defining attributes, e.g., those of flesh and of bones. The historically burgeoning insight here was promoted, for example, by Suarez using the example of the cooperating multiple substructures (‘partial forms’) of plants: That in diverse, heterogeneous parts of such beings [e.g., a living tree] there are diverse heterogeneous parts of the form. For in a tree that part of the form which is in the branch is really not of the same nature as that which is in the fruit, etc. Those forms are, nonetheless, partial and suited to be united to one another and joined together, and in that way they constitute one complete form of the whole. Hence, it is false to imagine that there is another form of the whole which is added to these partial forms and which also informs all those parts.19 (my insert)

Here Suarez is asserting that a complex structure (e.g., a tree) can have substructures—parts (e.g., roots, branches, leaves, fruit)—each with its own structuring cause (i.e., partial substantial form) and that some of these can be conjoined pairwise in a structurally relevant way, i.e., inter-related, so that the resulting chain of structuring conjunctions jointly effect the total structure that is the whole, and so, contra A8, without a single element connecting all the substructures. This ‘decentralization’ of substantial form can be pressed in a telling way: if local relations among pairs of parts can collectively give structure to some complex whole, then the same could be the case with the substructure that is each part, and this with the latters’ substructures, and so on down to some atomic ontic level of relations among non-structured subjects. The latter relations (as

|| 18 See Pasnau, Metaphysical Themes 1274-1671, pp. 630–32. 19 Francis Suarez, On the Formal Cause of Substance: Metaphysical Disputation XV (Disputationes Metaphysicae XV), trans. J. Kronen and J. Reedy (Milwaukee: Marquette University Press, 2000), Sect. 10, Par. 30, p. 143. See Kronen’s notes 102 & 103, p. 172.

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instances) would then be the ultimate ‘partial forms’ from which all hierarchical organization can be built up from successive layers of inter-relationships. Generalized to include monadic properties, this is a key thesis advocated below. In this way is corrected the narrow A8 understanding of the Aristotelian definition that ‘unity means undividedness’ (e.g., Meta. 1016b1-6, 1052a15-35). More accurately and detailed as thesis T6 in Chapter 5: unity means either literal undividedness (continuous composition) or inter-connectedness (articulated composition), what are, respectively, the inner unity of a whole of non-identical but non-discrete parts (viz., attribute instances), or the outward transitive unity across chains of (‘path-connected’) pairwise-shared entities (e.g., facts and all other structures). It will be argued that all unification among the discrete is that of articulated composition by attribution, or derivative from it by associations, and that only at the atomic ontic level is there between universals and individuating combinatorial acts unions among the non-discrete—continuous compositions. Taking advantage of the latter and previous points as context, it is instructive here to anticipate briefly and in relevant aspects how they give warrant to the instance ontology advanced in this work. First and foremost is the above analysis’ support for the truth of thesis A7—attributes are agent-combinators and thereby the ordering principles among their relata subjects. This characteristic is ‘writ large’ in polyadic relations, and is grounds for assumption A1 asserting that attributes are dependent upon their subjects. It follows immediately that, contrary to A2, attributes are individuals—instances—not universals. For, an expression of agency is an event and all events/acts are particular. Moreover, recognition of the outwardly unifying nature of relational attribution frees us both from the conceptual hold of the inherence model as a necessary account of attributional unity, and concomitantly from the distortion that monadic properties are categorically different from relations. With this the monadic tail no longer wags the polyadic dog. Once attributes of all adicities are seen to be, outwardly, instance-unifiers, external to (contra A5) but forming with their subjects atomic articulated composites, i.e., facts or states of affairs, it follows that they can form molecular wholes via the sharing of relata subjects, analogous to the various shared nodes in a lattice of relation ‘rods’. And, molecular wholes can be single subjects for further emergent attributes, and so upwardly all other entities are generated hierarchically as iterated structures of structures, all ultimately of attribute instances. The entire cosmos and all sub-complexes are hierarchical lattices of attribute instances. Except for atomic facts, the unification of articulated composites is not by any single attribute thread running through all the other con-

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stituents, contrary to A8 (Unity by the Constituent One). Now downwardly, it is logically possible and ontologically necessary, and perhaps physically required under our present understanding of quantum reality, that at the atomic ontic level there are attribute instances that have only other attribute instances as relata, these forming closed loops of mutually supporting attributes. Here we avoid an infinite regress of dependent entities without the need to posit a foundation of per se subjects (A3). In articulated complexes the parts are ontically prior to the whole. Inwardly, attribute instances must have the dual aspects of an outwardly-directed unifying act and its necessary delimiting and guiding intension. There are no arbitrary or random acts of indiscriminate collection, i.e., the unity of sets, sums, or ‘heaps’, outside of intellectual abstraction and association, willed or not. In composing an attribute instance, an intension is a universal and so is not identical to a concomitant unifying act. Hence, contrary to A6, an intension itself is a non-attribute yet not unrepeatable entity. The two aspects of an attribute instance form a continuous composite in being undifferentiated in the subsuming instance whole, the latter in this way being ‘simple’. And the part of an instance that is its outwardly unifying act is not ontically prior to, but simultaneous with, the instance, and the act’s delimiting intension is differentiated from it only in abstraction. This type of unity has been variously recognized, for example and famously by John Duns Scotus under the term ‘distinctio formalis a parte rei’. All of these points will be defended in Chapters 4 and 5.

3.3 Denying Attribute Dependence: Bundle Theories Another standard response to problems identified above has been to reject theses A1 (Attributes as Dependent) and A3 (Per se Subjects) by way of allowing at least some attributes to be intrinsically independent entities. These exceptions are then minimal one-intension ‘little substances’, what can thus go proxy as per se subjects for other attributes. This being plausible only for monadic properties, the strategy is to adopt the general inherence theory in the form of a ‘bundle theory’ where an ordinary ‘thick particular’ is assayed as the union of all its characterizing monadic properties. For these properties the ontic dependence of A1 is reversed: subjects are dependent upon attributes as non-dependent parts. If, in addition to attributes being independent, they are held to be universals, i.e., A2 is retained, then one has what is termed ‘Universalism’, a theory

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once advocated, for example, by Bertrand Russell, A. J. Ayer, and Brand Blanshard.20 Among the troubles peculiar to construing wholes as consisting of only compresent universals are that, as each and every constituent of a bundle is a repeatable universal then the bundle itself is repeatable, and hence the theory’s analysans for any entity whatsoever cannot be an unrepeatable individual. Also, Universalism is committed to the necessary truth of the Identity of Indiscernibles, i.e., entities having the same attributes are identical, what intuitively would seem not to be an ontic necessity.21 Again on the assumption that attributes are independent (the denial of A1 and so doing away with the need for per se subjects, A3), the alternative to Universalism is to reject A2, i.e., take attributes to be individuals, this being definitional of nominalistic trope theory.22 Specifically, a trope is a non-dependent unrepeatable attribute—a hybrid of both object and attribute—having both an individuating and a qualitative aspect, but where the qualitative aspect is not a universal, and the whole is simple. Trope theory has a number of serious problems, including first the nature of the union necessary to bundle tropes together into ‘thick particulars’. Advocates posit, as they must, a selecting cause of unity: ‘Compresence’, what (and what is passed over in silence) achieves its intended role here only by being an agent-unifier among, and so intrinsically dependent upon, the non-dependent properties it bundles. But this makes polyadic instances of Compresence either relations or associations, and as either they are of a completely different ontic category than their independent subjects. If Compresence is a relation then we have with trope theory the bifurcation of attributes into, on the one side, non-combinatorial/non-dependent propertytropes and, on the other, combinatorial/dependent relations, and this violates their uniform natures as both types of attributes: as all equally characterizing/

|| 20 Bertrand Russell, Inquiry into Meaning and Truth (London: Allen and Unwin, 1940), p. 98, and Human Knowledge, Its Scope and Limits (New York: Simon and Schuster, 1948), pp. 292– 308. A. J. Ayer, ‘The Identity of Indiscernibles’ (1954), in Michael Loux, Universals & Particulars, 2d. ed. (Notre Dame: Notre Dame University Press, 1976), pp. 263–70. Brand Blanshard, Reason and Analysis (LaSalle: Open Court, 1962), pp. 399–401. 21 Michael Loux, Metaphysics: A Contemporary Introduction (New York: Routledge, 1998), pp. 106ff. 22 Campbell, Abstract Particulars (Oxford: Blackwell, 1990); D. C. Williams, ‘The Elements of Being’, Review of Metaphysics 7 (1953): 3–18, 171–92; John Bacon, Universals and Property Instances: The Alphabet of Being (Oxford: Blackwell, 1995); Peter Simons, ‘Particulars in Particular Clothing: Three Trope Theories of Substance’, Philosophy and Phenomenological Research 54 (1994): 553–74, and ‘Farewell to Substance: A Differentiated Leave-Taking’, Ratio 11 (1998): 235–52.

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qualifying—being descriptors of—subject-others. This sameness of nature of the monadic and polyadic is reinforced indirectly by their seamless integration within our predicate logics and the latters’ power of translation and inference. Monadic properties are but the limiting 1-adic case of n-adic attributes, and not a separate category. There is, however, a more fundamental reason why Compresence, commonly construed, cannot be a relation. Broached in Section 1.2 and to be expanded upon in Section 4.2, a relation as an attribute prescribes through its intension necessary and sufficient conditions prerequisite for its prospective relata. Entities of an n-tuple that respectively satisfy these conditions are necessarily attributionally connected by (an instance of) a relation of this intension. I.e., in being so described, the entities of an n-tuple could not not be related (by an instance) under this intension—their connection being literally this ‘fact of the matter’. However, it is evident from the literature that Compresence is often taken as stipulating only a necessary condition for its dual subjects, viz., that they be tropes. (I take Compresence to be dyadic, though the following argument applies regardless of its adicity.) Beyond this stipulation the understanding is that any two tropes whatsoever—independent of anything either compositional of their beings or external in their connections with other things—can be, but need not be, connected by Compresence; any two entities connected under Compresence need not have been so connected.23 Hence, Compresence—thus understood—stipulates no sufficient conditions that otherwise in being satisfied by a pair of entities would necessitate that they be linked by the Compresence ‘relation’. I.e., nothing about any two tropes is sufficient to necessitate their being connected under Compresence, and so Compresence is not an attribute and so not a relation. Compresence is, then, only association—an arbitrary selecting and collecting of tropes into pairs, each thus a non-fact-forming unification imposed externally and indifferent to anything specific about the tropes selected, except for the imposed necessary (but not sufficient for fact-forming)

|| 23 I take this as the point being made by Anna-Sofia Maurin in If Tropes (Dordrecht: Kluwer, 2002), p. 133, where she asserts: “If compresence is a founded relation then it seems that there must be (just as there arguably is in the case of exact resemblance) something about the tropes themselves that, simply given their existence, makes them enter into specific compresence relations with other tropes. But what about specific trope, red1, makes it enter into a compresence relation with tropes round1, and soft1, instead of with tropes square1, and hard1? …It makes no sense to say, for example, that a red-trope, a round-trope, and a soft-trope, simply in virtue of being this redness, this roundness and this softness, must be related [by compresence] so as to form a bundle (e.g., this ball).” (her emphasis; my insert) I would finish this by saying that compresence in being a thus unfounded ‘relation’ is properly no relation.

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condition that the selecting be from the domain of tropes.24 This fact is behind, for example, the plausibility of the view that a bundle of compresent tropes is a mereological sum25, what implies that the kind of unity essential to a sum is the same as that provided by Compresence among tropes, and I have argued that the unity of a mereological sum is implicitly but necessarily by subject-irrelevant associations (Sect. 1.5). Yet as but one point against this, we have already seen in Section 2.4 the implication that Compresence as association cannot prevent the same bundle from having contrary properties, e.g., composed of both tropes Squarei and Roundj, and so Compresence cannot go surrogate for attribution.26 Further impugning the claim that Compresence is a relation, and not just arbitrary association, is the failure of the attempt by some to have it be a spatial relation, i.e., make it intensionally specific in requiring foundations of spatial co-location. Expanded, the claim is: trope Fi is compresent with trope Gj if and only if Fi is at location L and Gj is at location L. Here there are required two cases of the Is-At relation. I note that, in arguing for his reductionist program for all relations (Sect. 2.6), Campbell started with the reduction of Compresence to the Is-At relation, and then proposed that the latter reduces to just a trope and its location.27 Yet my point is that Compresence, reducible or not, cannot be

|| 24 That compresence is just arbitrary association has been argued, in effect, by Christopher Austin in ‘The Relation of Compresence in the Bundle Theory: Four Problems’, Percipi 2 (2008): 49–65. He argues that compresence is unfounded, and that it cannot account for why certain complex wholes are their own source of specific actions and passions. Reinforced are my points that compresence is not a relation, and that it thus cannot contribute to the internal structure of a resulting whole in a way necessary for certain actions and passions to be dispositions of it. 25 This is the thesis adopted, e.g., by Douglas Ehring in Tropes: Properties, Objects, and Mental Causation (Oxford: Oxford University Press, 2011), pp. 12–14, 98. 26 These observations make precise, I propose, a critique of bundle theory by Reinhardt Grossmann who concludes: “The bundle view, to repeat, cannot reconcile its conception of predication [attribution] in terms of a part-whole [Containment] relation with the existence of relations. Thus if there are relations, as we shall take for granted, then the bundle view must be abandoned…. In view of these considerations, most bundle proponents have chosen the more radical alternative of denying the existence of relations altogether [e.g., the early Campbell; see Sect. 2.6].” (my inserts) This from Grossmann, The Categorical Structure of the World (Bloomington: Indiana University Press, 1983), pp. 81–2. 27 Keith Campbell, ‘The Place of Relations in a Trope Philosophy’, Proceedings of the Colloque International de Philosophie de Grenoble: La Structure du Monde; Objets, Propriétés, États de Choses, in Recherches sur la Philosophie et le Langage, Universite Pierre Mendes France, Grenoble, 2003, and ‘Unit Properties, Relations, and Spatio-Temporal Naturalism’, The Modern Schoolman 79 (2001): 151–62.

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construed as a spatial relation, and this, first, for a reason that Campbell himself once observed. Viz., if for tropes Fi and Gj to be compresent means that they somehow share the same location L, then they could not be moved to a different location Lʹ without ceasing to be compresent. I.e., no whole composed of compresent Fi and Gj could change positions. Secondly, let s be a red iron sphere, what as such would be composed in part of the tropes Redi and Massj. On the current assumption these tropes are compresent and so contribute to the being of s because each is at the same location. Now, trope theory, like all inherence theories, makes attributes their own foundations, which means here that the trope Redi is that part of the being of s that makes it to be red, and trope Massj is that part of the composing being of s that makes it to have mass—Massj is b’s mass. But then Redi and Massj cannot be at the same location L, for what makes s red is a two-dimensional surface characteristic while what makes s have mass is distributed over its three-dimensional material volume. This second argument points to a further critique of trope theory. Let e be an extended entity, say in two dimensions, and so in part is composed of the trope Extendedi. Again by the inherence assay of attribution essential to trope theory, Extendedi is that part of e’s being that makes e extended in two dimensions—it is e’s two-dimensional extension. But then Extendedi, like all extension, has distinguishable parts, and this contradicts the posited simple nature of tropes. In addition to positing the Compresence relation, trope theorists, in order to make up for the explanatory loss of universals, also posit a primitive ‘Resemblance’ relation as a means of explaining the type-sameness of some entities. The resulting equivalence classes then each go proxy for a shared universal, e.g., replacing the universal Red would be the equivalence class of all entities that Red-resemble every other. Now what the latter brings into focus is the much-observed fact that entities do not simply resemble, but they resemble or not in qualitatively specific ways, e.g., Red-resemble, Spherically-resemble, Sixunit-diameter-resemble, etc. And so to have a viable alternative to universals, trope theory must admit a resemblance relation for each such way. But this significantly weakens the theory’s touted simplicity. Also, it is often observed that, intuitively, the order of explanation is backwards here: that things exactly resemble is derivative of their sharing something in common, and not that things have something in common because they resemble. Further, the many kinds of resemblance relations are real relation attributes, unlike Compresence as at best association, each a selective linking and so a subject-dependent attribute. Hence, they would have to be in a completely different ontic category from independent monadic property-tropes, what was argued against above. I

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note that Resemblance is proposed by Campbell and others as a straight-forward example of a relation that is reducible to properties of its relata. I will give a counter-argument in Section 4.2. Other charges brought against trope theories so described, what apply equally to Universalism, are that: 1) they cannot account for persistence through accidental change—all attributes, in composing their subjects, are essential to them, 2) they cannot account for the fact that tropes, or universals, of certain kinds must necessarily be bundled together (e.g., of Shape, Size, and Color; or of Pitch and Intensity), and that 3) in rejecting A1 (Attributes as Dependent) and making attributes ‘little substances’, or our ‘objects’, these theories cannot account for the distinction everywhere observed in subject/predicate discourse between subject entities and what is asserted of them—asymmetrically, attributes ‘are inherently about (predicates of) other entities’ (their subjects), whereas subject substances are not.28 To solve the persistence and kind-concurrence problems also requires complicating trope theory with additional relations beyond Compresence and Resemblance, what not only further diminishes the theory’s simplicity but points to the telling fact that the theory requires an expanded repertoire of non-eliminable, non-trope, dependent (‘actually predicative’) attributes, each as such a further exception to the theory’s denial of A1 for all other attributes. First for kind-concurrent tropes, e.g., Rectangulari and Redj, as constituents of entity a they must be linked by a trope of some contingent relation R other than Compresence whose intension/‘meaning’ implies a prior necessary relation of co-exemplification between respective genera tropes, e.g., Shapek and Colorm, the trope of relation R then a constituent of a. As to the first problem, to account for persistence through accidental change of an entity construed as a bundle of tropes requires modifying the basic strategy of bundle theory, viz., requires treating some properties of an entity, the ‘accidental’ ones, as not constituents of it. For, to solve the problem a core or nucleus of compresent tropes must persist through the change of gaining and/or losing accidental tropes, this being possible only because the latter are ‘externally attached’ by a contingent non-Compresence relation to the tropes of the nucleus.29

|| 28 The problems for bundle theories listed here are found variously in Loux, Metaphysics: A Contemporary Introduction, pp. 99ff., and Simons, ‘Particulars in Particular Clothing’. 29 In response to both the kind-concurrence and accidental change problems, Peter Simons in ‘Particulars in Particular Clothing’ has proposed a theory involving a two-stage bundling of tropes derived from something like the relations just described, the tropes of the core or ‘nucleus’ being ‘mutually founding’ and so held together by a necessary Husserl-type “foundation

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A related final point against any trope bundle theory, and, in particular, its adopting the inherence model for at least monadic properties (generalized A5 for properties), is that it cannot consistently account for the fact that tropes themselves have properties. For example, the trope Redi would itself have the attributes Is-a-Color, Has-Saturation-A, Has-Brightness-B, Is-Individual, Is-Simple, etc., what on the theory would themselves be tropes, Colorj, Brightness-Bk, …, and all proper constituents of Redi. But this contradicts the fact that as a trope, Redi is supposed to be simple and to be of only one intension. So these properties, just as all relations (e.g., Compresence, Resemblance, etc.), must be exceptions to the theory’s paradigm self-founding inherence conception of attribution, exhibiting rather attribution as externally-founded adherence. In sum, there is with trope bundle theory a duality of conflicting assays of attribution: some monadic properties as paradigm tropes are not dependent entities (contra A1) but are constituents of the entities they characterize, whereas all relations and some properties are dependent (A1) upon but not possibly constituents of their subjects.30 In contrast, the ontology argued herein provides a consistent and uniform adherence assay of attribution whereby there is no problem with an attribute instance being characterized by an externally adhering attribute instance, for attributes of any adicities.

3.4 Hume and the Denial of the ‘Inseparability’ of Attributes Recall that a motivation for bundle theories is the desire to avoid the difficulties of per se substrata asserted in classic assumption A3, what are thought, mistakenly as we shall detail (Sect. 5.2), to be necessitated by the prior assumption of a dependent nature for attributes, A1. That is, A1 asserts that attributes of their very nature are ontically dependent upon other entities—the subjects they descriptively qualify—and in this way are intrinsically ‘incomplete’ and ‘inseparable’ from (‘necessarily connnected’ with) what, it is assumed, must be some supporting substratum of categorically distinct self-sustaining/‘separable’ entities—‘substances’ (A3). Yet as we have seen in Sects 2.4-2.5, despite all attempts to save the per se subjects of A3 by the possible modifications of classic assump-

|| relation”. However, Arda Denkel has argued that Simons’ strategy cannot account for observed substantial change, e.g., the change from a tree to resulting lumber. See Denkel, ‘On the Compresence of Tropes’, Philosophy and Phenomenological Research LVII (1997): 599–606. 30 This and other arguments against tropes themselves having properties are found in Grossmann, Categorical Structure of the World, pp. 82–4.

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tions A4 and A5 (this in order to avoid the Dependence Contradiction), the unacceptable results are entities either completely without attributes or insufficient in attributes to serve their purpose. Now avoiding all of this, the philosopher most prominent in making the explicit denial of the dependent/inseparable nature of attributes (i.e., the denial of A1) a starting point of his ontology and drawing out its implications was the (and thereby) skeptic, David Hume. Because of both his influence in this regard, e.g., the promoting of bundle theory (generalized A5) and of mereology as ontology, and his work being, I argue, a detailed reductio of an assay of attribution where description (/intension) is divorced from connection (/combinatorial-agency), the latter then as only association, it will be instructive to devote some effort to the critique of Hume’s theses and their implications. Among the long-contentious “fictions” from which Hume sought to free the tradition was that of “unknowable” substance, and his method was to promote what has been termed ‘Hume’s Dictum’, viz., that there are no necessary connections between distinct entities, i.e., between entities having no shared composing being.31 Expanded upon below, the crux of the doctrine is that “The understanding never observes any real connexion among objects, and that even the union of cause and effect, when strictly examin’d resolves itself into customary association of ideas.” (1.4.6.16)32 Particularly in regard to causation, “We are never able, in a single instance, to discover any power or necessary connexion.”33 In their contrast with associations, what Hume intends by ‘real connexions’ among distinct existents are ones conditioned by mutual relevances that are objective to the things connected—something about each that makes it ‘fit’ with or be specifically appropriate to the others. Such entities could not be what they are without being so mutually relevant and so are necessarily connected-in-this-specific-way. Here the intension-determined necessity is ontological/metaphysical, what is in addition to logical/analytic necessity and is the

|| 31 This is my wording. For a discussion on other ways of stating Hume’s Dictum see Jessica Wilson, ‘What is Hume’s Dictum, and Why Believe It?’, Philosophy and Phenomenological Research, LXXX (2010): 595–637. A version of Hume’s Dictum is what D. M. Armstrong terms Hume’s ‘deflationalry doctrine of distinct existences’ and which Armstrong strives to uphold: that of distinct entities there is no contradiction in one existing without the other. See Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997), e.g., pp. 18, 263. 32 David Hume, A Treatise of Human Nature, David Norton and Mary Norton (eds.), (Oxford: Oxford University Press, 2005). 33 David Hume, Enquiries Concerning Human Understanding and Concerning the Principles of Morals, P. H. Nidditch (ed.), (Oxford, Clarendon Press, 1978), Sect. VII, Part I, par. 50, p.63.

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foundation for nomic causality. But with nullifying implications, Hume’s denial of such composition and necessity is precisely the denial of all attribution properly assayed, viz., as linkings necessitated on or among subject-others— what in every case are ‘necessary connexions’—due to the subjects satisfying the conditions set by the intensions of the attributes. With this denial what he asserts of things causally connected applies to all ‘ties’: such entities are “conjoined [in association] but never connected [in attribution]”34 (Hume’s italics, my inserts). Motivated to eliminate such “chimeras” as ‘substance’ and working in the absence of a correcting proper assay of attribution, especially of relations, Hume claims that monadic properties (the tradition’s paradigm attributes) are both given in perception as, and can by an argument he advances (below) be, entities whose natures are devoid of any necessary outward connections to, and so dependencies upon, other entities. But what this means as a consequence is that properties have no intensional/qualitative relevance to other entities, including to subjects that they would otherwise characterize and thus be tied to as ontic predicates of them. For, if entities are qualitatively relevant one to the other (e.g., as Round and Square are each relevant to the other as contraries) then they are necessarily connected-in-this-qualitative-way (e.g., as with the specific relation in :Is-Contrary-ofi(Round,Square)).35 Now, maintaining a consistency across all attributes, Hume extended his ‘no necessary connections’ claim to polyadic relations by recasting them as, in fact, psychologically constructed connections: virtual ones of comparison, and, closer to ‘real’ relations, actual ones of association. Contrary to Hume’s denial of the interposing nature of comparisons, both types are linkings, but as Hume intends both are arbitrary in being neither necessary nor conditioned by any descriptiveness of the relations’ intensions on their relata. I.e., neither comparisons nor associations require of their subjects grounds or foundations—something pertinent about them—in order to connect them. They obtain independent of any thing about the entities they link, except for their existences. These psychological connections can in a sense be non-random under the ‘gentle forces’ (1.1.4.1) found in the mind according to Hume’s “principles of association” (1.1.4.1; Abstract, 35),

|| 34 Ibid., Sect. VII, Part II, par. 58, p. 74. 35 A clarifying subtlety here in regard to necessity is that entities qualitatively mutually relevant need not be so relevant necessarily, and if not, yet it so happens they are thus relevant, then they are necessarily connected but in what is a contingent fact. Entities whose existences depend upon conditions that render them qualitatively mutually relevant are necessarily so, and their connection because of it is a necessary fact. These points are expanded in Sect. 4.2.

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but they are arbitrary in being indifferent to the natures of the things connected or to any other connections (e.g., attributions) the things may have. Central to the critique to follow, it is precisely with his assay of relations that we have an amplification of Hume’s program for attribution that ‘writes large’ its problems. Crucially, his comparisons and associations can no more go proxy for real relations than can a heap of randomly selected parts go proxy for a properly structured automobile, and Hume both needs and makes implicit use of real relations which, as we shall detail, his official analysis eliminates.36 Exemplified by the parts analogy, Hume’s resultant ontology must substitute mereological sums for structured wholes, a strategy advocated in contemporary ontology by David Lewis who in this way admits his inspiration is Hume (Sects. 1.1 and 1.5). More fundamentally for relations, what Hume’s theses do, despite his rhetoric to the contrary, in eliminating subject-relevant/informative interconnections in favor of, at best, subject-indifferent/uninformative associations (‘conjoinings’), is not only to deny the pervasive given of plural unities that are relational structures, e.g., the self, but, in particular and correlative with the loss of the latter organized reasoner, his theses are self-destructive of his program in being a structure of logical arguments intended to convince us of it. And, it is Hume’s elimination of polyadic relations as ‘real connections’—as linkings intensionally descriptive of their relata—that removes all informing epistemic bridges between knower and known, what is the root-source of Humean skepticism. Building upon the work of previous scholars I will below give an analysis of Hume’s theory of relations offered as instructive of both Hume’s ontology and of our assay of attribution as its correction. Hume’s assertion of the no-necessary-connections doctrine and the drawing out of its consequences are found in Book 1 of A Treatise of Human Nature, and in its restatement in the Enquiry Concerning Human Understanding.37 Here we shall focus mainly on the Treatise (text references to which are given in parentheses). Hume synopsizes the doctrine as: “Every quality being a distinct thing from another, may be conceiv’d to exist apart, and may exist apart, not only from every other quality, but from that unintelligible chimera of a substance || 36 For details on how Hume both needs and appeals to what are real relations see Yumiko Inukai, ‘Hume on Relations: Are They Real?’, Canadian Journal of Philosophy 40 (2010): 185– 210. For other arguments how Hume’s theory of relations implies inconsistencies in his atomistic ontology see T. H. Green’s long introduction to David Hume, A Treatise on Human Nature, vol. 1, T. H. Green and T. H. Grose (eds.), (London: Longmans, Green, and Co., 1874). Also, Alexander Klein, ‘On Hume on Space: Green’s Attack, James’ Empirical Response’, Journal of the History of Philosophy 47 (2009): 415–49. 37 See notes 32 and 33.

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[i.e., from per se subjects (A3)].” (1.4.3.7; my insert) In more precise statements Hume divides the doctrine into two theses, several times repeated and central to many arguments in the Treatise: “that all our distinct perceptions are distinct existences, and that the mind never perceives any real connexion among distinct existences.” (Appendix, 21; Hume’s italics) With the second thesis Hume is effectively denying classic assumptions A1, A3, A4, and A7. In particular regard to the denial of A7 (Attribute Agent-Organizers), Hume eliminates another of the tradition’s ‘fictions’, that of substantial forms (1.4.3.1 and .5-.6), but selfdestructively and more generally he eliminates all structured wholes, starting with the simplest form of simple facts, including propositions as themselves implicit semantic/linguistic facts, the former truth-makers for the latter. The denial of structure and these classic assumptions follows from what is the more fundamental elimination of attribution of any adicity on Hume’s counter-intuitive assertion that the epistemic given contains ‘no real connections’. And all of this is possible, I argue, on the tradition’s failure to properly assay attribution as intension-determined (‘real’) combinatorial-agency (‘connexion’). We will see on this proper assay that from the above group of assumptions only A3 (Per se Subjects) is to be rejected. Specifically in regard to the latter, Hume, like the tradition, assumed that attribute dependence, A1, implies the necessity of supporting per se subjects, A3, i.e., that on the assumption that attributes “cannot subsist apart [A1], [they then] but require a subject of inhesion to sustain and support them [A3]” (my inserts), what as ‘substances’ Hume would have us (rightly) reject as “fictions of ancient philosophy” (1.4.3.7 and 1.4.3.1; also see 1.4.5.24 and Appendix, 14). Hume’s ‘no necessary connexions’ thesis denies A1 and so eliminates the substances of A3. Hume thinks of both of his theses as pertaining to all ‘perceptions’, what in their atomic form are paradigmatic monadic properties he characterizes as each individual (he denies all universals, i.e., denies A2 and affirms A6 (1.1.7.6)), independent, and simple. These simple perceptions and their compounds are either primary ‘impressions’ from ‘sense’ or ‘reflection’, or are the weaker remembered copies of impressions—‘ideas’. Originating in or copied from sense, the atomic perceptions are instances from the species of “colour, taste, figure, solidity, and other qualities” (1.4.3.5), and from reflection they include instances from the “passions, desires, and emotions” (1.1.3.1). Under his theses, perceptions as epistemic ‘raw materials’ are for Hume analogs of classic particular and self-sufficient substances: “Taking it for something, that can exist by itself, ’tis evident every perception is a substance, and every distinct part of a perception a distinct substance.” (1.4.5.24; Hume’s italics) Simple perceptions are psychological and ontological atoms, what, in effect, are principally property

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tropes, and from which complex perceptions can be formed, these dividing into “RELATIONS, MODES, AND SUBSTANCES” (1.1.4.7). Despite his use of the term ‘Relation’ and his appeal to real relations obscured under phrases like ‘objects… dispos’d in a certain manner’ (1.2.3.4; 1.2.3.10)38, all complexity in Hume’s official ontology has as its unifying principle only psychological subject-irrelevant association. It is “association of ideas… [that] are the only links that bind the parts of the universe together… [being] really to us the cement of the universe…” (Abstract, 35; Hume’s italics, my inserts). Officially, every complex whole, e.g., ordinary objects (‘substances’) and their modes (e.g., dance), consist of given simple trope-perceptions bundled by associations not given in perception but constructed by the mind. In this way attributes as property tropes are intensioned non-connecting (inert/non-agent) constituents of the entities they characterize (A5 (Inherent Essential Attributes)), and attributes as relation tropes are non-intensioned connecting (achieving/agent) associations that structurelessly bundle the former. The proper assay argued herein is that every attribution, monadic or polyadic, is an intension-determined combinatorial-act, individuated by its unifying agency and structuring the resultant fact according to its intension. Hume’s intent was to develop a ‘mental mechanics’ of atomistic perceptions linked variously by ‘gently’ motivated associations formed in the imagination and falling under a few general types. With the identification of these “principles of association” he hoped to lay the foundations for a science of human nature whose explanatory power would be comparable to that achieved by the Newtonian corpuscular physics of the day, the latter being Hume’s inspiring model. This science was to stand in contrast to the “many chimerical systems [of philosophy], which have successively arisen and decay’d away among men” (1.4.7.14; my insert), Hume disposing of the latter in large part with the denial of A1–A4, and A7, and with them the implied problems we have detailed in this and the previous chapter. However, it is an implication of the analyses herein that Hume’s sweeping denials are not curative, but self-destructive: analogous to treating lung disease with asphyxia. The critique will be that his founding denial of ‘real’, i.e., intension-determined, connection and the agency that this would require (and so crucially his denial of A7) is an endemic source of ‘decay’ in his own system. This includes its inconsistency with what must be the unifying agency of Hume’s only official ‘connector’: association.

|| 38 Inukai, ‘Hume on Relations’.

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Let us turn, then, to the instructive details of our negative assessment of Hume’s ontology, introductory points providing context for our extended critique of Hume’s telling treatment of relations. Under Hume’s Dictum attributes are ‘separable’, by which he means that each is ontically independent, i.e., has a being that does not necessitate a connectedness with any other entity discrete from it. Hume, in addition to asserting it to be a fact that perceptions (attributes, qualities) are nowhere given as ontically dependent, proposes an argument for this ‘separability’. The compressed argument is given at paragraph 1.4.5.5 of the Treatise, and has been detailed in the literature, e.g., recently by Jani Hakkarainen.39 The argument is so constructed to allow him to infer from conceptual separability to real separability, a key assumption (and one found among the scholastics from which Hume may have inherited it40) being that if something is conceivable then it is possible. Hume holds that non-identical entities are discrete and as such can be conceived as separable, i.e., conceived as not necessarily connected, and so on the latter assumption it is possible that any two non-identical entities are not necessarily connected, or simply: no two entities are necessarily connected. I would, however, propose as instructive an ‘objective’ parallel to the argument, one that avoids a detour through the conceptual, has premises I take Hume to endorse, and, importantly, highlights Hume’s errors in not recognizing in addition to association the two and more fundamental forms of composition—attributions and wholes whose non-identical parts are only ‘formally distinct’. Required is ‘objectifying’ Hume’s term “distinguishable” from presumably ‘can be conceptually told apart’ to ‘are discrete in the sense that the composing being of neither presupposes that of the other’. With Hume’s terms in single quotes, the analog I propose is: 1) Nonidentical (‘distinct’, ‘different’) entities (fundamentally attributes/qualities as

|| 39 At Treatise 1.4.5.5 Hume argues: “For thus I reason: Whatever is clearly conceiv’d may exist; and whatever is clearly conceiv’d, after any manner, may exist after the same manner. This is one principle, which has been already acknowledg’d. Again, every thing, which is different, is distinguishable, and every thing which is distinguishable, is separable by the imagination. This is another principle. My conclusion from both is, that since all our perceptions are different from each other, and from every thing else in the universe, they are also distinct and separable, and may be consider’d as separately existent, and may exist separately, and have no need of any thing else to support their existence. They are, therefore, substances, as far as this definition explains a substance.” For a detailed analysis of the argument see Jani Hakkarainen, ‘Hume’s Argument for the Ontological Independence of Simple Properties’, Metaphysica 12 (2011): 197–212. 40 See Stephen Boulter, ‘The Medieval Origins of Conceivability Arguments’, Metaphilosophy 42 (2011): 617–41.

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tropes) are discrete (‘distinguishable’). (I.e., non-identical things as discrete share no common reality or being, the situation the medievals referred to as ‘thing and thing’ (Sect. 4.6), and so any union among them would, in order to bridge the ‘ontic distance’ between them, be by the externally unifying agency of one or more proper parts among the others. Hume, consistent with the conclusion of this argument, simply denies any such agency.); 2) Discrete (‘distinguishable’) entities have no necessary connections among them (are ‘separable’); hence 3) No non-identical entities have necessary connections among them (are ‘inseparable’). Specifically in regard to attributes Hume can conclude that every quality may exist apart from every other quality and from supposedly supporting substance (1.4.3.7). On the analyses herein the latter argument errs in both premises. Concerning premise 1), in particular that: “What consists of [non-identical] parts is distinguishable into them [i.e., has each part as discrete]” (1.2.1.3; my inserts)—to the contrary, non-identical (‘distinct’) entities need not be discrete, i.e., as ‘thing and thing’. If it were otherwise this would indeed require any union among them be by the bridging outwardly unifying agencies of one or more parts. Rather as noted and will be detailed in Section 4.6, there exist what I term ‘continuous composites’, e.g., attribute instances composed of intensions and combinatorial acts, that are wholes whose non-identical parts have their unions, not by the linking agencies of one or more of the proper parts of the resulting whole, but by the whole in whose undivided being the parts share. Here parts are differentiated as ‘thing and thing’ only conceptually—this abstraction being the classic ‘formal distinction’. The scholastic Suarez described the distinction as that “which is found in nature prior to any activity of the mind [i.e., non-identical entities], and that such distinction is not so great as the distinction between two altogether separate things or entities [i.e., between ‘thing and thing’41].”42 (my inserts) Tellingly, Hume considered the topic under the phrase ‘distinction of reason’ and claims, in effect, that assertions 2) and 3) do not require him to draw the conclusion that thus distinguished parts, e.g., his example attributes of figure and body, have no necessary connection. He avoids this by asserting that the parts of such wholes are “in effect the same [not

|| 41 Suarez, On the Various Kinds of Distinctions, Disputationes Metaphysicae VII, Sect. I, 15, p. 26. 42 Ibid., Sect. I, 16, p. 27.

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‘distinct’] and undistinguishable” (1.1.7.18; my insert), i.e., are identical.43 But this is simply counter-factual—their identity conditions are not the same. Premise 2) of the above analog argument is likewise in error; it is false that no discrete (‘distinguishable’) entities have necessary connections among them (false that any two entities are ‘separable’, or that without contradiction one can exist without the other). It is a principle point argued herein that all attributions are falsifying counter-examples. I.e., an attribute is completely external in its being from that of its subject(s), but necessarily it exists in a union of relevance with it(them) because of the subject(s) satisfying conditions prescribed by the attribute’s intension. Attributes are inter-entity connectors, as such dependent upon their subjects and existing in a union of ontological (not logical) necessity with them because the subjects satisfy the conditions prescribed by their intensions. Contra Hume, attributes as such are given to consciousness (are ‘perceptions’), yet abetting Hume is the possibility for each to have abstracted away conceptually its unifying agency and so its dependence (making it ‘separable’), the then stand-alone residuum—the attribute’s intension—being an ‘attribute’ only by courtesy. The error here, and what makes plausible Hume’s Dictum, is the easy equivocation that identifies abstracted and as such non-dependent intensions, e.g., Red or Square (or what Russell intended by relations “in the abstract”), with subsuming and actually characterizing attribute instances, Is-Redi or Is-Squarej (or what Russell intended by “actually relating relations”). I will amplify the nature of this distinction in Section 4.5, arguing that it is the error of confusing an attribute with its intension that gives rise to Bradley’s Regress (Sect. 3.1). Just as Hume’s official doctrine (though not his practice) would have us conceptually ignore the structuring/‘gestalt’ elements in perceptual fields in favor of residual isolated atomistic ‘sensa’ (a point I will return to below), he would have us in the limiting case abstract away the outwardly structuring connectedness of each attribute with its subject(s) (the connectedness being in fact the cause of the attribute’s individuation as an instance, and of its inherent dependence), the remainder being the attribute’s inert ‘separable’ intension. He would then have us, as would modern trope theorists, replace real attribute instances with surrogate tropes reconstructed by a stipulated melding of the individuation aspects of the former instances with their ‘separable’ substance-like intensions, eliminating, as it were, the ‘middle men’ of outward combinatorial agencies. Hume subjectifies his tropes as intensional atoms existing in a psychological realm closed under cognitive associa|| 43 Donald L. M. Baxter, ‘Hume, Distinctions of Reason, and Differential Resemblance’, Philosophy and Phenomenological Research LXXXII (2011): 156–81.

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tions as their only trans-entity connectors. But whether objective or subjective, if the only connections attributes as tropes have with their subjects is arbitrary associations, then all ‘attributions’ are possible, and any sets of propositions can be simultaneously true, e.g., those asserting Hume’s ontology and those contradicting it. With the above as context, let us now focus on Hume’s theory of relations and what I argue are the lessons of its distorting errors. Hume’s Dictum that denies any necessary connection among distinct/discrete existents is contradicted most forcefully by our intuitive understanding of polyadic relations. For, an intension R, e.g., Betweenness, specifies for each of its distinct relata certain necessary and sufficient conditions that must be met in order for an instance of the relation to exist between them, and when these conditions respectively obtain, e.g., say as they may with physical objects a, b, and c, then a relation instance of this intension could not not exist between them, i.e., there would exist necessarily a connection that is an instance Is-Betweeni, joining in an order the intension specifies, objects a, b, and c. It is not an optional matter— not a matter of arbitrary association—whether or not an instance of a relation exists between distinct relata when these relata respectively conform to the conditions set by a relation’s intension. And, it is not relata being in a relation whose intension is R that causes the relata to have the conditions set by R, but conversely. Though the relational connection is necessary, depending upon the intension (e.g., Betweeness), its founding conditions themselves need not necessarily obtain and because of this the resulting fact is contingent. (This is contrary to the erroneous inherence construal of attribution where a property being a part of its subject gives the latter the foundations for having the property.) In regard to Hume, then, the question is: What theoretical filter did Hume adopt in regard to relations that would nullify these pre-theoretical prima facie intuitions? Not surprisingly and abetting his dictum and project, the answer is: Hume adopted a then prominent assay of polyadic relations where their interentity linking aspects were taken to be, in fact, arbitrary connections, i.e., associations. With relations so understood, no entity is by its relationships necessarily connected with, and so does not depend for its existence upon, any other entity. Common at the time was the view that relations are products of the mind, entia rationis, being derivatives of certain conceptual comparisons, but what in themselves are not “real connexions” (1.4.6.16; Appendix, 21) between the compared relata. The foundations for this view are evident, for example, in Suarez’s late scholastic and widely influential Disputationes Metaphysicae (1597). He asserts that a relation (e.g., similarity, as in the fact that Socrates is similar in

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being white to Plato) is identical to its foundation (e.g., Socrates’ whiteness) inherent in a single subject (e.g., Socrates), but nevertheless requires definitionally an external ‘terminus’ (e.g., Plato) for the subject to be linked to (‘to be toward’) as related.44 The apparent inconsistency here is that a relation must have essentially both a foundation in one subject and an external terminus, but yet its total being is to be identified with only the former. Underlying its plausibility is the failure to recognize that essential to a relation is a relational intension (e.g., Similarity2) and essential to a dyadic relational intension—part of its identifying meaning—is the fact that it specifies a single joint characterization of two entities, and in this way the relation is a qualitatively specific inter-posing connection between two subjects. I.e., specified by its intension, with a relation there is one simultaneous characterization of multiple subjects, not one or more single subject characterizations united non-characterizingly (as with the ‘being toward’ (esse-ad) or with the logical conjunction ‘and’). The contrary view that a dyadic relation must characterize one subject and somehow involves noncharacterizingly a second one follows from the long-dominant inherence conception of attribution. Under the latter it was conceptually an easy matter to ontically discount a relation’s link to the external terminus, and so historically we have it being declared ‘ideal’ in somehow having no offending reality in the way that the relation’s foundation and terminus do. Suarez takes this stance against the view of Henry of Ghent who held that relations are actual ‘intervals’ between relata, Suarez asserting that such an interval would be “something of reason only”.45 As was observed (Sect. 2.6), the view was later adopted by Leibniz, who in conformity with his strict adherence to the praedicatum-inestsubjecto conception of attribution, held that a relation cannot be an accident because it would have to be simultaneously ‘in’ each of two distinct subjects— “with one leg in one and the other in the other”—and this is impossible (a thesis found prior in Suarez46). Hence a relation, “being neither a substance nor an accident, it must be a mere ideal thing.” With relations “the mind uses, upon occasion of accidents which are in subjects, to fancy to itself something answer-

|| 44 Francisco Suarez, On Real Relation (Disputatio Metaphysica XLVII), trans. John Doyle, (Milwaukee: Marquette University Press, 2006). Suarez asserts: “That a relation is not a thing or a real mode that is distinct from the foundation and added to it, but it is the very entity of the foundation as so denominating a subject. For since that denomination is purely respective, it consists only in a certain disposition that has arisen from the con-existence of a terminus.” (Sect. 8, 14, p. 141) For details of Suarez’s treatment of relations see Sydney Penner, ‘Suarez on the Reduction of Categorical Relations’, Philosopher’s Imprint 13 (2013): 1–24. 45 Suarez, On Real Relation, Disputationes Metaphysicae XLVII, Sect. 6, 4, p. 119. 46 Ibid.

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able to those accidents out of the subjects.”47 The conceptual assay is also explicit in Locke who asserts that relation “consists in the combination and comparing of one idea with another”48, and is “not contained in the real existence of Things, but something extraneous and superinduced.”49 That this was a popular view at the time is further evidenced in the ‘Relation’ entry of the 1728 Cyclopaedia by Ephraim Chambers where it is asserted “that Relation, take it which way you will, is only [of] the Mind; and has nothing to do with the things themselves.”50 (my insert) Taken literally, this is a gross overstatement: as if the mind is free to assign any relation, e.g., Taller-than, to any pair of subjects, e.g., the numbers 2 and 3. The lack of constraint here evidences how badly the notion of relation had come to be mis-construed. Hume’s assay of relations, at least as I understand it, avoids this overt absurdity but, I argue, replaces it with more subtle ones that follow from his retaining a sense in which relations have ‘nothing to do with the things themselves.’ To anticipate, Hume held that conceptual comparisons give rise to relation intensions as impressions/ideas jointly descriptive of ways compared subjects have ‘some degree of resemblance’, yet these comparisons and their intensions themselves involve no actual interposing connectors between the subjects. Such additional links were possible and often generated by the mind as motivated by these ‘resemblances’ or by the mind’s natural dispositions (1.4.2.32), but in every case these actual connections are arbitrary associations, what in each case is a union not conditioned by the subjects satisfying requirements set by the intension, but conditioned only by a psychological propensity that itself can only be associated with an intension and its subjects. Even with some mathematical relations that Hume describes as ‘necessary’, this necessity “lies only in the act of the understanding” as “but || 47 Gottfried W. Leibniz, Philosophical Papers and Letters, 2d. ed., L. Loemker (ed.), (Dordrecht: Reidel, 1969), p. 704. Also at p. 609 Leibniz refers to the paternity relation of Solomon to David as “a merely mental thing”. 48 John Locke, An Essay Concerning Human Understanding, P. Nidditch (ed.), (Oxford: Clarendon Press, 1975), II, XII, 7, p. 166. 49 Ibid., II, XXV, 8, p. 322. 50 This important reference is identified by Treatise editors Mary and David Norton. The full paragraph in Chamber’s entry ‘RELATION’ relevant here is; “Relation may be considered in two Ways; either on the Part of the Mind referring one thing to another; in which Sense Relation is only a Mode or Affection of the Mind, whereby we make such comparison: Or on the Part of the things refer’d, which being no other than Ideas, Relation, in this Sense, is only a new Idea resulting or arising in the Mind, upon considering of two other Ideas,—So that Relation, take it which way you will, is only the Mind; and has nothing to do with the things themselves.” Much the same description of relations is given in the 1751–72 Encyclopédie of D. Diderot and J. d’Alembert, under the Relation entry. Available at http://encyclopedie.uchicago.edu.

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that propensity, which custom produces, to pass from an object to the idea of its usual attendant” (1.3.14.22-.23). I.e., necessity is an idea that arises as itself attendant to a comparison among certain ideas, but is not a property of any connection between them. The comparison assay of relations is obscure, both in Hume and in the tradition. In regard to Hume, however, and expanding upon the work of Hume scholars, I would propose that one can glean from the Treatise the following assumptions at work in his statements regarding relations and their division into ‘philosophical’ and ‘natural’ (1.1.4-5; 1.3.14.31).51 First, by an act of conceptual comparison of two entities and their properties there is introduced to the context a “quality” (1.1.4.2; 1.1.5.1-.2; 1.4.6.7 & .16), i.e., relation intension, e.g., Resemblance, Identity, Contiguity, Above, After, Causation (1.1.5), which is simultaneously descriptive/specifying of aspects of each entity compared. What Hume here assumes, rightly, but inconsistent with his explicit claims, is that the identified intension has a qualitative relevance to the particular subjects compared in that they have the respective foundations prescribed by (are part of ‘the meaning of’) the intension as necessary for it to jointly describe them. Hume recognizes this, albeit obscurely, when he asserts that “no relation of any kind can subsist without some degree of resemblance” (1.1.5.8; also 1.1.5.3), implying that there is some basis in each relatum whereby they then ‘resemble’ in sharing a certain respect/intension. For Hume relation intensions are known by inspection (1.3.14.28), and would be his “impressions of reflection” or “secondary” impressions, or their derivative ideas (1.1.2.1; 2.1.1.1), i.e., products of the mind reflecting on other prior ideas (e.g., 1.4.6.7 & .16). Now consistent with his thesis that “the mind never perceives any real connection among distinct existences”, Hume holds that neither the act of comparison nor the resulting intension, nor both jointly, involve any actual inter-subject connection. Such comparisons and their derived intensions are Hume’s ‘philosophical relations’, relations he describes as not ‘connecting principles’ in themselves (1.1.5), i.e., not some third entities “interpos’d betwixt” the entities compared. (1.1.4) Such a relation is then a comparison that assigns an intension, e.g., Taller-than, to pairs of subjects, but without the bases for this assignment being any

|| 51 For other attempts to explicate Hume’s theory of relations see Ralph Church, ‘Hume’s Theory of Philosophical Relations’, The Philosophical Review 4 (1941): 353–67; Alan Hausman, ‘Hume’s Theory of Relations’, Nous 1 (1967): 255–82; Donald Gotterbarn, ‘Hume’s Troublesome Relations’, The Southwestern Journal of Philosophy 4 (1973): 119–24. Also see Charles Hendel, Studies in the Philosophy of David Hume, (Princeton: Princeton University Press, 1925), especially Section IV, ‘The Theory of Relations and Mental Habits’, pp. 103ff.

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complex whole consisting of the subjects and a connecting intermediary between them, i.e., without either a corresponding fact or a whole by association. No doubt as a historical influence on Hume’s analysis, we saw in Section 2.6 that something like it was proposed for all relations in the esse-in/esse-ad conception of relations by the medievals and going back to Aristotle, and it continues into contemporary ontology for some relations termed ‘internal’. Relations so conceived are somehow each an intension in a virtual union or ‘togetherness’ with a pair of relata (Hume’s ‘comparisons’), yet a union that is an ontological ‘free lunch’ in not being an actual additional polyadic connector between the relata (what for Hume is an association). In addition to philosophical relations, and indeed presupposing them as cognitive comparison-intension complexes, are what Hume terms ‘natural relations’. Here the mind is said to go beyond relational comparisons and generate actual interposing links between the relata, each such connection being an arbitrary association (1.1.4-5). In particular and as part of his ‘mental mechanics’, Hume asserts that the human mind has a natural propensity—is subject to a “gentle force” (1.1.4.1)—to associate entities under the “qualities” that arise from certain comparisons, these falling under the three general types of “RESEMBLANCE, CONTIGUITY in time or place, and CAUSE and EFFECT” (1.1.4.1). (Note: for Hume Resemblance, Contiguity, and Cause and Effect are each both a natural and a philosophical relation.) I.e., a quality Q generated from a comparison among entities a and b does not necessitate (and is not part of) an actual link among a and b, but Q ‘gently’ motivates the mind to form a link of association between them. For, according to Hume, associations provide the only actual “bond of union” or “uniting principle” between distinct entities (1.1.4.1); what, to re-quote him, are “the only links that bind the parts of the universe together”, being “to us the cement of the universe”. (Abstract, 35; Hume’s italics) Hume is clear, however, that the bond of association is not a “real bond” or “real connection” (1.4.6.16; Appendix, 20-21). Now crucially, what Hume must mean by asserting that an association is ‘not real’ is that it is an unfounded connection, i.e., an association, though conceptual, is an actual inter-entity unifier, but one unconditioned and irrelevant to or non-descriptive of anything about the subjects it links, whether of their composing natures or external attachments. As Hume puts it: “nothing is more free” than association (1.1.4.1). The ‘freedom’ here stems from the fact that the ‘principle of connection’ (the agent (contra Hume)) is the mind which can arbitrarily associate any things whatsoever, but what then results in wholes that are but proper sets or sums (Sect. 1.5). These stand in contrast to unions by (agent) attributes—what Hume denies— that exist only among subjects when they satisfy the conditions prescribed by

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the attributes’ intensions, making for wholes that are non-arbitrary facts. In this way Hume must contradict himself in his implied assumption that entities a and b in ‘resembling’ under quality Q have some mutual qualitative relevance described by Q, for if Q, e.g., Heavier-than (from Hume’s class of comparisonsin-degrees (1.1.5.7)), has such a relevance it would specify foundations that if had by a and b, e.g., weights of 5 lbs and 4 lbs, respectively, would necessitate their connection under Q, i.e., would necessitate the (possibly contingent) fact :Is-Qi(a,b). But for Hume no actual unifying connection is by qualitative relevance nor of real necessity. Hence for Hume, with neither philosophical nor natural relations do their intensions enter into the composition of the only unities involved: cognitive comparisons or associations. Rather, the relational intensions are ideas of reflection generated by the mind subsequent to operations of comparison, and they dispose but do not necessitate the mind to generate associations between their relata.52 Locke had insinuated the post-comparison emergence of relation intensions when he asserted that relations are ‘superinduced’: from the Latin meaning ‘to introduce as an addition’.53 So in sum, on either of the above divisions of Hume’s analysis of relations there is no bond between entities that requires or is determined by anything specifically descriptive of (‘about’) these entities, and in this way his assay of polyadic relations reinforces the ‘separability’ characteristic Hume explicitly attributed to their monadic property versions. On Hume’s assay, no relation among any two entities requires one be ontically dependent upon—‘inseparable’ from—the other. Now in critical response to Hume’s assay of relations I observe the following. First, despite the above attempts to do away with ‘real relations’ by reconstructing them as mind-generated associations, Hume nevertheless makes use of and explicitly refers to (because it is impossible to avoid) interposing and

|| 52 E.g., “Among the effects of this union or association of ideas, there are none more remarkable, than those complex ideas, which are the common subjects of our thoughts and reasoning, and generally arise from some principle of union among our simple ideas. These complex ideas may be divided into RELATIONS, MODES, and SUBSTANCES.” (1.1.3.7) And, referring to the relation of identity, Hume asserts that it “is nothing really belonging to these different perceptions, and uniting them together; but is merely a quality, which we attribute to them, because of the union of their ideas in the imagination when we reflect upon them.” (1.4.6.16) 53 Locke asserts that the mind “exerts several acts of its own, whereby out of its simple ideas, as the materials and foundations of the rest, the others are framed”, among these are acts of comparison “by which way it gets all its ideas of relation.” Essay Concerning Human Understanding, II, XII, 1, p. 163. The implication is that the ideas that are relations, i.e., relational intensions, emerge from acts of comparison and so are not conditioning elements of them.

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relata-descriptive relations, some said to be just as much given in perception as their relata. These and other inconsistencies have been detailed by Donald Gotterbarn and more recently by Yumiko Inukai.54 Inukai observes how in regard to spatial relations Hume asserts that they are “conveyed” by the senses as “colour’d points, disposed in a certain manner” (1.2.3.4, also .7), and similarly for temporal relations as “nothing but different ideas, or impressions, or objects dispos’d in a certain manner, that is, succeeding each other” (1.2.3.10). Implicit here is that spatial and temporal relations are given equally as perceptions in and among specific perceptions that are their relata—given as their relata’s ‘dispos’d manner’—and not constructed by the mind as associations. Indeed, this is necessarily the case since many such relations are asymmetrically ordered, and association is a symmetric connector. Inukai points to a passage where Hume is explicit about the perceptual given of relations of identity and time and place: “When both the objects are present to the senses along with the relation, we call this perception rather than reasoning; nor is there in this case any exercise of the thought, or any action, properly speaking, but a mere passive admission of the impression thro’ the organs of sensation.” (1.3.2.2; Hume’s italics) Despite this, later and after reminding the reader of his argument for the ‘no necessary connexion’ thesis, Hume asserts that “Five notes play’d on a flute give us the impression and idea of time, tho’ time be not a sixth impression, which presents itself to the hearing or any other of the senses. Nor is it a sixth impression, which the mind by reflection finds in itself.” (1.2.3.10) We see in all of this Hume both appreciating the need for real relations but officially on his assumptions forced to denounce them. As a second point of criticism, consider his two assumptions: that neither the descriptive relevances of relation intensions to their relata nor the comparisons of entities involve inter-entity connections, and, that connections, limited to associations, involve no unifying agency. In regard to the first, insofar as relation intensions, e.g., Resemblance, Copy-of, Above, Prime-Divisor, are descriptive of subjects and not just randomly assigned to them (the latter not requiring a ‘comparison’, but only an association), they have ties of selective relevance to their subjects, and these are ‘real’—non-arbitrary—connections.55 Hume and those in the shadow of the esse-in/esse-ad assay of relations are misled by a metaphorical construal of the esse-ad—the ‘being-toward’—aspect. It is

|| 54 Gotterbarn, ‘Hume’s Troublesome Relations’. Inukai, ‘Hume on Relations’. 55 This is behind Gotterbarn’s observation in ‘Hume’s Troublesome Relations’ that Hume’s admittance of relations is inconsistent with his thesis that impressions are isolable without loss.

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as if related subjects are like people who point toward each other without actually touching, the pointing making for relatedness but the absence of physical contact demonstrating that the relatedness is not an actual connection. The error here is to confuse what are two distinct relations: the one of reference achieved by the pointing, what though not physical is nonetheless an actual trans-subjects linking, with the touching relation which is absent here and so absent is any connectedness by it. Third, comparisons as cognitive acts are as much actual interposing links among subjects, if only brief ones, as are associations. Comparisons are real, temporally located events mostly outside of consciousness, what science tells us are complex mental processes, i.e., dynamic neuro-cognitional structures, composed as such of attributional facts, some containing the subjects compared. Indeed, Hume refers to comparisons of resemblance as “acts or operations of the mind” (1.4.2.32; also 1.2.5.21, 1.3.14.23), yet conflicting with this is his crucial thesis that there is no such thing as agency or production. And, Hume can properly admit only those portions of comparison processes available to consciousness—perceptions, but here and second, there is a conflating of these processes with their results: in acts of comparison ideas are brought together— associated, contra Hume—by the mind and examined with the intent of finding foundations corresponding to relational intensions, this prior to the recognition of any such attributional connections. The subsequent recognition of the existence of such an attribute ‘between’, i.e., characterizing, these subjects, but not this latter fact itself, would be a product/result of such a comparison. But this distinction is not available to Hume. Again, and despite his constant use of language to the contrary, he must officially reject processing/productive ‘acts’ as part of his denial of all causation, agency, efficacy, etc., and so must collapse the difference between comparing processes and their thereby discovered relational facts. But thus identified, then just as there is no relational connection yet in the process of comparison, there can be none in its results of a thereby recognized relational fact—Hume’s ‘philosophical relations’. And in this identity of comparison and relation, just as comparisons are freely-made and subjectindifferent, so then relations, if they are to involve any actual links between relata, the links must respect these conditions of being freely-made and subjectindifferent, and this is precisely the nature of association—Hume’s ‘natural relations’. Underlying the issues here and ontically primary, what is as crucial to Hume in its denial as it is to what I propose in its affirmation, is the fact that comparisons, associations, and attributions are all equally trans-entity ‘connectors’, and that this necessarily implies ‘efficacy’, i.e., unifying agency. Hume

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broaches the connecting-agency thesis in his explicit denial: “Now nothing is more evident, than that the human mind cannot form such an idea of two objects, as to conceive any connexion betwixt them, or comprehend distinctly that power or efficacy, by which they are united.” (1.3.14.13) Taken literally this asserts that there is nothing inherent in the beings of either of any two entities that is a connection with the other, or is a unifying agency that is necessary to achieve this connection. Indeed, Hume includes ‘connexion’ in a list of terms he says are “nearly synonimous” but have no corresponding reality: “efficacy, agency, power, force, energy, necessity, connexion, and productive quality.” (1.3.14.4) Yet, he repeatedly characterizes association as a connection—as a “union or cohesion” (1.1.4.6)—and, as noted, describes associations as themselves motivated by a ‘gentle force’, in this way resemblances being “most efficacious” (1.4.2.32). Thus contradictorily, Hume denies universally the reality of agency, what is aimed particularly at attribution as intuitively involving agent unification, “something that really binds” (1.4.6.16), but he makes, as he must, an exception for instances of association that are to be surrogates for attributions. The latter is necessarily so on the following. Consider two entities, a and b, and the unification: a-association1-b. Focusing on the left-two entities: a and association1, on Hume’s assertion we cannot “conceive any connexion betwixt them” nor “efficacy” that unites them, and so to get the unification Hume implies we would have to introduce a further association as “the only links that bind the parts of the universe together” (Abstract, 35), i.e., the original unification becomes: a-association2-association1. This, of course, is the beginning of a vicious regress, and one duplicated on the right-side of the original unification, what together form an analog of, and provide the same illustrative service as, Bradley’s Regress concerning attribution. The only way to avoid this regress, as with Bradley’s, and for there to be unity among ‘distinct existences’ is that one or more of the parts must each achieve something beyond itself, viz., its bonding with some of the others, what in this self-attachment is ‘inseparable’ from its subject(s). And this outward-achieving is precisely agency, efficacy, power, etc. It is what Aristotle intended by the term ‘energeia’ = ‘at-workness’ and attributed to substantial forms in their roles as unifying organizers of structural wholes (A7 (Attribute Agent-Organizers)). These points will be expanded in Section 4.3. It is the unity-achieving connections of both arbitrary associations and intension-controlled attributions that are the primary and only exemplifications of agency, power, productive quality, etc.—of, contra Hume, causation.

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In addition to the above negative assessments there are the following impossible consequences of Hume’s assumptions. The official Humean world is one of sensa-tropes “conjoined but never connected” 56, i.e., composed of tropes some of which are conjoined by association but none of which are connected via attribution. Limited to such unities/wholes, it is an impoverished world where, principally: there is no causation as relations of nomic necessity and of various types/intensions, and so no epistemic access to the extra-subjective (Appendix, 19); there is no structured complexity, including in its simplest form of single facts, and so no truth-makers for other facts that are sentences and propositions as grammatical/semantical structures (this itself a reductio of the written Treatise); and, with the absence of structured complexity, there is no personal identity (e.g., necessary to generate and assent to the arguments of the Treatise). Only the latter caused Hume anxiety, this expressed in the Appendix to the Treatise. Yet, all of this is counter-factual. Particularly in regard to the first two points, Hume’s denial of real relations eliminates the means of epistemic access to the extra-conceptual. Unlike an association, a relation obtains among a set of relata only when the latter have the specific aspects and so ‘fit’ the conditions prescribed by the relation’s intension. In this way and like all attributes, the obtaining of relations carries information about their relata. Only by instances of epistemic relations, objective in existing only because their relata satisfy conditions set by intensions inherent to the beings of the instances, is there an informative link between a knower and something x not itself given in awareness, extra-conceptual or conceptual—these relation instances ‘transmit’ information descriptive of x. It is by epistemic relations that the mind, in the roles both of relatum and as comprehending the intensions involved, can achieve what Hume denies: that these relations “can be trac’d beyond our senses [i.e., the immediate content of perception], and inform us of existences and objects [distinct from but in ways represented by perceptions], which we do not see or feel.” (1.3.2.3; my inserts) More specifically, awareness of the existences and intensions of instances of epistemic relations informs the knower that the instances’ subjects have the foundations specified by their intensions, though these subjects and foundations are beyond awareness. Real epistemic relations are prerequisite to a correspondence theory of truth, and to answering Berkeley’s challenge of how to get beyond one’s own ideas to warrant the ‘fit’ between them and the subject(s) of the correspondence. The answer to solipsism, epistemic relations are the ‘lines of information transfer’, analogous to trans-

|| 56 See note 34.

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mission wires or fiber-optic cables, between the content of consciousness and any other entities. In contrast, arbitrary associations are both creations of the mind and depend upon nothing about, and so can provide no information concerning, their subjects, subjects which to be known must be given independent of their associations. Associations are then analogous to simply connecting but otherwise inert ropes. Hume’s associationist tropism uncouples intensions from any required subject-specificity on inter-entity connections, and without this the connections are uninformative—here no message can be transmitted by the medium. Hume’s standard of truth is then coherence among association bundles (‘systems’ (1.3.5.2; 1.3.9.3)) of perceptions. Refining some of these points and at the crucial starting place for the data of Hume’s empiricist ontology, it is simply a fact that the immediate contents of our perceptual fields are not atomistic sensa, but are organized/structured wholes. I.e., the phenomenal given is of structured wholes consisting then of multiple real, inter-connecting and intension-determined attributes. This point is central to Gestalt psychology, and was stressed by philosopher and psychologist William James. James observes: The statement of fact is that the relations between things, conjunctive as well as disjunctive, are just as much matters of direct experience, neither more so nor less so, than the things themselves. The generalized conclusion is that therefore the parts of experience hold together from next to next by relations that are themselves parts of experience. The directly apprehended universe needs, in short, no extraneous trans-empirical connective support, but possesses in its own right a concatenated or continuous structure. 57

James argued this against both the ‘elementarists’ and the ‘intellectualists’ psychologists who maintained, respectively, the above reductive-elimination and intellectual-act assays of relations.58 Now further, the more important point is that the given of a subjective sensory structure carries information beyond itself because of an interfacing isomorphic causal structure (what in most cases will be a long sequential chain of such) between the experience and substructures of the objective world. This point was emphasized by Russell:

|| 57 From the Preface of William James’ The Meaning of Truth: A Sequel to ‘Pragmatism’ (1909), pp. xii–xiii. Available at http://www.gutenberg.org/files/5117/5117-h/5117-h.htm. For a sketch of James’ account of spatial perceptions relative to Hume see Klien, ‘On Hume on Space: Green’s Attack, James’ Empirical Response’. 58 Marian Madden and Edward Madden, ‘William James and the Problem of Relations’, Transactions of the Charles S. Peirce Society 14 (1978): 227–46.

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It appears generally that if A and B are two complex structures and A can cause B, there must be some degree of identity of structure between A and B. It is because of this principle that a complex of sensations can give us information about the complex that caused them.59

Modernizing an analogy given by Russell, consider the sequence of isomorphic causal structures involved in a radio broadcast of a prior musical performance: it is first a complex event structure of vibrations in air that is then transformed so as to be recorded as a digital structure in a memory device, this is then transformed and transmitted as an electro-magnetic wave structure, what is received and transformed into motions of speakers and so into vibrations of air. Because each transformation preserves identity of structure, the vibrations of the original performance will be duplicated in the received one. Analogously, structurepreserving transformations across event structures in our neuro-sensory apparatus provide knowledge of objective structure beyond it. But relative to Hume, there is no structure, simple or complex, without attributes as intension-conditioned unifiers to effect it, and associations, singly or in chained lattices, carry no information (other than existence) about the elements so unconditionally linked. And inter-connecting associations, because they are created and sustained only in the intellect, are not available to bridge the objective|subjective divide. Further and reemphasizing a point broached above, a structure-less world contradicts Hume’s advocacy of it. The Treatise presents arguments and makes assertions of fact, both requiring cognitive propositions composed of semantic and syntactical relations among referring units. For certain sets of propositions these composing relations are necessary and sufficient for logical relations of implication to exist between them and further propositions properly so composed. But neither propositions nor implications between them can be just associations: propositions can be asserted, but wholes by associations—sets or sums—cannot, and implications exist necessarily based upon the particular structures of the propositions involved, whereas associations are arbitrary and not determined by their subjects. Moreover, to assert propositions is to presuppose a truth-context and so facts and a truth-maker relation between the facts and propositions. But, propositions taken as wholes by association are not the sorts of things that can be true or false, and the truth-maker relation cannot be just association, for then any fact would make any proposition true. What this means is that, worse than epistemic solipsism, Hume’s denial of subject-rele-

|| 59 Russell, Human Knowledge, p.468. Also see pp. 250–55, 460–75.

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vant attribution eliminates all rational thought whatsoever. In short, the whole point and force of Hume’s Treatise as arguments for a true description of the real dissipates if what he is arguing for is true. Finally, I note that against Hume’s atomistic ontology of separate and arbitrarily associated monadic attributes are results of contemporary physics. As pointed out in the literature, quantum and relativity physics evidence an ineliminable structural holism. For example, the relations of quantum entanglement are necessarily connecting and subject-dependent but not supervenient upon nor reducible to properties of their subjects. And, physical properties of the particles, e.g., Has-Spini, are “fixed only by the interconnected web of entangled relations among particles.”60 The implied ontic structuralism of current physics will be considered in more detail in Sections 5.2 and 5.3. In general and contrary to Hume, the data of immediate perception and everyday experience, of systematic science, and the arguments of this work are jointly of a reality replete with irreducible hierarchical structures composed of the intension-controlled unifying-agency of attributes on and among (A7), and so what are intrinsically dependent upon (A1), their subjects. It is through the specific lattice of certain kinds and combinations of attribute instances that form a structure, whether, e.g., a quantum entanglement, a computer, a living body, a self, or a logical argument, that the whole or its parts are foundations for emergent attributes, e.g. and respectively, determinate particle spin, complex computer functioning, homeostasis, continuous awareness (required to understand an argument), and validity. Hume’s second thesis, “that the mind never perceives any real connexion among distinct existences” is a wholesale denial of all of this, as it is of single facts from which all these complex structures are built and what are required truth-makers for corresponding asserted propositions (including all of Hume’s assertions to the contrary). Given the conditions prescribed for its subjects which are what is known in knowing the intension Prime-Divisor, and an understanding of 3 and 6 which includes knowing that they satisfy these conditions, then the mind does ‘perceive’ a necessary connection under the intension Prime-Divisor between these numbers, the resultant whole being the fact :Is-a-Prime-Divisor-ofi(3,6). And knowing the intension Orbits, which means knowing the conditions it requires of its respective subjects, and that the earth and sum respectively satisfy these conditions, then

|| 60 Vassilios Karakostas, ‘Humean Supervenience in the Light of Contemporary Science’, Metaphysica 10 (2009): 1–26. Also see James Ladyman, ‘On the Identity and Diversity of Objects in a Structure’, Proceedings of the Aristotelian Society, Supplementary Volume LXXXI (2007): 23–43.

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the mind ‘perceives’ a necessary connection under this intension between the earth and the sun, the emergent fact being :Orbitsi(earth,sum). The latter fact is contingent because though the earth and sun satisfy conditions prescribed by the intension Orbits, and so necessitate an instance Orbitsi unifying the earth and sun, these conditions need not themselves have obtained (Sect. 4.2). Succinctly and what will be detailed in Chapter 4, attribution is a, and I would argue the, principle of what are ontological/metaphysical necessary connections, efficient causal relations being one subclass. Contrary to what Hume claims we do not have for causation, it is the case for all attributions/onticpredications that, in fact, “we are acquainted with that energy [i.e., combinatorial (‘actually relating’) agency] in the cause [in a property or relation (instance)] by which it operates on its effect [more accurately: operates on its subject(s) so as to effect an emergent fact]; that tie, which connects them together; and that efficacious quality [i.e., the attribute’s specific intension], on which the tie depends.” (1.4.7.5; my inserts) A Humean denial of necessary connection is plausible only after the given is filtered through an ontological doctrine that reductively eliminates relations and so paradigm structure in favor of psychologically constructed associations. Motivation for this doctrine in turn was the (correct) assessment by Hume and the philosophers of his time that the notion of ‘substance’ (i.e., the per se subjects of A3) yields absurdities, substances thought (erroneously) to be necessitated by the outward subject-dependence of attributes (A1). The corrective was then taken to be the denial of attribute dependence, this requiring the elimination of relations proper because of their obvious attributional dependence on and among multiple subjects. It is ironic that it was the increasing knowledge of precisely the internally complex (contra A8 (Unity by the Constituent One)) causal-mathematical structures observed in nature that gave corpuscular ‘natural philosophy’ its explanatory advantage over Aristotle’s blunt substantial forms, and the reason why the former so much impressed Hume and his contemporaries. But a canonical Humean world is devoid of structure: it is one of fictional inert atomic tropes, what then can be joined to form collections only by the theory’s non-attributional associations. And, associations are conceptual and arbitrary, and their hypostatized results—theoretical sets and sums—are logical fictions (‘chimeras’). The latter are good for constructing formal models and for being the freely assigned correspondence mappings between a model and the structures modeled. But it is a mistake to identify associations and their resulting models with the corresponding non-arbitrary extra-conceptual and conceptual attributes and their resulting structures. And ontology concerns principally the latter.

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In brief, then, the further critique of classic assumptions A1-A8 that is this chapter has produced the following results: In reverse order, I have argued that Hume’s denial of any ‘real connection’ and so of agent attribution, and what is principally the denial of A1 (Attributes as Dependent) and A7 (Attribute AgentOrganizers), implies absurdities. That in regard specifically to the denial of A1 and this in the context of bundle theories that the denial underlies, we have seen a number of profound problems, particularly in regard to the there required Compresence unifier and its impossibility as either a relation or as association. Prior to that we saw how A2 (Attributes as Universals) and A7 yield Bradley’s Regress concerning the unity of facts, and how A2 and A8 (Unity by the Constituent One) imply either the loss of polyadic relations and so structure, or a counterfactual substance monism. And initially it was argued that A2 and A8 imply that subjects are the cause of their unification with their attributes, and this contradicts A7. The net implication from the chapter is warrant for the veracity of A1 and A7, and the falsity A2 and A8. Extended are the implications of Chapter 2 where it was concluded that A5 (Inherent Essential Attributes) and A8 are false and that A4 is true. All of this will be reinforced in Chapters 4 and 5, and where the remaining classic assumptions A3 (Per se Subjects) (Sect. 5.2) and A6 (Non-Attribute Individuals) (Sect. 4.5) will be shown to be both false.

4 Atomic Structures: Facts and Their Natures 4.1 Structural Unity via Attribution; Facts as Atomic Structures Let us regain perspective. Recall T1 (Sect. 1.1) as an overarching thesis of this work: that structure (organization, system, gestalt) is a ubiquitous feature of all the given, and that an extended analysis of the types of unity characterizing structure provides the founding insights for a complete ontology having as its single primary category that of individuated attributes or instances. It will be theses T2-T10 developed in the next two chapters that will detail this claim. Fundamental to the latter are a sequence of recognitions, viz., that structural unity is kind(s)-specific inter-connectivity, what in its most obvious form is relational attribution; that this type of unity likewise characterizes structure in its simplest form of single facts—one attribute characterizing its subject(s); and that within the latter this structuring and existential unity of agent interconnectivity can be by either polyadic relation or monadic property attribution. The broader thesis, then, is that every unity among the discrete requires one or more entities to be each the agent of an outward-achieving bond, what by their unifying acts they and their resultant whole are thereby individuated, and these unifiers are primarily intension-determined attribute instances, or derived from these are arbitrary cognitive associations. All other entities (‘objects’), types of unions, and ontic dependence are derivative of property and relation instances and the structures they compose. This promised analysis and the details warranting these claims will now be our direct focus. Chapters 2 and 3 have provided a context and motivation for this assay; there a number of classic ontological assumptions, tellingly all relevant to structured wholes, were made explicit and seen, in various combinations, to imply inconsistencies, vicious regresses, or other problematic implications. The joint sources of these problems have otherwise remained obscure to and so have retarded the current debate. Included among these assumptions as closest to and reinforcing of our thesis T1 is the Aristotelian-scholastic A7: structured wholes require agent-causes of their organized unities, but what were taken to be attributes restricted to certain kinds, viz., ‘substantial forms’ for substances (living creatures as paradigm) and ‘accidental forms’ for artifacts. Correcting the error in this myopic restriction, we shall in this chapter assay attributes in their defining ontic roles of forming characterizing/qualifying unions with subject-others, what will then display every attribute’s common nature to be, out-

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wardly, a cause of the structural unity that is its resultant subsuming fact, and so, inwardly, being an intension-controlled combinatorial agent. This potent insight will found an ontology of individuated attributes and their derivative facts, facts being the simplest form of structure and what, via the agency of their composing instances, combine and emerge so as to form all other compound and hierarchical structures of our thought, experience, and science. Removing much ontological distortion that would replace structured wholes with theoretical sums or sets is the recognition that the latter are fictions derived from wholes by cognitive associations, and that the latter emerge upon neuro-cognitive fact-structures that are minds. Surviving our analysis as veridical will be only three of the classic assumptions: A1 (Attributes as Dependent), A4 (Required Essences), and A7 (Attribute Agent-Organizers). The errors inherent in the remaining assumptions will become apparent and dissolved in the course of developing instance ontology. Our assay of structure and the warrant for thesis T1 start with the recognition that every single attribution, whether by a polyadic relation or a monadic property, is an intension-conditioned linking, effecting as such a structured whole, and what is the minimum such, viz., a fact (or state of affairs). I.e., proposed is Thesis T2: T2. Structure as qualitatively conditioned unification has as its simplest form single facts or states of affairs, i.e., :Rni(a1,a2,…,an), n ≥ 1, where an n-adic attribute, Rni, qualifies jointly an n-tuple of subjects. Included here are monadic properties as the limiting 1-adic case with general form :P1i(a1). The unification of a fact involves a descriptive ‘fit’ or relevance of the constituent attribute’s intension Rn with corresponding ‘foundations’ had by each subject, these foundations being either aspects of the subjects’ internal composing natures, and/or some external contextual unions had by the subjects. In this way unity of a fact contrasts with the nature- and context-indifferent unifications composing mere sets, mereological sums, random lists, or ‘heaps’. We will in this chapter warrant the claims motivating our notation, viz., that ontic predicates exist only as unrepeatable instances, Rni (individuation indicated by a subscript), but where each instance has as a proper constituent a repeatable/universal intension Rn (indicated by the absence of subscript), what conditions each of its instances as to the nature, order (if any), and number n of its subjects (its n-adicity). A historically enduring mistake has been to assign unifying attribution to the latter universals (A2). The differentiation herein

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between an attributive instance Rni and its non-attributive and constituent intension Rn eliminates both otherwise intractable problems, e.g., Bradley’s Regress, and the charge that admitting both individuated attributes and universals is redundant.1 Concerning the simplest or atomic structures, these are wholes whose composing intra-connectedness is conditioned in one qualitative way, i.e., by only one intension Rn, and this among the intension’s required n subjects. These are single facts or states of affairs. The structured nature of facts is usually highlighted by contrasting them with the unordered unities of arbitrary or random wholes, viz., sets, mereological sums (or fusions), ‘heaps’, or random lists, a contrast I have previously made use of in Section 3.1. Returning to this device and, for perspicuity of introduction, setting aside temporarily the use of suband super-scripts on attribute terms, let us compare structured facts we will here indicate simply as :Red(a), :Love(John,Mary), and :Between(b,a,c), with their corresponding sets, {Red,a}, {Love,John,Mary}, and {Between,b,a,c}. Different from their roles in the sets, it is immediate that the attributes Red, Love, and Between respectively condition the unifications that are their facts. First, each set exists independently of whether or not the respective and contingent fact exists, each fact’s existence requiring in addition that the given attribute ‘actually characterize’ the other elements. I.e., a set is a union among elements that is indifferent to anything about or specific/descriptive of the connected elements except their existences. In contrast, a fact is via an attributional union conditioned by a specific and differentiating kind—the constituent attribute— and its descriptive qualitative ‘fit’ or appropriateness with co-relevant aspects of its subjects. Epistemically, because of the latter a fact has one constituent—the attribute—that is informative about the other constituents, but this is not the case for any element relative to the others in the unity that is a set. Restating this point, in a set the unification among the elements is ‘free’ or arbitrary, any entities whatsoever being formable into a set, and no set precluding the existence of any other. Likewise for mereological sums. However, in a fact the characterizing attribute conditions what is then a non-arbitrary union with its subjects in that the attribute specifies and requires of its subjects that they have certain inward natures and/or outward connections, what are ‘foundations’ or ‘grounds’ necessary and sufficient for the attribute to obtain on them. More on this presently. It is in requiring certain foundations be internal and/or external aspects of an attribute’s subjects that the attribute precludes other facts with || 1 D. M. Armstrong, Universals: An Opinionated Introduction (Boulder: Westview Press, 1989), p. 132.

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contrary attributes from obtaining on these subjects, e.g., fact :Circle(b) precludes the existence of fact :Square(b), whereas set {Circle,b} does not preclude the existence of set {Square,b}. And, contrary attributes, e.g., Dog and Whale, are such because they each prescribe sets of foundations that overlap at a proper-subset, the latter founding a common genus attribute, e.g., Mammal. And, in terms of the refinements and notation justified below, an intension Rn though simple, can specify multiple conditions required on or among n subjects in order for an instance Rni to characterize them, and subsets of these foundations may each found other attributes that as such can be used jointly as a definiens for intension Rn. Second and in regard to order, attribution in general has a ‘directionality’ in the sense that every attribute proper qualifies (and so carries information about) its subject(s), and not vice versa, i.e., attribution itself is asymmetric. This directionality evidences the intrinsic ontic dependence of attributes, what is asserted in classic assumption A1 and whose sources we shall make explicit. In this fundamental way all facts are structured. Also, in a further more obvious way and as a function of their specific intensions, certain attributes can provide an ordering among certain n-tuples of subjects if the attributes are polyadic and asymmetric or non-symmetric, or analogs of the latter for adicities n > 2. For example, the facts :Love(John,Mary) and :Between(b,a,c) are not identical to, respectively, the facts :Love(Mary,John), and :Between(c,a,b), and with each pair the difference is clearly a function of the relation and the specific and different conditions it sets on each relatum and how jointly they are to be ordered. In contrast, with a set (or mereological sum) there is no internal ordering, and no element conditions the inclusion or exclusion of any others. For example, irrelevant to the typographical order among their term tokens, the set {Love, John,Mary} is identical to the set {Love,Mary,John}, and has the unity of its elements independent of any element being ‘descriptively distributed’ across the others, what without the latter it has no internal ordering. As much emphasized in the previous chapters, this is the unity of associations. But for the facts Mary loves John and John loves Mary, if one or both obtain, they do so because Mary and John each have aspects that are foundations specified and ordered under the relation Love. For example, the fact that Mary loves John obtains because Mary and John each satisfy the appropriate foundational conditions set by the relation Love: Mary knows John, and internally Mary is in certain psychological and physiological states, including dispositions toward John. A key lesson here

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can be put as a slogan: Only intensioned connections—attributes—have ordering directions.2 Particularly obvious with ordering relations, it is because of an attribute’s conditioning of an attributional union it has with its subjects that the resulting whole—a fact—is ‘more than the sum of its parts’; more than an arbitrary or random collection of these subjects. This is evidenced by the emergence on such wholes of non-formal attributes, e.g., the relational fact that Joe is in debt to Bill has real and possible moral, legal and causal consequences, some of these for Bill and, because of the order, different from those for Joe, but none of which are had by the mere collection or set {Joe,Debt,Bill} or its elements because of their inclusion in it. The kind of unity involved in an unstructured (‘arrange-less’) list, set, or sum, e.g., Joe+Debt+Bill, is not constrained, and so not ordered, by the natures of the elements. It is the general nature of arbitrary wholes, e.g., those of set theory and mereology, that of the things united all that is required is their existences, though as I urged in Chapter 1, for their selective unification and collective differentiation from other such wholes, one or more constituent unifying causes are essential, viz., cognitive associations. In fact and necessarily, sets and sums proper are each a ‘sum (via intra-connecting associations) of its parts’. But within their respective formal theories, sets and sums are construed in abstraction from their constituent associations—what are then logical fictions of each a delimited ‘many’ absent the prerequisite differentiating ‘selecting and collecting’ unifiers. To confuse hollowed-out fictions with what are sets or sums proper—cognitive constructions via associations—is to succumb to a profound error, one that contributes to the masking of what is the fundamental ontological role of trans-entity unifiers, not just of associations but

|| 2 It would be an error to think that the set-theoretic Wiener-Kuratowski (W-K) modeling of ordered pairs as sets of sets, e.g., = {{a},{a.b}}, demonstrates that one can have orderings without intensions (i.e., that ordered pairs are reducible to unordered sets). The W-K modeling is sufficient to formally distinguish from (={{b},{a.b}}) for a ≠ b. This is so, however, because the symbol ‘’ itself carries information of an ordering typographically, e.g., via the intension Left-of2 in the fact :Is-Left-of2i(‘a’,’b’). And in the W-K modeling the correspondence rule is: take the unit set of the left-most term of ‘’ and join it with the set using both terms of ‘’ to form corresponding set symbol ‘{{a},{a.b}}’. Of course one could achieve the same formal results if the modeling’s correspondence rule had been: take the unit set of the right-most term of ‘’ and join it with the set using both terms of ‘’ to form corresponding set symbol ‘{{b},{a.b}}’. The point is that a relation ordering its relata by its specific intension, e.g., Left-of2 or Right-of2, is presupposed in the W-K type modeling. For similar observations see Herbert Hochberg, ‘The Wiener-Kuratowski Procedure and the Analysis of Order’, Analysis 41 (1981): 161–63.

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of attributions as well. Perhaps a psychological motive for this error is the slide from the vaguely appreciated fact that constituent unifying associations are irrelevant to the natures of the elements unified to the error that associations are irrelevant to the natures of the resultant wholes. Historically, that the attributive unity of a fact is more than that of a ‘mereological whole’, but is rather a structuring via an intension-conditioned cause, has been central to the ontologies of a number of philosophers, from Aristotle, as we have observed concerning his constituent substantial forms, to recently Armstrong in his dual thesis of attributes as ‘ways’ and of states of affairs as sources of their own internal non-mereological unity.3 Yet, little advance has been made in analyzing the unity of ontic predication and so in mining its implications. This explains why in the literature we have no developed theory of complex structure as it derives from atomic facts. The analytic void allowed Armstrong, for example, to advocate the thesis that, outside of single states of affairs, there is no composition that is not mereological, what runs counter to, I have urged, the ubiquitous given of complex and hierarchical structure.4 To the contrary, on the analysis herein there is a uniform theory of non-mereological structure from facts up through all forms of complexity, this via fact-structures compounded both ‘horizontally’ and ‘vertically’ into more complex forms. Made precise in the sequel, inter-attributional (horizontal) and emergent (vertical) composition provide an account of all complex structure, including that of dynamic forms and by which it solves related problems such as identity through change. Both the latter account of upward complex structure and the refined downward analysis of composing facts advance this work over that of others who have promoted the fundamental ontological status of facts or states of affairs, e.g., Bertrand Russell, Ludwig Wittgenstein, and Armstrong.5 Central here, in its clarifying details our analysis corrects the error that is the Wittgenstein-Armstrong thesis of ‘fact-independence’: that no sets of facts entail the existence or non-existence of other facts.6 To the contrary and warranted by experience and science, reality is a vast hierarchical network of facts, composed of upwardly emergent and so downwardly dependent lines of nested structures, || 3 Aristotle’s analysis of structure is found principally in Books VII and VIII of the Metaphysics. 4 D. M. Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997), pp. 25, 30, 118–22. 5 Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London: Routledge & Kegan Paul, 1961), p. 7, Prop. 1.1; p. 13, Prop. 2.05. Bertrand Russell’s views on facts are made succinctly in his summary My Philosophical Development (London: Allen & Unwin, 1959), pp. 112–13. Armstrong, A World of States of Affairs. 6 See Armstrong, A World of States of Affairs, pp. 139ff.

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each stratum composed of facts where at least some of their composing attributes derivatively emerge upon prior strata as wholes, i.e., the latter ‘sets of facts’ being the necessary and sufficient grounds for the generation of new facts. Or in short, Reality is not one all-encompassing fact, but an articulated and stratified lattice of all facts.

4.2 On Intensions and Their Prescribed Foundations As key to our analysis of attribution/ontic-predication, let us sharpen our understanding of the correlative nature of attribute intensions and their foundations. It is appropriate hereafter, with only a couple of exceptions, to utilize the refined notation anticipating our fundamental distinction, argued for presently, between a non-unifying attribute intension/universal, ‘Rn’, and a subsuming attribute instance, ‘Rni’, that is the actual attributional unifier of itself with its subjects. It has been emphasized that in a fact the attribute exists in a union not just of irrelevant juxtaposition with its subject(s), but in one conditioned on the subject(s) conforming to specifications set by its intension and whereby the attribute is descriptively ‘about’ its subject(s)—the difference here being that between association and characterization. I.e., and contrary to an easy mistake that there is a class of ‘external’ relations that are exceptions, all attributes specify what are necessary and sufficient conditions—foundations or grounds—that subjects must have in order to be characterized by them. More precisely and in recognized dispositional terms7, attribute intensions Rn (e.g., the intensions Circularity1 or Marriage2) are both directive and selective: An intension is directive in that part of what gives it its identity is the non-mental intentionality that is its descriptiveness of possible n-tuples of entities beyond itself—its ‘pointing-toward’ subject-others (hence my use of adicity superscripts on intension terms). Concomitantly, an intension is selective in being a ‘criterion of application’ requiring specific ‘selecting’ conditions that define it be satisfied by hence just certain n-tuples of entities in order for them to be qualified by instances of (argued in Sect.4.4), and so be included within the extension of, it as an attribute universal (argued in Sect.4.5). Attributes being both directive and selective is implicit in their common description as ‘ways’ other things are.

|| 7 C. B. Martin, ‘On the Need for Properties: The Road to Pythagoreanism and Back’, Synthese 112 (1997): 193–231. The terms ‘selectiveness’ and ‘directedness’ used herein are adopted from Martin. Also see John Heil, The Universe as We Find It (Oxford: Oxford University Press, 2012), and George Molnar, Powers: A Study in Metaphysics (Oxford: Oxford University Press, 2003).

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Further and to be argued in Section 4.3, if each subject in an n-tuple respectively satisfies the conditions set by an intension Rn, then, contra Hume, some instance Rni effects ‘a necessary connection’—is necessarily attributionally combinatorial/collective—of itself with these subjects resulting in a unified whole that is the fact :Rni(a1,a2,…,an). What will be established is, in a primary sense I would urge (more in Sect. 5.5), an intension (‘quiddity’) Rn is ‘dispositional’ in that it ensures that an instance Rni possessing it (though significantly, not as an attribute of it) behaves in a certain way when certain circumstances obtain. Or in detail, an intension Rn is dispositional in that it specifies conditions where, if circumstances are such that these conditions are respectively met by each of an n-tuple of subjects, then an instance Rni necessarily both exists and exercises causally an Rn-conditioned unifying act—an attribution/characterization—among these subjects. Because each attribute instance Rni is a conditioning intension of a combinatorial act, we have thus the characterizing slogan: attribute instances are each directive, selective, and collective. The resulting unions, whose emergent wholes are facts, are the fundamental form of ontological/metaphysical necessity. This, however and in a manner we shall see shortly, does not make every resultant fact itself ‘necessary’ in the sense of denying contingency to facts that are intuitively so. In sum, it is argued that attribution as an asymmetric union necessitated by a criteria-prescribing intension and subject(s) that fulfill, and thus are described by, these criteria is the principle of all non-arbitrary connection and de re necessity and contingency. The prerequisite foundations prescribed by an intension can be composing elements of, and/or certain external unions among, would-be subjects. Significantly, it is the possibility of foundations being external connections that is ignored under the inherence model of attribution. For entities that are absolutely simple, such as intensions, e.g., Parthood2, the foundations for intrinsic attributes of them, e.g., Is-Dyadic1i, are just the entities themselves. In all cases the relevance of an intension to its foundations is why knowing a subject’s attributes tells us something about the subject, and is the warrant for the common maxim that we have no epistemic access to entities except through their attributes. The point is made dramatically with ‘category mistakes’. For example, the proposition that ‘Rock r loves Mary’ is a category mistake, what as such is absurdly false because among the foundations the intension Love2 prescribes for its subjects is that the first be an entity capable of certain emotional states, and a rock cannot possibly have these. There are no analogs to category mistakes with arbitrary associations. Importantly, the foundations prescribed by an intension Rn can also be in part those for other intensions, and this makes possi-

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ble definitions of Rn using other attributes—identification by a kind of ‘foundational parallax’, e.g., by ‘operational definitions’. It is characteristic of an advance in knowledge, for us individually and collectively, that intensions for some predicate terms are replaced over time as the foundations required for their attribution change to conform to conventional usage or are refined by observation and analysis, e.g., as the intension for ‘is water’ expands along with its prescribed foundations from those for a child’s ‘is a refreshing clear and odorless fluid’ to those for an educated adult’s ‘is composed of H2O molecules’. It would seem a tacit assumption by some that, contrary to the above, spatial and temporal relations are ‘completely external’ to their relata in the sense that their intensions put no conditions on and are irrelevant to anything about— require no specific foundations be had by—their subjects except existence. Yet if this were the case, it would make spatial and temporal relations not attributes with each its own differentiating intension, but simply arbitrary associations. Even ‘naturalists’ who would make being relata for such relations a universal criterion for existence presuppose that their instances are not randomly assigned and subject indifferent, but that their intensions specify certain composing foundations that their relata must have in order to be so related and on this so exist. Among the entities that naturalists wish to eliminate (by various reductionist strategies) as not having the prerequisite composing foundations are numbers, intensions, sets, propositions, and instances of numerical and logical relations. Indeed, it is nonsensical (as category mistakes) to say, for example, that 2 is some distance from 5 or that Red1 is temporally related to Yellow1, or, with ‘semantic ascent’, to say that these two propositions themselves are relata for spatial or temporal relations. But none of this is relevant to the ontic status of these subject entities nor gives spatial and temporal relations a special status as a criterion for existence, this on the simple observation that instances of spatial and temporal relations are not themselves relata for instances of spatial or temporal relations. Intensionally specific spatial and temporal relations, like all attributes, require foundations, and for them some are internal to their relata and some external. The foundations internal to their relata are what are presupposed by referring to these relata as ‘physical’ or ‘concrete’, and the absence of which is meant by calling entities ‘abstract’. And foundations external to the relata of spatial relations are instances of other specific spatial relations on these objects. Indeed, definitional of the relational theory of space (or spacetime) is that the intension of a spatial relation, e.g., Left2, will specify as necessary external foundations for the relata of its instances only instances of various other spatial relations, e.g., those constituting orientation relative to a point of observation. For, on the relational theory, space is just the dynamic complex

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structure of all facts consisting of physical objects standing in instances of spatial relations, and there is nothing else available to define and support the existences of composing instances of spatial relations other than contexts of other composing instances of spatial relations. This description is near-analogous to and is bolstered in its plausibility by what I claim must constitute the composition of an atomic ontic stratum, viz., a closed system of mutually supporting attribute (property and/or relation) instances, this possibility perspicuously explained in Section 5.2. The relational theory of space stands in contrast to a substantival conception that takes space to be a plenum of dimensionless spatial points, spatial relations then obtaining among these, or sets of, ‘spatial substances’ as their necessary relata, and objects then being subjects of instances of spatial relations in a derivative way by being related to sets of spatial points by instances of the At2 relation (cf. Sect. 2.6). Here spatial relations emerge upon or are reducible to certain n-tuples of more fundamental points or sets of points. On the substantival theory space could exist devoid of all occupying objects, but not so for the relational theory. It is a commonplace that modern physics favors the relational theory of space, though details remain unclear and controversial. This work is intended in part as providing clarifications of these issues and details of how the relational theory is possible. Further, I note as an ontological argument against the substantival alternative that its dimensionless points would seem to be nothing but bare particulars posited as necessary relata to spatial relations (e.g., Theodore Sider’s suggested assay of space-time points in support of bare particulars (Sect. 2.4)), and it was argued in Chapter 2 that the notion of a bare particular is incoherent. Analogous points to the above can be made regarding temporal relations, or combined as spatialtemporal relations. Reinforcing some of the above points, I would, first, re-emphasize how the classic and erroneous inherence model (A5 and its generalizations) recognizes attribute-subject relevance. It does so by identifying the foundations for an attribute with the attribute, either as an instance or intension, and then holds that the attribute itself founds its relevance to its subject(s) by being a constituent of it(them). As observed, this assay is both the underlying, if tacit, motivation for bundle theories, and is antithetical to relation attributes. Central to the ontology advocated herein are the theses that an attribute through its intension prescribes and so is correlative with—‘meshes with’ and is thus informative of (like the shape of a key is to the mechanism of a corresponding lock)—but is distinct from its foundations, what is prerequisite for polyadic relations, and that these foundations are not necessarily components of their subjects (the lock in these cases being disanalogous). And, though the foundations that

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intensions specify can be multiple and complex, themselves involving articulated wholes by either attributions or associations, intensions themselves are simple entities—would-be complex intensions are just two or more intensions each prescribing its own foundations, and ultimately such intensions must be simple. It is worth noting also that the relevance/mesh but not identity of an attribute with its foundations answers the ‘old dilemma’ made prominent by F. H. Bradley. Viz., “If you predicate what is different, you ascribe to the subject what it is not; and if you predicate what is not different, you say nothing at all.”8 The first part of the dilemma could be re-written as the false assertion: “If you attribute to a subject an attribute that is not a part, proper or improper, of the subject, then you ascribe to the subject an attribute whose foundations it prescribes are not satisfied by the subject, and so an attribute the subject cannot have.” The naïve and rejected assumptions here are that an attribute is identical to its foundations and that a subject satisfies these foundations by having them as parts. Second in reinforcing the central point concerning how intensions Rn set prerequisite conditions on subjects in order for their instances Rni to characterize them, we can observe briefly its relevance to, and I propose some clarification of, the classic distinction of intrinsic versus extrinsic attributes, and relatedly the distinctions of necessary versus contingent facts. First, in the literature intrinsic attributes are described as those that depend upon what their subjects are like ‘in themselves’, and not with respect to other entities. Members of the subclass of intrinsic monadic properties are sometimes described as founded even in ‘contracted’ worlds where their subjects would exist ‘alone’.9 Now on our assay, there are attribute intensions Rn such that, among the foundations they prescribe for each of some n subjects, those prescribed for a k-th subject ak, 1 ≤ k ≤ n, are all internal as part of the composing identity-bestowing being of ak. I.e., for an instance of Rni to have ak as its k-th subject, intension Rn does not require of ak that it have any external unions, attributional or via associations. In this way such an instance Rni, and by extension the intension Rn, is ‘intrinsic’ to ak. An instance Rni, and by extension the intension Rn, that is intrinsic to all of its n subjects is, I propose, what is intended by ‘intrinsic attribute’. Examples

|| 8 F. H. Bradley, Appearance and Reality (Oxford: Clarendon Press, 1978; reprint of 2d. ed., 1897), p. 17. 9 Robert Francescotti, ‘How to Define Intrinsic Properties’, Nous 33 (1999): 590–609. Rae Langton and David Lewis, ‘Defining ‘Intrinsic’’, Philosophy and Phenomenological Research LVIII (1998): 333–45. Gene Witmer, William Butchard, and Kelly Trogdon, ‘Intrinsicality without Naturalness’, Philosophy and Phenomenological Research LXX (2005): 326–50.

178 | 4 Atomic Structures: Facts and Their Natures of intrinsic attributes would be Is-Individual1i, Has-Mass1j, Is-a-Vertebrate1k, IsExtended1m, Is-a-Component-of2o, Is-Contrary-to2p, Implies2q. The non-attributional intensions here, what are ‘intrinsic attributes’ in a derivative sense, I would then term, respectively, Individual1, Mass1, Vertebrate1, Extension1, Component2, Contrariety2, Implication2. Complementary to intensions that are intrinsic are those termed ‘extrinsic attributes’, what are described in the literature as characterizing their subjects because of the latters’ ‘accompaniments’.10 Clarified on our assay, an extrinsic attribute intension Rn is one that prescribes for one or more subjects in each of its subject n-tuples foundations that are external unions—either attributions or associations—with other entities. E.g., such attributes, again properly as instances, would be Is-a-Roof1i, Is-Famous1j, Sits-on2k, Is-One-Meter-from2m, Occurred-an-Hour-Before2n, Caused-the-Collapse-of2o. The respective non-attributional intensions could be termed, respectively, Roof1, Fame1, Sitting1, OneMeter-Distance2, Hour-Precedence2, Collapse-Causation2. In the case of prescribed foundational unions external to the subjects of these attributes, they themselves make up structured or non-structured plural wholes subsuming these subjects.11 Some extrinsic attributes require among their foundations some that are also internal to their subjects, e.g., spatial relations as I have contended above. As an example of a pure extrinsic attribute, consider a fact that s is a subject (of an external unifying agency), i.e., :Is-a-Subject1i(s). The intension Subject1 (or Subjecthood1) requires nothing specific of the composing nature of s, but requires of s only that it be in an external union with something else, what is either an attribute or an association.12 Now, in addition to the intrinsic|extrinsic distinction there is the related necessary-fact|contingent-fact distinction. That is, intuitively the modal properties of de re necessity and contingency are attributes (through their instances) of facts, and our analysis is relevant in suggesting the following definitions. A

|| 10 Ibid. 11 The question might be asked: If for an instance Rni its external foundational unions are attributes (as opposed to associations), the latter themselves having foundations, will these foundations be included as a subset of those of the original attribute Rni? It would seem yes, but I confess to being somewhat uncertain. Perhaps my difficulty turns on confusing epistemological with ontological issues here. 12 I observe here the subtle point that an association between a and b, a+b, has a corresponding but non-identical fact :Is-Associated-with2i(a,b). In the fact the attribute’s extrinsic intension, Association2, is non-arbitrarily descriptive of—has as its foundations—external aspects of each of a and b existing because of the prior non-attribute association, viz., that each is arbitrarily linked with the other.

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necessary fact :Rni(a1,a2,…,an) is one where ‘things ordered as could not have been otherwise than as Rn’, and what this means on our assay is that given the existences and identifying beings of each subject in, and in the order of, an n-tuple , they could not not jointly satisfy the conditions prescribed by the intension Rn. Or alternately, given the identifying beings of these subjects, their existences as such presuppose, in the sense of logically imply, the foundations for the intension Rn, and therefore they could not have existed without an instance Rni attributional of these subjects. E.g., that the measure of the internal angles of a Euclidean triangle is equal to two right angles is a necessary fact, and this is so because the properties that are the subjects in have as what is defining of them foundations satisfying the intension Is-Equal-in-Internal-Angular-Measure-to2, and so could not be what they are without having an instance of the latter intension as an attribute. This is seen in the sequence of logical inferences that yields this theorem. In contrast are contingent facts where ‘things might have been different’, i.e., ‘things ordered as (e.g., ) could have been otherwise than Rn’ (e.g., Is-Shorter-than2). With a contingent fact :Rni(a1,a2,…,an), though the subjects and in the order of do ‘as it so happens’ satisfy intension Rn, and so an instance Rni jointly characterizes them, one or more of identically the same subjects could exist without their satisfying the foundational conditions prescribed by Rn, and in that case an instance Rni would not exist among all of them. E.g., for the fact :Is-Shorter-than2i(Socrates,Plato), the existence and identity of neither subject, Socrates or Plato, presuppose the particular spatial conditions required to found the Is-Shorter-than2 intension and thus the fact is contingent. More precisely, then, I would propose the following definitions: If a subject ak of an instance Rni depends for its existence and identity upon the obtaining of the foundations prescribed by intension Rn, then ak necessarily has (could not not have) Rni. Otherwise ak contingently has Rni. Then in total, if each subject in an n-tuple necessarily has Rni, then resultant fact :Rni(a1,a2,…,an) is a necessary fact. Here we would have the higher-order fact of :Nec1j(:Rni(a1,a2,…,an)) where ‘Nec1j’ designated an instance of the intension Necessity1. If things are otherwise, then the fact :Rni(a1,a2,…,an) is a contingent fact, and we would have the higher-order fact :Con1j(:Rni(a1,a2,…,an)) where ‘Con1j’ designates an instance of the intension Contingency1. And by terminological extension, instances Rni, and derivatively their intensions Rn, of necessary facts would be designated ‘necessary attributes’, and otherwise, ‘contingent attributes’. In its favor, this analysis extends directly to de dicto necessity and contingency. E.g., as with assertions of the form: ‘Proposition p is necessarily true’.

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Here we simply extend by ‘semantic assent’ to propositions the de re analysis of facts, e.g., :Nec1j(:True1i(p)).13 Concerning the latter example, the fact :True1i(p) has the attribute of being necessary because the subject proposition p could not not satisfy the conditions prescribed by the attribute Is-True1. And the latter is the case, for p in its simplest form of having as a referent a single fact :Rni(a1, a2,…,an), when the fact :Nec1j(:Rni(a1,a2,…,an)) obtains. When p is a complex proposition, its de dicto modality would also be a function of the logical connectives involved. Given the above definition of intrinsic attributes, i.e., instances with intensions all of whose prescribed foundations contribute as components to the identities of the instances’ subjects, then every fact whose attribute is intrinsic is a necessary fact. Our assay of attribute instances makes those of Resemblance-F1ly2 for some definite F1, e.g., as in fact :Resembles-Red1-ly2i(Red1j,Red1k), examples of intrinsic and so necessary attributes—intrinsic in having as foundations only the intensional components of the subject instances, and necessary in that given just the existences of these relata in their composing identities we have the foundations sufficient for the existence of an instance of the relation Resemblance-F1-ly2, and so it is impossible that the emergent fact not exist. Other examples of intrinsic and thus necessary attributes would be instances like IsIndividual1i, and Implies2j—if the latter obtain on subjects, the same subjects could not, ‘under any other external circumstances,’ not have these attributes and yet retain their same identifying beings. Here I observe a plausible alternative definition for essence (cf. A4): the essence of an entity x is jointly all the foundations for the necessary intrinsic attributes of x.14

|| 13 See Colin McGinn, Logical Properties (Oxford: Clarendon Press, 2005), p. 79, for a similar account of de-re/de-dicto modality where the latter is by ‘semantic ascent’ on the former. McGinn treats these modalities as ‘modes of instantiation’, whereas I propose they are attributes of facts. 14 These distinctions may also provide some clarification of the semantic analytic|synthetic distinction. On the Kantian definition, analytic propositions, e.g., ‘7 + 5 = 12’ and ‘All bachelors are unmarried’, are true and necessarily so because ‘their predicates are contained in their subjects’, whereas for synthetic propositions, e.g., ‘The moon has water’ and ‘All bachelors are unhappy’, this is not the case. Sharpening these intuitions, on the above, analytic propositions are such and necessarily true because the foundations prescribed by the predicate’s attribute are a subset of those had necessarily by (required for the identity of) the subject. In the case of propositions where subject and predicate terms designate attributes, e.g., are of the form ‘All F’s are G’s’, the proposition is analytic when the foundations for G, e.g., Is-Unmarried1, are a subset of those for F, e.g., Is-a-Bachelor1. So necessarily, to be an F is to be a G. In the case where the subject-term is an object (Sect. 2.1), e.g., of the form ‘a is F’, the proposition is analytic when the foundations for F are had necessarily by (required for the identity of) a. However,

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However, there are also necessary facts whose attributes are extrinsic, i.e., ones where the subjects depend for their existences and identities upon external unions. For example, an intension Circle1 is a necessary extrinsic attribute— extrinsic because the intension Circle1 prescribes as foundations for a subject curve c the external conditions that all points composing c be equidistant from a non-constituent center point, and necessary because the subject curve c would not exist and have its identity if it did not satisfy these conditions. In this way fact :Is-a-Circle1i(c) is a necessary fact. The relation Is-Prime-Divisor-of2 is also a necessary extrinsic attribute: it is extrinsic in that it requires of its subjects that they be subjects of certain other mathematical division relations, and necessary because the subjects of this relation would not have the identities they do if they were not subjects of these other relations. In contrast are, for example, instances of the relation Ownership2 as in a fact that a owns b, instances that are contingent extrinsic: extrinsic in having as required foundations certain external moral and legal relationships between owner and thing owned, and contingent in that neither subject requires for its existence and identity these foundational unions—both subjects could retain their identities and not be so related. Illustrating an interesting sub-type of contingent extrinsic relations is the historically often-used example of Fatherhood2. Let it be a fact that Abraham is the father of Isaac. Here Abraham and Isaac are linked attributionally under the intension Fatherhood2 and so have the respective foundations the intension requires and that are spelled out in its definition, viz., a) that internally the subjects be certain biological creatures, the first a ‘male’, and not, e.g., rocks or numbers, and b) that externally the subjects be part of a certain diachronic causal structure where the first ‘male’ subject initiates as a cause this sequence which has the second subject as a product. Consistent with what is described in the literature as ‘origin essentialism’, these foundations/conditions are had contingently by Abraham—his identifying being does not depend upon or imply his having all of the requisite foundations for being the first relatum in the relation of Fatherhood2, yet are had necessarily by Isaac—Isaac would not exist as the being he is if he did not satisfy all of the relevant conditions set by the intension Fatherhood2. So in general, an instance Is-a-Father-of2i will be for its second subject necessary extrinsic, whereas for its first subject it will be contingent extrinsic, with the emergent fact then classified as contingent. It is instructive to see our proposed account of necessary and contingent facts alongside of the evolving assays of Armstrong. Initially he held, as I read || depending upon F, the foundations prescribed for a and had necessarily by it, may or may not be intrinsic to a.

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him, that for contingent facts to be possible the instantiation nexus or tie between subjects and an attribute (for him what is an intension universal) cannot flow from the natures of either, i.e., from any kind of qualitative relevance, fit, or mesh between them.15 If it were otherwise, then the view was that the existences of subjects conforming to—‘fitting’—the foundations required by an attribute intension would make the resulting fact a necessary one, contingent facts then being impossible. What this view does is, in effect, to make instantiation between an attribute and its subject(s), if between distinct entities (as I hold they are), just arbitrary association. We saw this with Hume (Sect. 3.4), and Armstrong seconds Hume’s Dictum in the form: “There are no necessary connections between wholly distinct existences.”16 (Armstrong’s italics) But subsequently Armstrong had a change of view: that the instantiation nexus is in every case a necessary one under his assay of instantiation as ‘partial identity’ of a subject particular and a property universal. Adapting a proposal of Donald Baxter, Armstrong holds that in the ‘partial identity’ that is instantiation “property-universals are actual parts of the particular,” and for any of these universals “it will be necessary that the particular instantiates that universal.”17 (Armstrong’s italics). Yet despite all of this, Armstrong argues that all resulting states of affairs (facts) are contingent. This is so because the existence of particulars are contingent, as is that of universals, on his view, and so “therefore, the states of affairs involved are also contingent beings.”18 I.e., the partial identities that make for states of affairs might not have existed since neither the subject particulars nor attribute universals need have existed. Now, this account of contingent facts has been challenged, e.g., by Peter Simons19, but here I

|| 15 Armstrong, Universals, p. 109. Also Armstrong, A World of States of Affairs, p. 267. 16 Armstrong, A World of States of Affairs, p. 263. 17 D. M. Armstrong, ‘Particulars Have Their Properties of Necessity’, 2004 Pufendorf Lecture, Lund University, Sweden. Available at http://www.pufendorf.se/2004_lecture_4.html. Also, Armstrong, ‘How do Particulars stand to Universals?’, in Oxford Studies in Metaphysics, Vol. 1, Dean Zimmerman (ed.), (Oxford: Oxford University Press, 2004). Donald Baxter, ‘Instantiation as Partial Identity’, Australasian Journal of Philosophy 79 (2001): 449–64. I note that Armstrong in discussing instantiation in his 2010 survey of his positions does not mention the ‘partial identity’ thesis but says he has a “new suggestion to make”. It is that universals must be instantiated by particulars and particulars must have properties, and so apparently sufficient jointly, “There would then be a mild necessary connection between particulars and universals, and this would be the ‘fundamental tie’ [of instantiation]”. (my insert) This in D. M. Armstrong, Sketch for a Systematic Metaphysics (Oxford: Clarendon Press, 2010), pp. 32–33. 18 Armstrong, ‘Particulars Have Their Properties of Necessity’. 19 For a critique see Peter Simons, ‘Negatives, Numbers, and Necessity: Some Worries about Armstrong’s Version of Truthmaking’, Australasian Journal of Philosophy 83 (2005): 253–61.

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would only point to, on what I have argued, would be Armstrong’s fundamental nullifying error, viz., his adopting the inherence conception of attribution. I have argued against inherence in previous chapters, including as a principal flaw its forcing the elimination of polyadic relations. In particular, we have seen how Armstrong’s current strategy for reducing external relations to structural properties fails (Sect. 2.6). Our above assay of contingent and necessary facts both clarifies points broached by Armstrong and avoids the errors of inherence and relation reduction. For in brief, it is on the conditions that a) an intension Rn specifies certain necessary and sufficient requirements that subjects must satisfy, and, b) the entities of some n-tuple respectively satisfy these requirements, that then necessarily an instance Rni has these entities as a subject n-tuple. Or in short, if conditions a) and b) are satisfied, then necessarily there exist instance Rni and its resultant fact :Rni(a1,a2,…,an). But, this does not make the latter a ‘necessary fact’ as clarified above. Rather, :Rni(a1,a2,…,an) is a necessary fact only if conditions a) and b) are necessarily satisfied, and this particularly for b) means that the requirements set by Rn are necessarily satisfied by the respective subjects in . Yet the latter is the case only if these entities depend for their respective identities and existences upon these requirements. If so then things could not have been different than asserted in the fact. With the examples facts :Is-Even1i(4) and :Has-an-Appendix1j(Socrates), the first fact is necessary because the requirement set by the intension Even1 for its subjects, here of 4, is necessary to the existence of 4, whereas the second fact is contingent because the requirements set by Appendix-Possession1 for its subjects, here Socrates, is not necessary for the existence and identity of Socrates— as usually defined, Socrates could retain his identity without an appendix. Importantly, these results—that an attribute intension Rn sets necessary and sufficient conditions on an n-tuple of entities such that if these subjects respectively satisfy the conditions then there is necessarily an emergent unified fact—combined with the results for the next section—that fact-effecting unity is via the combinatorial agency of the attribute—provide an explanation of our intuitions that, contra Hume and Lewis, there are necessary connections between distinct existences. The above intrinsic|extrinsic distinction also sheds light on what in the literature is the confused debate over ‘internal’ vs. ‘external’ relations. For example, in the classic debate between Russell and Bradley, Russell’s arguments for ‘external’ relations is for the above pure extrinsic relations, this giving his position maximum contrast with Bradley’s ‘internalist’ view that Russell characterized, in part, as holding that all relations are intrinsic. More specifically, he

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described Bradley’s ‘Doctrine of Internal Relations’ as asserting “that every relation between two terms expresses, primarily, intrinsic properties [i.e., foundations] of the two terms and, in ultimate analysis, a property of the whole which the two compose.”20 (my insert) The latter point is clarified when one understands Bradley as asserting, in addition to all attributes being intrinsic, that attributes are to be identified with their foundations, and that these foundations are essential to the beings of their subjects. We saw in Section 3.2 how this can make the relation a ‘property of the whole which the relata compose.’ We also observed in Section 2.6 how recently Armstrong, in keeping with a common view, has termed as ‘internal’ any relation whose existence in unifying a set of relata is entailed by the existences of these relata.21 And, he proposes that such relations ‘supervene’ in adding nothing to reality—have no separate being—over and above their subjects, whereas ‘external’ relations, whose subjects in themselves are not sufficient for guaranteeing the foundations in order to be so related, thereby have a reality beyond these subjects. Internal relations are then an ‘ontological free-lunch’. Now, in addition to the critiques of Section 2.6 against this reductive elimination of internal relations, our current work allows us to add the following. First, note that Armstrong’s ‘internal’ relations, in order to have no being beyond that of their subjects, must be our intrinsic attributes, i.e., their foundations—what is prerequisite for their existence—must all be constituents of the defining identities of these subjects. If such an attribute was also to require foundations external to its subjects in their defining identities—some external unions—then the attribute could not be identical with, and so reduce to, just the narrower beings of its subjects. Yet, this is in fact what is required of at least some paradigm internal relations called ‘comparatives’, such as Is-Taller-than2i. For example, the fact that a is taller than b is held to reduce without remainder to, or to what founds, monadic properties of height had by each of a and b, say, that a is 6 ft. tall and that b is 5 ft. tall. However, what goes unrecognized is that properties like Is-6-ft.-Tall are indeed extrinsic, e.g., the foundations for the obtaining of an attribute Is-6-ft.-Tall includes not only the subject’s internal spatial extension, but also this extension being isomorphic to a portion of an external standard of linear feet. Analogously for the attribute Is-5-ft.-Tall. It is isomorphisms to portions of this standard, what is external to both a and b, and

|| 20 Russell, My Philosophical Development, p. 42. Also see Russell, ‘The Basis of Realism’, 1911, in Stephen Mumford, ed., Russell on Metaphysics (London: Routledge, 2003), pp. 85–90. 21 Armstrong, A World of States of Affairs, pp. 87–94.

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the subsumption of one measure by the other, that is necessary to found the fact that a is taller than b. Consider as another standard example of an internal attribute, one supervenient according to and in the reductive sense of Armstrong, the previously referenced Resemblance2 relation. As utilized above and as often asserted, things do not just resemble, but always resemble-in-some-specific-respect-F1, i.e., a resembles-F1-ly2 b, e.g., a resembles-Red1-ly2 b, or a resembles-Square1ly2 b. Now, in an example like a resembles-Square1-ly2 b, the foundations for the entire dyadic attribute, what on our assay is some instance ResemblesSquare1-ly2i, are taken to be those required under the sub-intension Square1, the latter then taken to be intrinsic to each of the subjects. In this way instance Resembles-Square1-ly2i would be held to reduce to nothing but components of these subjects. But, in fact, for all F1, all instances Resembles-F1-ly2i are extrinsic, and so not so reducible. For, even if it is the case that for the fact :Resembles-F1-ly2i(a,b) the intension-part F1 prescribes only intrinsic foundations to a and b, the intension-part Resemblance2 requires a match through an external comparison of each subject’s F1 foundations with those of the other subjects. This comparison is not (an instance of) the relation Resembles-F1-ly2, but is prerequisite to it. Because of this, instances Resembles-F1-ly2i cannot be eliminated in favor of just their relata.22 In passing I would also offer a proposal for making precise the commonly observed but contentious distinction between sortal (‘substantival’) intensions, e.g., Tiger1, Planet1, Table1, and non-sortal intensions, e.g., ‘mass’ intensions such as Water1 or Clay1, and ‘adjectival’ intensions, e.g., Red1, Extension1, Thing1. Peter Strawson’s classic offering is that “A sortal universal supplies a principle for distinguishing and counting individual particulars it collects.”23 All other intensions are non-sortal. I.e., a monadic intension F1 is sortal if a subject a in satisfying the conditions prescribed by F1 is numerically differentiated from and so countable together with any other entities satisfying the conditions prescribed by F1. In this way it makes sense to say, for example, ‘There are two tables’ but not to say ‘There are two reds’ or ‘There are two waters’. The || 22 I would argue that the comparison here is a cognitive act/event, like association, and thus being in mente is a motivation for some to discount its reality. But, having an ontic dependence upon a mind does not make certain operations, nor the facts they effect, unreal, any more than each attribute being ontically dependent upon its subjects makes it unreal. 23 P. F. Strawson, Individuals (London: Methuen, 1971), pp. 168. For an overview of problems with sortals see Richard Grandy, ‘Sortals’, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = .

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latter would make sense only if they are to be understood as compressed ‘restricted sortals’, e.g., ‘There are two red balls’ and ‘There are two cups of water’. And so I propose: an intension F1 is sortal if and only if the foundations in a subject a required by F1 in order for an instance F1i to characterize a are sufficient to prevent another entity b, a ≠ b, and that shares its being with a, to also be characterized by an instance F1j. Or more succinctly: a monadic intension F1 is sortal if and only if, for any entity a, if a fact :F1i(a) were to obtain, it is not possible that there is an entity b such that a ≠ b, b shares part of its being with a, and fact :F1j(b) obtains. Otherwise, monadic intension F1 is non-sortal. For example, let a be a planet. It is not possible for there to be something b such that a ≠ b, b shares part of its being with a, and b also satisfies the conditions set by the intension Planet1. However, if a is, say, water, then it is possible for there to be a b, e.g., some sub-quantity of a, such that a ≠ b, b shares part of its being with a, and b is water. With the latter we see that a and b having the foundations for satisfying the intension Water1 is not sufficient to render them numerically distinct and distinguishable, and so countable. It is appropriate here to observe the relationships between intensions and their foundations and the corresponding extensions. First, intensions Rn and Sn are identical (i.e., synonymous) if and only if the foundations prescribed by each are the same. And, if intensions Rn and Sn are identical then their extensions are identical. The converse is, of course, not the case, e.g., the intensions Equilateral-Euclidean-Triangle1 and Equiangular-Euclidean-Triangle1 are not identical, though their extensions are. Now, an implication is that if the extensions of intensions Rn and Sn are not identical, then neither are these intensions nor their prescribed foundations the same. We can use this fact and the above identification of intrinsic intensions to make a succinct argument against per se subjects and so prime-matter or bare-particulars as implied under classic assumptions A1, A3, and A6—what require that such entities be both simple (in the broad sense of not having non-identical components (Sect. 4.6)) and particular/individual. That there can be no such entities is seen as follows: Let x have both attributes of the intensions Simple1 and Individual1. Both intensions are intrinsic as defined in Section 4.2 and so each has all its prescribed foundations as components of x. These foundations, however, cannot be numerically the same. For, there exist a myriad of individuals—indeed, most things of ordinary experience—that are not simple. Hence, because these extensions are not the same neither are the intensions nor their prescribed foundations that are constituents of x. Thus x is composed of non-identical components—is complex—and this contradicts the initial assumption that x is simple. In short, for

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an entity x to be individual, it must be complex. This is in line with the analysis herein that the ontically basic individuals are complex attribute instances.

4.3 Assaying Attributes as Intensioned Combinators We now have the proper context to take up the question whose answer is fundamental to this work and to all ontology in its broad and synthesizing implications: How, precisely, are we to understand the nature of the unity that is attribution/ontic-predication? Anticipated and picking up some inductive warrant in prior chapters, the answer I shall now argue for directly is summarized in the principle: T3. In a fact :Rni(a1,a2,…,an), the characterizing attribute (instance) Rni functions as an intension-determined agent-combinator, i.e., by means of a constituent externally-directed agency, Rni is the cause of a sustained union of itself with and among its intensionally relevant subjects/relata, a1, a2, …, an. The attributional unity that Rni effects preserves itself and its subjects as each discrete, and is such that Rni is completely external to each subject—Rni is not a component of the beings of any of its subjects. As intrinsically an outward-directed unifier, an attribute Rni is ontically dependent upon concomitant subjects as recipients of its unifying agency. Hence, the Principle of Instance Instantiation: Attributes proper do not exist independently of their subject n-tuples, and hence do not exist independently of the subsuming facts whose unities and so existences they effect. The founding and potent insight here is the general one—essential to both attributions and associations—that every plural whole is a controlled unification across the discrete, i.e., a unity that is both a bridging of each element’s otherwise isolation from the others and correlatively one that ‘selects’ just these joined entities and not others. All unity among the discrete requires what is jointly a collecting and selecting of the entities unified. These two aspects, and the ‘directedness’ they each (though differently) presuppose, are what give any plural whole its identity as a singular and differentiated being, distinct as such from every other unit entity, including other collections. It is essential, then, to plural wholes—facts, complex structures, sums, etc.—that they each have as constituents one or more principles/sources of this selective trans-entity linking. In particular and of its essence, a whole of discrete elements requires one or more of these parts to have the ontic role of outwardly directed unifiers—

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unifiers whose natures as such are ‘to-go-beyond-themselves’ to effect connections to and among the other elements, and just these. I.e., each such unifier must be the cause of—bring about the existence of—something beyond its own composing being, viz., an external union or nexus with a target subject or subjects (‘patients’), both union and subjects being non-identical to (other-than) this source. Without a category of entities whose natures are to outwardly bridge ‘ontological distance’ and ‘hold themselves together with’ things with which they share no composing being, i.e., without entities that are ontoglial (Greek: ‘glue of being’), discrete entities would each remain absolutely isolated from every other. Every entity would exist as a radically segregated atom, an extreme ‘monad’ completely devoid of inter-connections—physical, cognitive (e.g., associations), etc., with any others—and with any such entity, because of this total mutual isolation, no mind (assuming per impossibile there are minds, what necessarily are dynamically functioning structures) would have epistemic access since this would require real epistemic relationships linking knower and known-other. The latter points, I urge, to the fact that polyadic relations as a category are intuitively obvious examples of ‘outwardly directed connecting and selecting’ entities, an ontic role we will clarify as had by all attributes. Also, a plural whole as intrinsically certain-elements-linked, requires the ‘selecting-links’ be as essential/intrinsic to and parts of the whole as the elements unified, i.e., be elements themselves. To deny this is to either confuse internal unifiers with external efficient causes that effect them, the latter being remote causes of the wholes effected immediately by the constituent unifiers24, or to confuse the effect of unifying agency—the whole—with a cause of this agency, the error, for example, of taking sets or sums to be the causes of the unities of their elements. The latter confusion is abetted by the inherence metaphor for attribution (see Sect. 2.6). The crucial point in these observations is: Every plural whole composed then of discrete entities must have at least one element that can bring about something other than and not constitutive of itself, viz., a union of itself with others whereby all and just these exist jointly as the singular whole. This

|| 24 In this I argue the contrary of a view advanced by William Vallicella that the unity of factual wholes requires external agency. See his ‘Three Conceptions of States of Affairs’, Nous 34 (2000): 237–59; ‘Relations, Monism, and the Vindication of Bradley’s Regress’, Dialectica 56 (2002): 3–35; and A Paradigm Theory of Existence: Onto-Theology Vindicated (Dordrecht: Kluwer, 2002). For my response see ‘The Nature and Necessity of Composite Simples, E.g., Ontic Predicates’ in Mertz, Essays on Realist Instance Ontology: Predication, Structure, and Identity (Frankfurt: Ontos Verlag, 2006).

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‘achieving-beyond-its-source’ is traditionally termed ‘agency’, from the Latin agere = ‘to do’, and is fundamental to all forms of causation and definitional of the concepts of power, efficacy, production, operating, energy, and the like. But in particular and relevant here, the term agere is used to translate Aristotle’s technical term energeia = ‘at-work-ness’ or ‘functioning’—what scholars emphasize carries for Aristotle the meaning of ‘an exercise of a capacity’ or ‘a capacity in operation’, where, importantly, the ‘doing’ need not involve change or motion.25 Indeed, for Aristotle motion is an incomplete form of energeia.26 Better still, I propose, in capturing what Aristotle intends for its role in the unity of structured entities, his energeia is to be understood as ‘a continuous state of achieving an unchanging state’. Or in expanded form, ‘the continuous bringing about of something determined in its nature by, but external-to/beyond the being of, its cause or source’, and where this ‘achieving’ can be ‘the maintenance of a static state’. E.g., a power-line achieves a continuous state of static pull on each and between two supporting poles. It is this type of constant-state causation that is required to account for any union among discrete things, viz., in its simplest form, a continuous state of achieving (‘producing’, ‘generating’, etc.) by one of these entities of a constant external connectedness with the others—‘a-persisting-unifying-action-across-an-ontic-distance’. Here change oc-

|| 25 Among contemporary authors: Ronald Polansky, ‘Energeia in Aristotle’s Metaphysics IX’, Ancient Philosophy 3 (1983): 160–70; Jonathan Beere, Doing and Being: An Interpretation of Aristotle’s Metaphysics Theta (Oxford: Oxford University Press, 2009); Aryeh Kosman, The Activity of Being (Cambridge: Harvard University Press, 2013). 26 Reinforcing what Aristotle intends by energeia as an outward-achieving-beyond-its-source is his use of the term in characterizing motion. This point has been detailed recently by Kosman, Ibid., focusing mainly on Metaphysics 9.6, Physics 3.1, and De Anima 2.5. Motion as a process of changing from one state to another, i.e., from having one set of attributes to having a contrary set, is characterized by Aristotle as appearing “to be a kind of activity [energeia], but one that is imperfect [i.e., incomplete].” (Physics 201b31; my inserts) On Kosman’s analysis, this is so because for Aristotle motion “is a certain kind of activity, its active exercise of its ability to be other than it is.” (p. 67) Or in my words, at any moment that is part of a motion of x there is by that fact an other-directed achieving by x of a transition to the having of properties it does not now have (e.g., different spatial positions). Insofar as something is in motion it does not complete this transitional achieving and so is incomplete. Motion qua motion is always in the process of achieving its completion. As I understand Aristotle and Kosman’s analysis of him, both motion and energeia proper are to be understood as accomplishing something beyond themselves: a motion qua motion of x being a continuous achieving of a dynamic and uncompleted (i.e., at no time during its existence fully realized) sequence of created and destroyed attributional unions of contrary properties with x; the energeia proper of the substantial form F of x being the continuous achieving of a static and completed (i.e., fully realized at all time during its existence) structured unification that is the attribution of F on x.

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curs only on the cessation of the unifying-agency—the dissolution/destruction of the whole qua whole. Detailing, then, what this must mean: First, a unifying agent’s continuous/sustained act of unification with and among other discrete entities (whose effect is either a fact or a whole by association) is not identical with either the being of the agent (an attribute (instance) or an association) or the beings of the entities unified. However and in distinction with ‘extrinsic’ efficient causation, with the causation of unification the agent and its connecting agency/act contribute their beings jointly to that of the resultant effect (fact or a whole by association)—what is ‘intrinsic’ causation. In this way an effected whole that is an inter-entity unification among the discrete (an articulated unification the scholastics described as among ‘thing and thing’) cannot exist independently of a persisting unifying act, the latter itself not existing independent of a producing agent. And fundamental to my assay, though an act of unification is not identical to its agent (an attribute instance or an association), the act is not separate from that of its agent but is rather a proper part of the agent’s being, e.g., as the combinatorial act of an attribute on its subjects is a component aspect of the attribute (as an instance, (Rni)) along with a controlling intension aspect (Rn). It will be argued in Section 4.6 that these two aspects of an attribute instance—an outwardly unifying agency and an intension that delimits this agency—though not identical, are not discrete as ‘thing and thing’ and so their union does not require one to be an agent-unifier connecting itself with the other. As emphasized, Aristotle ascribes continuous-achieving unifying agency— energeia—to the nature of form in order to explain how when it is an ontic predicate of matter the resultant is an organized whole, in contrast to a mere “heap”. And in general, according to Aristotle, it is this ‘continuous achieving of an external unification’ by an agent (only one by A8) on something(s) that has (have) the potential for receiving it that “is the cause of unity and of a thing’s being one” and whereby “the whole is something besides the parts”. (Meta. 1045a7-b24; also see 1040b5-10, 1041b11-33, 1043b5-14, 1044a4-5) Later Aquinas emphasizes the unifying-act nature of form: “Each individual thing is actually a being through a form, whether in the case of actual substantial being or in the case of actual accidental being. And hence every form is an act, and as a consequence it is the reason for the unity whereby a given thing is one.” (De Spirit. Creat., Art 3)27 Latter still, Suarez would add detail concerning the causality of a substantial form, saying that this causation “can be nothing else besides the || 27 Thomas Aquinas, On Spiritual Creatures (De Spiritualibus Creaturis), trans. M. Fitzpatrick and J. Wellmuth (Milwaukee: Marquette University Press, 1949).

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actual union of the form to the matter”, the point of connection being where the form “exercises its causality”, i.e., its act of unification, with the resulting substance being the effect.28 He asserts that the unification by formal causality, what he terms a “union”, is different from that of efficient causality, what he terms an “action”.29 As I read Suarez, he asserts that with efficient causality the agent-unifier and a unifying act (‘action’) share no being with each other or with the effected whole: The “causality [‘actual union’ or ‘action’] is something really distinct by nature from the entity of the form”, and “the agent, insofar as it is acting [and hence the act itself], remains outside the effect.”30 (my inserts) Whereas with formal causality the agent-unifier form and unifying act (‘union’) share their beings, as they do jointly with matter as all components of the effected substance: In particular regard to the link between agent-form and its act-‘union’, Suarez holds that the union of a substantial form with matter is a ‘mode’ of the form, and that the mode and form exist in “a certain mode of identity”, the two being “not properly distinct”.31 (The unity here is that of ‘continuous composition’ detail in Sect. 4.6.) With substantial or formal causation so described, we have what is my above assay of the type of unification involved in any attributional whole or fact, its analog being the nature of causation involved likewise in wholes by association. Suarez notes a problem, however, with substantial forms that are rational souls, due to their being able to exist independent of unions with matter.32 Because of this their acts of outwardachieving unification cannot be parts of their constituting beings as agents, and in this way, on the above specifications, the unions of such forms with matter are that of efficient causation, and not formal causation. After further consideration he concludes that the union of soul to matter can be of “two kinds of cause, namely, the efficient and the formal.”33 Underlying Suarez’s difficulties

|| 28 Francis Suarez, On the Formal Cause of Substance: Metaphysical Disputation XV, (Disputationes Metaphysicae XV), trans. J. Kronen and J. Reedy (Milwaukee: Marquette University Press, 2000), Sect. 4, Par. 6, p. 83. 29 Ibid., p. 84. 30 Ibid., pp. 83, 84. Also see Francisco Suarez, On Efficient Causality: Metaphysical Disputations 17, 18, and 19, trans. by Alfred Freddoso (New Haven: Yale University Press, 1994), 17, 1,6, pp. 9–10. 31 Francisco Suarez, On the Various Kinds of Distinctions (Disputationes Metaphysicae, Disputatio VII, de variis distinctionum generibus), trans. Cyril Vollert, S.J. (Milwaukee: Marquette University Press, 1947), I, 20, pp. 31–32. 32 Suarez, On the Formal Cause of Substance, Disputationes Metaphysicae XV, Sect. 6, 8, pp. 84–85. 33 Ibid., Sect. 6, 9, p. 85.

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here are the many errors involved in the Aristotelian conception of organizing forms we have pointed out in prior chapters. Properly understood, all attribution involves formal causation in the sense I ascribe to Suarez and as expanded upon herein. Returning to Aristotle, it is worth making a point here in passing. On his energeia theory of form there is established by form qualitatively-specific links among constituents of the resultant substance when these constituents are specifically suited or fit—have a passive dunamis, i.e., ‘capacity’/potency/ability —for the form (classic assumption A7; Meta. 1045b8-24,1046a19-29). Aristotle asserts that dunamis/potency is primarily “an originative source of change in another thing or in the thing itself qua other” (Meta. 1045b11). The active potency of a form allows it to be an agent of unification with subject-others insofar as the latter have a corresponding passive potency for this agency, this, according to Aristotle, being the account of non-random, structured unity. Reconceptual-ized on our assay, every attribute intension has, by the conditions it sets as prerequisite for each of an n-tuple of subjects to have an attribution union under it, an ‘active potency’ for being part of such an act, the n-tuple of subjects satisfying these conditions thereby having a ‘passive potency’ for receiving this act of unification among them. So refining Aristotle’s notion of structuring energeia as relevant to thesis T3 and to all attribution, it was brought into relief in the last section that for every fact :Rni(a1,a2,…,an), e.g., :Is-Prime-Divisor-of2i(3,6) or :Is-Electically-Repulsedby2i(a,b), it is both an intension controlled and a structured unity, the latter via at least the asymmetry of attribution generally, if not by the specific intension of Rni. These are obviously the functions of constituent attribute Rni. What this requires, then, for instance Rni is that in its fact it be a constituent trans-constituent unifier, an entity that as such is the cause of all across-the-whole ordering, and that conditions/constrains the admissibility of its co-constituents, what in these ways differentiates the whole for the corresponding unstructured set. A connecting link unconditioned by a specific intension, i.e., an arbitrary association, cannot satisfy these conditions. And attribute Rni cannot achieve its unity with its subjects by jointly sharing or coinciding in any composing being with them. This is evidenced by the problems with inherence seen across Chapters 2 and 3, and with the ‘meldings’ required by substance monists (Sect. 3.2). More directly, for any contingent fact if its attribute Rni has its unity with its subjects by being wholly and numerically the same component of each of its subjects, then if the fact were no longer to obtain because instance Rni has gone out of existence, then each of the subjects of which Rni is a part of its composing being would, as such, also have to go out of existence, and this is counter-factual.

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Attributes are external unifiers, and so to bridge the ontic gap between themselves and their subjects requires that they act to achieve beyond themselves an inter-entity unification. Hence, it is the nature of every attribute that in one act it both unifies itself with, and qualifies under an intension, subjects that have the intension’s correlative foundations, a nature not restricted to just the select monadic infimae species—forms—to which Aristotle assigned these roles. By T2 an n-adic attribute’s intension sets conditions that constrain its linking agency to or among, and in an order (if any), the subjects of n-tuples that jointly satisfy these conditions. Or in short, every attribute in its defining ontic role as a qualifier of subject(s) is an external intension-conditioned agent-combinator. To re-emphasize a point made above, the outward unification an attribute (instance) effects with its subject(s) is to be understood as a continuous or sustained achieving—a ‘constant exertion’ as it were—persisting as long as the attribute is thus characterizing its subject(s). The assumptions to be avoided are that all causal effects have beings separate from the acts that effect them, and that acts are only instantaneous or over short intervals, e.g., as with the continuing effect-motion of a billiard ball after the brief energy-transfer-act of a prior collision. The unity an attribute instance achieves with (and among) its subject(s) is not just a brief act occurring when the instance comes into existence (what would apply only to contingent attributes), as on a misunderstanding of the analogy of the connecting two boards by an initial act of nailing them together. Even on the latter what holds the boards together are the continual forces exerted by parts of the nails on the respective boards. I would interject here a note on the difference between the ‘directedness’ of an intension Rn and that of a combinatorial act, as intension and act compose an attribute (instance) Rni. The intension is outwardly directed in the (nonmental) intentional sense of being descriptively/selectively-of-something(s)other, whether or not subjects so-described exist, i.e., there is potentiality involved here in that the intension and its directedness can exist whether or not there are subjects that satisfy its conditions. Whereas with the directedness of an attribute’s unifying act (as well as with the unifying act of an association) we have a case of ‘actualism’: the act and its directedness exist only when the act’s subjects/termini exist and it is effecting a union (an energeia) of itself with them. In these ways there are two senses of ‘power’: for an intension its power is dispositional-potential, and for a subsuming instance its power is a state of achieving—an actual enduring exercise—of intension-controlled combinatorialagency. Having powers so understood and with their intensions termed ‘qualities’, it is accurate to say that all attributes are “powerful qualities”. This is the description of attributes given by C. B. Martin and John Heil, though in a differ-

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ent sense.34 Their assay of ‘properties’ is done in a prevailing dialectical context that fails to recognize the outward combinatorial aspect of attributes, and dispositionality, if admitted, is taken to be not an intrinsic characteristic of the intension but, at least for Martin and Heil, as something concomitant with it in composing and being a characteristic of the resultant attribute. In this dialectic the dispositional aspect of attributes, if admitted, is construed as doing all the causal work, and the intension (or ‘qualitative’) aspect is taken to be ‘categorical’ in a Humean sense of a specific quality/kind minus any dispositionality, what within its own nature is totally self-contained and inert, undirected and causally irrelevant to anything else (‘making no difference to its possessors’). All of this is an error on my analysis. Martin and Heil would have what is dispositional about an attribute—what is ‘directive and selective’—to be distinct from the attribute’s intension but to be united with it in way other than in a composition of yet discrete parts, a kind of union they find difficult to explain but what is, I suggest, a misplacement of the kind of ‘continuous composition’ I detail in Section 4.6. On my assay the continuous composition forming an attribute instance is between a dispositional intension and a non-dispositional combinatorial act; the former powerful potentially, the latter powerful actually. It is appropriate here to stress that for an entity ‘to achieve a unification with something(s) beyond itself’ is not for it, contradictorily, ‘to be something beyond or in addition to itself’. To hold otherwise is to require a resultant unification to be internal to the agent of unification, and for attribution the only plausible possibility for such agents would be the subjects. Hence, the bogus inherence conception of attribution. Crucial to ontology, without the sui generis nature of agency as an achieving-beyond-its-source, i.e., the production of a unifying linking by one of the entities linked, there would be among the discrete no unity whatsoever—no attribution or association, neither structures nor sums or sets, and no efficient causation. Indeed, the existence of plural unities, even those minimal ones by Humean associations, presupposes and so demonstrates, contra Hume (Sect. 3.4), the reality of causation at least of the requisite type. The fact of plural wholes of any kind proves the existence of unifying agency. So even associations, Hume’s surrogates for attributions, are, despite his assertions to the contrary, ‘real connexions’, ‘real bonds’, though without the ‘necessity’ that is inherent in attribution, and with them alone and as such the above analysis shows how, contra Hume, we can in fact “comprehend distinctly

|| 34 See references in note 7, and C. B. Martin and John Heil, ‘Rules & Powers’, Philosophical Perspectives 12 (1998): 283–312; C. B. Martin and John Heil, ‘The Ontological Turn’, Midwest Studies in Philosophy XXIII (1999): 34–60.

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that power or efficacy, by which they [associated things] are united” (1.3.14.13; my insert), and in this way how the reason can “give rise to the idea of efficacy” (1.3.14.6).35 It is the abstracting away of this agency and the effecting associations that yield the logical fictions of theoretical sums and sets, what are formally appealing in their conceptual simplicity, but ontologically falsifying. Plural unity via outward-achieving-agency is the warranted mean between the counter-factual extremes of radical atomism, e.g., monadism, and homogeneous monism. For, without unity via mediating agency, the ontic possibilities are the extremes of either the radically discrete in a vacuum of absolute mutual isolation, or a divisionless One in which all differentiating identities are obliterated in a homogeneous blend, both extremes in the end unknowable and ineffable. Concerning the homogeneous One, Bradley’s monistic assumption regarding unification is instructive: the only means of unification is mutual absorbing identity. Observed previously (Sect. 3.1), in the context of analyzing the unity of a relational fact Bradley asserts that a relation must be both a ‘between’ and a ‘together’, i.e., a relation must be both its own entity distinct from its subjects and the means whereby these subjects are unified into a relational fact—“Relations are nothing if not conjunctive.”36 But under his unity-bymutual-absorption assumption the only way a relational unity is possible is for the relation and its relata to “pass beyond themselves” and so “self-surrender” their own separate identities, i.e., contradictorily, for the relation to cease to be distinct from its relata.37 The unified entities “must ‘enter’ one into the other, and yet again are ruined if they do so.”38 That is, for Bradley there is no intension-determined unification via outward agency (what is also Hume’s thesis (Sect. 3.4)), rather unity is only where there is a sameness of being—where two entities overlap identically at a shared part, and to that extent in which the two are unified they are not distinct (Hume, to the contrary, allowing for arbitrary external ‘associations’ among the distinct). But, as seen in Section 3.2, Bradley’s construal of unification via internal-absorption reduces the would-be diverse into a homogeneous One of monism. For an ontology to recognize and account for unity among what remain distinct some constituent must act externally to itself, this being either attribution or association. These constituents

|| 35 David Hume, A Treatise of Human Nature, David Norton and Mary Norton (eds.), (Oxford: Oxford University Press, 2005). 36 F. H. Bradley, ‘Relations’, in Collected Essays, Vol. 2 (Westport: Greenwood Press, 1970), p. 655. 37 Ibid., p. 644. 38 Ibid., p. 638.

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must ‘achieve beyond themselves’ without ‘passing, i.e., being, beyond themselves’, and this is precisely the nature of agency. When the union is descriptive of the entities unified, this agency is attribution (T3). The externality of all attributes contradicts classic assumption A5 (Inherent Essential Attributes) and so prevents as a consequence the Dependence Contradiction and Individuation Regress of Section 2.3. Important for avoiding confusion is the recognition that there is no unconditioned/uncontrolled agency—no undirected just-doing. (This, and relatedly by T4, any more than there are just-individuators (e.g., bare particulars).) All exercises of outward-achieving are either controlled by intensions and their objective relevance to internal and/or external foundational aspects of the objects of the agency (i.e., are attributions resulting in facts), or are controlled by external psychological mechanisms (involving will or not) in subjective associations external and indifferent to the objects of the unifying agency (e.g., are willed associations as in memorizing a list). Arbitrary associations are products of minds, but minds themselves are cognitive-neural structures emergent upon a hierarchy of biological-physical structures composed of facts, facts themselves plural wholes via the agency of attribution. In all of this, attributes proper are the underlying ontoglial. And, the denial of the objectively-founded unifyingagency of attribution, what Hume meant in asserting there is no “real connection among distinct existences” (1.4.6.16) but only associations that are “for us the cement of the universe” (Abstract, 35; Hume’s emphasis)39, insofar as the denial is argued for, involves a self-contradiction. For, to reiterate a point made in Section 3.4, an argument must utilize implicational structures that have warrant precisely because they are composed of the non-arbitrary attributional unions of logical and semantical facts, yet all of these would be denied on the intended conclusion. An analog would be the absurdity of someone proposing an argument for the thesis that people are completely incapable of rational thought. The ‘cement’ of subject-indifferent association is via the subjective agency of a mind, and is fraudulent and self-defeating when identified with the objective and founded intensional fit of attributional agency—what is in fact, and not ‘just for us’, the cement of the universe. And as a further source of error, because connecting associations are unconstrained by any relevance to aspects of their subjects, they are psychologically facile and so easily ignored, and in this way unities by constituent associations are construed as just the subjects unified. And insofar as the subjects are objective, then these fictional || 39 That intensions (‘qualities’) do not determine outward unifying agency also see 1.3.12.20, 1.4.3.7 and Appendix 20–21.

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wholes are taken to be objective, and since they are unconstrained as to the elements connected, any plurality is as such a whole, hence, e.g., mereology’s Axiom of Unrestricted Composition (Sect. 1.1): Any entities, however disparate and mutually irrelevant, and yet absent any principle of selecting and collecting them, form a single and delimited sum. The delusion here is that ontology gets a free lunch in that any needed plural unity is ready-made, and all without regard for intensions, facts, or minds. Over the Western tradition various philosophers have been explicit about the need for, in effect, agent-combinator aspects of attributes in order to account for their unity with their subjects. We have noted this in regard to the scholastic Francisco Suarez40 and his positing of ‘modes’, though these have as analogs the prior ‘dispositions’ of John Buridan41. With Suarez, the unifying mode that an attribute has with its subject is distinct from the attribute but joined with it in a way closer than ‘thing and thing’—the differentiation of a unifying mode and its attribute being a ‘formal’ one. He held that an attribute (instance) can continue to exist even if its mode of union with a subject is dissolved, as with a soul-substantial-form upon death, or with remaining accidents in the miracle of the Eucharist.42 Here the cause of the unification of an attribute and its subject(s) is not something constitutive of the attribute, but is auxiliary to it. Contrary to this and more recently one finds the unifier nature of attributes, and so their implied dependence (A1), stressed in Gottlob Frege’s metaphorical use of the term ‘unsaturated’ as definitional of ‘concepts’, i.e., attributes.43 What he intended is that attributes themselves—as constitutive of their beings—provide the “liaison” whereby they “adhere” to their subjects. Reverting to the less accurate (on the analysis herein), Gustav Bergmann44 and Peter

|| 40 Suarez, On the Various Kinds of Distinctions, Disputationes Metaphysicae VII, Sect. I, 17–29, pp. 28–38. 41 John Buridan, Questiones in metaphysicam aristoteles, V, Q. 8, fols. 31, 33. Portions translated by Calvin Normore, ‘Buridan’s Ontology’, in How Things Are, J. Bogen and J. McGuire (eds.), (Dordrecht: Reidel, 1985), p. 198. 42 Suarez, On the Various Kinds of Distinctions, Disputationes Metaphysicae VII, Sect. I, 18, p. 29; On the Formal Cause of Substance, Disputationes Metaphysicae XV, Sect. 6, 6, p.83; and Disputatio Metaphysica XXXII, Sect. 1, trans. Sydney Penner, at www.sydneypenner.ca/su/ DM_32_1.pdf, Sect. 1, 18, p.14. 43 Gottlob Frege, ‘On Concept and Object’ in Translations from the Philosophical Writings of Gottlob Frege, P. Geach and M. Black (eds.), (Oxford: Blackwell, 1970), pp. 42–55, and ‘On the Foundations of Geometry’ in Essays on Frege, E. Klemke (ed.), (Urbana: University of Illinois Press, 1968), pp. 559–75. 44 Gustav Bergmann, Realism (Madison: University of Wisconsin Press, 1967), pp. 9, 42ff.

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Strawson45 have emphasized the necessity of an attribute, construed as an intension, to have an accompanying unifying agent, a non-relational “tie” or “nexus” in order to provide the connection of it with its subjects. Presumably, Russell intends this in saying that a relation as it occurs as an attribute in a fact, in opposition to its contribution to a set of the same elements, has the ontic role, relative to the whole, of being an “actually relating relation”.46 All of the philosophers here mentioned observed that the unifying agency of attributes is the answer to Bradley’s Regress, the latter usually directed against the reality of polyadic relations, but what is, as Bradley intended, applicable to attributes generally. Specifically, it was recognized that an attribute must be, or have concomitant with it, a cause of an immediate union of itself with is subject(s), and that it be a ‘non-relational tie’, i.e., that it be ‘closer’ than an otherwise mediated union via a further interposing relation, the latter the start of a vicious regress. To be corrected by our assay under theses T3-T6, Bergmann and Strawson, like the scholastics, confuse an attribute, e.g., Is-Square1i, with its intension-universal component (the error of classic assumption A2), e.g., Square1, what then requires an additional unifier—‘tie’, e.g., expressed grammatically with the copula ‘is’—having the intension and the subject(s) it is said to qualify all as subjects of the tie’s agency. Since to avoid vicious regress (or its arbitrary termination) the tie cannot be a further attribute under Exemplification2 or Instantiation2 47, it must be in fact merely blank association, what we have seen cannot go surrogate for the union of attribution. The subtle but crucial correction is that an attribute is as a single entity a composite intensionconditioned-‘tie’ (detailed in Sect. 4.6), and is not just its component and combinatorially inert intension which would otherwise itself have to be a subject of the needed tie. Coming closer to the correct assay but making, with Frege, the intension-universal itself the agent-tie, D. M. Armstrong, E. J. Lowe, and others refer to the crucial unifying role attributes have in the context of facts or states of affairs as ‘ways’.48 And, an attribute cannot be a ‘way’ “with no thing to be

|| 45 Strawson, Individuals, pp. 167ff. 46 Bertrand Russell, ‘Some Explanations in Reply to Mr. Bradley’, Mind 19 (1908): 373–8. 47 Exemplification2, or Instantiation2, are intensions for real but derivative or secondary formal relations. The fact :Is-Exemlified-by2j(Rni,) obtains only because the prior fact :Rni(a1,a2,…,an) obtains, each attribute instance having its own fact-forming agency, the unifying agency of Is-Exemlified-by2j not being identical with and not accounting for the unifying agency of Rni. 48 Armstrong, A World of States of Affairs, pp. 30, 38, 99 (though at pp. 118–19 he would seem to hold that a subsuming state of affairs (fact) is the cause of the unity of its parts) and Univer-

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that way”49, i.e., attributes cannot exist independent of subjects (classic assumption A1), though they can be isolated in selective abstraction from these subjects. Armstrong argues that this is a justification for his attributes-asuniversals version of my Principle of Instance Instantiation stated in T3.50 Finally and anticipated in previous chapters, indirect warrant for the agentunifier nature of attributes (T3) is found, for one, in its providing a positive account of the intuitive dependent nature of attributes (A1). To be intrinsically an outward acting unifier is to be ontically dependent upon the subjects of this agency. Second and crucially, the agent-unifier nature of attributes (T3) is the prima facie response to Bradley’s Regress—if an attribute is the achieving unifier of itself with and among its subjects, e.g., a relation is an ‘actually relating relation’, then no further cause (i.e., no further relation) is needed to account for this unity. As a relevant point, we saw in Section 3.1 that Bradley’s Regress follows from classic assumptions A2 (Attributes as Universals) and A7 (Attribute Agent-Organizers). Since A7 and T2 above imply T3, the error is with A2, what will be dissolved in the next section with the demonstration of T4, the contradictory of A2. An important clarifying point relevant here is that the intrinsic subjectdependency of attributes, derivative as it is from their outward combinatorialagent natures, reflects no ‘deficit of being’ or a less than full reality that would require them to share in the beings of subjects of a different type and having full realities. Without our assay the contrary seems a plausible assumption, and was the explicit view of at least some scholastics.51 Rather, an attribute is subject-dependent because its being has as a positive aspect a causal act of unification with a subject or subjects external to it. And, the Eleatic Principle (Sect. 1.6) is correct in asserting that to act (or be acted upon) is a mark of the (fully) real, though all acts require a patient or patients distinct from them in order to exist. And as we are about to see, the linking agency of attributes implies their existing as individuals, what can only be a further mark of their being ‘fully real’.

|| sals: An Opinionated Introduction, pp. 96–7; E. J. Lowe, The Four-Category Ontology: A Metaphysical Foundation for Natural Science (Oxford: Clarendon Press, 2006), pp. 90–91. 49 Armstrong, A World of States of Affairs, p. 38. 50 Ibid., pp. 38, 154, 267. 51 See Robert Pasnau, Metaphysical Themes: 1274-1671 (Oxford: Clarendon Press, 2011), pp. 192–3.

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4.4 The Individuation of Attributes Given their natures as combinatorial agents (T3), it is an immediate implication that attributes proper are not universals (contra classic assumption A2) but are particulars/individuals, and are each ontically dependent upon the subjects of a single n-tuple that the attribute jointly qualifies/characterizes. Specifically, T4. In a fact :Rni(a1,a2,…,an) the attribute/ontic-predicate Rni, in effecting an act of unification of itself with and among the elements of the subject n-tuple , is both unrepeatable, i.e., is an individual (an ‘instance’), and is existentially dependent uniquely upon this subject n-tuple. From this follows the Principle of Subject Uniqueness: If Rni(a1,a2,…,an) and Rni(b1,b2, …,bn), then a1 = b1, a2 = b2, …, an = bn. The arguments for T4 will demonstrate that the outwardly-directed combinatorial-agent nature of attributes proper provides an ontic underpinning for the long-persistent doctrine of individuated or ‘unit’ attributes, a foundation compelling of the doctrine, and what historically has been otherwise absent. In particular, it is a common assertion of trope theorists that the unrepeatability of tropes must be taken as an unexplainable primitive. They advocate for the reality of individuated attributes indirectly by arguing their relative virtues over the negatives of substratum theories whose central claims are classic assumptions A1 (Attributes as Dependent) and A3 (Per se Subjects), including realist versions that adopt A2 (Attributes as Universals), theses all of which nominalistic trope theorists deny. We, however, are now in a position to give direct and relatively simple arguments of attribute instances.52 As a first argument for T4 I would return to one given in Section 3.1 but here utilizing dyadic relations. Temporarily omitted will be subscripts on attribute terms that would otherwise anticipate our conclusion. Let :R2(a,b) and :R2(c,d) be any two non-identical contingent facts with ‘the same’ attribute R2, e.g., :IsLeft-of2(a,b) and :Is-Left-of2(c,d). For the present we will leave open whether ‘the same’ is to be understood in a nominalist or realist way. Under T3, each fact exists as a structure via a unifying agency of the attribute R2 linking the || 52 I have come across only one other author who has explicitly offered direct arguments for individuated attributes—Avicenna (Ibn Sina, 980–1037). His arguments are based upon false premises found at places in Aristotle, including a particularly interesting argument utilizing the esse-in/esse-ad property reduction of relations. See my Moderate Realism and Its Logic (New Haven: Yale University Press, 1996), pp. 120–25.

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respective relata. Now assume that it is one and numerically the same unifying agency that is a constituent of each fact, i.e., that this agency is as repeatable/universal as is, I will argue, the attribute’s component intension. And further, let it be the case that a is no longer related to b by R2, e.g., a is moved to the right of b. The contingent fact :R2(a,b) would then cease to exist since the unifying agency of attribute R2 (e.g., Left-of2) essential to the resultant fact has ceased to exist. But then on the assumption that this agency is exactly and numerically the same in all facts with R2 as their attribute, it will likewise cease to exist for each of them, and so the facts themselves will also all go out of existence, e.g., for this reason alone c will no longer be left of d. This is absurdly counter-factual. Generalizing, though an attribute can in some sense be ‘the same’ across distinct facts, fact-forming unifying agency under it is unique and particular to each relata n-tuple whose elements jointly with it make up a fact. Hence, our initial facts :R2(a,b) and :R2(c,d) are more accurately designated by our refined notation: ‘:R2i(a,b)’ and ‘:R2j(c,d)’, where R2i and R2j are unrepeatable ‘instances’ and R2i ≠ R2j, and where ‘R2’ is used to designate that which the two facts share as ‘the same’, what on T5 below is a numerically identical component universal. I note that this argument in its general form, but utilizing monadic properties, is found in Alexius Meinong’s Hume Studien I (1877).53 He argues that if a property of Triangularity ‘adheres’ to a and a property of Triangularity adheres to b then these two properties cannot be numerically identical since b and so its Triangularity could go out of existence while a and its Triangularity remain. In his analysis of this argument Benjamin Schnieder54 has identified the crucial but implicit and unaddressed premise to be: Every attribute adheres to its bearer in such a fashion that the attribute vanishes if its bearer vanishes. But this is precisely what T3 substantiates: A monadic property of Triangularity adheres to and so characterizes a subject b because it is a combinatorial agent and in this way its act of unification of itself with b (its ‘fashion of adherence’) is dependent upon the existence of b. If b ceases to exist then so does the adherence whereby || 53 Alexius Meinong, ‘Hume Studien I, Zur Geschichte und Kritik des modernen Nominalismus’ in Sitzungsberichte der philosophisch-historischen Klasse der Kaiserlichen Akademie der Wissenschaften, Wien, Band 87 (1877): 185–260. Translated by Kenneth Barber as part of his dissertation, Meinong’s Hume Studies: Translation and Commentary, University of Iowa, 1966, pp. 98–193. The argument is also quoted in Benjamin Schnieder, ‘Particularized Attributes: An Austrian Tale, in The Austrian Contribution to Analytic Philosophy, (London: Routledge, 2006), pp. 130–58. 54 Ibid. Schnieder critiques arguments for particularized attributes found mainly in Meinong and Bolzano, with some discussion of relevant views of Brentano and Husserl.

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the property of Triangularity links itself to b, but since this adherence is a composing part of this property had by b, this property must itself cease to exist. Since another triangle a can remain in existence as such when b ceases to exist, then what characterizes it as Triangular must be numerically different from what characterized b as Triangular—the property of Triangularity, and equally all attributes, occur as individuated instances. As a second argument for T4, let :R2(a,b) and :R2(b,a) be two contingent facts with a ≠ b and R2 a non-symmetric relation, e.g., :Loves2(John,Mary) and :Loves2(Mary,John). Because R2 is non-symmetric it orders its relata in each fact, and so for a ≠ b, :R2(a,b) ≠ :R2(b,a), as seen in our example where the two facts exist independently of each other. In particular, in the fact :R2(a,b), a occupies position-1 and b occupies position-2, whereas in fact :R2(b,a), b occupies position-1 and a occupies position-2. Now, assume that the unifying agencies effecting facts :R2(a,b) and :R2(b,a) are numerically the same. This means that these facts’ orderings of their relata are numerically the same since it is in an attribute’s trans-relata connectedness—through its combinatorial agency (T3)—that it orders its subjects. With this we have, say a, occupying position-1 in fact :R2(a,b) and occupying position-2 in fact :R2(b,a), and though these are two distinct facts, the connecting-ordering agency is now assumed to be numerically the same in both. Thus, for numerically the same connecting-ordering under R2, a occupies position-1 and position-2, and this is simply to say that a is related to itself under R2, i.e., that fact :R2(a,a) obtains. But this is counterfactual: just because, for example, :Loves2(John,Mary) and :Loves2(Mary,John), it does not follow necessarily that :Loves2(John,John). Again our two facts are properly :R2i(a,b) and :R2j(b,a) where R2i and R2j are individual instances and R2i ≠ R2j. The latter argument can be generalized in the following way. If acts of ordering unification among subjects under an attribute Rn are identical for all of Rn’s subject n-tuples, then whatever occurs in the first position of an n-tuple for this single act of ordering will be ordered under Rn with whatever occurs in the second position of any n-tuple by this numerically identical act of ordering. So that if, for example, :Loves2(John,Mary) and :Loves2(Bill,Pegg), then necessarily :Loves2(John,Pegg), which is absurd. Acts of connected-ordering must be particular and numerically unique to each n-tuple of entities ordered. As a third and more general argument for T4, consider simply this: An agent is such because it produces an effect, this production is an act, and every act is individual/unrepeatable. Numerically the same production/act cannot be shared by numerically distinct agent-patient pairs, nor can it exist discontinuously for the same agent-patient pair. Therefore the unification-achieving and

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unification-sustaining act that is essential to an n-adic attribute as it characterizes n subjects is unrepeatable, and thus likewise is its subsuming attribute, i.e., attribute instance. Hence, contra the classic assumption that attributes are universals (A2) (and in this way avoiding the Individuation Regress of Sect. 2.3), they are, in their defining nature as intensioned (T2) combinators (T3), unrepeatable particulars (T4). That is and also contrary to a common view that attributes are individuated by the prior individuation of their subjects, they individuate themselves via their acts of unification that are necessarily dependent upon, but not caused by, their external subjects (‘patients’) which can be individuals or universals. Specifically, attribute instances are numerically distinct in qualifying distinct n-tuples of subjects, what is formalized in the Principle of Subject Uniqueness: If Rni(a1,a2,…,an) and Rni(b1,b2,…,bn), then a1 = b1, a2 = b2, …, an = bn. And, since the identity of a particular attributional union is determined by the attribute’s intension and the unique n-tuple of subjects it unites, then there cannot be two different instances Rni and Rnj of the same intension Rn having the same subjects. This is formalized as the Principle of Instance Uniqueness: If Rni(a1,a2,...,an) and Rnj(a1,a2,...,an), then Rni = Rnj. Combining both principles, instances are non-transferable and not multiply instantiated by the same ntuple, i.e., unlike with tropes and for which trope theory is criticized, instances so assayed cannot be ‘swapped’ or ‘piled’.55 Further, with the demonstration of thesis T4 we have identified what is ontology’s long sought principium individuationis. As will be detailed, the combinatorial agency of attribute instances founds a universal account of individuation, and its does so by providing an external ‘contextual’ (cum aliud) refinement (i.e., where a necessary element in the individuation of x is something external to x) on yet necessarily self- (per se-) individuating entities. The contextual aspect of instances as individuators is said to be needed in an ontology of quantum entities56, and having this component our account stands in contrast to the much-troubled traditional non-contextual posits for such individua-

|| 55 For the problems and references here see, e.g., Jonathan Schaffer, ‘The Individuation of Tropes’, Australasian Journal of Philosophy 79 (2001): 245–57. In regard to ‘swapping’, we have here a justification for the scholastic maxim: Accidentia non migrant de subjecto in subjectum. 56 For a description of the need and references see James Ladyman, ‘On the Identity and Diversity of Objects in a Structure’, Proceedings of the Aristotelian Society, Supplementary Volume LXXXI (2007): 23–43. Also see Ladyman, ‘Structural Realism’, The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.), URL = .

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tors57. The latter have included: ‘matter’ as an underlying subject for the attribution of universals (under classic assumptions A2, A3, and A6; e.g., Aristotle (as historically widely interpreted) and Aquinas)58; primitive haecceitas ((Latin: ‘thisness’) Scotus, Elshof)59 and bare particulars (e.g., Bergmann, Moreland, LaBossiere)60. With all these entities there is no account of how they are unrepeatable; they are simply posited as self-individuated in order to account for the individuation of other entities. And, theories of individuation that are contextualist without recognizing the necessity of self-individuating entities selfdestruct because of it. For example, the proposal that entities are individuated by being relata for spatial or spatial-temporal relations (e.g., Schaffer, Demirli)61 would require that the spatial-temporal relations themselves be individuated— i.e., be instances—(since sets of relations as universals are non-unique), and hence to account for the individuation of the latter relation instances would require they be relata for further instances of spatial-temporal relations, which, even if possible, would lead to vicious regress. Another example is the holding

|| 57 Jonathan Lowe observes that: “Certainly it seems that any satisfactory ontology will have to include self-individuating elements, the only question being which entities have this status— space-time points, bare particulars, tropes, and individual substances all being among the possible candidates.” He then gives an overview of problems with such posited individuators. See Lowe, ‘Individuation’ in The Oxford Handbook of Metaphysics, M. Loux and D. Zimmerman (eds.), (Oxford: Oxford University Press, 2003), p. 93. 58 Aristotle, e.g., Meta. 1016b31-32, 1034a5-8; Aquinas, e.g., On Being and Essence, 2d. ed., trans. Armand Maurer (Toronto: Pontifical Institute of Medieval Studies, 1968), pp. 36–37. 59 E.g., Scotus, Ordinatio II, d.3, part 1, q. 6, in Paul Spade, Five Texts on the Mediaeval Problem of Universals (Indianapolis: Hackett Publishing Co., 1994), pp.101–02; Gregg A. Ten Elshof, ‘A Defence of Moderate Haecceitism’, Grazer Philosophische Studien 60 (2000): 55–74. 60 Gustav Bergmann, Realism, passim; James P. Moreland, ‘Theories of Individuation: A Reconsideration of Bare Particulars’, Pacific Philosophical Quarterly 79 (1998): 251–63; Michael LaBossiere, ‘Substances and Substrata’, Australasian Journal of Philosophy, 72 (1994): 360–70. LaBossiere’s paper is relevant here also because of his argument that a trope theory requires a further category of entities that can bind tropes together into bundles. These cannot be further tropes because to succeed as ‘binders’ they must have, in effect and in terms of my assay, an agency(A7)/dependency(A1) that inert substance-like tropes do not have. Under the constraints of trope theory, LaBossiere sees the alternative for needed binding to be a primitive characteristic of posited underlying substrata, what must be bare particulars each with the primitive characteristic of individuator. On my analysis the problem here is with the making of attributes to be inert independent tropes. When this is corrected, attributes, especially as ‘writlarge’ with relations, are seen to be the needed agent-binders, and what parry the need for primitive substrata and individuators. 61 Schaffer, ‘The Individuation of Tropes’; Sun Demirli, ‘Indiscernibility and Bundles in a Structure’, Philosophical Studies 151 (2010): 1–18.

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of individuation to be via the instantiation of specially endowed substance universals (e.g., Loux, Lowe)62. Here the problem is how can the instantiation of a repeatable universal effect the categorical contradictory of an unrepeatable particular? It would seem that on this tack if instantiation is universal the question remains, and if it is particular then the account for this would have to be that it instantiates the universal Instantiation2, and this is the first step to vicious regress. All of these difficulties bolster in a negative way a further view that simply declares individuation an unexplainable primitive (e.g., Ockham, Campbell)63. Now in contrast to all this, our analysis of attribution expanded later to include fact complexes will provide a uniform and complete account of the individuation of all entities. T4 provides the foundational component: the above assay of the intuitive qualifying nature of attribution, especially as amplified in relations, implies an outward-achieving unifying-agency, and every attribution is by its combinatorial act individuated as an unrepeatable eventinstance. And, in ways we will detail in Chapter 5, since all other individuals are either systems of attribute instances composing hierarchical lattices of facts, or are individuated cognitive acts of association, or networks thereof, emerging on such fact-systems, all complex particulars inherit their individuation from the outward-directed combinatorial agency of thereby self-individuating constituent instances. The lesson will be that what are fundamental to ontology are not some ultimate self-supporting/independent per se ‘substances’ (A3), but rather self- or per-se-individuating attribute instances, each dependent as an externally unifying agent, but where at an ultimate ontic level some jointly form independent closed systems of mutually supporting instances (T8), these resultant structures being ontology’s atomic non-attribute ‘objects’ (Sect. 2.1). Attribute instances emerging upon and having these atomic objects as subjects form further structures, and so on, iterated hierarchically (T7), this up through the macro-complexes that are the objects of ordinary experience.

|| 62 Michael Loux, Metaphysics: A Contemporary Introduction (New York: Routledge, 1998), pp. 117ff., and ‘Beyond Substrata and Bundles: A Prolegomenon to a Substance Ontology’ in Contemporary Readings in the Foundations of Metaphysics, S. Laurence and C. Macdonald (eds.), (Oxford: Blackwell Publishers, 1998); E. J. Lowe, The Possibility of Metaphysics (Oxford: Clarendon Press, 1998), pp. 180–83, 197, 201–02, and ‘Form without Matter’, Ratio XI (1998): 214– 34. 63 For Ockham see Spade, Five Texts on the Mediaeval Problem of Universals, p.172; Campbell, Abstract Particulars (Oxford: Basil Blackwell, 1994), p.69.

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4.5 Attribute Intensions as Universals Under theses T2-T4 we have established that an attribute instance Rni in a fact :Rni(a1,a2,…,an) is an intension-controlled combinatorial agent. We can now demonstrate that as such instances are not simple entities (in the sense that they have non-identical components), but are, contrary to the posited nature of nominalistic tropes, composed of two aspects: in addition to but controlling of its outwardly unifying act, an instance has a qualitative content or intension that is identical across all synonymous instances, i.e., is a universal. More specifically, T5. An attribute instance Rni has two non-identical components: its outwardlycombinatorial agency and the latter’s controlling intension. For exactly resembling instances, Rni, Rnj, Rnk, ..., they share numerically the same qualitative content or intension: the universal Rn. Intensions/universals exist primarily as components of instances, separate from which they exit only conceptually as either derivative abstractions, or subjective creations prior to any instantiation. Intensions in themselves are non-agents/non-combinatorial, i.e., are not attributes/ontic-predicates. As indirect support for the universals of T5, I reference a number of arguments against various attempts by nominalists to explain away as only apparent qualitative identity across numerically distinct entities. These are given by D. M. Armstrong, Reinhardt Grossmann, Michael Loux, and J. P. Moreland. 64 Also as an indirect argument for both universals and their concomitant instances is their formal integration into an analytically and deductively powerful higherorder logic I have detailed elsewhere and termed Particularized Predicate Logic (PPL).65 In PPL there are both instance and intension variables and constants, but the quantifiers and their scopes are such that quantifiers with intension variables bind instance variables within their scopes, even within quantifiers— this formalizing the ontology of individuated instances as attributes and their

|| 64 D. M. Armstrong, Nominalism and Realism (Cambridge: Cambridge University Press, 1978); Reinhardt Grossmann, The Categorical Structure of the World (Bloomington: Indiana University Press, 1983); Loux, Metaphysics; J. P. Moreland, Universals (Montreal: McGill-Queen’s University Press, 2001). 65 See, ‘The Logic of Instance Ontology’ in Mertz, Essays on Realist Instance Ontology.

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sharing numerically the same non-attribute intensions.66 Relevantly, it has been said that the ontology of relations has not benefited from the muchexpanded logic of relations occurring in the late nineteenth and early twentieth centuries67, yet the power of application of PPL (e.g., formalizing inferences involving predicate modifiers, and diagnosis and avoidance of self-referential paradox), derived as it is from a refined ontological analysis of attribution especially as writ large in polyadic relations, does give, I propose, support to the motivating ontology of individuated attributes and shared universals. Now in addition to these, I offer the following three more direct arguments for intension universals, the introductory one given in expansive detail, and where crucial aspects of all of them are made possible by our prior analysis. The general structure of these arguments is that for an instance R1i, e.g., IsRound1i, the constituent foundations necessary for it (not its subject) to be an individual and for it to characterize its subject R1-ly, e.g., to characterize as round its subject, are non-identical, and that to assume the latter foundation, e.g., intension Round1, is also individual/unrepeatable leads to unacceptable consequences. For the first part of the first argument, let R1i be a monadic property instance, e.g., Is-Round1i, and such that it has contraries, e.g., Square1m. By contraries I mean a relation between two intensions of the same genus, and between instances of each, when instances of each can characterize the same subject, though not simultaneously, and no instances from either need characterize it. E.g., Round1 and Square1, Red1 and Blue1, Hot1 and Cold1, PositiveCharge1 and Negative-Charge1, are pairwise contraries. Now, instance R1i itself is the subject for at least two intrinsic attributes, it having within its composing being foundations necessary and sufficient for it to be the subject of attribute instances Is-Individual1m and Is-Contrary-to2n. Let U be the component foundation within instance R1i founding its satisfying the intension Individual1 (or Unrepeatable1, hence the ‘U’). As such, U is the component of instance R1i that renders it a ‘this’ (is its ‘haecceitas’) and what makes R1i numerically distinct from other individuals. Similarly, let R be the constituent foundation in instance R1i for it satisfying as a relatum the intension Contrariety2 (or Contrariness2),

|| 66 E.g., consider the ‘Principle of Instantiation’ for monadic predicates, i.e., for every property intension P1 there exists an instance of P1, P1i, and there exists an individual x, such that P1i characterizes x (a thesis I deny). It would be symbolized in PPL as: (P1)(∃P1i)(∃x)P1i(x). By the ‘extended binding’ of the leading intension quantifier, ‘(P1)’, if we instantiate its variable with ‘phlogiston1’, or ‘Phlo1’, the inference would then be the false: (∃Phlo1i)(∃x)Phlo1i(x). 67 Peter Simons, ‘Relations and Truthmaking’, Proceedings of the Aristotelian Society Supplementary Volume LXXXIV (2010): 199–213.

208 | 4 Atomic Structures: Facts and Their Natures e.g., R the foundation in instance Is-Round1i whereby it is contrary to the instance Is-Square1m. For this paragraph and the next I will leave off the superscript ‘1’ on the ‘R’ in order to avoid visual confusion. The foundation R is the intensional/qualitative aspect of instance R1i (and what is the necessary foundation in R1i for it to exactly resemble other instances R1j, R1k, ...). Now, this setup allows us to establish the important point that in composing the instance R1i the two foundations are not identical, i.e., U ≠ R. In this regard first observe that the intension Individual1 and its instances have no contraries. The genus here is that of Entity1, and of its species there are no contraries to Individual1 and its instances, only the contradictories of Universal1 and its instances (cf. Aristotle, Cat. 3b25; Meta. 1087b2). So, instance R1i qua individual—per what makes it an individual and so founds it having the property Is-Individual1m—cannot have contraries, i.e., constituent U cannot provide a foundation in instance R1i for it being the relatum for a relation Is-Contrary-to2n. Yet, based upon instance R1i having constituent foundation R, R1i is a relatum for a relation Is-Contrary-to2n. Thus, if U = R, then R1i would by the same foundation both have and could not have contraries. I.e., the same aspect of R1i (which if R1i is simple, as trope theorists posit, would be R1i itself) both founds and cannot found R1i as a subject of an instance Is-Contrary-to2n. Therefore, U and R must be non-identical components of R1i. To be explicated in thesis T6, the unity between the distinguishable aspects U and R internal to an instance R1i I term ‘continuous composition’, what stands in contrast to the ‘articulated composition’ externally effected by the combinatorial agency of attribute instances. Now for the second part and core of the first argument, assume constituent intension R, the aspect of instance R1i that founds it having the attribute IsContrary-to2m, is itself an unrepeatable individual. On this assumption foundation R itself will be the subject for the two attributes of Is-Individual1o and now Founds-Contrarity-Relations1p, these requiring of R constituent foundations U* and R*, respectively. But on an argument exactly analogous to that above, U* ≠ R*. I.e., U* in founding in R it being an individual—being R’s ‘thisness’—cannot found contraries; U* does not have the attribute Founds-Contrarity-Relations1p. Yet, R* is the foundation in R for R having contraries, and so R* has the attribute Founds-Contrarity-Relations1p. Hence, U* ≠ R*. Now, to be consistent with the above, R*, what founds the attribute of Founds-Contrarity-Relations1p, must itself be assumed to be unrepeatable. Clearly this is the beginning of what is both an infinite progression of individuators, U, U*, U**,…, and a vicious infinite regress of individuated intensions, R, R*, R**,…, each presupposing for its existence the next. The dual regresses are illustrated in Figure 4.1. So, on our assumption the initial instance R1i decomposes into an ontically bloated infinity

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of individuals, and unsuccessfully chases after a foundation for the initial instance R1i having contraries. These unacceptable consequences are avoided only at the initial step by recognizing the foundation intension R in the instance R1i, whereby the latter has a relation attribute Is-Contrary-to2n, must be repeatable, i.e., be a universal.

Fig. 4.1: Vicious Regress Showing Intension R of Instance Rni is not Unrepeatable

Returning to adicity superscripts for all intension terms, the first part of the above argument appeals to contraries making the argument appropriate to monadic property instances R1i; however, it can be extended to involve instances of any n-adicity Rni and a demonstration of the universal nature of their contained intensions Rn. As a second and more general argument, let U1, U2, U3, …, be all the individuators constituent of an instance Rni, i.e., all the foundations in Rni whereby it would have an instance Is-Individualni. And, let Rn be the intensional content of Rni, i.e., what makes Rni synonymous or not with other instances (e.g., the content of Is-Taller-than2i making it synonymous with IsVertically-Longer-than2j and not synonymous with Is-Same-Length-as2m). Now Rn is distinct in its being from any of U1, U2, U3, …, for the following reasons. First, synonymy, though an identity condition for intensions, is not an identity condition for individuators qua individuators. This is the basis for the falsity of the Identity of Indiscernibles. Second, intensions have extensions, but there is no equivalent sense in which individuators qua individuators do. And third and on the assumption that U1 is the only individuator constituent of instance Rni, then, by T4, U1 is the combinatorial act that connects Rni to its subject n-tuple, and it is intension Rn that conditions this act as to the subjects’ natures and order (if any), but the unrepeatable aspect U1 of Rni as itself simply a combinatorial act has no such qualitative relevance to the subjects unified. Reinforcing the latter is the fact that associations have combinatorial acts but they are not controlled by any qualitative relevance they have with the natures of their sub-

210 | 4 Atomic Structures: Facts and Their Natures jects. In these ways, then, intension Rn has attributes that none of the individuators U1, U2, U3, …, have and so Rn must be distinct in its being from each of them. Now, intension Rn cannot itself be an individual, i.e., be a subject for an instance Is-Individual1i. For otherwise, Rn would have to be or contain a foundation for this attribute—some individuator Un—what then would also be an individuator for subsuming instance Rni and so identical to one of U1, U2, U3, … But it was argued that intension Rn is distinct from each of these. Hence, intension Rn is not an individual, and thus is a universal. As a third reductio argument consider the following. Again for any attribute instance Rni let U be its individuating combinatorial agency and Rn be its intension. For reasons given above, U ≠ Rn. Now assume that intension Rn is also individual/unrepeatable. Since both U and Rn are individuals they are discrete, the situation that, as noted, medievals referred to as ‘thing and thing’ (Sects. 4.3, 4.6), and any whole composed of them would have to be that of an ‘articulated’ unity having a constituent agent unifier to bridge the ontic distance between them as each an individual. This constituent unifier of instance Rni would have to be either an attribute or an association. If it is an attribute, then, because neither U nor Rn are themselves attributes, it would have to be some third entity, some relation S2j, between them. But now S2j must get the same analysis as the original instance Rni, and this is the beginning of a vicious regress of successively needed unifiers among the combinatorial and intension parts of prior instances. On the alternative, if the needed constituent unifier between U and Rn forming instance Rni is that of arbitrary association, then intension Rn would not condition the combinatorial agency U that instance Rni has with its subjects, which would make Rni itself not an attribute, but rather a mere association. Hence, the assumption that intension Rn is an unrepeatable individual is false. In sum, the force of the arguments of this chapter thus far is for an immanent realism where an attribute instance Rni , e.g., Has-Mass1i, is composed of two non-identical components: an outwardly achieving unifying agency U and a qualitative content or intension Rn, e.g., Mass1, the instance’s ontic dependence being derived from the former, and it descriptive relevance to and ordering of its subjects being a function of the latter. The latter illustrate that each component has its own positive composing being (a ‘nature’) that founds attributes descriptive of it and not of the other component, with principal among these: the unifying agency U founds an instance Is-Individual1i (T4), and the intension Rn founds an instance Is-an-Unum-in-Multis1j descriptive of Rn being numerically the same component of numerically distinct instances Rni, Rnj, Rnk, … (T5), e.g., the attribute instances Has-Mass1i, Has-Mass1j, Has-Mass1k, …, all share

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numerically the same intension Mass1. And also in regard to the attributes of intension Rn, we saw in the analysis supporting T3 (Sect. 4.3) that Rn is dispositional, this in the sense that it prescribes as its defining meaning conditions on possible subjects such that, if the conditions obtain, then an instance Rni containing Rn acts causally with an agency U to unify itself with these subjects—to generate a fact. An intension Rn is essential to the determinants of, but does not itself causally effect, factual unities, and independent of any such unifying act an intension exists only in and dependent upon human intellects, this not just in abstraction from actual instances but when its descriptive conditions are not now, or will never be, satisfied by subjects, e.g., as with Tyrannosaurus-Rex1 or Phlogiston1. The dispositional nature of intension-universals Rn, e.g., PositiveCharge1, Fatherhood2, Betweeness3, Numerical-Proportionality4, answers a classic challenge brought against them. The critique is that because universals are not themselves relata for spatial or temporal relations, this brings into question any causal role these ‘abstract entities’ may have, which in turn casts doubt upon their existence.68 But on our assay, intensions set necessary and sufficient conditions prerequisite to the obtaining of attribute instances which are one of two primitive forms of causality, and on the form of the Eleatic Principle found, e.g., in Armstrong69—that everything that exists makes a difference to the causal powers of something—then insofar as attribute instances (attributions) are real, their constituent intensions are real. Because instantiated intensions make an ontic difference by constraining the combinatorial causality of their instances, they on the Eleatic criterion exist. Uninstantiated intensions have the reality of the generating minds upon which they are dependent, as do all arbitrary associations, the other form of primitive combinatorial causality. Spatial and temporal relations and their intensions have no special status as prerequisites to the basic form of attributional causality. Further, with attributes as instances (T4) we have the analog of Armstrong’s ‘victory of particularity’70; an instance inherits its unrepeatability from the unrepeatability of its agency component. Intension universals ‘characterize’ subjects only in a secondary and derivative sense, and not as constituents of subjects (contra classic assumption A5 (Inherent Essential Attributes)). Rather, intensions (‘types’) are constituents of attribute instances (‘tokens’), the latter characterizing subjects in the primary sense of each being externally attached to a subject or subjects based upon a qualitative relevance between the instance’s

|| 68 E.g., see Armstrong, A World of States of Affairs, pp. 5–6, 8, 41–43. 69 Ibid., p. 41. 70 Ibid., pp. 126–7.

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universal and internal and/or external aspects of the instance’s subject(s). Intensions, e.g., Round1, Red1, Love2, do not in the primary sense characterize the instances they are constituents of, e.g., though the instance Is-Round1i contains the intension Round1, the instance itself is not round. And, even though, for example, it is true that ‘An instance Is-Individual1i is individual’, this is so because of a corresponding fact :Is-Individual1j(Is-Individual1i), where Is-Individual1j ≠ Is-Individual1i, and the attribution is based upon the condition prescribed by the intension Individual1 of the attribute Is-individual1j being satisfied by the agency aspect of its subject instance Is-Individual1i. Because intensions themselves are neither attributes nor unrepeatable individuals, they contradict classic assumption A6 (Non-Attribute Individuals). The fundamental entities argued for thus far are to be seen in the context of a sequence of simplifying abstractions, what starting with facts are the results of a process of increasing conceptual distillation. Viz., with the arrow representing increasing selective abstraction, we have: Facts, :Rni(a1,a2,…,an) → attribute instances, Rni, → dependent-intensions, Is-Rn, → intensions, Rn. For example, consider it a fact that Romeo loves Juliet, what in expanded symbolic form would be :Is-in-Love-with2i(Romeo,Juliet). First, if we conceptually ignore the subjects here, Romeo and Juliet, and consider only the particular case of love had by them, retaining still its intension and concomitant subject-linking agency (and hence the outward directedness of both), and the latter’s dependence/incompleteness and unrepeatability, we have the instance Is-in-Lovewith2i. If, further, we conceptually set aside the instance’s agency and so its unrepeatability, but retain the instance’s subject-dependence and incompleteness along with its repeatable intension (and its inherent directedness), then we have, for lack of a term, a ‘dependent-intension’, Is-in-Love-with2. The conceptual confusion of attribute instances with dependent-intensions makes plausible both classic assumptions of true A1 (Attributes as Dependent) and false A2 (Attributes as Universals). Finally, if we conceptually isolate the repeatable intension from the sense of dependence/incompleteness, the result is the intension proper, e.g., Love2. The residual intension still retains as part of its content/meaning, however subtle as now unreinforced by the setting aside of the dependence of its agent source, the intentional directedness of setting joint criteria that n-tuples of other entities are to have (whether or not these conditions are or can be satisfied jointly by any n entities). Hence the appropriateness of superscripts on intension terms. These resulting intensions, though repeatable, are substance-like as non-dependent, and, if confused with their now twice-removed instances, require further agent/dependent attributes— Exemplification2 or Instantiation2—to connect them and the subjects they char-

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acterize. E.g., our initial fact :Is-in-Love-with2i(Romeo,Juliet) would be identified with what is actually a derivative ‘second-intention’ fact :Is-Exemplifiedby2i(Love2,). Instructive is the observation that if one takes intensions and reconstructs them by both denying their descriptive intentionality and positing them to be individuals then we have attributes construed in the manner of Humean trope theory. Overall, Humean individuated attributes are devoid of any directedness, selectiveness, or collectiveness, and are unrepeatable by stipulation. In semantic terms, the abstraction sequence from dependent-intensions to intensions follows the ‘nominalizing’ of linguistic predicates: from predicate adjectives, e.g., ‘is bald’, ‘is human’, ‘has mass’, and transitive verbs, e.g., ‘is the cause of’, ‘is a father of’, ‘is identical to’, ‘implies’, to their respective abstract nouns or ‘abstract singular terms’: ‘bald’ or ‘baldness’, ‘humanity’ or ‘humanness’, ‘mass’, ‘causation’ or ‘causality’, and ‘fatherhood’, ‘identity’, ‘implication’. In English grammar, ways of marking this last level of abstraction are numerous, including adding suffixes such as ‘-ness’, ‘-hood’, ‘-ity’, ‘-ence’, ‘kind’ and ‘-tion’, though, and significant in abetting distortions, in the case of monadic properties the single noun absent the verb is also used, e.g., ‘human’, ‘red’, ‘mass’. Facts and their instances can be either extra-conceptual or conceptual, but all isolated intensions are conceptual only. In this distilling process intensions retain their adicities (indicated by the superscripts), for we do not have the full sense that is an intension until we understand its number of subjects, what is more apparent with ordering polyadic attributes in that understanding an ordering via such an attribute’s intension, e.g., Betweenness3, presupposes that the intension carries with it the number of subject-places ordered. So importantly, we have intensions, e.g., Mass1, Even1, True1, Love2, Fatherhood2, Implication2, Betweenness3, Proportionality4, etc., that in themselves have no nature of outward agency or dependence, but rather, like classic ‘substances’, are self-contained and ‘inert’ non-qualifiers. It is their subsuming instances, e.g., Has-Mass1i, that qualify their subjects as intension-determined agent-combinators and in this are both individuated and dependent upon their subjects. A principal point of this work is that it is the confusion of a unifyingagent instance with its inert intension that is a primary source of the tradition’s errors regarding attribution. This conflation renders plausible, for example, such diverse errors as the Platonic Theory of Forms (it being the basis of the Platonists’ confusion of ‘this’s with ‘such’s71), Hume’s ‘separability of attributes’ || 71 Aristotle brought the charge of ‘this’-‘such’ confusion against the Platonists, saying that from it “many difficulties follow and especially the ‘third man’ (Meta. 1038b35), the Third Man

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thesis (Sect. 3.4), and Bradley’s Regress. In regard to the latter, the mediating dependent but non-agent ad-intension, Is-Rn, makes it easy to confuse a dependent agent attribute instance, Rni, with its contained independent non-agent intension, Rn, and so makes plausible the construal of an attribute successively as a plural unifier and then not so, the latter requiring the posit of a further attribute unifier, and so on. Also abetted in providing a basis for them are bundle theories, whether of universals or tropes, where non-dependent intensions need no further subjects to bear them (as otherwise required under A3 (Per se Subjects)) and so are speciously plausible as ontology’s explanatory urelements. Returning to a point made earlier (Sect. 1.3), the failure to distinguish an individuated attribute proper from its component universal intension is the source of the apparent contradiction in the scholastic claim that attributes are ‘individuated in things’ but ‘universal in the intellect’, an obscurity reinforced by the inherence model of attribution that removes the need for attributes in their full and defining natures to be outward agent unifiers and as such necessarily individuated. A confused and vaguely understood distinction of individuated attributes from their universal intensions, with then subsequent inconsistences, is seen in Aristotle. On the one hand, Aristotle conflates an attribute with its intension in his dominant theses that attributes are universals (A2) and yet they are inherently predicable of subject-others and so dependent (A1). A proper understanding of the latter where each attribute is seen to involve structuring agency, which he had worked out only imperfectly and for some attributes under the energeia assay of ‘forms’ (A7), would have shown straightforwardly and in the manner of Section 4.4 that the former was false—that attributes are unrepeatable, though they have repeatable components. A consequence of this failure surfaces in a crucial way, for example, in the often-observed inconsistency of Metaphysics VII. Here Aristotle seems committed to the three theses: 1) No universal can be a substance, 2) A substantial form is a universal, and 3) A substantial form is that which is most truly substance. If Aristotle would have distinguished between intension universals and their subsuming instances the contradiction would be dissolved as: 1ʹ) No universal can be a substance, 2ʹ) The intension F1 of an individuated substantial form F1i is universal, and 3ʹ) The individuated substantial form F1i is that which is most truly substance. And perhaps not unrelatedly, there are texts in the Metaphysics where Aristotle ap-

|| Regress being a principal argument Aristotle brings against Plato’s theory of Forms (Meta. 990b9-17).

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parently admits, though this is disputed, individuated substantial forms.72 If so then they would add to the texts where, on the other hand, Aristotle was willing to admit a distinction between an attribute and its intension. Specifically, these texts allow exceptions to A1 (i.e., allowing some attributes to be non-dependent or non-predicable) or A2 (i.e., allowing some attributes to be individuals—nonuniversals). Included here is the early Categories where Aristotle would have some intensions/universals be independent—‘never-in-a-subject’, viz., genus and species of substance, e.g., Man1 and Animal1, and also some attributes be unrepeatable instances—‘never-said-of-a-subject’, e.g., instances of accidents like Is-White1i. Also, in his semantic-logical works Aristotle has the same attributes at places be intrinsically predicable and so subject-dependent, and in other places be non-predicable and so independent. In this regard and made much of by Peter Geach, Aristotle’s treatment of propositions changes from the heterogeneous term-predicate analysis of the De Interpretatione to the homogeneous term-term analysis of the Prior Analytics’.73 And, I take Geach to imply rightly, this carries with it a distortion of the nature of corresponding facts: on our refined assay, from attribute-instance-combining-itself-to-(‘predicative-of’)-its-subject to that of attribute-intension + subject, where the ‘+’ (corresponding to the grammatical copula) stands for some further relation, e.g., class-subsumption. (For Aristotle, his semantic distinctions of “predicable of or present in some other thing” apply “to things themselves” (Cate. 1a20; De Inter. 16b10-11)). Geach refers to this distortion as comparable in its negative consequences to ‘the Fall of Adam’, and he gives as an example the fact that under the term-term theory (further specified as the ‘two-name theory’ by Geach) “there can be no relations—no res answering specifically to relative terms.”74 Without polyadic relations not only is there no account of ubiquitous structure, but the most obvious cases of outward-unifying agency are removed and in the vacuum monadic properties are more easily misconstrued as their agency-less universals. It is abetting the view that attributes proper are not unifying agents and thus not individuated events that is the cardinal sin here.

|| 72 E.g., see Rogers Albritton, ‘Forms of Particular Substances in Aristotle’s Metaphysics’, The Journal of Philosophy 54 (1957): 699–708; Edwin Hartman, ‘Aristotle on the Identity of Substance and Essence’, The Philosophical Review LXXXV (1976): 545–61; Mary Gill, ‘Aristotle’s Metaphysics Reconsidered’, Journal of the History of Philosophy 43 (2005): 223–51. 73 Peter Geach, Logic Matters (Berkeley: University of California Press, 1980), pp. 44ff, 289ff. 74 Ibid., p. 293.

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Significant in adding to the confusion between attribute instances, dependent-intensions, and intensions, and in this the promotion of nominalism, is the fact that we can also freely construct conceptually intensions independent of any known exemplifying subjects. Some are posited from the start as fictions, as not intended to be, and in some cases theoretically not possibly constituents of attribute instances of anything, e.g., Unicorn1, Leprechaun1, FrictionlessSurface1, Free-of-External-Forces1, Unrelated-to-Anything1, Essenceless-Entity1. Intensions are also freely constructed in scientific theories, the existence of their instances warranted by their fit within the conceptual structure of current accepted theory and range of observation. These would include Natural-Place2, Phlogiston1, Hyper-Light-Speed1, Blackhole1, and Graviton1. It is clear for both types that these intensions have a conceptual existence, with perhaps the existence of extra-conceptual attribute instances containing the latter intensions. Not to be confused with these are ‘formal attributes’ and their intensions, the scholastics’ ‘second-intentions’, that exist only conceptually though non-arbitrarily in founded instances. The intensions here are, for example, Exemplification2, Instantiation2, Identity2, Genus1, Existence1, True1, Absence1, and all logical and mathematical properties and relations, e.g., Negation1, Implication2, Even1, Addition3. These formal intensions and their instances are both parts of and serve as analytic tools for expanding the conceptual structures that are our understandings of the real.75 The analysis herein, then, is contrary to a ‘Principle of Instantiation’ which asserts that every n-adic intension universal is instantiated by at least one ntuple of subjects, what has been advocated, e.g., by Bergmann, Armstrong, and

|| 75 Reinforcing the instance-intension distinction, I have argued elsewhere, following Frege, that cardinal numbers as applied descriptions of quantity and asserted adjectivally/predictatively, e.g., ‘There are four apples in the bowl’, are attribute instances that qualify other intensions, e.g., (∃4i)4i(Apples-in-the-Bowl), whereas numbers treated substantivally/non-predicatively as subjects of theoretical/‘pure’ arithmetic propositions, e.g., ‘4 is an even number’, are intensions common to instances, e.g., as intension 4 is common to instances 4i, 4j, 4k, … See my Moderate Realism, pp. 259–71. I also note in passing another possible clarification due to the instance-intension distinction, this in regard to semantics. A particular affirmative proposition is to be seen as a complex semantic structure involving what are the senses of its sentence’s subject and predicate terms, these senses involving attribute intensions. If the predicate term has a referent or denotation this will be an instance of the intension which is the sense of the predicate term. The proposition is then true if the instance exists in an attributional union with the referent of the subject term. The latter union effects the fact that is the truthmaker for the proposition.

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Lowe76, and is intended as a denial of ante res Platonism. Rather what we have argued for is the more refined Principle of Instance Instantiation (T3) where attributes as unrepeatable n-adic instances (T4) and containing intensions as components (T5) exist only in each being instantiated by exactly one n-tuple of subjects. Most intensions Rn are constituents of instances Rni, whether the latter are extra-conceptual (e.g., physical attributes) or conceptual (e.g., semantic, logical, mathematical attributes), and in this way they fit the classic realist description of in rebus. For conceptual instances (and so their facts), their intension universals emerge within minds, some freely constructed and not abstracted from any prior qualifying instance, e.g., Average-Reader1, Aether1, Unicorn1, what as existing only conceptually fit the classic nominalist description of post res. With intensions so understood we avoid an artificial distinction between instantiated intensions and uninstantiated linguistic ‘predicates’. In short, there are no uninstantiated attributes proper—instances—but there are ‘uninstantiated’ intensions/universals—intensions not constituents of any instances. In current terminology, this assay makes for a theory that is ‘sparse’ in regard to attributes but ‘promiscuous’ in regard to universals. Some of the latter intensions—those that can be instantiated but in fact are not—are what Armstrong has recognized as ‘possible properties’, but unlike Armstrong we do not have to declare them ‘unreal’.77 I note that this assay of intensions is compatible with a form of naturalism (a version motivating, e.g., Armstrong) that holds that all entities are, or are ontically dependent upon entities that are, in time and space, i.e., are relata for spatial and temporal relations (e.g., fictional intensions as entities emergent upon neural networks), but where intension universals of any kind are not themselves the subjects for spatial, temporal, or physicalcausal relations. At any rate, bringing together results of Section 2.4 and those above we have as fundamental principles concerning attribution that: No entity exists without being characterized by an attribute proper—an instance Rni; No attribute instance Rni exists without a constituent subject-determining intension Rn; however, there can and do exist conceptually created intensions/universals that are not constituents of any instances and so characterize nothing. In passing I would offer some speculative extensions to the latter points. As typically conceived, there are facts that with their attribute instances and the latters’ intensions all exist independent of human cognition, and that may or may not ever be known, e.g., through sense experience. E.g., what would give

|| 76 Bergmann, Realism, pp. 43, 88–9; Armstrong, States of Affairs, pp. 38–43, and Nominalism and Realism, pp. 113, 137; Lowe, Four-Category Ontology, pp. 99, 114. 77 Armstrong, Sketch for a Systematic Metaphysics, p. 15.

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truth to the proposition that there was at any time life on Mars. There are also, however, facts that, with their composing instances and the latters’ intensions, are purely conceptual, and so ontically dependent upon and proprietary to individual minds. Unlike with extra-conceptual facts, with conceptual facts their intensions come into existence by emerging (willed or not) within individual minds, e.g., Truth1, Justice1, Exemplification2, Phlogiston1, Not-Round1, Round-or-Square1. However, like extra-conceptual instances, no instances Rni having conceptual intensions Rn are under the power of the mind to create. When a mind recognizes that each of an n-tuple of subjects respectively satisfy the conditions set by a conceptual intension, (e.g., Exemplification2), then there comes into existence a fact-forming instance of that intension (e.g., Is-Exemplified-by2i), i.e., the union of an instance with its subjects is not arbitrary and subject-indifferent (e.g., as seen in the fact :Is-Exemplified-by2i(Love2,))—it is not just association (e.g., as in the set {Exemplification2,Love2,}). A mind, and only a mind, can create a subject-indifferent union, i.e., an association, but the alternative of subjectrelevant unification conditioned by an intension—requiring the agency of an attribute instance—the mind is not free to create. In this sense, a conceptual fact is as ‘objective’ as those ‘out there in the physical world’, though its existence, as that of its intension, is dependent upon the mind that has them. A mind can create intensions but it cannot create attribute instances and so facts. To illustrate this last point I would touch on briefly the topic of semantic satisfaction relations. Consider the proposition that ‘Baseball a is spherical or cubical’, and assume that baseball a is spherical, i.e., that there exists a fact :IsSpherical1i(a). The truth-maker for the given proposition would be a cognitive fact had by a mind m, and one whose cognitive intension would be that for ‘is spherical or cubical’, say, fact :Spher-or-Cub1j(a). This fact, however, would obtain because the intension Spher-or-Cub1 prescribes as a foundation a prior cognitive fact, viz., ‘in’ mind m, a semantic structure for ‘is spherical or cubical’ and a semantic satisfaction relation Disj-Sat2 (for ‘Disjunctive Satisfaction’) such that, with m having the additional knowledge of the extra-cognitive physical fact :Is-Spherical1i(a), there would come into existence in m a cognitive semantic fact :Disj-Sat2k(a,semantic structure for ‘is spherical or cubical’). Crucial for the obtaining of this fact is the obtaining of the extra-conceptual physical fact :Is-Spherical1i(a), the latter a necessary condition prescribed by the semantic intension Disj-Sat2. The semantic fact then being the primary truth-maker for the initial proposition. I shall return again in passing to semantic issues when considering ‘negative facts’ below.

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As a final and synthesizing point for this section we can reinforce our full analysis of attribution by observing how an attribute instance’s dual intensioned-linking aspects provide an account of the truth of negative propositions directly in terms of absences. The account avoids the posit of negative facts or states of affairs without having to resort to the device of ‘totality states of affairs’, e.g., as recently advocated by Armstrong.78 Consider some true contingent proposition that ‘a is F’. Assume with Armstrong that what makes this proposition true—its truth-maker—is just the union of subject a and universal/intension F in a fact, but where this factual union is nothing more than just the existences of both a and F (what in more detail for Armstrong would be their mutual ‘partial identities’ (Sect. 4.2)). Then, if things were to change so that, with no change to a or F, the negative proposition ‘a is not F’ is now true, its truth-maker cannot be the absence of something from the truth-maker for ‘a is F’ since the only constituents of the latter, subject a and universal F, remain each in existence, and this is sufficient as truth-maker for the contradictory ‘a is F’. This is perhaps what motivates the thinking that the truth-maker for ‘a is not F’ is something positive in the form of a totality state of affairs. Armstrong holds that the latter consists of a relation between a property F and a mereological whole such that the relation asserts that the sum is all of the subjects that instantiate F, a state of affairs he designates with ‘Tot(property F,mereological whole of the F’s)’.79 With this positive fact and with a outside of the totality of all things that F, it is then this ‘absence’ of inclusion that founds the truth of ‘a is not F’. Now, against all of this I first recall in passing a point previously made: that Armstrong himself came to the realization that mereological unity is not real unity (Sect.1.5)—the connecting and selecting unification essential to the sum as its own entity is missing—and so, with this real absence of a second subject in Armstrong’s proffered state of affairs, there is no such state of affairs. More straightforwardly, our assay of attribution avoids all of this as more economical and not contrived, and along the lines advanced, for example, by Peter Simons against Armstrong.80 For us, the truth-maker for a simple positive proposition like ‘a is F’ is a fact :F1i(a) where instance F1i consists of universal/intension F1 and the combinatorial act it conditions. If things change so that the negative ‘a is not F’ is now true, what makes it true is the absence—the nonexistence—of any instance F1i unifying itself to a. More specifically, the truthmaker here is the absence on a of any combinatorial act determined by inten-

|| 78 Ibid., pp. 74–81. Also see States of Affairs, pp. 134–35, 196–201. 79 Armstrong, Sketch for a Systematic Metaphysics, p. 80. 80 Simons, ‘Negatives, Numbers, and Necessity’.

220 | 4 Atomic Structures: Facts and Their Natures sion/universal F1, this in turn due to a not now satisfying the conditions set by F1 as prerequisite to it being descriptive of subjects. These ‘absences’ can be the case even though subject a and intension F1 remain in existence. What Armstrong asserts, but we, along with Simons, deny, is that: Every true claim about the world is made true by something that exists.81 To the contrary, some true claims are made so because of what does not exist. So in this regard let us return to the issue of conceptual facts and touch again briefly on the topic of semantic satisfaction relations. Assuming once more the existence of a standard baseball a, and so extra-conceptual fact :IsSpherical1i(a), consider the proposition that baseball a is not a cube. The proposal is that this negative proposition is true because there is a conceptual fact involving the intension for ‘not a cube’, say, :Not-Cube1j(a). But this is so because the intension Not-Cube1 prescribes as a foundation a further cognitive fact :Neg-Sat2k(a,semantic structure for ‘not cubical’). And the latter fact obtains because the Neg-Sat2 (for ‘Negation Satisfaction’) intension sets as a necessary condition for it being part of an instance Neg-Sat2k the absence of an attributional union with a involving the intension Cubical1. This second cognitive fact and the primary truth-maker for the original negative proposition would come into existence in the mind that has the semantic structure for ‘not cubical’, and knowledge jointly of the extra-conceptual fact :Is-Spherical1i(a), and of the contrariety of intensions Cubical1 and Spherical1. The second cognitive fact, and not an extra-cognitive one, is the truth-maker for the proposition ‘Baseball a is not a cube’. The second fact obtains because of the combinatorial agency of the instance Neg-Sat2k, and the latter exists because satisfying the descriptive intension Neg-Sat2 is the absence of any agency under the Cubical1 intension on a. In these ways the absence-assay of negation, and our agent-combinator theory of attribution that explains it, offers clarification for avoiding the traditional controversies over ‘negative facts’. In addition to a way to handle truth-makers for propositions involving logical operators, it would seem also proper for propositions whose predicates are impure, e.g., ‘is left of Socrates’.

4.6 The Simple ‘Continuous Composition’ of Attribute Instances The results thus far pertain to an analysis of factual unity, the simplest form of qualitatively-determined unity among the yet discrete. To be examined later are || 81 Ibid., p. 74.

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the more complex forms of inter-attribute and stratified composition. The latter provide counter-examples to classic assumption A8 (Unity by the Constituent One) in that these are wholes whose unities are by more than single shared constituent ‘ones’. Corresponding to the outwardly-directed unifying agency of instances, but without concomitant controlling intensions, is arbitrary association. Both intensioned and non-intensioned types of unifying agency make for what I term the ‘articulated composition’ of plural wholes, i.e., wholes ontically dependent upon discrete parts and what require as such that some of these parts be unifiers among the others, e.g., facts, complex structures, sets, mereological sums. The claim herein is that, directly or indirectly, attribute instances are the source of the articulated composition defining all plural wholes. But now, in addition to the outward unities attribute instances effect, they are each themselves the effect of a different and fundamental form of inward unity. Viz., each instance is a whole whose being is undivided yet non-homogeneous, and so a whole that in its unbroken oneness provides the inward unity of subsumed yet virtual parts, parts at least some of which are as ontically dependent upon the whole as the whole is upon the parts. Such unity is appropriately termed ‘continuous composition’; Aristotle in the Metaphysics’s lexicon under the entry ‘wholes’ asserts that among continuous wholes there are those whose several parts “are present only potentially”, i.e., parts that are distinguishable but not distinct in the whole (Meta. 1023b26-34). With attribute instances being continuous composites they in another way contradict A8: here the unifier of the whole is the whole and not a constituent of it. More specifically: T6. In composing the being of an attribute instance Rni, the aspects of combinatorial agency and its controlling intension Rn are a unified whole not by attribution or association, and so though these aspects are non-identical, they are in Rni undifferentiated/non-discrete and form a seamless ‘continuous composite’. The differentiation of these aspects is posterior and external to Rni in the tradition’s ‘formal’ abstraction. In a continuous composite at least some of the parts, e.g., the combinatorial agency of an instance Rni, are reciprocally ontically dependent with the subsuming whole, e.g., instance Rni—neither prior to the other, and the unity of all the parts is by the whole, what stands in contrast to a plural ‘articulated composite’, e.g., a fact, that is ontically dependent upon prior and remaining discrete parts, and requiring as such one or more of these parts be agent-unifiers among the others.

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It has been argued that the agent-combinator and intension aspects of an instance Rni are non-identical, and that the combinator aspect does not have the intension as an additional implicit subject. An instance’s dual aspects, then, require something else as the cause of their unity. This cause cannot be a further attribute instance since this is the beginning of vicious regress. Nor can the cause be arbitrary association for then the intension Rn would not truly condition the unifying agency of Rni among its subjects, i.e., instance Rni would not be a characterizing attribute. What all of this implies is that in contributing to the being of the instance whole the two aspects of combinator and intension are not discrete, what, as noted, the medievals described as ‘not thing and thing’— there is no ‘ontic distance’ between them insofar as they contribute to the being of the whole—for otherwise their unity would require an impossible constituent outward-unifying agent to bridge their discreteness. Now, if it is not one or more of the parts that are the cause of the then derivative being and unity of the whole, it is the whole itself that is the cause of the being and unity of the nonidentical but non-discrete parts, what is then a continuous whole of virtual parts, the latter distinguished and separated only conceptually in abstraction. The distinction can be summarized, I propose, as: With articulated composites, e.g., a fact :Rni(a1,a2,…,an), the plural whole has its existence separate from but derivative of the thus ontically prior existences of discrete parts and their unification by one or more of these parts’ bridging combinatorial agencies, whereas in a continuous composite, e.g., an attribute instance Rni, it has non-identical components of which at least one, e.g., an instance’s linking agency, has no existence prior to or separate from (i.e., its ‘act of existence’ is numerically the same as) that of the whole, and the union of these parts (‘aspects’) is derivative of their inclusion in the oneness of a divisionless/‘seamless’ whole. Thus, with an articulated composite the whole emerges from the ontically prior parts, requiring one or more of them be unifiers among the others to effect the plural unity, whereas with a continuous composite one or more of the non-identical parts have their beings reciprocally with the whole and the unity of all the parts is by the whole, these parts being rendered discrete only in abstraction. In particular and correcting classic Assumption A3, ontic dependence in general is to be understood as non-symmetric, not asymmetric, and specifically when restricted to the dependence of articulated facts upon their parts it is asymmetric, and when restricted to the mutual dependence of a continuous attribute instance and its part that is a combinatorial act it is symmetric.

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Philosophers recognizing continuous composition have proposed various geometric analogies to explicate its subtle nature as a ‘divisionless unity among the non-identical.’ There is, for example, the analogy given by Proclus82 of a closed continuous circle and contained virtual semi-circles. A continuous circle is in itself unbroken and undivided, and in this is simple in its oneness, yet we can conceptually divide it into, say, two discrete semi-circles. Prior to this external separation there is no division in the continuous circle, yet in fact the composing being of each semi-circle enters into the composing being of the subsuming circle. Semi-circles distinguished/discrete from each other can compose a then posterior circle-whole but only with a constituent cause of the unity between the two, viz., a sharing of end-points by the two curves, analogous to articulated wholes that require constituent agent unifiers. A continuous closed circle requires no constituent connectors of parts as in itself it has no discrete parts to connect.83 Using a similar example, Aristotle, in arguing the point that “in complete reality two are never in complete reality one”, is apparently referring to continuous composition when asserting that a continuous line, though one, consists of two halves potentially: “The double line consists of two halves— potentially [non-discrete within the whole]; for the complete realization of the halves [i.e., rendering them discrete] divides them from one another [and so as discrete and two are not identical to the original one subsuming line].” (Meta. 1039a5-6; my inserts). Elsewhere in defining ‘continuity’ Aristotle asserts that “Things are continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other; continuity is impos-

|| 82 Proclus, Commentary on Plato’s Timaeus: Vol. III, Book 3, Part 1, Proclus on the World’s Body, ed. and trans. by Dirk Baltzly (Cambridge: Cambridge University Press, 2007). pp. 55–6. 83 Jonathan Schaffer alludes to Proclus’ circle—semi-circle analogy as contributing to the plausibility of ‘priority monism’, the view that reality as a whole is prior to its parts, the latter dependent for their natures and existences upon the whole. This in ‘Monism: The Priority of the Whole’, Philosophical Review 119 (2010): 31–76. Also see ‘Monism’, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = . In contrast, a priority pluralism is argued herein where reality is an inter-connected hierarchy of structures, each of whose nature and existence derives ultimately from composing attribute instances, but where only at the lowest level of instances do we have a unity where ‘many parts exit in virtue of the one whole’, what Schaffer would universalize as priority monism. Schaffer would have the ultimate whole or cosmos be ontically prior to all differentiable parts, whereas I argue that nowhere within total reality is this the case, and that even with the continuous unity of attribute instances they as ontic atoms are mutually ontically dependent with their subpart combinatorial acts—here and only here are neither wholes nor some of the parts prior or posterior to the other; whole and some parts require each other in order to exist.

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sible if these extremities are two [i.e., the things are divided/dis-crete].” (Physics 227a10-13; my insert) The medieval Peter Auriol used the similar geometric example of discrete points composing a continuous line to illustrate the continuous composition he held to be the union of inherence between an accident and its subject. He asserts that “the very composition of an accident with the substance” is “that of lack of division”, what would otherwise require them to be “linked (per copulationem) in the way one complete thing is linked together with another compete thing”. Rather as “relationally indivisible” the union of an accident with its substance subject is “just as a point makes one thing with a line through internal indivisibility rather than through simultaneity or union.”84 Among contemporary ontologists Reinhardt Grossmann has used the geometric analogy of the continuous area of a square and its potential divisibility by a diagonal to illustrate the point that “To be simple [i.e., to have no discrete parts requiring unification] is not the same as to be indivisible [i.e., not to have nonidentical aspects contributing to one’s being].”85 (my insert) To help drive home the insight here, consider a somewhat different analogy involving a uniformly black dot, •. Phenomenally the dot is an unbroken, continuous whole, yet it is composed of what must be non-identical foundations for the intensionally and extensionally distinct attributes Is-Extended1i and Is-Black1j. Though ontically distinct, these foundations or aspects are not discrete or separate—not ‘thing and thing’—that would require some additional constituent to connect the two. A separation of either of these aspects from the whole is a product of selective abstraction, like viewing the same continuous object from two different and partially informative perspectives. Hume used a similar example to illustrate our ability to distinguish color and figure within a given perception, what is a “distinction of reason” separating aspects that in the ‘simple’ perception are “in effect the same and undistinguishable.” (1.1.7.17) Along the same line Armstrong gives the example of an object’s size and shape. These aspects are dis-

|| 84 I am using a translation by Robert Pasnau of Section IV Sent. d. 12 q. 1 a.1 of Peter Auriol, Commentariorum in quartum librum Sententiarum (Rome, 1605), and found at URL: spot.colorado.edu/~pasnau/research/aureol4-12.pdf. Also provided by Pasnau is a relevant passage from a Coimbran commentary on Aristotle’s Physics and describing the highest of five degrees of unity: “The fifth is the per se unity of simple things and of substances free from mixture with matter [i.e., free of a subject of attribution and so free of the articulated unity of attribution, e.g., presumably souls, angels, and God]. This unity is far superior to the others, since it is lies outside all composition of really discrete parts [i.e., its unity is that of continuous composition].” (I.9.11.2; my inserts) This from Pasnau, Metaphysical Themes: 1274-1671, p. 556. 85 Grossmann, Categorical Structure of the World, p. 90.

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tinguishable and non-identical, yet in composing the object they are “far too intimately conjoined to speak of their being related.”86 Common to these examples, however, is the fundamental mark of a continuous composite and what distinguishes it from an articulated composite. Viz., it is the nature of a continuous composite that, though having non-identical parts, none of these parts are attributes (specifically, attribute instances) of others of its parts. In a continuous composite there is no ‘ontic distance’ between the parts that would otherwise require an attribute instance to bridge—in the words of Armstrong, there is here “a distinction without a relation”.87 This is so because in a continuous composite the being and the unity of the externallyconceptually differentiated parts is that of the being and prior undifferentiated oneness of the whole. The parts are virtual as non-discrete in their contribution to the being of the whole. In an articulated composite the reverse is the case, the being of the whole is derivative of the prior and internally differentiated beings of the parts, what requires some parts be external unifying agents among the others. It is to be noted that Bradley, in denying the possibility of articulated composition—the supposed lesson of his regress—held that Reality in which differentiation is founded must be, in effect, a continuous composite: “..a whole in which distinction can be made [i.e., for which there is an intrinsic basis], but in which divisions do not exist.”88 (my insert) What Bradley held is the continuous unity of all-encompassing and undifferentiated “Reality” I am inverting to the unity of only atomic attribute instances from which is built the plural and articulated whole that is Reality. It is the continuous composition of attribute instances that locates and explicates the ‘fundamental tie’ necessary to connect the ‘realms’ of the particular/extensional and the universal/intensional. On this topic, Armstrong, for example, has taken the view that a subsuming fact or state of affairs is the cause of the unity of its subject particular(s) and an attribute universal, the unity between the two being necessarily “closer than relation” 89 (on our assay unity of

|| 86 Armstrong, Nominalism & Realism, p. 110. 87 Ibid., p. 111. 88 Bradley, Appearance and Reality, p. 128. 89 Armstrong asserts that between a subject and a universal composing a state of affairs (a fact) “That although particularity and universality are inseparable aspects of all existence, they are neither reducible to each other nor are they related. Though distinct, their union is closer than relation.” A Theory of Universals: Universals and Scientific Realism, Vol. II (Cambridge: Cambridge University Press, 1978), p. 3. Also see Armstrong, A World of States of Affairs, pp. 113–19, and Universals: An Opinionated Introduction, pp. 96–7. My analysis differs from Armstrong’s in that Armstrong would have universals be attributes and the union between them

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the particular and the universal being more accurately described as ‘closer than attribution’). On the above more refined analysis it is the attribute itself as an instance whose continuous being unifies its composing but undifferentiated constituent aspects of the particularizing outward-combinator and the latter’s controlling intension universal, a view more closely approximated by the scholastics John Duns Scotus and Francisco Suarez. We have noted that Suarez held that an attribute’s ‘mode of adherence’ to a subject exists in a unity with the attribute that is closer than ‘thing and thing’. Rather, the two aspects are joined in “a certain mode of identity”, their distinction being external and of a type he describes as one sense of distinctio rationis ratiocinatae—(a ‘distinction of the reasoned reason’).90 To avoid confusion Suarez prefers the term “modal distinction”.91 He argues that, though both the adherence mode (our combinatorial agency) and its attribute (our attribute intension) are real and not identical, they are “not properly distinct . . . as thing and thing” (what I have described as not ‘discrete’), for otherwise a further mode of adherence would be required to unify them, what would be the beginning of a vicious Bradley-type regress of modes of adherence.92 Prior and relatedly, Scotus had argued that to account for the individuality/unrepeatability of a substance, e.g., Socrates, the substantial form must be ‘contracted’ from within by a positive principle he termed “haecceitas” or ‘thisness’, and that the distinction within the individuated form of the universal intension or quidditas (Latin: ‘whatness’), e.g., Humanity, and its haecceitas must be of a general type that was termed a distinctio formalis a parte rei (a ‘formal distinction on the side of the thing’, i.e., a formal distinction objectively based).93 Here the mind distinguishes what is not extra-conceptually separated as ‘thing and thing’94, yet there is an extra-conceptual basis for the conceptual distinction. In general, I take Scotus to intend as a basis for his

|| and their subjects into facts be ‘closer than relation [attribution]’ (my insert), whereas I would have universals join with combinatorial agent-linkings to form individuated attributes, the union of these two aspects being ‘closer than attribution’, but the union between these instances and the subjects they qualify to form facts being precisely that of attribution. 90 Suarez, On the Various Kinds of Distinctions, Disputationes Metaphysicae VII, Sect. I, pp. 16–39. 91 Ibid., Sect. I, 16, p. 27. 92 Ibid., Sect. I, 18–19, pp. 29–31. 93 For Scotus’ views see his Ordinatio II, d.3, part 1, qq. 1–6, in Spade, Five Texts on the Medieval Problem of Universals, pp. 57–113. Also Peter King, ‘Duns Scotus on Metaphysics’ in The Cambridge Companion to Duns Scotus, Thomas Williams (ed.), (Cambridge: Cambridge University Press, 2003), pp. 15–68. 94 Scotus, Ordinatio II, d.3, part 1, q. 6, pp. 107–08.

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‘formal distinction’ a unity among non-identical components, what in this way “is not absolutely simple”95, and yet is in a proper sense divisionless (not between ‘thing and thing’) and so simple-as-seamless, what would otherwise require a constituent unifying agent to bridge the ontic divide. The distinction is of a ‘moderate simplicity’ that allows for metaphysical complexity.96 And in particular regard to ontic predication and the assay advocated herein, the relevant relation between the views of Suarez and Scotus is that what is the agentunifier aspect of an attribute instance and what individuates it (makes it a ‘this’) are identical—an unrepeatable combinatorial act/event. In contemporary literature, Keith Campbell has appealed to Scotus’ formal distinction as an account of how a trope can have both a qualitative nature and be a particular.97 And, Bergmann describes this union between ‘sorts’ (intensions) and ‘individuators’ as a ‘Two-in-One’, what as a “simple is a composite of two”.98 The latter quote points to how recognizing continuous wholes forces the clarifying differentiation of two senses of the term ‘simple’: a) an entity is simple in the sense of not having two or more parts, and b) an entity is simple in the sense of being with-

|| 95 Ibid., p. 108. 96 The term ‘moderate simplicity’ is used by Yann Schmitt to describe the kind of unity I term ‘continuous composition’ and that he proposes as a solution to the problem of divine simplicity—how God can be simple and yet characterized by the non-identical divine attributes of omniscience, omnipotence, goodness, etc. His proposal is that “we accept a moderate conception of simplicity as absolute indivisibility instead of absolute lack of complexity.” See his ‘The Deadlock of Absolute Divine Simplicity’, International Journal for Philosophy of Religion 74 (2012): 117–30. 97 Keith Campbell, Abstract Particulars, p. 56. I note that Douglas Ehring in also advocating a nominalist trope theory, but of a ‘natural class’ type, argues that, contra Campbell (and our assay), a trope cannot be both simple and have the dual constituent aspects of individuator and a ‘nature’. Ehring avoids this by asserting that the nature of a trope is not a constituent of it but is determined solely by its external membership (p. 186) in “the set of all the natural classes of which it is a member.” (p. 188) Ehring recognizes that this would make a trope a residue ‘bare particular’ but argues that as a trope in his sense it does not succumb to standard objections against bare particulars. I would claim the contrary, for reasons given in Sects. 2.4 and 2.5. Further, Ehring is explicit that the memberships that determine a trope’s nature “are not grounded intrinsically in the trope.” (p. 186) But then a trope’s nature is determined by only what can be arbitrary associations with either natural classes or elements that jointly by association make up natural classes, and so a trope could equally and with no difference to itself have the ‘nature’ of a round trope or a square trope, and this is impossible. See Douglas Ehring in Tropes: Properties, Objects, and Mental Causation (Oxford: Oxford University Press, 2011), pp. 175ff. 98 Gustav Bergmann, New Foundations of Ontology (Madison: University of Wisconsin Press: 1992), pp. 56–59, 90.

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out internal division, i.e., does not have discrete parts. An entity simple in the sense of a) will be simple in the sense of b), but not necessarily conversely, attribute instances being examples of the latter exceptions. With the continuous composition of T6 we have an actual account of the ‘missing link’ between particulars and universals for which historically attribute instances have been posited to ‘forge’. In the being of a continuous composite an intension does not characterize/qualify (i.e., is not an ontic predicate of; is not ‘rooted-in’) the individuator (i.e., the combinatorial agency) it is joined with, nor is it simply associated with (‘tied-to’) its individuator, nor does it qualify the whole that it and its individuator compose. This is opposite the intended connection intensions are to have with posited supporting and collecting ‘bare particulars’, and what makes our assay free from their flaws. There is no ‘ontic space’ between an intension and its individuator, what would require either attribution or association (the ‘rooted-in’ or ‘tied-to’ relation, repectively) as a further outward unifying principle to join them. The divisionless union of continuous composition is differentiated only in the selective attention of conceptual abstraction, wherein we have the basis for the scholastics’ formula: Universalitas est per intellectum cum fundamento in re. Though I would re-emphasize that intensions are also freely constructed in the intellect, e.g., Unicorn1, Frictionless-Surface1 (and hence there can be ‘uninstantiated universals’ in the sense of not occurring in any subject-characterizing attribute instance). And, on our assay we have the Chapter 1 promised clarification of the slogan-characterization of moderate realism: Universals are individuated in things, but repeatable in the mind. The claim here is not the contradiction that intensions are unrepeatable ‘in things’ they qualify but the very same thing is repeatable when abstracted from these subjects. Rather, intensions are repeatable universals inside and outside the intellect, but outside they exist only in simple-asseamless unions that are attribute instances, and they have no independent existences whether internal or external to instances.

4.7 Summary In this chapter there have been argued a number of clarifying and potent ontological theses. We can summarize these gains relative to the classic assumptions examined in Chapters 2 and 3: Attributes are the structuring elements of facts (T2; conforming in this way to A7). As such, attributes are outwardly unifying agents of themselves with the subjects they characterize (T3), and thus attributes are not constituents of their subjects (contra A5 and its generalization), are ontically dependent upon their subjects (A1), and are unrepeatable

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individuals—instances (T4; contra A2). Attribute instances Rni are controlled as to the nature, number, and order of the subjects they qualify by their constituent intensions Rn, these intensions being repeatable universals (T5; contra A6). The unity among an instance’s constituent dual aspects of qualifying agency and the latter’s controlling intension is that of the prior undivided oneness of the subsuming instance (T6), an internal continuous composition that stands in contrast to the external unity an instance effects among its prior and discrete subjects—articulated composition. With all this we have an account of the plausibility of and the correction for the inherence model of attribution (A5 and its generalizations): the union of intension universal Rn, for any adicity n ≥ 1, with an attribute instance Rni is indeed that of internal containment but not of attribution, whereas the union of attribution of Rni in a fact :Rni(a1,a2,..,an) is not that of an impossible containment, for n ≥ 2, of instance Rni in each of subjects a1, a2,…, an, but is rather an external linking to/among these subjects controlled by a compatibility/fit between their natures and/or external unions and intension Rn. With the elimination of classic assumption A5 (Inherent Essential Attributes) there is also eliminated the Dependence Contradiction and Individuation Regress of Section 2.3. Providing insights for solving a number of classic ontological problems was the assay of intensions as both directive—having the intentionality of being inherently relevant to subject-others—and selective— specifying certain conditions that subjects must have in order to be characterized by attributes with these intensions (T2, T3; essential to A1, A7). These characteristics are the source of all de re necessity and of all necessary and contingent facts. An n-tuple of entities could not not be linked and ordered (if any) by an instance Rni if they respectively satisfy the internal and/or external conditions—have the foundations—prescribed by the intension Rn, and it is the cases where these subjects happen to but need not satisfy these conditions that the resultant fact is contingent. Details of the external qualitative/descriptive relevance or fit an intension has with its subjects—crucially, how an intension or attribute is not its own foundation—and of the possibilities of an intension’s prescribed foundations being internal and/or external to their subjects, where offered as shedding light on the classic but disputed distinctions of intrinsic| extrinsic attributes, ‘internal’ verses ‘external’ relations, necessary|contingent facts, and sortal|non-sortal intensions. The results of this chapter lay the foundations for the important advances of the next. There it will be detailed how all structured wholes derive from certain combinations of facts (T7), wholes that have multiple and not single constituent unifiers (contra A8). And it will be seen how all these structures can rest on a foundational stratum consisting of only closed chains of attribute instances

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having other instances as relata—of facts about other facts (T8). This nullifies the need for per se subjects (contra A3). And by this attribute instances are the fundamental building blocks of all reality, what as continuous composites (T6) are the truth behind Aristotle’s assertions that “Primary things are those which do not imply the predication of one element in them of another element.” (Meta. 1030a10) With this chapter and the next we will have eliminated classic assumptions A2, A3, A5, A6, and A8, and along with them all the implied traditional problems identified in Chapters 2 and 3 (including the indicative Dependence Contradiction and Individuation Regress). Only theses A1 (Attributes as Dependent), A4 (Required Essences), and A7 (Attribute Agent-Organizers) survive as veridical.

5 Complex Structures and Ontic Atoms 5.1 Complex Structures by Inter-Attribute and Emergent Composition The work of Chapter 4 was analytic: there we detailed the structuring nature of attribution, the principal results given in theses T2-T6. The key points were that an attribute with an n-adic intension Rn, e.g., Spin1, Prime-Divisor2, Between3, in its defining role of qualifying/characterizing the elements in an n-tuple of subjects, , is an intension-determined combinatorial-agent of its unity with and among these subjects, and as such is an individual/unrepeatable instance Rni unique and irreducible to that n-tuple. With the exception of isolation in abstraction, an instance Rni, e.g., Is-Prime-Divisor-of21, exists only in the context of its resultant fact :Rni(a1,a2,…,an), e.g., :Is-Prime-Divisor-of21(3,6), where it is the cause of a structured union among thus discrete-but-linked subjects, and upon all of which the fact has an asymmetric dependence. In contrast, a constituent attribute instance Rni is itself and internally a continuous whole of two non-identical but non-discrete components: its intension Rn and its outward unifying agency. Here, as with all wholes, an instance is ontically dependent upon its parts, but also reciprocally the combinatorial aspect is ontically dependent upon the whole—neither can exist separate from the other, whereas intensions can exist outside of instances but only in minds upon which they are ontically dependent. The unity among the dual aspects of an instance consists in their non-differentiated contribution to the continuous being of the whole. I.e., the two aspects of an instance Rni are differentiated posterior to it in ‘formal’ abstraction. In regard to ontic dependence, facts are, to borrow phrasing from Armstrong, the least things that can have independent existences.1 Building upon these results, the work of this chapter will be, in contrast, synthetic: we will outline how attribute instances so assayed are sufficient for the derivation of all other types of entities, ontic dependencies, and forms of unification (T1). The latter will be seen to derive hierarchically from combinations of inter-attribute (‘horizontal’) and emergent (‘vertical’) composition (T7), and this upward from a base stratum consisting of only mutually dependent atomic instances (T8) (‘metaphysical coherentism’), the latter correcting the specious classic assumption of per se subjects (A3) (‘metaphysical foundational-

|| 1 D. M. Armstrong, Sketch for a Systematic Metaphysics (Oxford: Clarendon Press, 2010), p. 27.

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ism’). Clarifying criteria for the identity (T9) and indiscernibility (T10) of structures will follow. These results liberate fact-ontology from the overly-restrictive Tractarian thesis that all facts are first-order, a view Armstrong extends only slightly with two types of facts of facts.2 Our results dispose of these errors with warrant in explaining the observed common nature of complex hierarchical structure given in ordinary experience and this extended by scientific instrumentation and theory, the latter including the apparent completely structural and relational nature of foundational quantum reality. With this and all our previous analysis, we have strong grounds, both metaphysical and physical, for the thesis that ontically dependent attribute instances are the founding ontic category; all entities whatsoever derive from instances. They are what Aristotle sought as the ‘primary beings’. First toward establishing the thesis that attribute instances are the single primary ontic category is the observation that all complex structures—physical, logical, mathematical, psychological, social, etc.—are built up iteratively of instances by what are their two modes of composition. It is these two modes that account for the two defining characteristics of complex structures, and do so as simple and natural extensions of our assay of atomic structures, i.e., facts. For intuitively, complex structures are given 1) as composed of either multiply intensioned or ‘kinds’ of connections, or of multiple ‘occurrences’—instances— of the same kinds, and 2) as some themselves structured hierarchically, what involves composing ‘emergent’ attribute instances having entire substructures as single subjects. These conditions are made precise when understood as in fact the two ways multiple attribute instances can share common relata, transitivity across the latter giving the unity-via-multiple-unifier nature (contra A8) to complex structures. Anticipating the following clarifying analysis of these points, we assert here the summarizing result that all complex structural composition can be specified recursively as: T7. All complex structures (organizations, systems, gestalten) are composed, some hierarchically, from atomic structures, i.e., facts (T2), :Rni(a1,a2,…, an), combined as follows: a) If x and y are two structured wholes (e.g., facts :Rni(a1,a2,…,an) and :Smk(b1,b2,…,bm)) having at least one constituent in common (e.g., a1 = b2), then there is a structured whole that contains as constituents all and

|| 2 Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London: Routledge & Kegan Paul, 1961), p. 13, Props. 2.04 and 2.05. D. M. Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997), pp. 2, 196ff, 220ff.

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only the constituents of both x and y (Inter-Attribute (‘Horizontal’) Composition). b) For any fact :Rni(a1,a2,...,an), if for 1 ≤ j ≤ n, aj is a structured whole, then Rni as emergent upon aj is part of a hierarchically structured whole whose constituents are all and only the constituents of the fact and constituents of aj (Emergent (‘Vertical’) Composition). T7 is a ‘recursive definition’ of complex structures, i.e., inter-attribute or emergent composition among or on facts, the atomic simple structures, effect molecular or complex structures, these modes of composition then applying to the latter to effect more complex structures, and so on. Jointly and built upon our assay of attribute instances, these two modes of composition are for ontology (and General Systems Theory in particular) the long-sought explication of the ‘intra-connectiveness’ definitional of complex structures or systems. Indeed, it is primarily the insights of inter-entity unification via attributes (T3) and thereby their individuation as instances (T4), together with instances’ two modes of complex composition given in T7, that provide a rigorous and intuitively consonant account of structure and so a powerful counter to eliminativist and reductionist theories. Or in short, with these theses we will have a perspicuous account of how arrangements-of-entities are as much ‘additions to being’ and themselves single subjects for attributes (including, e.g., of efficient causality) as are the things arranged. To make the two modes of complex structural composition more perspicuous we can utilize the following ‘rod & node’ models for facts. Smooth curves, e.g., here straight lines, will represent attribute instances and the dots they contain will represent the instances’ subjects (what, more specifically, could be other instances or entire structures, as will be seen below). For example,

Structure A represents the fact :F1i(a), with its single subject a and monadic property instance F1i. Similarly, Structure B represents the dyadic fact :R2j(b,e), and Structure C the triadic fact :S3k(a,b,c). In general, facts with n-adic attribute instances are modeled as smooth curves, herein mostly straight lines, having n dots. Now, given structures A, B, and C, and assuming that here token subject

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terms of the same type name the same subject, these structures can be seen to be each substructures of the more complex structured whole D:

Here we have a completely inter-connected and in this a single complex whole, one whose unity is via shared relata among three attribute instances. Specifically, there is in Structure D a connectedness of each of its constituents, whether instance or subject, with every other, this through either the mediation of two instances having one or more common elements (here common subjects), or by a transitive unity across chains of such connections. Such mediated unity is accurately termed inter-attribute composition. By means of it wholes like D are structured or organized each due to all of its inter-entity connectedness being by the mutual and direct contribution of each of its constituent intension-determined attribute instances. For example, instance F1i is linked with remote entity e, what is not its subject, through the connected links of fact :F1i(a) sharing subject a with fact :S3k(a,b,c), and then the latter fact sharing subject b with fact :R2j(b,e). There is between F1i and e a ‘path-connectedness’ across D, i.e., F1i and e are at opposite ends of an articulated sequence of instances of D whose connecting joints are, here for inter-attribute composition, shared subjects (the connecting joints for emergent composition will be seen to be definingly different).3 Clearly, Structure D could likewise be a substructure of an expanded lattice of further and subsuming structures, their graphs imagined to radiate outward from D, and with each element being unified with any other across chains of composing attribute instances and their pairwise sharing of constitu-

|| 3 Peter Simons has proposed that the topological concept of ‘path-connectedness’ points toward the defining characteristic of integrated wholes generally. See his Parts: A Study in Ontology (Oxford: Clarendon Press, 1987), p. 327. Our two modes of composition in fact detail the general path-connectedness that effects all structured/integrated wholes. Indeed, we could define path-connectedness so as to then define complex structure in the following way: P is a path-connection between a and b if and only if P is a set of attribute instances such that for every partition of P into S and T, where a is an instance or a subject for an instance in S and similarly for b in T, then there is an instance Fi in S and an instance Gj in T such that Fi and Gj are joined by either inter-attribute or emergent composition (appropriately restated). Then, a set of instances form a complex structure if and only if any two subjects of these instances are path-connected.

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ents. Each such plural whole is a structure—more than just an arbitrary collection of its parts—in a way derived from the primary and atomic structures of its composing facts and how these links share certain entities—the ‘arrangement’ of the facts. Via shared relata thus contiguous facts are chained together to form non-arbitrary lines/paths of transitive unification, each of whose interconnecting segments are intension-determined and all jointly forming a networked whole. Hence, T7a). Such segmented composites are counter-examples to classic assumption A8 which asserts that all unity is by a constituent one. A8 is accurate to the unmediated unity that a single instance Rni causes among its n subjects—metaphorically, like a single thread holding together multiple beads of a necklace. But, with examples like D we observe not a single unifier but the mediated unity across multiple unifying instances sharing common elements, like the transitive unity across the links in a chain, or, three-dimensionally, like the lattice of molecular bonds structuring a single crystal. Described by the second mode of complex composition—emergent composition—is the fact that structures can as wholes and in their entirety be single subjects for further attribute instances. As an example from semantics, a fact though itself complex can be one relatum for an instance of a truth-correspondence relation with a proposition descriptive of it as the other relatum. When this is the case, the latter proposition, itself a complex semantic structure, is as a single entity the subject for an instance of the intension True1. Or more generally, every fact and proposition, indeed every plural whole, is as one entity a subject for an instance Is-Complex1i. Other more obvious examples are our oftmentioned biological structures, e.g., organs, that themselves have attributes, e.g., specific functions that their substructures do not have, and what in their proper structuring makes the resultant whole, e.g., a living human body, found attributes, e.g., local motion, sexual reproduction, consciousness, that the organs in themselves and not specifically inter-related do not have. Analogously for machines, e.g., computers and their subparts. In general, in an emergent composition it is jointly the specific intensions and the mutual arrangement of attribute instances (and so the subjects they presuppose) that in their connected totality found as one subject a thus descriptive emergent attribute instance, e.g., Is-True1i, Produces-Insulin1j, Imply-as-Premises2k, Is-President-of2n, Does-Addition1m. We can represent emergent composition graphically using braces, ‘}’, to indicate that an entire structure is to be one subject for further attribute instances.

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In Structure E we have four cases of emergent composition indicated by the four braces. The left-most brace has the Structure D to its left and is intended to indicate that D as a whole and in its entirety is one subject for the attribute instance whose graph is attached at the point of the brace, viz., dyadic attribute instance R2i, what has f as its other subject. Implied here is that some or all of the intra-organization of D is a necessary and sufficient foundation, as specified by intension R2, for a first subject of an attribute instance R2i, as is the nature of f for its second subject, the two subjects then joined in the fact :R2i(D,f). As given in Structure E, the latter ‘second-level’ fact forms an inter-attribute composite with fact :M2k(f,g) through shared relatum f. These then jointly form a complex structure that, as indicated by the upper-middle brace, is as a single entity a subject for triadic instance Q3i. Then in regard to triadic instance Q3i, in addition to the latter structure and entity m, its third subject, indicated by the lower-middle brace, is the inter-attribute structure of instances S3j and R2n and their subjects, as such a single entity. The right-most brace indicates that the entire hierarchical structure to its left is a single subject for the monadic property instance T1i. With emergent composition as in Structure E the transitive ‘path-connectedness’ of any two elements of the resulting whole is still through shared entities, but not in the way of inter-attribute composition where pairs of instances share the same subjects. Here the sequenced inter-connectedness of elements, say, a with f, is trans-strata (‘up-and-out’) at the point of a shared emergent whole D, where on the one side is the upward connectedness of part a to its derivative/emergent plural whole D, and on the other side the outward connectedness of D as a single subject of instance R2i to f. With these observations generalized, we have T7b). And as above, we can imagine Structure E increasingly augmented with attribute instances entering into both inter-attribute and emergent compositions with its components, jointly forming a hierarchy of increasingly more complex and stratified structures having E as a substructure.

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In particular, contrary to the claim that there are only first-order facts, by emergent composition of T7b) there are vast hierarchies of n+1-order facts of n-order facts. Our example structures of bodily organs, computers, and automobile engines remind us of the fact that the vast majority of structures given as such in everyday experience or hypothesized in science are dynamic, i.e., attribute instances come into and go out of existence at various rates, and thus also the structures they are parts of. More accurate in modeling such dynamic wholes, structures like A-E above can be imagined as animated, with instances going out of existence, new ones perhaps replacing them, or the whole being augmented by new instances joined to old in inter-attribute or emergent composition. In such continual change a preponderance of new instances makes for structural growth (e.g., human maturation), a preponderance of disappearing instances makes for de-structuring (e.g., organ atrophy), and a certain balance between the two maintains the whole in a steady state or equilibrium (e.g., the autopoiesis of a body functioning in good health). These considerations point to how attribute instances and their T7 modes of composition can provide an ontological account of observed emergent characteristics and ‘mechanisms’ of complex dynamic systems, e.g., from General Systems Theory the mechanisms of homeostasis, autopoiesis, and onto- and phylogenesis. Importantly, what some of this would require, and what is not, to avoid visual confusion, modeled in Structure E, is ‘downward causation’. I.e., among the emergent relations a structure, say E, could have and of which it would be one relatum are ones having one or more of E’s composing substructures, say D, as other relata. The coming into existence of such a relation instance on E and D may effect changes in substructure D, where then resultant substructure Dʹ effects a different emergent structure Eʹ. A simple example is the ‘feed-back loop’ that is a dynamic furnace—ambient-temperature—thermostat system. I emphasize again that all such complex wholes, static and dynamic, are ‘one’ via the cooperative agency of multiple unifiers—attribute instances—contra classic assumption A8 (Unity by the Constituent One). As pointed out in Section 2.6, A8 is implied by the premises that a structured whole has essentially an attribute with intension Unification1 or Oneness1 (what on our assay would be instances Is-a-Unity1i or Is-a-One1i) and classic assumption A5 (Inherent Essential Attributes) which asserts that essential attributes are constituents of their subjects where they serve as foundations for their attributions to these subjects. It would follow, though I think with reductio incredibility if made explicit, that a property with the intension Unification1 would be the single constituent foundation, and so the internal cause of (the single ‘connecting thread’ providing) the

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unity of the subject structure it characterizes (this analogous to how a universal was considered a single unifying thread holding the entities that exemplify it together as a unified extension). Our contrary lessons are that A5 and A8 are false—attributes are not to be identified with their foundations, and so in this minimal extended sense all attributes are ‘emergent’, and that a single unity can be by multiple unifying causes. Structure E models the latter when T1i of the diagram is assigned as its intension Unification1. I note that, though not indicated within the diagram, if T1 were the intension Unification1 then every component of Structure E—‘node’ subjects and ‘rod’ attributes—would have an instance of T1 emergent upon it. Further concerning emergence proper, we can use Structure E to illustrate points made in Section 1.4. On our assay of attributes as instances, there are two ways attribute instances can be new and non-eliminable, and so emergent in the full sense: The first is simply that an attribute instance, e.g., R2i in Structure E, can obtain only on its unique subject n-tuple (T4), and so, a fortiori, cannot occur at any prior level of composition forming each of its n subjects. Though as in Structure E, it is possible that, depending upon the intension, e.g., R2, different instances of it can occur at different levels of a complex, e.g., R2j and R2i. We have noted this with regard to the intension Unification1, and for other intensions, e.g., Mass1, Extension1, instances of them occur at all but perhaps the most elementary sub-levels of any complex whole qualified by instances of them. Closer to the common intent of ‘emergent’ are those attribute intensions that have no instances below certain levels of specific complexity and so are novel at that level4, e.g., as instances of Capable-of-Consciousness1 (say, T1 as above) occur only at a neural level of an immensely complex hierarchically structured physical brain (abbreviated by the part of structure E left of the rightmost brace). Or, the less but still highly hierarchically complex structure that is an automobile engine (abbreviated similarly) has as emergent in this sense the attribute instance Is-a-Continual-Source-of-Motive-Power1i (modeled with T1i above)—the engine but none of its parts, e.g., an alternator, nor the latter’s parts, e.g., bolts or wires, nor the latters’ parts, e.g., metal molecules, nor etc., have this attribute.

|| 4 For an overview and references see Timothy O'Connor and Hong Yu Wong, ‘Emergent Properties’, The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.), URL = . For a detailed argument that there are novel emergent attributes in molecular biology see F. Googerd, F. Bruggeman, R. Richardson, A. Stephan, and H. Westerhoff, ‘Emergence and its Place in Nature: A Case Study of Biochemical Networks’, Synthese 145 (2005): 131–164.

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In Structure E, intension T1 whose instance T1i characterizes the whole hierarchical substructure to its left, could, if the latter substructure were a classical ‘substance’, be an infima species, e.g., Rational-Animal1. Or, if intension T1 is descriptive of all the exact compositional details—all the relative ‘arrangements’ of the parts—of this substructure, then T1 would be what all structures that are strictly isomorphic to it have in common—it would be their ‘kind’ in this detailed sense. In general, an intension T1 can as a ‘kind’ or ‘sort’ be more or less specific or selectively descriptive of the details of a subject’s composing structure, e.g., due to the various substructures of its molecular matter and from them hierarchies of geometric formations, an artifact can be characterized by instances T1i of the different descriptive kinds: Container1, Bottle1, Glass1, GlassBottle1, Air-tight1, etc. Consider as a further relevant example and one muchdiscussed as a supposed quandary for common-sense ontology: that of a statue, say a miniature of a horse, fashioned from a continuous lump of clay. Ostensibly, the statue and the mass of clay are not identical, the persistence conditions of one not being those of the other. However, it is argued that if the statue cannot be identified with the mass of clay composing it, then we have two objects occupying the same space-time, and this is implausible. Moreover, if, say the mass of clay weighed 10 pounds, then so would the statue, but if they are not identical then when the statue is placed on a scale the reading should be 20 pounds, the sum of the weights of the two non-identical items, and this is counter-factual. On our analysis and consonant with common-sense informed by science, the statue s is but one hierarchically structured whole that at its highest level has a complex geometric shape sufficient for s to satisfy the intension Statue-of-a-Horse1, but contains as a proper molecular substructure what is sufficient for s to satisfy the intension Lump-of-Clay1. The ‘horizontally’ structuring relations of the latter molecular substructure are spatial relations of general proximity, not of particular geometric configurations, whereby the molecules are joined in a continuously extended but amorphous ‘lump’. What we have with the statue-clay example is one total hierarchical structure s—the statue—composed of substructures, one being the mass of clay as continuous but amorphous, and instances of two intensions, one descriptive of s in its highestlevel structure and one descriptive of s as it has a substructure of simply juxtaposed clay molecules. This explanation is unavailable to theorists who do not recognize structuring components in addition to the material parts of organized wholes. They are left with no answer to the so-called ‘Grounding Problem’5: || 5 See Kathrin Koslicki, The Structure of Objects (Oxford: Oxford University Press, 2008), pp. 181–83.

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How can entities with the same ultimate material parts, say atomic parts, be distinct? The answer is simply that the same parts are differently structured by constituent attribute instances in the manners of T7. With these observations as a part, our analysis of structural unity clarifies and extends, for example, the recent work of Kathrin Koslicki in her attempt to also give an account of ‘restricted composition’ (Sect. 1.1). This is particularly so in her advancing the thesis that structural components of organized entities are to be counted among their proper parts. Following upon her analysis, Koslicki proposes a ‘Restricted Composition Principle’ (RCP), what in its atemporal version reads: Some objects, m1, …, mn, compose an object, O, of kind, K, just in case m1, …, mn, satisfy the constraints dictated by some formal components simpliciter, f1, …, fn, associated with objects of kind K.6

By ‘formal components simpliciter’ of O, e.g., of a table, Koslicki means those structural components explicitly prescribed by kind K (say, T1 in Structure E), e.g., the kind Table, which would not include the formal components at lower levels of composition of O, such as the structural properties of the molecules making up a table. For that matter, the specific geometric shapes of the top or legs do not count among the foundations for instances of the intension Table1. The possibility of less detail-specific intensions, e.g., Table1, and their instances under T7b) account for this. Indeed, Koslicki’s RCP is made precise and expanded on our analyses by their explaining how the formal components, f1, …, fn, are in fact attribute instances, and can be of any intensions (and not particular ones posited to effect structured wholes, e.g., Baker’s ‘constitution relations’7 or Fine’s relations that serve as ‘principles of rigid embodyment’8), and how their resultant facts are themselves ‘organized’ in the manners of T7, what as a thus unified whole can then be accurately described as of a ‘kind K’. Koslicki is careful to say that the structuring components, f1, …, fn, organizing an object O are “associated with” a kind K, and not that K is also a formal component of O that orchestrates—meta-structures—the “recipe”9 that is f1, …, fn, in their joint structuring of O. Though, one might infer otherwise from her statement that “kinds really do pose constraints on the mereological composition of their

|| 6 Ibid., pp. 187–88. 7 Lynne Rudder Baker, The Metaphysics of Everyday Life: An Essay in Practical Realism (Cambridge: Cambridge University Press, 2007). 8 Kit Fine, ‘Things and Their Parts’, Midwest Studies in Philosophy XXIII (1999): 61–74. 9 Koslicki, The Structure of Objects, pp. 172, 182.

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members.”10 For this would seem to make a kind K a second-level formal aspect of O structuring (‘constraining’) O’s formal aspects, f1, …, fn, and for the same reasons the latter are components of O so should K be a component of O. Consistent with Koslicki’s apparent view and explicit on our assay, a ‘kind’ intension, again say T1 involved in Structure E above, specifies conditions that must be satisfied by its subject in order for an instance of the kind, our T1i, to characterize it, but the instance T1i is not a constituent contributor to—not inherent in—the structuring of the subject nor is it an external cause of it. In general, it is not an instance of a kind that internally causes a whole to be structured as one of that kind, but it is the prior structuring of the whole that provides the foundations causing it to be externally characterized with an instance of a kind descriptive of that structure. Complex wholes being hierarchical structures are not created and differentiated from others by the ‘top-down’ imposition of monadic forms on some single stratum of matter, but rather are composed ‘bottom-up’ of attribute instances via T7 modes of lateral and emergent composition, where the specific ‘configurations’ of each of these hierarchies founds it having certain attributes demarcating it from other substructure wholes within the total structure that is Reality.

5.2 Attribute Instances as ‘Primary Beings’ In addition to the above account of the two modes of unification involved in complex structured wholes, there remains the ontological task required by the analyses of Chapters 2 and 3 of showing how attribute instances, though inherently outwardly dependent entities, are sufficient unto themselves, i.e., as a single category, to provide an ontic foundation for all other entities. Once established, this will do away with the need for the classic and insidious posit of per se subjects (A3)—independent simple entities thought needed to support dependent attributes and complex wholes. Per se subjects as individuals (A6) is the concept behind classic ‘prime matter’ and contemporary ‘bare particulars’, and I have argued in Section 2.4 that these posits are incoherent. As an instructive reminder consider a slightly different argument against per se subjects. Let p be a per se subject, what as such has the essential attributes, and hence the foundations for, Is-Independent1i and Is-Simple1j (Simple1 in the strict sense of having no non-identical components (Sect. 4.6)). For each of these attributes their foundations are intrinsic to, and necessary and sufficient for the attributes

|| 10 Ibid., p. 200.

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to characterize p. However, these foundations as components of p cannot be numerically identical, for there are entities that are simple but not independent, e.g., the combinatorial agency of instances. But this makes p complex, contradicting its having the attribute Is-Simple1j. The conclusion follows as a contradiction to the lemma that if the foundations in a subject a (here posit p) for it having intrinsic properties F1i and G1j are numerically the same, then, if a subject b founds an instance F1m it must also found an instance G1n. Avoiding such problems, our thesis is that the ultimate subjects of attribution are themselves attributes—as instances—what as such are neither independent nor without distinguishable parts (though parts that are not discrete (T6)). In sum, the necessity of dependent entities, i.e., attributes properly assayed (A1, T3-T4), together with the impossibility of a substratum of ultimate independent and simple supporting per se entities, requires a substratum composed of attribute instances only. That is, required is a foundational level consisting of only dependent attribute instances. And given our assay of instances thus far, and independent of arguments against per se subjects, it is a simple matter to account for such a foundational stratum, this alone sufficient to render the posit of supporting and categorically different per se subjects superfluous and thus a target for Ockham’s Razor. In detail: T8. Attribute instances, Rni, Smj, Tok,…, as a category of inherently ontically dependent entities, do not require further categories of inherently independent per se entities in order to avoid a vicious regress of dependence. In particular, it is possible that there is at some base ontic level atomic attribute instances that have their dependence satisfied by only other atomiclevel instances as subjects, and this via shared instances forming closed chains of atomic facts; :Rni(..,Smj,..,Tok,..), :Smj(..,Tok,..,Rni,..), :Tok(..,Rni,.., Smj,..), … I.e., there can be an ontic atomic level of mutually sustaining dependent instances. T8 follows from the fact that, given their individuated outward combinatorial natures, attribute instances, Rni, Smj, Tok,…, are sufficient as a category to supply an atomic subset of mutually supporting instances, where the latter are individual links in closed chains jointly forming completed structures. This is demonstrated in diagrams like the following:

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Structure F consists only of monadic attribute instances M1i, N1j, and O1k, but arranged in a closed sequence of inter-attribute compositions where each instance has another instance as its subject, e.g., line M1i in meeting obliquely and not extending beyond O1k symbolizes that instance O1k is the subject of M1i. I.e., Structure F consists of the closed sequence of facts :M1i(O1k), :O1k(N1j), and :N1j(M1i). Here each instance’s ontic dependence is satisfied by another instance in the structure, requiring nothing outside the thus completed loop to support the existence of each instance and so that of the whole. Importantly, the circularity here is non-vicious because instances depend in part for their existences upon the existences of subject-others, but their composing beings do not derive from—are not parts of—the beings of their subjects, what would be a vicious dependence.11 And, we can easily imagine a structure like F extended to any number of monadic instances (‘sides’), each instance a subject for another constituent monadic instance. Structure G consists of a closed system of three dyadic instances, relations J2i, K2j, and L2k, though here, to illustrate each instance’s dependence being satisfied by the other two, they are each modeled, not by straight lines, but curved open-‘C’s. For example, at one of its endpoints K2j meets but does not extend beyond L2k, indicating that L2k is one of its subjects, and at K2j’s other endpoint the same for J2i. Illustrated thus is the fact :K2j(L2k,J2i). Modeled in the same way are the other facts :L2k(K2j,J2i) and :J2i(L2k,K2j), what jointly with fact :K2j(L2k,J2i) compose Structure G. Here the dependence of each dyadic instance upon two other subjects is satisfied by entities within the structure—nothing outside the composing instances is required for the existence of the whole. Now generalizing, one can see the possibility of other such diagrams consisting of any number of instances and of various intensions and adicities, and where the subjects of each composing instance are other composing instances. With each we have a closed system/ network of instances that are, directly or indirectly, mutually sustaining. The possibility of such lowest-level structures composed of only dependent instances (‘metaphysical coherentism’) both avoids a vicious regress of ontic dependence—‘turtles all the way down’ (‘metaphysical infinitism’)12—and removes the || 11 As an analogy, think of boards upright because they are leaning against each other. Each has an existence as an upright board because of the others, but the composing being of each board is distinct from that of the others. 12 The argument against foundationaless infinitism with regard to attribute instances is that with it we have an infinitely regresssing chain of instances, each dependent upon the next, and so a dependence that in its transitivity gets passed on but never satisfied. The situation here is like the unending sequence of promissory notes, each written to pay off the former but none of which pay off the debt.

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necessity of positing some foundational stratum of non-attribute non-dependent entities—per se subjects (bare particulars, prime matter)—i.e., it nullifies classic assumption A3 (‘metaphysical foundationalism’). Thus within T8 atomic structures every element is an attribute instance, of possibly any adicity, that characterizes other elements, not the whole, and this necessarily by an outward unifying agency (i.e., attribution is adherence) rendering it both individual and intrinsically ontically dependent, and hence on the latter no element in the atomic whole is a per se subject (thus avoiding the attendant problems). This contrasts with classic trope theory bundles taken as atomic wholes, where for each the constituent tropes are monadic properties that characterize the whole (i.e., attribution is inherence), and each trope is a combinatorially inert per se subject with posited individuation, their unity into a whole requiring a categorically different unifying, dependent, and (at least) dyadic Compresence attribute (problems with the latter described in Sect. 3.3). I note that with T8-type purely attributional structures all composing instances must come-into or go-out-of existence simultaneously. Thus, if for such a structure a all of its composing instances are intrinsic in the sense of Section 4.2, then each part and the resultant object a would exist necessarily and independently of any other external facts (a kind of unchanging Democritian ‘atom’). However, if one or more of a’s composing instances Rni is extrinsic in the sense of Section 4.2, i.e., Rni obtains among its subjects because one or more of these subjects exist in external unions (attributions or associations) prescribed by Rni’s intension, Rn, then, if these unions are contingent, so will be the existence of Rni and so likewise the existence of emergent a. The above then is the finishing component of our global thesis (T1): that all entities whatsoever are or derive from attribute instances, as either composing them (intension universals and combinatorial acts (T2-T5)), as composed of them, i.e., as structures (T7, T8), or as emergent from specific structures of them (e.g., the arbitrary associations and abstractions by cognitive faculties that emerge from certain neural structures). Alternately, objects (in our sense of non-attribute entities (Sect. 2.1)) are secondary and derivative of property and relation instances. I.e., attribute instances are the ontic atoms—Aristotelian ‘primary beings’—and so together are the primary ontological category. With all of this we have a detailing and justification of classic assumption A7 (Attribute Agent-Organizers) and a refining extension of an Aristotelian insight: ‘that there are exactly as many species of being as there are species of unity provided by attribute instances’ (an extension of Meta. 1003b33). The latter corrects the

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maxim ‘to exist is to have an attribute’13 to the proper ‘to exist is to be, or be derivative from, attributes—as instances’. In this way all existents whatsoever (including single facts, contra, e.g., Armstrong) are ontically dependent—noninstances dependent upon instances, and at bottom some instances dependent upon other instances. Existential dependence does not mark a deficit of being, but is a condition of all that exists, and in its root form as that of attribute instances derives from their natures as each a positive act of outward characterizing unification.14 In addition to what I have argued is their ontological necessity, the assay of ultimate/foundational entities as closed structures of mutually sustaining instances (T8) is both reinforced by and serves to refine a popular proto-ontology for our current micro-physics—Ontic Structural Realism (OSR). Touched upon in Chapter 1, OSR is the general thesis that an accurate ontology for Quantum Mechanics and General Relativity will be one that shows how relational structures can be the fundamental entities and in a way where there are no relata subjects/‘substances’ with beings independent of the relational structures in which they are embedded.15 In other words, it is held that warranted in these domains is the existence of individuals, e.g., quantum particles and space-time points, whose composing essences—their existences, identities, and individuations—and so the attributes founded on these, are determined at least in part by their specific types of unions with other entities—by their positions in subsum-

|| 13 James Moreland, ‘Theories of Individuation: A Reconsideration of Bare Particulars’, Pacific Philosophical Quarterly 79 (1998): 251–63. 14 Among the implications of our conclusion is its requiring us to be careful in formulating one of the standard arguments for the existence of God, viz., the supposed necessity of an ‘uncaused-cause’ in the sense of an underived nondependent source of the derived dependent. One could argue that in order to avoid vicious regress there must be some ultimate underived entities, but the latter need not be inherently independent entities. This is the case in Christian Theology in the Doctrine of the Trinity, where the three Persons are taken to be each a relatedness among (and so relationally dependent upon) the other two. See, e.g., Thomas Aquinas, Summa Theologica, 3 Vols., trans. Fathers of the English Dominican Province (New York: Benziger Brothers, Inc., 1947), Pt. I, Q. 27–40. 15 For an overview see James Ladyman, ‘Structural Realism’, The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.), URL = . Also see Ladyman, ‘Scientific Structuralism’, Proceedings of the Aristotelian Society Supplementary Volume LXXXI (2007): 23–43; Steven French, ‘The Interdependence of Structure, Objects and Dependence’, Synthese 175 (2010): 89– 109; Peter Ainsworth, ‘What is Ontic Structural Realism?’, Studies in History and Philosophy of Modern Physics 41 (2010): 50–57; F. A. Muller, ‘Withering away, weakly’, Synthese 180 (2011): 223–33.

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ing ‘relational webs’. These entities have no beings independent of or prior to certain external unions with other entities. Specifically in regard to quantum entities, held as motivations for the relational-web thesis are the apparent facts that such entities are variously: indiscernible on permutation (as are space-time points), have indefinite location, exhibit wave-particle duality, have certain properties only on measurement, and are necessarily linked though separated when in entangled states. OSR advocate James Ladyman assesses these and other relevant facts as implying “That relational structure is ontologically more fundamental than individual objects,” and that we are to reject “The metaphysical article of faith that objects and properties must have intrinsic natures prior to entering into relations.”16 Central to the ongoing OSR debate over such claims have been the issues of: 1) whether the relevant relations have beings distinct from that of (i.e., do not just ‘supervene’ upon) their subjects?, 2) whether quantum entities and space-time points as relata exist at all, or rather are just the ‘meeting points’ of structuring relations?, and 3) if they do so exist whether they have intrinsic natures, and, if the latter, how do these natures contribute to the fact that their identities and individuations are dependent upon the relational systems they are parts of?17 Our assay of dependent relation and property instances, with quantum entities taken as either attribute instances or as closed systems of mutually sustaining instances (T8), provides direct and clarifying answers to these issues. First and toward this point, Peter Simons has outlined a now prominent structuralist quantum ontology built up from T8-like closed bundles of ‘mutually founding’ tropes.18 Founding the stratified compositions that make up physical reality, he proposes that certain mutually and immediately unifying (thus avoiding Bradley’s Regress) and so dependent tropes form tight ‘nuclei’ or ‘kernels’ (where “each trope requires the other”), these wholes then themselves existing in looser unions of ‘generic dependence’ with other peripheral accidental tropes, e.g., particular velocities. A peripheral trope is fully specific, e.g., a velocity of 5m/sec, and requires for its existence a kernel, however the kernel does not require for its existence this specific trope but only one from the same || 16 Ladyman, ‘Structural Realism’. 17 Ibid. 18 Peter Simons, ‘Particulars in Particular Clothing: Three Trope Theories of Substance, Philosophy and Phenomenological Research LIV (1994): 553–75; ‘’Farewell to Substance: A Differentiated Leave-Taking’, Ratio XI (1998): 235–52; ‘Identity Through Time and Trope Bundles’, Topoi 19 (2000): 147–55; ‘The Ties that Bind: What Holds Individuals Together’, in Substanz: Neue Überlegungen zu einer klassischen Kategorie des Seienden, Käthe Trettin (ed.), (Frankfurt am Main: Klostermann, 2005).

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generic kind, e.g., some one of the type velocity. For Simons tropes can be either monadic or polyadic. In line with Simons’ proposal, Matteo Morganti has added details on how what are currently considered fundamental particles under the ‘Standard Model’, viz., 12 fermions (6 quarks and 6 leptons) and 12 bosons (photons, 3 gauge bosons, and 8 gluons), can be seen as composites of tropes of four elemental attribute-kinds: color, mass, electrical-charge, and spin.19 One is reminded of Aristotle’s physics where the basic elements of earth, air, fire, and water, are theorized to derive from pair-wise non-contrary combinations of the qualities wet, dry, hot, and cold (Gen. & Cor. 330a30-332a3). Morganti observes that this trope account is general enough to cover entities construed in terms of quantum field theory, and others have argued specifically that fields, what are assessed as dynamic structures composed of events, not objects, are best accounted for in terms of a trope ontology20, in this way field theory being subject to our instance refinements. It is, of course, an empirical question whether color, mass, charge, and spin are the elemental attributes; it may be the case that instances of these attributes emerge on wholes composed of attribute instances of some more elementary theory, e.g., String Theory. In particular, for our assay of attribute instances to apply, physical ‘atoms’ would have to be intensionally-delimited (‘of a kind’) agent-unifiers, presumably instances of specific and causally unifying elemental forces and these understood as relation attributes. Closed chains of facts, in the manner of T8, involving these force-attributes would be Simons’ ‘kernels’ and they would be as wholes single subjects for instances of, perhaps, color, mass, etc. Physics will have to supply the deciding details. Continuing Simons’ outline, the theory he proposes to be tested is one of kernels of mutually dependent and thus somehow mutually unifying tropes of elemental physical kinds, these the subjects for ‘halos’ of dependent peripheral tropes, and that jointly form, ‘under dependence closure’, the analogs of traditional simple and independent substances. Simons then suggests how various hierarchical wholes are formed from these simple substances by other unifying ‘ties’, the latter including causal relations forming causal chains, constitutive succession relations unifying successive episodes that make up a dynamic entity’s endurance across change, unity by constituent contemporaneous forces, and ‘Gestalt qualities’ that give structured unity to organisms, societies, and

|| 19 Matteo Morganti, ‘Tropes and Physics’, Grazer Philosophische Studien 78 (2009): 185–205. 20 See, e.g., Andrew Wayne, ‘A Trope-Bundle Ontology for Field Theory’, in The Ontology of Spacetime II, Denis Dieks (ed.), (Amsterdam: Elsevier, 2008), and Meinard Kuhlmann, The Ultimate Constituents of the Material World (Frankfurt: Ontos Verlag, 2010).

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nations.21 Now our analysis thus far, and bolstered later in regard to the identities of changing structures (Sect. 5.5), fills in, unifies, and clarifies Simons’ account: Simons’ tropes posited as dependent, individuated, and founded correspond to what we have been able to ontologically warrant are attribute instances, Rni, dependent and individuated as combinatorial agents, and ‘founded’ by their subjects satisfying conditions set and required by their intensions, Rn, (the necessity or contingency of such unions explained in the manner of Sect. 4.2); his quantum kernels are our T8 mutually supporting closed attributional loops; his wholes by simultaneous forces, causal chains, and succession relations are all just complex structures formed as static or dynamic interattribute and/or emergent composites (T7), e.g., Structure E; and Simon’s Gestalt qualities, contrary to his holding that they are constituent structuring unifiers of organized wholes, they correspond to our emergent attribute instances (T7b)) and characterize a prior structured whole because of the specific intensions of the composing relations and their T7 ‘arrangements’. And so relatedly and answering the OSR question above concerning specifically the quantum or ‘kernel’ level, we have argued that all attributes, and so whatever are the ultimate physical properties and relations, as instances have, in answer to 1), beings distinct from—not reducible to or constituents of—their subjects to which they externally attach via their natures as connecting agents (T3). This agency is both the principle of individuation (T4)22 and part of the identity (along with an intension (T5)) of an attribute instance, and implies necessarily subject-others, i.e., it is the internal composing nature of an instance to exist only in an external context of its intension-controlled connectedness with other entities. In answer to 2), the atomic ontic level is structured not via a transitive linking of relations across shared characterless ‘meeting points’, the latter the bogus logical residue of evaporated ‘substances’ (what would be ‘bare subjects’ analogs of ‘bare particulars’), but is structured by attribute instances having other instances as relata they characterize (T8), all instances in the efficacies of their intension-controlled attributional acts proved fully and equally real. Providing the transitive unity at this level, the ‘meeting places’ or ‘nodes’ are not categorically different from their interconnecting instance ‘rods’: every composing instance having the role of both an inter-connecting rod and a

|| 21 Simons, ‘The Ties that Bind’. 22 In regard to individuation, this assay clarifies what in advocating OSR Ladyman refers to as “contextual individuation”, individuation that does not require the posit of haecceitas or bare particulars. See James Ladyman, ‘On the Identity and Diversity of Objects in a Structure’, Proceedings of the Aristotelian Society, Supplementary Volume LXXXI (2007): 23–43.

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connected node, the resultant particle-system then being composed solely of structuring instances/‘rods’. And with space or space-time treated relationally, it is a lattice of variously mutually dependent spatial or spatial-temporal facts, ‘extensionless’ points like their cousins ‘bare’ particulars, having been dispensed with. In these ways the OSR slogan ‘All there is, is structure’ is true at the level of elemental physics, as it would be for all hierarchical reality emerging from this stratum via the modes of composition of T7. Finally in regard to 3) above, under T8, quantum particles are not just parts of attributional structures but are closed loops of atomic attribute instances, each loop in its complete unity is a single structure with its own intrinsic nature, the latter derivative of the particular configuration and the intensions of the composing instances, and providing the foundations for the whole as one subject having descriptive emergent instances in the manner of T7b). A quantum field would be a hierarchical structure composed in the manner of T7 around and upon a base of T8particles, and as the composing acting instances can come-into and go-out-of existence and so are properly events, the field is in this way a dynamic event structure. And in general, the attribute instances of T8-structures depend for their defining natures upon the closed attributional structures they are parts of, whereas all other structures emerging upon the latter have natures derived from the attributional structures that compose them. Finally, I think it is now clear that the often-made assertion in the context of OSR that relations and relata must be categorically different23 is based upon the same error that motivated the tradition to think that classic assumption A3 (Per se Subjects) is required, given veridical assumption A1 (Attributes as Dependent), i.e., the error that dependent attributes require independent—thus nonattribute—subjects. Recalling the observations of Chapter 2, I suggest that resistance to the contrary view stems from the implicit and facile beliefs that monadic properties are the paradigm ontic predicates (relations reducible to or ‘supervening’ upon them) and that the union of predication is that of inclusion of an attribute in the composition of its subject, i.e., generalized A5 (Inherent Essential Attributes). As such, properties cannot form mutually sustaining closed loops since by the transitivity of the Part-of2 relation the composing properties would each and absurdly end up being proper parts of themselves. Hence on these assumptions, properties (and so relations) cannot depend upon only other properties (and so relations) for their existences. To the contrary, we have

|| 23 E.g., bringing this charge is Michael Esfeld and Vincent Lam, ‘Moderate Structural Realism about Space-Time’, Synthese 160 (2008): 27–46. For other references see Ladyman, ‘Structural Realism’.

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seen reasons to reject A5 and its generalization—attributes attach externally to their subjects (T3), what then and intuitively makes polyadic relations paradigm and properties but the limiting case, parries the Part-of reductio, and provides the ontological possibility of fundamental independent systems composed of only mutually dependent attribute instances (T3, T4, T7, T8).

5.3 The Identity and Indiscernibility of Structured Entities Our results concerning the composition of structures, from single facts (T2-T4) to complexes of them (T7, T8), provide a criterion for their identity. Intuitively, entities x and y are identical if and only if the composing beings of x and y are not two distinct things, i.e., there is no numerical difference in the intrinsic beings of the referent of ‘x’ and the referent of ‘y’.24 Hence literally, ‘Composition is Identity’, but where composition is understood properly as not simply the pale abstraction of mereological summation. For plural wholes it is their total constituents, as both the entities unified and the inter-linking causes of the unity among them (viz., attribute instances or arbitrary associations), that determine the natures/identities of the resultant wholes, these natures founding and known through the wholes’ emergent attributes. In particular for structures, on the above analysis and particularly T7 and T8, every structured entity whatsoever is exclusively and at every level composed of individuated attribute instances or the wholes that emerge from them. In this way we have a criterion of identity for all structured wholes, from simple facts to what are their hierarchical complexes. Viz.: T9. For any structures x and y, x = y if and only if, for every intension Rn and every instance Rni of Rn, Rni is a constituent of x if and only if Rni is a constituent of y. Succinctly, structures are numerically identical if and only if they are composed of numerically the same attribute instances. This is so because all entities of discrete parts are composed ultimately of only attribute instances, and since instances are unique to their subjects, with numerically the same instances

|| 24 I have elsewhere proposed a four axiom contextual definition for the identity relation itself. See Mertz, ‘A Definition for Identity and the Implying of an Infinity of Logical Entities’ in Essays on Realist Instance Ontology: Predication, Structure, and Identity (Frankfurt: Ontos Verlag, 2006), pp. 215–35.

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implying numerically the same subjects and with these jointly forming a network of facts ‘arranged’ in numerically the same structure, then the same composing instances make for the same resultant structure/whole. In turn and on our analyses of Chapter 4, the ultimate composing ontic atoms of attribute instances, say, Rni and Snj, which are not structured entities but continuous wholes, have as their identity conditions that intension Rn and Sn be synonymous and that each instance have the same subject n-tuple. Importantly, T9 gives for all structures, and so for all physical objects and systems, not just a criterion for synchronic identity—identity at any instance of time for a then static whole (a ‘temporal slice’)—but also for what has proved the more challenging diachronic identity—identity across time and change. We recognize a dynamic physical system to be the same structure even though it changes over time, i.e., while retaining an identity-bestowing trans-temporal oneness, it consists of components, including entire substructures, that at various times come into and/or go out of existence. On our assay, for a given dynamic structure its changing component attribute instances, e.g., instances of spatial, temporal, and/or causal relations, come into or go out of existence at the ‘moving present’, but in the modes described in T7 these composing instances form, together with those components that endure, a continuous diachronically evolving lattice. Thus, across time, as in some cases space, these mutually connected instances, those current and their ancestors under T7 connections, form a single trans-temporally unified structure. A current oak tree can be considered a substructure of a subsuming dynamic historical structure of continuously linked (especially through causal growth relation instances) substructures, many cumulatively emerging, and going back to the structure that was an initiating acorn. Like all entities, composed ultimately of only attribute instances, oak trees with the same dynamic history of variously composing attribute instances are identical. This account of identity across change combines rectifying elements of both endurance and perdurance theories of persistence.25 A dynamic structure, such as the growth of an oak tree from an acorn, consists in part, if not totally, of ‘a linked succession of attribute instances as temporal parts’ and in this way can be said to perdure. Equally however and on our assay, each composing instance itself endures as ‘wholly present at each time it exits, i.e., it is numerically the same entity across the temporal span of its existence. For some composing

|| 25 For a discussion of endurance vs. perdurance theories of persistence see, e.g., Theodore Sider, Four Dimensionalism: An Ontology of Persistence and Time (Oxford: Clarendon Press, 2001). Sider argues for a perdurance conception.

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instances their duration may be instantaneous, and for others they may differ in the durations of their endurances, some enduring perhaps for the entire existence of the dynamic structure (and even beyond its destruction as an organized whole), e.g., those instances involved in a certain molecule may endure as retained from acorn to mature tree (and perhaps beyond as the tree is made into lumber). A dynamic diachronic structure is then a perduring entity consisting of an inter-connected lattice of variously enduring attribute instances, the latter staggered and overlapping in the intervals of their persistence. Standardly, endurance and perdurance theories are construed as mutually exclusive and this because as perduring an entity is considered a succession of non-identical temporal slices or stages, typically instantaneous in duration, and each slice encompassing the entire entity at that time—the entity being like a very finely segmented worm. In contrast to this counter-intuitive assay, our account of persistence is of structures composed each of multiple instances enduring for varying intervals, but all ‘path-connected’ to each other and across time in the ways of T7 and thus forming a trans-temporal inter-connected and so single whole whose identity conditions are given by T9. On our account, a metaphor more proper to a dynamic structure is not as a sum of sequentially juxtaposed and ontically distinct temporal slices, but a changing tapestry of interwoven threads, some threads enduring while others go out of existence, these perhaps exactly replaced or not, and the whole augmented by the inter-weaving of entirely different substructures. The inter-weaving here is metaphor for the transentity unity described in T7—a transitive oneness beyond just numerical oneness, and change without total annihilation–creation. Not explicit in this metaphor, however, is that fact that path-connectedness in any structure is not random or component indifferent, but via chains of attribute instances each objectively selective of and necessarily obtaining on its subjects due to a match between conditions set by its intension and these subjects. This contrasts with a prominent but unintuitive construal of the ‘segmented-worm’ conception of perdurance where the whole is but a mereological sum of segments, the unity of sums being, I have argued, by means of arbitrary and subjective association. We will return to the topic of change in Section 5.5. In addition to that for Identity, also available at this point is a diachronic criterion for indiscernibility of structures. Intuitively, entities are indiscernible if they are ‘qualitatively the same but only numerically distinct’—they differ solo numero. This is precisely the nature of attribute instances as our ontic atoms, e.g., for facts :Is-Prime1i(3) and :Is-Prime1j(5), Is-Prime1i and Is-Prime1j are numerically distinct but intensionally identical as instances of the same universal Prime1. If structures are composed ultimately of only instances, then complete-

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ly isomorphic structures where instances are mapped to indiscernible instances, and in such a way as to preserve the relative arrangement of instances in the one structure with the arrangement of instances in the other, then the two structures, though not identical, would be indiscernible at every substructure and as wholes. We can make these observations precise with the recursive definition: T10. Entities x and y are (absolutely) indiscernible if and only if a) x = Rni and y = Rnj, where Rni and Rnj are instances of the same intension Rn, or b) x = :Rni(a1,a2,...,an) and y = :Rnj(b1,b2,...,bn) and ak and bk are indiscernible for 1 ≤ k ≤ n, or c) x and y are fact complexes with a one-to-one correspondence φ between their constituents, i.e., between the instances, resultant facts, and emergent wholes that compose each, such that φ(:Rni(a1,a2,...,an)) = :φ(Rni)(φ(a1),φ(a2),...,φ(an)), where :Rni(a1,a2,...,an) and :φ(Rni)(φ(a1), φ(a2),...,φ(an)) are indiscernible and respective constituents of x and y. Condition c) states the requirement that for two networks of instances to be indiscernible, not only must the inter-connecting instance ‘rods’ be indiscernible, i.e., distinct but have the same intension (by b), :φ(Rni) must be some instance Rnj), but the instances must be arranged properly—they must share their subject ‘nodes’ in exactly corresponding ways. I.e., and leaving off superscripts here to avoid confusion, for two structures to be indiscernible, if in one structure an entity a is an n-th subject for an instance Ri and jointly an m-th subject for an instance Sg, then in the second structure it must be the case that φ(a) is the n-th subject of φ(Ri), the latter some instance Rj, and the m-th subject of φ(Sg), the latter some instance Sh. In this way not only do instances that ultimately compose the two structures correspond in indiscernible pairs, but their relative ‘meeting-places’ and so mutual ‘arrangements’ correspond indiscernibly, and so the resultant wholes are themselves indiscernible. To illustrate these points consider again Structure D above and a further structure Dʹ composed of instances of the same types/intensions and sharing in the same ways subjects that are indiscernible:

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That fact-structures D and Dʹ are indiscernible on the conditions of T10 is seen through the indiscernibility of their metaphorically representing typographical diagrams, minus the labels. I.e., if the particular geometric structures just above were brought together spatially they would exactly coincide, and if permuted to each other’s position there would be no difference to the types/intensions of relations (though there would be changes to the instances) forming the spatial structure between and subsuming both. This is so because the spatial diagrams are isomorphic in a way analogous to the conditions specified in T10: there is an obvious one-to-one correspondence between the constituents of each such that corresponding typographical symbols (dots and lines) are indiscernible, and in corresponding positions. The latter are due to implicit non-represented spatial relations among the marks, and are essential for these diagrams to be metaphors for indiscernible structures composed of instances and their relata. Importantly, consider Structure D as it occurs contained in subsuming Structure E of Section 5.1. If there D were replaced by indiscernible Structure Dʹ, relation instance R2i that has D as a whole as one relatum would either stay numerically the same or change to another instance, R2o, this depending upon the intension R2. On the former and depending upon the intension Q3, instance Q3i in E would remain the same or change to another instance Q3p, and, on the latter—the change of R2i to non-identical R2o—Q3i would change to another instance Q3p. Similarly for instance T1i. But with all such changes the resulting new structure Eʹ would be indiscernible from the original E (E and Eʹ being two structure-tokens of exactly the same ‘structure-type’). One can think of Structure E as a complex experimental context, including instrument responses, involving substructure D as its object of study. Swapping object D with indiscernible object Dʹ, an experimental situation Eʹ would obtain and be indiscernible in the strict sense here from that of E. In epistemic terms, empirically there would be no observable difference between E and Eʹ. This situation occurs for certain quantum particles and is a source of the debate central to Ontic Structural Realism (OSR) over the nature of, and particularly the individuality of, entities like D and Dʹ.26

|| 26 Ladyman uses graphs similar to mine as evidence that certain objects are individuated by external context and not intrinsically. I take him to be arguing that swapping numerically different but indiscernible entities in the context of a subsuming structure ought to make a difference to the individuality of the subsuming structure—it should be numerically different after the swap. And he claims that his geometric examples as well as permutation invariance under the swapping of certain quantum entities shows there is no difference in subsuming

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These problems dissolve on our analysis. It is in conforming to the conditions of T10 that entities can be numerically distinct but ‘qualitatively the same’ in both senses of 1) they are internally composed exclusively of corresponding instances that are distinct but exactly resemble and are correspondingly mutually arranged (c), and 2) as wholes derivative from these instances and their proper arrangements they are single subjects of corresponding intrinsic27 property instances that are distinct but that exactly resemble. In this way the analog of the Identity of Indiscernibles (PII) for properties as instances is false, i.e., restricting ‘P1’ to range over only intensions of intrinsic properties and allowing under ‘extended binding’ its instantiation scope to include all instance symbols containing ‘P1’, then for every structure x and y, if (P1)[(∃P1i)P1i(x)  (∃P1j) P1j(y)]28, this does not necessarily imply x = y. Further and in regard to OSR, the established existence of indiscernible quantum particles, and so the falsity of PII, has led some to conclude that since the grounds for these particles’ individuality and identity are not the properties of them, then these entities are either some yet-to-be-understood ‘non-individuals’, or we must posit as their principles of individuation some mysterious or disreputable ‘transcendentals’ as haecceitas or bare particulars.29 In response, some propose as a third alternative, articulated for example by Ladyman, that “In so far as they [quantum particles] are individuals it is the relations among

|| structure before and after the swap. E.g., he says, “Permuting exactly structurally similar individuals in a mathematical structure results in exactly the same structure.” Now on our analysis what should be said is that with such permutations ‘what results are two exactly structurally similar—indiscernible—subsuming structures,’ the subsuming structures before and after the swapping are indeed numerically different individuals, though they are observationally indiscernible. See Ladyman, ‘On the Identity and Diversity of Objects in a Structure’. 27 Recall from Sect. 4.2 that an intrinsic property instance is one whose foundations are all internal to the composition of its subject. 28 The expression ‘(P1)[(∃P1i)P1i(x)  (∃P1j)P1j(y)]’ can be read: ‘For every monadic intension P1, there exists an instance of P1, P1i, characterizing x if and only if there exists an instance of P1, P1j, characterizing y’. The ‘extended binding’ involving ‘P1’ here is intuitive, and I have provided more explanation in note 66, Chapter 4. The full formal details are given in ‘The Logic of Instance Ontology’ reprinted in Essays in Realist Instance Ontology. 29 Steven French, ‘Identity and Individuality in Quantum Theory’, The Stanford Encyclopedia of Philosophy (Summer 2011 Edition), Edward N. Zalta (ed.), URL = . Steven French and Michael Redhead, ‘Quantum Physics and the Identity of Indiscernibles’, British Journal for the Philosophy of Science 39 (1988): 233– 46. Steven French, ‘Identity and Individuality in Classical and Quantum Physics’, Australasian Journal of Philosophy 67 (1989): 432–46.

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them that account for this”, what is extended to space-time points as well.30 The often-noted problem here, however, is that relations as inherently relatadependent presuppose subjects distinct from them and with their own identities, including their individuations, and not conversely. The assumption behind both the apparent loss of identity of quantum particles and the Ladymantype solution is that the properties (explicit in the formulation of PII) or relations that are relevant to an entity’s individuation and indiscernibility are those predicable of it as (one of) their subject(s), 2) above. Rather, on our assay it is not the attribute instances predicable of a structured subject but rather those that compose it that give it its identity/being and that are the bases for both its individuation (inherited from the unrepeatable combinatorial agency of each composing instance) and its indiscernibility from others (inherited from the intensions of each composing instance and their resemblance correspondences dedescribed in T10). It is possible then that numerically distinct but indiscernible quantum particle-structures (analogous to Strucs. F and G above) can spatially coincide or be permuted without changes in any larger and subsuming structure-types—without changes in their ‘physical situations’ (and so effect no observable differences), while ontologically each is still fully an object, with an identity and individuality completely constituted by attribute instances just like but in simpler combinations than in derivative macro physical object. And their composing attribute instances, the true physical primitives/atoms, though they have individuators that require unions with other entities, these individuators as outward-directed (ad aliud) combinatorial agencies are internal to the composing beings of their instances. Alternately and in response to Ladyman, an external union (but not a ‘relation’) is required for the individuation of an attribute instance, but this as an external union of attribution/predication that is derivative of an ontically prior and individuating agency inherent to, but not as an ‘intrinsic property’ of, the being and identity of the instance. Described by T10 is absolute indiscernibility: the complete indistinguishability of two entities due to their being composed exclusively of structuring attribute instances (T7 and T8) and in such a way that between the resulting structures and involving every instance of each there is an isomorphism where corresponding instances have the same intensions. Such pairs would be exact copies at every level and substructure of their respective beings, corresponding substructures being characterized by indiscernible intrinsic attribute instances, i.e., instances with the same intension, differing only numerically (i.e., in their

|| 30 Ladyman, ‘On the Identity and Diversity of Objects in a Structure’.

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individuating combinatorial acts). However, indiscernibility as we ordinarily experience it, or seek to achieve as crucial to practical concerns, is partial, i.e., two structures with instances of the same intensions arranged in the same way, i.e., structures that are isomorphic, but where the respective subjects of these instances need not themselves be indiscernible. This is isomorphism at a certain level and in a general manner in abstraction from refining details that are structurally differentiating. The idea here can be made precise by modifying T10c: Two structures x and y are partially indiscernible if and only if there is a one-to-one correspondence φ between their composing attribute instances such that φ(:Rni(a1,a2,...,an)) = :φ(Rni)(φ(a1),φ(a2),...,φ(an)), where :Rni(a1,a2,...,an) and :φ(Rni)(φ(a1),φ(a2),...,φ(an)) are respective constituents of x and y, and :φ(Rni) is some instance Rnj but where a1, a2,..., an are not necessarily respectively indiscernible from φ(a1) ,φ(a2),..., φ(an). Unlike with absolute indiscernibility, the two facts :Rni(a1,a2,...,an) and :φ(Rni)(φ(a1),φ(a2),...,φ(an)) need not be indiscernible, there being the possibility of differences of structures within their respective subjects. Here we have exact copies but only in general or ‘surface’ features of the two structures, not in their more specific components—‘not all the way down’. Partial indiscernibility is what we strive for in practical affairs. For example, in many circumstances a corporation in replacing an employee seeks to maintain an indiscernibility of certain general corporate functionings, but to which many particular differences between new and old employee are irrelevant. Or, the replacing of a machine gear, for example, with a duplicate of the same shape results in a partial indiscernibility between the before- and after-machine, an isomorphism at the level of gross geometric form and related mechanical function that allows the machine to continue operating in the same manner as before. But no two manufactured gears, no matter how phenomenally indiscernible they are, are in their composing beings absolutely so, e.g., the parts always having at least microscopic differences of material composition and surface form. However, the latter differences, within certain engineering ‘tolerances’, make no difference to the less-specific geometric form and correlative operations of the machine, and so (assuming the same compositional strength) it is only the partial indiscernibility of the gears with respect to their surface geometric forms that we are interested in maintaining. We will return to partial indiscernibility in Section 5.5.

5.4 Answering the Problem of Composition We have now completed our analysis of structure and structured wholes, what is a form of complexity ubiquitous to external and internal experience and as

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hypothesized in warranted science. These results are central to this work’s overarching thesis, T1. In the process and more generally we have identified five forms of unions and so of composition, including three types of structuregenerating unions (that of single facts and their inter-attribute and emergent unions), and all, I have argued, deriving from the single ontic category of attribute instances. All then derivative wholes conform to and clarify the proper ‘Composition is Identity’ thesis. These forms of unification are ontology’s crucial but historically undifferentiated principia compositionem, what jointly provide a complete answer to the fundamental ontological Problem of Composition, what has been made contemporarily prominent by Peter van Inwagen as the Special Composition Question: Under what conditions does composition occur?31 I have put it in the form: What are the nature and kinds of selective unities where, to the exclusion of others, some non-identical entities are unified, ‘made one’, but in such a way that each retains its differentiating identity? Our answers joined in one principle are: The Principle of Composition (PC): All composition and thus all entities and forms of ontic dependence derive, directly or indirectly, from the single category of attribute instances Rni (T1), and take one or more of the following five forms: 1) Continuous Composition: the union between non-identical but non-discrete entities via the being of a subsuming whole that is ‘simple’ in having no internal division. E.g., the union of an intension Rn and an act of combinatorial agency within the being of a subsuming attribute instance Rni (T5,T6). Here ontic dependence is symmetric between at least some of the

|| 31 Peter van Inwagen, Material Beings (Ithaca: Cornell University Press, 1990), p.39. And more directly related, our results satisfy and clarify the ‘Desiderata for any Principle of Qualitative Unity’ observed by David Robb as necessary for a ‘bundle theory’ where the being of every object is generated by composing attributes. On my paraphrase of Robb’s desiderata, the account should explain systematically unifications among certain attributes and how these unifications are related to unifications among wholes emerging from the former (explained by our PC-2a) and -2b)); explain how attributes are dependent, not prior to their subject(s), and why the having of some attributes excludes others (explained by T2,T3, and T8); and these explanations should be accomplished without postulating ad hoc, specific primitive relations (what we achieve with PC-2a) and -2b)). See Robb, ‘Qualitative Unity and the Bundle Theory’, The Monist 88 (2005): 466–92.

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parts and the whole, the distinction of parts only posterior to the whole in ‘formal’ abstraction. 2) Articulated Composition: the inter-linking among discrete entities via necessarily the agency of one or more of them. The resultant plural/complex whole is asymmetrically ontically dependent upon the parts. Articulated composition is by, or emerges on, the intension-determined and outward unifying agency (T2,T3) of attribute instances Rni (T4), this directly in either: a) the atomic form of facts, :Rni(a1,a2,…,an), what are the simplest forms of structure (T2), or, b) the molecular form of multiple facts that form complex structures (T7,T8) by either or both: i) Inter-Attribute Composition: instances having parts of other facts (viz., the facts’ instances or the latters’ subjects) as subjects, or, ii) Emergent Composition: instances having entire structures as subjects; Or articulated composition is effected indirectly and emergent upon attribute instances as: c) Linkings via the agencies of arbitrary associations, these necessarily by and dependent upon minds that themselves emerge upon hierarchically complex structures of form 2b). Abstraction of the constituent associations from such wholes yields the logical fictions of theoretical sums or sets. Importantly, PC presupposes what is our answer to the more fundamental problem, formulated by Lewis as: “What is the general notion of composition, of which the mereological form is supposed to be only a special case?” (his italics; Lewis holding that there was no such notion beyond that of mereology)32, and termed by van Inwagen as the General Composition Question: What is [the nature of] composition?33 (my insert) Our answer: Composition is a union or ‘oneness’ of the non-identical, what in its simplest form requires one thing be a trans-entity unifier of itself with each of, and so a shared unifier across, entities non-identical to itself. Expanded as PC, such unifiers are either the internal intra-unifying beings of wholes composed of their non-discrete parts, or the outward-directed inter-combinatorial agencies of parts (attribute instances or

|| 32 David Lewis, ‘Against Structural Universals’, Australasian Journal of Philosophy 64 (1986): 25–46. 33 Van Inwagen, Material Beings, p. 39.

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associations) among other discrete parts. These results were anticipated in Figure 1.1 which we reproduce here:

Fig. 1.1: The Five Kinds of Unification/Composition (arrows indicating direction of dependence)

Beyond just the composition of material/physical objects on which much of the relevant literature has centered, the argument herein has been that PC-2 precisely characterizes all inter-connectedness among the discrete, and, if controlled by an intension, the connectedness and resultant whole are equally real no matter the category of the intension: material-causal, spatial-temporal, psychological, conceptual, semantic, mathematical, logical, corporate, familial, ethical, etc. In this way PC-2 and its background analysis provide solutions to problems that in a widely-joined dialectic center around ‘restricted composition’, viz., in providing necessary and sufficient conditions for how certain entities and not others form thus ‘restricted’ wholes, it corrects the unintuitive and explanatory impotence (especially in regard to structure) of composition restricted in kind to just the extensionally unrestricted hypostatized abstractions of sums or sets (2c). It is appropriate here, then, to consider briefly how our analysis counters the debate’s prominent ‘Vagueness Argument’ against restricted wholes proposed by David Lewis34 and detailed by Theodore Sider35. As a preliminary recall an observation made in Chapter 1: that if all composition is

|| 34 David Lewis, On the Plurality of Worlds (Oxford: Basil Blackwell, 1986), pp. 211–13. 35 Theodore Sider, Four-Dimensionalism, pp. 120–39.

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that of sums or sets, the effecting unions for the latter being necessarily via arbitrary cognitive associations that yet their theories abstract away, then, without constituents providing and delimiting element unifications, there are no constraints on fixing and differentiating sub-groupings within a given universe of entities. In particular and a point made by Trenton Merricks36, equally plausible are the two extremes that any things, no matter how random and without mutual relevance, compose something (‘mereological universalism’), or nothing does (‘compositional nihilism’). For, each sub-sum/set has as such its own essential and identifying ‘togetherness’ of just its elements and not others, a particular togetherness that is not identical to any of its elements singly and is prior to, as making the resultant whole, ‘all’ of its elements. That is, for sums or sets it is not the qualitative essences/natures of elements that conditions their mutual unification to the exclusion of others, nor can it be simply their existences that account for their delimited unities, since everything satisfies this criterion and on it there would be only one universal sum or set. What differentiates any plural whole from another as all and only its exact elements, neither less nor more, must be a ‘collecting and selecting togetherness’, it and its causes being particular to and constitutive of the whole, but this the respective theories ignore—a sum/set is, to restate our analogy, like the grin that is left when Lewis Carroll’s Cheshire Cat is made fictitiously to disappear. It is the explanatory vacuum where differentiating unifications are denied that allows David Lewis, for example, to claim that mereology is “ontologically innocent”37, i.e., a sum of x’s is no addition to being beyond the x’s. Confirming my point, Lewis understands a sum not to be the resultant of any unifiers among the component x’s. He asserts, for example, that “Take them [x’s] together or take them separately [i.e., independent of any union that would bring them and just them ‘together’], … [the x’s] are the same portion of Reality [i.e., the sum just is the x’s].”38 (my inserts) Lewis seems to imply what I urge: that it is the unions among x’s that makes the resultant whole more than—an addition to reality beyond—just the x’s, but Lewis holds that there are no component unions in sums. This despite the fact that elsewhere he asserts that “What’s true of the many [x’s] is not exactly what’s true of the one [the sum of the x’s]. After all, they are many while it is one.”39 (my inserts) Contra Lewis, the difference between x’s and any plural whole, whether a sum/set or structure, that subsumes them, are unifiers—

|| 36 Trenton Merricks, ‘Composition and Vagueness’, Mind 114 (2005): 615–37. 37 David Lewis, Parts of Classes (Oxford: Basil Blackwell, 1991), p. 81. 38 Ibid. 39 Ibid., p. 87.

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associations or attribute instances, respectively—among the x’s that jointly with them are necessary to compose the whole, the unifiers causing a particular togetherness that makes this whole ‘something more than’ just the x’s, including a single subject for an emergent attribute instance Is-a-One1i. Consider now the Vagueness Argument against ‘restricted composition’, what, as I understand it, runs as follows. The argument assumes that there will always be some vagueness in the intensions of properties and relations that would be criteria for an “arrangement” fixing a delimited whole, and there is no such thing as objective, ‘in-the-world’, vagueness. A whole does not exist until what composes it is each and all definitely so and thus differentiated from what does not, and a vague intension cannot supply this yes-or-no decidedness of inclusion or not. The argument is put in the following form: Given vague intensions as criteria for what composes, say, a certain physical object, e.g., “qualitative homogeneity, spatial proximity, unity of action, comprehensiveness of causal relations, etc.”40, they will be relevant to a continuous series of very slightly different cases where somewhere in this continuum there will be on the one side composition by these criteria and on the other side the criteria will not apply and there is no such composition. But this requires a “sharp cut-off” between adjacent cases in a continuous series, and there can be no such thing because of the vagueness of the criteria as to whether or not composition occurs.41 For, as Sider rightly asserts, “In any case of composition, either composition definitely occurs, or composition definitely does not occur”42, i.e., there will always be a ‘sharp cut-off’ between when the unions causing delimiting wholes exist and when they do not. Now indeed, this latter point is precisely how our assay of composition among the discrete leading to PC-2 answers the Vagueness Argument. Viz., such composition is by either constituent cognitive associations or attribute instances, both being cases of definite individuating acts of unifying agency—they either exist and unify, and so effect a composite whole, or neither and so in this way there is no resulting composite. Seconding Lewis’s point43, there are no vague acts that ‘sort of and sort of not’ make for composition, anymore than there is vague existence—as if something could ‘sort of and not sort of’ exist. There are degrees of complexity, but there are no degrees of composition—certain things are inter-connected or they are not. As developed in Section 4.3, unifying agency, a necessary and sufficient condition for compo-

|| 40 Sider, Four-Dimensionalism, p. 123. 41 Ibid. 42 Ibid., p. 125. 43 Lewis, Plurality of Worlds, p. 212.

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sition among the discrete, is a ‘doing’ or ‘at-work-ness’ that is either happening or it isn’t, like electrical current through a switch that is either on or off. This is the relevance of the phrase ‘sharp cut-off’ here. And, vagueness is a characteristic only of certain intensions, such intensions being necessarily conceptual constructs indeterminate as to whether or not they apply to certain n-tuples of subjects e.g., Spatial-Proximity 2. Lewis is right is saying that “The only intelligible account of vagueness locates it in our thought and language.”44 Intensions existing independent of human cognitive construction, e.g., those intrinsic through their instances to objective physical structures, are not vague, it being our understandings’ approximations to them that are vague. Yet also for a vague cognitively constructed intension (e.g., the sortal Ship1 (see ‘Ship of Theseus’, Sect. 5.5)), and independent of any ‘precisifications’ of it into a related intension, in those cases when an n-tuple of entities unambiguously satisfies the intension, there fully and definitely exists an instance of it that acts to unify these and just these n subjects into a restricted composite. I suggest that the Vagueness Argument turns on the tacit assumptions that properties and relations are intension universals and are themselves the causes—the selective unifiers—of then restricted composites. If these intensions are inherently uncertain as to whether or not they characterize some entities, and are themselves taken to be the internal causes of the selective unities essential to their restricted wholes, then on such subjects these unifying acts would themselves be inherently uncertain—not acting nor not not acting to unify them, which is impossible. On our assay intensions can be vague, but attributional acts by their instances for which these intensions are sufficient to specify are not. Summarizing this section and thus the implications of much of this work up to now, we have with PC achieved one of ontology’s crucial desiderata: a universal theory of composition—an account of all forms of unity or ‘oneness’ among the non-identical. Built upon our agent-assay of properties and relations, and so their full reality and individuation, along with the non-attributional manner in which they contain controlling intension universals (T2-T6), PC both distinguishes and provides integrated solutions to problems of composition that in the tradition have been either confused or seen as involving separate issues. These include principally: 1) the unity between repeatable universals and unrepeatable particulars; 2) the attributional unity linking properties and relations with the subjects they characterize; 3) the structuring unity among parts that make them hierarchically organized wholes (e.g., machines, living creatures);

|| 44 Ibid.

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and 4), receiving less attention, the ‘looser’ unity among entities irrelevant to them in any qualitative way and rendering them jointly a ‘heap’, sum, or set. Much current work on what I have sought to establish as the epistemically and ontologically primary problem 3) has involved nascent attempts at explaining the ‘manner of arrangement’ which intuitively is essential to organized/structured wholes (e.g., structuring by Aristotelian-like ‘kinds’ (Koslicki, Baker), or by ‘rigid embodiments’ of composition relations (Fine)). My claim is that PC2a)-b) accomplishes this perspicuously and in full. More generally, central to our analyses leading to PC has been an argument for the thesis that all unification is ‘restricted’, and in particular this because composition exists only by delimiting causes—required principles of simultaneous differentiating selection and unifying collection. I.e., with continuous composition among the nondiscrete the unity is via the specific being of a subsuming whole, and with articulated composition among the discrete the unity is by one or more combinatorial constituents that are either attribute instances conditioned as to their subjects by their intensions, or cognitive associations controlled as to their subjects by selecting minds effecting them. Continuous composition conforms to Aristotle’s inaccurate formula that ‘oneness is absence of division’45, but it does not conform to the formula’s classic corollary that unity among the diverse is by the constituent one, A8. For in general, every composite is ‘a one and a many’—a unity among the nonidentical—where the foundations for it having the property Is-Many1 include those for it having the property Is-One1. The converse relation among these foundations does not hold, viz., with simples not having multiple parts. A composite is then a many in either a continuous or articulated manner. With continuous wholes, e.g., attribute instances or, what would seem necessarily (but counterfactually) the nature of the monistic One under ‘priority monism’46, the unity is of non-identical but non-discrete—not divided ‘thing and thing’— aspects, e.g., the combinatorial and intension aspects of attribute instances,

|| 45 E.g., Aristotle asserts that “Wholeness [composition] is a sort of oneness” (Meta. 1023b35; my insert), and that “For in general those things that do not admit of division are called one in so far as they do not admit of it” (Meta. 1016b4). 46 See Jonathan Schaffer, ‘Monism’, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = . With priority monism the parts and necessarily their unity is derived from the subsuming whole. But, if the parts are discrete—‘thing and thing’—then their unification(s) would have to be by attributes, especially relations if the whole is complexly structured, but then it is not the whole as a single entity providing the unity among the parts but multiple attributes as parts of the whole.

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and the unity is by the subsuming whole and not a constituent of it. Recall the example of the two semicircles composing a continuous circle prior to their being made discrete/‘divided’. However, in contrast, articulated composition contradicts the ‘oneness is absence of division’ thesis, as well as its corollary A8 except in the limiting case of atomic structures—single facts. Unity among the discrete is precisely a ‘bridging-of-the-divided’, or succinctly, a trans-division, it is not an absence of division. Unity among the discrete does not obliterate division—‘discreteness’—within the one. And as we have seen, an articulated composite can, contra A8, be a single entity by multiple unifiers—the unity need not be like a single thread through beads, but can be like links jointly forming a chain or a system of connectors forming a lattice. Single facts conform to a unity-by-the-constituent-one thesis, but the transitive unity across articulated facts does not, and the latter is the source of what is ubiquitous organization and structure. Further, only with continuous composition is there unity by ‘inherence’ (though no component characterizes another nor the whole), all other unification being by outward-directed agency, and in every case of attribution where this external linking is conditioned by an intension the union is, contrary to the Humean thesis, a necessary connection between distinct existences (as explained in Sect. 4.2). The Humean thesis describes only wholes by arbitrary associations, and hence the motivation for those that find the thesis appealing to promote a mereology of sums or set theory as a theory of composition, giving the Part-of2 relation a fundamental ontological and explanatory status. The expansive fact, however, is that instances of the Part-of2 relation emerge upon all the types of wholes identified in PC, though it, like all attributes, generates through its instances its own fact-structures. The latter are all meta-structures, presupposing and thinly descriptive of ontically prior and richer either fact-structures composed of attribute instances of any other intensions and adicities, or complexes by associations emergent upon particular factstructures that are minds. Underlying all of this is the fundamental insight that the ontically primary form of unification and dependence is that of agent-uponsubject(s), with that of whole-upon-parts being derivative from it, and primary among the former are combinatorial acts each controlled/conditioned by an intension—the intensional is prior to the extensional. And contrary to what some apparently assume of sets or sums, the only case where a whole provides the unity among its elements, though in a way where at least some of the elements are equally ontically dependent upon the whole, is when the whole is an attribute instance and so is an internal continuous composite of its composing intension and outwardly combinatorial aspects. It is a related mistake for monists who would hold all unification to be the internal continuous composition of

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an all-encompassing One, what as such would be devoid of any composing relatedness; indeed, as Bradley urged, devoid of all characterizing/attributional unions.

5.5 Some Implications: On Dispositions, Causation, and Change As a means of adding further inductive warrant to our assay of composition, particularly to the articulated structural forms of Thesis T7 and so the ontology of attribute instances supporting it, I will in this section outline briefly what I propose is its potential for solving certain contentious problems concerning dispositions, causation, and change. Let us first consider how our analysis can clarify the concept of disposition, the preliminaries also shedding light on the nature of causation. In a broad sense of the term, something x (e.g., salt) is ‘dispositional’ (e.g., is soluble) if when some fixed set of circumstances S involving x obtain (e.g., salt is placed in water), these are sufficient for x to be part of a causal act of a fixed kind correlative with circumstances S (e.g., the dissolving of the salt). It was noted in Sect. 4.5 that this is the nature of intensions: an intension Rn (e.g., Circular1), in circumstances consisting of the satisfaction of foundational conditions it prescribes (e.g., composed of points equidistance for a center point) on an n-tuple of subjects (e.g., the 1-tuple of some figure a), is sufficient for it to be part of an instance Rni (e.g., Is-a-Circle1i) consisting of it and a causal act of attributional unification to and among these n subjects (e.g., the conditioned unity that is the fact :Is-a-Circle1i(a)). In this way every instance is derivatively dispositional, and so in terms of a distinction found in the literature our analysis of attribution would be a ‘pan-dispositionalism’ or ‘dispositional monism’. This stands in contrast to ‘categoricalism’ that denies that attributes either have foundations that are, or themselves achieve—cause—anything that is, beyond themselves. Humeans, for example, assert that all attributes are categorical in this sense—in effect, for them attributes are self-contained and inert, having no ties with anything else except via arbitrary and externally imposed connections (what I argue can only be cognitive associations). This then is the basis for the Humean claim that all attribution is contingent. Our pan-dispositional analysis of attribution is the basis for further insights into the nature of causation, central here: that all causation is or is derivative of the presence or absence of attributions. In its broadest and positive sense causation is a production or achieving—a more or less sustained bringing-about of the

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existence of something numerically distinct, whether an object, attribute instance, or association. It was argued that each attribute instance Rni is a case of static positive causation—a single outwardly unifying act enduring as long as the n subjects of Rni satisfy the conditions of intension Rn. When an instance comes into existence on an n-tuple of subjects, each of which may themselves be structures (emergent composition), there is causation of a new augmented structure of increased complexity. But causation can also be negative: the diminished state after one or more attribute instances and their subsuming structures composing a larger structure ceases to exist, this because the instances’ ntuples of subjects no longer jointly satisfy the conditions prescribed by their intensions. Our ordinary attention is on what in fact are complex chains of dynamic causation—of evolving and/or devolving structures (e.g., a bat hitting away a ball, or the decomposition of organic matter). Such a causal sequence is often described in terms of events, and we can clarify the concept of event, and subsequently that of process, in terms of instances by refining a proposal made by Lowe47: an event is the coming into or going out of existence of attribute instances, Rni, or derivatively of structures coming into or going out of existence because their composing instances do.48 A case of dynamic causation is then a sequence of events linked in a single diachronic structure, such an ‘event structure’ being what is intended by the term ‘process’, Within an event structure the first substructure (e.g., the forces involved in hitting a ball with a bat, or the death of a living body) being a ‘cause’ and the last substructure in the sequence being an ‘effect’ (e.g., motion and kinetic energy of the ball, or a certain residue of simpler molecules). It is the atomic unifying act-events of subject-grounded—and so nomically necessitated—attribute instances that bring into existence—are positive causes of—evolving event structures, i.e., single facts and their complexes (in the manners of T7). And for already existing structures, if some subjects of their composing attributes change (possibly because they are

|| 47 E. J. Lowe, The Four-Category Ontology: A Metaphysical Foundation for Natural Science (Oxford: Clarendon Press, 2006), pp. 80–1. Lowe does not explicitly include the going-out-ofexistence of instances, his ‘modes’, as events. The assay of events presented here corrects my earlier view that confused events and processes. This in Moderate Realism and Its Logic (New Haven: Yale University Press, 1996), pp. 78–9. 48 This account of events can provide answers to a range of questions found in the literature concerning them, e.g., why events are more similar to properties than objects (i.e., structures composed of attribute instances), but yet how events are closely related to facts and to objects, and how events are linked to times. See Roberto Casati and Archille Varzi, ‘Events’, The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.), URL = .

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subjects of new emergent attributes) so that the foundations necessary for these attributes to unify their subjects into a certain network of facts no longer obtain, then these absences of unifying acts bring with them—are negative causes of— the going-out-of-existence events of the facts and so the destruction events of certain structures subsuming them. The dynamic generation and/or destruction of facts makes for new evolving and/or devolving structures that then found their own attributes and so cause further subsuming and inter-locking dynamic structures. E.g., the event structure that is an explosion involves the combination of negative and positive causation in the form of a very rapid destruction of some and creation of other molecular bonds as relational attributes. Extended maximally, all Reality is a vast event structure (T1): the totality that through T7 compositions is the inter-connected and dynamic hierarchical web or lattice of all facts. Everything is causally connected with everything else via a transitivity across the atomic units of causation: attribute instances Rni of every kind, sort, or ‘category’ Rn, where each instance’s linking agency (T3) is conditioned on the obtaining of certain external states prescribed by its intension (T2). The thus Total-Structure and each of its sub-structural event chains is a dynamic interplay between positive and negative causation in the form of its facts’ attribute instances (T4) coming into and/or going out of existence, and this according to the nomic necessity built into the instances’ condition-specifying intensions. Causal chain structures evolve or devolve, not because their composing attributes do or cease to bestow causal powers upon their subjects, but because the attributes as instances are themselves causal agents that when they exist generate new facts and when they cease to exist so do their subsuming facts. Thus in forming this vast tapestry of inter-woven causal chains, its temporal leading edge consists in part of changes of attribute instances as actualities to their absences, or vice versa, and so likewise of derivative facts, these changes determined by whether or not the criteria set by relevant intensions obtain. Descriptive of certain event structures, ‘laws of nature’ and their necessity derive from the intensions/universals (T5) involved in these structures’ changing sequences of composing facts. The Humean ‘constant conjunction’ construal of laws of nature is correlative with the thesis that the only unification among the discrete is in effect by subject-irrelevant and arbitrary association. And the latter is a consequence of the identification of attributes with their intensions and further these taken in abstraction from any outwardly directed subject-selectiveness (contra Thesis T2 and classic assumption A1). Hume is explicit that this is the nature of attributes when he asserts of the example attributes solidity, extension, and motion, that “these qualities are all complete in themselves [i.e., are without dispositionality or combinatorial agency], and

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[hence] never point out any other event which may result from them.”49 (my inserts) And because for Hume arbitrary and random associations are the only trans-entity agent unifiers (though he could not admit this characterization) for bundling ‘qualities’ into things/‘substances’ and giving them attributes, we have the Humean maxim that anything whatsoever can happen. To the contrary and in sum, it is with the composition that is attribution properly assayed—in particular, with intensions prescribing conditions on subjects that if satisfied necessitate thus characterizing acts of unifying agency with and among such subjects, and if not satisfied preclude or eliminate such unions—that there are certain event structures having nomic necessity and what are described in their general forms as laws of nature. That part of the Total Structure that is Nature is, nevertheless, contingent in that the conditions set by some intensions can begin to be or cease to be satisfied, or be possibly satisfied but are never so. In passing it is instructive to see Aristotle’s four kinds of causation in the above context. Since all causation rests on attribute instances and the creation and/or destruction of them as unifying agent-causes (including the unifications caused by associations as derivative from instance structures that are minds), and since instances exist only in the structures their agencies are necessary and sufficient to effect, then all causation is fundamentally structural, or, in Aristotelian terms, all causation is at bottom ‘formal’. Moreover, if under T8 the foundations upon which all entities are ontically dependent—the ‘ultimate subjects’—are themselves some kinds of each dependent but together mutually supporting instances, then at that level Aristotelian formal and material causation are identical. In the structural hierarchy that is all reality, at all levels above this atomic stratum formal and material causes are distinct. Aristotelian ‘efficient causation’ describes the above dynamic event structures, and consists of chains of formal causation. Lastly, there is Aristotle’s ‘final’ (teleological) causation—activity directed toward an ‘end’, ‘goal’, or ‘purpose’ (Physics 198b10-199b33, Parts of Animals 639b12-640b4). Apparently at least part of what Aristotle intended by final causation, particularly in regard to biological entities, is, loosely, a type of event structure that through its progression of stages manages the effects on it of its environment so as to achieve an end that its environment might otherwise defeat. More specifically, these are event structures that can each at any stage merge with any of a correlative range of possible external structures and still effect what would be the same type of subsequent (further stage) composing structure, e.g., the structural homeostasis and || 49 David Hume, Enquiries Concerning Human Understanding and Concerning the Principles of Morals, P. H. Nidditch (ed.), (Oxford, Clarendon Press, 1978), Sect. VII, Part I, par. 50, p.63.

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autopoiesis of living bodies. I.e., each stage (e.g., an acorn) in such an event structure controls the effects of its combination with any of a range of environmental structures (e.g., a certain range of kinds of soil and amounts of moisture) so that there is a predictable sequence of substructure types (e.g., certain root, trunk, and leaf structures), what without this control would be defeated. Any later stage of such an event structure is an ‘end’ of the prior subsequence. In particular concerning the ontogenesis of biological entities, Aristotle apparently had in mind event structures that each when it reached a progression of stages M where one is very similar to another, as compared to the progression of stages preceding subsequence M (e.g., the constancy of structural form of a mature oak tree compared with diverse forms involved in the growth from an acorn to a sapling), then these stages M represent a kind of completion or maturity and are to be considered the ‘end’ or ‘purpose’ of their preceding subsequences. A plausible sign that a biological being has reached its proper end is its ability to reproduce, i.e., to effect another entity that can recapitulate its entire predictable event structure type. In these ways an end (telos) is not just the last step in any causal sequence, but the last stage (or stages) in an event structure (e.g., growth leading to a mature oak tree) that could have been otherwise defeated in achieving this end (e.g., a sapling dies) because either an external structure (e.g., soil absent of moisture) at some prior stage was outside the range of external substructures compatible with the internal structure’s selfmaintenance at that stage, or because the internal controlling structure was at some stage destroyed (e.g., by disease). Assisted with the above preliminaries let us now consider the concept of dispositionality in the form of ‘dispositional attributes’, e.g., Is-Brittle1 or IsSoluble1, a topic for which there is an extensive literature and classic problems. Recognized in Section 4.3 was the fundamental dispositional nature of all intensions, but dispositional attributes involve dispositionality at a more complex structural and commonly observed level The work here will serve as a context for displaying the explanatory power of our prior analysis of attribute instances and derivative structure. Dispositions as attributes are said to be properties that describe latent powers, efficacies, or potentialities, e.g., Is-Elastic1, had by entities such that in the right ‘initiating conditions’, e.g., being stretched and released, these efficacies manifest themselves or are actualized, e.g., the resumption of an original shape. Hence, dispositional properties, D1 (e.g., Is-Fragile1), are correlative with at least two other kinds of properties, ones describing initiating conditions C (e.g., Is-Struck-with-Mild-or-Greater-Force1) and others being manifestation properties, M1 (Is-Broken1). Dispositions are then said to entail subjunctive conditionals, pre-critically in the manner of the ‘Simple Conditional

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Analysis’ (SCA): An entity x has a dispositional property D1 relative to a manifestation property M1 and initiating conditions C if and only if x would have M1 if it were the case that C. Most dispositional properties are never manifest because it so happens that their subjects are not subjected to the necessary specific initiating conditions. It has been established in the literature that the initial SCA characterization of dispositional attributes is inadequate and alternatives have been offered for its amendment.50 Our prior clarification of the nature of structure along with the following observations of how structure has multiple roles in founding dispositions provides solutions to fundamental problems here. In particular and making precise what is left undeveloped in the debate, I propose that a disposition property D1 is to be defined in terms of a manifestation property M1 as it derives causally from the merging of instances of two structure types, one internal and one external to the subject. In detail, the proposal is: (Disp) An object x (e.g., a crystal bowl) with an internal substructure of type S (e.g., a certain type of molecular structure) has a dispositional property D1 (e.g., Is-Brittle1) relative to a manifestation property M1 (e.g., Is-Shattered1) and initiating circumstances C (e.g., a type of dynamic force-structure of being struck sharply) if and only if, as the foundations for D1, if the type S substructure of x is joined in the manners of T7 with a certain external structure of type C, then there results a new structure y (e.g., spatially separated pieces) with property M1. Note that only in a derivative sense is the manifestation property M1 a property of x, being rather and primarily a property of y as the causal resultant of the interaction of structures S and C. We can illustrate this analysis and example with the following Figure 5.1 (the lines representing structuring attribute instances are left unlabeled). The left-to-right sequence, a) - c), represents three successive ‘snapshots’ of a continuous event structure composed of at a) an intact crystal bowl x subjected at b) to an external force structure resulting in what at c) are shattered parts y, the latter all of formerly intact x.

|| 50 See Sungho Choi and Michael Fara, ‘Dispositions’, The Stanford Encyclopedia of Philosophy(Spring 2012 Edition), Edward N. Zalta (ed.), URL = .

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Fig. 5.1: Event Structure for Shattering x Due to It Having Disposition D1

The resultant state y, having the attribute instance Is-Shattered1n, derives from two essential and mediating structural contributions: a certain molecular substructure of x of type S (so characterized by an attribute instance Is-S1i) and a correlative external force structure of type C (so characterized by an attribute instance Is-C1j), the double lines representing instances of force relations connecting parts of x with parts of what has structure C, e.g., a striking hammer. It is x having composing substructure of type S, and from the joining of the S-type with the initiating C-type structures there resulting a manifestation structure on y characterized as Is-Shattered1n, that collectively are the foundations for x having the property Is-Brittle1m, and for it and derivatively in this way its intension Brittle1 being classified as each a dispositional attribute. In our particular example of the shattered bowl y, the momentarily combined structures of types S and C remove foundations prerequisite to the existence of some of the attribute instances making up the structure of bowl x and hence the disintegration of this structure, i.e., its shattering into y. In other cases of dispositions, e.g., a key x with shape-structure of type S having the disposition D1 to open a lock with a slot-structure of type C, the combined structures of entities of types S and C create new foundations and so new attributes so that now we have a more, not less, complex structure y with emergent property of kind M1, e.g., Rotates1, and so unlocks the lock. A categorical attribute is one whose foundations differ from those specified in Disp. The Disp assay provides solutions to a number of problems raised against proposed definitions of dispositional properties. First and among the standard problems addressed, the above shows how dispositional properties as instances, D1m, 1) are not identical to their foundations but emerge upon them, 2) are not intrinsic to their bearers, x, on our definition of ‘intrinsic’ made precise in Section 4.2, 3) are related to their causal foundations—substructure types S and

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C—but are distinct from them, and 4) are ‘causally relevant’ to their manifestations but not themselves causally efficacious. Moreover, Disp diagnoses and eliminates difficult counter-examples to previous attempts at refining the definition of dispositions, viz., those of ‘maskings’ and ‘antidotes’.51 The disposition intension Fragile1, for example, is sometimes loosely described as having an initiating condition of being sharply struck, this then causing a manifestation property instance of the intension Broken1. A proposed counter is the wrapping of a fragile object in packaging—masking it— such that if it were dropped it would not break, this then showing that SCA cannot accurately characterize dispositions. This is true and what it points to is the necessity of the further refinements of Disp: specifically, reference to the proper substructures S and C. Maskings that prevent a merging of a certain internal molecular structure with an external force structure do not falsify Disp. Similarly for disarming the case where certain compounds that have the disposition to poison humans are defeated by the simultaneous taking of antidotes. An antidote defeats the would-be effects of a poison x which has a relevant destructive substructure C because it prevents the latter from merging with and destroying the relevant metabolic substructure S of a patient. Under Disp this does not falsify the left-side analysandum which asserts that x has the disposition to poison, for the right-side analysans remains true—the antecedent of its conditional is false since the prerequisite merging of structures S and C does not obtain here. As a final reinforcing topic of our assay of structure, let us return to and amplify its role in regard to change considered briefly in Section 5.3, what will include displaying its power to shed light on the classic ‘Ship of Theseus Problem’. Change is to be contrasted with creation and/or extinction in that, unlike the latter, with change something persists—maintains its unified identity— across one or more creations and/or extinctions, the latter including necessarily those of attributes, e.g., as the same apple a persists in changing from green to red. In the example of an apple changing color the account seems straightforward and Aristotelian (Physics, Book I): the apple as the same underlying entity persists through the creation and extinction of external accident instances having it as their subject, e.g., some instance Is-Green1i goes out of existence and is replaced by an instance Is-Red1j. Here the apple is considered other than its accidental attributes and so there is no problem with it persisting while it changes colors. I note that pointed to here and reinforcing this work is the fact || 51 See Michael Fara, ‘Dispositions and Habituals’, Nous 39 (2005): 43–82. Also Choi and Fara, ‘Dispositions’.

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that attribute instances are required to explain change of attributes, whether accidental or essential. This is so because when, for example, subject x persists but ceases to be characterized by a property with intension F1 (and so the fact :F1i(x) ceases to exist), what goes out of existence is neither subject x (e.g., our apple a) nor intension/universal F1 (e.g., intension Red1), but rather and as the only alternative the particular attributional union that was unique to them. This individual combinatorial act is either: what I have argued, a non-relationally (continuous) union with intension F1 and so jointly forming an instance F1i, what ceases to exist when x changes, or alternately is a relational (articulated) union and so an instance of the specific relation of Exemplification1 (or Instantiation1), this individual instance Is-Exemplified-by1i then going out of existence when x changes.52 I have argued that Exemplification1 is a relation of conceptual analysis whose instances are derivative of the obtaining of prior attribute instances, e.g., F1i. Now returning to apple a, the more difficult problem is accounting for change that is essential to the apple, and this in the following way. We think of an apple a maintaining its identity across its entire growth—across a continuous sequence of evolving stages of a long event structure teleological in the above sense—from fertilized blossom to mature fruit. Yet, some at least of what is essential to form and function at one stage goes out of existence and is replaced by different things that are essential to the next stage of the apple’s existence. If identity is determined by what is essential, and what is essential must be numerically the same for all times an entity exists, then there is no persisting identity across the growth sequence of the apple. Presupposed here is the classic and false assumption identified in Chapter 2 as Unity by the Constituent One (A8): that identity-maintaining unity is always by a shared one. I.e., the view that for apple a to persist through change what is essential to it and gives it its identity must be numerically the same across all times that it exists. Asserted by Aristotle in the Physics, with change “there must always be an underlying something…[what is] always one numerically…” (Physics 190a15; my insert). This is the ‘endurance’ conception of change: that across change an entity is wholly present (as what is essential to it) at all times of its existence. And on the latter the standard blunt form (i.e., not refined with predicate instances) of the Indiscernibility of Identicals restricted to essential attributes would have to be true, i.e., if a = b then (F)[(F(a) and F is essential to a)  (F(b) and F is essential to b)]. || 52 Along other lines Jiri Benovsky has argued that proffered accounts of change imply trope theory. See his ‘New Reasons to Motivate Trope Theory: Endurantism and Perdurantism’, Acta Analytica 28 (2013): 223–27.

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But now the properties an apple a has as essential to it at fertilization—as a zygote + endosperm + ovary—are different from what it has as a mature edible fruit b, and so under the Indiscernibility of Identicals there is not the same apple across these changes of essential attributes—a ≠ b. Responding to the latter problem, as previously noted the standard alternative to the endurance conception of change is that of ‘perdurance’ (or ‘fourdimensionalism’): that an object like the apple is composed of temporal parts or stages, one temporal part for every instance or small interval of time that the object exists in. The apple then is a sequence of temporal slices, or ‘worm’, each stage the composing structure of the apple at that moment. Different temporal parts can consistently have different essential attributes without the inconsistency of the whole as a single entity having different essential attributes. But now crucial to perdurantism, since, as it presupposes, there is nothing numerically the same running across all the temporal stages of an entity to act as their unifier, like a thread through the beads of a necklace, the question is: What links each such stage to all and just the other stages before and after it so as to make up a singular entity? For most advocates of perdurantism the unities among the temporal stages of perduring entities are those of mereological wholes, sums corresponding to each such entity guaranteed under the promiscuous abundance of Unrestricted Composition—that every possible collection of temporal slices of any manner exists, however mutually irrelevant their elements are to each other. An example of the latter is an allowed apple-banana sum that is all the time-slices of apple a up to some time t together with all the time-slices of banana b after time t. But, it was argued in Chapter 1 that mereological ‘unifications’ and their resultant sums are falsifying abstractions, each posited as an objective plural whole whose prerequisite unifications among its parts are unconditioned by the natures of these parts, yet what as such can only be the abstractive residue left when what is its actual unifiers—arbitrary subjective associations—are conceptually ignored. Mereology is not ontology, but is hypostatized psychology, and it cannot account for the objective unity and being of perduring entities, e.g., apple a. To the contrary and reiterating points made in Section 5.3, it was a crucial argument above that a structured whole whose complexity is beyond that of a single fact is unified, not by a shared single entity, but through transitive chains of connectedness across the intension-controlled combinatorial agencies of attribute instances in the manners of Thesis T7. Now, we tend to think of the transitive unity of a given structure, e.g., apple a, as a unity distributed spatially but as it exists at one time or as static over a short interval, as in a photograph. But identity-bestowing transitive unity across articulated attribute instances

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can be ‘hereditary’ linkings across time as well as space, e.g., as continuous growth displayed in dynamic video. Indeed, this is what is intended by ‘eventstructure’, and the apple as a unified temporally-extended event structure is as such one thing both at any given time and across all its times from fertilization to mature fruit, the latter while retaining some as well as gaining and loosing other constituent and inter-connecting instances of physical, causal, spatial, and temporal attributes. That is, in such dynamic structures some composing instances may endure through its entire existence (e.g., a cluster of molecules composing a seed of apple a) whereas some and their substructures come into and/or go out of existence, enduring for various time intervals, some of these being essential to the whole for the interval of its existence (e.g., those composing the initial zygote substructure of apple a). The being and identity of an apple across its life cycle is the manifold unity of a temporal system composed, mostly, of emerging and/or going out of existence attribute instances continuously articulated at any given time and across time. The ‘temporal parts’ of an apple are not temporal slices each of the entire apple at some instance or interval, the apple then their juxtaposition in an arbitrary sum, but are its composing attribute instances of various durations and mutually inter-connected through non-arbitrary attributions. Diachronic unity here requires no persisting underlying per se subject or ‘substance’. In sum, for the ubiquitous changing structures of our experience, e.g., ordinary physical objects, they neither endure nor perdure in the usual senses, but rather it is for each the path-connectedness across its composing linking and evolving instances that it has its oneness (T3, T7) and being, i.e., ontic identity (T9). This contrasts with the fact that, phenomenally and for practical purposes, it is usually instances of external relations, especially spatial ones, that serve to re-identify such entities, e.g., to reidentifying apple a as the same entity from fertilized blossom to mature apple we would rely upon its spatial position on a certain tree and the latter’s spatial position relative to other trees in an orchard. Though I cannot pursue it herein, it is important to point to the fact that our account of the identity of apple a as a dynamic structure persisting in an identity-bestowing oneness via diachronically articulated instances would apply equally to persons or selves. We are conscious (have ‘perceptions’) of ourselves precisely as such dynamic structures and with memories of ourselves as such. Contra Hume and the source of his problem with personal identity confessed in the Appendix (10-22) of the Treatise53, the mind does perceive ‘real connection || 53 David Hume, A Treatise of Human Nature, David Norton and Mary Norton (eds.), (Oxford: Oxford University Press, 2005).

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among distinct existences’, i.e., attributional unions forming structured wholes. And as Hume observes, “Did the mind perceive some real connexion among them [perceptions], there wou’d be no difficultly in the case.” (my insert) Utilizing some of the above points concerning identity across time, let us consider briefly the classic Ship of Theseus Problem, what is sometimes argued as best solved by a perdurance theory of persistence.54 The problem can be formulated as follows: A wooden ship T has each of its composing parts— planks, masts, etc.—replaced one after another with parts that are closely similar in their physical attributes to the originals. After all the parts are eventually replaced the resulting ship is Tʹ. The common assessment would be that the ship remains ‘the same’—as to it being recognized, its capabilities, legalities, etc.—across these changes and so that T is ‘identical’ to Tʹ. Now, the story continues, as the original parts of T are replaced they are set aside in a pile and that after the completion of Tʹ they are themselves reassembled in the same manner they were in T, the resulting ship being Tʹʹ. But then Tʹʹ likewise has some, indeed it might seem better, claim to being identical to T, Tʹʹ having not only the same organization of parts, but also the very same parts as T. Yet, if all of this is the case, then we would have T = Tʹ, T = Tʹʹ, and Tʹ ≠ Tʹʹ, which violates the transitivity of identity. Our assay of entities in terms of structure, and the latter in terms of attribute instances, allows us to accurately describe and solve the above ‘paradoxes’. We do this graphically with Figure 5.2 (for ease of reading I here omit superscripts on the relation instances that would indicate their adicity). What the diagram illustrates is that, as ontologically precise, there is no pair-wise identity, in the proper sense of ‘no difference in being’ and explicated in T9, among any of T, Tʹ, or Tʹʹ. There is, rather, first a partial indiscernibility between T and Tʹ, and, as intended by the setup of the problem, what we are to take as an absolute indiscernibility between T and Tʹʹ. With the latter we have indiscernibility at every level of compositions of T and Tʹʹ, and in this way is explained why we might think T is ‘more identical’ to Tʹʹ than to Tʹ. In these ways we do not have with T and Tʹ a numerically identical entity with different sets of parts, or with T and Tʹʹ what would be a numerically identical entity discontinuous (at the pile) in its existence across time. With partial and absolute indiscernibility we have two further and needed senses of the phrase ‘the same’ beyond strict identity (i.e., without-numerical-differences).

|| 54 Sider, Four-Dimensionalism, pp. 4–10.

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Fig. 5.2: Ship of Theseus T Transformed into Ships Tʹ and Tʹʹ

The partial indiscernibility of T and Tʹ is at the gross level of relations among visible parts and overall phenomenal structure, having stipulated in setting up the problem that replacements for material parts a, b, c, d, viz., e, f, g, h, be respectively similar (in order that they ‘fit’ in their respective places within the ‘same’ structural form), but not necessarily indiscernible. This is the case with all ordinary replacement parts (e.g., ship planks, masts, etc.)—no two are absolutely (at all substructures) indiscernible. All the ship-structures from T to Tʹ are partially indiscernible. In terms of persistence, we have with the transitions of T-to-Tʹ and T-to-Tʹʹ two evolving/devolving continuous event structures (two ‘histories’), each divisible into non-identical but overlapping substructures as temporal parts. For each, as a dynamic lattice of composing attribute instances connected in the manners of T7, it has a diachronically articulated and so transitive unity that gives it a persisting identity. For each we can trace objective composing connections among its parts back through time, just as we can at any time trace such connections among their then parts through space. The difference between event structures T-to-Tʹ and T-to-Tʹʹ is that the sequence of substructures making-up T-to-Tʹ are all partially indiscernible in being of the same general structure-type—presumably the general form of some class of ancient Greek ships—and it is this persistence of general type, i.e., the exemplification of the same intension/universal , that reinforces the false impression that we have numerically the same entity throughout. The apparent contradiction here is that T and Tʹ in not having numerically the same material parts cannot be iden-

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tical. Our ontology of attribute instances and their forming structure-tokens of structure-types, , that can be partially indiscernible removes the contradiction. In the event structure T-to-Tʹʹ, however, there is no continuity of indiscernible general ship-form  and so no incentive to think that T and Tʹʹ are identically the same ship. Given this, the paradox then arises from the assumption that Tʹʹ has exactly identical material and formal/structural parts as T, and thus T and Tʹʹ would be identical. Again on our ontology, the refinement of absolute indiscernibility shows how entities can be numerically distinct—non-identical—and yet be absolutely and totally indistinguishable in every detail of material and structural components. It is said in the literature that it is the vagueness of the sortal ‘ship’ that is the source of the Ship of Theseus paradoxes, but on our refinements they derive from a prior vagueness of the term ‘identity’ that fails to distinguish between true identity (ultimately T9) and partial and absolute indiscernibility (based on T10).

5.6 Conclusion: The Route to Realist Instance Structuralism The topics briefly touched upon in the previous section illustrate, I propose, the further explanatory promise had by the single-category ontology of attribute instances developed and defended across this work, and what I suggested in Section 1.1 is appropriately termed Realist Instance Structuralism (RIS). What is the expansion of our initial thesis T1, RIS details how all reality is primarily a single dynamic, hierarchically emergent, and multi-dimensional structure or lattice composed of attribute instances, together with derivative cognitive constructs, including associations and their wholes, which emerge upon the particular neuro-psychological structures that are minds. To have being is to have a place in the stratified and emergent system of attribute instances—the active structure that is all facts. RIS represents a holism without any form of monism. Founding and unifying it all are attribute instances, what in fact are what Aristotle sought as ‘primary being’, and where in and through them is his claim true that being and unity—specifically, being and agent-unification—are correlative. To be is to be, or be derivative of, outwardly-achieving combinatorial agency, and this ultimately that of attribute instances. Within the derivative total ‘Webof-Being’, substructures, e.g., an apple, a person, an argument, a nation, or a galaxy, each is differentiated by composing unities that found concomitant emergent attributes, e.g., attributes of spatial continuity, sequences of causal relations, shape, reasoning and emotions, validity, foreign policy, angular momentum, etc., and what we use to focus on these substructures because of our practical and theoretical interests. Accounted for are not only the unities of

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each of the vastly diverse phenomenal and theorized structures we have as given or warranted, but more, how these are integrated in an all-encompassing emergent hierarchy of attribute instances, this up from a lowest ontic level of only mutually dependent instances. The latter holds the promise of an ontological account of our current understanding of quantum reality, and in its integrated completeness RIS is a desideratum ontology for General Systems Theory. Also brought into clarifying relief in the context of RIS is the fictional status of theoretical sets and mereological sums (fusions), what then restricts their explanatory roles to formal modeling, it being a mistake to identify them with the reality modeled. I promoted in outline what I take to be at the core of a case made by Philip Kitcher (Sect. 1.5) that real sums and sets are like lists and what is intended by one sense of the term ‘heap’, viz., conceptual wholes necessarily having prior but subject-irrelevant—and thus easily ignored in abstraction— composing unifiers, i.e., cognitive associations. The theoretical counterparts to real but psychological list-like sums and sets are on this assay fictionalized versions of the latter, e.g., the ‘iterative’ conception of sets—what would be the results not just of idealizing and removing constraints on association-generating operations by the human mind (what might be thought possibilities of God’s intellect), but also and per impossibile, these wholes are held to exist absent any constituent associations, i.e., devoid of any unifying-delimiting causes (like smiles without supporting faces, impossibilities even for the Divine Intellect). So unconstrained, we have the basis for the hypostatized ‘Platonic paradises’ of theoretical sums or sets posited for any plurality of entities. This pseudo-ontological ‘free lunch’ of wholes ready-made for all explanatory occasions, and particularly with CEM mereology the added thesis that sums are nothing more than their elements, make for a false but seductive economy, especially for philosophers at-home in the formal systems of mereology and set theory, and admiring of their logical precision and perspicuity. Avoiding the error of identifying subjectively constructed sums and sets with objective and structured wholes is one sense I intend by terming RIS ‘realist’. But in a technical sense more fundamental to ontology and supported by direct arguments given in Section 4.5, RIS is ‘realist’ because of its implication that there is shared as a component of each of exactly resembling instances, Rni, Rnj, Rnk,…, what is numerically the same real universal/intension, Rn. By way of conclusion I would reinforce RIS by synopsizing our route to it in the following way. In an order from greater to less generality, a starting point is the recognition that the most general features apparent across all of which we are aware are the existence of a plurality of entities, these differentiated both qualitatively and numerically, and existing variously unified or grouped togeth-

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er. A then specifying insight is that each such whole or composite is something more than just two or more non-identical things—it is a delimited grouping of them, i.e., it is all and only, and so ‘just certain’, things—and this requires constituent causes that ‘collect and select’ just these entities. For, all entities would exist in absolute isolation unless one or more of them could bridge the ontic distance between themselves and others, and insofar as they do this they create and fix the limits and identities of resultant composites. Without selecting unifiers there would be no discriminating collecting—no differentiating out from among everything that exists what are limited non-identical wholes—nor would there be even a maximum universal whole of everything that exists. (Removing a possible confusion here, in this last statement the phrase ‘everything that exists’ is to be understood in a ‘distributive sense’, the alternative ‘collective sense’ making the proposition self-contradictory.) Crucial for ontology, then, is the advancing insight of thesis T3 that all delimited composites of the yet discrete presuppose connecting agents that as such effect selecting acts of unification upon which these wholes qua wholes emerge. Each such act is a sustained achieving (Aristotle’s energeia) of a bond that makes for a oneness beyond the being of the unifying agent. The ‘selectiveness’ as to the particular subject(s) of each of these acts is by either concomitant intensions or minds via their associations. Concerning the former, these claims are exhibited intuitively with polyadic relations, and their denial in the vacuum of this a proper theory of attribution leads to such errors as Bradley’s Regress, and ultimately to either of the extremes of homogeneous substance monism or an atomism of absolutely mutually isolated entities. The untenability of the latter and yet continued failure to recognize the necessity of element agent unifiers motivates the tack of identifying all plural wholes with mereological sums or sets of set theory misconstrued as unifierless fictions. Supporting these theses is the recognition that exhibited across all we know and how we know it are wholes that distinguish themselves into those whose unities are a function of qualitative—intensional—relevances among the constituents, i.e., facts via attribution (or ontic predication), and those whose unities require no such relevance but only the numerically distinct existences of their constituents, i.e., unities by arbitrary cognitive associations: again, these being sums, sets, lists, and ‘heaps’. Epistemically, insofar as human thought involves any form of qualitative analysis, synthesis, distinction, or comparison, intension-determined attribution or its absence is essentially involved. And insofar as we have cognitive access to anything beyond our own thoughts it is necessarily a function of real ‘bridging’ relations and the supporting attributes of their relata. Only non-qualitatively founded numerical differences are rele-

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vant to the operation of association; associations are epistemically impotent— they carry no information about their subjects other than their existences. Ontologically, associations are unique to and dependent upon the minds that create and sustain them. In contrast, attributes can have either objective or subjective existences, and exist insofar as their subjects satisfy specific conditions prescribed by the attributes’ intensions, the latter being either objective or conceptually constructed. Central to the tradition’s distinction between wholes by intension and wholes by extension, attributions and associations are causes of unification, extra-conceptual and conceptual. Importantly, however, they are not exhaustive: there is also the more subtle and what I have termed ‘continuous composition’. The latter is what is required to found the scholastics’ ‘formal distinctions’ and what contemporary philosophers intend when holding attribution involves ‘a union closer than relation’. It is also, I suggest, what would have to be the unity of reality taken as a whole if any of the forms of monism were true. Toward clarifying the distinction I have argued that in ‘articulated’ wholes by attribution or association the constituents remain discrete, what requires that some be unifying causes in the specific sense of outwardly-linking combinators (attributes or associations) among the others, whereas in a continuous whole the constituents, though non-identical, are not distinct from each other, and as such do not require inter-part combinators but have their unity intra-whole—by the undifferentiated being of the subsuming whole. The latter is the necessary type of union between intension universals and individuating outwardly-unifying acts that compose the ontic atoms of attribute instances. The distinction and realities of articulated and continuous composition are the necessary foundations for RIS ontology. In regard to intensions, their role in attribution is intrinsic, with one exception, to the classic and continually, if implicitly, influential Aristotelian assumptions, A1-A8, identified and critiqued in Chapters 2 and 3. Relevant to the thesis that intensions set conditions on what attributes can have as their subjects are assumptions A1 (Attributes as Dependent), A3 (Per se Subjects), A4 (Required Essences), and A5 (Inherent Essential Attributes); relevant to the thesis that the same conditions can be multiply satisfied are A2 (Attributes as Universals) and A6 (Non-Attribute Individuals); and relevant to the thesis that intensions control unifying and organizing attributional acts effecting structures is A7 (Attribute Agent-Organizers). Among the arguments herein is that all three general theses are true, but that a number of the classic assumptions regarding them are false. In particular, it was argued, principally in Chapters 2 and 3, that various combinations of assumptions A1-A8 yield contradiction, vicious regress, or other unacceptable implications. The net conclusion was that only three of the

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classic assumptions are veridical: that attributes proper are intrinsically dependent upon their subjects (A1); that every entity has a positive qualitativelydelimiting composing being or essence, what is the grounds or foundations for it being characterized by then essential attributes (A4); and that structured wholes are such by the organizing agency of constituent attributes (A7). It was indicated how, historically, influential responses to the problems of substanceattribute ontology have been, in effect, to deny not only one or more of the five false assumptions but also those from among veridical A1, A4, and A7. The results have been nexuses of errors spawning a multitude of further ontological distortions, e.g., objects as structureless bundles or essenceless particulars, or attributes as all reducible to monadic properties, or construed as either independent ‘little substances’ (e.g., Humean tropes), certain mereological sums or sets, or subjective linguistic predicates or concepts. Central among these destructive assumptions has been the denial of veridical A1 (Attributes as Dependent); specifically, the denial of attributes being ontically dependent and other-directed/other-referring. For to the contrary, on the analyses herein the necessary dual aspects of ontologically fundamental attribute instances imply these characteristics: ontic dependence is intrinsic to an instance’s combinatorial agency, and other-directedness is intrinsic, though in different senses, to both the combinatorial and intension aspects of an instance. It was argued that historically the denial of attribute dependence results principally from the erroneous assumption that a category of dependent entities must presuppose a category of ultimate supporting independent entities—nonattribute per se subjects (A3). When the latter is combined with the common background assumptions that 1) every object, at least other than per se subjects, has some attributes descriptive of what is a composing and defining essence (A4), and that 2) at least essential attributes of an object must be constituents of—inhere in—it (A5), then implied is that such an object must have a constituent per se subject that is essenceless and so without defining attributes. If it were otherwise we would have with per se subjects the Dependence Contradiction identified in Section 2.3. But, per se subjects so construed—entities that can found no characteristics descriptive of them essentially—are essenceless and so cannot found any specificity whatsoever. These posits are the tradition’s ‘prime matter’ or ‘bare particulars’, what historically have been much ridiculed and, indeed, on our analysis are shown to be incoherent: nothing can answer to their defining assumptions. The misreaction was and is to reject A1, thinking that it necessitates A3. The result is to make attributes themselves inert ‘substances’, this the nature of the proposed ontic atoms that are Humean ‘perceptions’ and the common construal of now popular individuated attributes as ‘tropes’. We

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have observed major defects with these theories and, more fundamentally, how not only is their motivation short-circuited by the fact that, by T8, A1 does not necessitate A3, but prior to this how an attribute as such is necessarily an outwardly-directed agent unifier of itself with its subject(s) and in this way is intrinsically a dependent entity. The latter is most apparent in the inter-linking nature of polyadic attributes, but is lost with the inherence theory of attribution (A5 and its generalizations). Analogous to combinatorial acts that are obviously other-directed in the achieving of unions of themselves with other things, intensions are intentionally other-directed in being intrinsically descriptive (criterial, specifying) of other entities (though some are also ‘true of’ themselves, e.g., Abstractness1). Essential to an intension Rn is its stipulating conditions for itself or other entities to satisfy, whether or not this is possible (logically or physically) or if there are any such entities (examples of unsatisfied intensions are Is-a-Square-Circle1, Is-aFrictionless-Surface1, or Is-a-Golden-Mountain1, the first two being unsatisfiable). If an n-tuple of subjects does satisfy these requirements then necessarily there exists an instance Rni that, in a combinatorial act so delimited by intension Rn, characterizes these subjects jointly. In this way the intentionality of intensions founds their dispositionality (Chapter 4). The condition-prescribing that is the other-directedness of intensions is what makes unions that are attributions, contra Hume, objectively ‘real’ and ‘necessary connexions’. The general Humean denial of the ‘other-directedness’ nature of attributes stems, it would seem, from the failure to distinguish the concept of ‘other-dependence’ from that of ‘other-directedness’, and particularly in the sense of intentionality. I have emphasized the point that intensions in abstraction for their actually combinatorial instances are intrinsically non-dependent but yet remain otherdirected intentional entities, the latter being marked by the placing of adicity superscripts on intension terms. This other-directedness is evident with polyadic intensions, e.g., Electirical-Repulsion2 carries with it as intrinsic to its sense its being descriptive jointly of other things beyond itself—there is no repulsion without two things being mutually repulsed. When, as classically, attributes are confused with their constituent intensions, then attributes themselves are taken as non-dependent, and so, on the confusion here, are held as not intentionally other-directed, and so as having no role in ‘necessary connexions’. The only identified classic Aristotelian assumption not specific to attribution, but applying equally to association, is A8—Unity by the Constituent One. The thesis that oneness is by one thing among others by which they are all unified pertains to the ontologically crucial nature of the actual link or connection—the ‘how’ of cohesion—essential to any form of unification among the non-identical.

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The singularity of this assumption in contrast to the rest, and, further, its falsity as argued herein, evidence the historical weakness in our understanding of unity and composition, an absence abetting both the errors that are assumptions A2, A3, A5, A6, and A8, and the long failure to properly and explicitly differentiate attribution from association. Consequences of the latter failure, and the role in them of A8 and relatedly the inherence model, can be seen as follows. As a preliminary, observe that inherence is related to A8 when a whole is taken to be an ‘improper’ constituent of itself and is held to be the cause of the unity of the parts composing it. Now as the pre-theoretical given, attributes make their ontic contributions, and in resulting increasing complexity, either singularly as properties (each a characterization of a single subject) or as relations (each a simultaneous characterization of multiple subjects), or jointly, and particularly obvious as relations, in multiply intensioned inter-connected ‘arrangements’ forming complex structures (each a network of relations and/or properties as they each characterize their subjects). Historically, however, and in the absence of a proper understanding of attribution, the latter sequence has been subject to various collapsing theoretical reductions. In the reverse order of successively eliminating structural complexity the theorized proposals have been: multiple connecting relations composing a complex organization (e.g., living Socrates) reduce to a single attribute (A8 as unity by one attribute; e.g., a ‘substantial form’), relations reduce to monadic properties of their relata (A8 as unity by one subject; e.g., the Aristotelian esse-in/esse-ad analysis), properties reduce to their foundations taken as proper parts of their subjects (inherence and A8), or attributes reduce to their extensions—to sums or sets of their subjects (reverse inherence and A8; e.g., class or mereological nominalism), or subjects reduce to sets, sums, or compresent bundles of their monadic attributes (inherence and A8; e.g., trope bundle theory). Each reduction has its problems, some well-worn, some new on my analyses. But distilled down to the last two options, here either attributes are eliminated in favor of their subjects unified into the attributes’ extensions, and so are not available to have a role in the unity of these extensions and thus leave only association to do the job, or attributes are absorbed into their subjects held composed of two or more of them and where the attributes’ mutual unifications are either by some relation of ‘Compresence’, a hypocritical exception to the reduction strategy and with other problems observed in Section 3.3, or are unified simply by associations dedicated to this service. Maintaining consistency, after all this distillation attribution will in effect reduce to association. With it, then, all unification among the nonidentical is non-factual, being arbitrary, non-necessary, and with no union excluding any other (e.g., contradicting the nature of contrary predicates), what

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in a self-nullifying way applies equally to would-be facts of semantics and logical inference necessary to argue for this unintuitive conclusion. Each step in the sequence of reductions leading to these and other untoward consequences derives from a failure to understand the proper nature of attribution and this in contrast to association. I have detailed this failure in the context of a sustained critique of Aristotelian substance-attribute ontology centered on its assumptions A1-A8, and what are some historically prominent responses to it. On the positive side and with lessons learned from this critique, I then offered an analysis of attribution and its role in composition starting from an assay of the same structural given as the reductions above, but, being now forewarned, one that avoids the easy misdirections of the erroneous Aristotelian assumptions. Again, the pervasive given is that of hierarchical structures (e.g., living animals, complex machines, ecological systems), each composed most obviously and essentially of numerous and qualitatively/intensionally varying inter-connecting polyadic relations, these in their specific intensions and jointly in their specific ‘arrangement’ determining the resultant single whole to have specific emergent attributes (e.g., and respectively: metabolism and reproduction; certain computational powers; specific weather conditions). The immediate second step in the analysis was to see ‘writ large’ in complex structures what then is equally the nature of simple relational structures, i.e., relational facts: each a single relation occurring as an external and intension-determined interconnection among discrete relata, the resulting fact then having its own emergent attributes, e.g., causal relations with other structures. Freed of reductive biases, facts involving monadic properties are then seen naturally to be but the limiting case of all simple structures and to which the same analysis would apply. I.e., the simplest structures are facts consisting each of an n-adic attribute whose intension conditions its selective adherence to or among some n subjects. Expanding upon this preliminary understanding of attribution and drawing out its implications was the work of Chapters 4 and 5 and resulted in our theses T1-T10. Primary to all of our ten theses are T2 and T3: their crucial parts are, respectively, that a) an attributional union is conditioned by a qualitative relevance or fit of the attribute’s intension with aspects of its subject(s), i.e., the intension sets necessary and sufficient conditions that when satisfied by the subject(s) there is a resultant fact, and that b) the actual connection between attribute and subject(s) is effected by the outwardly achieving combinatorial agency intrinsic to the attribute. These two theses describe what are the ontic foundations for the truth of classic assumptions A1 and A7, and, directly or indirectly, for the other eight theses: T1, T4-T10. Centrally important in following from T3—the

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fact that attributes as externally achieving acts—is not only their natures as dependent entities, A1, but also their individuation, T4 (contra A2)—they exist as individuated instances, Rni. Also following from T3, no attribute is a component of—is ‘inherent in’—its subject(s); all attributes adhere to their subjects (contra A5 and its generalizations). Further, following from the nature of an attribute proper, an instance Rni is composed of both an individuator, i.e., its combinatorial act (T3), and an intension Rn, what controls the act as to the nature, number, and order (if any) of its subjects (T2), and what is itself a universal (T5). (These two aspects of an attribute instance are what make it a structuring agent (A7)). The union of an intension and a combinatorial act composing an instance cannot be that of articulated attribution or association, but is rather the continuous composition of a whole of non-identical but non-discrete parts (T6). The intension components of attributes are not individuals nor themselves attributes (contra A6). We have here, then, an immanent realism where, except in the selective attention of conceptual abstraction, an attribute proper—an instance Rni—because of its intrinsic ontic dependence upon patients of its outward unifying agency, can exist only in its union with the subjects of some unique n-tuple, , i.e., it cannot exist outside of some fact :Rni(a1, a2,…,an). And, what is intrinsically an ontically inert and independent—‘thinglike’—intension Rn can exist separate from any instance Rni but only conceptually, though this existence may be one of conceptual construction and not of abstraction from some prior instance. The misidentification of agent attribute instances Rni with their component inert intensions Rn is, I argued, the source of much error in the tradition, e.g., besides misidentifying agent attributes with ‘inert’ Humean perceptions, or with tropes, it also abets the construal of attribution as association. Once attributes were established as individual agents for structuring single facts (T2, T3), it was a straightforward demonstration of how they can combine in either inter-attribute or emergent composition to form complex hierarchical structures, T7, and how this hierarchy can derive from an ultimate atomic ontic stratum of only mutually dependent attribute instances, T8 (contra A3). The unifications of the latter are each, not by a single constituent unifier (contra A8), but by the transitive, ‘cooperative’, agencies of multiple attribute instances. In these ways theses T2-T8 give in refined detail the long and distortingly absent ‘how’ of attributional cohesion, and what are the hitherto missing insights necessary for a perspicuous and comprehensive Principle of Composition (PC). Definitions of structural identity, T9, and indiscernibility, T10, follow immediately from this assay of complex structure. The remaining classic assumption A4—that every entity has a specific positive essence that founds certain essential attributes (what by T3 do not compose it)—is a funda-

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mental ontological principle, and is supplemented by T2 that gives further specificity to how attributes are founded with respect to their subjects. The structuralism I have defended differs from and corrects standard and stalemated ontologies in key ways that I would re-emphasize in summary. Fundamental to RIS are two ‘Copernican reversals’: First and contrary to substanceattribute ontology, attributes as subject-dependent instances are exclusively ontically primary; all independent objects (‘substances’) are derivative of these dependent entities. This parallels their fundamental epistemic status: we have no cognitive access to other entities except through their attributes as founded in them. Second and contrary to bundle theories that react to substance-attribute ontology, attributes as instances do not enter into the composition of their subjects, but adhere externally to them and form subsuming facts—the simplest structures. Implied by the details of these ontological reversals are corrections to standard realist and nominalist/eliminativist strategies. Important here are the following. Linking epistemology and ontology, explanation is not reductive elimination, but the observance of contextual inter-relation, i.e., conceptual placement within a structure of thus mutually explanatory items, the only explanation possible for simple entities.55 Relatedly and in general, the extensional (e.g., sums, sets, and constructs out of them) is ontically derivative of and posterior to the intensional. In particular, all unity among the yet discrete requires controlled combinatorial agency, the control as to things unified being either objectively by intensions on their instances or subjectively by minds on their associations. Attributions being acts of unification are individuated as instances, and, since instances are the ‘primary beings’, attribution is for ontology its principium individuationis. In addition to articulated unity among the discrete, made more precise was the continuous unity forming attribute instances, a clarification on the classic ‘formal distinction’ and how it avoids the perennial and fundamental problem of Bradley’s Regress. Specifically and a potent differentiation absent from traditional ontologies, identified was five forms of unification/composition, what crucially for hierarchical structure includes emergent unification. And, following upon these is the distinction of two

|| 55 The point is an important one and one made classically by Strawson against Quine who asserted that “Explication is elimination.” Rather, Strawson rightly observes, “For philosophical explanation is not a steady reductive movement in the direction of the intrinsically clear, but rather an exhibition of connections and relations between notions none of which are immediately transparent to philosophical understanding. The clarity is in the connections.” W. V. O. Quine, Word and Object (Cambridge: MIT Press, 1960), p. 260; Peter Strawson, Subject and Predicate in Logic and Grammar (London: Methuen, 1974), p. 37.

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forms of ontic dependence: a) the primary form of combinatorial agents upon their subjects—that of attribute instances and associations—and b) the derivative dependences involved with wholes and their parts—the dependence of all wholes upon their parts, and the dependence of at least some parts upon their subsuming wholes, the latter characterizing instances as continuous composites. Since necessity and contingency characterize types of dependence, a), b), and the five forms of composition provide the basis for an integrated account of these modalities. Emerging upon structures that are minds are mental faculties and operations, their resulting structures themselves yielding emergent products (e.g., abstracted and created intensions, propositions, arguments). Intensions are numerically repeatable universals, primarily (i.e., if not conceptual constructs) proper constituents of attribute instances, not constituents of the subjects of the latter, and are intrinsically independent entities in the sense of being simple and non-agents, contrasting with their subsuming intrinsically dependent instances. The union of attribution is not that of self-founding inherence, the contrary being also a cause of much distortion in the tradition, but is rather that of external intension-founded adherence. As the latter, properties and relations are equally and fully attributes, differing only in adicity determined by their intensions, but neither one being reducible to the other. In these ways and in regard to intension-universals, we have none of the traditional ‘isms’ as standardly defined: neither immanent realism (Aristotle), transcendent realism (Plato), nor various forms of reductive nominalism. And thus globally and consonant with our intuitions, Reality is not just a sum or set of things whose natures are irrelevant to its unity—‘just one little thing after another’—nor even just the space-time-causal network. Rather and subsuming the latter, it is a hierarchical lattice of inter-connecting attribute instances of physical and non-physical intensions, and their resulting wholes (including minds and their associations). And this all-encompassing hierarchy avoids dependence vicious regress—‘turtles all the way down’—by resting on an atomic ontic level of closed chains of mutually dependent instances, what would include particle-forming mirco-physical attributes. Because instances do not share parasitically in the beings of their subjects, the transitivity of dependence in these closed loops of instances having other instances as subjects is non-vicious—each composing instance ‘leaning upon’ one of the others and jointly supporting each other. Hence, absent is the need to posit characterless substrata (‘prime matter’ or ‘bare particulars’), what are impossibilities on the analysis herein, or to deny the intrinsic dependence of attributes (as with most trope theories). Within the total structure that is Reality, causation is not constant conjunction, nor real but of just a few intensions, but is real and ubiqui-

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tous in the agency of every attribute instance as conditioned by any intension. And, we have indicated how causal interaction among structured wholes can provide a more complete account of dispositions, and how persistence through change can be accounted for in a way that retains the internally-grounded integrity of the persistent. The latter is opposed to turning persistence into a sum or set of temporal slices each of whose unifications with the others are arbitrary and without relevance. Realist Instance Structuralism represents a ‘paradigm shift’ from the prevailing alternatives of substance-attribute and bundle theory ontologies. I have argued for its need due to combinations of errors from among classic assumption A1-A8 or their denials inherent to the latter theories, and for its necessity as defined by theses T1-T10 and following straightforwardly from an assay of structure, the ubiquitous given. With the latter theses we have, I propose, the foundations of a potentially rich research program for solving further ontological problems, including those implied by modern physics.

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Index absences, 219 abstraction, 36, 59, 64, 65, 101, 137, 171, 195, 212, 213, 221, 224, 244, xviii – intrinsic vs. extrinsic, 177 accidental forms, 15, 72, 85, 167, xi actualism, 193 adherence, 2, 47, 89, 110, 289, xii, xiv agency, 29, 32, 41, 136, 159, 189, 194, 195, 196, 201, 202, xiii, xvii agent-combinators, 26, 42, 45, 75, 78, 84, 91, 127, 129, 136, 138, 192, 209, 210, 222, 282, xii, xvii aphairesis, 101 Aquinas, Thomas, 43, 55, 68, 83, 85, 100, 106, 108, 135, 190 Aristotelian ontology, 7, 15, 17, 72, 81, x, xiv – four causal types, 269 Aristotle, 5, 10, 12, 18, 24, 46, 51, 67, 68, 70, 75, 76, 78, 79, 80, 83, 84, 88, 90, 91, 101, 105, 106, 108, 127, 128, 160, 172, 189, 192, 214, 221, 223, 230, 264, 270, 274, 279, xiii, xiv, xvi, xx Armstrong, D. M., 7, 43, 62, 65, 87, 99, 103, 119, 121, 123, 181, 198, 211, 219, 224, 225, xx associations, 5, 6, 16, 18, 19, 24, 30, 38, 39, 41, 65, 102, 103, 109, 111, 118, 139, 145, 148, 154, 156, 157, 162, 194, 196, 198, 210, 218, 268, xi, xii, xiii, xx Attribute Agent Organizers, Assumption of (A7), 75, 78, 80, 82, 84, 86, 91, 92, 96, 117, 119, 125, 126, 128, 129, 132, 136, 147, 148, 160, 164, 166, 167, 168, 192, 199, 214, 228, 229, 230, 244, 282, 286, 287, xv Attributes as Dependent, Assumption of (A1), 18, 74, 79, 80, 87, 92, 94, 99, 114, 118, 125, 134, 136, 137, 138, 142, 143, 147, 164, 165, 166, 168, 186, 197, 199, 200, 212, 214, 215, 228, 229, 230, 242, 249, 268, 282, 284, 286, xiv Attributes as Universals, Assumption of (A2), 74, 80, 82, 91, 92, 93, 94, 96, 99, 104, 110, 118, 126, 127, 128, 129, 130, 131,

132, 133, 134, 136, 138, 166, 168, 198, 199, 200, 203, 204, 212, 214, 215, 229, 230, 282, 287, xiv attribution, 4, 73, 167, x, xii, xvi – accidental, 4, 6, 79, 82, 87 – as 'partial identity', 124, 182, 219 – asymmetry of, 170 – contingent, 4, 6, 152, 165, 179, 181 – essential, 4, 6, 79, 82, 98 – foundations for, 53, 87, 89, 107, 109, 110, 112, 113, 114, 120, 139, 152, 168, 169, 173, 179, 183, 207, 208 – intension-conditioned combinatorial acts, 2, 5, 8, 9, 17, 20, 29, 32, 67, 97, 148, 150, 168, 174, 187, 193, 199, 231, 275 – necessary, 4, 6, 179, 180 – 'rooted-in' subjects, 102, 104, 111 – 'tied-to' subjects, 102, 104, 111 Auriol, Peter, 224 Austin, Christopher, 140 Avicenna (Ibn Sina), 200 Axiom of Extensionality, 54 Ayer, A. J., 138 Baker, Lynne, 25, 240 bare particulars, 27, 33, 73, 92, 96, 99, 102, 103, 104, 108, 125, 196, 204, 241, 255, 283, 289 Baxter, Donald, 182 Bergmann, Gustav, 98, 197, 216 Berkeley, George, 161 Black, Max, 55 Blanshard, Brand, 132, 138 Bostock, Simon, 121 Bradley, F. H., 129, 131, 132, 177, 183, 225 Bradley’s Regress, 6, 19, 27, 37, 84, 90, 126, 128, 129, 132, 151, 160, 169, 198, 199, 214, 246, 281, 288 bundle theories, 6, 20, 87, 88, 137, 142, 144, 148, 176, 214, 258, 285, 288, xii Buridan, John, 197 Cajetan, Tommaso, 105

302 | Index

Campbell, Keith, 105, 118, 119, 120, 123, 141, 142 Cantor, Georg, 53, 63 Carrara, M., 63 categories, 1, 3, 5, 6, 241 category mistakes, 174 causation, 144, 145, 159, 161, 165, 188, 190, 191, 193, 194, 211, 266, 289 – 'downward', 13, 237 – negative, 267 Chambers, Ephraim, 154 change, 273, 274, 276 combinatorial agency, 144, xviii composition, 1, 3, 60, 76, 83, x, xii – articulated, 136, 225, 259, xiii, xviii – continuous, 35, 137, 150, 191, 194, 221, 223, 225, 227, 228, 258, 264, 282, xiii, xviii – emergent, 233, 259, xix – five forms, 34, 44, 70, 258, 263, xii – inter-attribute, 233, 259, xix – is identity, 250, 258 – principia compositionem, 70, 258 – Principle of Composition, The (PC), 258, 287 – Problem of, 25, 70 – Vagueness Argument, The, 262 Composition-as-Identity Thesis (CI), 21, 42, 44, 45, 58, 62, 65 compresence, 5, 19, 37, 88, 119, 138, 139, 140, 285, xi, xx contingency. See attribution Cope, Glen, xxi Copernican reversals, 288, xx correspondence theory of truth, 161 cosmos, 2, 10 Cross, Richard, 46 de dicto necessity and contingency, 179 De Monticelli, Roberta, 21 de re necessity and contingency, 178 Dedekind, Richard, 63 Denkel, Arda, 143 dependence, 6, 69, 74, 93, 108, 145, 242, 243, 288, 289, x, xii, xix – agent-on-subject prior to whole-on-part, 19, 265 – avoiding 'turtles all the way down', 243

Dependence Contradiction, The, 94, 95, 97, 99, 107, 108, 118, 125, 144, 196, 283 dispositions, 266, 290 – dispositional attributes, 9, 270 – 'maskings' and 'antidotes', 273 – pan-dispositionalism vs. categoricalism, 266 Dorr, Cian, 22 Ehring, Douglas, 35, 37, 227 Eleatic Principle, The, 8, 71, 199, 211 emergence, 10, 12, 14, 44, 49, 171, 222, 238, 286, 289, xi Emergent Attribute Principle, The (EAP), 46 energeia, 80, 84, 160, 189, 190, 192, 214, 281 – characterizing motion, 189 epistemology, 4, 11, 41, 73, 132, 146, 161, 169, 281, 288, x, xi – explanation, 288 essence, 75, 81, 82, 84, 87, 96, 97, 101, 105, 108, 180, 245 – general, 98 – individual, 98 events, 91, 136, 267 exemplification, 5, 6, 18, 37, 103, 118, 198, 218 facts, 2, 22, 29, 44, 136, 167, 168, 169, ix, x – 'fact-independence', 172 – necessary vs. contingent, 178 Fine, Kit, 22, 25, 240 Frege, Gottlob, 197, 198 Geach, Peter, 215 General Relativity, 14, 245, xx General Systems Theory, 13, 233, 237, 280, xx Gotterbarn, Donald, 158 Grossmann, Reinhardt, 140, 206, 224 Grounding Problem, The, 239 Hallett, Michael, 64 Heil, John, 47, 52, 93, 100, 118, 122, 193 Henry of Ghent, 153 holism, 71, 279 homoeomerous, 83

Index | 303

Hume, David, 19, 32, 39, 40, 68, 126, 144, 174, 183, 194, 196, 213, 265, 268, 277, 284 – comparison assay of relations, 155 – 'distinction of reason', 150, 224 – Hume's Dictum, 144, 149, 151, 152, 182 – perceptions, 147, 149 – 'philosophical' vs. 'natural' relations, 155 – separability argument, 149 Humphreys, Paul, 49 identity, 3, 33, 250, xvi, xix Identity of Indiscernibles, The, 33, 116, 138, 255 indiscernibility, 252, xvi, xix – absolute, 256 – partial, 257, 278 individuation, 68, 75, 80, 98, 200, 203, xviii – Aristotelian forms, 92 – haecceitas, 33, 92, 204, 207, 255 – of substantial forms, 215 – principium individuationis, 6, 27, 33, 203, 288 Individuation Regress, The, 95, 97, 99, 108, 114, 118, 125, 196, 203 Individuation, Problem of, 27 inherence, 2, 6, 18, 31, 47, 86, 87, 88, 89, 91, 103, 109, 112, 113, 115, 123, 127, 136, 137, 174, 176, 183, 194, 285, 289, xi, xiv – by accidents as 'kooky' entities, 88 – praedicatum-inest-subjecto, 115, 153 Inherent Essential Attributes, Assumption of (A5), 75, 77, 79, 82, 86, 88, 89, 92, 93, 94, 95, 97, 99, 101, 104, 107, 109, 110, 113, 114, 115, 125, 126, 131, 134, 136, 143, 144, 148, 166, 176, 196, 211, 228, 229, 230, 238, 249, 282, 283, 287, xv Instance Instantiation, Principle of, 187, 199, 217, xvii instance notation, 32, xvi instances, attribute, 1, 164, xii, xiii, xvii – not 'swapped' or 'piled', 203 instantiation. See exemplification Instantiation, Principle of, 216 intensions, 1, 4, 22, 32, 73, 151, 152, 153, 168, 206, 217, 282, ix, x, xii, xvii – as dispositional, 193, 284

– as intentional, 173, 193, 284 – being simple, 177 – extensions of, 173, 186 – sortal vs. non-sortal, 185 Inukai, Yumiko, 158 isomorphisms, 11, 39, 163, 257 James, William, 11, 162 Karakostas, Vassilios, 14 Kitcher, Philip, 63, 280 Koslicki, Kathrin, 11, 22, 25, 240 LaBossiere, Michael, 204 Ladyman, James, 14, 246, 254, 255, 256 Lango, John, 11 Laycock, Henry, 61 Leibniz, G. W., 105, 115, 117 Lewis, David, 14, 21, 22, 24, 42, 45, 60, 62, 65, 70, 146, 183, 259, 260, 263 – 'trout-turkey', 24 Linzee, David, xxi Locke, John, 39, 154, 157 logic, 11, 139, x – Particularized Predicate Logic (PPL), 54, 206, 255 Loux, Michael, 109, 206 Lowe, E. J., 31, 41, 68, 125, 198, 217 Marchal, J. H., 13 Martin, C. B., 193 Martino, E., 63 matter, 72, 78 Meinong, Alexius, 201 mereological sums (fusions), 3, 5, 23, 41, 53, 54, 140, 146, 169, 171, 280, xi, xiv mereology, classical extensional (CEM), 20, 42, 45, 58, 197, 265, 275, 280 Merricks, Trenton, 62, 261 moderate realism, 36, 228 monads, 116, 117, 126, 188, 195 Monaghan, Patrick, 6 monism, 18, 126, 128, 130, 132, 134, 192, 195, 223, 265, 279, 282 Moreland, J. P., 86, 102, 206 Morganti, Matteo, 110, 247 Munson, Ronald, xxi

304 | Index

near-bare particulars, 109, 111, 112 necessity. See attribution nominalism, 20, 23, 216, 285 Non-Attribute Individuals, Assumption of (A6), 75, 76, 77, 80, 82, 92, 93, 94, 96, 98, 101, 110, 137, 186, 204, 212, 229, 230, 241, 282, 287, xv non-relational tie, 2, 6, 18, 35, 198, xi, xii numbers, cardinal – adjectival vs. substantival, 216 objects, 73 ontic predication. See attribution Ontic Structural Realism (OSR), 13, 33, 164, 245, 254, xx ontological dichotomies, 2, 72, 79, xi origin essentialism, 181 Pasnau, Robert, 6, 106, 129 path-connectedness, 29, 38, 136, 234, 236, 252 Per se Subjects, Assumption of (A3), 67, 74, 76, 79, 81, 82, 85, 87, 89, 92, 93, 94, 96, 99, 100, 101, 107, 108, 110, 118, 125, 126, 127, 134, 137, 138, 143, 147, 165, 166, 186, 200, 204, 205, 214, 222, 230, 231, 241, 244, 249, 282, 283, 287, xiv persistence, 142, 239, 251, 273, 278, 290 – endurance, 251, 275 – perdurance, 251, 275 Pickavance, Timothy, 102, 103 Plato, 18, xiii – the 'Receptacle', 100 Platonic Forms, 40, 90, 213, xi plural reference, 61 potency, 192 primary being, 67, 72, 76, 81, 82, 84, 91, 92, 232, 241, 244 prime matter, 18, 73, 77, 79, 85, 89, 96, 98, 99, 102, 105, 106, 107, 108, 241, 283, 289 – pure potentiality, 78, 100, 106 processes, 267 Proclus, 223 propositions, 4, 28, 33, 118, 120, 133, 147, 161, 163, 216, 218, 219, 220, 235, xi, xvi – analytic vs. synthetic, 180

prōtē ousia, 67, 76, xii quantum entities, 2, 67, 137, 164, 203, 246, 249, 254, 255 Quantum Mechanics, 13, 245, xx quiddity, 1, 226 Quine, W. V. O., 288 real accidents, 88 Realist Instance Structuralism (RSI), 26, 279, xix relations, 9, 17 – Doctrine of the Trinity, 55, 245 – ens ad aliud, 16, 79 – esse-in/esse-ad modeling, 117, 119, 120, 153, 156, 158 – external, 119, 124 – in mente, 118, 152 – internal, 52, 119, 121, 124 – internal vs. external, 183 – multigrade, 85 – supposed reduction of, 16, 84, 87, 114, 115, 116, 120, 131, 165, 285 – Wiener-Kuratowski modeling, 23, 171 Required Essences, Assumption of (A4), 75, 77, 84, 86, 92, 93, 94, 98, 99, 101, 107, 108, 110, 113, 125, 126, 144, 147, 166, 168, 230, 282, 283, 287, xv resemblance, 88, 141 Restricted Composition Principle, The (RCP), 240 Robb, Robert, 258 Rosen, Gideon, 22 Russell, Bertrand, 42, 55, 57, 117, 123, 129, 130, 138, 151, 162, 172, 183, 198 Schaffer, Jonathan, 134, 223 Schmitt, Yann, 227 Schnieder, Benjamin, 201 Scotus, John Duns, 46, 127 – distinctio formalis a parte rei, 36, 137, 226 sets (classes), 3, 5, 23, 41, 53, 54, 63, 128, 169, 171, 265, 280, xi, xiv – iterative conception, 58, 64, 280 Ship of Theseus Problem, The, 277 Sider, Theodore, 21, 58, 105, 109, 176, 260 Simons, Peter, 25, 142, 220, 246, 247

Index | 305

Simple Conditional Analysis, The (SCA), 271 spatial relations, 30, 105, 119, 123, 140, 158, 175, 204, x – Relational Theory of, 175 – Substantival Theory, 31, 176 states of affairs. See facts Strawson, Peter, 198, 288 structure, 5, 7, 10, 11, 16, 28, 29, 73, 75, 77, 83, 84, 128, x, xii, xvi, xvii, xx – dynamic, 237, 251, 268, 270, 276 – hierarchical, 2, 12, 13, 71, 77, 83, 136, 164, 172, 232, 236, 268, 280, 286, 289, xi, xvi Suarez, Francisco, 68, 108, 135, 150, 152, 153, 190, 197 – distinctio rationis ratiocinatae, 36, 226 Subject Uniqueness, Principle of, 200, 203, xviii substance, 12, 67, 72, 77, 142, 143, 144, 165, xx substance-attribute ontology, 73, xx substantial forms, 5, 15, 17, 57, 72, 79, 81, 85, 87, 96, 108, 135, 147, 160, 165, 167, 190, xi supervenience, 34, 119 synonymy, 29, 35, 186, 206, 209, ix T1, Thesis, 26, 73, 167, 168, 231, 244, 258, 286, xvii T10, Thesis, 232, 253, 254, 255, 256, 279, xix T2, Thesis, 168, 193, 199, 203, 228, 229, 250, 268, 286, xvii T3, Thesis, 128, 187, 192, 196, 199, 200, 201, 203, 211, 217, 228, 229, 233, 242, 248, 250, 268, 276, 281, 286, xvii

T4, Thesis, 128, 196, 199, 200, 202, 203, 205, 209, 210, 211, 229, 233, 242, 248, 250, 268, xviii T5, Thesis, 201, 206, 210, 229, 248, 268, xviii T6, Thesis, 136, 208, 221, 228, 229, 242, 287, xviii T7, Thesis, 205, 231, 232, 233, 235, 236, 240, 248, 249, 250, 251, 252, 256, 266, 267, 275, 276, xviii T8, Thesis, 205, 230, 231, 242, 244, 246, 248, 249, 250, 256, 284, 287, xix T9, Thesis, 232, 250, 252, 279, 287, xix Third Man Argument, The (TMA), 90 tode ti, 77 trope theory, 1, 73, 97, 118, 138, 141, 143, 151, 204, 227, 244, 247, xiii, xx truth-makers, 5, xi, xvi Unity by the Constituent One, Assumption of (A8), 38, 43, 53, 57, 76, 77, 78, 80, 83, 84, 85, 86, 91, 92, 93, 96, 114, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 165, 166, 190, 221, 229, 230, 232, 235, 237, 238, 265, 274, 284, 285, 287, xvi universals, 1, 34, 74, 91, 95, 99, 113, 128, 129, 136, 137, 141, 206, 209, xiii, xviii Universals, Problem of, 27 van Inwagen, Peter, 25, 70, 258, 259 virtus dormitiva, 87 Wittgenstein, Ludwig, 38, 172