Aristotle’s Theory of Knowledge 9781472597908, 9780826494856

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Acknowledgements

I would like to thank the following people for their help, encouragement, instruction, and advice: My parents and family – Kiefer, McMahon, and Honey, Harry Ide, Lex Newman, John Turner, Luc Brisson, Tim Black and Peter Murphy, Lisa Wilkinson, David Pitt, Phil Hugly, Jim Rosowski, Sarah Douglas and James Fieser at Continuum Publications, and the philosophy departments of Creighton University and the University of NebraskaLincoln. I would like to thank the students from my Senior Seminar in Epistemology at Nebraska Wesleyan University, from Creighton and from Southeast Community College. I am grateful to the city of Olomouc, Czech Republic, where much of this work was first written. I would like to make a special acknowledgement to several people without whom this work would not have been possible. First, I thank Albert Casullo and Edward Becker. Like Kant in his day, they both demonstrate that first-rate philosophy can, and is, being done in places that seem far from the centers of learning. I am incredibly grateful to Michael Chase, whose hospitality, advice, and assistance during a trip to Paris and the Centre Nationale de la Récherche Scientifique was exemplary. All scholars should help each other in the way he helped me. Finally, I would like to thank Maureen Honey, without whom much in my life would not have been possible.

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Introduction

Aristotle’s work is very difficult. It has reached us in a condition like a fossil bed, whose contents have been lost, jumbled or broken, mixed about, all at the mercy and whim of history. The volcanoes, plate shifts and erosion it has had to suffer came in the form of irresponsible book collectors, Roman armies on the rampage, editors and scribes filling in gaps with guesswork and cramped hands, among many other things. Miraculously, significant pieces remain intact, some preserved quite well, others with evident gaps, chips, and cracks. Others clearly have been broken, with parts lost or reassembled. Yet for others, only their shadows remain, like the imprint of a fish swallowed by a predator just before the predator itself succumbed to the mud. One can imagine how incredibly hard it would be to understand Kant if all we had of his three Critiques, and some ethical and political works, were some notes based on them and the notes his students took during his lectures. This is what we have of Aristotle’s work, and, unfortunately, Aristotle is about as good a writer as Kant! This mess makes our job like that of a paleontologist. In order to get a glimpse of the creature that once lived, we have to sort through what remains in the fossil bed. We then have two choices: We can make an attempt to put the skeleton back together, and from that skeleton estimate as best we can what that creature’s life was like, how it appeared, ate, moved, who its enemies were, how it interacted with its environment. Alternatively, we can examine each fossil fragment on its own, independently of the bones found together with it or of the skeleton to which it belonged. In this case, we might firmly determine the proportions and composition of any one fragment. However, without examining it in the context of the bed in which it was found, or of its position in a skeleton, or even in comparison to more intact coeval remains found elsewhere, we will have a very difficult time in establishing the role it played in that creature’s

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life, let alone the kind of creature to which it belonged. Any skeletal fragment clearly belonged to some creature, as no bone comes into being just by rising out of the earth on its own as a bone. Fortunately we have plenty of material work with. The analysis of the fossil bed may ultimately indicate that there is more than just one creature preserved in it. It would be a mistake, though, to assume that the way in which remains are preserved is indicative of the nature of the creature or creatures from which they came, with complete, intact remains indicating a fully-formed creature, and disjointed, disconnected remains indicating an incomplete, unorganized, or at least quite unusual, one. Any endeavor like this has to begin with some plausible working assumptions in order to get underway. We know that Aristotle’s immediate philosophical forebears, Plato and Socrates, asked basic ‘what is...?’ questions. From those basic questions, they attempted to work out answers, especially answers that were coherent with others given to different questions. Socrates asked questions like ‘what is piety?’ or ‘what is virtue?’; Plato asked ‘what is justice?,’ ‘what is the good?,’ ‘what is knowledge?,’ ‘what are the best laws for a state?,’ and many others. One of Aristotle’s principal philosophical terms utilizes this ‘what is...’ in its construction: to ti estin. From the evidence of this tradition, I started this project with the assumption that Aristotle worked in a like manner: I assumed that Aristotle took the basic questions with which Socrates, Plato, the Academy, and others worked and provided answers of some sort to them. Accordingly, a sound technique for dealing with Aristotle’s philosophical remains is to ask such a question, like ‘what is knowledge?,’ and then determine his answer or answers to whatever extent the material allows. I also assumed that an answer to one question had to cohere and be consistent with the others, unless the remains themselves evinced otherwise. For the era in which Aristotle was working, the goal of the philosopher was to offer an explanation of everything. In order for such a goal to be achieved, an answer to one question, like ‘what is?,’ had to be interwoven with the answers to all the others so addressed, like ‘what is knowledge?’ or ‘what is good?’ Accordingly, I took all of Aristotle’s surviving work as potential material for my question. A third working assumption comes from Aristotle’s philosophy itself. The evidence is overwhelming that Aristotle used language very carefully, deliberately, and technically. For example, Metaphysics V describes the crucial different senses of key philosophical terms. The Topics repeatedly rails against using vague or ambiguous terms in definitions and other philosophical discussions. It also encourages us to seek out inconsistencies in the use of language by others in order to refute their views. Aristotle, like

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Plato, also introduced many new terms, as well as technical uses of existing terms, into the ancient Greek vocabulary, for example ‘to ti ên einai’ and ‘sumbebêkos.’ Accordingly, I assumed that the key terms in his philosophy are technical and have specific meanings which are the same throughout, albeit recognizing that Aristotle might be utilizing, emphasizing, or playing off a certain connotation that term has at the expense of another. I also assumed nothing in regard to the specific meaning of these terms. The drawback to this approach is that one often has to sift through a lot of material with key pieces remaining unidentified for a period of time. The benefit of it is that one discovers (to at least some extent) Aristotle’s real intent behind these terms. You will be able to see this approach in action for yourself concerning such terms as ‘hupolêpsis,’ as well as the notorious ‘kath’hauto’ – a term which, given the structure of my work, cannot receive a proper examination until Section III. These assumptions turned out to be very fruitful. I uncovered four preserved answers that form the backbone of Aristotle’s response to the question with which I am concerned, namely ‘what is knowledge?’ I then discovered that these four share many presuppositions and interconnecting details. I failed to find any fossil remains that clearly, or even probably, came from entirely different creatures – that is, from entirely different, mutually excluding philosophical positions. The pieces of this theory fit together into one relatively complete skeleton.1 It is a pretty big, very sophisticated and complex creature, and is lurking around, either in the foreground or background, in multiple works. The results of my reconstruction show that much of the last 1700 years of interpretation of Aristotle is flawed. (I leave it to the reader interested in this to note where my accounts differ from or directly challenge this tradition as they read along.) From what I can tell, there are two main reasons why this has occurred, setting aside the problems that naturally arise from Aristotle’s style of writing and the condition in which his work has reached us. The first reason why so much interpretation has been flawed is, I think, due to the misunderstanding and careless translation of his technical terms. I mentioned this problem above and how I avoided it as best I could. So that we do not make the same mistake, you will see the application of a strict one-to-one correspondence between these terms and appropriate English counterparts in my translations and usage, with variants of the English term strictly corresponding to their ancient Greek variants wherever possible. If no appropriate English term or variant was available, I transliterated the ancient Greek term. The benefit of such consistency is that any use of one term can be invariably understood as standing for the corresponding ancient Greek term. Adherence to this principle sometimes

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resulted in unintelligibility. In such instances, I tried to translate Aristotle’s Greek into fluid English, but retained unambiguous use of the key technical terms.2 Where I take Aristotle to be using a term to refer to a genus, form, or universal, I put that term in italics. I also include a Greek–English glossary of my translations at the end of this work. I tried to choose appropriate English terms with little or no philosophical baggage – especially baggage found nowhere in Aristotle! By doing this we avoid the extraordinary philosophical uses or connotations so many of Aristotle’s terms have acquired over the centuries, many of which are highly obfuscating. Thus no philosophical or interpretative conclusion is grounded upon the ambiguity of terms or some translational decision. There is the least amount of static interference between Aristotle’s work, the reader, and myself. By my translating all of the passages under examination in this way, we can escape the trap of reading contemporary philosophical concerns or issues back into Aristotle’s work, a trap that drastically distorts what Aristotle was trying to do. This is the second reason why so much interpretation of Aristotle has been flawed. Our understanding of it has suffered greatly throughout the ages at the hands of commentators who have done this, for whatever reason. This injustice however is not the same as putting Aristotle’s work into modern terms, or noting similarities between it and contemporary authors. The former way takes foreign debris and forces it into the fossil bed, and then the commentator declares that this debris is a part of Aristotle’s work. The latter way reconstructs the skeleton by using contemporary techniques and methods without introducing foreign matter, and by comparing it with similar creatures living today. If any pieces are missing, they are inferred from the surrounding structure and in comparison with analogous creatures whose corresponding skeletal pieces we do have. I am completely unconcerned by Aristotle’s theory of knowledge looking unfashionable or implausible to contemporary eyes. If in modern terms Aristotle’s positions and concerns coincide with ours today, great; if they do not coincide, or even seem ludicrous in our eyes, great – at least we really understand what he was getting at, and we can be sure that the views of someone as smart as he have legitimacy even if we do not see it, or cannot see it due to the violence of history or our ignorance. One issue needs to be settled right now, and that concerns the word ‘knowledge’ itself, ‘epistêmê.’ Many interpreters understand Aristotle’s use of the Greek term as meaning ‘understanding,’ not ‘knowledge,’ and translate it accordingly. There are two camps carrying this banner. The first is comprised of scholars of ancient philosophy persuaded by Miles Burnyeat’s paper ‘Aristotle on Understanding Knowledge.’3 He does not offer a formal argument in defense of this interpretation of the term,

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and it does not seem to have ever been presented or examined in this manner. Such an argument, though, can be constructed from his paper, and it runs as follows: 1. Contemporary discussions about knowledge primarily concern belief, justification, and related matters. 2. Aristotle’s discussions about epistêmê do not primarily concern belief, justification, and related matters. 3. If the topic of a discussion does not primarily concern belief, justification, and related matters, then that topic does not concern knowledge, but something else. 4. Therefore, Aristotle’s discussions about epistêmê do not concern knowledge, but something else. Versions of (1) and (2) are usually what is explicitly stated by the proponents of the ‘understanding’ position. (1), even though it seems to be based on a rather narrow view of epistemology over the last fifty or so years, might be true if one takes ‘belief, justification, and related matters’ broadly enough. However, (2) is downright false. Unfortunately, it takes a book-length project like mine to show its falsity conclusively.4 You will see, for example, that the role logic has for Aristotle works in pretty much the same way as it does for the Stoics as Burnyeat describes it for them but not for Aristotle: A demonstrative proof is a valid argument which deduces from premises which are both true and evident a conclusion which in itself is nonevident, where ‘evident’ and ‘non-evident’ are strictly epistemic terms… The non-evident conclusion is then made known to us by the proof… This approach makes of demonstration an instrument for the increasing of knowledge, for inferring or justifying explanations, rather than for systematizing explanations and understanding knowledge which for the most part has been independently acquired. (Burnyeat 1981, 137) Thus, contrary to Burnyeat and his followers, I am convinced that there was no gap in, or shift away from and then back again to, the theory of knowledge between Plato and the Stoics (Burnyeat 1981, 133–9). As you will also see, Aristotle’s theory of knowledge shares some strikingly similar features or notions with epistemologists like Panayot Butchvarov, Carl Ginet, Paul Moser, and Ernest Sosa. So, if such a similarity, along with this present work, does not show Aristotle’s use of ‘epistêmê ’ to mean ‘knowledge,’ then among other things I have terribly misunderstood contemporary epistemology.

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This talk about contemporary epistemology leads us to the second camp that likes to take ‘epistêmê ’ as ‘understanding,’ namely the virtue epistemologists like Linda Zagzebski and Jonathan Kvanvig. They are part of a new philosophical trend that is placing more emphasis on understanding instead of knowledge. Many of their epistemological views are clearly inspired by Aristotle’s virtue ethics, as well as what they take to be the ancient Greek conception of ‘epistêmê.’5 For a work like mine, their work is beneficial in that they are beginning to offer clear accounts of what ‘understanding’ means in a theory of knowledge. For example, Zagzebski states: The important point is that understanding ought to be an important concept for us as well [as it was for Plato and others], it clearly has been neglected, and this neglect cannot be remedied if epistemology persists in making the locus of evaluation individual propositions or states of believing single propositions, as is the case of justification. Understanding is not a state directed toward a single propositional object at all. This is not to deny that there is a sense in which one can be said to understand a proposition p. But the understanding of p is not directed primarily at p itself. One understands p as part of and because of one’s understanding of a system or network of truths, or to follow Kvanvig’s advice in getting away from the atomistic terminology, we could say that one understands p as part of one’s understanding of the pattern of a whole chunk of reality. [emphasis mine] (1996, 49) In his chapter on the nature of understanding, one which begins with the debate concerning the translation of ‘epistêmê,’ Kvanvig’s view is that ‘[u]nderstanding requires the grasping of explanatory and other coherence-making relationships in a large and comprehensive body of information. One can know many unrelated pieces of information, but understanding is achieved only when informational items are pieced together by the subject in question’ (2003, 192). Given these complimentary accounts of understanding, you will see that Aristotle does not use the term ‘epistêmê ’ in this way, and in at least two ways it is directed to a single propositional object, although he would not use those terms. (These are an immediate statement and the conclusion of a proof.) Moreover, as I will show, Aristotle was a strong opponent of coherentism. So given Zagzebski’s and Kvanvig’s conception of the term, Aristotle is concerned with knowledge, not understanding. You will also see by the end of this work that even though he might be the inspiration for virtue epistemologists, Aristotle himself was not one.

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I am interested in not only what Aristotle said, but also how his view works and why he sets it up this way. Therefore, my goal is to provide a plausible account of Aristotle’s theory of knowledge in a way that is clear, interesting, and useful for those working in contemporary epistemology, as well as students and scholars of ancient philosophy. In order to establish sufficiently an interpretation for Aristotle, sometimes some considerable textual exegesis has to take place. Moreover, sometimes an interpretation has interesting consequences for other, non-epistemological aspects of Aristotle’s philosophy. Understanding that this could be potentially uninteresting or deterring for those whose focus is just epistemology, I mark out such material by starting it with the term ‘aside,’ followed with a phrase summarizing the topic covered. I mark the conclusion of that material with ‘end of aside.’ If such material occurs at the end of a chapter, I mark it with ‘coda.’ If it is less crucial for the argument, I place such material in endnotes. This way, readers can skip over it if they so choose. At other times, when such material seems absolutely necessary for the argument, I do not so bracket it, but I do include signposts along the way to keep the reader informed as to where I am going, and why I am going this way. By doing this, I hope the reader stays informed of the direction I am headed. I have tried very hard to reconstruct Aristotle’s theory of knowledge using modern terminology and methods, and in a way that both students of ancient philosophy and of epistemology would find readily recognizable. Even though it might not outstrip my interpretative abilities, Aristotle’s theory of knowledge likely outstrips my epistemological ones. So I realize that there will probably be things which a full-time epistemologist will see that escaped my notice, or connections between Aristotle’s theory and contemporary ones that I missed. I ask these readers to note and to fill them in as they go along, and should they ever have the chance, to let me know what these things are. I also ask them to forgive my shortcomings! I hope both kinds of readers find a work here that is not only interesting, but also helps them come up with new ideas or approaches to their own endeavors. Section I covers what I call ‘the metaphysics’ of knowledge. This material forms the backbone and structural support of Aristotle’s epistemology. Without it, I found any attempt to understand the various parts of the theory to be wild conjecture. I think the failure to get this foundational structure straight is the cause of so much divergence among commentators. Chapter 1 begins with Aristotle’s notion of a hexis. This misunderstood and barely analyzed piece of Aristotle’s philosophy is actually the tailbone for everything that follows. Not only is this notion the central axis for his theory of knowledge, but also for his ethics. If my interpretation of hexis is correct, then much interpretation of Aristotle’s ethics is seriously

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jeopardized. Chapter 2 extends into Aristotle’s theory of relations, and 3 brings 1 and 2 together to explain how knowledge is a hexis. So chapters 1 through 3 form the backbone of this epistemological structure. Chapter 4 moves into the philosophy of mind, and affixes the skull onto this backbone. Here I set out in detail Aristotle’s taxonomy of the human psyche, and the position of knowledge and belief within it. The almost completely neglected term ‘hupolêpsis’ receives a total reinterpretation, and we also get glimpses of the function of nous. Chapter 5 moves back into more metaphysical anatomy, and affixes the hips to our emerging creature. Here, the key epistemological terms ‘logos’ and ‘aïdon’ get repositioned, and we begin talking about proofs. Chapter 6 makes the transition into solid epistemology with a treatment of ignorance, primary knowledge, and theory. Section II puts the arms, legs, tail, and teeth onto our creature. Chapters 7 through 13 examine in detail Aristotle’s necessary and sufficient conditions for knowledge. Chapter 7 concerns causes and what I call the ‘starting points’ (arkhai) for knowledge. Chapter 8 concerns the requirements of truth and relevance. So for something to be derivative knowledge for Aristotle, the statement at issue cannot just come from any foundational, primary statement by means of a logical procedure, it has to so come from an appropriate foundation. Chapter 9 examines in detail Aristotle’s notion of necessity in the context of his epistemology, and the connection this necessity has with his four causes theory. Necessity can be either axiomatic or compositional. Chapter 9 also examines Aristotle’s conditions for something to be a universal, and this conception is one that is more detailed than, and different from, the stereotypical view. This chapter also includes a new interpretation of his notorious notion ‘for the most part,’ epi polu. Chapter 10 revisits Aristotle’s four causes theory, and discusses some important features it has that seem to have gone unnoticed before. Chapter 11 does the same for the ‘for the most part’ notion discussed in chapter 9. Chapter 12 moves to the requirements involving ‘recognition’ (gnôsis and variants). Recognition itself involves ‘seeing’ in a non-ocular sense (eidenai) and discernment (sunesis). Matters concerning self-evidence also come into play here. Chapter 13 is an analysis of Aristotle’s sole strong internalist requirement, confidence (pistis), which is involved not only with knowledge, but other kinds of discursive thinking as well. Section III then addresses this question about our reconstructed creature: ‘given Aristotle’s theory of knowledge, is knowledge possible?’ This entire section provides a detailed, ‘unpacking’ analysis of Posterior Analytics I.19–23. (I encourage those readers who know German and are interested

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in these passages to compare my work in this section with Wolfgang Detel’s excellent, but in many instances competing, commentary.) I found these texts to be the most difficult and intractable in the entire Aristotelian corpus, and figuring out where these pieces belonged in the skeleton of our creature was enormously challenging! Chapter 14 examines in detail the first known appearance of the famous regress problem on this planet. Chapter 15 nails down all the important terminology Aristotle uses to resolve the problem. Chapters 16 and 17 examine Aristotle’s reformulation of the regress into terms which he finds more tractable. Chapter 18 is a substantive analysis of one half of his solution to the regress, which he calls the ‘universal’ argument. It involves a lot of material from the philosophy of language, in particular Aristotle’s categories of being. Chapter 19 is a substantive analysis of the other half, which he calls the ‘analytical’ argument. It involves a lot of metaphysics, particularly about essences and genera. It also includes a new interpretation of ‘kath’hauto.’ Chapter 20 recaps this kath’hauto material and shows how it resolves all the interpretative problems commentators have raised about it over the years. Chapter 21 summarizes Aristotle’s theory of knowledge in a modern format. I feel Aristotle’s work deserves serious consideration by everyone – not the kind of consideration akin to the curiosity shown towards the skeleton of a now extinct ferocious beast, only later to be used in fiction or forgotten once we leave the museum, but the kind of consideration that is shown towards an ancestor from which we, and much of our work, descends, and whose genetic material is coursing through the veins of philosophy today.

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What is a Hexis?

Aristotle’s metaphysical concept hexis has not received much consideration. Due to this lack, and the complete confusion a misunderstanding of this concept results in, I pause for a moment and focus on some purely translational issues first. Aside: Translating the term ‘hexis.’ The orthodox interpretation takes ‘hexis’ to mean simply ‘state,’ ‘disposition,’ or even ‘habit.’1 I conjecture that Alexander of Aphrodisias is the original source of taking ‘hexis’ just to mean ‘a mental or physical state or disposition.’ Alexander explicates the concept in terms of virtues and vices, like health, justice, and skills -– all apparently dispositions, physical or mental states (In Meta. 417,36–418,12). It is questionable though whether he thought these were the only type of hexeis (the plural of ‘hexis’), or whether his examples were just one-sided. D.S. Hutchinson, apparently the only modern commentator in English who has provided any analysis of this concept, takes ‘hexis’ as ‘disposition’ or ‘state’ in a restricted sense, even though Aristotle seems to use the concept in ways that do not fit modern philosophical or ordinary usage: Hutchinson argues initially that hexeis should not be understood as dispositions, but later that they should be understood as dispositional traits, which are dispositions (Hutchinson 1986, 8–38, 108ff.; esp. 10, 35–8). Translating ‘hexis’ as ‘habit’ is not worth comment, even though the Latin ‘habitus’ corresponds in form and origin to ‘hexis.’ The orthodox treatment of ‘hexis’ as ‘disposition’ is a serious mistake. First and foremost, it prohibits one from distinguishing between occurrent and dispositional hexeis, like belief or knowledge. Aristotle is very careful to make this distinction, although he uses different terminology: ‘actual’ for ‘occurrent,’ and ‘potential’ for ‘dispositional.’ For example, I am disposed to believe a great many things about politics, my environment, my family and friends, and so on; I am occurrently believing stuff about

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Aristotle and certain concepts of his. All are hexeis. It makes no sense to speak of a dispositional or occurrent disposition. Second, many of Aristotle’s examples of a hexis are not dispositions at all. One might consider them as states, but only in the sense of states of affairs, so taking ‘hexis’ as meaning ‘state’ can be misleading. For example, the fact that I am wearing jeans and a t-shirt, that I have allergies, that my glass has water in it, that my house has a yard and garden, that my fence keeps my dogs from running away are all hexeis (Cat. 15.15b17–27, Meta. V.23.1023a8–25). These facts are not dispositions in any plausible sense of the term. Although they are various states of affairs, one might call them ‘states,’ but it is a somewhat peculiar use. The phrase ‘the fact that I am wearing jeans and a t-shirt is a state’ is odd; ‘the state of wearing jeans and a t-shirt’ is a little less so. Third, the defenders of the ‘disposition’ interpretation will retort that Aristotle derived the word ‘hexis’ from the intransitive use of ‘to have’ (‘ekhein’), followed by an adverb in ancient Greek, which translates in English as ‘to be x.’ Accordingly, they say, a hexis is just the way something is, which is a disposition. There is a significant problem with this. Since knowledge is a hexis, the disposition interpretation commits Aristotle to a kind of adverbial theory of knowledge, which is much more implausible than the adverbial theory of perception: ‘I have knowledge’ becomes, under this interpretation, ‘I am cognized to knowingly’ or something along those lines. I know, for example, given certain natural laws and as a human being, that my DNA follows a certain basic sequence. The only way I can understand this fact in the orthodox interpretation’s terms is to take it as meaning that I am somehow cognized to ‘my DNA follows a certain basic sequence’-ly. This is nonsense, even though, like its perceptual counterpart in regard to sense objects, it frees one from making any sort of ontological commitments to some object of knowledge. Aristotle does not fear any such commitments. Moreover, in interpretation, one should be as charitable as the evidence allows, and assigning a thinker like Aristotle such a view is not. Aristotle clearly takes knowledge to be the product of a relation that has two members, the thinker and the knowable object. Using the example above, the hexis is the relation between I and my DNA follows a certain basic sequence. This is much less problematic than what the orthodox interpretation is stuck with, and almost all modern epistemologists will have no problem with Aristotle’s basic metaphysical set-up. Now I will admit that I need to be disposed in a certain way in order to know (in Aristotle’s terms, that I need a capacity or potential in order to know): at minimum, I need a body with a certain degree of cognitive ability, and some degree of understanding a

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language. However, this is not what Aristotle means when he says that knowledge is a hexis. These considerations give enough reason to see that a hexis is not a disposition. One could say in a peculiar way it is a kind of state, and the term ‘attitude’ fits well in psychological contexts. Due to Aristotle’s unique use – which we will now see – I will simply use the transliteration and corresponding variants. I leave it to others to correct the decades of misunderstanding of Aristotle’s ethics that has occurred based on the ‘disposition’ or ‘habit’ interpretation. End of aside. Aristotle classifies hexis into two different kinds. The first kind corresponds to an active, positive sense of the verb ‘to have,’ where the haver controls in a broad sense what is had according to their nature (kata phusin) or some impulse (kata hormên) (Meta. V.20.1022b4–10, 23.1023a8–11). This kind of hexis is an actualization of an appropriate relation between two members, with the appropriateness being determined by (i) some subject that has a certain nature or impulse, and (ii) a possessible and usable object for fulfilling this nature or impulse. Aristotle often uses the example of wearing clothes to show what he means.2 The wearer, by the controlling activity of choosing, putting on, arranging and then wearing that clothing for a period of time, actualizes or fulfills some nature or impulse. The relationship between the wearer and the worn is the hexis. When that person gets undressed, this actualization of the wearer’s impulse or nature – and thereby the hexis – disappears. This kind of hexis includes instances where the reverse occurs, and the haver somehow controls the had in a way that prevents the actualization of its (the had’s) nature or impulses (Meta. V.23.1023a17–23). This is an ‘actualized negation’ of the nature or impulses of the had, instead of a fulfillment of the haver’s. For example, my fence negates my dogs’ nature or impulse to run wild. If my dogs escape, the hexis disappears. The appropriate relation for this kind of hexis is determined by (i’) some object that has a certain nature or impulse, and (ii’) a subject preventively controls the actualization of that nature or impulse. The second, and much more complicated, kind of hexis is the one involved in knowledge. A proper understanding of it requires a brief but substantial foray into some interconnected metaphysical territory. As Aristotle was not adverse to marching back and forth between epistemology and metaphysics, I hope the reader will, in his honor, tolerate it. The booty, though valuable on its own, will pay some significant epistemological dividends down the road. He states:

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...In another way, it is said that a hexis is a constitution by virtue of which the thing constituted is constituted either well or poorly, and either kath’hauto or in regard to something else, as health is a kind of hexis, for such a thing is a constitution. Moreover, it is said that a hexis will be a section of such a constitution; on account of this, the virtue of the parts is a kind of hexis. (Meta. V.20.1022b10–14) The crucial concept here is ‘constitution’ (diathesis).3 ‘A constitution,’ according to Aristotle, ‘is an order (taxis) of the thing which has parts, either in terms [1] of place, [2] of potential or [3] of form...’ [emphasis mine] (Meta. V.19.1022b1-2). In the Categories, Aristotle says that hexeis and constitutions are one form (eidos) of qualification (Cat. 8.8b26–27). Both are also relations (Cat. 7.6b2–3). (Notably, the categories relation and quality are not mutually exclusive: ‘Moreover if the same thing happens to be a quality and a relation, it is not absurd to include it in both genera’ [Cat. 8.11a36–37].) However, although all hexeis are constitutions, not all constitutions are necessarily hexeis: ‘Those who have hexeis are also somehow constituted by virtue of these things; those who are constituted do not in all cases have a hexis also’ (Cat. 8.9a10–13). This asymmetry is due to differences in durability: A hexis is ‘more stable and longer in duration,’ or ‘longer in duration and more difficult to change’ than a constitution (Cat. 8.8b27–28; 9a5, 9–10). Constitutions on the other hand are ‘easily changed’ (ibid., 8b35, 9a9). In these passages Aristotle reveals a broader and a narrower use of the term ‘constitution’: The order of the parts of a thing is the constitution broadly speaking of that thing. If this order of parts is stable, durable and resistant to change, it is also a hexis. If this order is unstable, easily changed and more temporary, it is a constitution in the narrower sense, and not a hexis. Aristotle says that a constitution in this narrow sense can become a hexis if given enough time and the right conditions. One can understand the conditions of stability, durability, and resistance to change as necessary conditions for reliability, and that only hexeis are reliable. Knowledge and virtue are each a hexis, and not a constitution, for reasons of durability: Knowledge seems to be among the things which are steadfast and unchangeable – even if one acquires some knowledge partially – if presumably no great change occurs by illness or some other such thing. Similarly with virtue also, as justice, self-control and each of these sorts of things do not seem to be easily changeable or transitional. Constitutions however are called what is easily changeable, i.e., are

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things which transition quickly, like hotness and coldness and disease and health and so many other such things: A human is constituted in some way according to these, and transitions quickly from hot becoming cold and from being healthy into being sick. Similarly too in the other cases, unless one of these same things would happen to have become natural, and to be incurable or quite unchangeable, on account of length of time, which one might then perhaps call a hexis. It is clear that people want to call hexeis what are longer in duration and more difficult to change: they do not say that those barely in possession of instances of knowledge have a hexis, but are easily changeable, although they are constituted at least somehow, either better or worse, in respect to knowledge. (Cat. 8.8b29–9a8) Knowledge is a hexis because upon its acquisition, someone is constituted in some manner and this constitution is resistant to change. Someone does not easily transition back and forth between knowledge and ignorance, or between self-control and wantonness. Thus hexeis are that ‘by virtue of which we are good or bad in regard to modifications (pathê), e.g., in regard to anger, if having been angered we become violent or unrestrained, we are bad, if we are moderate, good...’ [emphasis mine] (EN II.5.1105b25–28; cf. II.3.1104b19–28, Phys. VII.3.246a10ff.).4 This general immutability also occurs even if one has acquired only partial knowledge or virtue. If knowledge or virtue were merely constitutions – constitutions in the narrow sense – then someone could make the transition back and forth between knowledge and ignorance with the same amount of ease as the body can move from being hot to being cold, or from being healthy to being sick.5 Since this kind of hexis is a kind of constitution, one can apply Aristotle’s account of constitution to it. Such a hexis is the order of the parts of some thing in terms of [1] place, [2] potential or [3] form, out of which that thing is constituted, and by virtue of which that thing’s constitution is good or bad. By being a hexis, this order of parts is durable and resists change. A hexis of this kind is applicable not only to the whole of some thing, and whether the entirety of the parts of that whole is constituted well or poorly, but also to a section of that thing, and whether the parts of that section are constituted well or poorly. Whenever Aristotle refers to a hexis as a potential (dunamis), he means this second kind of hexis.6 The first kind of hexis, recall, is an actualization. ‘[P]otentials are said to be those hexeis by virtue of which things are generally impassive, fixed or not easily changed over to something worse’ (Meta. V.12.1019a26–28, cf. IX.1.1046a13–15). Since it is a potential, a hexis of this kind is either an active starting point (arkhê) of transition or

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change either to do something to another or to itself (as Aristotle puts it, ‘in something else or in that thing itself but qua something else’), or a passive starting point to undergo something by another or by itself (‘by something else or by that thing itself but qua something else’). The doing or undergoing can be achieved either well or poorly (Meta. IX.1.1046a10–11, 16–19; V.12.1019a19–20). Just as the first kind of hexis corresponds to a certain use of the verb ‘to have,’ so does this second kind, and just as there are two variations for the first, so there are for the second. These variations involve a part-whole relation. Aristotle’s use of health as an example corresponds to ‘to have’ in a sort of static, internal sense, where ‘in what something belongs as a recipient (dektikos); e.g. the bronze has the form of the statue and the body the illness’ (Meta V.23.1023a11–13). The mirror image corresponds to the verb in a static, but ‘external’ sense, where ‘the thing which contains (to periekhon) the things which are contained (ta periekhomena): in a container, it is said that that thing is had by this container, as we say the vessel has the water and the city people and the ship sailors, so also the whole has its parts’ (ibid., 1023a13–17). The relationship between a donor and a recipient, or a container and what is contained, is a hexis of this second kind. The haver-had relationship characterized with the first kind of hexis seems applicable to both the subject and the object of this second kind. For example, in the case of a bronze having a certain form, the bronze is not somehow controlling the form, or vice versa, yet has a form. In the case of a container (for example my glass, which has water in it), one might say that the nature of water is to flow, and the vessel preventively controls this flowing from occurring. Likewise, sailors have their ship under control. However, the difference with these cases is that both the haver and the had are an ensemble, are used together as a unity by someone or something extraneous to or outside them in order to fulfill some nature or impulse that person or thing has. Only then does a hexis of the first kind come into being. The haver or the had involved in the second kind of hexis are themselves only complete when the other is present: Sailors are truly sailors only with a ship. Conversely, a ship is useless without sailors. Potable water is available for drinking only when it is in a vessel of some kind; a drinking vessel achieves its function only when it holds some drinkable liquid. In turn, a ship and its sailors together are under the leadership of a captain, or the glass filled with water is under my control. Assuming we know what we are doing, we control them in an active, positive sort of way. If the captain is incompetent, or control of the ship is taken over by a storm, then the ship and its crew are controlled in an active, but negative, sort of way.

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If I have terrible motor control, then my glass of water is going to be spilled, not drunk. What is the difference between the container-contained, and what I will call for lack of a better term, the donor-recipient, relationships? The answer does not lie in Aristotle’s accounts of part and whole, because both relationships involve parts and wholes. He says that a whole has its parts, or that parts are in a whole, in the same way a ship has its sailors or a vessel its liquid (Meta. V.23.1023a16–17). However, in his account of part, the angularity (the form) and the bronze (the matter) of a bronze cube are its parts, and together form a whole. Moreover, he states that either the form, or the thing which has the form, are wholes. Thus, molten bronze, or a lump of it, by itself is not a whole, but the form by itself is: In one sense, a part is ‘into what the form, or the thing which has the form (like the bronze sphere or the bronze cube; both the bronze is a part – this is the matter the form is in – and the angularity is a part), is divided, or out of what the whole is composed’ (Meta. V.25.1023b19–22; cf. V.2.1013b17–22). However, one difference between the two relationships is whether there is some sort of change occurrent in the haver when it comes to hold what is had: When the bronze comes to have a form, it changes; when a ship for example comes to have its crew, it does not change.7 Aristotle also holds that each use of ‘to have’ in his senses can be appropriately reformulated into an ‘in something’ form (Meta. V.23.1023a23–25). So, with the donorrecipient relationship, the form is in the matter, or the matter has the form, and the form changes the shape, structure or nature of the matter. With the container-contained relationship, the matter is in the form, or the form has the matter. The whole is either the form, or the form-in-matter complex. No change in either occurs here. One must take the terms ‘matter’ and ‘form’ in a broader sense, so that ‘form’ also includes things like a ship as well as the shape of a cube, and ‘matter’ things like sailors as well as bronze.8 Accordingly then, the hexis that is the result of a donor-recipient relationship involves some degree of change, and a form-in-matter relation. The had is in the haver in the sense that the shape, structure or nature of the haver is changed upon receiving the had, and remains in this changed state until the haver-had relationship itself is changed. No control of one by the other is involved. For example, the bronze has the form of a cube, or the human being has an illness, and these hexeis will remain until something changes this relationship, say by melting the bronze or curing the patient.9 The hexis that is the result of a container-contained relation involves a matter-in-form relationship, and no degree of change. When a glass has

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water in it or a ship has sailors, the object is in the subject, and one is not controlling the other. (In the former case, I am doing the controlling by moving the glass around, drinking from it, and so on. In the latter case, the captain is controlling the ship, not the sailors.) The shape, structure or nature of the haver here is not changed when the had is in it, despite the fact that the end for which that container exists is actualized only when it has what it is supposed to contain. Each is full or empty, occupied or unoccupied, accordingly.10 Aside: Matter and individuals. The relationships at issue support the view that Aristotle made a distinction between proximate and ultimate matter. In the donor-recipient relation, the matter involved is ultimate, like bronze. In the container-contained relation, the matter involved is proximate, like the bodily organs, various kinds of sailors or citizens, and not the stuff out of which they are made. Furthermore, whenever a whole is a whole qua container, this whole has the potential of having certain kinds of parts. These parts are in this whole. The shape, structure or nature of the whole is not changed by the presence or absence of the parts. For example, assuming an individual is an ousia, a reality, Aristotle consistently states that the parts of someone’s body, like a head or a hand, are some of the matter which that individual whole contains: ‘...Plato did not state poorly that forms are what is by nature (if indeed there are forms), but not of things like fire, flesh, head: all these are matter, the last one of reality most of all’ (Meta. XII.3.1070a18–20).11 Assuming Socrates is a reality and a whole qua a container, Socrates contains all of the parts of his body, and these parts are the entirety of the matter that comprises him. Socrates is a full or complete whole. In the case of any natural body then, if the anatomical parts of a body are to that body as parts to a whole, and if a natural body is a reality, then the loss of a member of, or perhaps even all of the parts of, that body does not entail a change in the shape, structure or nature of the whole. The whole would be empty in extreme cases, or in other words, would contain nothing and is just form without qualification.12 When the whole lacks a certain part at a certain time, it is deformed (kolobos).13 Regardless, the shape, structure or nature of the whole (i.e., the form) is such that it is not changed by any change in its parts (i.e., matter). End of aside. Now that we have solved the problem concerning the difference between the donor-recipient, and container-contained, relationships, we can take the next important step. Since our focus is epistemology, knowledge involves this second kind of hexis, and since such a hexis is a constitution

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that satisfies certain criteria (durability, etc.), one can combine their respective accounts. By doing so, one discovers that this kind of hexis comes in six different forms: [1] In respect of place (i) kath’hauto14 (ii) in regard to something else (pros allo); [2] In respect of potential (iii) kath’hauto (iv) in regard to something else; [3] In respect of form (v) kath’hauto (vi) in regard to something else. The problem now is to figure out what the difference is between a kath’hauto hexis and one ‘in regard to something else.’ (I hope the reader has seen by now that Aristotle’s terminology is not felicitous, and that he has a proclivity to making distinctions.) So, our foray into Aristotle’s metaphysics needs to press on a little further into the realm of relations, especially the part-whole one, the potentially-actuality distinction and some discussion about universals, before we can return to more epistemological territory. One will hopefully begin to see how tightly interconnected the different parts of Aristotle’s philosophy are. All six variations above involve the part-whole relation. Aristotle says: A whole is said of what there is no part absent – parts out of which a whole is said to be naturally, and that which contains the things which are contained, such that these are some one thing. This works in two ways: either as each thing being one, or as the one being composed out of these things. (Meta. V.26.1023b26–29)15 Aristotle also adds that a natural thing is more of a whole than a manufactured thing. According to this passage, parts, and the whole to which they belong, can be related in two different ways. First, the array of parts, or each part itself, is one thing; the whole, whose parts they are, is another thing. For example, a human, a horse, and a divine being are each one thing, but all of these are parts of one universal – living thing – that contains them. This universal is one thing different from these parts, taken either individually or as a group.16 In this case, due to their nature as a part, these parts are potentially prior to the whole in the same way as matter is potentially prior to reality. In terms of fulfillment

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(entelekheia17) though, the whole by its nature is actually prior to its parts. Therefore, it is possible for this whole to exist without its parts in its formation. However, since the parts are naturally potentially prior to the whole, it is possible for these parts to exist without the whole when it is in dissolution (Meta. V.11.1019a5–14).18 Second, the parts themselves, taken together, comprise one whole thing: The array of parts, which is ‘both continuous and limited,’ is some one thing – a whole – and the parts themselves are in this one thing actually only in a few cases. In most cases, the parts are in this one thing just potentially (Meta. V.26.1023b29–36). It is important to note here that the parts here form an array or have a certain structure, and it is this array or structure with the parts that form the whole. It is not just a group of parts that form a whole, but a group of parts that fits together in a certain way that is complete to an adequate degree. An individual human being for example is a whole comprised out of interconnected organs, tissues, and the like, which are its parts. The (whole) human being is simply the sum of its parts arranged according to a certain structure. How does potentiality and actuality work in this kind of part-whole relationship? The human being, for example, is in actuality prior to its parts because the whole needs to exist for any of the parts to exist, and in fact does come to be prior to it having all of its parts: an infant is a whole even though it does not have any of its teeth, or even some sections of its brain. In turn, these parts are in that whole potentially in two ways: first, the fulfillment of the thing (here, a human being) means that even though these parts are not present, they shall be present assuming nothing interferes with the course of nature; second, they do not functionally come to be apart from, or independently of, the whole. Regardless, the array of parts make up the whole, and the whole would not exist without the arrayed parts, so these parts are potentially prior to the whole they comprise. This potential priority means then that, upon the dissolution or disassembly somehow of the whole, it is possible for the parts to exist actually on their own. So the heart, liver, and other organs (and more grisly, the head, arms and so forth) can exist apart from the whole they used to comprise, say upon the death of that human, and whose organs are thereupon donated. The order of priority and posteriority is changed when the parts are actually in the whole. Take for an example the Delian League that came to be after the Persian Wars, which was the union of Greek city-states formed under the stewardship of Athens. The Delian League is a whole, and is simply the sum of its parts, like the individual human being in the previous example. Its parts are its member city-states, as well as any bureaucracy created to help run it. In contrast to the case of the human being, the parts

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– Athens, Delos, and so on – are in actuality prior to the whole, even though they provide the matter for the League. The League in turn is a form, one of regional organization and co-ordination. The member citystates also can be treated as potentially prior, insofar as any individual member was potentially a member of the League before it joined. So in contrast to the human being, the whole is not naturally prior to its parts, and the whole could not exist without its parts in its formation. Furthermore, during the existence of the League, its parts were something actual – namely viable city-states or island communities – while being in this whole, the League. Like the human being though, it is possible for the parts here to exist actually upon the dissolution of the whole, that is, for the city-states to exist apart from the League. In conclusion, when parts are actually in a whole, and the whole is simply taken as the sum of its parts, the parts are actually (and not just potentially) prior to the whole in the natural or manufactured order of the thing at issue. These parts, since they are actual, are not just simply matter – not simply organs, tissues, and the like – but matter and form. Aside: Interpreting the part/whole distinction. This distinction between taking the whole and its parts as two different things, and taking the parts as the whole, seems to have gone unnoticed before. Perhaps this is because commentators have interpreted Aristotle as distinguishing a whole qua universal and whole qua continuous thing. Alexander interprets this passage as stating that each part (here, each thing or individual) is one thing in that all are instances of one thing (here, a universal). Using the same example I do above, a human, horse, and divinity are all one thing, namely living thing, because living thing is the universal predicated of all of them (In Meta. 425,12–25). In other words, by analogy using set terminology, each member of a set is one thing together in that they all are members of one set. This either does not make any sense, or seems to be an instance of the second way, where the whole is nothing more than the parts comprising it. Alexander seems aware of this, so in order to have a distinction and a viable interpretation, he classifies the first way as being about universals, and the second about continuous but discrete objects (In Meta. 425,25–426,1). W.D. Ross follows Alexander on this point (1997, I.340–341). I think an underlying motivation for Alexander’s interpretation is that he does not want to say anything that might sound like realism about universals, something my interpretation does, but does not necessarily entail. End of aside. From this part/whole material, we can now determine what the difference is between kath’hauto and ‘in regard to something else.’

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A hexis that stands in respect of something kath’hauto is one where the array or order of parts itself comprise one thing, and is treated as being the whole. The order of parts itself is the hexis; the hexis exists only as the order of parts. These will be potential starting points for making or undergoing some kind of transition or change by means of itself alone. The hexis which stands in respect of some one thing in regard to something else is one where the parts are one thing (either each individually or as a single group) and the whole is another one thing. These parts are typically in the whole potentially, but sometimes actually. These will be potential starting points for making or undergoing some kind of transition or change to or by something else. The array or order of the parts on one side, and the whole on the other, form the hexis, typically in potential, but sometimes in actuality. Knowledge involves hexical variations (iv–vi) above. Before we can completely return the realms of the epistemological, there is one other metaphysical region that needs to be briefly explored, and it is that of relation. For those who might be impatient, Aristotle’s account of relation has some very significant exploitable resources, and will lead us back into our home territory, where we can fully understand what an epistemic hexis is.

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Relations, Epistemic and Otherwise

When one has something, like knowledge, or when something is of or about something else, like knowledge of my genetic makeup or about Aristotle himself, the things involved bear some relation to each other. Accordingly, hexeis (including constitutions and also what Aristotle calls ‘deprivations’) comprise a form of the ontological genus relation (pros ti).1 Included in this form are position, perception, knowledge, virtue and vice (Cat. 7.6b2–3, 15–16; 8.8b26–27).2 This form of relation, which I call hexical, is one of three specified by Aristotle, the other two being what I call proportional and dynamic (Meta. V.15.1020b26ff.). All three forms of relations share the same basic characteristics. ‘It is said that relations then are those things that are of other things, or are in regard to some other thing in any manner whatsoever,’ [emphasis mine] (Cat. 7.6b6–8).3 According to Aristotle then, there are two independently sufficient conditions for some thing x to be a member of a relation, or in other words, for two or more things x and y together to comprise a relation: (R1) x is of y (hosa auta haper estin heterôn); (R2) x exists in any way in some regard to y (hopôsoun allôs pros heterôn). In the case of (R1), when one term properly takes another term that is in the genitive case, this is indicative of a relation between two things in the world. In the case of (R2), when one term properly refers to another term by means of certain kinds of grammatical devices, this also is indicative of a relation between two such things in the world. What these two criteria indicate is that each member x in a relation must have, and is explicitly or implicitly spoken of in reference to, a counterpart y (antistrephonton). This requisite makes what is relative contrary to what is kath’hauto (Cat. 6.5b15ff.).4 With (R1) or (R2), if someone says that something is a relation

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or a member of a relation, and yet is unable to state the counterparts or counterpart involved, then either one probably has not considered the relation or its counterparts properly, or one may need to invent names for the counterparts (Cat. 7.6b36–7a22). This notion of a counterpart (and not David Lewis’, although one could take them as related) is crucial for, and crucial for understanding, Aristotle’s theory of knowledge. Hexical relations are the most important for our purposes. Aristotle distinguishes hexical relations from the others as follows: Proportional or dynamic relations are relations due to the fact that there is some thing in the world (prâgma), which is represented linguistically by a term in the nominative case, that involves some other thing in the world, which is in turn represented linguistically by some appropriate grammatical marker. With these two kinds of relation, the primary counterpart directly implies the presence of its opposing secondary counterpart: they are existentially symmetrical. Due to this symmetry, the linguistic representations of these two counterparts can be reversed, with the one that was formerly in the nominative being indicated by some appropriate grammatical marker, and the latter taking a nominative form. (This ability is more easily apparent in an inflected language like Greek, than in an uninflected one like English.) For example, a mother involves someone of whom she is the mother, some child implies a mother of whom she or he is the child. Something small involves something it is smaller than (namely, something large), and what is large in turn implies something it is bigger than (namely, something small). Since each pair of counterparts in a relation is relative by virtue of themselves, by virtue of their very nature and what they are, these things in the world are relative kath’hauto (Meta. X.6.1056b34). Although Aristotle holds that ‘kath’hauto’ is contrary to ‘relative,’ this does not entail that things cannot be relative kath’hauto, as seen in this passage. The difference between relative kath’hauto and relative relatively will play a very important role later.5 Hexical relations in contrast are relations due to the fact that there is some one thing in the world, which is represented linguistically by a term in the nominative case, that involves some other thing in the world, which is appropriately represented linguistically by some grammatical marker – however, the latter does not necessarily involve the former. In Aristotle’s terms, one counterpart in a hexical relation exists ‘in the respect of some other thing being said in relation to it’ (Meta X.6.1056b36; cf. V.15.1021a28ff.). The presence of one counterpart in a hexical relation does not imply the presence of its opposing counterpart, unlike the other two kinds. It is a counterpart not by virtue of its very nature, but by virtue of some other thing being in relation to, being said of, it. Thus, hexical

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relations are asymmetrical (Meta. V.15.1021a26–29).6 Consequentially, counterparts in a hexical relation are relative relatively.7 This symmetry or asymmetry of relational counterparts is connected to the modality of the relation, that is, whether a relation between two counterparts is necessary, possible or contingent. Aristotle often uses temporal terms to express modalities, and so counterparts in relations are either called ‘simultaneous’ or not (Cat. 7.7b15ff.; cf. Cat. 13).8 Symmetrical, relative kath’hauto relations are simultaneous by nature: with the occurrence of one counterpart is the occurrence of the other counterpart and vice versa; likewise, the annihilation of one results in the annihilation of the other. Thus, one counterpart in either a proportional or dynamic relation necessarily has its corresponding counterpart.9 The counterparts in hexical, asymmetrical, relatively relative relations are not simultaneous. The primary counterpart is prior to the secondary counterpart, and this priority does not entail that the secondary one will either come into existence or remain thereafter. To use a previous example, a ship exists in a hexical relation with its crew. However, a ship can completely come into being without ever having a crew, say by becoming militarily obsolete by the time it is built, by being torched the moment it is completed, or by there being no one qualified to man it. So in this case, the ship is the primary counterpart, which is prior to the secondary counterpart crew. In contrast, a mother or a father is strictly speaking not a mother or a father until their child is born. The annihilation of the primary counterpart in a hexical relation entails the simultaneous annihilation of any occurrent secondary counterpart, and the impossibility of any secondary counterparts in the future for it, unless the primary counterpart were to return to existence. In the case of the ship, once it ceases to exist, the ship’s crew also ceases to exist, even though all of the sailors might still be alive: they are no longer the crew of that ship. ‘Ship of Theseus’ problems aside, if that ship were reassembled, those sailors would become its crew again. This priority of a primary counterpart in a hexical relation determines the secondary counterpart in more than just temporal terms: Since the primary counterpart can exist without the secondary one, the primary one is not simultaneous with its secondary counterpart. The former is prior to the latter. Take a ship that has come to be. If it were just a matter of time for a secondary counterpart to come into existence for it, any completed ship would at some point come to have a crew. However, this consequent is clearly false. Therefore, it is a matter of possibility, and not a matter of time, that this ship has a crew. By extension, it is a matter of possibility and not of time that a primary counterpart in a hexical relation comes to have a

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secondary counterpart. Indeed, Aristotle states that primary counterparts are prior to their secondary ones by virtue of reality, that is, naturally: ‘things which are possible to be without other things, but those are not possible to be without them’ are things which are prior naturally (Meta. V.11.1019a2–4). The relation between counterparts can now be formalized in the following way, with the modality in both cases being natural, and not merely logical10: For every x and y that are counterparts in a proportional or dynamic relation, necessarily (x if and only if y). For any x that is a primary counterpart in a hexical relation, and any y that is a corresponding secondary counterpart, (i) not necessarily (if x then y), and (ii) necessarily (if y then x). Following Aristotle’s lead, I will now introduce perception into the mix, and Aristotle does make parallels between knowledge and perception. Knowledge is a hexis, and knowledge is of something knowable. Perception too is a hexis, and is of something. Accordingly, the relation between knowledge and its objects, or perception and its objects, is hexical. If someone says they have knowledge or a perception, but cannot specify what it is of, then either they genuinely do not know or perceive (misunderstanding what they are), or they need to create names for it (Cat. 7.6b28–36; see also 7.7a22–b14, 7.8a36–8b15). Now which counterpart is primary, and which is secondary, in knowledge and perception? Aristotle states: We say that both knowledge and perception are the ‘unit measures’ (metron) of things in the world for the same reason – because we recognize (gnôrizomen) something by means of them – when in fact these [knowledge and perception] are measured rather than a measure. For us, it is just as if, while someone else was measuring us by laying a cubit ruler on us a number of times, we recognized at that moment how tall we were. Protagoras asserts that a human being is the unit measure of all things, just as if he were saying the knower or the perceiver – these because they have knowledge and perception respectively, what we assert to be the unit measures of underlying things. While saying nothing really, they appear to say something extraordinary. (Meta. X.1.1053a31–b3)

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Aristotle later says: The one and the many are really opposed numerically as a unit measure to that which is measurable. These are like the relations that are not of the kath’hauto relations. It has been distinguished by us in other places that relations are said in two ways, some as contraries, others as knowledge in relation to that which is knowable, in the respect of some other thing being said in relation to it. ... Plurality is like a genus of number, for number is a plurality measurable by one, and one and number are opposed in some way, not as contraries but just like some relations – these are opposed in this way, as a unit measure and that which is measurable – on account of which not everything that might be one is a number, as if it were something indivisible. While spoken of in a like manner, knowledge in relation to that which is knowable does not reciprocate in a like manner: it would seem that knowledge is the unit measure and that which is knowable the thing which is measured; however, while every instance of knowledge implies there being something knowable, not every thing which is knowable implies an instance of knowledge, because knowledge is in a kind of way measured by the thing which is knowable. (Meta. X.6.1056b32–1057a12) Due to language or our perspective, it seems that knowledge and perception are both primary counterparts – the unit measure, a ruler for measuring things in the world – while the knowable or perceptible – that which is measured by us – are secondary. Using Aristotle’s terminology, this Protagorean perspective takes the thinker as prior to what is knowable. ‘Knowability’ becomes metaphysically dependent upon creatures like us, and if no one has the ability to know anything, then nothing is knowable. This perspective has in fact been the dominant thread running throughout the history of epistemology: The thinker is an active agent who satisfies certain criteria in order to obtain knowledge; what is knowable is a passive thing that is there, standing to have those criteria applied to it. It is up to a thinker as to whether something is knowable, or in other words, it is the responsibility of the thinker to come to know something. The Aristotelian perspective is the reverse: What is knowable is so independently of any such criteria or of any thinking creatures. It is prior to us, and thus our knowledge is metaphysically dependent on knowable things in the world: But not in all cases of relations does the simultaneity by nature seem to be true: For the thing which is knowable would seem to be more prior

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than knowledge – as for the most part we acquire instances of knowledge of pre-existing things in the world; in few or no cases would someone see knowledge coming to be simultaneously with the thing which is knowable. Moreover, when the thing which is knowable is destroyed it destroys knowledge together with it, but knowledge does not destroy together with it the thing which is knowable. Without there being something which is knowable there is no instance of knowledge – for knowledge will no longer be of anything – but nothing prevents that which is knowable from existing without there being knowledge, even the square of the circle for example, if at any rate it is knowable, there is no knowledge of it yet, but it itself is knowable. Moreover, when life is destroyed there will be no knowledge, but it is possible that there will be many things which are knowable. (Cat. 7.7b22–35) For the Aristotelian perspective, it does not matter if no one has the ability to know anything, or indeed if there is anything living. The knowable is still there. Knowledge is what is dependent. Unlike the opposing perspective, when we come to know something, instead of us grasping things according to our will, that something has in a way come and grasped us, just as if we were standing and someone came up to us with a measuring stick and measured us, and by that, we came to recognize how tall, or short, we in fact were. All you need to do in order to know is just put yourself in a position such that the knowable ‘hits’ you. (Matters get complicated once you try to put what hit you into words.) Aristotle does have criteria that one must satisfy in order to know, but it might be a stretch to call these normative: His criteria are a kind of checklist to make sure your thinking corresponds to how the world works, instead of a kind of tablet of commandments that one has to follow in order to earn knowledge as a reward. Perception works in the same way as knowledge, except here Aristotle emphasizes its physicality: Perceptions concern body, are in body, and when something perceptible is destroyed some body is also destroyed. When that perceptible is destroyed it destroys perception together with it, but perception does not destroy the perceptible if it ceases to be, either individually or even if life itself were destroyed, for there will still be things like ‘body, hot, sweet, bitter, and all the other things which are perceptible.’ Moreover, perception comes to be simultaneously with the perceptive – for perception and life come to be simultaneously – but the perceptible at least exists even before perception exists – fire and water and the like, out of which life is composed, exists even before life or perception is in

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general. Therefore, the perceptible would seem to be more prior than perception. (Cat. 7.7b35–8a12)11 To emphasize then: what is knowable or perceptible is prior to knowledge or perception naturally, i.e., by virtue of reality. The annihilation of the things in the world, or of their features that were knowable or perceptible, would bring about the destruction of knowledge and perception, but the reverse is not the case: the destruction of life on earth would bring about the end of knowledge and perception (at least here), but that which was knowable or perceptible would still exist. If things in the world were in no aspect knowable, then knowledge would never exist, regardless to whatever justification, evidence, processes or faculties we possessed. Knowledge and perception are therefore secondary counterparts.12 The hexical relations of perception and of knowledge can now be characterized formally for Aristotle as follows: Perception: For any x which is perceptible, x exists if and only if x is a body. For any y which is a perception of x, (i) necessarily (if y then x), (ii) not necessarily (if x, then y), and (iii) if y, then there exists some z such that z is a living thing and z has y. The possibility here is natural, i.e., by virtue of reality. Knowledge: For any x which is knowable, and for any y which is knowledge of x, (i) necessarily (if y then x), (ii) not necessarily (if x, then y) and (iii) if y, then there exists some z such that z is a living thing, z is a potential knower and z has y. The possibility here is natural, by virtue of reality. Here is a consequence of the Aristotelian, in contrast to the Protagorean, perspective: since the primary counterparts are different, knowledge and perception cannot be about the same things, or about the same feature of one thing. The knowable or perceptible determine the general character of knowledge or perception, even if there are certain conditions to be met in order for either to occur. If those conditions are met, what is known or perceived is limited due to the potential of each organ or apparatus being restricted to certain unique aspects of those things. We are incapable of apprehending whatever features such things in the world might have beyond those aspects, even though these features exist. Such features are indiscoverable.

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Coda. Like commentary on almost all of Aristotle’s philosophy, commentary on his account of relations is contentious. I think future debate on matters such as substitution, extension, and intension can be smoothed out considerably if commentators (1) are careful to use examples that involve counterparts related to each other in Aristotle’s sense; (2) distinguish what kind of relation is involved; and (3) make clear as to whether the counterparts involved are related derivatively, that is, are related because the genus to which a particular belongs is a relation. Take an example from a noteworthy article by Mignucci (1986, 104–105). Assume being a lover is a relative property. Assume that all and only men with dark eyes are lovers. If this identity is extensional, then the property being a man with dark eyes is relational, something which is absurd Mignucci says. It is not absurd if one takes being a man with dark eyes as indicative of a genus and difference, and being a lover a quality of that. Aristotle would allow this property to be relational derivatively and extensionally. It is important to note though, that being a lover is relational in Aristotle’s terms only if it is a secondary counterpart in a hexical relation, with being loveable as the primary counterpart. Someone can be loveable without having a lover, and so lover-loveable is not a dynamic relation like heat-heatable (and it obviously is not proportional as number is not involved). Also in his discussion, Mignucci does not note the difference between hexical and non-hexical relations: Formulation [1] in his article is based on non-hexical relations, but is applied to a hexical one. I grant that [1] is workable for secondary counterparts, but it is not so for primary ones.

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Knowledge as a Hexis, for Us and by Itself

We can now address what Aristotle means when he says that knowledge is a hexis. Knowledge is something we can have. We have it by being constituted somehow: Knowledge is an order or array of parts that is very durable and resistant to change, and it is by virtue of this order of parts that we know well, poorly or not at all. Knowledge is a relation, for it is of something, namely that which is knowable. Corresponding to the relative kath’hauto and relative relatively distinction discussed above, this epistemic hexis can be approached from two directions: from the point of view of living beings that can know (the relative relatively approach), and from the point of view of knowledge by itself, independently of any such being (the relative kath’hauto approach). The former involves a container-contained relation; the latter involves a donorrecipient relation. This differentiation resolves many interpretative difficulties both in regard to knowledge and to other issues.1 The three levels of being, according to levels of potentiality and actuality, that Aristotle uses in the De anima and in Physics VIII.4 facilitate this analysis: the first level is that of a potential potential; the second, an actual (active or fulfilled) potential, or equivalently, a potential actuality (activity or fulfillment); the third, an actual actuality (active fulfillment, fulfilled activity, etc.).2 Knowledge for us is a hexis (vi) in terms of form in regard to something else. From the point of view of a thinker, this being has knowledge as a potential potential in the sense that knowledge is something that can be contained by that cognizer by virtue of what they are, by virtue of being an appropriate container for knowledge: ‘A knower is so, we might say, as a human is a knower because humans are among knowers and the things that have knowledge’ (DA II.5.417a22–24). The whole is the form of a human or other creature that can know. This form is a psyche (psukhê)

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(e.g., DA II.1.412a19–21ff.). Knowledge is a part – i.e., some of the matter or potential of – of this form. Knowledge has yet to have anything knowable applied to it. The transition to this level of knowledge, like perception, begins when that creature is in the process of formation, and no deprivations (like birth defects) connected to the presence of knowledge are occurring (DA II.5.417b16–18). Knowledge for us is a hexis (ii) in terms of place in regard to something else. A creature attains knowledge as an actual or fulfilled potential by ‘being altered by means of learning and transitioning often from the contrary hexis’ (DA II.5.417a31–32). It is by learning, what learning involves, and its quality, that a thinker comes to have knowledge of something (and either excellently or poorly). It is by means of learning that knowable things in the world or their features apply themselves to this thinker, like someone coming up to them repeatedly with a ruler (either skillfully or crudely), and measuring them over and over until that thinker finally comes to recognize their height. For Aristotle, this ultimate recognition occurs by means of instruction through a teacher (who repeatedly presents one with what is knowable until one ultimately ‘gets it’), or by means of an inductive procedure (empeiria), which occurs when the knowable itself does the presenting to one until one ‘gets it.’ Once one does ‘get it,’ the thinker attains this level of knowledge, or in other words, our epistemological container has something in it. This fulfilled potential is a hexis that is in an individual, or in there for some purpose, as something contained in a container, but is not manifested or occurrent, in the same way as an adult male in ancient Greece had in him the potential fulfillment to be a general simply by winning a specific election for that post (DA II.5.417b29–418a1).3 The part or matter in this instance – knowledge – is in this whole, the individual, as such a potential ‘because, being wished,’ she or he ‘is capable of theorizing if something from outside does not prevent it’ (DA II.5.417a26–28). Importantly, knowledge at this level is of something specific, like grammar, mathematics, culture etc., and so is no longer a relation, but a qualification (poiotês): It is said that genera in almost all such cases, but no particulars, are relations: It is said that knowledge, being a genus, ‘is the very thing that is of another’ – knowledge is said of something. Among particulars, not one is said to be ‘the very thing that is of another,’ like grammatical knowledge is not said ‘grammatical of’ something, nor is cultural knowledge said ‘cultural of’ something, but these are also called relations (if at all) by virtue of their genus. For example, it is said that grammatical

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knowledge is knowledge of something, not grammatical of something, and culture is knowledge of something, not culture of something. Therefore the particulars are not of relations. We are said to be of a certain quality by particulars – we also have these, and we are said to be knowers by having some of the particular instances of knowledge – therefore these particulars will also be qualifications, by virtue of which at times we are said to be of a certain quality. These are not relations. (Cat.8.11a22–36)4 Knowledge at this potentially active level remains a hexis, because, Aristotle says, one has this knowledge. By having it, we contain a certain actual quality: we are constituted in a certain way, and this constitution is reliable because it is durable, difficult to change, and we do not easily make the transition from it to ignorance. We have fulfilled a potential for knowledge, and in a fine or crude way. This psycho-physiological constitution is an order of parts, and is excellent or poor due to that order. Knowledge by itself is a hexis (iv) in terms of potential in regard to something else. Knowledge by itself is a hexis in terms of potential in regard to its primary counterpart, the knowable. In the same way as shapeless bronze has the potential to receive certain forms, so knowledge, without being of anything, has the potential to be the recipient of what is knowable (which is the ‘donor’ in this case). In Aristotle’s terms, knowledge has the potential to have knowable things in the world applied to it, but which have not yet been applied. It is a recipient without any donor. Knowledge at this level is a potential potential, like bronze devoid of any form. Since knowledge is a relation, it can be characterized as ‘knowledge of ________.’ In one way, the potentially potential knower – a potential knower who has had no or insufficient learning – could be said to have this kind of knowledge.5 In another way though, purely formal knowledge – or in Aristotle’s terms, ‘knowledge in respect of the universal’, e.g., the syllogistic devoid of content – can also be considered as potential potential knowledge (e.g., AnPr. II.21.67a27ff.).6 Aristotle offers to explain the relation between what is knowable and knowledge by analogy to the relation between one and plurality. (The analogy also applies to the perception-perceptible relation.) The relation of mother to child or triple to third is a kath’hauto relation because, being without qualification that very thing that a mother or a triple is (as Aristotle would put it) includes something in relation to whom or what that mother or triple is. In contrast, the relation between the one and plurality is a relative relation: What the one is does not without qualification include some plurality in relation to which it stands. The one, like what is knowable, does

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not entail the presence of plurality, although the presence of plurality entails there being the one. Hence, the one is prior to plurality. If the one did not exist, then plurality would not exist. In this way, the one goes beyond or transcends plurality, just as what is knowable goes beyond or transcends knowledge. The one is what measures plurality: Plurality is the genus of number; when the one is applied to plurality, a specific number (which in Aristotle’s terms is a form), is obtained, say 6 or 33. The numbers 6 or 33 would not exist without the one. In parallel, the knowable measures knowledge: Knowledge is a genus; when something knowable is applied to it, specific instances of knowledge are obtained (which is a form). This knowledge would not exist otherwise. This is what Aristotle means when he says that knowledge is ‘the unit measures of the underlying things’: According to Aristotle, the genus is the underlying thing of the form, so when one has knowledge, this knowledge is of an underlying thing (the genus), and thus this knowledge itself is generic (Cat. 8.11a24–25). When something knowable is applied to knowledge, as a unit measure to that which is measured, a specific instance of knowledge comes to be, like a specific number, and is thereby not generic anymore. Moreover, just as the one is not contrary to plurality, what is knowable is not contrary to knowledge: knowledge is contrary to ignorance (agnoia, Cat. 7.6b16–17), plurality is contrary to indivisibility. If something is indivisible (adiareton) – if that thing is not a member of the genus plurality – it cannot be a number, it cannot be assigned a quantity or measurement, only because the one cannot measure it. Likewise, if something reveals ignorance – if that thing is not a member of the genus knowledge – then it cannot be a specific instance of knowledge without qualification because the knowable cannot measure or determine it. Knowledge by itself is a hexis (vi) in terms of form in regard to something else. This kind of knowledge is an actual or fulfilled potential. It is the kind of knowledge had by a thinker who is capable of theorizing, but is not utilizing it, say in the case of sleep, illness, intoxication, preoccupation and the like. Importantly, knowledge at this level is not something on its own – it has found a donor. The blank in ‘knowledge of ________’ has been filled in. Knowledge in this case is of something, say grammar, mathematics or culture, but is, or is considered as, something apart from grammar, mathematics or culture. Knowledge is a part qua a genus, underlying thing or matter (perhaps intelligible) for, and is the secondary counterpart of, these forms, which are the primary counterparts. Grammar, mathematics, culture or other forms have been applied to knowledge. However, knowledge, and whatever differences are involved, are in this whole by potential, and, like the bronze in the sculpture, knowledge and those differences

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cannot exist apart from some whole, i.e., some form, except as (iv) the hexis in terms of potential described above. So at this level, the thing that knowledge is of is the form: The form (grammar, mathematics, culture) is a whole, the genus (knowledge) and differences of that form are treated as parts, and each is, or is considered as, one thing. Those subjects are examples of the things in regard to what (pros ha) knowledge is at this second level of being. Knowledge is a relation here only because the genus is a relation, or is a relation only by potential.7 The attainment of this level of knowledge is complete (teleios) once no part of this knowledge is missing (Meta. V.16.1021b12–13). Continuing with the parallel example of the one and plurality, at this level of being, the one has been applied to plurality to obtain a number, say 6, but this number is abstract, i.e., taken apart or separate from things in the world that are six in number. Under this characterization, the form (grammar, mathematics, 6) is the primary metaphysical unit in that it is something actual or active, and its parts (knowledge, plurality) are potential, even though they are just as much one thing as the form. This is why the knowledge in this case is in actuality a quality, but only potentially a relation: at this level it is a relation only because it qua genus is a relation.8 In terms of actuality, the form is prior to its genus and differences, but in terms of potential, the genus and differences are prior to their forms (Meta. V.11.1019a2–4ff.; DA III.7.431a2–4). The parts involved in knowledge by itself can be understood in two ways, corresponding to the proximate/ultimate matter distinction mentioned in an aside above: In one way, grammar has knowledge as a part (namely, as its genus), along with the differences that comprise the logos that reveals what grammar is, in the same way that animal, mammal, and bipedal are a part of the form human. For example, concerning grammar, its genus is knowledge, some of its differences are natural, human, linguistic, SinoTibetan, and so on down. Here, knowledge is like ultimate matter. In the other way though, grammar has vocabulary, idioms, verbal, nominative, and prepositional syntax and the like as parts, in the same way that head, hand and the like are parts of the form human. Here, knowledge is like proximate matter. One’s knowledge of grammar then would be excellent or poor, would exhibit virtue or vice, not due to the order of parts in the former way, but in the latter: Due to what it is, the logos of grammar, revealing what it is in the former sense, is arguably ordered in one way only by necessity, namely as a genus with its differences. However, the logos revealing grammar in the latter way can be ordered or exhibited in any number of ways, some of which are deep and profound, others of which are confusing and shallow. Even though there may be no part missing to

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one’s knowledge here, and is thereby complete, it might be considered as incomplete insofar as one’s knowledge exhibits any kind of vice (Meta. V.16.1021b14–17). Furthermore, as Aristotle says, the section of a hexis is also hexis, and is excellent or poor as well. So for example, the syntactical section of one’s grammatical knowledge could be excellent, but the vocabulary poor.9 These examples of knowledge, combined with Aristotle’s account of the three levels of being, show it is incorrect to hold that only (iii–iv) hexeis in terms of potential are potentials, and the remainder are actualities. Something can be an actuality, and still have or be a potential. Even though health is a hexis in terms of potential kath’hauto, it is nevertheless something actual, namely a general insusceptibility to illness. When someone is ill however, they potentially have the potential to be healthy, though not the actual potential because they are in fact sick. Health is just an actuality (i.e., an actual actuality) when a person has achieved a physical and mental well-being (eudaimonia) that is complete for them. A completely outfitted trireme with crew on the open sea is something productive, yet, so long as it is not involved in combat, it still is, or has, only a potential of some kind, namely, to attack and destroy other ships. If the ship is under construction and the crew in training, then one might say that this ship has or is the potential to attack and destroy other ships twice removed. Only when the trireme is in fact attacking and destroying other ships could one say it is an actuality without qualification. I have now explained Answer 1. As you can see, it required a lot of complicated metaphysics just to explain Aristotle’s take on the simple little statement ‘you have knowledge.’ These metaphysics though provide a foundation for understanding all the other answers, besides being important in their own regard. They also help us, I think, take another look at our ingrained Protagorean epistemological mindset. The subtle distinction between knowledge for us and knowledge by itself reveals some careful thinking on Aristotle’s part too. There is more like this to come with Answer 2.

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Knowledge as a Kind of Linguistically Expressed Thought

Answer 2 takes us out of the realm of pure metaphysics and into that of some philosophy of mind. As in the case of Answer 1, this material provides more of the skeletal framework for Aristotle’s theory of knowledge. I hope the reader does not think that, due to its antiquity, Aristotle’s work has nothing to offer to the philosophy of mind. At minimum, his work is unburdened by more than two thousand years of tradition, prejudices, and assumptions, and so is refreshing as well as interesting. At maximum, perhaps Aristotle on some level is right! This material also establishes the underpinnings of Aristotle’s ethics, so I hope the readers interested in those issues will find this rewarding. Aristotle differentiates the faculties – or in his terms, the parts – of our psychology according to differences in things in the world. All are accordingly differentiated extensionally, not intensionally. Some thing or feature in the world is knowable, not by how it is described or stipulated, but by what it is. Therefore, Aristotle’s theory allows for a single thing or feature, apprehended by a single part of the psyche that together form the hexis, to be described validly in multiple ways. Nature does not build anything superfluous into our minds, so if a certain kind of primary counterpart did not exist, that part of the psyche would not exist. Nature also did not give human beings total situational awareness, so some things in the world, or their features, that do exist do not function as primary counterparts to any part of our psyches. In such cases, we cannot directly apprehend anything at all about them.1 Aristotle’s taxonomy of the human psyche is constructed on the basis of these metaphysics. We can firmly understand in Answer 2 what a hupolêpsis is, and how knowledge is one, within it. Answer 2 is consistent and complimentary with Answer 1, as both concern the hexeis of the psyche. I beg the reader to be patient with my use of the term ‘hupolêpsis’

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for now, as I find it important to take you through the taxonomy first before translating it. Prior to his presentation of this taxonomy, Aristotle focused on the behavioral (êthikos) part of the psyche. The one that concerns us now involves pursuits about which there is knowledge (EN VI.1.1138b20–21, 26–27, 32–34, 35–1139a3). (Notably, behavioral virtues too are hexeis [e.g. EN VI.2.1139a22–23].) This break between the behavioral and epistemic parts of the psyche means that there is some disconnect between action and knowledge: the psychological bases of behavior are separate or apart from (khôris) those of knowledge. Knowledge for Aristotle has no motivational force, and ethics and action have no epistemological force. Aristotle constructs this taxonomy by means of the method of division (diairesis) (e.g., EN VI.1.1138b35ff.). Divisions are made according to differences within genera, at times treating forms (eidê; sing. eidos) of a genus as subgenera with their own forms. Before unraveling this taxonomy, I want to emphasize an important characteristic of hexical relations, one which is crucial for seeing why knowledge for Aristotle is not belief with certain strings attached. Hexical relations are between primary and secondary counterparts. Primary counterparts are naturally prior to their secondary ones, which means that the latter are metaphysically dependent on the former. Due to this priority, the existence or presence of different primary counterparts entails correspondingly different secondary counterparts, for the starting point of each secondary one is different (e.g. Meta. V.1.1013a7–10). For example, let A and B be different primary counterparts – either as two different features of one thing in the world, or as two different things. Let a and b be their corresponding secondary counterparts. Thus A is prior to a, and B prior to b. Now suppose b is in the same hexical relation with A as a is with A. If b is in the same hexical relation with A as a is with A, then by definition of primary counterpart, A is the starting point (arkhê) for b. If A is the starting point for b, then A is the same as B. However, it was assumed that A is different from B. Therefore, A is not the starting point for b, and b is not in the same hexical relation with A as a is with A. Again, this difference can stand as either a difference between different things in the world or a difference between different features of one such thing. First, it does not follow from the argument above that if primary counterpart A is not the same as B, then A and B are two different things in the world; A and B can be two different features of one thing in the world, which happens to have both A and B. Second, it also does not follow that A has (or can have) only one individual secondary counterpart a; A is (or can be) the starting point for one kind or type of secondary counterpart.

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Third, it seems that A can be the starting point for more than one secondary counterpart, say a' and a''. However, crucially, from the argument above, the hexical relation between A and a is not the same as that between A and a', nor between A and a''. Fourth, it does not follow that if A stands in a hexical relation to a, then if A is not the same as C then C does not (or cannot) stand in a hexical relation to a at all; it simply follows that the hexical relation between A and a is different from any between C and a: A is the starting point for one feature of a; C is the starting point for a different feature of a. Differences in primary counterparts therefore entail differences in secondary counterparts, again either as a difference between different things in the world, or a difference between different features of one such thing. Thus different psychological hexeis – for example, knowledge as opposed to factual belief, or factual belief as opposed to prudence (phronesis) – can have the same primary counterpart, but just cannot stand in relation to the same features of that thing. Again, these differences in secondary counterparts are due to what these things or features are, and not due to how they are described or stipulated.2 By means of these primary counterparts, Aristotle has a very clear way of distinguishing different parts of the human mind. He does so as follows: Parts of the Human Psyche (Virtues only) I. Behavioral — (…) II. Thought A. epistemic 1. knowledge B. reckoning (deliberative, doxastic) 2. deliberative belief i. prudence

ii. skill

iii. factual belief

Primary Counterparts (Things in the world) I. What one strives for or avoids: what is good or bad II. What is true or false 1. what is necessary

2. what is contingent i. the practicable, what concerns the good or advantageous in a general way ii. the makeable or doable, what concerns the good or advantageous in a partial way iii. what is contingent, but neither practicable nor makeable (it does not concern the good in any way)

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My defense of this schema starts with Aristotle’s initial assumption that there are virtues of the psyche; that is, that there are certain features a psyche may have which are excellent, exemplary, and make it surpass other psyches in which those features are absent. First division: Aristotle divides these virtues into two parts, those of behavior (êthos) and those of thought (dianoia). (I ask the reader to be patient in waiting for my argument translating ‘dianoia’ as ‘thought.’) The former are rooted in desire (orexis) and the resultant striving and avoidance. The latter are rooted in nous, and the resultant true and false (EN VI.2.1139a22, 26–28). By now, the use of the term ‘part’ here should be no surprise.3 ‘Part’ in either Greek or English does not necessarily entail a lack of activity or of doing something. A gear is a part of a watch, but yet does something crucial for the proper functioning or activity of the watch. ‘Part’ also does not necessarily imply physicality. Take a mathematician thinking through a proof in her head. A line in this proof is a part of that proof, does something (namely, helps to demonstrate the necessity of the conclusion), but is not something physical, not at least in any intuitive sort of way. ‘Part’ also does not necessarily entail a fixed location. Nitrogen is a part of our atmosphere, and actively plays a role in its nature and what it does (for example, it makes the sky blue), but in contrast to a gear or a premise, it has no fixed or set location; it is just diffusely there. Playfulness is a part of my dogs’ character, yet is not fixed in some spot somewhere in their brains or hearts, detectible by some sort of electronic scan, but instead is just there. In all these examples the part is something actual or active and does something. ‘Part’ in Aristotle’s taxonomy should be understood in this sort of way. Second division: He then takes thought and divides it into two parts: the one having a logos, and the other which is without a logos (EN VI.1.1139a3–5). (I leave ‘logos’ untranslated too for now. The most important thing to note about the term is that it signifies language is involved.) Notably, the division Aristotle makes at this stage is only of the parts of the thinking part, and not the virtues of that part. My focus is on the thinking part. Third division: Aristotle focuses next on the part which has a logos and divides this part into two: the one by which we theorize ‘such things, of the things that are, whose starting points are not possibly otherwise,’ and the one by which we recognize such things, of the things that are, which are possibly otherwise (EN VI.1.1139a6–8). Thus, the primary counterparts at this division are different in the following way: some are necessary (i.e., are starting points that are not possibly otherwise) whereas the others are contingent (i.e., are starting points that are possibly otherwise).4

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Fourth division: The part of the psyche whose primary counterparts cannot be otherwise is the epistemic (epistêmonikon) part. The secondary counterpart to these is knowledge, and is the hexis that results from this part of the psyche. Aristotle notes that knowledge concerns not only matters that are necessary, but also things that come to be from necessity (EN VI.4.1140a24–25).5 For these reasons, this hexis is apodeictic (e.g., EN VI.3.1139b19–23 et al.; AnPo. I.33.88b36–37). Fifth division: The part of the psyche that has a logos, and whose primary counterpart is what can be otherwise, is the reckoning part (logistikon). This part is the same as what is called the ‘doxastic’ part (doxastikon), and the verb ‘to reckon’ (logizesthai) means the same as ‘to deliberate’ (bouleuesthai) (EN VI.1.1139a11–14; 5.1140b25–26). Thus these three different labels all are different ways of marking this single part of the psyche. Sixth division: There are three hexeis that comprise the reckoning part of the psyche: prudence, skill, and belief. (Note that prudence does not belong to the behavioral part of the psyche!) Each one is demarcated according to its primary counterpart. This demarcation means that the things in the world or their features that are contingent are of three different kinds (e.g., EN VI.4.1140a21–23; 5.1140b4–6, 28–30). Aristotle states that ‘...the practical hexis with a logos is different from the productive hexis with a logos’ (EN VI.4.1140a3–5). Prudence is ‘a practical hexis, with a logos that is true, concerning the goods and evils for human beings’ (EN VI.5.1140b4–6). So whatever is practicable (praktikon), or doable or makable (poiêton), but does not fall under the provenance of any skill, is the primary counterpart to prudence. Otherwise, the makable or doable is the primary counterpart to skill: ‘...skill will be the same as a productive hexis with a logos which is true’ (EN VI.4.1140a9–10). Things in the world which are contingent starting points, but which are neither doable, makable nor practicable, are the primary counterparts to belief (e.g., AnPo. I.33.89a3–4, DA III.3.428a19).6 Aside: Two senses of ‘belief.’ Aristotle’s term ‘belief’ requires some analysis. (‘Belief’ translates ‘doxa.’ ‘Opinion’ might be better but I chose ‘belief’ in order to emphasize the similarities between Aristotle’s project and contemporary epistemology.) Aristotle arguably uses it in a broader and in a narrower sense. What I will call ‘deliberative’ belief is the hexis whose primary counterpart is simply everything contingent, i.e., everything in the world that is possibly otherwise, regardless as to whether it is practicable, makable or factual. What I will call ‘factual’ belief is the hexis whose primary counterpart is the contingent that has nothing to do with doing anything.

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Primary evidence for this broader usage occurs when Aristotle identifies the reckoning and the doxastic parts of the psyche, and also when he says that ‘to reckon’ is the same as ‘to deliberate,’ as cited above. He uses ‘to deliberate’ and its variants mainly in the context of prudence, and ‘to reckon’ mainly with factual belief and skill. The doxastic part of the psyche is clearly connected to belief. Furthermore, Aristotle says that if one is deliberative, or has the ability to reckon well, then this person is prudent (phronimos): ‘It is significant that we also call people prudent concerning something whenever they will reckon well for themselves in regard to some end which is excellent, of which there is not a skill. Therefore too the deliberative person in general could be a prudent person’ (EN VI.5.1140a28–31). Aristotle also offers an argument within this taxonomy that evinces this broader use of ‘belief’: No one can deliberate about what is not possibly otherwise, and knowledge concerns this. Therefore, prudence is not knowledge. Skills concern things which are good and expedient (spoudaion) for oneself partially (kata meros). Prudence is about living well – i.e., the good and the advantageous – in general. Therefore prudence is not a skill, even though both concern what can be otherwise, goods, and involve deliberation or reckoning. Now there is virtue or excellence of a skill. (The Greek term ‘aretê ’ encompasses both virtue and excellence.) For example, there are doctors who adequately diagnose and treat an illness, but there are others who do so well, and these latter are the ones who are excellent doctors. However, there is no virtue and excellence of prudence: one is either prudent or not; one either sees what is best for oneself and others or not. There is no distinction between acting prudently and acting prudently well. Analogously, willed error is a sign of skill (say in the case of a Michaelangelo sculpture), but not of prudence. ‘It is clear then that it [prudence] is a certain virtue and not a skill. There are two parts of the psyche having a logos, and excellence is of one of them – the doxastic: belief (and prudence) concerns the thing which is possibly otherwise’ (EN VI.5.1140a31ff; b24–28). Prudence therefore is the excellence or virtue of the deliberative part of the psyche. Prudence is deliberative belief, belief in the broader sense, at its best. Correspondingly, the contrary of prudence – impracticality (aphronsunê 7) – is deliberative belief at its worst.8 Furthermore, from these passages, and from Aristotle’s account of skill at Nicomachean Ethics VI.4, one can conclude that skill is a kind of belief that concerns something which is good and advantageous (sumpheronta) for someone partially, in some respect, for example strength or health (EN VI.5.1140a27–28). Aristotle therefore differentiates prudence from skill in at least four ways, not including by means of counterparts: (1) Prudence

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concerns what is doable broadly speaking but is not the provenance of any skill. (2) Skill concerns the good, expedient, and advantageous partially or in some respect, whereas prudence concerns the good and expedient in general. (3) Skill can exhibit virtue and excellence, whereas prudence cannot. (4) Willed error can be a sign of skill, but not of prudence.9 There remain matters that are factually possibly otherwise and do not concern the good and advantageous generally or partially. As we clearly think and speak about such things, there must be a psychological counterpart to these contingencies. This is factual belief, belief in the narrower sense. Henceforth, when I use ‘belief’ without any adjective, please understand it as ‘factual belief.’ When I want to refer to belief in the broader sense, I will use ‘deliberative belief.’10 End of aside. This taxonomy shows what a hupolêpsis is. Prudence, skill, belief, and knowledge all are parts of the psyche that have a logos, and each is differentiated by their respective primary counterparts. All are hexeis as well. Knowledge is ‘a hupolêpsis concerning the things which are universal, i.e., the things which are from necessity’ (EN VI.6.1140b31–32).11 In the De anima, Aristotle briefly notes that ‘[t]here are differences in hupolêpsis itself – knowledge and belief and prudence and the contraries of these...’ (DA III.3.427b24–26). Concerning skill, he states that ‘a skill arises whenever one universal hupolêpsis concerning things which are similar arises out of many options from an inductive procedure’ (Meta. I.1.981a5–7). Skill then is the hupolêpsis concerning what is doable or makable and can be otherwise. Concerning prudence, he states ‘...good-will (boulia) will be rightness in respect of the advantageous toward some end, of which prudence is a hupolêpsis that is true’ (EN VI.9.1142b31–33; cf. 5.1140b11–16).12 Prudence then is the hupolêpsis concerning what is practicable, or doable or makable but is not counterpart to skill, and can be otherwise. Concerning belief, he states that belief is ‘a hupolêpsis of an immediate and not necessary statement’ (AnPo. I.33.89a3–4). Aristotle also states: ‘There are five things in respect of which the psyche arrives at truth by means of affirmation and denial: these are skill, knowledge, prudence, wisdom, nous; it is possible to be mistaken in hupolêpsis – i.e., in belief’ (EN VI.3.1139b15–17).13 Factual belief then is the hupolêpsis concerning what can be otherwise, but which is neither doable, makable nor practicable. Knowledge, skill, prudence, and belief are now all hupolêpseis as well as hexeis. Each of these have contraries – ignorance, incompetence, impracticality, false belief respectively. These will also be hupolêpseis, because hupolêpsis includes both contraries. Each pair of contraries will concern the

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same primary counterparts.14 All are parts of the psyche that has a logos. Hexeis in contrast are not exclusive to just this part of the psyche or to even living beings; there are many kinds of hexeis which do not involve a psyche at all. The case concerning nous will be discussed below. From this evidence, I conclude that ‘hupolêpsis’ is the name for the part of our thinking that has a logos. Hupolêpsis then is a psychological genus which has a logos is its distinguishing characteristic, and knowledge, prudence, skill, belief, and their contraries are forms of this genus. Hupolêpsis – having a logos – is the matter, underlying thing or potential for these eight: a genus is ‘of which there is difference and qualification, this is the underlying thing, what we call matter’ (Meta. V.28.1024b8–9).15 Since hupolêpsis is a genus, it is a whole, in which these eight hexeis are parts, and each pair of contraries is in a hexical relation with one corresponding primary counterpart. Having a logos then comes in two forms, depending upon the necessity or contingency of things in the world, or comes in four forms, depending upon whether the logos concerns something knowable, makable or doable, practicable or factually believable. There are many passages that support this conclusion that hupolêpsis is a genus or whole. For example, Aristotle says, as in the quotation from the De anima above, that there are differences (diaphorai) of hupolêpsis, a term which indicates that hupolêpsis is a genus. In the Physics, Aristotle explicitly states that hupolêpsis is a genus, and knowledge is a form of it: ‘But if there are things which are both genera and forms at the same time, it is clear as it is that it will be as one in form, but not one in form without qualification, like learning, if knowledge is a form of hupolêpsis on the one hand, but a genus of particular instances of knowledge on the other’ (Phys. V.4.227b11–14). In the Topics, Aristotle describes hupolêpsis as a whole and as a genus, and knowledge as one of its parts: Also consider, in the shifting of names, if one no longer signifies the same thing, e.g. the one who says that theoretical knowledge is a hupolêpsis which is theoretical – hupolêpsis is not the same as knowledge; it would have to be, if at any rate one also intends the whole to be the same (for on the one hand ‘theoretical’ is common in both their logoi, on the other the rest is different). Moreover, [consider] if one making a substitute of another of the names has not made a shift in difference but in genus, just as in the case just now said. (Top. VI.11.149a8–16) What Aristotle is saying here is that when constructing or examining an argument or claim, be careful lest you replace the name of a part for the name of the whole, even if they share the same qualification (here,

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theoretical), or replace the name of a difference with the name of the genus to which that difference belongs, as in the case of replacing ‘knowledge’ for ‘hupolêpsis.’ There are other instances as well in the Topics where Aristotle clearly states that hupolêpsis is a genus (Top. IV.5.125b28–126a2, 126b13–34). For many reasons, one may choose to use a generic term instead of a more specific term in certain contexts. For example, one may choose to call something by the term ‘animal’ instead of ‘mammal,’ especially if one is unsure whether that creature is indeed a mammal. One may choose to say, for whatever reason, that someone ‘is going’ somewhere, instead of ‘is walking,’ ‘is flying’ or ‘is taking the bus.’ Similarly, Aristotle at times uses the term ‘hupolêpsis’ and its variants in this way. As in the instances of ‘animal’ and ‘is going,’ ‘hupolêpsis’ used in this way is a generic, ‘catch-all’ term for any kind of hexis or reasoning which has a logos, regardless as to whether one is confident as to what this specific kind is, or whether it is true or false. So when Aristotle uses the term ‘hupolêpsis’ in its verbal form (‘hupolambanô’ and its variants), one is either knowing or deliberatively believing something, or suffering the contrary of these, like being impractical or incompetent. Whatever then is the object of these terms may either apply to all the specific kinds of hupolêpsis, it does not matter, or he is unclear as to what specific kind of hupolêpsis is at issue. The examples of ‘animal’ and ‘is going’ above may exemplify any of these three applications. Although the subject matter could be either necessary or contingent, true or false, the one clear point with such use of ‘hupolêpsis’ is that the part of the psyche which has a logos is involved.16 One can find examples of such usage in the Physics and Metaphysics (Phys. IV.6.213a12–15; Meta. I.2.982a6–10ff., I.8.989a6 and a9–12, XII.8.1073a17–18). The generic use of the term ‘hupolêpsis’ also plays a prominent role in Aristotle’s citation of the views of other thinkers, again with the key point being that what is reported has a logos (DA I.2.403b28–404a16, 405a19–21, a29–405b1, 410b27–411a2, et al.; EE VII.1.1235a4–20ff.). There are two crucial cognitive functions that the genus hupolêpsis does not encompass: perception (aisthêsis) and nous. Perception and nous therefore do not involve a logos, even though each is a hexis (e.g., DA III.5.430a14–15). Regarding perception, and presuming that perception is part of the perceptive part of the psyche, Aristotle states that one will easily posit ‘the perceptive’ part of the psyche (to aisthêtikon) neither as something that has a logos nor as something being without a logos (DA III.9.432a30–31).17 In other words, perception is a hexis that on the one hand does not have a logos, but on the other, is not ‘without a logos’ either, because it is not deprived (sterêsis) of one – as hexis is opposed to deprivation, the deprivation

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of perception is non-perception, like blindness (see Meta. V.10.1018a21, 22.1022b22ff.; Cat. 10.12a26–34). A logos is not something that it should have but in fact lacks. If perception were a kind of hupolêpsis, then perception would have a logos. However, many different kinds of animals have perception, but do not have the ability to have a logos. Therefore, perception is not a kind of hupolêpsis.18 Regarding nous, Aristotle states that ‘[s]ince knowledge is a hupolêpsis concerning the things which are universal and from necessity, and there are starting points of the things which are apodeictic, that is, of every instance of knowledge – for knowledge is with a logos – there would be neither prudence nor skill nor knowledge of the starting point of the thing which is knowable,’ because prudence and skill involve things which can be otherwise, but the thing which is knowable is provable, and what is provable cannot be otherwise (EN VI.6.1140b31–1141a1). Wisdom (sophia) does not have these starting points either, because wisdom includes proofs of certain things.19 Thus, the part of the psyche which concerns these starting points is nous (EN VI.6.1141a1–8). Aristotle is arguing here that something which ‘is with’ a logos, like knowledge (whose logoi are proofs), requires starting points. As was cited earlier, the epistemic part of the psyche thinks things whose starting points cannot be otherwise; this part does not recognize these starting points themselves. Prudence and skill both are parts of the psyche that have a logos, and are of things which are possibly otherwise, so these do not provide any starting points either, but instead require them too. Factual opinion also involves a logos and can be false; the starting points of knowledge are never false. Wisdom does not apprehend these starting points because wisdom has proofs at times – i.e., wisdom is also something which, at least in some instances, is with logoi. There is not any knowledge of these starting points because knowledge is with a logos, this logos appears to be a proof, and there are no proofs for the starting points of proofs (AnPo. I.3.72b5ff.). Moreover, Aristotle states that: virtue saves the starting point, degeneracy (mokhthêria) destroys the virtue; in actions (praxeis) the ‘for the sake of which’ is the starting point, just as in mathematics declamations are the starting point. Neither with the latter or the former are there logoi of the starting points; instead, there is a virtue – either natural or behavioral – of correct thinking about the starting point. (EN VII.8.1151a15–19)20 Nous gets these starting points, and is also an excellence of correct thinking. It is also more recognized (gnôrimôteros) and precise (akribesteros) than knowledge. Aristotle states: ‘nous concerns the terms (horoi), of which there

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is not a logos’ and ‘...nous is of the first and the final terms, and not a logos’ (EN VI.8.1142a25–26; 11.1143a35–1143b1).21 Aristotle divides the parts of the psyche according to respective primary counterparts. There are no logoi of these starting points, nor are these starting points logoi. The part of the psyche which is the secondary counterpart of these starting points then does not have a logos. Nous is the secondary counterpart of them. Therefore, nous is not, does not have, and is ‘without’ a logos (AnPo. II.19.100b7–14). Therefore, nous is a part or form of the psyche that does not have a logos. Aristotle groups nous, perception, and desire together as the ‘ruling powers’ (ta kuria) of actions and truth, and these ruling powers are starting points in their own way (EN VI.2.1139a17–18; 6.1141a7–8). Perception is not deprived of a logos, as shown above. Desire too is without a logos, and is not deliberative in any way (EE II.4.1221b30–32, VII.14/ VIII.2.1247b18–19; DA III.11434a10–12).22 Since these two members of the group are without logoi, it is plausible to conclude that the third member of the group, nous, is also without a logos. As cited above, although Aristotle does state that nous is one of the five things by means of which the psyche arrives at truth (alêtheuei) through affirmation or negation, he is not stating that all five of these belong to the part of the psyche which has a logos (EN VI.3.1139b15–17). From these considerations, and from the fact there are no passages in the body of Aristotle’s work to the contrary, nous is neither a form nor a part of hupolêpsis. These facts about nous and hupolêpsis make clear what dianoia is in Aristotle’s taxonomy. Dianoia is the part of the psyche Aristotle contrasts with behavior. Dianoia concerns truth and falsity; behavior concerns desire, striving, and avoidance. The parts of the psyche that arrive at truth by means of affirmation and denial are knowledge, skill, prudence, nous, and wisdom. The first three are parts of the psyche which have a logos, nous is not. Wisdom is a combination of both knowledge, skill, and prudence on the one hand, and nous on the other (see e.g., EN VI.7.1141a9ff., VI.12.1143b15ff.). Therefore, dianoia is the part of the psyche that encompasses both hupolêpsis and nous. Notably, since dianoia concerns truth and falsity, and behavior concerns desire, striving, and avoidance, and Aristotle differentiates these two accordingly, behavior does not concern truth and falsity. Dianoia is then the kind of thought a human psyche has that (i) either has or does not have a logos and (ii) concerns the true and the false. Hupolêpsis then is a subgenus or form of dianoia, being the kind of thought that has a logos. With ‘dianoia’ meaning ‘thought,’ and with ‘having a logos’ as involving language and generally meaning ‘having words,’ one can understand the term ‘hupolêpsis’ as meaning ‘thought with words’ or ‘linguistically expressed thought.’ Nous in contrast is the form of dianoia

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that does not have a logos. One can understand ‘nous’ then as meaning ‘thought without words’ or ‘non-linguistic thought.’ For felicity’s sake, I will often use ‘discursive’ for ‘thought with words’ or ‘linguistically expressed thought,’ and ‘non-discursive’ for ‘thought without words’ or ‘nonlinguistic thought.’ Importantly, again, all thought here, with or without words, concerns what is true or false. One might be wondering why I am not using ‘propositional’ instead of ‘linguistically expressed thought.’ Propositions are generally understood as the meanings of sentences, are the same across different language speakers if they are about the same things, and are contentious in regard to what they are metaphysically speaking. For Aristotle, what is linguistically involved here is not the meanings of words but the words themselves. Moreover, I think Aristotle did not ‘believe in’ propositions, at least in any way most moderns do. So for Aristotle, my linguistically expressed thought about the moon (e.g., ‘the moon is pretty’) is different from a Parisian’s (‘la lune est jolie’), even though the proposition will be the same if they exist. Aristotle’s taxonomy of the human psyche, with their primary counterparts, can now be schematized completely as follows. Parts of the Human Psyche (Virtues and Vices) I. Behavior

Primary Counterparts (Things in the World) I. What one strives for or avoids: what is good or bad

— (…) II. Thought (wisdom/folly) II. What is true or false – non-linguistic thought (nous; does not have a logos) – linguistically expressed thought (hupolêpsis; has a logos) A. epistemic 1. knowledge/ignorance 1. what is necessary B. reckoning (deliberative, doxastic) 2. deliberative belief/ 2. what is contingent deliberative false belief i. prudence/impracticality i. the practicable, what concerns the good or advantageous in a general way ii. skill/incompetence ii. the makable or doable, what concerns the good or advantageous in a partial way iii. factual belief/false factual iii. what is contingent, but belief neither practicable nor makable (it does not concern the good in any way)

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Aristotle’s Answer 2 therefore is this: Knowledge is a kind of linguistically expressed thought concerning the things which are universal, that is, the things which are from necessity. Answer 2 then is Aristotle’s definition of the term ‘knowledge.’ It is that simple, once hupolêpsis was deciphered! Our journey through the metaphysics of knowledge is not yet complete though. Aristotle’s definition leads to further questions that require an answer in order for his theory of knowledge to be understood: What does ‘linguistically expressed thought concerning…’ actually mean? What are the things which are universal and from necessity? Another way of asking these two questions together is this: What kind of thinking corresponds to the objects of knowledge?

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Accounts, Unconditionality, Proofs

In Aristotle’s terms, all discursive thought has, or is with, a logos. Knowledge concerns that which is universal and from necessity. So the logos that knowledge has must somehow concern what is universal and from necessity. What are its unique characteristics, if any? The answer to this question will establish what is knowable, and in what way discursive thought must correspond to it in order to be knowledge. First, though, I need to talk about two Greek terms, ‘logos’ and ‘aïdon.’ Aside: What is a logos? ‘Logos’ is very difficult to translate, because it can function as a generic noun that refers to just about anything involving language. (Sometimes it is even translated as ‘reason.’) It can also function as a very specific term, meaning just ‘word’ for example. Unfortunately, Aristotle seems to use it frequently in that generic sense, so it is almost impossible to come up with a single English word to match his use. In the previous chapters I left it untranslated, in order to let you get a feel for how Aristotle was using it. At this point I am going to begin translating it by the single word ‘account,’ as some readers may find transliterated Greek cumbersome or off-putting. I ask the reader to treat ‘account’ as a placemarker for ‘logos.’ Aristotle holds that what makes any linguistic expression an account is a certain kind of unity. This unity is what makes any account ‘be’ (e.g., Meta. IV.2.1003b22ff.). He says that ‘an account is one in two ways: one in respect of a binding together (sundesmos), like the Iliad, one in respect of revealing non-coincidentally one thing of one thing’ (AnPo. II.10.93b35–37; cf. Meta. VIII.6.1045a12–14, Poet. XX.1457a27–30). According to the meaning of the term ‘sundesmos,’ something can be bound together not only in a physical sense, say by clasps or ligaments, or just by being a bundle, but also in a sense corresponding to how the laws of a state bind its citizens together.1

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According to Aristotle’s first sense, a work like the Iliad is one as an account, and not as a scroll, book or other kind of text but as something linguistic, in the sense that it is a continuous narrative that changes or flows by being bound by one theme or subject – in this case, the rage of Achilles. The Iliad is not a single account because of the contact of just any one word with some other word in a series, grammatically correct or not: Such a string, even though it is comprised of linguistic elements, is not an account (Meta. V.6.1015b36-1016a9). So an account will be complete in a grammatical or formal sense, but something which is complete in that sense is not necessarily an account. Multiple themes or subjects within a single work, a series of works or something like a collection of tales or stories, then will either comprise a single account in some broad fashion (say as being about the same characters or locale, or as being the artistic or intellectual expression of a single author), as a bundle of individual accounts (like a collection of papers or short stories), or do not comprise a single account at all (like an incoherent movie or philosophy book).2 An account in Aristotle’s second sense reveals a feature of some single thing in a way that is not coincidental. If it is such, this account reveals something that is either from necessity or for the most part (Meta. V.30.1025a14; AnPo. I.6.74b11–12). The Iliad then, even though it is an account in the first sense, is not one in this second sense because its composition is coincidental: the lines about Achilles’ rage are not necessary in that they do not necessarily follow given that rage; other words or an entirely different story could be (and have been) written about this very same theme. Importantly, two methods of Aristotle’s – division (diairesis) and his inductive procedure (epagôgê) – are kinds of accounts. They also can be either coincidental or non-coincidental. An example of coincidental division is animal into blue, red and yellow; an example of non-coincidental is animal into terrestrial and non-terrestrial. In either case, each posits one thing of one thing, and is thereby an account in the first sense. Only the noncoincidental division is an account in the second sense. From this material, an account for Aristotle may be characterized as follows: Something is an account if and only if it reveals one thing of one thing. If it reveals something coincidental, it is an account in the first sense (like the Iliad); if it reveals something not coincidental, it is an account in the second sense. Consequentially, an account is by its very nature something which is divisible (diairetos) (Meta. V.6.1016a34–35). In order to reveal one

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thing of one thing, it is necessary that there are at least two parts involved: (1) a subject, topic or theme, and (2) a predication, comment or narrative, with (2) revealing something about (1). Nothing precludes either (1) or (2) from having parts themselves. Thus ‘Plato,’ and ‘fearsome,’ or ‘the rage of Achilles’ and ‘a great philosopher’ for example are not accounts, and given that they are being used and not mentioned, the former pair does not have parts, whereas the latter does. (If they were being mentioned, all four would have parts, namely the letters.) I set aside the issue whether the term ‘reveals’ (dêloun) for Aristotle indicates that an account is expressible by some linguistic form, or only expressed in a linguistic form. If ‘reveals’ means ‘is expressible by,’ then for example, a dream or a silent movie, or a series of images or depictions, all of which reveal one thing of one thing, are accounts. If this is the case, a geometrical proof done by means of images (as Socrates does in the Meno) will be an account. However, if ‘reveals’ means ‘is expressed in,’ then these examples would not be accounts until they were put into language. A resolution of this issue involves Aristotle’s account of the imagination in thinking, something which would lead us too far afield, and is not needed for adequately dealing with the epistemological matters at hand. In either case, it is clear that if something can reveal one thing of one thing, and yet cannot be expressed in a linguistic form, then it is not an account. End of aside. Aside: What does ‘aïdon’ mean? In order to figure out what sort of account is involved in knowledge, we also need to understand the term ‘aïdon.’ The things in the world, or their features, that are universal are the primary counterparts to knowledge. What is universal ‘belongs to things in the world from necessity’ (AnPo. I.4.73b27–28). Therefore, these things, or their features, which are from necessity are the primary counterparts to knowledge. Therefore, in Aristotle’s terms, knowledge is about that which cannot be otherwise (e.g., EN VI.3.1139b18–24; AnPo. I.2.71b15–16). Aristotle states frequently that what is universal, what is from necessity, is ‘aïdon’ (AnPo. I.8.75b21–24). The contrary of ‘aïdon’ is ‘phthartos.’ ‘Phthartos’ is typically translated ‘perishable’ and the like.3 These translations however do not fully capture its meaning. For example, Aristotle claims the following: It is also evident that if the statements are universal, out of which the syllogism is constructed, it is also necessary that both the conclusion of such a proof is aïdon, and states a proof without qualification. Thus there is without qualification neither a proof nor knowledge of things which are phthartos, but just [a proof or knowledge] coincidentally, because it

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is not ‘beneath the whole’ of it, but is ‘sometime’ and ‘somehow.’ Whenever this is the case, it is necessary that the other statement is phthartos and not universal – phthartos because the conclusion will also be when it is the case, but not universal because it will be the case in respect of something yet will not be the case overall – therefore it is not to be syllogized universally, but that it is the case now. (AnPo. I.8.75b21–30)4 Aristotle’s use of ‘phthartos’ is revealing. Here he is classifying two kinds of syllogisms and their conclusions according to two kinds of statements. Universal statements result in conclusions – and thence syllogisms – that are universal. Since the conclusion is universal, it is aïdon, and hence knowable without qualification. However, when statements have things which are phthartos for their subject matter, the syllogisms comprised out of them are not proofs without qualification, but are proofs coincidentally. That is, they just happen to be proofs. (The Greek for ‘coincidental’ and ‘to happen’ are formed from the same linguistic root.) Correspondingly, the possession of such a proof results in what Aristotle calls ‘knowing coincidentally’: coincidental knowledge just happens to be knowledge, because it was just chanced upon while leaving some necessary criteria unsatisified (AnPo. I.6.74b32ff.). Conclusions of coincidental syllogisms do not cover the whole or the entirety of the subject matter – are not universal – because the conclusion contains an explicit or implicit reference to a particular time and manner. These statements, syllogisms and conclusions are accordingly the case ‘in respect of something.’ The important fact to note here is that Aristotle not only calls the subject matter of premises or conclusions ‘phthartos,’ but also the statements themselves. Earlier in the Posterior Analytics he also described some ‘middles’ (i.e., middle terms) as being ‘phthartos’ (ibid.). Therefore, if a statement is phthartos, the conclusion of a syllogism, in which such a statement appears, is the case only if that statement is the case. Since the statement contains a reference to a time and manner, by definition of ‘phthartos,’ the conclusion is the case only if it contains within itself that same time and same manner. Such a statement, and the resultant conclusion, will not be universal because the syllogism does not hold in accordance with the whole of the subject matter at hand, regardless of circumstances, but in accordance with only that subject matter in regard to that indicated time and manner, that is, in respect to something. Thus, such a syllogism holds now, but not universally: it does not hold over every now or over every manner. Therefore it is plausible to conclude that the term ‘phthartos’ for Aristotle is better translated as ‘contingent’ (as opposed to ‘perishable’ and the like) in logical and epistemological contexts, such as in the passage

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from Posterior Analytics I.8. Thus, a statement that somehow contains a reference to a time or to a manner, is the case just in some respect, is not necessary but contingent. Such statements, or syllogisms which contain them, are not knowable without qualification because they can become false beyond one’s recognition, or when one is not paying attention. For Aristotle, what can be true at one time or in one manner, but false at another time or in another manner, is not knowable, but only opinable. In order to possibly know something that is contingent without qualification, one literally could not take one’s eyes off of it, and must constantly change the statements about it in accordance with that thing’s changes. The moment one ‘blinks,’ the knowledge is lost or becomes coincidental. Now for ‘aïdon.’ ‘Aïdon’ is typically translated as ‘eternal.’5 Aristotle contrasts what is contingent with what is aïdon; so just as ‘phthartos’ is translated better by the term ‘contingent’ rather than by ‘perishable,’ so ‘aïdon’ is translated better by a term other than ‘eternal,’ one which is contrary to ‘contingent.’ Since what is contingent is the case given a certain time or a certain manner, is the case in respect of something, what is aïdon is the case given any time or any manner, not just in some respect. What is universal and from necessity is the case given any time, manner or respect. Therefore, what is universal and from necessity is unconditionally the case, unconditionally true. It is plausible then to take ‘aïdon’ as meaning ‘unconditional’ in the context of Aristotle’s theory of knowledge. Thus, the things in the world or their features that are unconditional are primary counterparts to knowledge. Accordingly, the account that knowledge has reveals one thing of one thing unconditionally. However, this fact does not automatically entail that universals are these primary counterparts; it just entails that those things or features that are universal due to their being from necessity are the primary counterparts.6 End of aside. A proof (apodeixis) for Aristotle is what reveals one thing of one thing unconditionally. Since what there is knowledge of without qualification is incapable of being otherwise, that which is knowable by virtue of apodeictic knowledge will be necessary, and apodeictic [knowledge] is what we have by having a proof. Thus, proofs are syllogisms which are from necessaries. One thus must take that proofs are also from some such things. (AnPo. I.4.73a21–25).7 Accordingly, a proof is one way by means of which human beings know. ‘If then there is also another way to know we will say later; however we are

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saying it is to see [eidenai] by means of a proof. I call a proof “an epistemic syllogism”; I call “epistemic” that by virtue of which we know by having it’ (AnPo. I.2.71b16–19). So a proof is a unique kind of syllogism – as indicated by ‘epistemic’– and it is by means of, and by virtue of, this kind of syllogism that we have at least a significant amount of knowledge. The feature that makes proofs unique, and a vehicle by which we acquire knowledge, is that they are able to reflect or correspond to the necessity of things in the world. A proof is clearly not one linguistic item in the sense the Iliad is one, but one in the sense of revealing one thing of one thing in a way that is not coincidental: Proofs prove by predicating one thing of another without qualification (haplôs), not coincidentally (AnPo. I.22.83a18–21). Aristotle contrasts ‘without qualification’ with ‘coincidentally.’ He also contrasts ‘coincidentally’ with (a) ‘from necessity’ (or ‘kath’hauto’) and (b) ‘for the most part.’ If it is the case that if some thing is not coincidental, then it is (a) or (b), then this passage indicates that ‘without qualification’ is another way to say ‘from necessity (or kath’hauto) or for the most part.’ A syllogism, of which a proof is a unique kind, is an account in which, by one having positioned certain things, something different from those positioned things occurs from necessity in respect of being these things. ‘In respect of being these things’ I mean ‘to occur on account of these things’; ‘to occur on account of these things’ ‘not to need in addition any outside term for their necessary arising.’ [emphasis mine] (AnPr. I.1.24b18–22) A proof, as well as a syllogism, is an account. In this account, certain terms (horoi) are arranged in certain positions within a statement (protasis). These statements result in a new statement, a conclusion (sumperasma), that follows from these statements from necessity. All statements are themselves affirmative or negative accounts, each of which predicates something of something (AnPr. I.1.24a16–17). So proofs and syllogisms show one thing of one thing: ‘It is truly a necessity that each proof and every syllogism shows that something belongs or does not belong...’ (AnPr. I.23.40b23–24). Proofs – epistemic syllogisms – are the only kind of syllogisms which capture or reflect universality, necessity, unconditionality. Therefore, one kind of account (if not the only kind) that knowledge has or is with is a proof. From the fact that proofs are composed out of statements entailing a conclusion, one may take Aristotle’s statement that knowledge is with, or has, an account, in regard to proofs, in two ways: generally, when the account

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is the entire proof, statements and conclusion together, with the former entailing the latter; or specifically, when the account is a conclusion which follows necessarily from a proof. Either way, the proof is about one thing, namely its middle term or primary subject. The passage just quoted at length also clearly indicates that Aristotle considered proofs to be a means by which to obtain new knowledge, and not just a means to organize previously attained knowledge for justificatory, explanatory or organizational purposes.8 Knowledge therefore is an apodeictic hexis, a hexis which is formed by thinking of a proof: We all realize that what we know is not possible to be otherwise. The things which are possibly otherwise, whenever they arise outside of our theorizing, escape our notice as to whether they are or not. Thus the thing which is knowable is from necessity, and thus it is unconditional: the things which are from necessity without qualification all are unconditional, and things which are unconditional are ungenerable and undegenerable... Thus, knowledge is an apodeictic hexis... (EN VI.3.1139b19–24, 31–32; cf. AnPo. I.4.73a21–27, 8.75b21–36) Aristotle later says that knowledge is ‘a discursive thought concerning the things which are universal, i.e., the things which are from necessity’ (EN VI.6.1140b31–32). Besides confirming that proofs are the accounts knowledge is with, these passages add that what is unconditional is not subject to either generation or degeneration. Those things in the world, or their features, which are subject to these are not the primary counterparts to knowledge. This position means that one cannot have knowledge of contingent things, i.e., things which both possibly are and possibly are not. Hence, according to Aristotle’s theory, one cannot know anything about material particulars as material particulars because anything material (save perhaps whatever is comprised of the ‘fifth element’) is subject to generation and degeneration. Any thing or feature in the world subject to formation or disappearance may or may not exist, be the case, be true or false, when one is not ‘theorizing’ about them. One can only have beliefs about them. Aristotle’s position by no means entails that we have no knowledge of the material universe. It just entails we have no knowledge of those aspects of it that are not unconditional. In contemporary terms, we can have knowledge of these aspects insofar as they are naturally necessary. So for example, one cannot know anything about Socrates qua Socrates; however, one may be able to know something about him qua a human being, qua an animal, and so on.

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Now the various forms of discursive thought are distinguished by their primary counterparts. Knowledge is distinguished from prudence, skill, and factual belief by being of what is universal and from necessity, whereas the others concern what can be otherwise. Now the account involved in knowledge is a proof, an epistemic syllogism. Proofs are not about contingencies and what is possibly otherwise. Prudence, skill, and factual belief are all about what is possibly otherwise. Therefore, the accounts involved in the other forms of discursive thought are not proofs. Therefore, there are no proofs of matters that concern skills, practical matters or conditionally factual matters. In short, there are no practical, technical or factually opiniative proofs.9

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Ignorance, Primary Knowledge, Theory

Since knowledge has a proof for its account, the kind of discursive thought contrary to knowledge would also have for its account a syllogism of some kind parallel to a proof. The contrary to knowledge is ignorance. If there is a kind of knowledge which has an account that is not a proof, then there will be a corresponding kind of ignorance which too has a similar kind of account. Aristotle does indeed hold this. He indicates that ignorance is either a denial or a constitution. Ignorance as a constitution is deception arising by means of a syllogism. In those things which do or do not belong primarily, this occurs in two ways: either [i] whenever one without qualification discursively thinks something to belong or not to belong, or [ii] whenever one acquires the discursive thought by means of a syllogism. From an unqualified discursive thought the deception is unqualified; from one by means of a syllogism it [the deception] is multiple. (AnPo. I.16.79b23–29) Passage (i) indicates that unqualified discursive thoughts, which are instances of ignorance, are not the result of syllogisms, but are acquired in some other way. These thoughts are instances of ignorance regardless as to whether they are used in syllogisms, for their truth value is not dependent upon such use. However, it is clearly admissible to use them within syllogisms. Passage (ii) refers to the multiple ways of being deceived by a syllogism. These ways can be summarized as follows, letting ‘Z ’ and ‘X ’ be appropriate terms: (ii.i) One concludes Z belongs to X, when in fact Z does not belong to X or does not belong to X universally. (ii.ii) One concludes Z does not belong to X, when in fact Z does belong to X universally (AnPo. I.16.79b29ff., I.17 respectively).

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In summary, the account ignorance has is one which states non-coincidentally one thing of one thing, but this statement is false, either by itself in the case of (i), or as the result of a syllogism with one or more false premise statements, as in the case of (ii.i) and (ii.ii).1 This material about ignorance hints at the other kind of account involved in knowledge. Aristotle holds that ignorance comes about in one of two ways: a discursive thought acquired by means of a syllogism, or not by means of a syllogism. One account knowledge has is a proof, and this may be taken generally (as the entire proof) or specifically (as the conclusion of that proof). In both cases, someone obtains an instance of knowledge upon gaining them. This knowledge is clearly contrary to the ignorance acquired by means of a syllogism – namely, one which has one or more false premise statements. Is there a contrary to (i) ignorance without qualification that just takes something to belong or not to belong? There is in fact such a contrary: ‘anapodeictic knowledge,’ knowledge without a proof. In parallel with its contrary, this anapodeictic knowledge is ‘a discursive thought of the immediate statement’ (AnPo. I.33.88b36–37). However, a discursive thought of an immediate statement that is not necessary – i.e., can be true at one time but false at another – is belief (AnPo. I.33.88b37–89a4). Knowledge is of what is unconditional. Therefore, anapodeictic knowledge is a discursive thought of an immediate statement that is unconditional. The kind of ignorance contrary to anapodeictic knowledge then is a thought of an immediate statement that is (i) always false, or (i') sometimes false. Ignorance of kind (i) involves deception by taking the statement to be always true. Ignorance of kind (i') involves deception about the general modality of the statement by taking it to be necessary when in fact it is contingent. Like its contrary, anapodeictic knowledge is a statement that is evidently not the conclusion of a proof, but is acquired in some other way, and is an instance of knowledge regardless of its use within a proof. Finally, when Aristotle says ‘[i]f there is also another way to know...’ as opposed to knowing by means of a proof, this other way of knowing refers to anapodeictic knowledge.2 Therefore, the starting points for apodeictic knowledge are not concepts, but statements.3 Similarly, when Aristotle says that ‘[o]ne thus must take that proofs are also from some such things,’ he is saying that proofs, which are of necessities, must come from things which are necessary. These are instances of anapodeictic knowledge, i.e., of immediate, necessary statements. Indeed ‘[i]f then to know is as we just posited,’ that is, if knowledge involves having a proof, ‘it is also necessary that apodeictic knowledge is from truths, primaries, immediates, and things more recognized than, prior to, and causes of the conclusion...’ (AnPo. I.2.71b19–22).

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This passage shows that apodeictic knowledge is derived from anapodeictic knowledge. Aristotle is a difficult philosopher, and his writing is difficult as well. Words like ‘anapodeictic’ are heavy and cumbersome. I hope the reader now understands what he means by it. So to make matters easier, from this point forward I will usually call anapodeictic knowledge ‘primary knowledge.’ Such knowledge will be an immediate statement of something unconditional. It may or may not be derivable from a proof; if it is, it has not yet been so derived by the person who has obtained it. (Matters concerning derivability will come up later.) The term ‘apodeictic’ is not as bad but can be awkward. So, I will alternate ‘apodeictic’ with ‘derivative’ depending on the context, and take them as equivalent. ‘Derivative’ is nice in that it can be taken figuratively in that derivative knowledge is posterior or secondary to primary knowledge, and literally in that derivative knowledge is derived somehow from primary knowledge. Many contemporary epistemologists might now be in a state of shock because Aristotle’s conception of knowledge is strong: one has knowledge only of things that are necessary, which they take to be a major concession to the skeptic.4 For those who are persuaded by Quine’s arguments against the concept of necessity, Aristotle’s position entails an even nastier skepticism: knowledge does not exist. However, there are a couple of features of Aristotle’s philosophy that might palliate this discomfort. The first concerns what he calls ‘theorizing,’ a technical term which I will discuss below. Aristotle accepts Plato’s worry that anything material is in constant flux: it is the case at one instant, but not the case at another. (Such a position seems quite in line with contemporary physics, by the way.) A necessary condition for knowledge is truth. The primary bearers of truth and falsity here are indeterminate in that one cannot get a fix and ‘lock on’ to them in their cognitive radar over any significant extent of time. Thus, the truth condition for knowledge in regard to material entities is never satisfied for any significant extent of time. One can however theorize about them on a moment-by-moment basis. The fact that I am seated as I am writing this is a contingent matter: a few moments ago it was not the case, in some moments it will not be the case. You can theorize about my being seated, but only if I am seated and present before you while you are doing that theorizing. So for Aristotle, not only is matter in flux, but one’s theorizing too. One might ask how one’s theorizing is changing if one is thinking about the same single thing over a period of time. Remember that for Aristotle, all discursive thought is a secondary counterpart, dependent upon its primary counterpart in a hexical relation. If one’s theorizing remains the

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same, but its object is changing, then one’s theorizing is changing too, changing from true to false, back to true, changing back to false again, and so on, in accordance or discordance with that object. The moment you stop theorizing, or leave my presence, the fact that I am seated may have changed without you being aware of it. One cannot have knowledge of something that is not the case, something everyone will accept. (Careful! One can of course have knowledge that something is not the case.) However, what about adding a temporal and spatial marker into one’s analysis of knowledge? Cannot one know that at time t in place p I was seated? This fact is always true once it occurred, correct? In again what many would take to be a major skeptical concession, the answer for Aristotle is no. If there is any theorizing about contingent matters, these matters must be occurring now, at the moment of theorizing. Otherwise, a human being cannot know this fact, but only believe it with a certain degree of evidence, with the truth of the matter being more or less probable depending upon that evidence. This includes anything based on testimony: If the testimony is about something contingent, there is no knowledge, just some degree of justified opinion or belief. If the testimony is about something necessary, at best only coincidental knowledge is obtained, not knowledge without qualification, unless and until the auditors come to theorize the testified fact on their own. Once they do so however, it is no longer based on testimony, but something else, with the testimony being a means to, but not the source of, knowledge without qualification. The case with memory is more complicated and cannot be discussed here. The second palliative feature is that Aristotle’s principal (and perhaps only) conception of necessity is natural. In contrast to many today, he holds that there are necessities in nature, and these can occur always or ‘for the most part.’ (The latter notion will receive more substantial treatment later.) So, anything necessary embodied in something material will be knowable. For example, if there are any features that human beings unconditionally have (say, involving DNA or our specific position in a systematic taxonomy of the animal kingdom), those features will be knowable. Moreover, anything that occurs according to natural laws will also be knowable. So for example, if astronomical phenomena like lunar eclipses, geological ones like tides or plate tectonics, biological ones like evolution, and so on, occur because of certain natural laws, one will be able to know something about them. Some very solid evidence for this is forthcoming, especially in the material on ‘for the most part.’ Now about theorizing. Recall that in chapter 3, I analyzed Aristotle’s concept of knowledge as a hexis according to his three levels of being, and

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made the distinction between knowledge by itself or for us. There I only did two levels. Theory (theôria) is knowledge at the third level, the actively actual, the actually fulfilled level: The matter is a potential, the form a fulfillment, and this is twofold: the one as knowledge, the other as theorizing.... It is a necessity that the psyche is a reality as a form of a natural body potentially having life. Reality is a fulfillment – thus it is the fulfillment of such a body. This fulfillment is twofold: one as knowledge, the other as theorizing. It is evident then that the psyche is like knowledge.... (DA II.1.412a9–11, 19–23) He states that the person who has knowledge at the second, potentially actual level, ‘being wished, is capable of theorizing if something from outside does not prevent it.’ Aristotle then says ‘[t]he one who is theorizing already, being in fulfillment and like a master, is knowing this x’ (DA II.5.417a28–29).5 So one who is theorizing is at the third level of actual actuality, actual fulfillment, ‘knowing this x’ like a master. What does it mean ‘to know this x’, i.e., to be theorizing? Aristotle states that ‘“to perceive actually” is said in a way similar to “to theorize”’ (DA II.5.417b18–19). To perceive actually is for what has the potential to perceive, by having undergone something, to ‘have been made similar’ somehow to the perceptible in actuality, to which the perceptive was not similar beforehand – although ‘to undergo’ is being used in a strictly correct sense (DA II.5.418a1–5). So, in parallel, to theorize is for what has the potential to theorize, by having undergone something, to have been made similar to, and to be just as, that which is knowable actually, to which that hexis was not similar beforehand. In fact, Aristotle says that ‘knowledge in terms of actuality is the same as the thing in the world’; ‘...theoretical knowledge and the thing which is so knowable are the same’ (DA III.7.431a1–2, III.5.430a4–5). (I take ‘theoretical knowledge’ and ‘theory’ to be the same.) So in order to theorize x, there must be potentially active knowledge of x (or in other words, there must be hexis x at the second level of being), just like there must be potentially active eyesight in order to see color. However, this hexis is not similar to x, except in potential. By undergoing something in a special sort of way, the hexis ‘has been made similar to, and is like,’ or ‘is the same as,’ x. According to the passage above, what accomplishes this is simply a thinker wishing it to be so, as long as nothing outside prevents its fulfillment. At this level, using the analogy Aristotle has employed, the theorizing human being is measuring herself or himself, and realizing how short or tall they are, on their own, ‘like a master.’ It is in this way that this x is

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theory. So knowledge, when it is becoming theory, ‘transforms into’ those unconditional things in the world or their features, though of course minus any matter those things or features have: knowledge and perception then are divided into the things in the world, those potentially into the things potentially, those actually fulfilled into the things actually fulfilled: the things of the psyche that are perceptive and epistemic are the same potentially, the one as the perceptible, the other as the knowable – and it is necessary that they are them or their forms, but them certainly not, for the stone is not in the psyche, but the form. (DA III.8.431b24–432a1) Theory then is the same as form, or its features, that exist from necessity. Perception works in the same way in regard to its own unique perceptible, like color in the case of eyesight. Theory by itself is a hexis (v) in terms of form kath’hauto. Theory x is this x, theory is the form itself. The ‘activity,’ ‘actuality’ or ‘fulfillment’ of theory is the form itself, and this is one of the reasons why Aristotle calls forms by these names. Theory is in actual fulfillment the same as (i.e., is like, or has been made similar to) the form itself. The parts which comprise the theory are taken as the whole. There is no whole (like knowledge) involved or under consideration in regard to which theory stands as a part. So for example, grammatical theory is grammar in terms of form, by virtue of this form itself: there is nothing in regard to which grammar is. Aristotle says there is nothing that ‘grammatical’ – i.e., grammar – is of. This means there is no relational counterpart to grammar; grammar is without qualification the very thing that it is. Grammar is not taken as one thing, and its parts something else. Instead, it is the whole or totality of these parts, like vocabulary, syntax, and so on. So with theory – with actual grammar – the parts of grammar constitute grammar, and it is by virtue of this constitution that the grammar is excellent or crude. If one’s grammatical theory is incomplete or exhibits any kind of vice, then the theory is the same as the form only partially. If the theory is complete or exhibits virtue, it is complete, and at this point one has mastery of grammar. Since this constitution is durable and resistant to change and transitions, it is a hexis, not merely a constitution. Accordingly then, grammatical theory is the same as whatever unconditional features – i.e., those that are from necessity and universal – the grammar of a language has. In fact, grammatical theory is grammar. The same is the case for mathematical, cultural, and other forms of theory. Speaking, doing mathematics, music, and other particular instances of theory will then work like skills, e.g., like the shipwright who is

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building the ship: one who is speaking is making something which is particular, although it is based on a something universal. In terms of the plurality analogy Aristotle makes, knowledge at the first level of being is like plurality; knowledge at the second level is like the one having been applied to it, but the number determined (which is something actual) is not some thing in the world, but abstract, and is thereby still a potential. Theory is like the presence there of that plurality.6 Theory for us is a hexis (ii) in terms of place in regard to something else. A theory is a part of the psyche of the theorizing creature, who is, or is taken as, the whole in regard to which the theory is a part. That psyche is an appropriate container for theory, which is contained in it. That theory is in that psyche in the same way as a reality, an ousia, is there. Since theory is the same as (is like, or has been made similar to) a form, the form in that sense is in the psyche without matter in the same way the stone is in the psyche without its matter: a part of our minds has in some way become identical to that form. The distinction between act (theory) and object (form) here is merely conceptual or descriptive. The grammatical equivalent to the actual ‘stone’ mentioned above is grammar as it is naturally used or occurring. Moreover, one’s psyche is constituted somehow by containing this form, and thereby one has a certain kind of quality one would not otherwise have. Theoretical activity is the cognizer knowing ‘how short or tall they are,’ and their ‘height’ here (which is a quality of theirs) is this x they are theorizing. Coda. How do proofs and immediate, necessary statements work according to this three level of being format? By itself, at the first level of being, the proof is just a potentiality, at best something merely a formal pattern without any content. However, this pattern has the ability to receive forms. By itself at the second level, as an active or fulfilled potentiality, the proof is the content of knowledge. It is the form or forms translated into language without having yet become them. The content is either the entire proof or just the conclusion of the proof. By itself at the third level, where knowledge becomes theory, a proof or its conclusion is the form or forms in language. This occurrence explains why sometimes Aristotle calls the form a ‘logos.’ For we who have knowledge, the proof at the first level of being is again just a potential. If knowledge by itself at this level is indeed formal, then correspondingly, our psyches are built in a way that corresponds to and is an appropriate container for this formal pattern. For us at the second level, the proof is the evidence we have. A conclusion is evidence for something unconditionally true; the entire proof itself

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is evidence for this conclusion. Insofar as potential knowledge for us has a formal character, this evidence will be molded or shaped according to that formal character while it is being attained. For us at the third level, the level of theory, we are actively going through the proof. In this case, the proof is both the content and the evidence, and somehow it contains in our psyche the form linguistically. Immediate statements work the same way. By itself, at the potentially potential level, an immediate statement is a formal pattern without any content. By itself at the second level, as an active or fulfilled potential, an immediate statement has content without yet having become the form to which it corresponds. By itself at the third level, when knowledge becomes theory, this immediate statement is the form itself in language. For us at the first level, we have the potential to form and think immediate statements. If immediate statements at this first level are truly formal, then for us, we have something built in the part of our psyche that thinks with language in a way that matches and is receptive to this formal pattern. For us at the second level, an immediate statement is content and a piece of evidence that we have, but are not occurrently thinking about. At the third level, where an immediate statement becomes theory for us, we will somehow have the form in us by means of language. This is both content and evidence for us.

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Requirements (1) and (4): Causes and Starting Points

Requirement (4) states that knowing involves the recognition of starting points. In his account of the term ‘starting point,’ Aristotle states that [i]t is common to all of the starting points to be the first thing from which something either is or comes to be or is made recognized: of these, some are things which are in, some are outside. On account of this, nature is a starting point, and elements, thought, choice, reality, and the ‘for the sake of which’ – truly, the good and the fine is a starting point of the recognizing and of the change of many things. (Meta. V.1.1013a17–23) Aristotle divides starting points here into two kinds: One kind is in – that is, is inside or internal to – the thing in the world whose starting point it is. Since ‘in’ has the same number of senses as ‘to have’ (Meta. V.23.1023a23–25), one kind of starting point has, or perhaps is had by, the things in the world whose starting points they are. The other kind is not in – is outside, is external to – those things whose starting point it is. Accordingly, this kind of starting point does not have, or is not had by, the thing in the world whose starting point it is. So for example, the starting point for one’s decline through aging is in one’s body, for the body has within itself this natural process. However (assuming any kind of pre-existence or reincarnation to be false), the starting point for one’s being born is outside one’s body: this starting point instead was in one’s parents. Aristotle states in the passage above that a starting point is the thing from which something either first is, first comes to be, or is first made recognized for someone. Since knowledge, factual opinion, and all such cognitive capacities about things in the world like recognition are hexeis, and are thereby secondary counterparts, they are dependent upon things in the world for their existence. So if someone genuinely recognizes a starting point of something, this recognition has to be of something real. Thus a

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recognized starting point is in fact a genuine starting point. A recognized starting point therefore is not something instrumental in or pragmatic for explaining or accounting for our experiences. In Aristotle’s terms, recognized starting points are not starting points only for us. Of course though, if someone thinks some a is the starting point of some thing in the world t, this thinking does not automatically make a the starting point of t: that person can simply be mistaken.1 Due to this metaphysical set-up, Aristotle does not need a criterion of certainty or a guarantee of correspondence between a subjective or perspectival recognition of a starting point and an actual, objective starting point – a requirement missing from Aristotle’s epistemology – in order to avoid a disparity between one’s recognition and reality. In fact, Aristotle identifies the meaning of the terms ‘starting point’ and ‘cause’: A starting point is that ‘from which the thing in the world is first recognizable, and this starting point is said of the thing in the world, like the declamations (hupotheseis) of proofs, and also the causes are said equally, for all causes are starting points’ (Meta. V.1.1013a14–17). If there were any disparity between a recognized and an actual starting point, then this identification of ‘starting point’ and ‘cause’ would be problematic, for there could be no correspondence between that thing and one’s psychological recognition of it. Aristotle also pre-empts any skeptical considerations about the external world by means of this set-up. Other than whatever ones someone might have involving necessity, the skeptical worries that arise from his theory instead concern how much the external world transcends our perceptual and cognitive abilities, or in other words, how much more there is to things in the world other than what we can perceive and think about. So the issue is not whether there is anything out there; instead, the issue is how much more there is out there that we cannot get! So, for example, taking a proof to be a thing in the world, a proof of something is first recognizable by the starting point of that proof, which (at least in some instances) is a declamation. A declamation is an existence statement made probable by the consensus of the appropriate authorities or experts, presuming the existence of that thing is not already taken as obvious (e.g., ‘there are geometrical points’ or ‘there is fire (lightning) in clouds’). If the existence statement is obvious, then this statement is automatically probable (AnPo. I.2.72a18–24). This declamation is a cause of that proof, and is said of that proof. This correspondence between an actual and a recognized starting point, and between a starting point and a cause, entails that a declamation is both (a) the thing that actually produces a proof and (b) is the thing by which we first come to recognize that proof. So, given the fact that geometers have declaimed the existence of

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points, the first thing by which one recognizes the existence of lines is by recognizing the existence of points. In turn, in order to prove that lines exist, one declaims that points exist. Since there is no disparity between a recognized and an actual starting point, and ‘starting point’ and ‘cause’ mean the same thing, if points exist (i.e., if the corresponding declamation is true), then points cause lines. Such a proof about lines then adequately matches or corresponds to a certain fact about things in the world. Therefore, the parity between a recognized starting point, an actual starting point, and a cause entails three important features of Aristotle’s theory of knowledge: the parity entails that a declamation is the cause of a proof (i) in terms of a potentially knowing creature; that is, the recognition of a declamation is a cause of the recognition of a proof for that being. The declamation is the cause of a proof (ii) in terms of the proof itself. The subject of the declamation is likewise (iii) the cause of the object of that proof. Since ‘starting point’ means ‘cause’ for Aristotle, and a cause, like a starting point, is the thing by which some thing is first recognized, requirements (4) and (1) are equivalent: In a way adequate for knowledge, (4) recognizing that from which some thing in the world is first recognizable is the same as (1) recognizing the cause on account of which that thing in the world is. Requirement (4) however clarifies what cause is the one required by (1): it is an initial thing from which some thing in the world at issue is, comes to be, or is made recognized for thinkers like us. Thus requirement (1) is not too stringent in that one must recognize the ultimate causes in order to have knowledge (cf. AnPo. II.12.95b22–26). For example, in order to know why thunder occurs (presuming this phenomenon is in fact knowable), one need not recognize the causes of clouds, of changes in weather patterns or of storms, all of which would be ultimate causes. Instead, all one needs to recognize in order to know why thunder occurs is that by which thunder first or initially comes to be or be recognized, which is fire (i.e., electricity) occurring in clouds. In order to know something about lines, one does not have to recognize something about the nature of space, some demiurge or certain innate psychological underpinnings; one needs only to recognize something about points. Since (1) and (4) are equivalent, I will henceforth refer to them with one symbol, ‘(1/4).’ ‘Primaries’ (ta prôta) is the name of the kind of statements that express the starting points and causes of requirement (1/4). If knowledge, Aristotle says, involves having a proof, then derivative knowledge is ‘from truths, primaries, and immediates, that is, things more recognized than, prior to, and causes of the conclusion’ (AnPo. I.2.71b20–22).2 For a proof

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to be from primaries is for it to be ‘from appropriate starting points, for I say that “primary” and “starting point” are the same. A starting point of a proof is a statement which is immediate,’ and an immediate statement is one such that there is not another statement prior to it (AnPo. I.2.72a5–8). Recall that there is no disparity between a recognized starting point and an actual one. If some thing a is a starting point of some thing in the world t (that is, of some t one is trying to prove), then a is the first thing from which t either is, comes to be or is made recognized. Since Aristotle holds the terms ‘starting point’ and ‘cause’ to be equivalent, a is the initial cause on account of which t is, comes to be or is made recognized. Take a statement s, which is about a, and from s, a conclusion c, which is about t. For Aristotle, just as a is the starting point or cause of t, so s is the starting point or cause of c; more broadly, s is the starting point or cause of the proof which entails c. Thus proofs for Aristotle correspond to the workings of the natural world. Now if a statement s is genuinely of a, then s captures the priority or ‘initiality,’ so to speak, of a in regard to t. Hence s is a primary statement, and this is the reason why Aristotle says ‘primary’ and ‘starting point’ are equivalent. By transitivity, ‘primary’ is also equivalent to ‘cause.’ Now Aristotle holds that one just needs to recognize the initial, and not the ultimate, cause of something in the world in order to know something about that thing. However, it seems that nothing precludes an initial cause from being the effect of some other, more ultimate cause. For example, the presence of static electricity in clouds is an initial cause of thunder; however, this presence itself seems to be the effect of some other cause, say the ionization of water vapor. Assuming this causal chain is so, then a, the presence of static electricity in clouds, is the effect of a*, the ionization of water vapor. In a corresponding proof then, a statement s of a will be the conclusion of another proof with a statement s* of a*. In this proof, s will be neither primary nor immediate. Since such a scenario – one where an initial cause is itself an effect of another, more ultimate cause – seems not only likely but also prevalent, the term ‘primary’ for Aristotle must mean that if s captures this priority, this ‘initiality’ of a in regard to t, then in a proof one will not need statement s*, from which s can be derived, in order to know the conclusion c of t. In short, it is not necessary that s be derived from s* in order to know c. Recognition of s is sufficient.3 By Aristotle’s definition of the term ‘immediate,’ s will be an immediate statement as well as a primary one. Given the above considerations about initial and ultimate causes in regard to proofs, an immediate statement is then best understood as one which is not necessarily mediated by, or not obtained by means of, another proof or syllogism.4 Due to this immediacy, Aristotle describes ‘from primaries’ also as ‘from primaries which are

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anapodeictic,’ that is, from primary statements which are not the result of proofs (AnPo. I.2.71b26–27). Anapodeictic (i.e., primary) knowledge is comprised of these primary immediate statements: ‘we affirm that not all knowledge is apodeictic, but that of the immediates is anapodeictic’ (AnPo. I.3.72b18–20). Thus, since it seems that an initial cause itself can be the result of a more ultimate cause, it in turn seems that the corresponding primary knowledge of that initial cause could at some point become derivative, upon recognition of a more ultimate cause. Primary knowledge is therefore not unprovable knowledge, just knowledge without a proof, or in modern terms, it is ‘non-inferentially justified.’5 If the terms ‘primary’ and ‘immediate’ are not equivalent, and all primary statements are immediate statements, then not all immediate statements are primary ones. If this conditional is true, then an immediate, non-primary premise is one which is not derived from another syllogism or proof, yet is not a starting point or some initial cause. Such statements would then be non-inferentially justified knowledge that does not justify anything else. As (i) all primary statements are immediate statements, (ii) primary statements are ones which are about the starting point or cause, and (iii) starting points are that from which some thing in the world first is, comes to be or is recognized, the items ‘things more recognized than, prior to, and causes of the conclusion’ listed in Posterior Analytics I.2.71b20–22 are explicative of the preceding items – ‘from truths, primaries, and immediates’– involved in derivative knowledge. They are not further, additional items. Due to (i)–(iii) and the above argumentation, if a statement is true, primary and immediate, and is recognized as such, it will be more recognized than (requirement [M]), prior to, and the cause of the conclusion derived from that statement, both in terms of the proof itself (such a statement causes and is the starting point of the conclusion) and in terms of the thing in the world the proof is about (the starting point in the statement is the cause of the thing in the world in the derived conclusion). Aristotle thus says that ‘it must be causes, more recognized and prior – causes because we then have knowledge whenever we see the cause, and prior if at any rate they are causes, and recognized beforehand not only in the way in terms of the conceiving, but also in terms of seeing that they are’ (AnPo. I.2.71b29–33).6 In summation, requirements (1) and (4) are equivalent. Statements which are of, or are about, starting points are primary statements. Since they are primary, they are immediate in that they are not necessarily the result of a proof. Primary knowledge is comprised of such statements. In turn, immediate, non-primary statements are ones which are without a

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proof, yet are not starting points or initial causes. The starting point of derivative knowledge stands for the starting point of some thing in the world, so the relationship between a starting point, and the thing whose starting point it is, is thereby somehow mirrored by the relationship between the starting point of a proof and the conclusion of that proof. Finally, recognition of a starting point entails, or is connected to, psychological requirement (M); this matter, however, will be examined later. Before determining which starting points are knowable – that is, which starting points are appropriate for derivative knowledge – I turn to requirement (2).

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Requirement (2): Truth and Relevance

In Answer 3, Aristotle says ‘[w]e think that we know each thing without qualification … whenever we think we (R) recognize (1) the cause on account of which the thing in the world is, (2) that the cause is of that thing….’ Requirement (2) is ambiguous. It has two possible general interpretations in multiple permutations. I need to go through all of them due to the importance of this passage and the difficulty in understanding its full meaning. Interpretation I. (2) is an object clause of ‘to recognize,’ and therefore states that in order to know, one needs to recognize that the cause (i.e., the starting point) is in fact the cause of that thing. Hence one not only needs to recognize the cause on account of which some thing in the world to be known is, but also needs to recognize that the cause is of that thing. There are several ways to understand this: I.a. (2) is redundant, and simply an alternative way of stating (1/4): by recognizing the cause on account of which some thing in the world is, one is recognizing that the cause is of that thing. I.b. (2) is not redundant, but instead is saying that one needs to recognize the truth of (1/4). In other words, (2) is saying that one must not only recognize (1/4), but also recognize that the expression of (1/4) is a true statement. One can now take this reading in two ways: I.b.i. Since expressions of (1/4) are primary, and constitute primary knowledge, one must recognize that one ‘is seeing’ that the cause is of that thing. That is, one must recognize that one has primary knowledge. (2) may therefore be another way of stating (M) or (P).

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I.b.ii. (2) is one about acquisition, learning, and investigation: In order to know, one needs to recognize that a purported or hypothetical cause of some thing in the world is in fact the cause of that thing, and this recognition may be obtained by teaching, by being shown the fact or by an inductive procedure or some other means.1 In short, one cannot just say or repeat (1/4) in order to know, but must obtain (1/4) by certain kinds of procedures or processes. By undergoing them, one recognizes the truth that the cause is of that thing. (2) then may be another way of stating (P). Interpretation II. (2) is not an object clause of ‘to recognize,’ and instead requires the cause be of that thing. There are three ways to understand this: II.a. (2) is redundant, and is another way of saying (1/4): One recognizes the cause on account of which some thing in the world is because the cause is of that thing, for recognition of a cause implies that cause is real or genuine. This reading takes the ‘hoti’ in ancient Greek as meaning ‘because’ more than just ‘that.’ II.a. is almost equivalent to, and has the same effect as, I.a. II.b. (2) is not redundant: One needs to recognize the cause on account of which some thing in the world is because the cause is of that thing, and not because of any other incident, as through testimony. In order to recognize a cause in this manner, one needs to go through certain learning processes or procedures. Hence this reading is ultimately the equivalent of I.b.ii. This reading also takes the ‘hoti’ as meaning ‘because’ and not ‘that.’ II.c. (2) is not redundant, but instead is saying that (1/4) needs to be true, and that the cause needs to be, in fact, of that thing in the world, and not something else. Thus, in order for one to know, the statements involved in a proof must be true and be relevant somehow to the entailed conclusion.2 Permutations (I.b.i), (I.b.ii) or (II.b), and (II.c) are not mutually exclusive, for the fulfillment of any one of these four does not negate, undermine or override the fulfillment of any of the remaining others.3 Are any of these permutations a more likely reading of (2)? (I.a) and (II.a) should arguably be the readings of last resort, because, out of charity, it is not likely that Aristotle would introduce something redundant

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or irrelevant at the point where he is first introducing and stating what his theory of knowledge is in his work on knowledge, even if this work was not intended for public consumption or was concocted in haste. This likelihood leaves (I.b.i), (I.b.ii), (II.b), and (II.c). Now the material that immediately follows requirement (2) explains and elaborates on the passage where (2) occurs. Aristotle takes the rest of Posterior Analytics I.2 to define and to explain his account of knowledge, the terminology and requirements involved. Much of Posterior Analytics I.4 and the following concern requirement (3); much of I.7 and I.10 concerns requirement (1). If immediately following material in a work has any bearing on the meaning of what preceded, then (I.b.ii) and (II.b) can be ruled out, for none of this material concerns the acquisition of knowledge.4 None of this material concerns the criterion of (I.b.i); moreover, Aristotle says that ‘[r]ecognizing whether one is seeing or not is difficult, for recognizing if we see from the starting points of each thing is difficult – which is the very thing seeing is’ (AnPo. I.9.76a26–28).5 By elimination, this leaves (II.c). Aristotle does in fact discuss the issues raised in (II.c). In Posterior Analytics I.2, he states that in order to know derivatively (and presumably primarily), the statements involved must be true. Right after the passage from which (2) is taken, he states that derivative knowledge is ‘from truths, primaries, and immediates, that is, things more recognized than, prior to, and causes of the conclusion’ (AnPo. I.2.71b20–22). The statements in proofs ‘must be truths, because it is not possible to know that which is not, for example the diagonal which is commensurable’ (ibid., 71b25–26). ‘That which is not’ means ‘that which does not exist in any way.’ Due to the connection for Aristotle between truth and being, if some ‘thing’ does not exist, then no affirmative statement about that ‘thing’ is true, and one cannot then have knowledge of this ‘thing,’ like the diagonal of a square which is commensurate with its sides, or a diameter commensurate with its circumference. However, it seems that some negative statements about non-existent things can be true – e.g., there is not a commensurate diagonal – and so, if such statements are unconditionally true, then they will be knowable. (With this connection between truth and being, there is presumably a corresponding connection between falsehood and non-being. If this correspondence is so, then any affirmative statements about non-being will be false – and hence unknowable – since they are about something non-existent.) Except for some radical coherentists or anti-realists perhaps, this rudimentary truth requirement is common to all theories of knowledge. Therefore, it is plausible for one to read (2), ‘that the cause is of that thing,’ as indicating this truth requirement.

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Truth of the statements in a proof alone is insufficient for knowledge: They must also be ‘appropriate’ (‘oikeios’) (AnPo. I.6.74b25–26). Statements that are appropriate are those which are ‘of the same lineage’ (suggenê) as the thing in the conclusion. ‘Of the same lineage’ means that for any proof, the genus to which the starting points in the statements belong must comprise the genus to which the thing in the conclusion belongs (AnPo. I.6.75a35–7.75b12). This comprising genus does so either without qualification or in some respect, i.e., in respect of a form or subgenus of that genus (AnPo. I.7.75b8–9).6 Thus, in order for a proof to be genuinely about some thing in the world, the cause or starting point stated in a premise must be relevant to – relevant by virtue of a common genus to which both belong – the thing in the conclusion. Without this relevancy requirement, one would be able to prove a conclusion from any starting point, as long as these starting points had any one feature in common with the thing in the conclusion. Aristotle reports that someone named ‘Bruson’ was able to show the squaring of the circle by using immediate, true, non-derivative, and presumably necessary, premises. However, according to Aristotle, Bruson’s demonstration was not a proof because its conclusion was not by virtue of (that is, not relevant to) the square or the circle, but by virtue of some common feature which both squares and circles coincidentally have. One thereby could also use this same kind of demonstration for things that are not geometrical figures, as long as those things also shared those common, coincidental features. So Bruson’s proof was not about these figures without qualification (AnPo. I.9.75b37–76a3). One’s putative knowledge here would be coincidental to triangles and squares. The common genus to Bruson’s putative proof was not geometrical figure, but feature F (Aristotle does not offer Bruson’s proof), and from feature F, Bruson concluded something about geometrical figure. One might say then that Bruson’s proof was founded upon a kind of category mistake. For Aristotle, by making such a mistake in a proof, one does not come to know anything, at least anything without qualification. Thus, Aristotle states ‘[w]e think that if we have a syllogism from some things which are primaries and agreeable to truth, we know – this is not the case; the thing must be of the same genus as the primaries’ (AnPo. I.9.76a28–30).7 Aside: Being and unity as genera. There is a notorious discrepancy in Aristotle’s works concerning whether being and unity are genera: In some places he seems to deny that they are genera, in others he seems to affirm that they are genera. When Aristotle denies that they are genera, he might be doing so just with this epistemological requirement in mind: Since

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everything that exists is and is one somehow – i.e., being and unity are relevant to everything – if being and unity were genera, one would be able to prove any conclusion from any starting point by means of them. This consequent is absurd; therefore, being and unity in this way are not genera. However, being and unity are not genera only in terms of not being genera by means of which one can learn something about anything more specific. This position does not entail that they are not genera simpliciter, that they are non-existent entities like goat-stags. One perhaps can know something about these genera by themselves, as Aristotle seems to think in Metaphysics IV, and what one knows about them can then be applied by extension to everything else. This knowledge then will be axiomatic. In this way being and unity are genera. Such a reading softens or obviates this apparent discrepancy. End of aside. Aristotle uses locutions similar to the one found in (2) for this relevancy requirement: [w]e know each thing non-coincidentally whenever, by virtue of that thing, we recognize by virtue of what it belongs, from that thing’s starting points qua that thing – for example having angles equal to two right angles – in respect of which the thing said belongs by virtue of itself, from the starting points of this thing. [emphasis mine] (AnPo. I.9.76a4–7) Take a conclusion c, which states that some feature F belongs to some thing in the world t. Aristotle is saying in this passage that in order to know c without qualification, one must recognize, by virtue of what t is, that by virtue of which t is F. This recognition must come from the starting points a, ... a′ of t qua t. This recognition cannot come from some starting points b, … b′, of which F is also predicated, but which is not an ‘ancestor’ of t.8 That by virtue of which F belongs to t (or t is F) is the genus g common to t and a, ... a′. In this respect then – in respect of a, ... a′ and t belonging to g – the thing said, F, belongs to t by virtue of t itself, and is from a, ... a′. In short, in order to know c without qualification, a, ... a′ must be about t, must be relevant or appropriate to t, and not about some b that coincidentally has a feature in common with t.9 For example, let t be a bronze isosceles triangle, let F be having angles equal to two right angles, and let c be that t is F (or equivalently, F belongs to t). In order to know c, one must recognize, by virtue of t, that by virtue of which t is F. What is the cause on account of which t is so? That is, what is the starting point or the initial, first thing (the ancestor) on account of which t is, comes to be or is recognized as being F? The answer should be

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a primary statement. Let bronze and isosceles be abstracted (aphairethês) from t. This t is still F. Now let figure and limit be abstracted from t. In this case, t is no longer F, because in order to have angles, something must be both a limit (that is, something with at least some ontological boundaries) and a figure. So, what is the first thing by virtue of which t is F? It is by triangle that t is first F. It holds unconditionally, and hence universally and necessarily, that a triangle has angles equal to two right angles. This is a starting point a of c, and is a primary statement. Thing t is isosceles; let this statement be a′. So the genus common to a, a′ and t is triangle, and it is by virtue of this shared underlying thing, and by virtue of what t is, that t is F (AnPo. I.5.74a32–74b4).10 If the common feature which grounded the proof was different from the genus triangle, one would at best know c coincidentally. It is the fact that a is of t, and that a is true, that c is true – i.e., that t is F. This is requirement (2). It is crucial to note that the relevancy requirement of (2) is applicable only to derivative knowledge, and not primary knowledge. Aristotle only talks about this relevancy requirement in the context of the former. In order for the relevancy requirement to be open to question, one needs a series of interconnected statements, and a primary, immediate statement automatically satisfies it since there is automatically only one underlying genus or matter. Only the truth requirement of (2) comes into play concerning cases of primary knowledge. To summarize, the most plausible reading of requirement (2) in Answer 3 is interpretation (II.c): (2) indicates that one of the requirements for knowledge is that the statements in the proof must be true and relevant to the conclusion. The foundations of knowledge do not function as such for anything non-foundational; there must be some sort of substantive tie between them. For Aristotle, in the world this tie is his genera-forms taxonomy; in thought this tie is his logical procedure that corresponds to that taxonomy. (One can now begin to see that Aristotle’s logic is not a logic in our formal sense, but a procedure by means of which to obtain derivative knowledge from primary knowledge without any loss in justification.) ‘Relevant’ means that the starting points or causes have a genus, underlying thing or matter in common with the thing in the world found in the conclusion. ‘A starting point’ for a proof ‘is not what is probable to us, but the thing which is primary of the genus...’ (AnPo. I.6.74b24–25). For this reason, Aristotle states that there are three things involved in a proof: ‘...one, the thing being proven, the conclusion (this is the thing which belongs to some genus by virtue of itself); another, the axioms (axioms are “from which”); third, the underlying genus, of which the proof reveals its modifications (pathê) and the kath’hauta coincidentals’

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(AnPo. I.7.75a38–75b2).11 Aristotle alternatively describes these three as follows: ‘All apodeictic knowledge concerns three things: what is posited to be (this is the genus, of which theoretical knowledge is of its kath’hauta modifieds [pathêma]); the things which are common, called axioms, from which, being first, one proves; third, the modifications, of which one takes what signifies each’ (AnPo. I.10.76b11–16).12 The most important thing to note from these lists is the genus: This genus is the thing which underlies or is the matter for all of the subjects in the proof. The conclusion indicates some modification that necessarily belongs to that genus. Axioms indicate what is shared by all genera; that is, the axioms indicate what underlies, or what is non-coincidentally common to, all things in the world.13 This fact is why Aristotle holds that one needs to have recognized these axioms somehow in order to be able to learn anything (AnPo. I.2.72a14–18). In turn, each body of knowledge – e.g., astronomy, geometry, harmonics, etc. – is differentiated by the one unique genus it is about. ‘...[O]ne body of knowledge is about one genus’ (Meta. X.4.1055a31–32). This body is composed from the primaries and the parts or the kath’hauta modifications are of these. One body of knowledge is different from another, whose starting points are neither from the same things nor are the others from its. A sign of this is whenever one comes to things which are anapodeictic, for these must be in the same genus as the things which have been proven. Also a sign of this is whenever the things shown through these, which are of the same lineage, are in the same genus. (AnPo. I.28.87a38–87b4)14 Epistemic genera (i.e., bodies of knowledge) are hexeis, and hence differentiated by their primary counterparts. Inasmuch as the primary counterparts are different generically (i.e., have different starting points), so too the corresponding epistemic genera will differ. These differences are ultimately revealed by primary statements: One body of knowledge will ultimately be grounded upon a select group of primary statements, another body another group; each group will be demarcated by the genus which underlies all of the statements in that group. Each part of one body of knowledge will have as its subject matter a corresponding part of that genus – that is, a kath’hauta modification or kath’hauta coincidental feature of that genus. Bodies of knowledge will ‘bleed’ into each other so to speak insofar as they partake in the same genus or share some kath’hauta concidentals or modifications of a single genus. According to Aristotle’s epistemology then, a body of knowledge will be complete or finished if and only

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if it has proved all of the possible kath’hauta coincidentals or modifications from this underlying genus. One can again see here a fine instance of the close interconnection between Aristotle’s epistemology and metaphysics: a proof mirrors the production, formation or formal arrangement of things in the world (here called ‘modifications’ or ‘kath’hauta coincidentals’) out of a genus, matter or underlying thing.15 Again, this mirroring is due to the fact that knowledge is the secondary, dependent counterpart in a hexical relation with things in the world; these things have a certain order which in turn is imparted upon the psycho-physiology of a creature that has the potential to know. It would be a tremendous oversight if Aristotle somehow omitted mentioning this crucial aspect of his epistemology in his account of it! He does not do so by proffering requirement (2).16

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Requirement (3): Necessity

For Aristotle, all knowledge concerns all and only what is unconditional. What is unconditional is universal and from necessity. So requirement (3), ‘it is not possible for this to be otherwise,’ is an obvious one for him. However, it is not obvious what its full significance is. The ‘this’ in (3) refers to the initial cause or starting point of requirement (1/4). Which of these are not possibly otherwise, and hence potential candidates for knowledge? Aristotle states that all four of his kinds of causes provide potential candidates for knowledge: Whenever we think we know, the kinds of causes that could be involved are ‘one...the essence (ti ên einai), one the “when there are certain things it is a necessity this thing is,” another what first changed something, fourth the “for the sake of something”’ (AnPo. II.11.94a20–24; Phys. II.3.194b23–195a3, 15–26; cf. ibid. II.7.198b5–9).1 In support of my position that requirements (1) and (4) are equivalent, these four causes as described here encompass the starting points Aristotle lists in Metaphysics V.1, cited earlier: nature, the elements of things, thought, choice, reality, and the ‘for the sake of which’ (which includes the good and the fine).2 Thus, contrary to what some commentators have claimed, Aristotle does not restrict knowledge to so-called ‘essential’ attributes, especially in the Posterior Analytics.3 Now what must an instance of these kinds of causes have in order to be knowable? Requirement (3) provides an answer: A cause or starting point a of some thing in the world t is knowable only if it is not possible for t not to be caused by a. In short, it is necessary that a causes t in order for a to be knowable. This requirement implies that, in order for one to be able to know that a is the cause of t, it is necessary that if t, then a is a cause of t. (3) also includes

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instances of causation that take the form ‘F is G’, with F being some thing in the world and G being a feature of F: In these cases, F (which is a here) is somehow the cause of G (which is t), due to what F is, either as form or as matter. For these reasons, what is from chance is unknowable and unprovable (AnPo. I.30.87b19–27). Any feature F that is universal in regard to t automatically satisfies requirement (3). Universals are therefore highly valuable in Aristotle’s theory of knowledge: ‘[t]he universal is prized, because it reveals the cause. Therefore, concerning such things, the universal proof is more prized than perception and noêsis, of which the cause is different...’ [emphasis mine] (AnPo. I.31.88a5–6). Indeed, he says ‘knowledge is of the universals’ (Meta. XIII.10.1086b33; cf. III.6.1003a14–15), ‘knowledge is the recognition of the universal’ (AnPo. I.31.87b38–39), ‘proofs are from the universals’ (AnPo. I.18.81a40–81b1), and ‘every account and all knowledge are about universals and not about the things which are final...’ (Meta. XI.1.1059b25–26). Universals are valuable because they are unconditional: what is universal will not be at one time but not be at another, nor will it be in one manner at one time, but in a different manner at a different time (AnPo. I.8.75b21–30). By recognizing the universal, one will satisfy both requirements (1) and (3): the universal reveals a cause of some thing in the world, and universals are things which are from necessity.4 If a single universal underlies a proof, one also satisfies requirement (2). This revelatory ability is further evidence that Aristotle’s logical procedure is a means by which to obtain new knowledge. Aristotle defines the term ‘universal’ as something that is both ‘beneath every’ (kata pantos) and kath’hauto. Equivalently, what is universal is ‘beneath every’ and qua itself, for the meaning of ‘kath’hauto’ and ‘qua itself’ are the same.5 However, three criteria must be satisfied for some feature – a unique property, quality, effect, etc. – of some thing in the world to be universal (AnPo. I.4.73b26–28, I.31.87b32–33): Universality: A feature is universal if and only if [i] this feature exists by virtue of what that thing is to which it belongs, [ii] it is from necessity, and [iii] it is always and everywhere whenever and wherever there is that thing to which it belongs. 6 Criterion (i) is the ‘kath’hauto’ requirement: In order for a feature to count as universal to the thing to which it belongs, this feature must have its starting point in the nature of that thing, and not outside it. For example, take two features of human beings which are potential candidates for being universals: user of a language and being an English

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speaker. The feature of being a user of a language arguably has its starting point in human nature; by extension it seems being a native English, Cantonese or Arabic speaker has its source or ground in human nature. Criterion (ii) is a modal requirement. Being the user of a language may necessarily be a part of human nature; however being an English speaker is clearly not necessarily a part of human nature. Criterion (iii) is the ‘beneath every’ requirement. I am not always and everywhere an English speaker whenever and wherever I am at: when I am in the Czech Republic, I speak (some) Czech, as well as some English and some German. The same goes for many other English speakers. So being an English speaker does not satisfy (iii), neither in a specific case (namely mine) nor in general (namely for English speakers in general). Being the user of a language is therefore universal to human beings, but being an English speaker is not.7 This ‘beneath every’ requirement reveals some very important points about Aristotle’s theory of knowledge. Aristotle defines ‘beneath every’ as follows: what is neither in some cases on the one hand, but not in some cases on the other, nor at some time on the one hand but not at some time on the other. For example, if living thing is beneath every human, if it is true to say that this thing is a human, it is also true it is a living thing, and if now another, also this one, and similarly if in every line a point. (AnPo. I.4.73a28–32)8 First, this ‘beneath every’ requires that every instance of t be caused by a. Since what is key here is every instance of t, and since it is plausible that something is an instance if and only if it is a particular of some kind, t here, and by extension in requirement (3), seems to be a particular of some kind.9 Second, the term ‘beneath’ here should not be understood in its spatial sense literally, but analogously, corresponding to the manner in which Aristotle takes particulars to be parts of a universal, in which a universal ‘underlies’ the particulars which instantiate it, or the manner in which a genus is a matter and underlies its forms: A genus is that ‘of which there is difference and qualification; this is the underlying thing that we call “matter”’ (Meta. V.28.1024b8–9).10 Third, and crucially, the ‘beneath every’ criterion is not sufficient for (3): (3) requires that it is not possible for t not to be caused by a. The ‘beneath every’ requirement is only statistical, and lacks any modal character. Thus, even though every instance of a crow is black (i.e., the

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nature of what it is to be a crow causes it to be black), thereby satisfying this ‘beneath every’ requirement, in order for one to be able to know that crows are black, it must also be impossible for crows to be any color other than black. This impossibility is natural, not logical, for it is grounded in the nature of the crow, or more broadly, in the nature of the physical universe. (3) in contrast is not a just statistical requirement, but a modal one with a statistical aspect. Since Aristotle differentiates the ‘beneath every’ requirement from the ‘kath’hauto’ one, it is clear that some things can be ‘beneath every’ but not kath’hauto. It can be true that F is the case of every t, but false that F is the case by virtue of t, for F could be the case of every t by chance. For example, it could be the case that every human being has been somehow affected by war, but it is not by virtue of being a human being (but say, by virtue of greed, hatred or ignorance, or by virtue of all current and preceding economic or political systems) that this is so. Every elected President of the United States has been male; however, it is not by virtue of being President, but by chance, that every elected President has been male.11 Conversely, something can be kath’hauto, but not ‘beneath every.’ Things which are ‘for the most part’ are of this nature, as are kath’hauto coincidentals or modifications.12 Things which are for the most part are the case in some instances, but not in others. Now (3) states that a cause or starting point a of some thing in the world t is knowable only if it is not possible for t not to be caused by a. An implication of this requirement is the following: (3′) A cause or starting point a of some thing in the world of t is knowable only if it is necessary that if t, then a is the cause of t. Let ‘a’ be ‘being a man’ and ‘t’ be ‘having a beard.’ Having a beard belongs to men kath’hauto: it is by virtue of being a man itself that men have beards. However, not every man has a beard, and so having a beard does not satisfy the ‘beneath every’ requirement (AnPo. II.12.96a9–11). Aristotle’s point here is not that some men shave, whereas others do not (pretty much all Greek men, save for Menander, grew beards, and he got flack for that), but that some men – for example, some Asians and Native Americans, and certain individuals of any ethnicity – cannot grow beards, whereas others can. Nevertheless, it seems that it is necessary that if someone has a beard, then it is by virtue of being a man that that person has a beard, even though, as Aristotle has said, it is not true in every case that men have beards. In fact, Aristotle says that something can be necessary without being universal, and that is by being kath’hauto (AnPo. I.6.74b6–7). He also says that things which belong kath’hauto are knowable (AnPo. I.6.74b5–10,

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I.4.73b16–21). So things which are kath’hauto can satisfy (3′), even though they do not satisfy the ‘beneath every’ requirement. Therefore, insofar as things which are for the most part are kath’hauto, and (3′) is a legitimate implication of (3), things which are for the most part, or are kath’hauto coincidentals or modifications, will satisfy requirement (3). Hence, these will be knowable, even though they are not ‘beneath every’ – and accordingly, not universal. What does Aristotle mean with the terms ‘necessity’ and ‘necessary’ in the contexts of proofs? Aristotle allows the involvement of two kinds of necessity: axiomatic and compositional. Axiomatic Necessity. This kind of necessity, Aristotle says, occurs in the sciences (mathêmata), exemplified quintessentially by mathematics. Axiomatic necessity is such that given some elements, primary statements or definitions, it is necessary that certain things follow (or in Aristotle’s parlance, are) from them. These elements, primary statements or definitions are the matter, underlying thing or genus for that science or body of knowledge, to which of course proofs are crucial: A proof is composed of things which are necessary, because if one has proven something without qualification, it is not possible for it to be otherwise. The primaries are the causes of this.… Certainly of some things, something else is a cause of their being necessary; of other things, nothing else, but on account of these, others are from necessity. Therefore, the primary and the unqualified are properly necessary: it is not possible for what is primary and unqualified to be in multiple ways such that it is not otherwise and otherwise, for just then it would be in multiple ways. Thus, if there are things which are unconditional and unchangeable, nothing is coercive to those or contrary to their nature. (Meta. V.5.1015b6–15)13 Some things in a proof are the source of other things being necessary, but there is nothing that makes these necessary. These things are most properly what is primary and unqualified, and are unconditional and unchangeable. In contrast, some things are necessary due to something else; it is impossible for these to be otherwise due to that something. For example, take the straight in geometry. (We would likely use ‘the line’ instead of ‘the straight.’) Since the line is of a certain nature, once one starts doing things with them, creating shapes with them, examining their relationship with other lines outside of shapes, and so on, certain things will necessarily follow. For example, Aristotle says that if there is the straight, from necessity a triangle has angles equal to two right angles: it is on

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account of, or due to (‘dia’+accusative), the straight or the line and what it is that triangles have angles equal to two right angles. However, the reverse is not the case, for the straight is not what it is due to triangles and what they are. The straight is unqualified and primary, and accordingly, necessary without qualification. Triangles and their nature are necessary due to the nature of the straight; the straight is the genus, matter or underlying thing; the triangle and its features are, or follow from, the straight from necessity. Such features are the kath’hauto coincidentals of the straight. However, Aristotle says, if it turned out that it was not the case that triangles had angles equal to two right angles, we would be able to determine that the straight was not what we took it to be either (Phys. II.9.200a15–19). Suppose there was in fact no genuine thing in the world that is the straight (or the line), despite the fact that one could still prove things about triangles from lines, say if Euclidian geometry were completely false. Aristotle says what would follow from these proofs would not be necessary without qualification, for the declamation that lines exist, agreed upon by geometers and mathematicians, would be false. Aristotle calls such proofs grounded in a declamation, not in matter (Phys. II.9.199b34–35). Compositional Necessity.14 In regard to compositional necessity, it is important to note that for Aristotle three of the kinds of cause ‘come into one: on the one hand, the specification [ti esti] and the “for the sake of which” are one, and on the other, from what the change initially is in respect of form, is the same as these’ (Phys. II.7.198a24–26). The ‘for the sake of something’ is in things which are and come to be by nature. The specification and the shape are examples of things which cause change while not being changed, and these are an end and are for the sake of something (Phys. II.8.199a7–8, II.7.198b1–4). Aristotle concludes that ‘since nature is twofold, the one as matter and the other as shape, and the latter is the end, and the rest are for the sake of the end, the latter will be the cause, the “for the sake of which”’ (Phys. II.8.199a30–32). What is necessary compositionally occurs whenever there is an end or a ‘for the sake of which.’ Compositional necessity is such that, given such an end, certain things are necessary in order for this end to be or to come to be. Take the wall of a house. Aristotle says one might think that a wall has come to be from necessity because things which are heavy are by nature borne downwards and the light upwards. This view treats the formation of the wall as involving a kind of axiomatic necessity, with weight being like the straight in the example above: It follows from the nature of weight that something heavier will rest more solidly on the ground than something lighter. Thus it follows necessarily that the heaviest and largest stones and foundations will be placed closest to or in the earth, bricks and the like are

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in the middle and come second, and the wooden rafters and beams on top comes third, since they are the lightest. In short, given weight, it is a necessity that the wall comes to be in this way. Although it is true that the wall does not come to be without these things (the stones, bricks, wood, and weight), regardless the wall is on account of these things only insofar as being matter for the sake of concealing, protecting or supporting something. The initial cause here then is the ‘for the sake of which,’ and not the weight. Thus, Aristotle says, given this end, the wall is necessary, and the stones, bricks, and the like are the matter necessary for the coming to be of this wall. For another example, take a saw. A saw exists for the sake of cleanly cutting wood. However, it is incapable of cleanly cutting wood unless it is made of a certain kind of matter, like iron. Therefore, iron is something necessary for a saw. Therefore, if a house will be, it is a necessity that these things come to be or belong, or are in short the matter for the sake of something, like bricks and stones, if a house. Nevertheless, the end is on account of these things only as matter, and will be on account of these. Generally then neither the house nor the saw will exist unless these things are, the one will not exist unless there are stones, the other unless there is iron.... (Phys. II.9.200a24–29)15 In general then, for any ‘for the sake of which’ or end, in order for this end to come about, certain materials, underlying things or genera are necessary; without this matter the end will neither exist nor come to be. So in the things which come to be for the sake of something, if the end will be or exists, the thing before it – i.e., the appropriate matter – will be or exists: ‘If the end will be or exists, also the thing which is ahead of this will be or exists’ (Phys. II.9.200a20). If there is not the appropriate matter, the end will not exist, just as if it were the case that without a conclusion the appropriate starting points would not exist. Therefore, compositional necessity is sequentially opposite to axiomatic necessity: for the former, given some last thing, some things are necessary first; for the latter, given some first thing, some things subsequently follow necessarily. If the necessity in geometry were compositional, the fact that a triangle has angles equal to two right angles would necessitate the existence of the straight. For this reason, Aristotle concludes that the ‘for the sake of which’ is in the account, the necessary is in the matter (Phys. II.9.200a14–15). In his commentary on the Physics, W.D. Ross has a very helpful characterization of the difference between axiomatic and compositional necessity. The necessity of the former ‘proceeds from ground to consequence’ or

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perhaps more in line with Aristotle’s terminology, from cause to effect. The necessity of the latter ‘proceeds from ends to preconditions; if the end is to be achieved the preconditions must be so and so, and if these are not present the end will not be achieved.’ Ross adds that both kinds can be considered as instances of necessitation as well as necessity: the premise statements necessitate a conclusion; an end necessitates certain preconditions (Ross 1988, 531–532).16

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The Four Causes

An interesting and apparently underappreciated feature of Aristotle’s four causes is that they are divided into two pairs, with each member of the pair being a causal precondition for the other. Since they are so interconnected, it is reasonable to hold that if any one cause is knowable, then its corresponding member is also knowable. Take for example the first pair of causes: ‘when there are certain things it is a necessity this thing is’

essence

Now take the following pairs of items: letters materials/ingredients elements parts declamations

syllables preparable things bodies wholes conclusions

Aristotle explains the columns as follows: Every item in the first column is a cause or starting point of the second as the underlying thing of that item (Meta. V.2.1013a24–26, b17–22). The second item comes to be from the first, so in this respect the second is in the first as a potential. With each first item (elements, parts, declamations, etc.), when they are established in a certain durable, change-resistant array, it is a necessity this second item exists (bodies, wholes, conclusions, etc.). Every item in the second column is a cause or starting point of the first as an essence. This essence is a whole, a form (or alternatively, a paradigm or a shape) and a synthesis, either of genera and differences, or of the elements or parts comprising the proximate matter of that essence. The second item has the first item, which is in the second, in an actual, active or

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purposive way. The form is also the account of the essence and its genera, which are the parts in that account. This kind of account is a definition (Meta. V.2.1013a26–29, b22–23, 8.1017b21–23, 25–26). The two meanings of the term ‘nature’ correspond to these two kinds of cause (Meta. V.4.1014b17–18, 26ff., 35ff.). The two meanings of ‘reality’ (‘ousia’) also correspond to these two causes: ‘It follows truly that “reality” is said in respect of two ways: the final underlying thing that is no longer said of something else, and what, being a certain this, is also separable – such a thing is the shape and the form of each thing’ (Meta. V.8.1017b23–26). Thus, (i) the essence (the whole, synthesis and form or nature and reality in one sense each), and (ii) the ‘when there are certain things it is a necessity this thing is’ (the parts, matter, elements and underlying thing, or nature and reality in another sense each) are two kinds of starting points that are potential, recognizable candidates for requirement (1/4). Each is in the other, either potentially or actually. Now take the second pair of causes: what first changed something

the ‘for the sake of something’

Now take the following pairs of items: seeds doctor one who has just deliberated

plants health object of pursuit or avoidance

Aristotle explains these as follows: Each item in the first column here is a starting point of transition, ‘stasis’ or stillness. Each first item initially changes something (Meta. V.2.1013a29–32, b23–25). So for example, one who has just made a certain choice about what to eat causes certain foods to be prepared and ingested, and this choice is the starting point of that preparation and ingestion. Each item in the second column is last or final (eskatê), the end (to telos) or the good of other things. The ‘for the sake of which’ one wishes is the best and the good of other things, and this good can be either genuinely or apparently good (Meta. V.2.1013a32–33, b25–28; Phys. II.3.195a23–26). The good, the fine, and the ‘for the sake of which’ are therefore also starting points for change and the recognition of many things. The first kind of cause in this pair is called ‘nature’ if it occurs as the primary source of change within some natural thing and as belonging to that very thing either potentially or actually, otherwise it is not called ‘nature’ (Meta. V.4.1014b18ff.; cf. Phys. II.8.199b15–18). The second kind in this pair can also be called ‘nature’ in some cases: ‘nature does make a

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“for the sake of something”’ (AnPo. II.11.94b36; cf. Phys. II.2.194a28–30, II.8.198b10ff.). These third and fourth kinds of causes, like the first two, are also internal in some cases. For example, the first source of change can be internal and natural either in a more literal sense (e.g., the source of degradation in one’s body) or in a more figurative sense (e.g., a choice made by a human being, for it is by nature that human beings have the ability to make choices). The ‘for the sake of which’ is internal and natural when it is the shape or the specification of something (Phys. II.7.198b1–5). In contrast, a first source of change that is external to a thing – for example, a doctor removing a tumor in an ill patient – is not called ‘nature,’ for the doctor’s removal does not occur within that patient, is not a part of what that patient is.1 However, she is the starting point of that patient’s return to health. Say this sick person submits to the doctor’s scalpel for the sake of his child. This child is outside that patient, and is not called ‘nature’ either (although the desire prompting such a ‘for the sake of which’ might very well be natural, if such desire is part of what it is to be a human being). In both of these cases, the things in the world that are the effects (removal of a tumor, submission to the scalpel) have a single underlying thing (the patient), which has the potential to undergo such effects by the causes involved (the doctor, one’s child). The two kinds of necessity discussed above match this pairing. Axiomatic necessity occurs in the reckoning or deliberation involved in skill and prudence. Given a certain end, say a good, certain things follow from necessity. This end is an instance of ‘the for the sake of which’ cause. One’s deliberation has determined what these things are (Phys. II.9.200a22–24). Compositional necessity occurs in the materialization of this skill or choice, and is sequentially opposite to axiomatic necessity. Corresponding to the above pairing, this is an instance of ‘the initial changer of something’ cause. The examples of the house and the saw above show how: given an end, certain material things are necessary before this last thing, the house or saw, comes to be. In a way then, Aristotle concludes, nature mirrors this deliberation: It is truly evident that the necessary in things which are natural is the thing which is said as matter and its [the matter’s] changes.... This [the end] is a cause of the matter, but not this of the end; the end is the ‘for the sake of which,’ and the starting point is from the definition, i.e., the account, as in the things which come about by virtue of skill – since the house is such, these things must belong and come to be from necessity, and since health is such, these things must belong and come to be from necessity – and so if human is such, these, and if these, these. Perhaps

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even in the account there is the necessary, for if you define the product of sawing that it is division of a certain sort, this will not exist unless it will have teeth of a certain sort, and these will not exist unless they are iron – in the account some sections of the account are as matter. (Phys. II.9.200a30–b8) Take a certain natural form, say human. This is an initial thing, a starting point. Say the account of human includes user of a language. A certain kind of matter thence follows by axiomatic necessity from this account: appropriate vocal and gestural apparatus, corresponding neural networks to use them, sufficient perceptual inputs, and so on. All of these in turn necessitate appropriate underlying chemical and physical materials. This account then is the cause of the matter in this sense; the matter in this sense is not the cause of the account. The products of skill work similarly. Say the end is shelter from the weather. (Shelter from the weather will be the good in this case.) A technician deliberates, and concludes a certain kind of house is the best way to satisfy this end. A house, he continues, thence necessarily requires, by means of an account obtained through skill, certain things: multiple walls, a roof, foundations, and so on. Appropriate materials for these walls, etc. then follow by axiomatic necessity from this account. (The deliberation of a more skillful technician will necessitate certain plans and materials over others, and the end product will be better than another technician’s work. She thence will not only build, but will build well.) Similarly with health and metalworking. For some things in the world, the matter will even appear in the account, for example iron in the case of the saw: what it is to be a saw, Aristotle says, is in part to be made of iron. The iron here is the ‘necessary’ appearing in the account. Compositionally however, both in regard to nature and to skills and deliberation, the matter comes first from necessity in order for the end to materialize, and in this respect, the matter is the cause or starting point of the form or end. In this way, say in regard to human, the genera and differences living thing, animal, mammal, primate, user of a language, and so on are compositionally necessary in order for human, and thereby a human being, to exist. These genera and differences are the matter for human. This is how a natural form is an end or final thing as well as a first thing. This material here further supports my contention that the parts of a form are not only the genus and its differences, but also things like head, hand, flesh, and the like. When taken as a final thing, the form’s matter are the genera and differences; when the form is a starting point, its matter is flesh, head, hand, larynx, and so on.

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For the Most Part

Aristotle’s requirement (3) for knowledge is this: A cause or starting point a of some thing in the world t is knowable only if it is not possible for t not to be caused by a. An implication of (3) is (3′): A cause or starting point a of some thing in the world of t is knowable only if it is necessary that if t, then a is the cause of t. This implication does not maintain that t always is present, that t is a necessary or ‘eternal’ existent, or that t is present with every instance of a. Instead, (3′) only maintains that, necessarily, if t is present, then a is the cause of t. It is not a problem as to whether t is present, nor is it a problem if a is present but t is not. The only problem is whether when t is present, a is the cause of t, and whether this conditional is necessary or contingent. Using Aristotle’s example, let ‘a’ be ‘being a man’ and ‘t’ be ‘having a beard.’ Having a beard belongs to men kath’hauto: it is by virtue of being a man itself that men have beards. However, not every man has a beard, and so having a beard does not satisfy the ‘beneath every’ requirement. Nevertheless, it seems necessary that if someone has a beard, then it is by virtue of being a man that that person has that beard, even though, as Aristotle has said, it is not true in every case that men have beards. Similarly, the ability to nurse is a kath’hauto feature of being a woman. However, not every woman can nurse, nor is an individual woman always able to nurse. Regardless, necessarily, if someone has the ability to nurse, then it is by virtue of being a woman that that person has the ability to nurse. Thus, men for the most part have beards, and women for the most part have the ability to nurse.

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(3′) is in my view the basis for the best interpretation of what ‘for the most part’ means for Aristotle. So Aristotle’s notion of ‘for the most part’ is a conditional bound by a necessity operator. Again, since such facts in the examples above satisfy requirement (3′), one can also know these two facts about the natural world, and not just believe them. However, Aristotle states that things which are for the most part are contrary to things which are ‘for the least part’ (ep’elatton, Top. II.6.112b10–11). Things which are for the least part will then also be of the form of (3′). Since things which are for the most part are kath’hauto, due to the nature of contraries for Aristotle, things which are for the least part will also be kath’hauto. Thus, that which will distinguish things which are for the least part from things which are for the most part will be a statistical requirement: instead of being ‘beneath every,’ things which are for the most part will be ‘beneath many,’ and things which are for the least part will be ‘beneath few.’ Thus for example, for human beings, births of maternal twins occur. It is necessary that if a birth of maternal twins occurs, then the division of one egg after fertilization is the cause of the birth of maternal twins occurring. It is by virtue of, or due to the nature of, this division that maternal twins occur. Births of maternal twins, however, occur statistically for the least part, i.e., ‘beneath few’ of the overall amount of births. Therefore, the birth of maternal twins is for human beings neither universal, for the most part nor by chance, but for the least part. These three requirements parallel the three requirements for a feature to be universal, as stated above: A feature is universal if and only if (i) this feature exists by virtue of what that thing is to which it belongs, (ii) it is from necessity, and (iii) it is ‘beneath every.’ Therefore, ‘for the most part’ and ‘for the least part’ seem not to be just modal, temporal or statistical terms, but terms of the same kind as ‘universal.’ The plausibility of this interpretation is augmented by the fact that it resolves two apparent difficulties involved with this notion that have been persistently raised by previous commentators. The first difficulty is that many think Aristotle is stuck in a skeptical morass between the necessity requirement in his account of knowledge, and his claim that things in the natural world – which provide many of his examples of knowledge – occur mainly for the most part. My interpretation shows how something can be for the most part, but also necessary – and hence, knowable. Thus there is no skeptical difficulty between his modal requirement for knowledge and his view of the natural world. The second difficulty is the apparently inconsistent things with which Aristotle contrasts and compares ‘for the most part.’1 My interpretation accommodates these contrasts and comparisons. In some instances,

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Aristotle seems to contrast ‘for the most part’ with ‘every,’ which makes it appear to be a statistical notion (e.g., HA V.14.545a14–18; PA III.2.663a28). In others, he contrasts it with ‘always,’ which seems to imply ‘for the most part’ is a temporal notion (e.g. AnPo. II.12.96a18–22; Top. V.1.129a6–16; Phys. II.5.196b10). Since ‘for the most part’ contains a conditional, and since the consequent of this conditional can be true with the antecedent being false (when a can exist without t existing), things which are for the most part are not ‘beneath every.’ Similarly, things which are for the most part are not always the case in that a sometimes exists without t. In other instances, Aristotle contrasts ‘for the most part’ with ‘necessarily,’ and even at times compares it to ‘possibly’ (e.g. DI 9.19a18–22, AnPr. I.13.32b5–10, Top. II.6.112b1–9 for the former; AnPr. I.3.25b14–15, I.13.32b4–11 for the latter). ‘For the most part’ contrasts with ‘necessarily’ insofar as the latter is ‘beneath every,’ whereas the former is not. Moreover, since what is for the most part is necessary, and what is necessary is also possible, what is for the most part can be compared to, and considered as, a kind of possibility, with universality and for the least part (and perhaps even chance) being other kinds of possibility.

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Requirements (R) and (M): Recognition and ‘Recognized More’

Aristotle’s theory of knowledge is a hybrid containing elements that can be called externalist and internalist. The more externalist requirements (1)–(4) concern causes, truth, and relevance based on genera, and what kind of causes are knowable. The internalist requirements are (R), (P), and (M). (R) requires that one recognizes (root gnô-) the initial cause or starting point. (R) is minimally internalist in that the thinker has to cognitively grasp or get the starting point in a certain way, but contemporary externalist theories all involve something like this, be it tracking the truth, processes, faculties or the like. So even though it barely seems to be a requirement, I examine (R) because it has received virtually no attention by Aristotle’s commentators (and in my view is perpetually mistranslated), and it is crucial for understanding (M). (M) is a more substantive internalist requirement, and states that one must recognize the starting point more than the conclusion in a proof, otherwise one will know only coincidentally. Requirement (M) then is the same as (R) except that it is somehow stronger, and passages concerning (M) help to illuminate (R). (P) is Aristotle’s strong internalist requirement, and indicates that in addition to this recognition, confidence (pistis) is requisite for someone to know without qualification. In order to know without qualification, one must satisfy all of the requirements. If one satisfies just the internalist ones, but misses one or more externalist requirements, one does not know at all. If one satisifies the externalist requirements (and basically one has to satisfy (R) in order to have them in mind), but does not satisfy (M) or (P), then one knows coincidentally. So overall one can classify Aristotle’s position as predominantly externalist – but not entirely! I will start with (R) and (M). Aristotle uses the term ‘recognized’ (gnôrimos) in his theory of knowledge in regard to both expressions and

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things. (I use ‘expression’ in order to encompass terms, statements, and accounts such as proofs or stories.) Unfortunately, a clear explanation of this term is available only for the former use. However, from this explanation, we can develop a general explanation for the latter use. In order to know something, either derivatively or primarily, Aristotle requires that all of the linguistic expressions involved must be recognized. Aristotle states ‘[i]t must be then that each of the words is recognized, that is, reveals something, and not many things, but just one; if it does signify several things, one must make evident towards which of these the name applies’ (Meta. XI.5.1062a13–16).1 Given sufficient competence in the language between the speakers involved, an expression is recognized in at least an epistemological context if and only if that expression has only one clear signification. In other words, one recognizes an expression if and only if the meaning of that expression is not ambiguous and not vague. Simply hearing, thinking or even generally understanding the expression is not enough. An expression reveals something only if it is not vague; an expression reveals just one thing only if it is not ambiguous. Recognition does not imply that that expression is true: one can recognize a false expression. One can also see that it is unlikely requirement (M) involves just this kind of linguistic recognition, for an expression genuinely available for a proof is either ambiguous or not, and vague or not. If this expression is ambiguous or vague to any extent, it will not be recognized according to the definition above, and hence will neither communicate nor lead to knowledge. This linguistic kind of recognition provides a rudimentary explanation for understanding what the recognition of things is: Let ‘a’ signify some thing which is recognizable, and ‘p’ signify a creature which has the potential to recognize a. Some a is recognized by p if and only if a has been revealed to p in some unambiguous and clear manner. Corresponding to the linguistic, this kind of recognition seems to be more than just thinking something, and need not be of something true. Both kinds of ‘revelation’ then require a truth condition, something I have argued Aristotle has provided. Support for this rudimentary explanation comes from passages concerning definitions. For example, Aristotle says one of the ways one might construct a poor definition is by using an unclear interpretation. (‘Interpretation’ (‘hêrmeneia’) here means approximately ‘representing linguistically some thing in the world.’) For the one who is doing the

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defining, one must use the clearest interpretation possible, since definitions are offered for the sake of recognizing (Top. VI.1.139b12–15, 11.149a26–27).2 This ‘recognizing’ can be understood in two ways. First, one is made to recognize what is signified by means of that clear definition, and this is a reality: ‘[I]f the definition is the making recognized of some reality, it is evident that such things [i.e., definitions] at least are not realities’ (AnPo. II.3.90b16–17; cf. Top. VI.4.141a26ff.). Definitions are not realities; however, one comes to recognize realities on account of, or by means of, them. In this way, definitions are offered for the sake of revealing a reality in an unambiguous and clear manner. So if definitions (or any statements in proofs more generally) are ambiguous or vague, one will not recognize the realities they signify. These realities then will not be revealed to some thinker by means of these definitions, at least not unambiguously or clearly. The second way of understanding ‘recognizing’ in the passage from the Topics above is as follows: Since there are some definitions which signify realities, and realities are starting points for proofs, ‘it is necessary to recognize each of these [starting points] by a definition’ (Top. VIII.3.158b3–4; cf. AnPo. II.3.90b24). These definitions are then the starting points for proofs, and from them one may prove or show other things. However, it is not possible (at least theoretically), to show or prove these definitions by means of other statements, declamations or definitions. Such definitions and what they signify are, in Aristotle’s terminology, by nature recognized (and hence recognizable) ‘by means of themselves.’ That is, they are somehow self-evident. Things which are not starting points, like non-primary, mediate statements and what they signify, are not recognizable by means of themselves (AnPr. II.16.64b34–36, 65a8–9). Instead, they are recognized by means of other things, namely by means of these definitions, other starting points like declamations, and what they signify (e.g., AnPo. I.2.72a14–24). These definitions and the rest are for the sake of recognizing non-primary, mediate statements and conclusions and what these signify.3 We can now develop the rudimentary explanation of ‘recognized’ above. If some thing in the world is revealed to a thinker without any intermediary – that is, it is self-evident – this thing is revealed in a clear and unambiguous manner. It is necessary that one recognize the starting point or initial cause in order to know something. Therefore, a is recognized by p if and only if a has been revealed to p and a is selfevident; a may be either a definition or declamation, or the reality signified by that definition or declamation.

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For Aristotle, one should understand ‘self-evident’ minimally as ‘selfrevealing,’ ‘self-presenting,’ or as ‘able to reveal itself to a thinker without any intermediary.’ In this way, something that is self-evident can be recognized ‘by means of itself,’ ‘just due to what it is.’ Self-evidence is not due to anything a thinker has done, and does not imply some sort of special normative trait or experiential quality. One can determine further that, given recognition of some self-evident starting point or cause a, anything properly determined from a will carry with it that clarity and unambiguity. It is the role of Aristotle’s logical procedures to guarantee that proper determination. Therefore, a non-primary, mediate s is recognized by p if and only if s is revealed to p by means of a in accordance with logic; s is either a non-primary, mediate statement or the reality signified by that statement. This s then is not self-evident, but comes to be recognized by means of something self-evident, together with a logical procedure. Both of these accounts presume that if expressions are involved, Aristotle’s criteria for linguistic recognition are satisfied.4 Upon consideration of these two accounts, one might object as follows: It seems likely that p will often recognize s, which is neither primary nor a starting point, before a, which is primary and a cause or starting point, especially if p is a child or a learner. If so, then p will come to recognize a by means of s. For example, a child will certainly recognize that mom is human before she or he will recognize that all mothers are animals that use a language. This order also seems contrary to what (M) requires, namely that one recognize a ‘more than’ s, for the child will clearly recognize s more than a in the process of learning and development. Aristotle recognizes this likelihood and divides recognition, and priority also, into two kinds, much like he does with knowledge: by nature or without qualification, and by us. ‘One must begin from the things which are recognized, but these are twofold: ones by us, and ones without qualification. Perhaps then, for us at least, one must begin from the things that are recognized by us’ (EN I.4.1095b2–3).5 In fact, Aristotle says, regarding most instances of learning, everybody proceeds from what is less recognized by nature (i.e., what is more recognized by us) to what is more recognized by nature (i.e., less recognized by us). The exception is when one recognizes a certain fact about some particular, not said of an underlying thing, simultaneously with the recognition of a universal that encompasses that particular (AnPo. I.1.71a17–24). So a child will recognize first that her

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mother is human, and perhaps later will come to recognize without qualification and by nature that all mothers are human. This order of recognition also occurs in other fields of learning. In respect of various kinds of action (praxis), Aristotle says one ultimately comes to make or do things which are good generally, and then turn these things into something good for an individual, initially by starting with doing or making things which were merely good for an individual. In the same manner, one ultimately comes to see things that are recognized by nature initially by starting with just seeing things that are recognized by oneself. Thus primary things recognized by oneself are often just slightly recognized, and often capture little or nothing of what reality is like. Nevertheless, one must try to recognize the things that are without qualification recognizable out of the things which are poorly recognizable, but recognizable by oneself. So, what is clear and is more recognized in regard to an account, like a definition, declamation, proof, other syllogism and so on, starts by coming from what is unclear but more readily apparent to us (Meta. VII.3.1029b3–11; DA II.2.413a11–12). What is recognized by nature or without qualification, and hence recognizable in general, and what is recognized, and recognizable, by us? Material concerning requirement (M) helps to answer this question. Aristotle states: ‘More prior’ and ‘more recognized’ are twofold, for ‘more prior’ by nature is not the same as ‘more prior’ in regard to us, nor ‘more recognized’ and ‘more recognized’ by us. I say ‘more prior and more recognized in regard to us’ are the things which are nearer to perception; ‘more prior and more recognized without qualification’ things which are farther. Farthest are the universals most of all, nearest the particulars, and these are opposed to each other. (AnPo. I.2.71b33–72a5) What is more prior and recognized by us are the primary counterparts to perception, namely particulars (ta kath’hekasta). What is more prior and recognized by nature are universals (ta katholou). Universals are, in Aristotle’s terms, farthest away from perception. Thus in most cases of learning or investigation, one begins with particulars: these are more prior and readily apparent to us, but are also more cognitively unclear. Ultimately, at the conclusion of one’s learning or investigation, one will end with universals. At this point, these universals will be recognized without qualification, seen as prior by that student or investigator, and will then be recognized more than the particulars with which they began: Unlike what is perceived, what is universal is clear, and is by nature more prior and

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more recognized than particulars. A universal is prior without qualification or by nature in that it encompasses all, or is ‘beneath every’ one of, its particulars as a whole. These particulars are as parts to this whole (Phys. I.1.184a21–184b14). In respect of an account, like a proof, the universal is prior to the particular – and hence will be recognized before, and be more recognized than, the particular. This occurs even though in respect of perception, the particular is prior – and here will be recognized before, and is more prior to, the universal (Meta. V.11.1018b30–34). It is important to remember that Aristotle is using the term ‘universal’ in his way, as I explained in chapter 8. So in learning, the order of recognition is like that raised by the objector at the beginning of this section: One starts with rudimentary perceptions, which are prior and more recognized by us, and perhaps ultimately arrives at some universals. This order, from particular to universal, is contrary to the natural order of things. However, in knowing, the order of recognition is the reverse. One starts with the universal, which is prior and more recognized by nature. This is unqualified recognition. The universal encompasses its instances as a whole to parts. These include the ultimate, final particulars. So by recognizing the universal, one has the potential to recognize all of the particulars encompassed and caused by it. However, by recognizing particulars, one, several or many, one does not necessarily recognize the universal cause of which they are the effects, but does have the potential to do so. A proof corresponds to this natural priority of what is more universal to what is less universal. Thus, in regard to knowledge and the recognition involved therein, the student or investigator will reverse the order with which one began their learning or investigation, and start with what is universal and then move to what is less universal, yet encompassed and caused by that universal. Take for example someone trying to teach a new, typical student some geometry. What is closest to perception, and hence more recognized by that student, are three-dimensional objects, e.g., a cube. What is farther from perception and more universal (and hence prior and more recognized by nature) are two-dimensional objects, and even farther away are such things as lines or points. In such instances, the teacher explains what a plane is using what is more recognized by that student, namely solids, and thus states that a plane is the limit of a solid. However, it must not escape one’s notice that it is not possible for those who are defining in this manner to reveal the essence of the thing being defined – unless it happens that what is more recognized by us is the same as what is more recognized without qualification – since one who defines

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finely must define through the genus and its differences, and these are of the things which are without qualification more recognized than and prior to the form: the genus and the difference destroys the form together with them, therefore these are prior to the form. These are also more recognized: when the form is being recognized, it is a necessity that both the genus and the difference are recognized (one recognizing human also recognizes living thing and terrestrial), but when the genus and difference is being recognized, it is not a necessity that the form is also recognized; therefore, the form is more unrecognizable. (Top. VI.4.141b22–34) The teacher who is defining plane in this way for the student is not revealing the essence to that student, for the definition that a plane is the limit of a solid does not capture the natural order of geometry and the axiomatic necessity involved in it. The solid is a form, Aristotle says, which is metaphysically dependent upon the genera and differences which comprise that form. Unqualified recognition mirrors the natural order of dependence, whereas the recognition of the student does not. This fact means the student is still recognizing what is final or ultimate, like a solid or a conclusion of a proof, more than what is prior or first, such as point: the former is more recognized and prior by us than the latter, but by nature this order is reversed. The student then will have at best coincidental knowledge about planes despite having that definition for the following reasons: First, they have not recognized the things in the world occurring in their natural order of priority and ontological dependence. Second, since they have not recognized the whole without qualification – that is, the genus and what follows from axiomatic necessity – it is still possible for them that there are particulars which are not encompassed or caused by the putative whole one does recognize. In short, the student has not recognized the essence of what is at issue. From both reasons, requirements (1), (2), and (3) have not been satisfied. Why is unqualified recognition important? In order to combat Protagorean subjectivism. Aristotle holds that if such ‘recognized by us’ definitions were, by definition of ‘recognized by us,’ ultimately in accordance with truth, then there would be multiple (and presumably mutually exclusive) true definitions: First, what is recognized by some people is not recognized by others (Top. VI.4.141b34–142a2). Second, the degree of one’s recognition of something can change for a single individual over time, even though the status of that thing does not change. For example, what is at first recognized more geometrically for that student is what is

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closer to perception, like solids. After many lessons, what is more recognized by nature becomes more recognized, and recognized without qualification, by that student, like points. Yet once the lessons are over, and the student has forgotten everything learned, then solids will be more recognized again (Top. VI.4.142a2–6). However, there is only one genuinely true order, and this is by nature. In regard to definitions, [i]t is clear then that one must not define by means of such things but by means of the things which are more recognized without qualification, for only so will the definition come to be one and the same. Perhaps too the thing which is recognized without qualification is not recognized for everybody, but recognized for those who are constituted well in terms of their thinking, just as what is healthy without qualification is healthy for those who are well in terms of their body. (Top. VI.4.142a6–11) So in order to know, one must recognize a statement and what it signifies without qualification. Even if one has a proof, say in the case of a new student, one will have only coincidental knowledge if one still has not recognized without qualification what is more universal. Once one has recognized the natural order of things in the world in this way, one will recognize the starting point or initial cause more than the conclusion, for this starting point will be the whole, of which the conclusion is a part, and it will be the cause of the conclusion, both in nature and in a proof. This analysis explains how Answer 4 works: one ‘knows whenever one is somehow confident and the starting points are recognized by one – if not more than the conclusion, one will have knowledge coincidentally.’ The ‘more than’ is a very succinct way of indicating requirements (2) and (3) from the third answer, with ‘starting points’ capturing (1). Also, the ‘more than’ here is a way of clarifying that the meaning of ‘by one’ does not mean the ‘by one’ that is contrary to ‘without qualification’ or ‘by nature.’ Due to the natural order of priority and recognition, in regard to a proof, if one recognizes starting points without qualification, one will recognize them before their conclusions. For this reason, Aristotle uses the phrases ‘recognize more’ in connection with ‘recognize beforehand.’ Since one must be confident and see the thing in the world by having the sort of syllogism that we call a proof ... it is necessary not only to recognize the primaries beforehand – either all or some – but also more, for on account of which each thing belongs, it belongs more to that. For example, on account of which we love, that is beloved more. [emphasis mine] (AnPo. I.2.72a25–30)

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In learning, the temporal order of recognition was the reverse of the logical order: we come to recognize what is more recognized by nature temporally after what is more recognized by us, even though the former is logically prior to the latter. Correspondingly, the ‘beforehand’ here is one of logical priority, and not temporal. For example, say one loves one’s dogs on account of their natural sweetness. Of all of the traits they have, this sweetness is beloved more than any of the others, for example, breed, size or color. One initially comes to recognize the dog’s breed, size or color before its sweetness; however, once one comes to love the dog, its sweetness is recognized before them. In regard to a proof, if one recognizes without qualification some thing in the world, which is a cause of another, one will recognize that cause before that other thing. In the same way as the case with the dogs, since that effect is recognized on account of its cause, that cause will be recognized more than – i.e, before in a logical sense – that effect. Such recognition is required in order to know by means of a proof, as indicated by (M). Furthermore, one can see that by genuinely satisfying requirement (1/4) – recognition of the starting point of some thing in the world – one will satisfy requirement (M). Such genuine recognition will be without qualification, and not in some respect by us. When this is the case, what is more recognized will also be recognized beforehand and vice versa. So when arguing that in order to know, the statements of a proof must be causes of, prior to, and more recognized than the conclusion, Aristotle explains these must be ‘causes because we know at that time whenever we see the cause, and prior if indeed they are causes, and recognized beforehand not only in respect of the discerning (xunienai), but also in respect of the seeing (eidenai) that it is’ [emphasis mine] (AnPo. I.2.71b30–33).6 I can now formulate a more satisfactory definition of recognition. For Aristotle, knowledge involves the recognition of the universal, proofs are constructed from universals and not particulars (‘finals’). Recognition of what is universal is recognition without qualification and by nature, not by us. Thus, adequately for knowledge: A starting point or cause a is recognized without qualification by some thinker p if and only if a has been revealed to p and a is self-evident; a may be either a definition or declamation, or the reality signified by that definition or declamation. A non-primary, mediate s is recognized without qualification by p if and only if s is revealed to p by means of a in accordance with logic; s is either a nonprimary, mediate statement or the reality signified by that statement.

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These accounts presume that the criteria for linguistic recognition are satisfied. By adding ‘without qualification,’ one handles the objection raised above that holds it seems likely that p recognizes s before a, which in turn seemed contrary to what (M) requires. I can also now explicate what ‘has been revealed’ means, thanks to this material and Posterior Analytics I.2.71b30–33 quoted above. This revelation requires a combination of both the discernment of some a or s and the seeing that a or s is. First, concerning ‘to see’ (‘eidenai’), Aristotle says that ‘[r]ecognizing whether one sees or not is difficult, for recognizing if we see from the starting point of each thing is difficult – the very thing that seeing is’ [emphasis mine] (AnPo. I.9.76a26–28).7 What ‘seeing’ means is apparently a kind of psychological apprehension that arises from the starting point of some thing in the world x. If x, or some feature of it, is self-evident, its starting point will not be different from x itself. For realities, some of their features and their linguistic significations, these starting points will be the realities, features or the significations themselves. For everything else, their starting points will be these realities and some of their features. (Aristotle is also indicating here that second-order recognition of one’s ‘seeing’ is very difficult to obtain.) Thus, recognition has as one component the apprehension from the starting point of some x that x is the case. Concerning ‘discerning,’ Aristotle describes discernment (sunesis) as more like prudence than either knowledge or belief: discernment, like prudence, concerns what one is puzzled and deliberates about, and neither what is necessary or universal, nor whatever is contingent. However, prudence commands (that is, it orders what one must or must not do), whereas discernment judges or determines. Discernment is neither the having nor the acquiring of prudence, but just as it is said that to discern is to learn whenever one uses knowledge, so in the use of belief for the purpose of judging about the things that prudence is about when another is speaking, one judges finely. (‘Well’ is the same as ‘finely.’) Thence the word ‘discernment’ has been acquired, by virtue of which people are ‘perspicacious,’ from which comes learning – for we say that to discern frequently is learning. (EN VI.10.1143a11–18) Aristotle says that discernment and perspicacity, and being discerning and being perspicacious, are the same. The members of an audience come to a teacher or to an instructor in order to learn something about which they are confused, trying to work out, or are ignorant. This teacher uses her

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knowledge in order to instruct this audience. In turn, while she is offering what they want to know, the members of the audience use their beliefs (the hexeis whose primary counterpart are what is contingent) in order to judge or to determine what is being said. To judge this information well – that is to discern, ‘to get,’ what is being said – is to be perspicacious. If a member of the audience is perspicacious, he grasps, by means of his own experience, the items that are salient for resolving their puzzlement or deliberation. By discerning frequently what is being said during the teacher’s presentation, one learns – that is, one comes to know for oneself. When something has been revealed to someone, that thing both has been discerned and has been ‘seen’ that it is the case or so by that person. Thus, presuming the criteria for linguistic recognition are satisfied, the final analysis of requirements (R) and (M) for Aristotle’s account of knowledge is as follows: Requirement (R): A starting point or cause a is recognized without qualification by some thinker p if and only if a (i) has been discerned by p, and (ii) has been seen to be by p, and (iii) a is self-evident; a may be either a definition or declamation, or the reality signified by that definition or declamation. Requirement (M): A non-primary, mediate s is recognized without qualification by p if and only if s (i) has been discerned by p, and (ii) has been seen to be by p, from a in accordance with logic; s is either a non-primary, mediate statement or the reality signified by that statement. This analysis of (R) and (M) allows one to mesh nicely the statements concerning recognition in Answer 3 and Answer 4: In 3, recognition involves only requirement (1/4); this fact is indicated by (R) above. In 4, it again involves (1/4), and then Aristotle adds ‘if not more than the conclusion....’ Thus, the derivative statements which follow from (1/4) are to be recognized after in a logical, not temporal sense, those of (1/4). This requirement is indicated by (M). Discernment is the judging, ‘getting’ or determination of a or s by means of belief (that is, by means of the prior and present apprehension of contingent things in the world), in regard to knowledge being provided by teaching or instruction. ‘Seeing’ is the cognitive apprehension that x is from the starting point of x. If x is self-evident, x will be its own starting point. Coda. One important conclusion follows concerning (M). The ‘more than’ of (M) does not entail that recognition in Aristotle’s view comes in

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quantities. According to the quantity interpretation of ‘more than,’ in order to satisfy (M), one would need to have more recognition units of a, so to speak, than of s. Under its most plausible reading, it would make Aristotle’s position very much like the one Hume offers in the Enquiry concerning Human Understanding, where ideas vary in degrees of liveliness and vivacity. So in order to know, one would have to have a more lively and vivid perception of the starting point or initial cause a than of s, in order to know without qualification by means of a proof. However, as has been shown above, especially with the connection between ‘more than’ and ‘beforehand,’ this quantity interpretation does not seem to work. This connection between ‘more than’ and ‘before’ plays a role in the confidence involved in our knowing, and with confidence, a kind of liveliness and vivacity does play a role.

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Requirement (P): Confidence

The final requirement that we need to consider in order to complete our study of Aristotle’s theory of knowledge is (P). This is the strong internalist requirement in his theory. In order to know, a cognizer must ‘be confident somehow’ (EN VI.3.1139b33). ‘A proof is composed out of things which are more conducive to confidence and more prior’ (AnPr. II.16.64b32–33). What is confidence (pistis), and how does it work?1 As we will see, Aristotle has in mind with confidence something akin to a subjective indefeasibility condition. Modern analogues can be found for example in the work of Carl Ginet, Panayot Butchvarov, and Paul Moser.2 Linguistically expressed or discursive thought is the genus that underlies knowledge on the one hand, and prudence, skill, and factual belief on the other. It does not underlie nous or perception. Aristotle ties confidence to discursive thought, not to nous or perception. In his discussion of problems and mistakes that often arise in the formulation of a definition or other accounts in the Topics, he states that sometimes people offer the genus as a difference and the difference as a genus, e.g., terror as excess of astonishment, or confidence as robustness of discursive thought. Neither excess nor robustness are a genus, but a difference, for it seems terror is astonishment being excessive, and confidence a discursive thought which is robust. Therefore, astonishment and discursive thought are a genus, excess and robustness a difference. (Top. IV.5.126b13–20) People also err by taking something that arises concomitantly with another thing as the genus of that thing,

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like pain of anger and discursive thought of confidence: Both the things said follow beside their given forms in some way, but neither is their genus. For one who is being angered is pained when prior pain arises in them. The anger is not about the pain, but the pain is the cause of the anger; therefore anger is not pain without qualification. In accordance with the same things neither is confidence an instance of discursive thought: it is possible for one to have the same discursive thought and not be confident in it. It is not possible for something to continue being the same if it transitions entirely out of its forms, just as it is not possible for the same animal to be a man at one time, but not at another. If one were to say that from necessity one who is having a discursive thought is also confident, discursive thought and confidence will be said equivalently, and therefore neither would be a genus in this manner, for the genus must be said more widely. (Top. IV.5.125b29–126a2) The first passage states that robustness or excess are not generic elements of the psyche in their own right, supporting certain kinds of qualifications. If one were to treat robustness in particular as a kind of psychological genus, confidence as a form of robustness, and discursive thought a difference of this genus, discursive thought will be confident. However, human beings are confident, not an aspect of their psychology, just as knowledge is not something which knows nor change something which is changed. The second passage adds that confidence is not a form of discursive thought: Two different people, or the same person at different times, may both be confident and not confident in the same thought. However, if confidence were a form of discursive thought, this phenomenon would be impossible, because it is impossible for some one thing, which is of a certain genus and form, to change its form while remaining in the same genus (Top. IV.5.125b35–39). Moreover, if discursive thought entailed confidence, then wherever there was discursive thought, there would also be confidence – but this clearly is not the case. Just as anger is not a form of pain but is an effect of pain, so confidence is not a form of discursive thought but is an effect of it. In turn, not every pain results in anger; not every discursive thought results in confidence. Discursive thought is a cause of the confidence, but not because it is a genus which, when differentiated somehow, becomes confidence. From these two passages, we can conclude that confidence is the robustness of a discursive thought, and this robustness, in regard to the same thought, can change for the same person, or be different for different people.3 Confidence then for Aristotle is a difference or qualification, but not a form, of discursive thought. That is, it is a qualification or difference of the

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part of the psyche which has a logos or account. Whenever one has a discursive thought – knows, believes factually, deliberates technically or prudentially – and this thought has the characteristics of being robust, one will be confident in what one is thinking of. In contrast, whenever one has a discursive thought of something, and this thought has the characteristics of being weak or enervated, one will doubt it. Some things will be more conducive to confidence than others. (Greater conductivity to confidence does not however entail greater likelihood of truth.) Moreover, since discursive thought is a genus, and this genus can be qualified in a certain way, a fortiori, all of the forms and instances under that genus can be qualified in the same way. For example, if the genus star can be differentiated (in Aristotle’s terms, ‘qualified’) by a certain color (say blue, red, yellow, etc.), then all of the forms of star and their instances – giant, dwarf, neutron, pulsar, etc.; Sun, Arcturus, Sirius, etc. – can be differentiated by a certain color. Similarly, all of the forms and instances of the genus discursive thought can be qualified by degrees of confidence. Confidence then is the robustness of discursive thought, either generically, or in terms of its forms or instances. Now discursive thought is the part of the psyche which has an account. Instances of discursive thought, like an instance of knowledge or deliberative belief, have, or are with, accounts. If an account is robust, that account will be conducive to confidence for the one who has it. An example of the kind of account that is more conducive to confidence than any other kind is the principle of noncontradiction: There is a kind of starting point, among the things which are, about which it is not possible to have arrived at falsehood, but it is always necessary to take the contrary – I mean to arrive at truth – e.g., that it is not possible for the same thing, in respect of some thing and at the same time, to be and not to be, and the others which are opposed to themselves in this manner. Furthermore, there is without qualification no proof about such things, but there is in regard to this: it is not possible for a syllogism to be made from a starting point more conducive to confidence than this one, and it must be at least if at any rate the ‘having been proven’ will be. (Meta. XI.5.1061b34–1062a5)4 Even though there is no proof, but at best elenctic or transcendental arguments, of the principle of non-contradiction, Aristotle holds that since this principle elicits more confidence than any other, one is compelled to take it, and others of this kind, as true. If one does not, then proofs, and thereby knowledge, will be impossible.

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In contrast, when one has an account that is weak or enervated, one will doubt that account. For example, in regard to claims concerning the psyche, Aristotle says ‘[i]n every respect in every way, to obtain some confidence about this is among the things which are most difficult’ (DA I.1.402a10–11). He says similar things about the existence of numbers: ‘Would someone know, in our consideration, even concerning numbers, from what one must take confidence that they exist?’ (Meta. XIV.2.1090a2–4). However, when an account is strong in certain respects, but weak in others, one will have neither doubt nor confidence in it. For example, Aristotle says ‘one must have a discursive thought that it belongs to the naturalist to theorize also about the void, whether it is or not, how it is, and what it is, just as concerning place, for through the discursive thoughts about them, one has both doubt and confidence to a nearly equal degree’ (Phys. IV.6.213a12–15). Discursive thought is the generic part of the psyche which has an account, one which does not include nous or perception. Confidence then has no causal connection with them, and is not something which comes from the vividness or liveliness of perceptions or of ideas. The robustness which constitutes confidence is applicable only to accounts, things involving language.5 Now when a psyche has an account that is robust, one is likely to be confident in it. Aristotle holds that one feature which distinguishes human beings from other animals is that humans are creatures which have accounts. Confidence therefore is restricted to such creatures. In his examination of imagination (phantasia), Aristotle states: It thus remains to see if it [imagination] is belief, for belief is both true and false. However, confidence follows alongside belief ... but confidence belongs to no non-human animal, imagination to many. Moreover, if confidence goes with each belief, the ‘having been persuaded’ confidence, and account persuasion: imagination belongs to some non-human animals, but not an account. (DA III.3.428a18–24)6 According to Aristotle’s technical use of the term then, animals like lions, sharks or eagles are not confident, not because they are lacking in emotions or are automatons, but because they do not have language capacity, even though they do have perception, and indeed imagination also. Now say one has a belief, and one is confident in it. Beliefs, since they are discursive thoughts, are hexeis which have accounts. Thus, if one is confident in a belief, one is confident in an account. If one is confident in an account, Aristotle continues, one ‘has been persuaded’ by it. Thus, confidence is a function of persuasion, and persuasion of accounts. If an account

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is robust, one will likely be persuaded by it; if it is weak or enervated, one will likely doubt it, and accordingly will probably not have been persuaded by it – even though one may still have that account in mind. So when Aristotle says, for example, that it is difficult to be confident in many of the arguments concerning the psyche, he is implicitly saying that these arguments are not persuasive, even though they might be from among the best available. Since confidence is a function of persuasion and this of accounts, Aristotle states for example that ‘[w]e are confident in all things either through a syllogism or from an inductive procedure’ (AnPr.II.23.68b13–14).7 Thus, the robustness of a discursive thought – i.e., confidence – is a function of the persuasiveness of the account with that thought. (P) states that in order to have knowledge, one must be confident somehow. So what kind of persuasiveness is involved in epistemic confidence? Knowledge is the only kind of thought that concerns what is unconditional. For Aristotle, the confidence requisite for knowledge is unpersuadability into changing one’s mind, into thinking that one is mistaken or deceived. This unpersuadability will be an internal analogue that would match the objective unconditionality of what is knowable. The confidence then is one of the unthinkability of mistake. He states ‘...one who is knowing without qualification must be unpersuadable’ (AnPo. I.2.72b3–4). In the Topics, Aristotle indicates that the unique property (idion) of knowledge is ‘a discursive thought unpersuadable by an account’ (Top.V.2.130b15–16).8 In regard to primary knowledge, one will be confident in it if one is unpersuadable, or finds it unthinkable, that the contradiction (which is the contrary in such instances) of it is true. In regard to derivative knowledge, given the satisfaction of the more externalist requirements, a potential knower will be confident in that proof if they find it unthinkable that the conclusion of that proof, or the proof as a whole, is erroneous. If one finds mistake in one’s conclusion or proof unthinkable, one will be unpersuadable into changing one’s mind by another account which purports to show that conclusion, or the proof itself, to be false. This unpersuadability or unthinkability of mistake is the feature that distinguishes knowledge from belief internally. (Remember that knowledge and belief are distinguished externally by having different primary counterparts.) Comparing knowledge to belief, Aristotle states: Belief is unsteady, and nature is such. Besides this, no one thinks that they believe whenever they think something is incapable of being otherwise, but that they know. Yet whenever that is so, but regardless nothing pre-

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vents it being otherwise, they then believe, since belief is of such a thing, but knowledge is of that which is necessary. [emphasis mine] (AnPo. I.33.89a5–10)9 I take ‘thinking’ here to be indicative of the consideration of one’s degree of confidence in the subject matter at hand. When someone thinks that something is conditionally true, one thinks they believe because one thinks it is possible for what they are thinking to be false. Thinking of the possibility of falsehood occurs if one is persuadable (or has been persuaded) by this possibility. If one does not give this possibility any merit, leaving aside stubbornness and the like, it is because they are unpersuadable into thinking that the subject matter is in fact conditionally true – they think they know, not just believe. This passage confirms that knowledge is distinguished from belief in two ways, and is not belief with some added features. The first difference is internal: one who knows something has been persuaded by the account involved to a maximal degree. They are unpersuadable by any other into changing their mind that what is at issue can in fact be different from what they are thinking. They are confident in what they are thinking, which is requirement (P). The possibility of being mistaken or deceived is to them in that instance unthinkable because their thought is so robust, because they hold it to be the case unconditionally: it cannot be other than the way it is, regardless of time or other particular circumstances. The second way knowledge is different from belief is that confidence, a kind of internal recognition of necessity, is not sufficient for knowledge: it must also be the case that the thing in the world at issue is in fact unconditionally so, which is requirement (3).10 As shown above, knowledge is distinguished from belief metaphysically in that, as secondary counterparts in different hexical relations, knowledge has primary counterparts different from belief’s (be it deliberative or factual): The ones in regard to knowledge are unconditional, necessary, and universal, and incapable of being otherwise (thereby satisfying (3)); the ones in regard to belief are contingent and particular, and capable of being otherwise (thereby violating (3)). Since the distinctive feature of nature is change and constant transition (e.g., Phys. III.1.200b13–15, Meta. V.4.1015a13–19), and since what changes is capable of being otherwise, nature then is the primary counterpart to belief – deliberative belief in general, factual belief in particular – except insofar as natural matters are necessary or for the most part. Two interesting conclusions now follow. First, according to Aristotle, there is no knowledge of natural things, just opinion, unless the changes or transitions involved are necessary or for the most part (which in my view

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would make them necessary in a sense anyway). Second, since he countenances that there are things which do not change (e.g., forms and genera) and change is nature’s distinctive characteristic, if things which do not change are not natural, Aristotle is not a naturalist in our contemporary sense. So if one is unpersuadable into changing one’s mind about something, but is wrong in thinking this way, then despite satisfying requirement (P), one does not satisfy requirement (3), and hence does not know. In turn, if one thinks that the thing in the world at issue could be otherwise, but the primary counterpart to this hexis is in fact necessary, one satisfies (3), but not requirement (P), and thereby knows coincidentally (AnPo. I.33.89a33–37). This is the fact that makes Aristotle’s theory externalist to a certain degree. Now if one thinks that what is at issue can be otherwise, one is clearly persuadable into changing their mind about that issue, persuadable into thinking that at some point what they are thinking will be mistaken. However, if one thinks that the thing in the world at issue is incapable of being otherwise, but was in fact persuadable into changing their mind that they were mistaken about that, one would then think that the same thing both could be otherwise and could not be otherwise, but ‘this very thing is not possible’ psychologically (AnPo. I.33.89a39–89b1). Thus, if one thinks the fact at issue cannot be otherwise, they satisfy requirement (P). Confidence is also connected to the ‘more than’ requirement of (M). Aristotle says ‘[p]roofs are from things which are prior and more conducive to confidence’ (AnPr. II.16.64b32–33). As was stated above, there are certain things in a proof which are self-evident. These are for example the starting points of proofs, which are primary statements. Each such starting point in a proof is itself an account, and knowledge of it is primary. One aspect of requirement (2) is that all the statements of a proof be true. Since confidence is a function of the persuasiveness of an account, and the starting point of a proof is an account, by recognizing such a starting point ‘by means of itself,’ one will be confident in it by means of this starting point itself: ‘Things which one has confidence in not by means of other things but by means of themselves are primary and true, for one must not seek out the “why” among epistemological starting points, but each of the them is itself conducive to confidence by virtue of itself’ (Top. I.1.100a30–100b21). ‘Therefore,’ Aristotle concludes, ‘if we really see on account of the primaries and are confident in them, we also see those and are confident in them more because the things which are posterior are also on account of those’ (AnPo. I.2.72a30–33). Self-evidence is then automatically conducive to confidence, and is more conducive to confidence than things which are not. The ‘more than’ of

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requirement (M) means that in order to know by means of a proof, the recognition of a starting point or initial cause in that proof must be without qualification, not by us. From this recognition, the statements which follow logically will be recognized by means of this starting point, and are thereby less recognized than, or recognized after, that starting point, since they are caused by or are on account of it, both in terms of the proof and metaphysically. One then will also be more confident in that starting point than in those statements which follow from it: it seems implausible that one would have more confidence in what one has less unqualified recognition of, for what is primary and recognized by means of itself will be prima facie more robust than what is derivative and recognized by means of something else. In fact, it is necessary to be confident more in either all or some of the starting points than in the conclusion. For one about to have knowledge through a proof, one must not only recognize the starting points more and be confident in these more than the thing which is being shown, but there must not be another thing more conducive to confidence to one, or more recognized, among the things which are opposed to these starting points, from which there will be deception, the syllogism of the contrary – if at any rate the one who is knowing without qualification must be unpersuadable. (AnPo. I.2.72a36–72b4)11 One’s satisfaction of (M) results in a greater degree of confidence in the starting point of a proof than in what follows from it. For one about to know by means of a proof, in order to be unpersuadable into thinking that the account they have is mistaken, requirements (M) and the correlated (P) are necessary not only in order to capture cognitively the metaphysical priority of the cause to the effect, but also in order to shield oneself against the persuasiveness of a syllogism or other account which purports to show the contrary. Without this greater degree of confidence and recognition, the starting point contrary to the one in the proof at hand could deceive one into thinking that one’s proof is incorrect, or that what cannot be otherwise could in fact be otherwise. In either case, one will not know, because one will be persuadable into changing one’s mind: one’s epistemic attitude will not correspond to or match the status of the starting point at hand. I can now summarize Aristotle’s more internalist requirements as follows. Requirement (R) states that a starting point or cause a is recognized without qualification by some thinker p if and only if a (i) has been discerned by p, (ii) has been seen to be by p, and (iii) a is self-evident. Here a may be either a definition or declamation, or the reality signified by that

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definition or declamation. Requirement (M) states that a non-primary, mediate statement s is recognized without qualification by p if and only if s (i) has been discerned by p, and (ii) has been seen to be by p, from a in accordance with logic. Here s is either a non-primary, mediate statement or the reality signified by that statement. Accordingly then, Requirement (P): p is confident in a or s adequate for knowledge if and only if p is unpersuadable into thinking that ~a or ~s is possibly the case. The ‘possibly,’ in conjunction with ‘~a’ and ‘~s,’ in this analysis indicates that p is to find the contingency of a or s unthinkable, as well as the opposing truth value of a or s, in order to know. The satisfaction of (M) by p entails a corresponding greater degree of confidence in a than in s, as well as in any s* derived from ~a. If p is persuadable into thinking that ~a or ~s is possibly the case, or that an s* derived from ~a is possibly the case, p will doubt a or s, and thereby will not know. The confidence of requirement (P) is a function of the robustness of a linguistically expressed thought. The more robust an account is, the more persuasive it will be, and hence will be more conducive to confidence. These considerations apply to any form of discursive thought, so one may have confidence or doubt in regard to any of its forms: knowledge, skill, prudence or belief. The persuasiveness of an account adequate for knowledge is maximal in that one will find mistake in it unthinkable. In contrast, since the subject matters of prudence, skill, and belief are contingent, not necessary, one will always find mistake thinkable, even if not likely, in the accounts involved with them. With other things being equal, the confidence involved in all three parts of deliberative belief will then be a function of the degree of thinkability of mistake (this is what persuadability or unpersuadability is based upon), which in turn is a function of the probability or likelihood of the falsehood of the account involved. The more likely it is that the account one has is false, the more persuadable one will be into changing their mind about it, and accordingly the contrary account will be more conducive to confidence than the original one. Therefore, one may conclude that one is confident in a or s in a way adequate for deliberative belief if and only if p is unpersuadable into thinking that ~a or ~s is more likely the case than a or s. The satisfaction of (M) by p in this regard would entail a corresponding greater degree of confidence in a than in s, as well as in any s* derived from ~a.

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The Regress Problem is Born

Knowledge is an apodeictic hexis. As such, it is a secondary, ontologically dependent counterpart in a relation with what is unconditional, its primary counterpart. No other hexis has this counterpart. Knowledge requires the possession of proofs: the necessary, logical connection between the statements of a proof and its conclusion corresponds to the unconditional, causal connection between the things in the world signified by the proof. Proofs begin with foundational starting points, primary statements about the initial causes of things in the world. Are these starting points known? At this point, the infamous regress argument makes its debut upon the philosophical stage. Aristotle formulates it as a dilemma in Posterior Analytics I.3: ‘For some it does not seem that there is knowledge because of the requirement to know primaries; for others, that there is knowledge, but that there is, however, a proof of everything’ (AnPo. I.3.72b5–7). This debut performance is as follows. Horn 1: If there is only one way of knowing, namely derivatively by means of proofs, then one knows every premise in a proof only as a conclusion of another proof. This horn now divides into two prongs. Prong (i): For every premise in a proof, there is a proof for that premise; moreover, each premise in that proof itself is the conclusion of another proof. However, it is impossible to complete an unlimited number of proofs in a limited period of time. Therefore, if there is only derivative knowledge, then knowledge is impossible.1 Prong (ii): Suppose proofs do come to a stop at some primary statements. Since these statements are themselves not the conclusions of proofs, they are not known. If the proofs do stop here, knowledge is based on things that are not known, but are posited by declamation (hupothesis) (AnPo. I.3.72b14–15).2 However, it is absurd that the conclusions of proofs are known, but that the starting points leading to them are not. Therefore, if there is only derivative knowledge, and proofs do come to a stop at some unknown primary statements, then knowledge is impossible.

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Horn 2: ‘On the other hand, others agree about knowing – that it is only through proof – but that nothing prevents there being a proof of everything, that it is possible that a proof comes to be by a circle and from one another’ (AnPo. I.3.72b15–18). So here, one accepts that there is only derivative knowledge, but that we are able to escape prong (i) by claiming it is possible that primary statements can be ‘mutually proving,’ either ‘by a circle and from one another.’ (I take ‘by a circle’ to mean ‘by a circular proof of more than two statements’; ‘from one another’ to mean ‘a circle of just two statements.’ One could however take the phrase ‘from one another’ – i.e., ‘mutually proving’ – to be another way of explaining ‘by a circle.’) One escapes prong (ii) by agreeing that all premises, even the starting points, are in fact proven, and hence known. Thus, if circular or reflexive proofs are possible, then the existence of only derivative knowledge is not self-defeating and knowledge is possible. This is the coherentist alternative. Aristotle rejects horn 2 for two reasons. First, its acceptance undermines requirements (M) and (P), for one could never recognize one statement more than another: ‘it is clear that it is impossible to prove simply by a circle, if at any rate a proof must be from what is prior and more recognized: it is impossible for the same things to be prior and posterior to the same things simultaneously’ in the same respect [emphasis mine] (AnPo. I.3.72b25–28).3 By admitting circularity, any starting point would be both prior and posterior to itself in the same respect, namely by nature: Any putative starting point of one proof would be prior and more recognized by nature than the conclusion; however, this same starting point would be the putative conclusion of a different proof, and hence posterior and less recognized by nature. Circularity ultimately violates the principle of non-contradiction, and therefore must be rejected. Second, the admission of the coherentist alternative will make every proof fallacious: Every proof will ultimately beg the question, and everything will be provable (AnPo. I.3.72b32–73a6). For example, take the statements A and B, with A being a starting point. Say one can prove the conclusion C from A and B. C then necessarily follows from A and B. Since proofs are circular or reflexive, one can also prove that A necessarily follows from B and C, with C being the starting point. Thus, C, which had been the proved conclusion, is also a starting point, which is begging the question in regard to C. (Similar moves could also be made with B.) Moreover, since C follows from A and B, and A follows from B and C, A ultimately follows from A. Thus, one ultimately proves that A is A, a move which is applicable to everything. Consequentially, the coherentist alternative results in everything being knowable, since everything is itself and provable from itself – and knowledge thereby becomes trivial.4

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The rejection of horn 2 leaves prongs (i) and (ii) of horn 1. Aristotle holds that prong (ii), if true, is an insuperable hurdle, and skepticism is definitively the result. First, if the starting points of proofs are not known, but taken by declamation, then in his terms, these starting points are at best probable (endoxa) by virtue of a group of authorities or experts, or by common sense. However, neither probability nor common sense guarantees the truth of these starting points, a condition which violates requirement (2). Second, if starting points are conditional, then what follows from them will also be conditional. Therefore, requirement (3) will be unsatisfiable, and more detrimentally, knowledge will be unobtainable, either ‘locally’ or ‘globally’: Since knowledge is a hexis, it requires an unconditional primary counterpart. If there is nothing unconditional for us, then knowledge will be unattainable by us. If there is nothing unconditional by nature, then knowledge is unobtainable period. This leaves prong (i). In order to be able to reject it, Aristotle must show that it is not necessary for proofs to be unlimited in length, but that they come to stopping points that are somehow known primarily. He explicitly states that this problem is ultimately the same as prong (i) of horn 1: ‘This consideration – whether proofs go on without limit – is the same as whether there is a proof for everything or they come to an end in regard to each other’ (AnPo. I.19.82a6–8).5 Aristotle also says that if proofs do not stop, ‘but there is always something above the thing which is taken, there will be a proof of everything – therefore, if it is not possible to go through things which are unlimited, of the things which there is a proof, we will not see these by means of a proof’ (AnPo. I.22.84a1–4).6 The recognition of such points, if possible, will satisfy requirement (1/4), and will constitute primary knowledge. I had shown earlier that Aristotle’s account of knowledge is not too stringent: in order to satisfy requirement (1/4) – recognition of the cause or starting point of the thing in the world at issue – one need not recognize the ultimate cause or starting point, just the initial or first one. For example, in order to know why thunder occurs, one only needs to know that static electricity in clouds is the cause, and not something about subatomic physics. Such initial causes are expressed as primary and immediate statements, and these will be the starting points of proofs. However, it seems that nothing precludes an initial cause from being the effect of some other, more ultimate cause. For example, the presence of static electricity in clouds seems to be the effect of some other cause, say a feature of water vapor. If there is that kind of causal chain, then what is initially primary and immediate is not necessarily ultimately primary and immediate, i.e., primary and immediate without qualification, which in turn entails that what is

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initially primary can also be derivative. This possibility does not result in a roundabout acceptance of the coherentist or infinitist alternatives because the ultimate stopping points will be primarily, not derivatively, known somehow. If my understanding of this here is correct, then what Aristotle is attempting to show in regard to the problem of the possibility of unlimitedly long proofs can be taken as being either modest or bold. The modest solution is that Aristotle is showing there are initial causes, which primary knowledge is about. The fact that primary knowledge can become derivative, once one’s recognition of the causes becomes more ultimate, is not problematic. The bold solution is that there are ultimate causes. Primary knowledge then either (i) follows from the existence of these, or (ii) is conditional or qualified by declamation until one recognizes these ultimate causes. Disjunct (i) holds then that if there are ultimate causes, then there are initial causes; (ii) holds then that there is no genuine knowledge, but only conditional knowledge, until one recognizes these ultimate causes. Which solution, bold or modest, does Aristotle proffer? There is some evidence from Section II that points in the modest direction. However, in order to answer this question properly, I would have to examine Aristotle’s metaphysics, specifically his account of causes and causal chains, in detail – a project which is impossible to fulfill here. The material below does provide hints to the right answer. Fortunately, adequate understanding of what Aristotle wants to say does not depend on answering this question: All one needs to do is adjust the terms ‘primary’ and ‘immediate’ once one has determined this answer. If the modest solution is correct, then ‘primary’ and ‘immediate’ below simply refer to initial causes. If the bold solution is correct, then these terms refer to the ultimate causes. One can then move to see whether disjunct (i) or (ii) of the bold interpretation is the right one. Aristotle tackles prong (i) of horn 1 by turning his attention to the possibility of unlimited chains, columns or series (sustoikhiai) of predication.7 Understanding what these chains are, and the work they do for Aristotle, requires a bit of his specialized terminology and a return to some metaphysical issues. I also think this material has not been understood or explicated very well before.

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Some Terminology

An ontological chain is a series of things in the world that are linked together, with each one somehow ‘belonging to’ (huparkhei) the one to which it is linked, either conditionally or unconditionally (e.g., AnPr. II.21.66b26ff; AnPo. I.15.79b5ff.). A term (horos) signifies one link on that chain (AnPr. I.1.24b16–18). Thus a term can be either a subject or a predicate, and can signify any of Aristotle’s categories. Aristotle might also treat definitions (horismos) as terms at times (e.g., Top. I.5.101b38–102a17).1 A statement (protasis) is formed by linking two terms together (AnPr. I.1.24a16–17ff). A true statement is one whose linkage successfully corresponds to or signifies a real linkage; a false statement is one whose linkage fails to correspond to or signify a real linkage. An immediate statement for Aristotle is one where there is not another statement prior to or before it (AnPo. I.2.72a8; see ch. 6). The linkage between two things in the world can be either primary (prôtôs) or non-primary, and coincidental (kata sumbebêkos) or kath’hauto. Two things in the world are linked together primarily if and only if no other link is, or can be, joined between (metaxu) the one and the other to form a new, viable connection. The statement that expresses such a connection is primary. The linkage is non-primary if some thing in the world is, or can be, placed between the two links to form a new viable connection (AnPo. I.19.81b31, 34–35, 82a2–3). The statement that expresses a non-primary linkage is itself non-primary. For example, the chain thing which breathes–living thing is primary because no connecting link can be placed between them to form a viable connection: there is no genus more universal than thing which breathes but less universal than living thing. On the other hand, the chain human–mammal is non-primary because primate can be placed between in order to form a viable link, and from which one may

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form the true statements ‘all humans are primates’ and ‘all primates are mammals.’ The process of interpolating a new link between two existing links in a non-primary predicational chain, thereby forming a new, viable connection, Aristotle calls ‘compressing’ (puknoô; e.g., AnPo. I.23.84b33–35). The difference between primary and immediate might seem blurry: Aristotle says ‘“primary” and “starting point” are the same,’ then says ‘a starting point of a proof is an immediate premise’ (AnPo. I.2.72a6–7). Thus, a primary premise is an immediate premise. However, an immediate premise is non-primary if it is not derived from another syllogism or proof, yet is not of a starting point or some initial cause. It may also be one which is taken from a division or an inductive procedure (AnPr. II.23, esp. 68b30–37; see ch. 6). Two things are linked together in a chain coincidentally if and only if the linkage is an accidental or conditional fact. For example, the chain human–brown is coincidental, because humans are only accidentally or conditionally brown in color. A corresponding statement, e.g., ‘some humans are brown,’ is likewise coincidental. Two things are linked together in a chain kath’hauto if and only if the linkage is necessary or unconditional.2 For example, the chain human– primate is necessary, because part of what it is to be a human is to be a primate. The corresponding statement, ‘all humans are primates’ is likewise kath’hauto. Each individual link and its corresponding term may also be considered as coincidental or kath’hauto when taken as the subject of a statement. For example, the subject in the statement ‘that white is a human,’ namely ‘that white,’ is coincidental. In contrast, the subject in ‘the human is white,’ namely ‘the human,’ is kath’hauto. These statements are very different in that with the former, although the subject appears to be the color white, the white is only a subject due to some other thing, which happens to be that color. However, with the latter statement, the subject – the human – is a subject due to itself, due to simply what it is, and not due to something else which happens to be human (AnPo. I.19.81b23–29). A proof (apodeixis) links together multiple statements in a way that corresponds to how unconditional things in the world signified by them are linked. A mere syllogism – sullogismos; a proof is a special kind of sullogismos due to its subject matter – is what corresponds to conditional chains. If the chain is real, then the corresponding proof or syllogism will be valid; if the chain is unreal, then the corresponding proof or syllogism will be invalid. Concerning just proofs, if unconditional ontological chains are unlimited in length, then proofs will be unlimited in length and knowledge will be

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impossible. If they are limited, the proofs will be too, and knowledge will be possible. These chains can run in either an ‘upwards’ or a ‘downwards’ direction: An upwards chain is one where some thing in the world, a link t, is more universal than the preceding link t–1. Thus any link t–n will be more universal than the subsequent link t–(n–1) (AnPo. I.19.81b39–40, I.20.82a23). A downwards chain, which means going ‘to the thing which is as a part’ (epi to kata meros), is one where some thing in the world, the link t′, is more partial or particular than the preceding link t′–1.3 Thus any link t′–n will be more particular or partial than the subsequent link t′–(n–1) (AnPo. I.19.82a1–2, I.20.82a23–24).4 The reader should understand that when Aristotle uses the above terminology, he makes no distinction between the linguistic item and the corresponding reality it signifies. So, when he uses the term ‘term’ for example, he almost invariably means both the linguistic item and the corresponding link in the world. The same goes for the rest of this terminology. The success or failure of Aristotle’s arguments does not depend upon the masking of this distinction. Hereafter, unless I say so explicitly, I follow Aristotle’s practice. Some readers might also dismiss Aristotle’s work here because much of it is connected to his ‘out-moded’ syllogistic. Although I think this conceit might be a little foolish due to the advances of category theory in mathematics and the work of Fred Sommers,5 I think it is unwarranted for another reason: Aristotle is demonstrating responsible philosophical behavior in that he makes sure his logical procedure, the one which gets him to derivative knowledge from primary knowledge, matches his metaphysics. His attitude is not like the kind of philosopher who loves possible world semantics but denies that possible worlds exist.

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The Regress Reformulated

The problem now is whether non-coincidental predicational chains for proofs can go on without limit. Aristotle excludes syllogisms more generally because these include dialectical syllogisms, as well as ones whose statements express beliefs. Truth is not an issue in the case of dialectical syllogisms, or can be otherwise in the case of opiniative ones. However, truth is an issue with knowledge (as indicated by requirement (2)), and knowledge concerns only what cannot be otherwise (as indicated by requirement (3)). This problem has three different permutations. In each of the permutations, let ‘A’ through ‘T,’ ‘A1’ through ‘T1’ etc. be constants which signify specific terms; let ‘U’ through ‘Z’, ‘U1’ through ‘Z1’ etc. be variables which signify any admissible term. A term can be either a single subject or predicate, or a predicational chain which is a definition. Permutation 1. Aristotle asks whether it is possible that a predicational chain for a proof goes upwards without limit (AnPo. I.19.81b39–40, I.20.82a23). First, take a term T1 which belongs to nothing else. This qualification means that T1 is not predicated of another term; i.e., T1 is maximally particular. Thus, there is no true statement of the form ‘X is T1,’ or equivalently, ‘T1 belongs to X,’ with X being a kath’hauto subject. Such a term as T1 is a last (hustaton) term, since it will be the last link in a chain (AnPo. I.21.82a39–82b1). Such terms (and what they signify) are particulars and things which are perceptible (AnPr. I.27.43a27, 33, 39–40). This notion of a last term (and of a first term, which is discussed next) is made plausible due to Aristotle’s restriction of the problem to non-coincidental predications. If both coincidental and non-coincidental predications were involved, then for any putative last term K, there would be another term Z, which would form a true statement ‘Z is K’ (or, in the case of first terms, ‘K is Z’). Consequentially, no term would be either last (or

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first), for any term could then become a particular (or universal) just simply by where it was placed in the statement. For example, Kallias would not be a last term because one could make Greek a subject, Kallias a feature of that subject, and say ‘a Greek is Kallias.’ However, the world does not work in this way, so such a statement is an example of coincidental predication (see e.g., AnPr. I.27.43a33–36). Now take the following chain, assuming for present purposes that each connection is primary and non-coincidental. Kallias human primate mammal chordate animal : Let ‘K’ signify Kallias. According to Aristotle, Kallias belongs to no other thing, such that there are no true non-coincidental statements of the form ‘Z is Kallias’: Kallias is maximally particular. In this chain, each link is more universal than the previous. Moreover, the chain can be used to form valid proofs, for example: Kallias is a human; a human is a primate; therefore, Kallias is a primate. Is it possible for this chain, or for any one going in the same direction, to continue on upwards without limit? Take T2 which belongs to K, and assume no other possible term Y occurs between T2 and T1. These mean that T2 is predicated primarily of K to form the statement ‘K is T2.’ Now take the term T3 which belongs to T2 similarly, and another term T4 which belongs to T3, and so on. Aristotle asks: is it possible that this predicational chain K,...T4,...Tn continues upwards without limit, such that for any term Tn in an upwards direction, there is a term Tn+1 which can be predicated truly and primarily of Tn? In other words, is there always possibly a noncoincidental, primary term Tn+1 which is more universal than a previous term Tn in such a chain? Or must such predicational chains come to a stop (AnPo. I.19.81b30–33)? If it is possible that predicational chains proceed upwards without limit, then it is possible that any statement one takes for a proof is the conclusion of another proof with statements more universal than that original statement. Now take any proof p which proceeds downwards, where the premise statements are more universal than the conclusion. Since this permutation is the case, any statement in p is possibly the conclusion of a

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different proof p* with more universal premise statements. Thus, it is possible that one never obtains a first term X such that no other term Z is predicated of, and belongs to, X, and thereby there is always possibly another premise statement of the form ‘X is Z.’ So, if this permutation is the case, then it will be possible that no statement universal in scope serves as a basis for derivative knowledge. Permutation 2. Aristotle now asks whether it is possible for there to be an unlimited sequence of predications moving downwards from the less partial or particular to the more partial. For example, take a term L, such that no other term W is predicated of, or belongs to, L. This qualification means that there is no statement or real link of the form ‘L is W,’ or equivalently, ‘W belongs to L,’ where W is more universal than L. This kind of term Aristotle defines as a ‘first’ term, and it is not possible to prove anything different of such things except ‘by virtue of belief’ (AnPo. I.21.82b2–3; AnPr. I.27.43a29–30, 37–39). Now take the following predicational chain: living thing breathing thing animal chordate mammal : Let ‘L’ signify living thing. Assume no thing in the world is predicated of ‘living thing’: nothing can be said to belong to a living thing such that one can truly form the statement ‘a living thing is Z’ non-coincidentally and primarily. In this chain, each link is more partial, or more particular, than the preceding link. As with the chain in the first permutation, this one can be used to form proofs as well: A thing which breathes is a living thing (or in other words, in order to make the ‘more partial than’ notion clearer, the genus of breathing things is more partial than the genus of living things). A thing which breathes oxygen is a thing which breathes. Mammals are things which breathe oxygen. Mammals therefore are living things. Is it possible for this sequence, or one going in the same direction, to continue on without limit? Assume that L belongs to S2 primarily (i.e., L belongs to S2 with no other possible term W occurring in between) and form the statement ‘S2 is L.’ Now take S2 to belong to S3 likewise, and S3 to S4, and so on. Aristotle again asks: Is it possible for such a chain, Sn, S4,...L to continue downwards without limit such that, for any term Sn, there is a term Sn+1 of which Sn is predicated, which then allows one to form the true

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statement ‘Sn+1 is Sn’? In other words, is there always possibly some term Sn+1 which is more partial or particular than the term Sn which preceded it, and with which one may form a new proof? Or must this kind of sequence always reach some limit (AnPo. I.19.81b33–37)? If it is possible that predicational chains proceed downwards without limit, then it is possible that any statement one takes for a proof is a conclusion of a different proof with premises more partial than the premise posited in the original proof. Now take any proof q which proceeds upwards, where the premise statements are more partial or particular in scope than the conclusion. So, since permutation (2) is the case, then it is possible that any statement in q is the conclusion of different proof q* with premise statements even more partial. Thus, it is possible that one never obtains a last term W such that W does not belong to, is predicated of, another term Y, and thereby there is always another chain of the form ‘Y is W.’ So, if this permutation is the case, then possibly no statement partial or particular in scope will be able to serve as a basis for derivative knowledge. Permutation 3. Aristotle then asks whether it is possible for there to be an unlimited number of predications between two links or terms. So assume the outermost terms or links of a chain have been delimited, e.g. P and R, with the connecting middle term Q. Now, is it possible that there is an unlimited number of non-coincidental terms A1,...An, An+1,... which ultimately and validly prove Q of P, or similarly B1,...Bn, Bn+1,... which validly prove R of Q (AnPo. I.19.82a2–6)? If this is possible, then it will be possible that no two statements in a proof will be immediate. For example, I prove that Kallias is an animal by the middle term ‘mammal.’ One responds that the premise ‘Kallias is a mammal’ is not immediate, because it is the result of proof involving the term ‘primate.’ Is it possible for the interpolating of proofs between ‘Kallias’ and ‘mammal,’ for example, to go on without limit? Using Aristotle’s technical term, is everything compressible?1 If it is possible that there is an unlimited number of predicational chains connecting a middle term with its extreme terms, then it is possible that there is an unlimited number of proofs between them. In this case then, one cannot prove – and hence cannot know – that one term ultimately and actually belongs to the others. Knowledge will then be impossible, because an unlimited number of proofs in between the extreme terms would undermine the possibility of constructing and completing a proof at all on the basis of some foundational predicational chains. So, even if one did have some such starting points – even some that were true – one could not use them to obtain new knowledge.

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This problem of possibly unlimited predicational chains applies equally to negative as well as to positive proofs, syllogisms, and statements. Aristotle says: for example, if P does not belong to any Q, either it will do so primarily, or there will be something between to which, being prior, it does not belong (e.g., R, which belongs to every Q), and again of this still another prior one, e.g., S, which belongs to every R. For also in these negative cases either the things to which, being prior, it belongs are unlimited, or stop. (AnPo. I.19.82a9–14) So, take the negative statement ‘No Q is P.’ If this predication of P to Q is not primary, then there will be some R such that ‘All Q are R, no R are P, no Q is P.’ Again, if P does not belong to any R primarily, then there will be some S in between P and R. Now do the terms or links between P and the denial of Q come to a stop, or are they possibly unlimited?2 Aristotle has established a secure means for obtaining derivative knowledge: the formation rules for affirmative and negative proofs are formal, and any model constructed according to those rules is valid. Anything obtained by this means will not result in any loss of confidence. It is impossible to prove either circularly or reflexively. Therefore, necessarily, if knowledge is possible, then some non-coincidental, primary predicational chains will provide statements for constructing valid proofs, but yet will not follow from other valid proofs (which themselves are predicational chains). That is, it is necessary that if knowledge is possible, then some terms provide the foundation for all subsequent chains by being the extremes or ultimates (eskhatos) of those chains. These ultimates will be either first or last terms (like living thing or Kallias respectively), and the ultimate causes of all that follows from them. Non-coincidental, primary statements comprised from those terms will then be foundational, and a confident linguistically expressed thought of them will be primary knowledge. Thus the problem in Posterior Analytics I.19–23 is epistemological, although some logic is involved – it is involved insofar as it is the means for Aristotle to get from primary to derivative knowledge.3 Aristotle’s notion of knowledge as a hexis helps us understand what sort of links he has in mind. As a secondary counterpart in a hexical relation, knowledge is causally dependent on something in the world for its existence. So Aristotle is asking, is there anything that is fundamentally particular? If so, these particulars will provide one potential basis, one primary counterpart, for primary knowledge. He is also asking, is there anything that is fundamentally universal? If so, these universals will provide the

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other potential basis for, and primary counterpart to, primary knowledge. It is easy for us to understand the effects that particulars have on us, but not so easy in the case of universals. Although it is impossible to address this matter in detail here, I think it is clear by now that Aristotle is using a much more restricted sense of ‘universal’ than we do, and that they are connected to genera and their forms. For these universals to have any causal efficacy, they have to exist somehow. So Aristotle is committed to holding that genera and species at least exist somehow in a somewhat robust sense, robust enough to have some effect on us. This issue leads to the question, do genera and species have to exist separately or apart from particulars in order to do this causing? This question of separation (root khôri-) leads down a perilous trail that is too far afield. Also, the issue as to whether there are other kinds of universals involved in primary knowledge, and what their metaphysical status might be, is just as treacherous. It suffices for us to realize that Aristotle thinks that if he can show they exist, particular objects, as well as certain kinds of universals, will provide the ultimate foundations for knowledge.

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The Regress Contained

Aristotle contains the regress problem in the following three ways. Containment Strategy 1. Aristotle limits himself to predicational chains which are specifications (ta ti esti). Specifications are true, primary statements that express what things in the world are non-coincidentally (AnPo. I.22.82b37). In strict chain form, a specification will be a column of links with the same subject in each of the first links, with a non-coincidental feature in the second link. In a less strict but equivalent form, a specification with its non-coincidental features will be linked together in a hubspokes form, with the subject being the hub, and the features being the spokes. In either case, the subject link or hub cannot trade places with any feature link or spoke: the subject link is not convertible with any feature link. Aside: Counterpredicability. Convertible, non-coincidental predications are counterpredicable (antistrephonta) terms. As Aristotle puts it, for among the things which are convertible, it is possible to show everything by means of each other (e.g., AnPo. I.19.82a15, 19–20; AnPr. II.5.57b35–36). Counterpredicable terms can be predicated truly of each other, and occurs in at least two cases. (CP1) Terms are counterpredicable when they belong mutually to each other, and thereby are mutually predicated of each other both non-coincidentally and primarily. Such a linkage violates the ‘not belonging to’ qualification involved with first and last terms of permutations (2) and (1) respectively. The most notable counterpredicable terms signify unique properties, idia. A unique property ‘is what does not reveal the essence but belongs to it alone, and is counterpredicable with the thing in the world.’ No one ‘calls the thing which possibly belongs to something else a unique property’ (Top. I.5.102a18–19, 22–23; cf. AnPo. I.3.73a6–7). Unique properties are thus non-coincidental and primary1. So for example, Aristotle says, the ability to obtain knowledge of grammar

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belongs to human beings alone, and it is not possible for something other than a human being to obtain knowledge of grammar. The use of photosynthesis to obtain food belongs to plants alone, and it is not possible for something other than a plant to use photosynthesis in order to obtain food. Therefore, the ability to obtain knowledge of grammar is a unique property of human beings, and the use of photosynthesis to obtain food is a unique property of plants. One can then say truly and convertibly ‘humans are beings which are able to know grammar’ and ‘beings which are able to know grammar are humans’; ‘plants are things which use photosynthesis to obtain food’ and ‘things which use photosynthesis to obtain food are plants.’ (CP1) also covers identity statements, including ‘K is K,’ or ‘that thing over there is K,’ as well as statements involving synonyms like ‘a book is a tome’ and ‘a tome is a book,’ for each term in such a statement clearly belongs to itself.2 (CP2) Convertibility also occurs in a syllogism or proof ‘by means of the conclusion and by means of one taking the remaining statement, reversing it in respect of predication, and taking the other to be concluded, which one possessed in the other syllogism’ (AnPr. II.5.57b18–21). For example, assume G belongs to H and F belongs to G; therefore, F belongs to H. Now, take the conclusion as a premise: F belongs to H. Reverse the second premise: G belongs to F. One now concludes that G belongs to H, the other premise that was taken in the original syllogism or proof. (Here, the only immediate and primary statement is the second premise; conclusions by definition are not immediate, so ‘F belongs to H’ and ‘G belongs to H’ are not immediate.) An instance of (CP2) also occurs in the case where one may convert particular affirmative, and universal negative, predicational chains. For example, Aristotle says ‘some good is pleasure’ is convertible to ‘some pleasure is a good’; ‘no good is pleasure’ is convertible to ‘no pleasure is a good’ (AnPr. I.2.25a5–10). For both (CP1) and (CP2), no term is either first or last, for all terms are similar in relation to all the others (AnPo. I.19.82a15–17). The ‘similar in relation’ means that the counterpredicable terms involved are related as elements (stoikheia) in each other’s specification, or are unique properties; it does not mean that F is predicated coincidentally of term G, whereas G is predicated of F without qualification. First or last terms preclude counterpredicability. With (CP1), it is possible for a proof and its conversion to proceed without limit, for example, ‘a book is a tome, therefore a tome is a book, therefore a book is a tome, therefore....’ Likewise, with (CP2), it is also possible for a proof like ‘H is G, G is F, therefore H is F; H is F, F is G, therefore H is G; H is G, G is F; therefore H is F’ to proceed without limit.

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Aristotle’s concern then is that since there is no first or last term in such chains, either the subject in them has an unlimited number of predicates, or the proofs in which counterpredicable terms occur is unlimited either upwards or downwards, assuming the terms are all similarly related (AnPo. I.19.82a17–20). So for Aristotle’s problem, the answer is automatically affirmative in every such case where the chains are comprised of counterpredicable terms. All such predicational chains are unlimited in length. At best, such statements (many of which nowadays would be called ‘analytic’) are immediate and not primary, which means that they are knowable primarily, but cannot be the source of any new knowledge derivable from them. (Perhaps another reason why Aristotle rejects coherence as a viable alternative is that in a coherent system, every term will ultimately be (CP2) counterpredicable with any other term in that system.) Definitions and declamations, which are for Aristotle central, potential starting points for knowledge, must therefore not be comprised of counterpredicable terms. Unique properties in particular are not admissible in definitions or declamations. End of aside. Containment Strategy 2. If permutations (1) and (2) of the problem are resolved, then permutation (3) is resolved without further work (AnPo. I.20.82a21–22). Say one wants to prove that R is predicated of P by means of Q, with P being a more universal term, Q and R progressively more partial in scope. P and R may not be a first or a last term here. Starting from P, if there is an unlimited number of terms ...Qn+1, Qn,...Q2, Q1 proceeding from P to Q, then this predicational chain is the same as the one in permutation (2). Now, start from R. If there are an unlimited number of terms going from R to Q, from the more partial to the more universal, i.e., Q1, Q2,...Qn, Qn+1,... then this upwards chain is the same as the one in (1). So, if one shows it is not possible that primary, non-coincidental predications are unlimited in length both downwards and upwards, then one shows a fortiori that it is not possible for predications to be unlimited in length between terms (AnPo. I.20.82a24–35). Containment Strategy 3. If the predications come to a stop in both directions in affirmative predicational chains, they come to a stop in negative predicational chains. Negative statements in a proof require a negative conclusion and vice versa. Two negative premise statements are not allowed in a proof, since the fallacy of exclusive premises will occur. Thus, any proof that employs a negative statement requires some affirmative statement for the proof to be completed. Negative statements are either primary (and hence immediate) or not. If that negative statement is not

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primary, it will be the conclusion of another proof with an affirmative statement in between it and another negative statement. The affirmative statement in that proof will then also be either primary or not. Negative proofs then will be unlimited in length only if that affirmative statement is never immediate. If it is not immediate, then that affirmative statement will be the conclusion of yet another affirmative proof. If predications do however come to a stop both upwards and downwards in affirmative predicational chains, and thence permutation (3) of the problem is not the case, then these predications will ultimately come to a stop at some immediate affirmative statement or chain of affirmative statements, as well as a primary and immediate negative statement (AnPo. I.21.82b6–8). Therefore, at some point, predications will come to a stop in between the two terms in that negative proof – or in any non-primary negative statement. Therefore, predications will come to a stop in negative predicational chains.3 Aristotle now argues that it is not possible for either downward or upward predicational chains to be unlimited in length. The starting points for proofs will be where these chains come to a stop. Primary – and subsequently, derivative – knowledge will then be possible, presuming some of these foundational statements are potential, epistemic, linguistically expressed thoughts. Aristotle presents his overall solution in conditional form: So, in the case of things which are predicated in the specification, it is clear: if it is possible to define, or if the essence is recognizable, and it is not possible to go through things which are without limit, it is a necessity that the things which are predicated in the specification have been brought to a limit. (AnPo. I.22.82b37–83a1) In his view, in order to solve this problem, he needs to show one of two things, assuming human beings cannot go or work through unlimited predicational chains: First, that it is possible to define; second, that essences are recognizable. If Aristotle can show either, predicational chains which are the specifications of things in the world will then be able to be brought to a limit successfully, and hence primary knowledge will be possible: the subject of a definition or the essence will provide the first or last terms for a proof, and will stop there. Aristotle proceeds to show both. For the first – that it is possible to define – he offers what he calls a ‘universal’ or ‘logical’ argument (AnPo. I.22.83a1, 84b2). Something is shown universally (taking ‘logical’ and its variants as being equivalent) ‘whenever it is shown in a random and primary case.’ For example, having two right angles is not universal for the

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genus figure, for some random figures will not have two right angles. Any random triangle will be shown to have two right angles, but in the case of isosceles, Aristotle holds, this holding is not primary, because triangle is prior. ‘That thing then, which is random and primary, is shown to have two right angles or any other thing whatsoever, belongs universally to this primarily, and the proof is of this kath’hauto universally’ (AnPo. I.4.73b32–74a3). This argument involves many considerations based on the philosophy of language. It is also important to note that ‘define’ is a technical term for Aristotle, and it has a much broader and more substantive function than the everyday English usage of the word: definitions for Aristotle are the linguistic means by which we get a firm grip on things in the world, and not just something by which we explain the meaning of a word. For the second – that essences are recognizable – he offers what he calls an ‘analytic’ argument (AnPo. I.22.84a8, 84b2). Aristotle does not make clear what he means by ‘analytic’; however, the term does seem to imply that the argument does not focus on any random, primary case, but focuses on certain theoretical claims and what follows from them. This argument involves many metaphysical considerations.4

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The Solution to the Regress Problem Part 1: The Universal Argument

Aristotle begins to show that it is possible to define as follows: It is possible to say truly ‘the white is walking’ and ‘the large is that tree,’ and again ‘the tree is large’ and ‘the human is walking.’ Now to speak in the latter way is different than in the former way: Whenever I affirm that the white is a tree, I mean then that that which happens to be white is a tree, but not as the white is the thing which is underlying for the tree. Furthermore, neither being white, nor what very thing that kind of white is, comes to be a tree such that it is not a tree except coincidentally. Whenever I affirm that the tree is white, I do not affirm that white is some other thing, and that thing happens to be a tree, as whenever I affirm that the thing which is erudite is white (for then I mean that the human being is white, who happens to be erudite), but the tree is the underlying thing, and what very thing that came to be, not being something other than what very thing a tree or kind of tree it is. (AnPo. I.22.83a1–14) Take for example these terms: the white, white, the large, large, tree, human, to walk. According to Aristotle, we recognize expressions such as ‘the white is walking’ and ‘the large is a tree’ as possibly true. (These statements sound much better in Greek or Shakespearean English than in contemporary English.) Likewise, we also recognize expressions such as ‘the tree is large’ and ‘the human is walking’ as possibly true. However, the former pair of expressions is different from the latter. Whenever one sees a birch for example, and then pointing to it says ‘the white is a tree,’ that speaker means, according to Aristotle, that that thing which happens to be white is a tree: there is some thing there – a tree – that coincidentally is white. The speaker does not mean that white, either as a universal

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‘one-over-many’ or as an instantiation of it, functions as the underlying thing or matter of the tree, or in other words, that white – in this case over there – coincidentally is a tree. When one says ‘the white is a tree,’ one is not affirming that white came to be a tree, but is affirming that some tree, due to what it is and its underlying nature, came to be white at some point in its existence, and happens to be white now. Similarly, when one says that ‘the erudite is white,’ one does not mean that the feature erudite has come to be a certain color, but that some human being, who coincidentally is erudite, is also by coincidence white. The human being in this case underlies both the white and the erudite. So the tree or the human is the underlying thing of the white or the erudite. In Aristotle’s terminology, neither the human nor the tree is anything else other than what very thing it is (hoper ekeino) to be a tree or a human, or what very kind of thing it is (hoper ekeino ti) to be tree or human. (Aristotle leaves it open here as to whether a particular human, or the specific form human or tree, is at issue.) In contrast, the walking, white or erudite is something different from what very thing is walking, or is different from what kind of things walk. The white, the walking, and the erudite all depend upon the presence of other things in the world, like the tree and the human. The human and the birch are not dependent upon the white, the walking or the erudite for their existence: a human or a tree is not something different than the very thing which is a human or a tree, or a kind of human or a kind of tree. Things like humans and trees are just the very things, or kinds of things, they are. Thus, according to Aristotle, it is the case, and we either explicitly or implicitly recognize, that certain things in the world function as underlying things or matter, which come to have and to support certain coincidental features by their nature, by what very things they are. These underlying things are particular objects that provide a possible foundation for knowledge. Particular features or their universals are not foundational in this way. It is the case, and we recognize, that these features are not themselves underlying things which come to be things like trees or humans.1 So, Aristotle says, the predications in the first pair of examples – ‘the white is walking’ and ‘the large is a tree’ – are not genuine predications at all, or are, strictly speaking, coincidental predications: Coincidental subjects, which are predicated, are ‘something different from’ what very things, or what kinds of things, those predicates say they are. The examples in the second pair – ‘the tree is large’ and ‘the human is walking’ – are predications without qualification: The unqualified subjects, which are predicated, are just the very things, or the kinds of things, those predicates say they are (AnPo. I.22.83a14–18). Thus, in the debate as to whether objects, or some

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variety of sensory phenomena, provide the foundations for knowledge, Aristotle comes down on the former side, insofar at least as those objects function as a matter or underlying thing for other things. Based on the distinction between unqualified and coincidental predication, Aristotle now states that unqualified predications reveal realities, whereas coincidental predications do not. Moreover, the things signifying realities signify what very thing that is, or what very thing that kind is, of which it is predicated. The things which do not signify realities, but are said of another underlying thing that is not what very thing that is, nor what very thing that kind is, are coincidental, like the white of a human. For human is not what very thing white is nor what very thing that kind white is, but is animal perhaps: animal is what very thing a human is. Those things that do not signify realities must be predicated of some underlying thing.... (AnPo. I.22.83a24–31) Take ‘the human is white.’ If ‘white’ were predicated of ‘human’ without qualification, then white would signify a particular feature of what very thing, or of what kind of thing, a human is. However, ‘white’ is not so predicated of ‘human’: there is no particular color which is part of what makes a human human, as opposed to something else. Thus, ‘white’ is a coincidental predicate; the person functions as an underlying thing that supports the presence of the color white, as well as its contrary black and the intermediate colors between them. The principal feature of coincidental predication then is that such predicates do not reveal what that subject is, or that it is a reality. In the first example – ‘the large is a tree,’ or in cases like ‘erudite is black’ – the subject of the predicational chain is not really a genuine subject at all, or is not considered as such. In the second example – ‘the human is white’ – though the subject is genuine, the predicate does not indicate what a human is, does not reveal the reality of that thing or indeed that it is a reality at all, even if that underlying thing is a reality in its own right: ‘the white coincides with the human because it is white, not because it is the very thing to be white’ (Meta. IV.4.1007a32–33). A coincidental predicate merely indicates that the subject functions as an underlying thing for the extension of the predicate. Since the possession of such features is coincidental, statements signifying such facts are not knowable, just believable. Now take a term like ‘animal’ and predicate it of ‘human.’ This term does reveal a particular feature of what very thing or kind of thing a human is: for any human being, one must predicate the term ‘animal’ of that being.

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(However, the particular feature revealed in this instance must not be a unique property, given Aristotle’s exclusion of counterpredicable terms.) A term like ‘animal’ signifies, at least in part, the reality of a human being or of humankind. Such terms are unqualified (or sometimes, ‘simple’) predicates, and thereby signify realities. A human, or humankind, does not function as an underlying thing for animal, its contrary non-animal, and any possible intermediates between the two. Instead, animal is one of those features that indicate what a human, or humankind, is. Thus, according to Aristotle’s universal argumentation, since the distinction between coincidental and unqualified predication applies in these random instances, the chains involved are primary, and since the test expressions in the argument are not special, more specific forms of more universal or general expressions, the distinction between unqualified and coincidental applies to all chains or expressions, most notably proofs. Of the two kinds of predication, only unqualified predications reveal reality, coincidental predications do not. Proofs, Aristotle ‘legislates,’ shall therefore employ only simple or unqualified predications, not coincidental ones. Whenever a term is predicated of a subject, it is in a specification of that subject, or signifies some non-specificational feature of that subject. Statements of the latter sort are inadmissible in proofs (AnPo. I.22.83a18–23). Consequentially, Plato’s Forms, like White or Large, have no use in proofs, because they are not underlying subjects of predication. Forms are superfluous for knowledge: White or Large would only play a role in proofs if coincidental predication were admissible. Aristotle hence declares: ‘Let one bid the Forms farewell: they are meaningless sounds, and if they exist, they are nothing…’ (AnPo. I.22.83a32–34). Aristotle has established the distinction between unqualified and coincidental predication. He now needs to show that it is possible to define: if it is so, then it is not possible that predicational chains are unlimited in length. Definitions and specifications are themselves specific kinds of predicational chains, and according to Aristotle reveal the reality of some thing in the world primarily and without qualification (e.g. Meta. VII.4.1030a22–23).2 Therefore, definitions and specifications are the special kind of statements that are comprised only of unqualified predications. If it is not possible for unqualified predications to be unlimited in length – that is, if it is not possible to represent a reality linguistically with an unlimited number of unqualified terms – then it will be possible to define, and thereby, possible to know primarily. Aristotle now provides this argument showing it is possible to define. Whenever one term is predicated of another without qualification, it is either (i) in a reality or specification, or (ii) because it is a quality, quantity, relation,

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doing, undergoing, somewhere or sometime (AnPo. I.22.83a21–23, 83b13–17).3 Why are the categories in (ii) still here, even though Aristotle has dismissed them as being genuine subjects of predication, calls them coincidental, and says they are not a part of specifications? He does so because some of these categories can be predicated kath’hauto of a subject, and thereby are necessary to that subject. Knowledge and proofs concern what is necessary; kath’hauto predications are necessary (regardless as to whether they are kath’hauto coincidentally or kath’hauto without qualification); some predications from (ii) are kath’hauto. Therefore, knowledge and proofs concern some predications from (ii). However, in order for this fact to result in the possibility of unlimited, unqualified predications, some quality or any other category would itself have to be a potential link between two terms, say erudite between Socrates and white. This fact would make a quality a reality as well as a quality, so that something else could be predicated of it without qualification. The same requirement applies to the other non-specificational categories similarly. Aristotle has shown that non-specificational categories like quality and quantity are not realities because, although such statements like ‘the white is a tree’ might be recognizable in ordinary language, this manner of predication is only coincidental. We recognize, either implicitly or explicitly, that non-specificational categories are not underlying things which support the existence of other things, but in fact require underlying things for their presence. Aristotle says that to predicate truly and without qualification something of a quality, quantity, and the like, is not possible, even if they are kath’hauto predicates (AnPo. I.22.83a36–39): Really, it is supposed that one is predicated of another, but these that are not a specification are not predicated of themselves, for all are coincidental, but some kath’hauta, some in accordance with a different way. We affirm that all these are predicated of some underlying thing, and that an underlying thing is not coincidental. We posit none of these such things to be what is said, not being something different than what is said, but it of another and this by virtue of another. (AnPo.I.22.83b17–24)4 Since qualities, quantities, and the like are not underlying things for other categories or realities, a quality like white is not a reality, of which color (or a tree for that matter) is a quality: white is not some underlying thing for color; white simply is a color. Aristotle concludes that predicational chains whose links are qualities, quantities, and so on will come to a stop in the downwards direction: All such predications are predicated of realities and

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are in realities (AnPo. I.22.83b10–15). Predication of a reality will stop at some quality, quantity or other such category, since it is not possible to predicate without qualification one reality, quality, quantity, and the like of any other such quality, quantity, and the like. The coincidental kath’hauto predicates will be last terms, and since they are kath’hauto, are knowable. Such predications will also come to a stop in the upwards direction, because every such predicational chain is said of a single reality, and this will function as the first link in a chain, either in terms of a reality itself or functioning as an underlying thing. Non-specificational categories will be posterior to this first item. Aristotle does not think he is out of the woods yet. He asks: Can a link like Socrates–erudite itself function as a single term in a predicational chain, with other qualities, quantities, and the like being predicated of it coincidentally but kath’hauto? Aristotle states: If everything is said coincidentally, nothing that is said of another will be first, if the coincidental always signifies a predication of some underlying thing. Thus it is a necessity to go into the unlimited. But this is impossible: no more than two terms are interwoven, for the coincidental is not a coincidental to a coincidental, unless both coincide with the same thing, I mean for example ‘the white is erudite’ and ‘this is white’ because both coincide with the human. But ‘Socrates is erudite’ is not so – both coincide with something different. Since then some coincidentals are said in the latter way, and some in the former, those said in the latter – as white to Socrates – it is not possible to be unlimited in the upwards direction, like something different being coincidental to Socrates–white, for something which is one does not come to be from everything. Nor truly will something different be coincidental to the white, like the erudite, for this is no more coincidental to that than that.... Therefore not everything will be said coincidentally. Thus there will also be something signifying reality in the former way. [emphasis mine] (Meta. IV.4.1007a33–b17) Aristotle concludes further that contradictories cannot be predicated of the same reality at the same time in the same respect, e.g., ‘erudite’ and ‘uneducated.’ So realities are not something coincidental in regard to the things predicated of it, as it would be in cases like predicating a quantity of a quantity, or a quality of a quality, like ‘white’ and ‘erudite.’ Aristotle has said that an account (in this case, a statement, syllogism or proof), predicates one thing of one thing either coincidentally or noncoincidentally (AnPo. II.10.93b35–37; cf. Meta. VIII.6.1045a12–14; see

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ch. 5). For knowledge, this account is either a proof, the conclusion of one or a primary, immediate statement. Both are predicational chains. Insofar as chains are concerned then, only one comprised of two links is a possibly genuine account, like Socrates–erudite, when such categories are involved. The chain (Socrates–erudite)–white is not one chain, a unity or account because (Socrates–erudite) is not a single, unitary reality or link which coincidentally is linked to white. The linkage erudite–white confuses Socrates–white and Socrates–erudite. Therefore, since links like (Socrates–erudite)–… are not possibly genuine accounts, unlimited chains are not possible in this case either. The discussion so far has just concerned non-specificational categories, and whether they ‘go off into the unlimited.’ What about the category of specifications from (i) above? The predicational chain in a specification is comprised of the genera to which the subject (a reality) of the specification belongs, and the differences (diaphorai) of its genera (AnPo. I.22.83a39–83b1). It follows that genera and their differences are unqualified predications. For it to be possible that unqualified predications are unlimited in length, genera with their differences must be counterpredicable in the sense of (CP1): any genus distinguished by some difference has to possibly be the subgenus of some other genus, including genera being genera of each other. In other words, counterpredicable genera must possibly be mutually underlying, ‘co-inclusive,’ or perhaps unique properties of each other, in order for them to produce unlimited, unqualified chains. (Aristotle would also argue that this possibility is required in order for Quinean or other coherentist webs to exist in reality.) For example, in a definition or specification of what a human is, one might provide the following chain: human–bipedal, bipedal–terrestrial, terrestrial–animal, animal–bipedal, terrestrial–living thing, living thing–bipedal, and so on, with each of the genera, distinguished by some difference, being mutually underlying. In this case, one has a mesh or a web of links instead of a chain. In order to correspond to reality, the purported proofs representing such a web would proceed on without limit, probably in an orb web of some size. If the metaphysics of the universe worked in this way, Aristotle would insist on a robust skepticism, because one could never figure out what the initial (or ultimate) cause was of all the other links. Someone attempting to figure this out could never escape the predicational web, for in such a web everything is ultimately ‘responsible’ for everything else. (Greek has one word for both ‘cause’ and ‘is responsible for,’ ‘aition.’) No one could classify anything, and everything would be mixed with everything else. To help the reader see this point, using some contemporary examples, if the kingdoms of life on Earth were interconnected – one

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cannot use a term like ‘organized’ or ‘structured’ – along the lines of a Quinean or coherentist web, systematics would be impossible and evolution would be a joke. Since capitalism seems to work along the lines of such webs or circles, Aristotle would laugh at the thought of free-market economics being a science, assuming science involves knowledge and not just beliefs.5 However, we need not worry that the universe is ‘organized’ along capitalist lines. It is in fact not possible, Aristotle holds, for genera with their differences to be counterpredicable: any form partakes (metekhein) in its genus, but that genus does not partake in it; that genus partakes in a supergenus above it, but that supergenus does not partake in that genus below (Top. IV.1.121a10–14, IV.2.122a3–9). Aristotle defines ‘to partake’ as ‘to admit the account of the thing which is partaken’ (Top. IV.1.121a11–12). For example, the account of animal includes that of living thing, but not vice versa (plants are also living things). The account of human includes that of animal, but not vice versa (dogs and birds are also animals). For genera to be counterpredicable – i.e., for simple or unqualified predications to go on without end – the accounts of the genera involved would have to include the accounts of all the rest. However, the account of one genus cannot include the accounts of other genera that are on the same metaphysical level (AnPo. I.22.83b9–10, 15–16). Therefore, since genera with their differences are not counterpredicable, unqualified predications will come to a stop in specifications in the upwards direction at some ultimate genus. This genus will function as a first term or link. Since the subject of specifications are realities, namely the particular or form, and since Aristotle has shown by the previous argument that nonspecificational predications of realities reach a downwards limit (for these are somehow more partial than their subject), unqualified predicational chains will reach a limit in the downwards direction too, either with the final reality, or with a non-coincidental quality, quantity or the like of that reality. This link will be the last term (AnPo. I.22.83b17–31). Therefore, Aristotle concludes, it is possible to define, to formulate specifications, and therefore, it is not possible that unqualified predications are of unlimited length.6 These definitions or specifications will be foundational, and will not be conclusions of genuine proofs. Since they are unqualified predications, the terms comprising definitions or specifications are from necessity kath’hauto. Primary knowledge of them will be possible. This argument concerning specifications presumes that the genera and their differences of things in the world are limited in number. If they are not, then one could never possibly find a genus that could serve as a first term. Skeptics, or Quinean or coherentist webmasters, might insist that this

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is the reason we cannot have knowledge if Aristotle’s epistemology is correct. Whether this presumption of Aristotle’s is legitimate is a metaphysical question, not epistemological. Attempting to answer it could send us off into the unlimited!

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The Solution to the Regress Problem Part 2: The Analytical Argument

Having shown logically or universally that specifications are not possibly unlimited in length, Aristotle now offers his analytical argument. This argument shows, in his view, that human beings at least have the capacity to recognize essences: So logically from these things one might be confident about the things which were said, it is more concisely evident analytically by means of the following, that neither upwards nor downwards is it possible there are things which are predicated that are unlimited in instances of derivative knowledge, which our consideration is about. (AnPo. I.22.84a7–11) The starting point of the analytic argument is the claim that each thing in the world has certain features which belong to that thing, and these include locations in space and time. Some of these features are coincidental: For example, if I am walking along at night and shining a flashlight on certain objects I pass by, it is not on account of the walking that I am illuminating certain things. It is on account of the flashlight. The illuminating is merely a coincidental feature of my walking (AnPo. I.4.73b11–13). Although my walking in a way underlies or supports the illuminating at that moment and place, in that it would not be present without my having walked there at that time with the flashlight, it is the flashlight, and not the walking, that is the starting point of the illumination. A coincidental feature is then ‘what belongs to something and says something true, but not from necessity nor for the most part.... Therefore, since there is something belonging to something – and both “where” and “when” are among these – that something will belong, but not because this was either now or here. That will be coincidental’ (Meta.V.30.1025a4–24). Those features which are coincidental are expressible as terms in a true, believable statement. However, they do not belong necessarily, nor for the

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most part, to that thing in the world, or to that kind of thing in the world, which is the subject of that statement. Such features require a certain underlying thing for their presence, and are not self-supporting. Coincidental features of such a thing in the world are then ones which are present randomly or by chance, and not on account of what that thing in the world is. ‘There is in fact no defined cause of the coincidental but chance, and this is undefinable’ (Meta. V.30.1025a24–25). Since what happens by chance does not happen necessarily or for the most part, such happenstances will be unknowable. Here is an example Aristotle uses. Say one happens to come to the island of Aegina. However, one is on Aegina, not on account of having departed from Peiraieus in order to get to Aegina, but on account of having been brought there by pirates or by a storm. Although this happenstance, this coincidence – coming to Aegina – occurred or is happening, it did so not qua itself – not qua departing from Peiraieus in order to get to Aegina for its own sake – but qua some other cause that happened by chance, namely the storm or the pirates. Ending up on Aegina on this occasion was not a necessary consequence of departing from Peiraieus, and there was no way one could have known that they would have ended up there: being waylaid by pirates or a storm was a random, chance event. Such events are not explicable in a way that is knowable. However, not all features of a thing in the world seem to be coincidental. Say I am moving forward while walking on a trail. It is by virtue of the walking on the trail that I am moving forward, because I move forward on account of the walking. I am moving forward qua walking, and it is not a coincidence that I am moving forward while I am walking on the trail (AnPo. I.4.73b13–16).1 My walking is not a thing underlying somehow my moving forward, with the forward movement being caused by some other thing which happens to be present. Instead, it is part of what it is to be walking (on a trail at least) to be moving forward. The walking is the starting point or initial cause of the forward moving. Aristotle states that non-coincidental features belong kath’hauto to that thing in the world which exhibits them: ‘that which belongs to each thing on account of itself is kath’hauto; that which does not belong on account of itself is coincidental’ (AnPo. I.4.73b10–11).2 Importantly, some feature might be causally necessitated by some thing in the world, but still fail to be kath’hauto. So if some y is not coincidental to some x, like (y) my moving forward while (x) walking on a trail, then y is causally connected to x from necessity, or perhaps for the most part. (This causal connection is revealed by Aristotle’s use of the preposition ‘dia’ followed by the accusative case in this passage.3) Since y is the starting point of x, either from necessity or for

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the most part, this fact will be knowable. In contrast, if some y′ is coincidental to some x′, like (y′) one’s ending up on Aegina while (x′) departing from Peiraieus on a ship in order to get to Delos, then that y’ is not causally connected to that x′. Instead, the pirates or the storm is the starting point of one’s ending up on Aegina. Such a fact (ending up on Aegina) is unknowable. This causal connection between y and x reveals Aristotle’s general use of the term ‘kath’hauto’: ‘In general the “kath’ho” belongs in an equal number of ways as the “cause” does’ (Meta. V.18.1022a19–20). Thus, insofar as some x is the starting point or initial cause of some y, then y belongs to, or is predicated of, x kath’hauto, by virtue of x itself. If some x′ is not the initial cause or starting point of some y′ (and yet y′ is truly said of or belongs to x′ on account of x′ being the matter, genus or underlying thing for y′), then y′ belongs to or is predicated of x′ kata sumbebêkos, coincidentally.4 As indicated in the previous quote, the term ‘kath’hauto’ is a more particular instance of the general locution ‘kath’ho,’ ‘by virtue of that’ or ‘by virtue of what.’ Aristotle classifies two principal ways in which the general locution is used: (K1) ‘Kath’ho’ is said of the form, i.e., the reality; (K2) ‘Kath’ho’ is said of the thing in which something by nature primarily comes to be, i.e., the matter. Aristotle’s example of (K1) is the good itself is that by virtue of which one is good (Meta.V.18.1022a14–16). For (K2), colors come to be, by nature and primarily, in visible surfaces (Meta.V.18.1022a16–17). ‘So then, the thing which is said “kath’ho” primarily is the form, secondarily as the matter of each thing, i.e., the primary underlying thing for each thing’ (Meta.V.18.1022a17–19).5 Since ‘cause’ is said of things in an equal number of ways as ‘kath’ho,’ and ‘kath’ho’ is used principally in reference to the form and to the matter, ‘cause’ is also used principally in respect to the form and to the matter. Thus, ‘kath’hauto’ is equivalent to ‘cause’ in a way which is applicable to either form or matter: Something of which there is not another cause other than itself, or its kind, is kath’hauto. For example, there are many causes of human (Aristotle mentions life and bipedal) but for all that, an individual human being is human by virtue of itself (Meta. V.18.1022a32–35). Corresponding to each of the two main uses of ‘kath’ho,’ it is necessary, Aristotle says, that ‘kath’hauto’ is said of non-coincidental features of things in the world in a like manner. Corresponding to (K2), Aristotle offers one

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main description of ‘kath’hauto’: If some feature has been received by some thing in the world in itself, either primarily, or in some part of what belongs to that thing, then that feature belongs to that thing in the world kath’hauto. So, for example, the visible surface is white kath’hautên, by virtue of the visible surface itself, because visible surfaces are the underlying things, primarily and by nature, for colors. Colors are received by a visible surface in this surface itself. Likewise, an individual human being is a living thing kath’hauton, by virtue of being human itself, for the psyche is a kind of part of that human being, and the psyche is the thing in the world in which life is primarily and by nature (Meta. V.18.1022a29–32). Corresponding to (K1), Aristotle offers three variant descriptions of ‘kath’hauto’: First, what is kath’hauto is the essence for each thing. So for example, Kallias, by virtue of himself (kath’hauton), is Kallias and the essence for Kallias (Meta. V.18.1022a25–27). Second, what is kath’hauto is what belongs in the specification. So, using Kallias again, Kallias is an animal by virtue of himself, for animal is contained in the account of Kallias. Upon specifying what Kallias is, this specification will contain the term ‘animal,’ for Kallias is a kind of animal (Meta. V.18.1022a27–29).6 Third, ‘what belongs to a lone thing and qua lone thing’ is called ‘kath’hauto.’ In other words, whatever belongs to some ‘thing which has been separated’ – i.e., some thing which satisfies Aristotle’s criteria for separate, independent existence7 – is kath’hauto (Meta. V.18.1022a35–36). Kath’hauto features which belong to some subject, some thing in the world, belong from necessity, just as the features which belong coincidentally are contingent or by chance. As I have indicated earlier, things which belong from necessity can occur either always or for the most part. ‘The things which are said “kath’hauta,” in the case of the things which are knowable without qualification, are so either as being contained by the things which are predicated, or containing them, on account of themselves and from necessity’ (AnPo. I.4.73b16–18).8 (Note the ‘container’ terminology: see ch. 1.) Since what is kath’hauto is in some instances what belongs in a specification, what belongs in a specification (assuming it is proper) will belong from necessity: ‘all specifications are universal and categorical’ (AnPo. II.3.90b4). ‘Since it has been revealed to us in the things above that the things in the specification are universal, and things which are universal are necessary...,’ the things in a specification are necessary (AnPo. II.13.96b1–3).9 As indicated in the previous paragraph, the first two descriptions of ‘kath’hauto’ correspond to the essence and to the specification. There is a close bond between an essence and a specification: A specification is comprised of the terms which belong to something kath’hauto. What belongs kath’hauto are things which are necessary for that thing to be

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what it is. The ‘essence for each thing is what is said “kath’hauto”’ (Meta. VII.4.1029b13–14). Therefore, the specification reveals by means of language what the essence for something is in reality. (Since a specification is this kind of account, Aristotle thinks of such an account as a kind of reality.) Thus, the features signified by terms that reveal the essence of some thing in the world, and are indicated in a proper specification, are necessary features of that thing. Coincidental features are not a part of the essence. Correspondingly, coincidental features of a thing in the world will not then belong in a proper specification of that fact. Finally, unique properties will not be included in a specification or definition because, although they belong kath’hauto or necessarily to the things in the world of which they are predicated, they do not reveal the essence of those things.10 From the claim that began the analytical argument – that each thing in the world has certain features (including location in space and time) which belong to that thing – Aristotle has distinguished between two kinds of features: Those which are coincidental, contingent or by chance, and do not belong to the essence, and those which are kath’hauto (or by virtue of itself) from necessity and do belong to the essence for that thing in the world.11 Aristotle’s problem here concerns solely statements which are specifications and whether it is possible that predicational chains in specifications are unlimited in length. As was shown in previous chapters, derivative knowledge requires a proof and concerns what is unconditional. A proof is about things in the world; so, if one has a proof satisfactorily, then one knows some unconditional truths about certain things in the world, namely what belongs kath’hauto: So if derivative knowledge is from necessary starting points – for what one knows is not capable of being otherwise – and the things which belong kath’hauto are necessary to the things in the world (these belong in the specification, but they belong to the things which are predicated in the specification of them, of which it is a necessity that one of the two things which are opposed belong), it is evident that the apodeictic syllogism [i.e., the proof] will be from some such things: everything either belongs in this way or coincidentally, but things which are coincidental are not necessary. (AnPo. I.6.74b5–11) Moreover, ‘proofs are of the things that belong to the things in the world by virtue of themselves’ (AnPo. I.22.84a11–12). Specifications have a role of revealing the necessary features of the things in the world they signify: they state what belongs to those things kath’hauto, and thereby express the essence. Thus, it follows that what we have knowledge of when we have a

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proof is the essence for each of the things in the world at issue: ‘There is knowledge of each thing whenever we recognize the essence for each thing’ (Meta. VII.6.1031b6–7), and ‘...at any rate to know each thing is to know the essence’ (Meta. VII.6.1031b20–21). One can see now that Aristotle’s concern in this analytical argument is whether there are possibly an unlimited number of necessary features, excluding unique properties and perhaps things for the most part, which belong to a certain thing in the world.12 If it is possible, then knowledge will be impossible: any proof about such a thing would have to be unlimited in length, and it is impossible to go through something unlimited in a limited amount of time. For this reason, the possibility of specifications being unlimited in length is the same as the one that asks if there must be a proof for every statement in it in order for that proof to result in knowledge. Moreover, if the essence is recognizable, then predications in specifications will be limited, not unlimited, in length: If it were possible that the essence for some thing in the world t had an unlimited number of necessary features, then it would be possible for the specification of t to have an unlimited number of kath’hauto terms. Since Aristotle holds that ‘kath’hauto’ is equivalent to ‘cause,’ if t were the cause of an unlimited number of features, t would have an unlimited number of kath’hauto predications. Knowledge of t would clearly then be impossible. Such an essence for t would be unrecognizable by any creature with less than an omniscient degree of cognitive ability. Aristotle now focuses on these kath’hauto features of things in the world, and the predicational chains that signify them, in order to show that essences are recognizable, and accordingly that predicational chains in specifications are not unlimited in length. Proofs, recall, are about the features that belong to things in the world kath’hauta, by virtue of themselves. Aristotle says that the ‘kath’hauta’ in this statement has two different senses, with the second appearing to be more crucial for this analytical argument (AnPo. I.22.84a11–14). (Ka1) What those things contain in their specification; (Ka2) What ‘to which same things they in the specification themselves belong.’13 Sense (Ka1) clearly indicates that in a specification of a certain thing in the world, the features which belong to it kath’hauto (again excluding unique properties and perhaps things for the most part) will appear in that specification (AnPo. I.4.73a34–35, I.6.74b7–8). For example, Aristotle says, line

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will appear in the specification of triangle, and point will appear in the specification of line, for these belong to triangle and line by virtue of themselves: lines are necessary features of triangles, and points are necessary features of lines. ‘Their reality,’ namely, the reality of triangle and of line, ‘is from these,’ namely lines and points respectively, ‘and are in the account stating the specification’ (AnPo. I.4.73a35–37). Thus, sense (Ka1) here plausibly corresponds here to the first general sense of ‘kath’hauto,’ (K1), discussed above, which is said of the form, the reality of each thing in the world (Meta.V.18.1022a14–16). Sense (Ka2), ‘to which same things they in the specification themselves belong,’ occurs in variant formulations elsewhere when he is contrasting between these two senses. For example, Aristotle unfelicitously describes (Ka2) as indicating what ‘to the same things, of the things which belong, they in the account revealing the specification are in’ (AnPo. I.4.73a37–38).14 For example, straight and curved, and equilateral and oblong, are features which belong to line kath’hautê, by virtue of line itself. Similarly, odd and even, and prime and composite, are things which belong to number by virtue of itself in this same sense (Ka2). Thus, according to Aristotle’s characterization, each pair of contraries in the case of number (odd-even, primecomposite) are in number by virtue of number by nature, and each pair in the case of line (straight-curved, equilateral-oblong) are in line by virtue of line by nature: ‘they in the accounts stating the specifications are in each of these: here, line, there, number’ (AnPo. I.4.73b1–3). Slightly later, Aristotle describes (Ka2) in reference to the contraries being in, or belonging to, the thing which underlies them kath’hauto: Thus, in the case of things which are knowable simply, the things which are said ‘kath’hauta’ are so as [Ka2] being in or [Ka1] containing the things which are predicated on account of themselves and are from necessity. It is not possible not to belong either without qualification or the opposites (as straight or curved to line and even or odd to number), for the contrary is either a deprivation or a denial in the same genus, e.g., as it follows ‘even is not the odd’ in numbers. Therefore if it is a necessity that one affirms or denies, it is also a necessity that things which are kath’hauto belong. (AnPo. I.4.73b16–24)15 What I take Aristotle to be saying here is simply that for any feature F, which has a contrary ~F, there must be some underlying thing U which supports either F or ~F, but not at the same time or in the same respect. Features F and ~F belong to U. This belonging is signified by corresponding affirmative or negative statements. Likewise, if someone affirms or denies

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a contrary feature of some subject (and assuming the speaker is speaking sensibly), then this affirmation or denial is correspondingly reflected in that feature belonging or not belonging to that subject. Aristotle is not precluding differences of genera. With either (Ka1) or (Ka2) kinds of features, the containment (or the being in) occurs from necessity. With (Ka1), the subject of a specification contains the links predicated of it by virtue of itself, by virtue of what very thing it is. The specification describes what is said kath’hauto without qualification. With (Ka2), the things specified are in the subject of a specification by virtue of itself (i) either due to the subject itself being an underlying thing, matter or genus, or (ii) due to what is common to both the subject and the predicate, namely the underlying thing, of which the subject is an instance, form or species, and of which the predicates are differences or contraries.16 (Ka2) describes how contraries in a specification belong to their subject: ‘to which things they themselves in the specification belong, being predicated of those things which one of the two contraries necessarily belong’ (AnPo. I.6.74b8–10). For example, number is a genus, and even and odd are the differences qua contraries of that genus (Top. IV.2.122b18–24). Recall that some non-specificational categories, even though they are coincidental, belong kath’hauto to the things which have them. Since differences are a kind of qualification or quality, differences of a genus can belong kath’hauto: Denials or deprivations stated in specifications occur in respect to one of a pair of contraries, or anything that is in opposition to each other, which in turn occur in regard to some common underlying thing by virtue of that thing. This common thing is some genus or form: each contrary or deprivation has an opposing difference within that genus or form, and these differences belong kath’hauto. In this case, the genus or form acts as the matter to which the differences belong (Meta. V.28.1024b8–9). Following Aristotle’s example of number, in the specification of three – i.e., in stating what three is – one affirms that three is odd and prime. The odd (and its contrary even) and the prime (as well as composite) must belong to something in order to exist: odd and even, as well as prime and composite, are not independently existing things such that one could point to it, grasp it in the hand, or recognize it independently of anything else, and say ‘here, this is the odd,’ as one could with a flower (‘here, this is a flower’) or a dog (‘there, that is a dog’). The something which underlies three, as well as odd and prime along with their contraries, is in this example here number: number is the thing which is common (koinon) both to three, to odd, and to prime. Number functions as the matter for each of the contraries, with three

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(considered in abstraction as being separate from material things in the world) being a form of number. Clearly then (Ka2) corresponds to (K2), the second general sense of ‘kath’ho’ discussed above, which is said of the thing in which something by nature primarily comes to be, namely, the matter which is primary for each thing in the world (Meta.V.18.1022a16–17, 18–19).17 With (Ka2) Aristotle now solves the problem raised in the analytical argument. Odd belongs to number, or in other words, ‘odd’ is predicated of ‘number.’ However, number itself is in the account of odd (AnPo. I.22.84a15–16): In specifying what odd is, one must use number; alternatively, the concept of number is contained in the concept of odd.18 (Ka2) reveals the ground for this containment: odd is in number in that number is the matter or underlying thing for odd (and even); odd exists by virtue of number. Is there something which is to odd as odd is to number, something that would occur with unlimited kath’hauto predicational chains? If there were, [a]gain, another thing would be belonging to odd which it would be in. If this is the case, number, which is first, will be in those belonging to it. If then it is not possible that such things are unlimited in the one, they will not be unlimited going upwards. Nevertheless, it is necessary at any rate that everything belong to the thing which is first, e.g. to number, and number to these. Therefore, they will be reciprocating, but not exceeding in number. (AnPo. I.22.84a18–25) Assume some feature F belongs to odd kath’hauto, by virtue of odd itself. This belonging makes a statement like ‘odd is F’ true, primary, and necessary. (It is parallel to the statement ‘the birch is white,’ but not to ‘the white is a birch.’) Odd will be in F in that the account of F will contain the account of odd. F in turn will be in odd in the sense that odd, by virtue of itself, functions as the matter or underlying thing of F. Since each contrary has an opposing difference within a genus, and this difference belongs kath’hauto in sense (Ka2), F will have a contrary difference ~F which will also belong to odd. Now take the initial term in this series, the genus number: ‘...the first thing which is in that is said in the specification, this is the genus, whose qualifications are called differences’ (Meta. V.28.1024b4–6; Top. IV.6.128a26–27, VI.6.144a18–19). Number is now both in odd (and its contrary even) and in F (and ~F) from transitivity of belonging: F belongs to odd, odd to number; therefore, F belongs to number. Since it is presumed that this belonging is kath’hauto, number’s belonging both to odd and to F will be from necessity. Similarly, due to (Ka2), the qualification F will be in odd from necessity, and through odd, to number from necessity (Top.

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VI.6.144a24–27). It is a necessity in fact, as Aristotle says above, that everything in the series will belong kath’hauto in sense (Ka2) to the first link of that chain: the first link in this generic chain acts as the matter or underlying thing for all the subsequent contraries or differences, subgenera and forms.19 Now Aristotle wants to show that essences are recognizable. He is attempting to do this is through kath’hauto predications that reveal the essence for each thing in the world through specifications. ‘Definition seems to be of the specification’ (AnPo. II.3.90b3–4, Meta. VII.4.1030a17–18).20 Therefore, definition in Aristotle’s view signifies the essence of a thing in the world. Definitions and specifications, primarily, simply, and without qualification, reveal the reality (Meta. VII.4.1030a22–23). Essences will belong as such to realities in a similar manner as definitions and specifications, but either will not belong at all or just in a coincidental sense to the other categories (Meta. VII.4.1030a29–32). Now take a case parallel to the odd-number case: concavity to nose. ‘[S]nubness is the thing which is said from the two, a certain this [nose] in a certain this [Socrates], and not coincidentally at least is concavity or snubness a modification of the nose, but by virtue of the nose itself: It is not like white to Kallias or to human, but as male to animal and equal to quantity and everything that is said to belong kath’hauta.’ The nose, by virtue of itself in sense (Ka2), acts as the underlying thing for both concavity (which creates a snub nose) and its contrary convexity, just as number to both odd and even, as animal to both male and female, and as quantity to both equal and unequal. ‘These things,’ like male, equal, snubness, ‘are in what belongs, either the account or the name, whose modification this is, and it is not possible to reveal what these are separately, like it is possible to reveal white without human, but not female without animal.’ One cannot describe what ‘odd’ means without bringing in material concerning number; similarly, someone cannot describe ‘female’ or ‘male’ without discussing what an animal is, ‘snubness’ without bringing in noses. However, one can describe what white is separately or apart from what appears white, like visible surfaces or humans. ‘Therefore,’ Aristotle concludes, ‘either there is not any essence or definition of these things [like odd, male, snub], or if there is, in another sense, just as we have said’ (Meta. VII.5.1030b17–28). Aristotle offers two arguments as to why this conclusion follows. First, ‘it seems that the thing which is separable and the certain this belongs especially to reality’ (Meta. VII.3.1029a27–28). Differences in genera like odd, female, unequal, and snub are incapable of being separated from the genera or forms – i.e., their matter – to which they belong. Likewise, as was said above, something like odd is not a certain this, is not something

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that can be pointed to or grasped. The difference cannot be grasped independently from its genus that underlies it, either from the genus qua a form, or from a form which is linked to that genus in a chain. ‘Whenever one thing is said of another,’ as odd of number, equal of quantity, female of animal, and so on, it is not just what very thing a certain this is (e.g., the white human is not what very thing a certain this is), if at any rate the certain this belongs only to realities. Therefore, the essence is of those things whose account is a definition. A definition is not a name signifying the same thing as an account ... but if it is of something primary: such things are what is said, not in respect of one thing being said of another. (Meta. VII.4.1030a3–11) Second, following from sense (Ka2) of kath’hauto (what ‘to which same things they in the specification themselves belong,’ which in turn corresponds to (K1), the matter or underlying thing), odd, snub, and the like contain within themselves number, nose, and the like respectively: snub contains something about noses already in its account, likewise with odd and number. Now assume there are definitions of such things as ‘snub nose’ and ‘odd number.’ (This is like the link Socrates–erudite in the universal argument above.) Since ‘snub nose’ is defined as ‘concave nose,’ for example, ‘snub’ and ‘concave’ will mean the same thing – but clearly they do not mean the same thing. If they do not mean the same thing, then one could not say ‘snub nose’ (for snubness is concavity in the nose), or one will have to say ‘concave nose nose,’ which is redundant. Therefore, definitions in Aristotle’s sense of such terms like ‘snub nose’ or ‘odd number’ are impossible. Recall that definitions (like specifications) reveal the essence for some thing in the world. If there were an essence for snub nose or odd number, there would be an essence in an essence, for in the essence for snub nose, the essence of nose will be present; in the essence for odd number, the essence of number will be present. The essence for F above would be in that of odd, such that the purported corresponding predicational chain F–odd would in fact be (F–odd)–odd. Such a chain would proceed without limit. However, such essences would then fail to be separable – for the essence of F would be inseparable from odd (as signified by the chain (F–odd)) and so on – which would entail that essence would not be a reality. ‘It is clear then that definitions are of realities alone,’ Aristotle concludes, and coupled items like odd-number will not be definable, unless perhaps in some derivative or coincidental sense (Meta. VII.5.1030b14–1031a14.

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Such differences or contraries as odd–even, female–male, equal–unequal, and the like, and any of their possible intermediates, belong kath’hauto in sense (Ka2) to the things which underlie them. They therefore follow from axiomatic necessity on account of that underlying thing: Axiomatic necessity is such that given some elements, primary statements or definitions, it is a necessity that certain things follow (or in Aristotle’s parlance, are) from those elements, primary statements or definitions. For example, given the genus number and its nature, it is a necessity that odd and even, prime and composite, and so on exist. In other words, it is on account of number and what it is that differences like odd and even exist; number is the starting point or initial cause of these differences or qualifications. These differences or qualifications are not part of that underlying thing’s reality. Instead, they are coincidental to it: ‘“Coincidental” is said also in another way, as what belongs to each thing kath’hauto, not being in the reality, as the two right angles is for triangle. Also, it is possible that these are unconditional, but none of those’ (Meta.V.30.1025a30–33). Things like odd and even hence belong coincidentally kath’hauto to number. Odd belongs to number, by virtue of the nature of number, primarily and unconditionally, but odd or its account is not required in a proper specification of number. Assuming that number or triangle has an essence or is a reality, the fact is that odd or having two right angles is coincidental to the essence of number or triangle: such differences or qualifications, which exist by virtue of an underlying thing that supports their existence (here, a genus), are coincidental in a sense. The things which do not exist by virtue of some underlying thing are kath’hauto without qualification: Moreover, what is not said of some other thing by virtue of an underlying thing, like the ‘walking’ being something different from what is walking ... is reality and what signifies a certain this, not being something different, is just what it is. I mean the things which exist not by virtue of an underlying thing are kath’hauta, those which exist by virtue of an underlying thing coincidental. [emphasis mine] (AnPo. I.4.73b5–10) As examined earlier, such features that have a dual coincidental kath’hauto nature are modifications and hexeis. Moreover, some quantities are called kath’hauta, others coincidentally. For example, line is a kind of quantity kath’hauto, erudite coincidentally. Of those that are kath’hauta, some are by virtue of a reality – like line is a certain quantity (the certain quantity belongs in the account stating the

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specification) – and some are modifications and hexeis of such a reality, like many and few, long and short, broad and narrow, deep and shallow, heavy and light, and other such things. Also large and small and more and less, both are said kath’hauta and in relation to each other, are modifications of quantity kath’hauta. However, these names are also carried over to other things. (Meta.V.13.1020a14–26)21 Thus, things which belong to something kath’hauto in sense (Ka2) are kath’hauto coincidentally, and are thereby knowable for Aristotle, but not as part of an essence: the first member of the chain, which is the primary genus that functions as the ‘material’ starting point for the differences that fall underneath it, will be the only thing for which there is an essence. Therefore, the first term or link in the chain, which is the primary, underlying genus, will be the uppermost limit for that chain of kath’hauto predications. Thus predicational chains come to a stop going upwards. (Importantly, unique properties will then be knowable because they also belong to their subject kath’hauto coincidentally – i.e., belong in sense (Ka2) – but do not reveal the essence. Recognition of unique properties therefore will not entail recognition of the essence.) Aristotle adds that given any last term in a chain, this chain will come to a stop in the upwards direction at some first link, which will be this essence, regardless as to the number of links between the first and last: Of the things between, of which there is something final and prior, it is necessary that the prior is the cause of the things after it. If we had to say which one of the three [terms in a chain] is a cause, we will say the first: surely it is not the final, for the ultimate is [the cause] of nothing; however not the middle, for it is [the cause] of one (and it makes no difference if there are one or more [middles], nor unlimited or have come to a limit). Of things which are unlimited in this way, and of the unlimited in general, all of the parts which are middle are as far as the now alike. Therefore, if at any rate there is nothing first, there will be in general no cause at all. (Meta. II.2.994a10–19) Take any final term Z in a chain. The link which precedes it, Y, is a cause of that last link Z, and is the matter or the underlying thing for Z. Similarly, the link X is the cause of Y, W of X, and so on upwards, regardless as to whether this chain is really unlimited or limited. Moreover, Aristotle continues, each preceding link V, U... is causally effective in the same way to the subsequent link, e.g., W. Say W is primate. Every preceding link in the chain like (V) mammal and (U) animal is causally effective in primate. Now

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if there is no first link, this causal chain will not be able to get started: there needs to be a causal starting point for the chain in order for the account of every higher genus to partake in the account of each lower one, for such a starting point establishes the axiomatically necessary connections between the higher ones and the lower ones which follow from them. Such connections will otherwise be by declamation only, and will be only conditionally knowable. Thus, if the preceding links are unlimited in length, there will be no causal connection between the last link Z and any of the links which precede it – Z will not be linked to, and hence will not have been caused by, anything at all. If this is the case, in other words, there will be no matter for Z. Each preceding form, subgenus, genus, and so on will be in nothing, so for example, human will not be in the primate family, nor primate in mammal, and so on. Such a circumstance however is absurd. Therefore, Aristotle holds, any chain with a final term will come to an end in the upwards direction with some first term that is the material cause for everything beneath it. ‘Therefore,’ Aristotle concludes, ‘if the things which are predicated all are said kath’hauta, these things being not unlimited, will stop going upwards, therefore going downwards also’ (AnPo. I.22.84a26–28). Why do such chains stop going downwards, if they stop going upwards? Every term in a generic chain, like number–odd–F, is in the first link of that chain: It is necessary that every subsequent link in a generic chain belongs to the thing which is first – here, to number, and that number also belongs to these in the sense that the account of number is contained in the account of odd, and both likewise in F. Therefore, each of the links in a generic chain correlate to, but do not exceed, the number of genera and contrary differences. The account of number will be in the two links in the chain (odd and F), and the two subsequent links will be in number since it is their matter or underlying thing. Here now is the clincher: Aristotle says that it is impossible for an unlimited number of things to be in an underlying thing, genus or matter. In order for there to be an unlimited chain of predications going downwards, the number of links in such a chain would have to be more than the number of links that were in the first item. This scenario can occur only if links such as (F–odd)–odd are possible. However, since they are impossible, predicational chains stop going in the downward direction, if they stop going upwards (AnPo. I.22.84a18–25). In short, an unlimited number of differences is only possible if the underlying matter is unlimited. Since it is not, the number of qualifications that underlying matter can have is limited. There is no essence or definition for the links in a generic chain other than the first link of that chain. Since only a genus qua a form, or form itself, has an essence, and this first

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genus or form is more universal than the contraries, differences or qualifications that modify it, the kath’hauto predications will stop going upwards. Since the contraries, differences or qualifications predicated of that first link have neither definitions nor essences, and these are more particular than the first, the kath’hauto predications will come to a stop going downwards as well at the last terminal link. Therefore, essences are recognizable, and kath’hauto chains come to a stop in both directions. Aristotle offers an additional argument as to why things will come to a stop in the downwards direction, given some first thing. One could take some thing in the world like Kallias or Socrates not as a last thing, but as a middle or first thing, with their parts being more final – their head, a hand, flesh, and on down to the elements like earth and water – or with their progeny as more final. In this way, these parts or progeny follow from compositional necessity, and hence are kath’hauto. Their parts or progeny will come to a limit because the processes of formation and degeneration, the transitions from one part or element to another, require the dissolution of what came before. In order for this process to go without limit, the final elements or parts would have to be convertible, like water from fire, fire from water, or hand from arm or arm from hand, or from adult to child, child to zygote, zygote to child, and so on. However, this convertibility is not the case: in the parent–progeny case, each transition point in the process comes to an end at each subsequent moment (otherwise one would be stuck in a Zenoesque paradox in regard to one’s aging); in the part and element case, the formation of one element entails the degeneration of the other (otherwise one would get fire that was part air, air that was also water, and so on). Thus, the point at each stop of the process, where each element, part or individual is at, will be the final term (Meta. II.2.994a19–994b6). Now kath’hauto predications reveal the necessary features of things in the world, and knowledge according to Aristotle is about what is unconditional in this way. According to requirement (R) then, from the analytic and universal arguments, recognition of these essences, along with the definitions that signify them, will provide foundations for knowledge. In a hexical relation then, the essence will be the primary counterpart, and one’s recognition and the corresponding definitions of them, will be the secondary counterparts. The hexis the two form together will be primary knowledge. ‘If this is so,’ Aristotle states: also the things in between two terms always will have been brought to a stop. If this is the case, it is presently clear also of the proofs that it is necessary that there are starting points, i.e., that there is not a proof of

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everything.... For if there are starting points, neither [a] everything is provable nor [b] can it step off into the unlimited: the being of either of these two whatsoever [a & b] is nothing other than no interval being immediate and indivisible, but all being divisible.... But this cannot happen, if predications stop upwards and downwards. That they stop has been shown logically earlier, analytically now. (AnPo. I.22.84a29–84b2)22 Aristotle’s arguments have shown that there are intervals of predicational chains which are primary and immediate such that one cannot (or more weakly perhaps, need not) place another term or link between those intervals. Such chains are atomic (atomos). These chains will come to form definitions and specifications, and contribute to the recognition of essences. Since predicational chains come to a stop in both directions, there are starting points for proofs: there would be no need for them if every premise in a proof were provable, or if circular or reflexive proofs were possible. Those starting points that are primary, immediate and indivisible – the atomic ones – will contain either first terms (in the case of the primary genera) or last terms (certain thises or forms). Such atomic statements provide primary knowledge – knowledge obtained without a proof – and thus requirement (1/4) is satisfiable. Therefore, since (1/4) is satisfiable, requirements (M) and (P) are satisfiable as well: these atomic statements will be more recognized by nature and prior to what is dependent upon them. Once one has recognized them according to (R), one will be unpersuadable into changing one’s mind about them, which satisfies requirement (P). One will then be confident in anything that follows from them in accordance with logic. From this material about chains, one can see that requirement (2) has to involve a relevancy component: In order to know, there must be one underlying genus for a proof. This genus (matter or underlying thing) is the same thing that underlies a predicational chain, with the first genus being the initial cause or starting point for everything posterior in that chain. If two or more things in the world are in the same chain, they will be in the same genus, and the same in genus (Meta. X.3.1054b32–1055a2). All the contraries of a single category in the same chain will be different in form, but not in genus, for this genus is the common underlying thing that supports these differences (Meta. X.8.1058a13–14). Any two or more links or terms within a single chain, as long as the linkages are either axiomatically or compositionally necessary, will be knowable derivatively. Thus, in Aristotle’s theory of knowledge, the genus, matter or underlying thing is in fact the ultimate ground for the possibility of knowledge itself. If there are

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no fundamental genera – if the world is constructed along coherentist or Quinean lines – and everything ultimately partakes in everything else, there will not be any atomic statements, and hence no primary knowledge. Since all forms of perception and thinking are hexical, such that they are causally dependent on things in the world for their existence, Aristotle does not have to worry about the possibility that the world might be constructed along foundationalist lines, but can only be thought and talked about by us along coherentist or Quinean lines. If we are built such that our thinking cannot capture the way the world works, then knowledge will be impossible for us, but will exist by itself, and might be possible for different creatures with more representative cognitive abilities. It is highly important to note that there are two potential secondary counterparts to the essence: the recognition of it and its corresponding definition. Both are instances of thought, but the former is not discursive; the latter is. The recognition of an essence does not entail possessing a definition for it, and vice versa: It is possible that one could recognize an essence for something without having the equipment to represent it linguistically. Similarly, the possession of a definition or specification does not entail that one has recognized the corresponding essence, for one could obtain a definition from an instructor, or from a kind of Aristotelian dictionary, without recognizing the essence which that definition linguistically represents. A version of prong (ii) of horn 1 of the dilemma now sticks its point out again, threatening to pierce right through the heart of Aristotle’s theory of knowledge. The proponents of prong (ii) will grant that Aristotle has shown that there are limited definitions (atomic statements), and proofs will in fact come to a stop at them. They also will grant that Aristotle has provided a plausible account of derivative knowledge, and has shown that this kind of knowledge is possible. However, they will stress that what Aristotle has shown is only that his essences are recognizable, and that it is possible to define. It is obvious that we have the capacity to define, and that we do so all the time. It is not so obvious however that we have the potential to recognize these essences, and even if we do, that we actualize it. The skeptic now asks: Do we have such a potential? Other ways of putting the question are this: Do we have the means of thinking about a thing in the world, or the necessary features of that thing, without using language? Definitions, specifications, atomic statements are comprised of terms, which are the elements of statements: Where do these elements come from? It is clear that in order for someone to have genuine primary knowledge, instead of mere parroting of what she or he has heard or read, this essence recognition must come first, as essences are causally prior to such

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knowledge, and as the recognition of them is epistemically prior to one’s definition of them. (Conceivably, definitions could be causally prior if a definition prompted one to seek out its corresponding essence. In such a case though, that individual does not have knowledge until recognition occurs.) If we do not have such a potential (or less plausibly, that we do, but can never actualize it), then any atomic statements that could provide the foundations for knowledge are merely conditional (or in Aristotle’s terminology, declaimed). They are not known, and hence so-called derivative knowledge will be conditional: we could never be confident that our declamations are true – which means there will be no genuine knowledge at all. Aristotle himself, skeptics will note, has admitted that it is absurd for the conclusions of proofs to be known, but with the starting points of that proof not to be known. This admission can even be extended further: it is absurd that conclusions are known, but the starting points are recognized in a way that is epistemically weaker than the knowledge a proof can bring. Recall the necessary and sufficient conditions for primary knowledge from the previous section: p knows some a primarily if and only if (1′) a (i) has been discerned by p, and (ii) has been seen to be by p, and (iii) a is self-evident; (2′) a is true; (3′) a is necessary; (4′) p is unpersuadable into thinking that ~a is possibly the case. Genuine definitions and essences will satisfy (3′) and (2′). However, in order for Aristotle to meet this challenge, he needs to show more than the fact that we have the potential to, and sometimes actually do, recognize essences, which will lead to the satisfaction of (1′(i–ii)). He also needs to show that this kind of non-linguistic thinking is epistemically equivalent to or stronger than both primary knowledge – which will lead to the satisfaction of the self-evidence of atomic statements for requirement (1′(iii)) – and derivative knowledge, which is the only way (4′) will be satisfied. Aristotle holds that we do have this potential to recognize essences, and there is a way to actualize it. This is the potential to think without words, and the means by which we get terms for primary knowledge. This potential is nous, and its use results in thinking that is epistemically stronger than both primary and derivative knowledge. Why? There is no linguistic activity mediating one’s connection to an essence. In fact, corresponding with theory discussed in chapter 6, actualized ‘noetic’ activity results in the identity between act (thinking) and object (essence). One cannot get more justification or evidence than that – one’s mind has somehow become the

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essence. It is the act of putting this event into words that decreases its epistemic power, but it is power still strong enough for knowledge. An adequate treatment of this most difficult of topics from Aristotle’s philosophy must wait for a future work. However, I think I have provided the groundwork for it here.

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Kath’hauto Redux

Aristotle’s notion of kath’hauto has been a real bugbear to track down and capture, and it does not help matters that Aristotle deployed it so frequently. One can see its elusiveness throughout the commentarial literature as well as in Aristotle. From all the considerations above, especially those concerning kath’hauto and coincidental predication in the analytical argument, I think one can see now that Aristotle has only two principal senses of the term: one corresponding to form (sense (Ka1)), the other to matter (sense (Ka2), a.k.a. ‘kath’hauto coincidentally’). He does not have four senses for it, as many commentators traditionally hold.1 In Posterior Analytics I.4, where Aristotle first and most explicitly explains what he means by ‘kath’hauto’ in that work, some commentators hold that he presents third and fourth senses of it. The third is revealed, some argue, at I.4.73b5–10, and this sense indicates something not said of another subject, or a subject ‘in each science’s subject genus.’2 Others, for example Ferejohn, argue that there is not a genuine third sense of ‘kath’hauto’ in this passage.3 The fourth is revealed at I.4.73b10–16, which McKirahan says ‘sits awkwardly in its context,’ and concerns causal chains or connections between events.4 I think that it is much more plausible that Aristotle is employing examples in these passages in order to explicate the differences between what he means by ‘coincidentally’ and by ‘kath’hauto.’ I have five arguments in support of this position. First, the sentence in the Posterior Analytics which immediately follows the putative third and fourth senses begins with the particle ‘ara.’ This particle indicates a logical connection between these passages and what follows. What follows is a discussion only about the two senses of ‘kath’hauto’ that correspond to form and matter, (Ka1) and (Ka2). It is implausible that Aristotle would indicate a concluding summary, logically connected to the

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explanations occurring before, without also including the putative third and fourth senses in that summary. Second, as shown above, Aristotle’s treatment of ‘kath’hauto’ in Metaphysics V concerns only the two senses, ones which correspond to the two senses of ‘kath’ho’: (K1) form and (K2) matter. There is no treatment there, explicit or implicit, of a ‘kath’ho’ that corresponds to the putative third and fourth senses. As ‘kath’ho’ is a more fundamental notion than ‘kath’hauto,’ it is highly unlikely that someone like Aristotle would have only two senses of the base notion, but four senses of a notion derived from it. Third, Aristotle states that the senses of ‘kath’hauto’ have senses corresponding to the term ‘cause.’ If there were two other senses of ‘kath’hauto,’ they would clearly correspond to the other two kinds of causes mentioned by Aristotle, namely the so-called efficient and final causes. They would not correspond to the items offered in the commentarial literature. Indeed, Aristotle may regard that there are no such third and fourth senses of ‘kath’hauto’ because efficient and final causes are not necessary unless they are combined with a formal or material cause, and therefore, are not possible objects of knowledge except in that regard. This would explain why they make no appearance in his discussion of knowledge. Relatedly, as discussed in chapter 10, Aristotle appears to reduce his four causes to two, namely matter and form, with the efficient and final causes being encompassed within the formal cause. Fourth, the so-called third and fourth senses of ‘kath’hauto’ do no work for Aristotle. For example, Barnes states that ‘only the first two are directly relevant to the characterization of demonstrative propositions.’ Moreover, contrary to Barnes, the arguments in Posterior Analytics I.22 work without any reference to the putative third sense, as shown above. In fact, both the so-called third and fourth senses play no role in the solution to the problem as to whether knowledge is possible, nor in any of the other problems in the Posterior Analytics or the Metaphysics.5 Fifth, Ferejohn’s arguments for the existence of a fourth sense rest on his consideration of senses (Ka1) and (Ka2) of ‘kath’hauto’ as being ‘analytic’ in a derogatory, post-Quinean sense of the term (and thereby trivial or philosophically worthless). In order for Aristotelian ‘science’ not to be trivial or philosophically worthless, he thinks Aristotle needs to admit empirical, contingent statements (in the modern sense) into his proofs, which are satisfied by this fourth sense. Aydede offers similar arguments for the importance of this fourth sense.6 Most problematic with this reasoning is Aristotle’s explicit requirement that all premises in proofs must be necessary, a requirement that Ferejohn recognizes.7 Thus, such an introduction of this fourth sense of ‘kath’hauto’ creates a contradiction in Aristotle’s

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philosophy, one which Ferejohn tries to work out. Such work is a product not of Aristotle, but is the result of reading modern conceptions and prejudices of definition, necessity, analyticity, and ‘science’ into Aristotle. Barnes, as indicated above, and McKirahan, both hold in contrast to Ferejohn that this fourth sense ‘is not central to the theory of science,’ yet introduce it anyway.8 From these arguments here, and more importantly, from the material above, it is relatively clear now that Aristotle formulated and employed only two senses of the term ‘kath’hauto.’ This bugbear has at least been corralled!

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Aristotle’s Theory of Knowledge Summarized in Modern Form

For any potential knower p, starting point a (a may be either a definition or declamation, or the reality signified by that definition or declamation), thing in the world t and statement s of t, p knows s derivatively if and only if (1) a is the initial cause of t; (2) a (i) has been discerned by p, and (ii) has been seen to be by p, and (iii) a is self-evident; (3) s (i) has been discerned by p, and (ii) has been seen to be by p, from a in accordance with a logical procedure; (4) a and s are true; (5) s is relevant to a; (6) it is not possible for t not to be caused by a; (7) p is unpersuadable into thinking that ~a or ~s are possibly the case. Here, my (1) corresponds to Aristotle’s requirement (1), (2) to (R), (3) to (M), (4) and (5) to Aristotle’s requirement (2), (6) to his requirement (3), and (7) to (P). With p and a being the same as in the previous analysis, p knows some a primarily if and only if (1′) a (i) has been discerned by p, and (ii) has been seen to be by p, and (iii) a is self-evident; (2′) a is true; (3′) a is necessary; (4′) p is unpersuadable into thinking that ~a is possibly the case.

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Introduction 1

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For a very good defense of the ‘systematic’ or ‘unitary’ interpretation of Aristotle’s natural philosophy, one which fits well with my account of his theory of knowledge, see Falcon (2005, ch. 1). I sometimes transliterate important or controversial passages into Roman, italic characters in footnotes. I use two letters to signify one Greek letter where necessary, e.g., ‘th’ for ‘θ’ or ‘kh’ for ‘χ.’ The vowels ‘η’ and ‘ω’ are signified by ‘ê’ and ‘ô’ respectively. The iota-subscript is indicated by a ‘j ’. Burnyeat (1981, 101–102, 126–127, 132–133). Taylor begins his account of Aristotle’s epistemology with this argument, and it resurfaces throughout his discussion (1990, 116–117, 121, 123–124). In a recent article, Lesher describes this argument as having been ‘convincingly established,’ and notes its widespread acceptance (2001, 45–46). Harari uses ‘knowledge,’ but is a member of the Burnyeat camp and takes this term to mean ‘conceptual understanding’ for Aristotle (2004, 117–120, 139–141). One can check out Irwin’s much shorter argument against (2), which is based on Posterior Analytics I.3 (1988, 530, note 24). For starters, see Zagzebski (1996, Part II, chapters 1–5, especially 134–137). This work, along with Kvanvig’s and James Montmarquet’s, is foundational to this movement.

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Section I Chapter 1 1

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Instances are almost too numerous to mention. See Liddell & Scott (1996, ‘hexis’ II.1–3); Bonitz (1955, 261a13–24); Ross (1997, I.336); Hardie (1980, 103–116); Owen (1986, 337); Kato (1987, 193ff.); Barnes (1994, 260); Byrne (1997, 171); Gould (1994, 182–184). Ferejohn translates ‘hexis’ as ‘condition’ in a sense that includes ‘faculty’ (1991, 45, 147, note 17). Even magisterial works like Irwin (1988), Broadie (1991) or Annas (1993) do not examine this concept to any noteworthy extent. For support that what is at issue here is the wearing or using of the clothing, and not the mere possession, see e.g. Ross (1997, I.336); De Rijk (2002, I.466–471). ‘Diathesis’ is often translated as ‘disposition’ or ‘condition.’ Either has its problems. ‘Constitution,’ though perhaps sounding awkward at times, captures all the important different uses ‘diathesis’ had (including medical and physical), has intelligible variants that correspond with the Greek, and is philosophically neutral. ‘Constitution’ does at times imply ‘stability’ in English, whereas ‘diathesis’ need not in Greek. This passage is very important in the literature on Aristotle’s ethics, and where a lot of confusion has ensued due to the ‘disposition’ interpretation of hexis: hexeis de kath’has pros ta pathê ekhomen eu ê kakôs, hoion pros to orgisthênai, ei men sphodrôs ê aneimenôs, kakôs ekhomen, ei de mesôs, eu…. Hutchinson translates this passage as ‘by “hexis” I mean those things in virtue of which we are in a good or bad condition with respect to the feelings,’ and then argues that this definition is different from the one in the Metaphysics because ‘conditions’ are not the same as ‘being disposed,’ his translation of ‘diakeitai’ (1986, 8–9). This assertion is grounded solely on reading ‘condition’ into ‘ekhomen,’ which is unwarranted, especially in the face of the aforesaid use of ‘ekhein+adverb’ to mean ‘to be…,’ and in the face of the parallel (and seemingly more precise) rendering the Metaphysics: ‘kath’hên ê eu ê kakôs diakeitai’ versus ‘kath’has … ekhomen eu ê kakôs.’ (Recall how ‘ekhein’ is the grammatical root of ‘hexis,’ so one could argue that the definition in EN is circular.) ‘Pathê’ (sing. pathos) is one of those terribly difficult terms to translate, and ‘modification’ is to me the best option. Aristotle has multiple conceptions of change. ‘Change’ translates ‘kinêsis,’ ‘transition’ ‘metabolê,’ both with corresponding variants. Aristotle has both of Ackrill’s uses in mind with his criteria of ‘length

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of time’ and ‘changeability’ (1994, 104–105). Aristotle might appear inconsistent between using health and illness as examples of hexeis (in the Metaphysics) and of constitutions (in the Categories). Barring any simple change of mind, Aristotle simply can be using health and illness as examples of things that change quickly from one to the other and back again: although one may change quickly from being healthy to being sick, the prediliction to be healthy or to be sick (which is the hexis) is not easily changed. See De Rijk (2002, I.740–743), for his discussion of potential in regard to hexis. One might argue that the container is changed by containing something. Aristotle would respond that even if this were so, this change is coincidental, and not a kath’hauto change. The latter kind of change is what Aristotle is concerned with here. The first kind of hexis could also be understood using the form–matter distinction: On the positive side, the haver is the form that controls what it has, namely its matter. In this case though, the matter does not receive the form, nor is the form in the matter. On the negative, the had is a form, whose productivity is hampered by some matter. This matter is not in the form. The fact that having an illness here is a donor-recipient hexis is not that there are viruses or bacteria inside their human host (which is an example of a container-contained hexis), nor that pathogens or some distemper control the behavior of their host, say in the case of rabies (which would make it a hexis of the first kind), but that there is an imbalance or disruption, caused by the pathogens or distemper, in that person. The constitution of that human being is changed by the presence of these malignancies. Thus Aristotle would understand the ‘has’ in ‘she has a cold’ as having three different senses. Cf. Meta. IX.1.1046a19ff. et al. One can see from my discussion that there is a strong connection for Aristotle between ‘hexis’ and ‘to have.’ It is obscured if one uses only the account of ‘to have’ found in the Categories. Interestingly, De Rijk argues for the same point though using only the list from the Categories (2002, I.467–468). Ackrill in contrast holds there is no connection (1994, 112). De Rijk broadly explains the term ‘hexis’ in regard to ‘to have’ as ‘being so-and-so in virtue of the thing had’ or ‘being in-formed’ (2002, I.415–417, I.466–471). …ou kakôs Platôn ephê hoti eidê estin hoposa phusei, eiper estin eidê, alla [g’ou] toutôn hoion pûr sarx kephalê: hapanta gar hulê esti, kai tês malist’ousias hê teleutaia. I am inclined to read ‘alla g’ou’ with Christ as opposed to Ross, or indeed to read ‘alla’ alone, but as ‘– not.’ Ross claims that

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Notes such a reading is (a) very unnatural, and (b) he holds that Plato says there are forms for fire, flesh and head (1997, II.356–357). Claim (b) is very controversial, and Aristotle might have had a different interpretation of Plato. Claim (a) might be correct; however, Aristotle here is praising Plato for a position he held, and under Ross’s reading, it becomes very unclear as to what Aristotle is praising Plato for. The first part of the statement is that forms are what exists by nature, but it is immediately qualified by the statement ‘if indeed there are forms.’ So Aristotle appears not to be praising Plato for claiming that forms are what exists by nature, but something else – namely, that things like fire, flesh and head are not things which are most ‘by nature,’ but individuals or their form. Ross’s version of this text makes this reading very difficult to obtain. This interpretation does not presuppose the possibility of uninstantiated forms, although it seems to entail it. I cannot examine this issue with the care it deserves here. Aristotle’s account of this term in Metaphysics V.27 supports my position. ‘…Also, the reality (ousia) must remain: if a drinking-cup is deformed,’ that is, if is deprived of a part or parts, ‘it still is a drinkingcup...’ (Meta. V.27.1024a14–16). ‘Kolobos’ is better translated as ‘deformed,’ rather than the more usual ‘mutilated,’ because the Greek term can be used in reference to teeth or horns that have been worn down over time, to parts of the body whose growth is stunted, and even to truncated geometrical objects. ‘Mutilated’ has too narrow of a connotation (one of damage or injury through violence, usually with a knife) in comparison. I will not fully deal with ‘kath’hauto’ until Section III. For now, it suffices to note that the concept kath’hauto is the contrary of relative (Cat. 6.5b15ff.), which is indicated by the use of the preposition ‘pros’ in this passage. (‘The relation’ is a translation of ‘to pros ti.’) Thus, the basic meaning of the ‘kath’hauto’ qualification here can be understood as ‘according to or in respect of itself, concerning itself, by virtue of or owing to itself, or for the purpose of itself,’ or neologistically, ‘selfly.’ Holon legetai hou te mêthen apesti meros ex hôn legetai holon phusei, kai to periekhon ta periekhomena hôste hen ti einai ekeina: touto de dikhôs: ê gar hôs hekaston hen ê hôs ek toutôn to hen. I take it that, since Aristotle is using the ‘te...kai’ construction here (and not the more customary ‘eti’ or ‘hena tropon’ to indicate differences in senses), the ‘touto de dikhôs...’/‘this works in two ways’ affects both senses of ‘whole’ here, if indeed there are two. Moreover, the examples he uses later in the passage seem applicable to both, which inclines me to think there is only

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one general sense of ‘whole’ under discussion here. The ‘kai’ phrase would then be just exepegetic, indicating an alternative or an additional way of expressing what was said in the ‘te’ phrase. A strong reading of this example is that the relation between individual and universal can be understood in terms of a relation between part and whole. Evidence for this reading is the fact that Aristotle does not devote any (of the surviving) chapters in Metaphysics V to either universal or individual! However, the weaker reading of this example would be that the individual–universal relation is merely illustrative of the part–whole relation, say by analogy, but is different from the part–whole relation. I refrain from resolving this problem here. This term is very difficult to translate: At times it seems synonymous with ‘energeia’ – which I am translating as ‘actuality’ – but there are some instances where they seem to be used differently, e.g., Meta. IX.8.1050a22–23. Also, there is no felicitous English word that captures its full meaning. So I opted for translating each differently, primarily using ‘fulfillment’ for ‘entelekheia,’ but occasionally adding ‘actual’ to it for clarification or to indicate its closeness to ‘energeia.’ I also use ‘completion’ as an alternative. The term ‘purposiveness’ or ‘Zweckmäßigkeit’ is helpful when trying to understand ‘entelekheia.’ Cf. Alexander In Meta. 387,12–388,14; Ross (1997, I.319–320). Kirwan says ‘[a] whole must be without its parts in respect of coming to be, because the “absence” of the parts (in the sense of their not being actual) is implied by the whole’s coming to be’ (1993, 156). This is incorrect at least when the parts themselves are actually prior to the whole: see my example of the Delian League. Kirwan also sides with Alexander and Ross, even though his translation of the passage at issue is friendly to mine (‘…either as each being one thing or as making up one thing…’ [sic]), and he notes that in Aristotle’s chapter on parts, there is nothing that corresponds to this whole qua universal (Kirwan [1993, 60–61, 175–176]). My interpretation does not suffer this problem, and as we will shortly see, is key for understanding Metaphysics VII.10, and for seeing that ‘part,’ especially in regard to a logos, can either refer to genera, species and differentia, or things like head, hand, flesh and the like.

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What Aristotle means by ‘relation’ is somewhat different from its current, especially philosophical, use. Much of the modern philosophical notion is based upon its expression in logical systems, which is not the case with Aristotle. One could say that the root of the modern notion of ‘relation’ is ‘is related to,’ whereas the root of Aristotle’s notion is ‘relational’ (Mignucci [1986, 102–103]). Although the modern notion is broader than Aristotle’s, it would exclude many things Aristotle takes to be relations, e.g., the heat–heatable relation. The German ‘Verhältnis’ is a better translation of ‘pros ti,’ for it captures most (if not all) of the various nuances that ‘pros’ carries. ‘Even though lying, standing, and sitting are positions, and thereby relations, to be lying, to be standing, and to be sitting are not positions, are not relations, but are called positions paronymously…’ (Cat. 7.6b11–14). pros ti oun estin hosa auta haper estin heterôn legetai, ê hopôsoun allôs pros heteron. Ackrill and Irwin for example discuss only the ‘of’ condition (i.e., the genitive) and not the ‘in regard to’ condition (1994, 98–99; 1988, 73–75 respectively). Some things are also considered to be relations derivatively, either because the genera to which these things belong are relations (e.g., medical knowledge is considered to be a relation because the genus knowledge is a relation), because they are abstractions of things which are related (e.g., equality or similarity are considered relations because there are things which are equal or similar), or because they possess certain coincidental features which are relations (e.g., a human being is considered to be a relation because he is twice as tall as his child) (Meta. V.15.1021a29–1021b11). It is beyond the scope of this work to discuss proportional and dynamic relations, especially in intensional contexts. However, in brief, it is important to note two points when Aristotle says ‘whenever one sees definitively some thing relational, one will also see that in relation to which it is said’ (Cat. 7.8a36–37): (1) In my view, the verb here (‘eidenai’ ), although intensional, does not mean ‘to know,’ but is something weaker and more general, indicated by my translation. Thus one does not stumble over trying to translate ‘aoristôs eidenai’ (Cat. 7.8b9–10), which would be ‘to know indefinitively’ – something which does not make any sense – if one were consistent in their translations. (2) From (1), the conditional above does not exclude seeing relations tentatively, broadly or ‘indefinitively,’ thereby allowing someone to see that

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something is a relation and related to something else without knowing or seeing precisely what one or both counterparts are. For example, one can see ‘indefinitively’ that 1,515,798 is twice another number, simply by seeing that it is a number and that it is even, even though one cannot see definitively what that number is. If one sees definitively 1,515,798, one will see definitively that it is twice 757,899 (cf. Mignucci [1986, 109]). (1) and (2) help resolve some of the problems Ackrill and Mignucci face in their accounts of this passage (1994, 101–103; 1986, 108ff., esp. 119–121 respectively). This and the preceeding paragraph are my paraphrase and analysis of the Jaeger text, which is as follows: ta men oun kat’arithmon kai dunamin legomena pros ti panta esti pros ti tôj hoper estin allou legesthai, alla mê tôj allo pros ekeino.... There is an alternative reading cited which replaces the ‘hoper estin’ with ‘auto ho estin.’ This passage from the Metaphysics (V.15.1021a26–1021b4) is very difficult. In my view, the commentarial literature’s purported ‘second’ definition of relations in the Categories (‘to einai t’auton esti tôj pros ti pôs ekhein,’ Cat. 7.8a32), also found at Topics VI.4.142a26–31 and VI.8.146b3–4, is based on this distinction between kath’hauto relatives and relative relatives. This second definition is specifically of kath’hauto relatives, which are either proportional or dynamic, but not hexical. The broader definition encompasses both kath’hauto and relative relatives, as 8a33–34 states. Thus, a rudder is hexically related to a boat: the boat is the primary counterpart, the rudder secondary; the presence of a boat does not automatically entail the presence of a rudder, say in the case of a canoe, but the presence of a rudder implies the presence of a boat (note, either a potential or actual one). The rudder is the part, the boat the whole. The same goes for heads and hands: these are relatively relative to creatures, and are secondary counterparts to them (Cat. 7.7a7–21; 7.8b15–21). My interpretation fits nicely with the account above of parts and wholes, especially in terms of priority and posteriority, as well as hexis. Thus I agree with Mignucci, against Ackrill and many others, that holding the difference between the first and second definitions of relations in the Categories involves a secundum dici/secundum esse distinction is problematic (1986, 107–108, esp. footnote 8; 1994, 101–103 respectively). I take Aristotle to have a modalized conception of terms like ‘always’ and ‘simultaneous,’ and not a temporal conception of modal terms, like ‘necessary’ and ‘possible.’ This is a contentious issue, and I cannot treat it here. Support for my reading will be evident by the material that follows.

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Notes This position prima facie does not commit Aristotle to some sort of bizarre metaphysics, with some item called ‘the heatable’ coinciding with different items, say something called ‘water.’ It is unclear as to whether water would exist if heat were to disappear from the universe, so take the divisive and the cuttable for an example. It seems that on Precambrian earth there were cuttable things without there being things like knives, teeth, and the like. However, Aristotle might say in his defense, the cuttable qua quality did not exist (at least in actuality) until the divisive qua quality came to be (at least in actuality). It also seems plausible that the potentially cuttable necessarily requires the potentially divisive, and vice versa, for the denial of this claim seems nonsensical: it would be like saying there could be something twice as big, but without there being anything it could be twice as big as. Given Aristotle’s examples and use of the term ‘nature’ in this account, De Rijk’s claim that this symmetry is merely logical, i.e. that it is merely a logical and not natural or metaphysical co-existence between counterparts, is mistaken (2002, I.428). Irwin seems to hold a view like De Rijk’s by saying that relations are dependent on descriptions (1988, 74–75). Aristotle contends that sometimes one needs to create a term for a counterpart in order to properly talk about it. This contention means that the counterparts in a relation are prior to, or independent of, language: one can sometimes see the counterparts in a relation independently of one’s language. This fact would be impossible if relations were dependent upon descriptions or other logico-linguistic devices. Cf. Meta. IV.5.1010b30–1011a1. For the opposite claim about Aristotle’s position in relation to Protagoras, see Lee’s Epistemology after Protagoras (2005), chapters 6 and 7. She holds that one of the principal criticisms Aristotle has for the Protagorean perspective is that it makes thinking passive (ibid., 140, 154, 159). I think the passages from Meta. X.1, Meta. X.6, Cat. 7.7 (all quoted above at length), and my argumentation so far, show that the reverse is in fact the case: the Protagorean view makes the human being the active agent whose features at that moment determine somehow the features of object being perceived or recognized in some fashion. This view gets perceptual and epistemic relativism going, and from here leads one to conclude that compresence of opposites is a fact (namely, that everything has somehow contradictory properties in the same way at the same time). Although Aristotle accepts that nature is in constant change, since he adheres to the principle of non-contradiction, he has to reject compresence of opposites. Hence, he is committed to the rejection of perceptual and epistemic relativism, and hence,

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the ‘active agent’ view of knowledge and perception. Lee does not address these crucial passages from Meta. X, and she does not seem to offer a positive argument with textual evidence that Aristotle did in fact hold this ‘active agent’ or ‘thinking is active’ view. She briefly mentions Cat. 7, but does so in order to point Aristotle’s ‘realist metaphysical convictions,’ which she then says might amount to nothing more than a ‘prejudice’ (2005, 179). I believe my material so far has shown that his metaphysical realism has a firm philosophical basis, that he took Protagoras to hold the ‘active agent’ view and rejected it, and that Lee’s account is problematic.

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These two different ways of consideration seem to have been neither noted nor employed before. A possible exception is Burnyeat (1981, 97), but he drops the matter immediately. The ‘for us’ locution is analogous to Paul Moser’s characterization of knowledge as ‘perspectival.’ However, Moser has no analogue to knowledge by itself because he takes knowledge to require belief or assent, and both of these are perspectival (1989, 23). For Aristotle, since knowledge is posterior to the knowable, knowledge exists independently of belief, and since the knowledge I have of x is identical to the knowledge you have of x, knowledge is not perspectival. In fact, as an opponent of the Protagorean view, Aristotle would have to insist that knowledge is not perspectival. I supply the terminological variations in order to help the reader see what Aristotle is meaning with ‘energeia’ and ‘entelekheia.’ I cannot discuss here two very important issues involved with potential: (i) the difference between potential as a source of change (i.e., a capacity) and potential as a level of being (i.e., potentiality); (ii) the physics and metaphysics involved in the change or transition between one level and another. For (i), see e.g., Ide (1992, 1–26); for (ii), see e.g. Burnyeat (2002, 28–90). Following Ide, I take it that a potential qua level of being requires a potential qua capacity, but not vice versa. The application of the potential/actual distinction to various parts of Aristotle’s epistemology is very fecund (I use it elsewhere too), and I do not know why it is not more frequently used. For example, it can resolve all of the problems Harari raises concerning epagôgê, nous, learning, and evidence (2004, 19–25).

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Notes Thus both Hardie and Gould are correct to some extent in regard to a hexis like knowledge at this level of being. In short, Hardie takes a hexis to be a physical property, whereas Gould, who is challenging this view, takes it to be a psychological one. Hardie is correct in that it is a qualification of a psycho-physical organism; Gould is correct in that it exists regardless as to whether the hexis is being manifested empirically. Both however take a hexis to be a disposition in the modern sense, which, as I have shown, is incorrect (Hardie [1980, 103–116]; Gould [1994, 182–184]). A passage from the Metaphysics restates this point: ‘…even if the coincidental (to sumbebêkos) were said in the cases of genera, i.e., names of a kind of universal – e.g. that a human is the same as an erudite human, either because erudite coincides with human, being one in reality, or because both of the particulars [erudite and human] coincide with someone, like Korsikos – both do not belong in the same way, but the one perhaps as a genus and in the reality, and the other as a hexis or modification of the reality’ (Meta. V.6.1015b28–34). This kind of knowledge, though, is not ignorance, which I will discuss in chapter 6. In this section of the Prior Analytics, Aristotle characterizes the three levels of knowledge in a uniquely different way. He states: ‘“To know” is said in three ways: as in respect of the universal, as in respect of the appropriate thing, or as in respect of actualizing…’; to gar epistasthai legetai trikhôs, ê hôs têj katholou ê hôs têj oikeiaj ê hôs tôj energein (AnPr. II.21.67b3–5). Cf. Cat. 7.8a13–28. Irwin states that ‘the reasons for assigning these genera and species [i.e., of knowledge] to different categories rely wholly on features of the genus-words and the species-words’ (1988, 75). As one can see, this claim is incorrect: Knowledge is assigned to a category dependent upon the level of potential it is at. Thus Hutchinson, when he says that hexeis are either perfect or imperfect, excellent or crude with no third possibility, is correct when one takes the hexis in terms of genus, differences, and forms, but incorrect in terms of an ordering of parts, like grammar and syntax, in a knower (1986, 20ff.). Aristotle does state that hexeis can become better (EE II.1.1219a6).

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Wedin (1988, 13–14) for example agrees that the parts of the psyche are differentiated by their objects, i.e. counterparts. However, he holds that it is differences in the descriptions of objects, and not what the objects are, which accounts for the differences in the psyche and in hexeis. This cannot be correct given the nature of hexeis and the primary/secondary counterpart relation involved. Thus, the fact that hexeis are differentiated in this way is not ‘formal’ as he claims, but ‘material.’ Thus, Aristotle has good reasons for distinguishing the parts of the psyche in this way, contrary to Bostock (2000, 77–79). At one point, he calls Aristotle’s account of the division of the psyche ‘ridiculous’: ‘exactly the same thinking may be undertaken for either purpose [i.e., for theoretical or practical reasons], but surely it is ridiculous to credit it to one part of the soul [psyche] in the one case, and to a different part in the other’ (ibid., 78). Aristotle would clearly scoff at this claim, and would say instead (and indeed says at various points) that different kinds of thinking – in particular knowledge and belief – can be about the same thing in the world, just not the same features (or aspects) of that thing. Bostock errs in making the initial division as one between the part that has emotion versus the part which has reason, and then dividing the latter between the parts which deal with what is necessary versus what is contingent (2000, 75). kai hupokeisthô duo ta logon ekhonta, hen men hôj theôroumen ta toiauta tôn ontôn hosôn hai arkhai mê endekhontai allôs ekhein, hen de hôj ta endekhomena. It is unclear here as to whether Aristotle wants to say in the latter part of this passage either ‘…of the things which are, whose starting points are possibly otherwise’ or simply ‘such things that are possibly otherwise.’ At EN VI.4.1140a23, he uses ‘the thing which is possibly otherwise’; at 5.1140a33–34, he uses ‘whose starting points are possibly otherwise.’ Following Aristotle’s practice, I will also remain ambiguous on this issue for right now. It is also likely, as I will argue later, that he is not implicitly using theôreô in the last phrase. It will have to wait as to whether knowledge concerns things that are or arise ‘naturally’ – i.e., whether that which arises naturally is from necessity. It is clear however that there is no skill concerning these things, because the starting point for things that come to be or are naturally are not in the maker, but in the natural thing itself (EN VI.4.1140a15–16).

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Notes It is unclear how a commentator such as Anthony Kenny can note the equivalence of ‘logizesthai’ and ‘bouleuesthai,’ and the division here according to what is necessary and contingent, but fail to note that (factual) belief, as well as skill and prudence, also concerns what is contingent (1979, 91–92). Ando makes this mistake as well (1965, 216). There is no explicit evidence that ‘aphronsunê ’ is the strict contrary to phronêsis, in contrast to ignorance (agnoia) to knowledge and incompetence (atekhnia) to skill. (For ignorance as the strict contrary of knowledge, see e.g. AnPr. II.21.66b25–26, AnPo. I.16.79b23ff. For incompetence as the strict contrary of skill, see e.g. EN VI.4.1140a22–23.) However, there are several considerations for taking ‘aphrosunê ’ as such. First, there is some indirect textual evidence which supports treating this term as the strict contrary (e.g., EN VII.3.1146b27; EE I.2.1214b10). One might also conjecture ‘aphronsunê ’ for ‘aphronôs’ at EE VIII.1.1246b6. Second, this is the only term I have been able to find that would plausibly fit this role. Finally, it works well as a Greek placemarker for the contrary to phronêsis, even if Aristotle had used a different (and presently unknown) term, or no term at all, to mark its contrary. Of all the hupolêpseis, only prudence and impracticality are affected by pleasure and pain. Knowledge, skill, factual belief, and their contraries are not affected by them. ‘Pleasure and pain do not destroy or pervert every hupolêpsis – like that the triangle has (or does not have) angles equal to two right angles – but those concerning the thing which is practicable’ (EN VI.5.1140b13–16). So according to Aristotle, one would not genuinely change to the contrary their hupolêpsis that a triangle has (or does not have) angles equal to two right angles, even under extreme duress. However, any hupolêpsis concerning what is or is not to be done, what is bad or good could be genuinely changed, given the prospect or occurrence of a certain degree of pleasure or pain. De anima III.3 provides more evidence for this. Not noting these differences, Bostock says that Aristotle’s way of distinguishing prudence from skill is ‘mistaken,’ and couches it in terms of appraising ‘a series of bodily movements as a piece of making (a production)’ versus appraising ‘a series of bodily movements’ ‘as an action’ (2000, 81–82). Given my fourfold differentiation, Bostock is clearly wrong, and especially since the distinction between skill and prudence is not intensional (i.e., in terms of a difference in appraisal), but extensional (i.e., in terms of a real, material or psychological difference in things in the world).

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Recognition that belief has this broader sense works felicitously with other discussions, for example in the De anima, III.3.428a18ff. and III.7.431b2–12. The failure to notice clearly Aristotle’s differences in use of ‘belief’ dramatically affects Ando’s account of this taxonomy. For example, he at times conflates knowledge with belief, as well as knowledge with prudence and skill, in regard to their subject matters, while arguing that belief is not practical. He then seems to argue that the doxastic part is indeed the ‘practical intellect,’ but at times is ‘in part, if not entirely, theoretical cognition’ (1965, 222–224; 229–231). For a clear discussion of what would be factual belief, in contrast to deliberative belief, see Posterior Analytics I.33, where Aristotle asks whether there can be both knowledge – which is strictly only factual – and belief about the same thing. Cf. AnPr. II.15.63b40ff. Bostock claims that good-will (he translates the Greek as ‘good deliberation’) is a part of prudence, but not the whole of it, because ‘obviously Aristotle cannot have quite meant this’: namely, that good-will is something different from prudence, with prudence being identified with a true hupolêpsis about an end (2000, 85). This claim need not be true: it seems one can be excellent at determining an end, but terrible at determining the means to that end, and vice versa. Given Bostock’s claim, however, this does not seem possible, for in his view one who has excellence in the former will automatically have excellence in the latter. I quote the Greek here in full, as this is a passage any opponents to my account will use: estô dê hois alêtheuei hê psukhê tôj kataphanai ê apophanai, pente ton arithmon: tauta d’estin tekhnê epistêmê phronêsis sophia nous: huplêpsei gar kai doxêj endekhetai diapseudesthai. At first glance Aristotle seems to be saying here that ‘[i]t is possible to be mistaken in hupolêpsis and in belief.’ This translation however contradicts his classification of knowledge, prudence, and skill as forms of hupolêpseis. However, since belief can be true at one time but false at another, one can take the ‘kai’ as explicative. The point he is making here then is that one cannot simply say that the hexeis by which the psyche arrives at truth are hupolêpsis and nous and the combination of the two (which is wisdom), because hupolêpsis includes deliberative belief, which is sometimes false, either factually, practically or through incompetence. Aristotle uses ‘hupolêpsis’ in a similar way at AnPr. I.39.49b6–9 and at Cat. 7.8b7–13. Contrary hexeis, like knowledge and ignorance, share the same primary counterparts: such contraries are ‘the things most differing under the same potential’ (Meta. V.10.1018a29–30). The potential

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Notes here is being able to ‘see,’ or to recognize, things which are from necessity, which in turn are the starting points for knowledge and ignorance. My account may seem close to Wedin’s, who describes ‘hupolêpsis’ as ‘“taking or holding something to be the case”,’ and ‘appearing to be an essentially propositional notion’ (1988, 104). However, ‘having a logos’ is not equivalent to ‘propositional’ or to ‘taking something to be the case.’ Wedin does not discuss ‘hupolêpsis’ in terms of hexeis, which is crucial in my view for fully understanding the notion, especially in the case of Meta. IV.3.1005b23–32. In comparison, Irwin states that ‘[t]hough Aristotle lacks a special term for the entertaining of a proposition, he needs to distinguish it from belief and supposition (hupolêpsis)…’ (1988, 320). Barnes notes that hupolêpsis is a genus, but only states knowledge and belief as its species (1994, 201). Hamlyn says the term ‘appears to express a very general notion which functions somewhat as the notion of judgment did in the writings of the Absolute Idealists such as Bradley,’ without explaining what the Absolute Idealist account of judgment is (1968, 130). Ross says that Aristotle ‘sometimes uses doxazein and hupolambanein without distinction, but strictly hupolambanein implies a higher degree of conviction than doxazein, something like taking for granted’ (2001, 411). One can see that Ross is incorrect. Harari translates ‘hupolêpsis’ as ‘belief’ on one page, but then on the next translates it as ‘universal judgement’ (2004, 18, 19). Wedin says ‘[j]ust as there are many figures that count as a plane figure so there are many ways to hold that something is the case.’ He adds ‘[a]s a rule,’ ‘hupolêpsis’ and its variants ‘are employed when what matters is not how but simply that something is taken to be the case’ [emphasis mine] (1988, 104, 105 respectively). ...kai to aisthêtikon, ho oute hôs alogon oute hôs logon ekhon theiê an tis rhâjdiôs. Misleadingly, Ross, Hamlyn, and Smith all take this sentence to mean ‘one cannot easily ... either as irrational or as rational,’ which is very much unwarranted due to 1) the ‘oute ... oute’ construction, and 2) no negative modifies the verb. Their English translation might be warranted if there was another negative affecting the verb. The Seidel/Theiler German translation has ‘und den wahrnehmenden, den man weder ohne weiteres als irrationalen, noch als rationalen ansetzen wird...,’ and is equivalent to my English one. Aristotle does not make this additional argument explicitly. However, it is warranted by analogous arguments he makes concerning prâxis (where animals have perception but not prâxis, therefore prâxis is not perception) and imagination (phantasia, where many animals have

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perception, but only a few have imagination, therefore perception is not phantasia) (EN VI.2.1139a18–20; DA III.3.428a9–11 respectively). Bostock mistakingly claims that wisdom for Aristotle does not concern what is practicable or makable, a claim which is disproven by the texts cited above (2000, 77). hê gar aretê kai hê mokhthêria tên arkhên hê men phtheirei hê de sôjzei, en de tais praxesin to hou heneka arkhê, hôsper en tois mathêmatikois hai hupotheseis: oute de ekei ho logos didaskalikos tôn arkhôn oute entautha, all’aretê ê phusikê ê êthikê tou orthodoxein peritên arkhên (EN VII.8.1151a15–19). I paraphrase the last phrase as follows: ‘Instead, there is a virtue of correct thinking – either about natural matters (in regard to mathematics) or behavioral ones (in regard to action) – about the starting point.’ This interpretation is controversial: many interpret the ‘natural’ to refer to naturally acquired, and the ‘ethical’ (reading ‘êthistê ’ like Sushemil, instead of ‘êthikê ’ with Ob like I do) to refer to virtue acquired by habit – an interpretation in my view not warranted by the text due to the preceding disjunction between actions and mathematics. I take ‘orthodoxein’ to be Aristotle’s term for ‘*orthodianoeisthai,’ which would be the verb that would strictly correspond with his taxonomy of the psyche. Cf. Bostock’s account of the former passage, where he agrees ‘that we have nous (rather than logos) of the principles’ (2000, 100–102). See also EE II.8, where Aristotle discusses disagreement between a desire and a logos, e.g. 1224a24–25, and where he offers some considerations concerning desire which are parallel to the one I offer concerning perception: some animals have desire, but do not have logoi, therefore desires do not involve or are different from logoi. The parallels between nous and desire are deep, very complicated and interesting, e.g. at DA 433a9ff.

Chapter 5 1 2

Liddell and Scott, ‘sundesmos’ I.1, I.2, III. Cf. Hume’s An Enquiry concerning Human Understanding, Section 3, paragraphs 10–18, especially 10, where he directly refers to Aristotle and Achilles. Contrary to the orthodox view, I do not take the Iliad as a sundesmos in the sense of a series of sheets or scrolls bound together by glue or leather. The Iliad might be a sundesmos in this way, but not as an account. See e.g., De Rijk (2002, I.690ff.).

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Notes E.g., McKirahan (1992), Barnes (1994), De Rijk (2002, esp. I.623–624). Ross (2001) and Lloyd (1981) translate it as ‘non-eternal.’ I leave ‘phthartos’ undeclined for simplicity’s sake. E.g., Ross (2001), McKirahan (1992, esp. 129), Barnes (1994), Byrne (1997), Reeve (2000), Modrak (2001), De Rijk (2002, esp. I.623–624), and many others. This interpretation of ‘aïdon’ as ‘unconditional,’ and ‘phthartos’ as ‘contingent,’ in logical and epistemological contexts absolves Aristotle of two charges: (1) the charge of confusing the difference between the eternal holding of facts (which are in my view not eternal, but unconditional) and the eternal existence of objects (which could be eternal in the common understanding of the term); (2) the charge of being inconsistent, for Aristotle can hold at the same time, as he does at GA II.6.742b17–34, that certain items can be unconditional (‘aïdon’ in the epistemological sense), but that there are no proofs of things which are eternal (‘aïdon’ in metaphysical sense). See Barnes (1994, 132–133) and De Rijk (2002, I.622–623) for these charges. The ‘from some such things’ means ‘from such things which are also necessary,’ which in turn refers to ‘another way of knowing.’ The fact that proofs are a means to obtain new knowledge shows that Harari’s conclusion that ‘[m]odern thought conceives of a proof as leading from premises to conclusions, while Aristotle’s demonstration seems to lead from conclusions to premisses’ cannot be correct (2004, 137; see 132–139 and Conclusion). As you will begin to notice more and more, Aristotle’s logic is not so much a logic per se but a procedure by which one moves from primary knowledge to secondary knowledge without any loss of confidence (i.e., without any loss of evidence or justification). This conclusion does not entail that there are no syllogisms involved in prudence, skill or factual belief.

Chapter 6 1

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Cf. Ross (2001, 558–561); Barnes (1994, 164–166). Ross, unlike Barnes, notes the parallel between knowledge and ignorance. The parallel with ignorance is one of the principal arguments for holding that Aristotle is referring to anapodeictic knowledge when he says ‘if there is also another way to know…’ in AnPo. I.2.71b16–19. Another is that, since Aristotle is using ‘epistesthai’ in this passage and is generally rigorous with his terminology on principle, he is referring to another kind of knowledge, and not another kind of seeing (eidenai),

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thinking (dianoia), recognition (gnôsis) or anything else. The only other kind of knowledge is anapodeictic. Therefore, he is referring to anapodeictic knowledge. Most commentators take it that Aristotle is referring to nous here: e.g., Ross (2001, 509); Irwin (1988, 139ff.); Taylor (1990, 126–127); Ferejohn (1991, 44–48); McKirahan (1992, 258); Barnes (1994, 93); Aydede (1998, 23); De Rijk (2002, I.601–602, 726ff.). Barnes and Aydede do so by simply rejecting this second argument without countenancing the possibility of anapodeictic knowledge here (and also by accusing Aristotle of being sloppy). Ross, Ferejohn, McKirahan, and De Rijk do not make such a rejection, but they do not countenance this possibility either. Ross does argue later however that anapodeictic knowledge is another name for nous, mainly by reading ‘immediate’ not in a logical or linguistic sense, but in a psychological one, and hence as a contrary to ‘ratiocinative’ (2001, 606–607). Modrak seems to holds a view similar to Ross’ here (2001, 104, 108). Aristotle’s text here and use of this term however does not really seem to justify such a reading, and nous moreover is not another way of knowing, but another way of thinking, a way of thinking that, unlike knowing, does not involve language. Byrne seems to follow Ross in that he characterizes the distinction between anapodeictic knowledge and apodeictic knowledge as one between an act of knowing (i.e., psychologically immediate, like an ‘insight’) versus various habits of knowing, which can also be active. This ‘other way of knowing’ for Byrne then refers to these habits of knowing, and takes AnPo. II.19 to be about these habits, one of which is nous (1997, 179–181). A similar position is intimated in Burnyeat (1981, 129–133) and Lesher (2001, 49–50). This interpretation cannot be right in that Aristotle holds that all knowledge, whether active or potential, are hexeis (‘habits’ for Byrne). My interpretation resolves an objection Taylor raises here, one which is a variant of Sellars’ dilemma: Taylor takes nous to be the starting point for apodeictic knowledge, but nous seems to be about concepts, and not statements or propositions. So, he holds, Aristotle’s theory lacks a bridge between knowable concepts and knowable, yet unprovable, propositions (1990, 127–128). Some still endorse a strong conception of knowledge, for example Butchvarov (1970). His position, like Aristotle’s and Plato’s, is motivated in large part by skeptical considerations. ho d’hoti boulêtheis dunatos theôrein, an mê ti kôlusêj tôn exôthen: ho d’êdê theôrôn, entelekheiaj ôn kai kuriôs epistamenos tode to A. Contrary to other interpreters like Ross, I interpret the ‘A’ as being a variable, and not literally the letter alpha.

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Notes One can see here how numbers and other things are ‘things in abstraction’ (ta en aphairesei): a number like 6 (or snub) comes to be at the third level of actuality only insofar as there is some material thing that is six in number (or snub), and we treat 6 (or snub) as something kekhôrismenos, having been separated from these material things (see DA III.7.431b12–19, 8.432a3–6).

Section II 1

This quotation is very important, so I transcribe the Greek in full and provide substantial commentary on it here: epistasthai de oiometh’ hekaston haplôs, alla mê ton sophistikon tropon ton kata sumbebêkos, hotan tên t’aitian oiômetha ginôskein di’hên to prâgma estin, hoti ekeinou aitia esti, kai mê endekhesthai tout’ allôs ekhein. dêlon toinun hoti toiouton ti to epistasthai esti: kai gar hoi mê epistamenoi kai hoi epistamenoi hoi men oiontai autoi houtôs ekhein, hoi de epistamenoi kai ekhousin, hôste hou haplôs estin epistêmê, tout’adunaton allôs ekhein. Ross’, Barnes’, Taylor’s and Burnyeat’s comments on this passage are, in my view, exemplary of the confusion that ensues when one is not careful in translating Aristotle’s vocabulary: Barnes translates ‘epistêmê’ as ‘understanding,’ but translates both ‘gignôskein’ and ‘eidenai’ as ‘to know,’ and then develops his commentary based on these translations (1994, 90–93). Barnes even goes so far to criticize Aristotle here because (1) Aristotle’s definition of ‘epistêmê’ here does not fit the legitimate Greek use of the term, even though, he holds, Aristotle is providing an analysis of the common use of the term, and (2) Aristotle’s definition is bad because Aristotle is providing a theory of science in some sense, but science concerns what is contingent, not necessary. Burnyeat follows Barnes, except by taking ‘eidenai’ as synonymous with either ‘epistêmê’ or ‘gignôskein’ (Burnyeat 1981, 104, 128). Taylor seems to follow Burnyeat (1990, 122, 126). Ross translates all three as ‘to know’ or ‘to know a fact’ (e.g., 2001, 536). McKirahan takes ‘gnôrizein’ and its variants to mean ‘coming to know’ and ‘gnôrimôteron’ as ‘more intelligible,’ even though he prefers ‘better known’ (1992, 258, 30 respectively). Ferejohn and Modrak use ‘better known,’ although Ferejohn uses ‘recognized’ for ‘gnôrimos’ in at least one place (1991, 21, 45; 2001, 105–106 respectively). Irwin uses ‘known’ and variants for ‘gnôrimos’ and variants (e.g. 1988, 123, 135). De Rijk uses ‘awareness’ or ‘perception’ for ‘gnôsis,’ but ‘become familiar’ for ‘gnôrizein,’ ‘more familiar’ for ‘gnôrimôteron,’ and ‘recognize’ for ‘ginôskein’ (2002, I.726–727, 602, 601 respectively). Harari, who seems

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at times to have an understanding of these terms similar to mine, translates ‘gnôsis’ as ‘acquaintance’ but then ‘ginôskein’ as ‘to know,’ ‘gnôrimos’ as ‘cognitive value’ at one point, but ‘more familiar’ at another (2004, 13, 117, 70, 129 respectively). I would translate ‘aitia’ as ‘causation,’ and ‘aition’ as ‘cause,’ in order to capture the sense of the ancient Greek suffix ‘-ia,’ which, like ‘-tion’ in English, is used to express an abstract notion. The suffix ‘-io-’ in Greek has no such function; it indicates ‘belonging’ or ‘pertaining to’ (e.g., Smyth 1974, articles 840.9, 858.2). Unfortunately, this use sometimes sounds awkward in English. Also, Aristotle uses ‘aitia’ at times, as he does here, to mean ‘cause’ and not the phenomenon itself. The question as to whether such lack of care is the fault of Aristotle himself, or of a redactor or scribe, is unfortunately unanswerable. Often ‘aitia’ is translated as ‘explanation’ instead of ‘causation’ or ‘cause’ (e.g., Barnes 1994, Bayer 1997, Aydede 1998). However, one can see from the AnPo. I.2 passage here that ‘explanation’ is unacceptable: Aristotle states here that in order to know something, one must recognize that on account of which the thing in the world – to prâgma, die Sache – is (exists, is the case). If ‘aitia’ here is translated ‘explanation,’ then Aristotle is saying here that things exist or are the case on account of explanations. This statement makes Aristotle an idealist who holds that an idea is only linguistic and takes the position that things exist on account of explanations. Barnes then argues dubiously that ‘…explanations are not necessarily linguistic or propositional items’ (1994, 90). In support of my position, see e.g., Irwin (1988, 518–519, note 4), Moravcsik (1991, 33) and especially Freeland (1991, 49–51, 53–54, 68). Irwin however sometimes uses ‘explanation’ and the like as a translation for ‘aitia’ (e.g., 1988, 123). Ross uses ‘cause,’ and not implausibly takes Aristotle’s term as meaning something like ‘objective ground’ (2001, 509–510). McKirahan uses ‘(explanatory) grounds’ (1992, 23, 209ff.). De Rijk uses ‘cause,’ but apparently as connoting ‘because,’ ‘explanation’ and ‘reason’ (e.g., 2002 I.462, 602 et al.). Barnes translates ‘phamen ... kai’ as ‘here we assert’ (1994, 2).

Chapter 7 1

Moravcsik calls this view a ‘correspondence theory of explanations.’ He holds ‘Aristotle posits configurations of elements of reality corresponding to adequate explanations not in order to assign reference to certain linguistic expressions, but to account in a realist way for that in

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Notes virtue of which some explanations are adequate and yield insight,’ and thus causes (my terminology) are not description-dependent, but feature-dependent (1991, 31, 34, 36ff.). Freeland calls this ‘explanatory realism,’ which holds that ‘C is an explanans of E in virtue of the fact that C bears to E some determinate objective relation R. Let us call R, whatever it is, an “explanatory relation”.’ She then argues that for Aristotle R is one of his four kinds of causal relations (1991, 61). In contrast, De Rijk describes starting points as ‘dicta,’ with ‘dicta’ in his view seeming to mean either ‘concepts including their connotative “be”…’ or things ‘conveying a primitive state of affairs of the axiom type,’ which are propositional. Arkhai are thence ‘the starting-points for concept-acquisition and those bearing on the formation of primitive that-clauses’ (2002, I.735, 737; see also I.628). He later recognizes however that ‘cause’ and ‘principle’ are equated (ibid., II.244, note 1). It is unclear how he can reconcile these two positions, and how he can explain the correspondence, generally speaking, between concepts or propositions on the one hand, and things in the world on the other. My position and this paragraph above resolves how, in Bayer’s terms, ‘what X is’ and ‘the explanation [i.e., the cause] for X’ can be the same for Aristotle: recognition of a cause or arkhê (which is specified in filling out the ‘what X is’) is itself at the same time a cause or arkhê (which is the ‘explanation’ of X) (Bayer 1997, 330–333). Bayer’s resolution is by arguing that ‘[t]o treat defining X and explaining it as entirely separate tasks would be to ignore this unity,’ i.e., the unity of ‘phenomenal properties’ (which is what X is for Bayer), and the underlying thing which is ‘responsible for all of them’ (which is the explanation) (ibid., 332). Note in addition that the ‘what X is’ is also a cause or arkhê in the sense that it is the cause or arkhê for new knowledge. My position here appears similar to Irwin’s (1988, 97–98, 122–125 and 518–519, note 4) and McKirahan’s (1992, 212–213), and is connected to a kind of selfevidence of starting points. This is another important passage which requires the full Greek transcription: ...ex alêthôn t’einai kai prôtôn kai amesôn kai gnôrimôterôn kai proterôn kai aitiôn tou sumperasmatos.... Ross defends a similar interpretation of ‘primary’ in a different way: ‘prôta here does not mean “most fundamental,” for A. [Aristotle] could not, after saying that the premises must be fundamental in the highest degree, go on to make the weaker statement that they must be more fundamental (proterôn a22) than the conclusion. To say this would be to confuse the characteristics of the premises in themselves (alêthôn kai prôtôn) with their characteristics in relation to the conclusion

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(gnôrimôterôn kai proterôn kai aitiôn tou sumperasmatos). prôtôn, then, means just the same as amesôn or anapodeiktôn (b27) – that the premises must be such that the predicate attaches to the subject directly as such, not through any middle term’ [sic] (Ross 2001, 509). Ross’ last claim, namely that primaries are ‘anapodeictic,’ contradicts his claim that primaries are just ‘more fundamental,’ since he takes the term ‘anapodeictic’ as meaning ‘indemonstrable,’ as Irwin (e.g. 1988, 132, 139, 535, note 15), Barnes (e.g. 1994, 94), and McKirahan (e.g. 1992, 25) do. If something is indemonstrable, by definition it is not possible for it to be proven. If something is just more fundamental, then it is possible for it to be proven. Therefore, in order to avoid a contradiction, the term ‘anapodeictic’ must not mean ‘indemonstrable,’ but something weaker, like ‘without a proof,’ ‘not needing a proof,’ and so on. This is how I take the term ‘anapodeictic.’ Sextus states at adv. Math viii. 223 that something is anapodeictic if there is no need of a proof due its being self-evident or obvious (cited in Barnes 1994, 94–95). However, Barnes sticks with ‘indemonstrable’ anyway! De Rijk also holds a view somewhat like mine: ‘The word anapodeiktos literally means “undemonstrated,” or perhaps rather “not involved in any epistemonic proof,” which most of the time boils down to “being immediate” and accordingly, “taken to hold, without proof”’ (2002, I.603). Harari uses ‘indemonstrable’ or ‘non-demonstrable’ (2004, 18, 39 respectively). The interpretation of ‘immediate’ as ‘something is immediate if and only if there is no middle term’ (Barnes 1994, 94–95) is problematic, depending on whether one implicitly reads necessity into the biconditional, as Barnes seems to. ‘If and only if,’ by itself, just like ‘just in case,’ is amenable to my interpretation of ‘immediate.’ Cf. Moser (1989, 2, 144 et al.). aitia te kai gnôrimôtera dei einai kai protera, aitia men hoti tote epistametha hotan tên aitian eidômen, kai protera, eiper aitia, kai proginôskomena ou monon ton heteron tropon tôj xunienai, alla kai tôj eidenai hoti estin. In contrast to my position, Ross, Ferejohn, McKirahan, Barnes, and De Rijk take Aristotle as offering additional items, and not explicating the items at issue (2001, 509–510; 1991, 20–22, 24; 1992, 24, 29–33; 1994, 93ff.; 2002, I.603 respectively). Ferejohn takes these last three as being intensional requirements, and the first three (true, primary, and immediate) as being extensional requirements (1991, 24).

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Chapter 8 1

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Concerning the procedures for arriving at primary statements, see for example AnPo. I.23 and much of II. Some from the Topics might also be useful. Ross, McKirahan, Barnes, and Aydede provide another reading of (2): (2) does not say anything at all and thence can be ignored (2001, 507, 509; 1992, 22–23; 1994, 90–91; 1998, 23 respectively). I cannot see where they got this reading, and none of the four provide any arguments for it. A permutation that reads (2) as an alternative way of saying (1) is implausible: some y can be of another thing x without x being the cause on account of which y is. For example, keeping in mind the ancient Greek usage of the genitive case (signified by ‘of’ in English), my copy of the Analytics is of my library, but my library is not the cause or starting point of that copy. This reading, if it were plausible, would not be redundant, in contrast to (I.a) and (II.a). De Rijk takes (I.b.ii) as the appropriate reading, although he does not seem to offer any explicit argument for it (2002, I.601–602). One might say that it is possible Aristotle is holding all four to be involved. Aristotle could, for all we know, be playing on this very textual ambiguity in order to refer succinctly to more than one of these permutations. Moreover, (I.a) or (II.a) could be the correct readings, and yet Aristotle may accept any or all of the remaining ones. However, these seem unlikely because Aristotle is consistently careful to clarify ambiguities, and not to play on them. Such issues are discussed however at the end of AnPo. I.23 and at II.13ff., and also at I.1. khalepon d’esti to gnônai ei oiden ê mê. khalepon gar to gnônai ei ek tôn hekastou arkhôn ismen ê mê: hoper esti to eidenai. This quotation plays a very important role later. McKirahan treats ‘appropriate’ as a redundancy, and translates ‘suggenê ’ as ‘co-generic’ (1992, 26–27, 56). In contrast for example, Lloyd takes ‘appropriate’ in the same way I do (1981, 159), and my account is similar to Harari’s (2004, 49–51, 61). One of the reasons for what I call this ‘relevancy’ component of (2) is due to requirement (3), which I will discuss next. This requirement is applicable to bodies of knowledge, as well as instances of knowledge. So for example, one cannot use an arithmetical proof to prove something geometrical. However, one can use a geometrical proof to show something in optics, or an arithmetical proof to show something in harmonics, because the underlying thing (the

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genus) is the same for each pair – space in the former, number in the latter (AnPo. I.7.75b14–17, 9.76a9–15; cf. 13.78b35–79a6, II.8). However, if one were able to provide some common genus underlying both geometry and arithmetic (say by using category or set theory), then one would theoretically be able to use an arithmetical proof for something geometrical, and vice versa. ‘Ancestor’ plays off a meaning of the term ‘starting point,’ and also of ‘suggenês’; see Meta. V.1.1013a7–10. Ferejohn uses ‘ancestor’ and ‘descendant’ in his discussion of Aristotle’s account of division (1991, 27–32). Cf. Ross (2001, 537); Barnes (1994, 135). Neither apply Aristotle’s example to their interpretations in order to see if their interpretations work, which I do in the immediately following paragraph. Note the genus isosceles triangle is common to a′ and to t, but not to a, so this genus is not relevant, or relevant enough, for the proof. In comparison to my interpretation, McKirahan describes this passage as being about ‘what conditions a proof of equilateral triangle–2R [i.e., is equal to two right angles] will give universal knowledge’ and ‘how to locate the primary subject’ (1992, 172–174). There is some controversy in the commentarial literature as to how axioms are, or are the, ‘from which.’ See Ross (2001, 531–532); Barnes (1994, 139). pâsa gar apodeiktikê apistêmê peri tria estin, hosa te einai tithetai (tauta d’esti to genos, hou tôn kath’hauta pathêmatôn esti theôrêtikê), kai ta koina legomena axiômata, ex hôn prôtôn apodeiknusi, kai triton ta pathê, hôn ti sêmainei hekaston lambanei. What are kath’hauto coincidentals or ‘modifieds’? Aristotle calls things which are said of an underlying subject ‘coincidental’ (AnPo. I.4.73b5–10). A single genus or matter underlies any proper proof; such a proof proves something about that genus or about some form of that genus. A proper proof then proves something coincidental to that genus. However, given that it is a proper proof, these coincidentals will belong to that genus kath’hauto, since the coincidentals exist by virtue of that genus. Thus, the features proven in a conclusion will be the kath’hauto coincidental features of that genus. These kath’hauto coincidentals are the so-called ‘kath’hauta modifieds’ or ‘kath’hauta modifications’ of that genus. This matter is discussed further below. From all the material in this section, I have to disagree with Harari’s position that the passage from AnPo. I.2 is about premises, whereas AnPo. I.7 and I.10 are about the subject and predicate of a conclusion (2004, 14).

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Notes So for example, all genera are such that nothing both is and is not in the same respect at the same time, and are such that adding or removing equals from equals are equal. Since axioms underlie everything that is, one about to learn something about anything whatsoever must see these axioms (AnPo. I.2.72a16–17). I take Aristotle’s axioms as the fruit of his metaphysical investigations into being and the like. Barnes states without argument that Aristotle must hold ‘that a term belongs to at most one kind [i.e. genus],’ and then states that Aristotle ‘cannot prove’ that genera, bodies or branches of knowledge are genera in the sense underlying requirement (2) (1994, 131). The first statement is implausible, at least without further clarification and argumentation, for clearly human can belong to the genus mammal, as well as the (super-)genus animal. A generic difference like user of a language need not belong only to human: for example, some birds, cetaceans or bees could plausibly be differentiated in this way. Things which belong to at most one genus are unique properties, idia. Barnes’ second statement is wrong, and the quotation from Aristotle here and my explanation of it shows it to be so. This arrangement, as well other aspects of Aristotle’s epistemology and metaphysics, are obfuscated if one takes Aristotle’s genera to mean ‘natural kinds’ in the contemporary sense and not as ‘underlying things’ (e.g., Irwin 1988, 120–121). Natural kinds in this sense do not share this arrangement Aristotle has in mind between things in the world. Instead, they are groups, classes or types naturally separated from one another somehow. See the next footnote, and much of the material that follows, for more reasons to take genera as ‘underlying things.’ It is interesting to compare my analysis of this subject to that of McKirahan’s, whose interpretation assumes Aristotle is discussing a theory of science, and not a theory of knowledge. First, McKirahan takes genera to be natural kinds, and not underlying things. The function of genera here is to ‘serve as principles of identity and individuation for sciences’ (1992, 50). Thus, instead of a relevancy requirement for deriving knowledge, Aristotle is proposing here a ‘doctrine of subject genera’ which ‘implies that the sciences are radically separated from one another’ (ibid., 51, 63). This doctrine then has several consequences for Aristotle’s ‘theory of science’: no transference of proofs between sciences; there is no master science; and there is no single set of master principles over all sciences (ibid., 51–57). It also declares ‘the unity of science and scientific knowledge to be a myth and proclaims specialization, not empty generalization, to be the key of scientific

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progress’ (ibid., 63)! All of McKirahan’s claims here are based on the assumption that Aristotle is talking about science in some kind of modern sense; once this assumption is questioned (or rejected, as I have done), these claims become really dubious. McKirahan also raises the question: what philosophical justification does Aristotle offer ‘for his view that sciences have distinct subject genera’ (ibid., 60)? His answer seems to be that (i) it ensures that all subjects and attributes related kath’hauto to each other are in the same genus, and (ii) each science corresponds to some natural division of reality. This conception of subject genera ‘is different in origin, purpose and nature from his conception of genus/species hierarchies’ (ibid., 62–63). In my view, the primary counterparts, and not any doctrine, are what insures that all subjects and kath’hauto attributes are in the same genus, and are what make the divisions within knowledge match any divisions among these primary counterparts. Thus, subject genera are not different in origin, purpose or nature from genus/species hierarchies.

Chapter 9 1

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epei de epistasthai oiometha hotan eidômen tên aitian, aitiai de tettares, mia men to ti ên einai, mia de to tinôn ontôn anagkê tout’einai, hetera de hê ti prôton ekinêse, tetartê de to tinos heneka.... One can speak about the cause in terms of the individual causing thing or as the genus of that individual, as something coincidental to the actually causing thing or as the genus of that coincidental something, and these either without qualification or in combination. All of these are spoken of in turn in terms of producing (in this case, the cause and the effect are always simultaneous) or in terms of potential (in this case, the cause and the effect are not always simultaneous) (Meta. V.2.1014a15–25). The ‘when there are certain things it is a necessity this thing is’ cause can be understood in the following way: On the one hand, when there is a certain form or end, from necessity some matter (the ‘this thing’ in one sense) comes to be; on the other, when there are certain genera and differences, it is a necessity that a certain form (the ‘this thing’ in the other sense) comes to be. Note also how the proximate/ultimate matter distinction could work in two ways here: organs vs. elements, and form vs. genus. E.g., Lloyd (1981, 163–165); Irwin (1988, 219–220); McKirahan (1992, 103–121 et al.); Modrak (1996, 156, 161); Reeve (2000, 20); cf. Harari (2004, 56–58, 132–139). In support of my view, see Freeland (1991, 59–60, 60ff.).

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Notes It seems that recognition of the universal would satisfy the truth aspect of requirement (2) if and only if undergoing the inductive procedure in regard to some thing in the world, and then applying what was recognized or attained from that procedure back to that thing in the world, was an error-free process. Aristotle sometimes uses the terms ‘epi pantos’ (‘upon every’) or ‘epi panti’ (‘in every case,’ ‘in the power of every’?) in regard to universals, e.g. AnPo. II.12.96a14–15. Byrne seems to interpret Aristotle in these passages as describing three different kinds of universal predication (1997, 94–95). This interpretation cannot be correct, for everything universal for Aristotle is necessary, but things which are ‘beneath every’ need not be necessary. Also, as I will show in regard to things ‘for the most part,’ things which are kath’hauto need not be universal, even though everything which is universal needs to be kath’hauto. Byrne later argues though that at AnPo. 73b25–27 Aristotle is offering a single, redundant definition by synonymy for ‘universal belonging’ (ibid., 96ff.). In support of my unitary interpretation, see McKirahan (1992, 97, 101). McKirahan however holds that what is necessary is ‘beneath every,’ and what is kath’hauto is ‘beneath every,’ positions which I show below to be incorrect. Ferejohn replaces my (iii) with a ‘qua itself’ condition (1991, 69, 70ff.). Aydede says that the necessity of knowledge comes from the ‘kath’hauto’ notion, and hence grounds universality (and other things) for Aristotle (1998, 26–27). The texts and arguments here and below show that something can be kath’hauto without being universal. Posterior Analytics I.4.73b26–28 and I.31.87b32–33, paraphrased above, provide evidence that Aristotle disconnects ‘kath’hauto’ from ‘universal.’ Note that what is for the most part is not ‘beneath every.’ The question now is ‘what is a particular?,’ taking ‘particular’ as being equivalent to ‘kath’hekaston’: Do forms of a genus, or genera of a supergenus, count as particulars? Or are only composites of matter and form particulars? I cannot deal with this issue here. McKirahan takes ‘beneath every’ (‘in every case’ in his translation) to mean ‘A belongs to all B’s at all times’ (1992, 85). His definition hides the causal connection involved in the ‘beneath every’ requirement, and implies a temporal, and not statistical, account of this term. Ferejohn holds that this requirement refers to instances, but he does not note the causal connection involved. hou gar hê diaphora kai hê poiotês esti, tout’esti to hupokeimenon, ho legomen hulê. The term ‘genus’ in this sense includes the thing which is first in specifications (ta ti esti), and a genus’ differences are called ‘qualifications’ (Meta. V.28.1024b4–6).

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This fact provides some evidence against taking ‘chance’ in Aristotle as being synonymous with ‘rarely,’ as e.g. Judson does (1991, 76). In support of my view, see e.g., Freeland (1991, 56–60), who argues that things which are ‘for the most part’ are kath’hauto, and that all four kinds of causes can fall under this rubric. In the last sentence, I read ‘ouden’ with Ab, whereas Jaeger has ‘ouden .’ This kind of necessity is often called ‘hypothetical necessity’ in the commentarial literature, because Aristotle at times describes it as necessity ‘ex hupotheseôs,’ e.g. PA I.1.642a1ff. (In that passage Aristotle is distinguishing compositional necessity from the ‘for the sake of which’ by taking the former as coming to be naturally, but the latter by choice.) Some examples are Balme (1972, 76–84); Leszl (1981, 293ff.); Charles (1991, 119–124); Modrak (1996, 156–162 and 2001, 76–81). However, these commentators treat the term ‘hypothetical’ in its modern sense, but not in Aristotle’s, which is a mistake. For Aristotle, ‘hupothesis,’ which I have translated as ‘declamation,’ is a statement about existence, and not a hypothesis in the modern sense. Thus, what I am calling ‘compositional’ necessity might be more accurately, but more confusingly, called ‘existential’ necessity, or in my scheme, ‘declamational’ necessity – i.e., what is necessary for something to exist. Socalled ‘hypothetical’ necessity is therefore also not, as many medieval metaphysicians took it, ‘disjunctive’ necessity, which is based on a misinterpretation of ‘hupothesis,’ not only when it is directly mentioned as in the Topics, but also when it is indirectly mentioned, as in passages like AnPo. I.74b9–10. Harari interestingly argues that a hupothesis is a statement containing the predicate ‘is true,’ but this either does not work for some examples Aristotle provides of them (e.g., ‘points are true’) or is reducible to an existence statement based on the Greek use of ‘to be’ (2004, 44–46ff.; ch. 2.1–2.4 more generally). She also says that ‘[t]he existential interpretation of “hypothesis” stems from attempts to explain the distinction between definitions and hypotheses in terms of their sentential form’ (ibid., 46). This is not true in my case: I am simply working from what Aristotle says! Many identify the declamation/definition distinction and the primary term/non-primary term distinction, but this in my view is a terrible mistake – for starters, I cannot see how an existence statement is identical to a primary term. For a list of those who have committed to this identification, see Harari (2004, 15, footnote 2). For my account of the difference between primary and non-primary, see chapter 15. Section III provides a lot of evidence against this identification in regards to definitions as well.

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Notes This passage makes clear the connection between this kind of necessity and declamations of existence. I am reading Phys. II.9.200a13–14 (ex hupotheseôs dê to anagkaion, all’oukh hôs telos…) as ‘the necessary is from declamation certainly not when there is an end,’ for this seems to be the only reading which makes any sense, given the material that follows before and after. (See Liddell and Scott (1996), ‘hôs’ B.V. for ‘when,’ and Denniston (1996), ‘alla’ I.ii, pp. 1–2 for ‘not.’) Leszl and Balme view this difference in a way similar to, but less helpful than, Ross’ (1981, 298; 1972, 78 respectively). Given Ross’ plausible characterization and the fact that Aristotle uses the term ‘anagkê ’ in the context of both kinds of necessity, it seems Aristotle did not make the distinction between ‘necessity’ and ‘necessitation,’ or considered it to be philosophically unimportant.

Chapter 10 1

It would be natural and internal if the human body, by being what it is, had the ability to remove the tumor on its own without outside assistance, either by means of cellular and organ activity, or by innate surgical skill. See Phys. II.8.199b28–33.

Chapter 11 1

The citations and arrangement are from Barnes (1994, 192).

Chapter 12 1

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The verb ‘reveals’ (‘dêloun’) and its variants are technical for Aristotle. They have no religious or mystical connotations. They may also be understood as ‘make clear to,’ ‘indicates,’ ‘shows,’ or even ‘explains’ in some contexts. The term ‘reveal’ seems to encapsulate all of these connotations and is generally neutral philosophically. One also does not define well if one uses a definition that is too verbiose (Top. VI.1.139b15–18). Defenders of the ‘understanding’ interpretation often point to the lack of something equivalent to ‘self-evidence’ in Aristotle’s work as evidence for their position. Well, here it is. For a particular example, this

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material here refutes Harari’s interpretation of Aristotle’s theory of knowledge (2004, 37). This self-evidence of starting points involved in knowledge is much simpler than, and resolves the problems of, Ferejohn’s interpretation of starting points: He holds that starting points ‘are not, and cannot be proper parts of that science. This is just to say that by virtue of the very nature of justification, no scientific enterprise could possibly function as a bootstrap operation somehow capable of generating or grounding results ex nihilo. Rather, Aristotle insists, it can be entered into only by an epistemic subject who is already in possession of an adequate stock of preexistent (that is to say, prescientific) knowledge not in itself in need of justification’ (1991, 5). This interpretation of starting points cannot be correct, given all of the texts cited above which make recognition of the starting points requisite for knowledge and given their self-evident nature. The issue about pre-existing knowledge is a complicated one, and since it involves learning and inductive procedures, it goes beyond the scope of this work. Again, the presumption that Aristotle is concerned with science in some modern sense, as it is with Ferejohn, is the big source of problems! For a different argument for self-evidence for certain starting points, see Irwin (1988, 130–133). However, to me it is incorrect, as Irwin holds, that nous (‘intuition’ in his view) is for Aristotle the capacity which apprehends this self-evidence: In brief, (i) the non-inferentially justified or evident statements for a proof comprise primary knowledge, not nous; (ii) Aristotle characterizes self-evidence as recognizing something by means of the thing itself, not by means of or with nous or noêsis, so it is unclear as to whether we need a special capacity to detect or register this self-evidence. Thus, with my interpretation, Aristotle’s epistemology can escape the difficulties Irwin posits for it (1988, ch. 7, esp. 141–143, 145–146). Evidence that Aristotle uses the terms ‘by nature’ and ‘without qualification’ to indicate the same kind of recognition and priority is available at AnPo. I.2.71b33–72a5, quoted below. ...aitia men hoti tote epistametha hotan tên aitian eidômen, kai protera, eiper aitia, kai proginôskomena ou monon ton heteron tropon tôj xunienai, alla kai tôj eidenai hoti estin. First, the ‘discerning’ is to be understood as ‘getting it,’ as in ‘oh, I get it!’ Second, my explanation of ‘recognized more’ and ‘recognized beforehand’ resolves the purported syntactic ambiguity reported by Barnes at 71b31 between the ‘causes’ and the ‘and.’ He reports that most commentators alter the textual punctuation, then take the ‘recognized beforehand’ as a restatement of the ‘more recognized’ condition. Barnes, accepting arguments that these two terms are

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Notes different requirements, holds the ‘recognized beforehand’ as a restatement of the ‘priority’ condition. As my explanation above has shown, both interpretations are correct, and without any change in the traditional punctuation (1994, 96). Much of Barnes’ and other commentators’ problems here seem to be caused by their taking ‘gnô-’ and its variants as ‘to know,’ which then makes understanding the two terms at issue difficult, and also taking the ‘pro-’ in ‘proginôskomena’ as indicating temporal priority, and not logical. (Barnes translates ‘gnôrimos’ as ‘familiar,’ but only because ‘known,’ which he prefers, does not work well, if at all, in comparative contexts. Otherwise he uses ‘know’ for the ‘gnô-.’) McKirahan suffers similar problems (1992, 31–35). Khalepon d’esti to gnônai ei oiden ê mê. khalepon gar to gnônai ei ek tôn hekastou arkhôn ismen ê mê: hoper esti to eidenai. I use ‘to see’ as a translation for ‘to eidenai’ because it captures the root sense of the Greek verb. ‘To know’ is reserved for ‘epistesthai’ to prevent confusion and fudging of the issues. The English use of ‘to see’ in examples like ‘Don’t you see what’s wrong here?’ or ‘Oh, I see what the problem is now!’ matches Aristotle’s use here nicely. Moreover, it is fairly easy in English to distinguish this sense of ‘see’ from ‘see’ in the ocular sense just by means of the direct object of the verb. Unbelievably, Ross, McKirahan, Barnes and De Rijk have nothing to say about this passage!

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Ross translates ‘pistis’ and its variants as ‘conviction’ or ‘credible’ depending on the form of the Greek term, while Barnes uses ‘conviction’ and its variants only. Harari uses ‘conviction’ too (2004, 22). De Rijk uses ‘inner conviction’ or ‘sure belief’ (2002, I.607). Irwin uses ‘credence’ and ‘credible’ (1988, 131–132). ‘Belief’ is sometimes used – ‘belief’ in the sense of ‘I believe you’ or ‘he believes in her,’ not in the sense of ‘she believes that p.’ It is obvious this translation would be too misleading and confusing to use, especially since ‘belief’ is a fair translation of ‘doxa.’ An example of the confusion that ensues by using ‘belief’ occurs in McKirahan (1992, 33–35). ‘Confidence’ does not suffer such difficulties. Cf. Butchvarov (1970, 76–88); Ginet (1975, 13–26); Moser (1989, 136–140). It is interesting to compare Alexander’s take on these passages (In Top. 346,5–27, 351,12–352,3). His concerns focus more on the classificatory

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mistakes being made in these examples, and not what can be learned about confidence from them. In parallel to knowledge, the account that is the principle of non-contradiction is more conducive to confidence in one as evidence, not as content, at the second level of potentiality. At the third level, when it is an actuality without qualification – when one is actively thinking through this account – it is more conducive to confidence both as evidence and content. Aristotle does state however the following: ‘There is confidence not just in the case of perception but also in account, that it is necessary to be stopped’ (Phys. VIII.8.262a17–19). In other passages, he states ‘sufficient confidence is from an inductive procedure’ and ‘[c]hange which is not coincidental is not in all things, just in the things which are contrary, the things which are between, and in contradiction: Confidence in this is from an inductive procedure’ (AnPo. II.3.90b13–14; Phys. V.1.224b28–30 respectively). He is saying here in regard to perception that the discursive thoughts which result from it produce confidence. In regard to his inductive procedure, this procedure itself is a kind of account, and hence a kind of discursive thinking. leipetai ara idein ei doxa: ginetai gar doxa kai alêthês kai pseudês. alla doxêj men hepetai pistis... tôn de thêriôn outheni huparkhei pistis, phantasia de pollois. eti ei pasêj men doxêj akolouthei pistis, pistei de to pepeisthai, peithoi de logos: tôn de thêriôn eniois phantasia men huparkhei, logos d’ou. The passage here is corrupted. I read ‘ei pasêj’ with many of the manuscripts as opposed to Ross’ ‘pasêj,’ because, as I have shown above, there are opinions – i.e., discursive thoughts – one may have that one does not have confidence in. Ross’ reading appears to makes Aristotle say that confidence accompanies every opinion, which is false both intuitively and in regard to other passages – unless one reads ‘confidence’ here as implying the possible degrees of confidence, from the strongest to the weakest, and with the latter being equivalent to doubt. hapanta gar pisteuomen ê dia sullogismou ê ex epagôgês. This passage provides further evidence that Aristotle considers inductive procedures to be accounts and involving language. The passage from the Topics here occurs in the context of Aristotle showing examples of unique properties that are improperly formulated by including a feature that belongs to everything. So, he says, take for example one who is positing the unique property of knowledge to be a discursive thought that is unpersuadable by an account being one. This formulation is incorrect because one has placed within it the

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Notes ‘being one,’ which belongs to everything that exists, and not just knowledge (Top. V.2.130b11–18). Neither Ross, McKirahan, Barnes nor De Rijk offer any comment on this passage. This passage also provides further support to the claim that the ‘recognition’ in the third answer affects only (1/4), and not (2) and (3). For more information concerning Aristotle’s use of the term ‘deception,’ see Prior Analytics I.34–35. See Barnes (1994, 102–103), McKirahan (1992, 33–35) and Ross (2001, 511–512) for possible alternative readings of this passage. In my view, the issue about unpersuadability seems to make the reading I offer above the most viable one.

Chapter 14 1

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Richard Fumerton reports that Peter Klein thinks this regress is not vicious, and that knowledge is still possible despite it. He calls this view ‘infinitism.’ This report occurs in the context of Fumerton’s fine discussion of this famous dilemma. See Fumerton (2001, 7–9). A declamation takes something either to be or not to be: the mathematician’s taking a monad to be (i.e., to exist or to be the case somehow) is different from her stating what a monad is. A modern example is G.E. Moore’s ‘I have hands.’ Declamations can also take the form of statements like ‘the contrary is the being contrary to the contrary, for which there is something contrary’ (AnPo. II.6.92a20). Declamations are not hypotheses, they do not take whichever two sides of a contradiction, say for the sake of experimentation (i.e., something like a hypothesis in our modern English sense, and which might seem implied by the Greek). Evidence for my interpretation occurs at AnPo. II.1.89b31–35, II.2.89b37–90a5ff.; Top. III.6.119b35ff. The best way to understand them in the context of the regress is that if declamations are not known, they simply function as foundational conditional reasons concerning the existence of things (‘If I have hands, then….’). So in short, Aristotle is saying that if declamations are only conditional, then knowledge is impossible. Aristotle admits that things can be both prior and posterior at the same time; however, these would be in different respects: one, prior by nature, but the other, by us. Cf. Irwin (1988, 125–129). I disagree with Barnes that this statement of Aristotle’s refers only to ‘permutation 3’ of the problem (1994, 170; see below for these

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permutations). My reasons for so doing are shown in this section. I also disagree with Barnes’ translation of this passage, where he has Aristotle say that the ‘each other’ concerns the extreme terms of a single proof. Instead, I take the ‘each other’ to concern individual proofs: if there are proofs of everything – i.e., if every line in a proof is itself provable – then proofs, and not terms, will not come to an end in regard to each other. The full passage is this: ‘[I]f of things which are prior some are predicated, there is of these a proof – but of the things which there is a proof, in regard to these it is possible neither to improve upon seeing, nor to see without proof, but if this thing is evinced by means of these things, we do not see these nor improve upon seeing in regard to them, not even do we know the thing which is evinced by means of these. So, if it is possible to see something by means of a proof without qualification and not from some things nor from a declamation, it is necessary that the predications in between stop. For if they do not stop, but there is always something above the thing which is taken, there will be a proof of everything – therefore, if it is not possible to go through things which are unlimited, of the things which there is a proof, we will not see these by means of a proof. So, if we do not improve upon seeing in regard to these, it will not be possible to know anything without qualification by means of a proof, but we will know only by declamation’ (AnPo. I.22.83b33–84a6). Other uses of sustoikhiai in ancient Greek philosophy are for example the Pythagorean columns or chains listed at Meta. I.5.986a24–26: ‘Limit-odd-one-right-male-being still-straight-light-good-square’ is one chain or column, and ‘unlimited-even-plurality-left-female-being changed-curved-darkness-evil-oblong’ is the opposing one. However, these Pythagorean chains are quite different from Aristotle’s.

Chapter 15 1

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I am not sure about this, even though it seems to be a common view in the literature. The evidence from the passage is not definitive. A standard translation of the Topics, found in Barnes’ collection of Aristotle’s works, translates ‘horos’ in some places as ‘term,’ in others as ‘definition,’ e.g., Top. VI.1. This is a terribly confusing practice in my view, and I think ‘term’ is what Aristotle is talking about there, not ‘definition.’ A linkage is kath’hauto regardless as to whether it is kath’hauto without qualification or coincidentally kath’hauto.

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Notes I use ‘partial’ or ‘partial or particular,’ instead of just ‘particular,’ to translate ‘kata meros’: (1) I restrict ‘particular’ to ‘kath’hekaston’; (2) something can be more partial than another without being a particular, if just a composite form plus its matter is a particular for Aristotle. For example, the phylum chordate is more partial than the kingdom animal, but is not a particular. Again, for Aristotle, the terms ‘upwards’ and ‘downwards’ can qualify either chains with two links (thereby expressible in a statement appropriate for a proof or syllogism), or more than two links (thereby expressible as a proof, syllogisms or multiple proofs or syllogisms). Barnes, for example, does not make this point clear in his commentary on the Posterior Analytics (1994, 170). See Sommers (1982) and Oderberg (2005).

Chapter 16 1

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For other treatments of permutations (1)–(3), see for example Lear (1980, 18–25); Kal (1988, 19); Barnes (1994, 169–170). Lear offers a different interpretation of permutation 3, which, in order for the interpretation to work, brings into consideration Aristotle’s views on infinity and holds, for example, ‘[t]hat Aristotle says it is the finite length of chains which prevents a regress provides further evidence that he takes an infinite number of middles between fixed extremes to be dense’ (1980, 24). My interpretation here avoids the introduction of issues concerning infinity and density. Cf. Barnes (1994, 170–171). Many have held Aristotle’s concern is solely logical. Charles says the key concern is about definitions (2000, section 8.5, esp. 215–217). Though she focuses more on definitions, Modrak recognizes the significance Aristotle’s problem has for knowledge (2001, 163–164). Lear claims that in these passages Aristotle ‘is trying to show that the process of proving demonstrable premises will terminate after finitely many steps. His argument provides a fundamental test of the adequacy of the syllogistic’ (1980, 19). In short, Lear claims that Aristotle is aiming to provide in these sections a ‘compactness’ proof for his syllogistic (ibid., 32–33). Though Aristotle’s arguments in AnPo. I.19–22 might have that incidental result, given the textual evidence, I cannot agree that a compactness proof was Aristotle’s aim.

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Aristotle calls unique properties ‘coincidentals’ in the Metaphysics: ‘“coincidental” is also said in another way, namely what belongs to each thing kath’hauto while not being in its reality, like the having of two right angles to triangle. It is possible that these also are unconditional – but none of those. An account of this is in different places’ (Meta V.30.1025a30–34). For a somewhat similar interpretation of (CP1), see Ross (2001, 569). However, he does not discuss identity statements explicitly, and he apparently excludes (CP2). For a more detailed argument which arrives at the same result concerning AnPo. I.21, see Lear (1980, 25–26). My interpretation of AnPo. I.21 works for any specific interpretation of the negative proofs Aristotle discusses in this chapter. For an account of the interpretive problems in determining what negative proofs Aristotle has in mind here, see Barnes (1994, 172–173). For similar, yet broader accounts of ‘universal,’ ‘logical’ and its variants see Barnes (1994, 173); Irwin (1988, 494, note 46); Charles (2000, 286, note 25). Byrne describes Aristotelian analysis as ‘finding the intelligible connection among otherwise unintelligible facts.’ For this argument in particular, Byrne states that Aristotle is beginning with his ‘meta-logical conclusion’ – namely, a syllogism unlimited in length is not a proof – and then seeks to resolve this conclusion into its premises (1997, 25, 70–73 respectively). Irwin calls this kind of argument one ‘from the appropriate subject matter’ (1988, 494, note 46). For a different take of ‘universal’ and ‘logical,’ see Ross (2001, 573). Lear gives short shrift to the universal argument, and does not discuss the analytical argument (1980, 30–33).

Chapter 18 1

Contra Irwin, I hold that Aristotle is placing the weight of the argument here on the ‘common sense’ recognition of underlying things, and not of natural kinds (1988, 120–121): The ‘underlying’ aspect is what does the work here, and not any ‘kind’ aspect – but this ‘underlying’ aspect includes genera and forms insofar as each is a matter or underlying thing for something else. Moreover, particular things or their specific forms, and not the kind to which they belong, are at issue. This argument will, and needs to, work for unnatural kinds like the products of

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Notes skill and prudence, for if it does not, then technical and prudential syllogisms will possibly be unlimited in length. This common sense recognition of underlying things resolves the perplexities raised by Gyeke concerning this passage (1976, 104–105): he is perplexed as to why Aristotle did not take ‘the white’ for example as ‘the white thing’ or ‘the white object’ in this passage, and in turn why Aristotle did not allow such expressions to be admissible subjects of sentences. Concerning the latter, Aristotle does allow them to be such, just not without qualification; concerning the former, Aristotle would not be making any point if he did take ‘the white’ as ‘the white object,’ for ‘the white object is the tree’ would thereby be redundant. Cf. Modrak (2001, 156–157) and also Bayer (1997, 326–333). This list excludes ‘to have’ and ‘to be placed’ from the list found in Categories 4. This passage will be explained further in the context of Aristotle’s analytical argument below, where the distinction between kath’hauto coincidental and ‘coincidental coincidental’ predication is more crucial. A complete specification of something will include both purely kath’hauto predications and kath’hauto coincidental predications. In his discussion, Aristotle may have in mind the problems of mixing (meignumi), commingling (summeignumi) or interweaving (sumplokê) that arise with Plato’s Forms in the Sophist. My account here is an interpretation of the following passage, presented in full: ‘Moreover, if this is not of this quality and that of this, nor a quality of a quality, it is impossible to be counterpredicated of each other in this manner, but although it is possible to speak something true, to counterpredicate truly is not possible. For either, note, it will be predicated as a reality, e.g., being a genus or a difference of the thing which is predicated [, or not]. These things have been demonstrated that it will not be unlimited, neither downwards nor upwards (e.g., human–bipedal, bipedal–animal, and this another; or animal–human, human–Kallias, and this of another in specification), for on the one hand it is possible to define all such realities; however, it is not possible for one knowing primarily to have gone though things which are unlimited. Therefore neither upwards nor downwards [is it] unlimited, for it is not possible to define that reality of which things which are unlimited are predicated. So indeed genera will not be counterpredicated of each other – this will be what very thing this kind is. Furthermore, no quality or any other, unless it was predicated coincidentally – all these are coincidental and are predicated of realities. But it is a fact that they will not be unlimited going upwards either, for of

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each is predicated what will signify either some quality or some quantity or some such thing or the things which are in the reality – these have been brought to a limit, also the genera of predications have been brought to a limit, either quality or quantity or relation or doing or undergoing or somewhere or some time’ (AnPo. I.22.83a36–83b17).

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Aristotle uses in this passage the more gruesome example of something’s or someone’s throat being cut: if something or someone dies while having their throat cut, it is by virtue of the throat that it does so, because that living thing died on account of having its throat cut. In other words, it was not a coincidence that that living thing died by having its throat cut. ...to men di’hauto huparkhon hekastôj kath’hauto, to de mê di’hauto sumbebêkos.... As shown in the examples here, the expression ‘kath’hauto’ is for Aristotle equivalent to the expression ‘qua itself’ (hêj auto). ‘For example, a point and the straight belong to line kath’hautên – qua line as well – and two right angles to triangle qua triangle – the triangle is equal to two right angles kath’hauto as well’ (AnPo. I.4.73b28–32). I agree with Ferejohn in interpreting ‘dia’ here as indicating a causal relation; however, I disagree that this interpretation completely precludes a logical relation as well for Aristotle, as Ferejohn appears to hold. Unlike him though, I think this interpretation works without having to introduce a fourth kind of ‘kath’hauto’ predication (1991, 118–123). As one can figure out, I clearly disagree with those who hold that Aristotle is describing different senses of kath’hauto in the above passages from AnPo. I.4. I deal with some interpretative controversies concerning these passages in chapter 20. Aristotle also mentions a less philosophically significant sense of the word: ‘kath’ho’ is a different way of saying ‘where’ or ‘there,’ that is, of signifying place and position in ancient Greek. For example, ‘where she stands’ or ‘there she walks’ can be said in Greek as ‘by virtue of what she stands’ or ‘by virtue of that she walks’ (Meta. V.18.1022a22–24). Modrak calls this second use ‘a corollary of the first that extends the notion to cover the conceptual parts of a definition of essence’ (2001, 154). I agree, but hold that the second use does not ‘extend’ that of the first.

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Notes See e.g. Irwin (1988, 210–215, sections 113–115). The active/passive verb use in English is reversed in the Greek: ta ara legomena epi tôn haplôs epistêtôn kath’hauta houtôs hôs enuparkhein tois katêgoroumenois ê enuparkhesthai di’hauta te esti kai ex anagkês. This reversal I think has caused a lot of interpretative problems. Also, if some x belongs to y kath’hauto, then that x belongs necessarily to y. Lloyd offers this conditional conversely, namely, if... necessary..., then... kath’hauto... (1981, 159). epei de dedêlôtai hêmîn en tois anô hoti katholou men esti ta en tôj ti esti katêgoroumena (ta katholou de anagkaion).... The manuscripts have readings for both ‘universal’ (which is Ross’ reading) and ‘necessities’ for 96b2. The confusion I hold arises between whether one takes for one’s reference concerning specifications Aristotle’s statements in AnPo. I.4 (where ‘necessities’ occurs) or AnPo. II.3 (where ‘universal’ occurs). In either case, what is made clear is that the things in the specification are necessary to the subject of that specification. See Top. I.5.102a18–19, 22–23; V.5.135a11–12 (‘…the revealing of the being is not a unique property but a term’); Meta V.30.1025a30–34. It is beyond the scope of the present work to examine whether things which belong ‘for the most part’ are also a part of the essence of a thing in the world, even though they are knowable. For example, it is unclear whether having a beard will belong in the complete specification of man (in contrast to woman), even though having a beard belongs to man for the most part and kath’hauto. It is clear though that unique properties do not. Something could have infinitely many unique properties without raising problems for Aristotle’s theory. Whether something could have an infinite number of features which are for the most part is an open question. There is a flip-side to this concern too: if there are no necessary features of anything, then knowledge is impossible as well. hosa te gar [en] ekeinois enuparkhei en tôj ti esti, kai hois auta en tôj ti esti huparkhousin autois. For those interested in the Greek, the verbs ‘enuparkhei’ and ‘huparkhousin’ are technical terms and have different functions. Aristotle indicates that this sense is more important or crucial than the first by the conjunctions he uses: the first sense is conjoined with the particle ‘te,’ the second sense with ‘kai’: see Smyth (1974, 2974); Kaegi (1913, 208.39). ...kai hois tôn huparkhontôn autois auta en tôj logôj enuparkhousi tôj to esti dêlounti.... Here is the difficult Greek: to ara legomena epi tôn haplôs epistêtôn kath’hauta houtôs hôs enuparkhein tois katêgoroumenois ê enuparkhesthai

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di’hauta te esti kai ex anagkês. endekhetai mê huparkhein ê haplos ê ta antikeimena, hoion grammêj to euthu ê to kampulon kai arithmôj to peritton ê to artion. esti gar to enantion ê sterêsis ê antiphasis en tôj autôj genei, hoion artion to mê peritton en arithmois hê hepetai. hôst’ei anagkê phanai ê apophanai, anagkê kai ta kath’hauta huparkhein. McKirahan is wrong to take ‘huparkhein’ to be equivalent to ‘enuparkhein’ (1992, 86), and the effects of this disagreement can be seen in the difference between my interpretations and his. However, I agree with McKirahan, and disagree with Reeve, that ‘enuparkhein’ refers to kath’hauto sense (Ka2), and ‘enuparkhesthai’ to kath’hauto sense (Ka1). See Reeve (2000, 90); McKirahan (1992, 88–89). Both Reeve and McKirahan make too much of Aristotle’s use of the term ‘opposites’ here; indeed, McKirahan calls what Aristotle says about them ‘a hasty generalization’ (2000, 91; 1992, 89–90 respectively). My discussion of kath’hauto sense (Ka2) offers further evidence for this view, which is concordant with Ferejohn (1991, 99–100). However, Ferejohn (and also Reeve) takes Aristotle’s main point in this passage here to be revealing two different kinds of necessity, and not two different senses of the term ‘kath’hauto’ (ibid., 100ff.; ibid. respectively). ‘A genus is that which is predicated in specifications with regard to many things and differing in respect of form’ (Top. I.5.102a31–32). For an opposing interpretation, see Goldin (1996, 76–77). Other prominent discussions of this topic have, in my view, missed this fundamental feature of kath’hauto sense (Ka2): Sorabji (1980, 188ff.); Barnes (1994, 112ff.); Ferejohn (1991, 96–99); McKirahan (1992, 87–93); Reeve (2000, 89–92, 95); Modrak (2001, 67–68). Byrne describes (Ka1) as the predicate term being a part of the definition of the subject term, and (Ka2) as a predicate term not being able to be defined without inclusion of the subject term (1997, 95). This kind of kath’hauto predication raises another possibility for infinite predication, which Aristotle mentions later in Posterior Analytics I.23. For example, let D belong to F and to G by virtue of E. In this case, E is something common to both F and G. Now, E itself belongs to both F and G by virtue of something common, namely E’ and so on, ‘such that one would chance upon terms which were unlimited between two terms’ (AnPo. I.23.84b11–12). This is like the Third Human argument. But Aristotle holds that this sort of unlimited predication is impossible: ‘It is not always necessary that the same thing belongs to many things by virtue of something common, if at least there will be immediate intervals. However, it is necessary that terms are in the same genus and out of the same “atoms,” if at any rate the thing which is common will be of those

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Notes things which belong kath’hauta: It would not be possible for things which are shown to cross over from one genus to another’ [emphasis mine] (AnPo. I.23.84b13–18). Cf. Physics IV.3.210a18–20: ‘…human is in animal and in general the form in the genus. Another [way] is as the genus is in the form and in general the part of the form in the account.’ This manner of the genus being the matter for its differences explains, at least in a sense, how differences are ‘inherent,’ like qualities. Thus, Aristotle can say that differences are (at least in a sense) qualities: Irwin holds that since differences are not ‘inherent,’ they cannot be qualities, despite all this textual evidence to the contrary (1988, 65). ‘...[D]efinitions should be accounts of unified substances..., which say what it is to be that substance’ (Charles 2000, 276). This discussion of characteristics which have the dual kath’hauto/coincidental nature accounts for their place in Aristotle’s two senses of kath’hauto predications, an account mentioned as lacking in the literature by Goldin (1996, 145, note 9). For different views of kath’hauto sense (Ka2) vis-à-vis kath’hauto coincidental predications, see Ferejohn (1991, 96–99); McKirahan (1992, 100); Barnes (1994, 113–114). I omit ‘te’ in this passage in accordance with d, and read ‘kai’ as explicative.

Chapter 20 1

2

3 4

5 6

7

8

Sorabji seems to hold implicitly that there are only two senses as well (1980, 188–189). Byrne explicitly argues for only two senses (1997, 95–96). E.g., McKirahan (1992, 94); Barnes (1994, 114–117); Reeve (2000, 91–92). Ferejohn (1991, 109–115). E.g., McKirahan (1992, 95); Ferejohn (1991, 118–123); Barnes (1994, 117); Aydede (1998, 24–26); Modrak (2001, 68–69). Barnes (1994, 112). For a discussion showing that definitions and specifications are not trivial or analytic, see Bayer (1997). Ferejohn (1991, 73, 115ff.); Aydede (1998, 24–25). This position is endorsed by Modrak in (2001, 69). McKirahan (1992, 95).

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Glossary

Words are arranged in the order of the Greek alphabet, with the Greek in italics and the English in roman. Words which share the same root are grouped under a principal word. Only the masculine form of adjectives are given. Some Greek words are simply transliterated into English if I use the transliterated term in the text. Some translations are followed by brief explanations, or by other terms (English or otherwise), for making the sense of the word clearer. A adoxos – improbable aïdion – unconditional (in epistemological contexts); eternal (in metaphysical contexts) aisthêsis – perception aisthêma – percept aisthêton – perceptible aitêma – assumption aitia – cause (rarely ‘causation’; treated as equivalent to ‘aition’) aition – cause akribos – precise alêtheuô – to arrive at truth amesos – immediate. See chapter 15. It does not mean ‘immediate’ in a ratiocinative or temporal sense. anagkaion – necessary anagkê – necessity antikeimon – opposed antiphasis – contradiction antistrephonta – counterparts apatê – deception

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apeiras – unlimited haplôs – without qualification aphronsunê – impracticality apodeixis – proof apodeiktikos – apodeictic/derivative anapodeiktikos – anapodeictic/primary apophansis – assertion apophasis – denial apophatikos – negative (working as the adjectival form for ‘denial’) aretê – virtue (sometimes ‘virtue and excellence’) arkhê – starting point atekhnia – incompetence B bouleuesthai – to deliberate G genesis – formation (sometimes generation or ‘genesis’ itself) genos – genus gignôskein – (to make to) recognize gnôrizô – to recognize gnôstos – recognizable gnôrimos – recognized D diathesis – constitution diatithêmi – to constitute dialektikos – dialectical (‘opiniative’ might be better, for Aristotle’s use carries a sense of being grounded in belief or opinion, not knowledge). dianoia – thought diaphora – difference diapseudô – to arrive at falsehood diôxis – striving doxa – belief doxastikos – doxastic dunamis – potential dunamei – potentially dunatos – capable adunaton – incapable

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E eidenai – to see (in the sense of ‘oh, I see how this works now’ or ‘don’t you see what the problem is?’) eidos – form to einai – being to on – that which is empsukhos – animate hen – one henôtês – unity enantion – contrary endoxos – probable energeia – actuality (sometimes ‘activity’). A better literal translation would be perhaps ‘productivity’ – ‘product-in-act’ is even better – but this term would make the translations almost incomprehensible. So one should keep in mind the notion of productivity – just as it occurs in the phrase ‘worker productivity’ – when they read the term ‘energeia.’ energeiaj – actually (sometimes actively). ‘Productively’ might be a better literal translation. enoêô – to opt ennoêma – option entelekheia – fulfillment (sometimes ‘actual fulfillment’) entelekheiaj – in fulfillment enuparkhein – to be in enuparkhesthai – to contain hermêneia – interpretation hexis – hexis (not ‘disposition’ or ‘habit’!) epistêmê – knowledge to epistasthai – knowing epimeleia – pursuit ergon – product energeô – to produce (although poiêsis – production) energos – producive eskhatos – ultimate euboulia – good-will eudaimonia – well-being Z to zôjon – life

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Ê êmerêsis – stillness êthos – behavior TH theôria – theory (literally ‘knowledge in activity or fulfillment’) theôreô – to theorize theôrêma – theorem I idea – idea idion – unique property K kath’hauto – kath’hauto (by virtue of itself, etc.) kath’hekaston – particular kataphasis – affirmation kinêsis – change (eu)kinêton – (easily) changeable kolobos – deformed krinein – to judge kritikos – judicative L logizesthai – to reckon logistikon – logistical logismos – reckoning logos – account. This term does not mean ‘argument’ (that’s problêma); the key element is that language is involved. It is the linguistic equivalent to the imagistic ‘das Bild.’ M mathêsis – learning (‘instruction’ seems too restricted, for it implies the having of a teacher; I’m not sure ‘mathêsis’ entails a teacher. If so, then ‘instruction’ would be better.) mathêma – a science mêros – part metabolê – transition (eu)metabolon – (easily) transitional ametablêton – fixed metablêtikos – transitive

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223

metalêpsis – substitution metallagê – shift metron – unit measure metekhein – to partake morion – section morphê – shape mousikos – erudite (when modifying people); cultural (when modifying things) ta mousika – culture N nous – nous noêma – noêma noêsis – noêsis X xulon – tree O oikeios – appropriate holon – whole holotês – entirety hoper – what very thing horos – term (with the connotation of ‘limit’, as in ‘terminal’) horismos – definition hôrismenôs – definitively hormê – impulse orâsis – vision (actually or actively seeing) orexis – desire opsis – eyesight (potentially seeing) ousia – reality P pathos – modification pathêtikos – receptive patheô – to undergo pathê – modifications pathêma – a modified to pan – totality paradoxos – beyond general opinion peras – limit

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pistis – confidence pisteuô – to be confident (in...) pistos – conducive to confidence to plêthos – plurality poiêsis – production poiêtikos – productive poiôtês – qualification poion – quality hoi polloi – the majority poson – quantity prâgma – thing in the world (die Sache) problêma – argument proginôskein – to recognize beforehand pros ti – relation (das Verhältnis) protasis – statement prôtos – primary (‘first’ in non-technical contexts) prôtôs – primarily ta prôta – primaries S sêmainô – to signify sêmainon – it is significant... (impersonal construction) skopeô – consider spoudaios – expedient (in a positive sense) stasis – stasis sterêsis – deprivation stoikheion – element suggenês – of the same lineage suggeneia – lineage sullogismos – syllogism sumbebêkos – coincidental kata sumbebêkos – coincidentally sumpheron – advantageous suneimi – to discern sunesis – discernment eusunetos – perspicacious eusunesia – perspicacity sunthêkê – consensus sustoikhia – chain skhêma – figure (shape – morphê)

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Glossary T tekhnê – skill telos – end to ti esti – specification to ti ên einai – essence tode ti – a certain this U hupokeimenon – underlying thing hupothesis – declamation PH phantasia – imagination phantasma – image phthora – disappearance, degeneration (‘dissolution’ is another good translation) phartos – contingent (in epistemological contexts); perishable (in ontological contexts) phronesis – prudence phronimos – prudent phugê – avoidance phusis – nature ho phusikos – naturalist phusei – by/in nature pephukos – naturally KH khôristos – separate khôris – apart (from) PS psukhê – psyche

225

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Primary sources Alexander Aphrodisiensis In Metaphysica Commentaria. Edidit Michael Hayduck. Berolini: Georgii Reimerii. In Aristotelis Topicorum. Libros octo commentaria. Edidit Maximilianus Wallies. Berolini: Georgii Reimerii. Aristotelis Categoriae et Liber de Interpretatione. Recognovit L. Minio-Paluello. Oxonii: Clarendoniano. Analytica Priora et Posteriora. Recensuit W.D. Ross. Auxit L. Minio-Paluello. Oxonii: Clarendoniano. Topica et Sophistici Elenchi. Recensuit W.D. Ross. Oxonii: Clarendoniano. De Anima. Recognouit W.D. Ross. Oxonii: Clarendoniano. De Anima. Mit Einleitung, Übersetzung und Kommentar heraus. H. Seidel. Griechischer Text in der Edition von W. Biehl u. O. Apelt. Hamburg: Feliz Meiner Verlag. Physica. A Revised Text with Introduction and Commentary by W.D. Ross. Reprint of the 1936 Edition. Oxford: Sandpiper Books Ltd. De Generatione et Corruptione. A Revised Text with Introduction and Commentary by Harold H. Joachim. Reprint of the 1926 Edition. Oxford: Sandpiper Books Ltd. Metaphysica. Recognovit W. Jaeger. Oxonii: Clarendoniano. Ethica Nicomachea. Recognovit F. Susemihl. Editio altera curavit O. Apelt. Athenis: D.N. Papadimas; Lipsiae: B.G. Teubneri. Ethica Eudemia. Recognoverunt R.R. Walzer et J.M. Mingay. Oxonii: Clarendoniano.

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ALEXANDER On the Metaphysics (In Meta.) 387,12–388,14 183 417,36–418,12 15 425,12–25 25 425,25–426,1 25 On the Topics (In Top.) 346,5–27 351,12–352,3 ARISTOTLE Categories (Cat.) 6.5b15ff. 7.6b2–3 7.6b6–8 7.6b11–14 7.6b15–16 7.6b16–17 7.6b28–36 7.6b36–7a22 7.7a22–b14 7.7b15ff. 7.7b22–35 7.7b35–8a12 7.8a13–28 7.8a32 7.8a33–34 7.8a36–37 7.8a36–8b15 7.8b15–21 8.11a22–36 8.11a36–37 8.8b26–27 8.8b27–28

208 208

27, 182 18, 27 27, 184 184 27 38 30 28, 185 30 29 32 33 188 185 185 184 30, 184, 191 185 37, 38 18 18, 27 18

8.8b29–9a8 8.8b35 8.9a5 8.9a9–10 8.9a10–13 10.12a26–34 13 15.15b17–27

18–19 18 18 18 18 50 29 16

De Interpretatione (DI) 9.19a18–22

103

Prior Analytics (AnPr.) I.1.24a16–17 I.1.24b16–18 I.1.24b18–22 I.2.25a5–10 I.3.25b14–15 I.13.32b4–11 I.23.40b23–24 I.27.43a27–40 I.27.43a33–36 I.39.49b6–9 II.5.57b18–21 II.5.57b35–36 II.15.63b40ff. II.16.64b32–36 II.16.65a8–9 II.21.66b25–26 II.21.66b26ff. II.21.67a27ff. II.21.67b3–5 II.23.68b13–14 II.23.68b30–37

59, 133 133 59 143 103 103 59 136, 138 137 191 143 142 191 106, 116, 122 106 190 133 37 188 120 134

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232 Posterior Analytics (AnPo.) I.1.71a17–24 I.2.71b9–16 I.2.71b15–16 I.2.71b16–19 I.2.71b19–22 I.2.71b25–26 I.2.71b26–27 I.2.71b29–33

I.2.71b33–72a5 I.2.72a5–8 I.2.72a14–24

I.2.72a25–30 I.2.72a30–33 I.2.72a36–72b4 I.2.72b3–4 I.3.72b5ff. I.3.72b14–15 I.3.72b15–18 I.3.72b18–20 I.3.72b25–28 I.3.72b32–73a6 I.3.73a6–7 I.4.73a21–27 I.4.73a28–32 I.4.73a34–35 I.4.73a35–37 I.4.73a37–38 I.4.73b1–3 I.4.73b5–10 175, I.4.73b10–16

I.4.73b16–24

I.4.73b25–28

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Passages cited 107 73, 196–7 56 59, 74, 194 63, 77, 83 83 79 79, 112, 199, 207 108, 207 78, 133, 134 76, 87, 106, 202 111 122 123 120 50, 129 129 130 79 130 130 142 58, 60 91 161 162 162, 216 162 167, 201 156, 157, 175, 215 93, 159, 162, 216–217 56, 90,

I.4.73b28–32 I.4.73b32–74a3 I.5.74a32–74b4 I.6.74b5–11

I.6.74b11–12 I.6.74b24–25 I.6.74b25–26 I.6.74b32ff. I.6.75a35–7.75b12 I.7.75a38–75b2 I.7.75b8–9 I.7.75b14–17 I.8.75b21–36 I.9.75b37–76a3 I.9.76a4–7 I.9.76a9–15 I.9.76a26–28

I.9.76a28–30 I.10.76b11–16 I.13.78b35–79a6 I.15.79b5ff. I.16.79b23–29 I.16.79b29ff. I.18.81a40–81b1 I.19.81b23–29 I.19.81b30–33 I.19.81b31–82a3 135,

I.19.82a2–6 I.19.82a6–8 I.19.82a9–14 I.19.82a15–20 I.20.82a21–22 I.20.82a23 I.20.82a23–24 I.20.82a24–35 I.21.82a39–82b1 I.21.82b2–3

204 215 146 86 92–3, 160, 161, 163, 205 55 86 84 57 84 87 84 201 56–7, 60, 90 84 85 201 83, 113, 200, 208 84 87, 201 201 133 62, 190 62 90 134 137 133, 136, 139 139 131 140 142, 144 144 135, 136 135 144 136 138

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Passages cited I.21.82b6–8 I.22.82b37 I.22.82b37–83a1 I.22.83a1, 84b2 I.22.83a1–14 I.22.83a14–18 I.22.83a18–23 I.22.83a24–31 I.22.83a32–34 I.22.83a36–39 I.22.83a36–b17 I.22.83a39–83b1 I.22.83b9–10, 15–16 I.22.83b10–15 I.22.83b13–17 I.22.83b17–31 I.22.83b33–84a6 I.22.84a7–11 I.22.84a8, 84b2 I.22.84a11–14 I.22.84a15–16 I.22.84a18–25 I.22.84a26–28 I.22.84a29–84b2 I.23.84b11–12 I.23.84b13–18 I.23.84b33–35 I.28.87a38–87b4 I.30.87b19–27 I.31.87b32–33 I.31.87b38–39 I.31.88a5–6 I.33.88b36–89a4 I.33.89a5–10 I.33.89a33–37 I.33.89a39–89b1 II.1.89b31–35 II.2.89b37–90a5ff. II.3.90b3–4 II.3.90b4 II.3.90b13–14 II.3.90b16–17 II.3.90b24 II.6.92a20 II.10.93b35–37

145 142 145 145 147 148 59, 150, 151 149 150 151 215 153 154 152 151 151, 154 131, 211 156 146 160, 161, 216 164 164, 169 169 171 217 218 134 87 90 90 90 90 45, 47, 63 121 122 122 210 210 165 159 209 106 106 210 54, 152

233

II.11.94a20–24 II.11.94b36 II.12.95b22–26 II.12.96a9–11 II.12.96a14–15 II.12.96a18–22 II.13.96b1–3 II.19.100b7–14

89, 203 99 77 92 204 103 159, 216 51

Topics (Top.) I.1.100a30–100b21 I.5.101b38–102a17 I.5.102a18–23 I.5.102a31–32 II.6.112b1–9 II.6.112b10–11 III.6.119b35ff. IV.1.121a10–14 IV.2.122a3–9 IV.2.122b18–24 IV.5.125b28–126a2 IV.5.126b13–34 IV.6.128a26–27 V.1.129a6–16 V.2.130b11–18 V.5.135a11–12 VI.1.139b12–15 VI.1.139b15–18 VI.4.141a26ff. VI.4.141b22–34 VI.4.141b34–142a2 VI.4.142a2–6 VI.4.142a6–11 VI.4.142a26–31 VI.6.144a18–19 VI.6.144a24–27 VI.8.146b3–4 VI.11.149a8–16 VI.11.149a26–27 VIII.3.158b3–4

122 133 142, 216 217 103 102 210 154 154 163 49, 117 49, 116 164 103 120, 210 216 106 206 106 110 110 111 111 185 164 164–5 185 48 106 106

Physics (Phys.) I.1.184a21–b14 II.2.194a28–30 II.3.194b23–195a3 II.3.195a15–26 II.5.196b10 II.7.198a24–26

109 99 89 89, 98 103 94

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234 II.7.198b1–5 II.7.198b5–9 II.8.198b10ff. II.8.199a7–8 II.8.199a30–32 II.8.199b15–18 II.8.199b28–33 II.9.199b34–35 II.9.200a13–14 II.9.200a14–15 II.9.200a15–19 II.9.200a20 II.9.200a22–24 II.9.200a24–29 II.9.200a30–b8 III.1.200b13–15 IV.3.210a18–20 IV.6.213a12–15 V.1.224b28–30 V.4.227b11–14 VII.3.246a10ff. VIII.8.262a17–19 De anima (DA) I.1.402a10–11 I.2.403b28–404a16 I.2.405a19–21 I.2.405a29–405b1 I.2.410b27–411a2 II.1.412a19–21ff. II.1.412a9–11 II.2.413a11–12 II.5.417a22–24 II.5.417a26–28 II.5.417a28–29 II.5.417a31–32 II.5.417b16–18 II.5.417b18–19 II.5.417b29–418a1 II.5.418a1–5 III.3.427b24–26 III.3.428a9–11 III.3.428a18–24 III.3.428a18ff. III.5.430a4–5 III.5.430a14–15 III.7.431a1–2

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Passages cited 94, 99 89 99 94 94 98 206 94 206 95 94 95 99 95 100 121 218 49, 119 209 48 19 209

119 49 49 49 49 36, 66 66 108 35 36 66, 195 36 36 66 36 66 47 193 119, 209 45, 119, 191 66 49 66

III.7.431a2–4 III.7.431b2–12 III.7.431b12–19 III.8.431b24–432a1 III.8.432a3–6 III.9.432a30–31 III.11.434a10–12

39 191 195 67 195 49, 192 51

History of Animals (HA) V.14.545a14–18

103

Parts of Animals (PA) I.1.642a1ff. III.2.663a28

205 103

Generation of Animals (GA) II.6.742b17–34

194

Metaphysics (Meta.) I.1.981a5–7 I.2.982a6–10ff. I.5.986a24–26 I.8.989a6, 9–12 II.2.994a10–19 II.2.994a19–994b6 II.2.994b29–31 III.6.1003a14–15 IV.2.1003b22ff. IV.3.1005b23–32 IV.4.1007a32–33 IV.4.1007a33–b17 IV.5.1010b30–11a1 V.1.1013a7–10 V.1.1013a14–17 V.1.1013a17–23 V.2.1013a24–26 V.2.1013a26–29 V.2.1013a29–32 V.2.1013a32–33 V.2.1013b17–22 V.2.1013b22–23 V.2.1013b23–25 V.2.1013b25–28 V.2.1014a15–25 V.4.1014b17–18ff. V.4.1014b18ff. V.4.1015a13–19 V.5.1015b6–15

47 49 211 49 168 170 127 90 54 192 149 152 186 42, 201 76 75 97 98 98 98 21, 97 98 98 98 203 98 98 121 93

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Passages cited V.6.1015b28–34 V.6.1015b36–16a9 V.6.1016a34–35 V.8.1017b21–26 V.10.1018a21 V.10.1018a29–30 V.11.1018b30–34 V.11.1019a2–4 V.11.1019a5–14 V.12.1019a19–20 V.12.1019a26–28 V.13.1020a14–26 V.15.1020b26ff. V.15.1021a26–b4 V.15.1021a29–b11 V.16.1021b12–13 V.16.1021b14–17 V.18.1022a14–16 V.18.1022a16–19 V.18.1022a19–20 V.18.1022a22–24 V.18.1022a25–27 V.18.1022a27–29 V.18.1022a29–32 V.18.1022a32–35 V.18.1022a35–36 V.19.1022b1–2 V.20.1022b4–10 V.20.1022b10–14 V.22.1022b22ff. V.23.1023a8–25 V.23.1023a11–13 V.23.1023a13–17 V.23.1023a17–23 V.23.1023a23–25 V.25.1023b19–22 V.26.1023b26–29 182–3 V.26.1023b29–36 V.27.1024a14–16 V.28.1024b4–6 V.28.1024b8–9

V.30.1025a4–24 V.30.1025a14 V.30.1025a24–25

188 55 55 98 50 191 109 30, 39 24 20 19 168 27 28–9, 185 184 39 40 162 158, 164 158 215 159 159 159 158 159 18 17 18 50 16, 17 20 20, 21 17 21, 75 21 23, 24 182 164, 204 48, 91, 163, 204 156 55 157

V.30.1025a30–33 V.30.1025a30–34 VII.3.1029a27–28 VII.3.1029b3–11 VII.4.1029b13–14 VII.4.1030a17–18 VII.4.1030a22–23 VII.4.1030a29–32 VII.4.1030a3–11 VII.5.1030b14–31a14 VII.6.1031b6–7 VII.6.1031b20–21 VIII.6.1045a12–14 IX.1.1046a10–11 IX.1.1046a13–15 IX.1.1046a16–19 IX.1.1046a19ff. IX.8.1050a22–23 X.1.1053a31–b3 X.3.1054b32–55a2 X.4.1055a31–32 X.6.1056b32–57a12 X.8.1058a13–14 XI.1.1059b25–26 XI.5.1061b34–62a5 XI.5.1062a13–16 XII.3.1070a18–20 XII.8.1073a17–18 XIII.10.1086b33 XIV.2.1090a2–4 Nicomachean Ethics (EN) I.4.1095b2–3 II.3.1104b19–28 II.5.1105b25–28 VI.1.1138b20–1139a3 VI.1.1139a3–5 VI.1.1139a6–8 VI.1.1139a11–14 VI.2.1139a17–18 VI.2.1139a18–20 VI.2.1139a22–28 VI.3.1139b15–17 VI.3.1139b18–24 VI.3.1139b19–33 VI.3.1139b33–35

235 167 213, 216 165 108 160 165 150, 165 165 166 165, 166 161 161 54, 152 20 19 20 181 183 30 171 87 28, 31 171 90 118 105 22, 181 49 90 119

107 19 19, 180 42 44 45, 189 45 51 193 42, 44 47, 51, 191 45, 56 13, 60, 74 74, 116

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236 VI.4.1140a3–5 VI.4.1140a9–10 VI.4.1140a15–16 VI.4.1140a21–23 VI.4.1140a24–25 VI.5.1140a27–28 VI.5.1140a28–31 VI.5.1140a31ff.; b24–28 VI.5.1140a33–34 VI.5.1140b4–6 VI.5.1140b11–16 VI.5.1140b25–26 VI.5.1140b28–30 VI.6.1140b31–1141a1 VI.6.1141a1–8 VI.7.1141a9ff. VI.8.1142a25–26 VI.9.1142b31–33 VI.10.1143a11–18 VI.11.1143a35–b1 VI.12.1143b15ff. VII.3.1146b27 VII.8.1151a15–19

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Passages cited 45 45 189 45, 189, 190 45 46 46 46 189 45 47, 190 45 45 13, 47, 50, 60 50, 51 51 51 47 113 51 51 190 50, 193

Eudemian Ethics (EE) I.2.1214b10 II.1.1219a6 II.4.1221b30–32 II.8.1224a24–25 VII.1.1235a4–20ff. VII.14/VIII.2.1247b18–19 VIII.1.1246b6

190 188 51 193 49 51 190

Poetics (Poet.) XX.1457a27–30

54

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Index

account 54–6, 59–60, 63, 118–20 see logos act/object distinction 68, 73 actuality 23–5, 35, 40, 66, 68–9 aïdion 56–8 see unconditional Alexander Aphrodisiensis 15, 25 anapodeictic 63–4, 78–9 apodeictic 45, 60, 64 axiom 85, 87 Barnes, Jonathan 127, 176 behaviour 42, 44 being 84–5 belief 5, 45–7, 60, 113, 119–21, 124 beneath every 90, 91–3, 103 between 133, 139 Burnyeat, Miles 4–5 Butchvarov, Panayot 5, 116 cause Ch. 7 passim, 89–90, Ch. 10 passim, 140, 153, 176 initial/ultimate 77, 78, 131–2 see starting point certainty 76 chain 132, 133, 136–40, 152–3, 168, 171 atomic 171 coherentism 6, 83, 130, 132, 153–5, 172 coincidental 84, 133–4, 148–9, 152, 156–7, 167–8 common 163 conclusion 59–60

confidence 104, Ch. 13 passim constitution 18, 62 content 68–9 contingent 57–8 counterpart 27–33, 43 counterpredicability 142–4, 154 declamation 76, 106, 108, 129, 144 definition 105ff., 144, 150, 165, 169–70, 172–3 deliberation 45 desire 44, 51 Detel, Wolfgang 9 discernment 112, 113–14 disposition 15–17 division 42, 55 doubt 119 downwards 134, 138–9, 145, 154, 169–70 element 143 essence 97–8, 145, 156, 159–60, 165–6, 168–70, 172–4 evidence 68–9, 173 externalism 73, 104, 122 Ferejohn, Michael 127, 175, 176–7 for the most part 59, Ch. 11 passim, 161 for us vs. by itself 35ff., 107ff. see without qualification for the sake of which 94–5, 98–100 form 35–6, 38–9, 42, 67, 68, 141, 148, 150, 154, 169

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238 foundation 140–1, 148–9 see starting point fulfilment 23–4, 35, 66 genus 4, 34, 36, 38, 42, 48–9, 84–5, 86, 87, 116–18, 141, 153–4, 163–6, 169 Ginet, Carl 5, 116 have 16, 17, 20 hexis Ch. 1 passim, Ch. 3 passim, 167–8, 170 Hume, David 115 Hutchinson, D.S. 15 hypolêpsis Ch. 4 identity 143 ignorance 38, 62–4 immediate 78–9, 133–4, 139 impracticality 46, 47 in regard to something else 23, 26, 35ff., 68 incompetence 47 individual 22 see particular inductive procedure 36, 55, 120 internalism 73, 104, 116, 123–4 interpretation 105 justification 5, 73, 79, 86, 173 kath’hauto 23, 26, 27, 29, 59, 67, 87–8, 90–3, Ch. 11 passim, 133–4, 151–2, 157–70, Ch. 20 passim relative 28–9 Kvanvig, Jonathan 6 learning 36, 82, 85, 107–12 logical procedure 107, 112, 127 logos 44, 48, 54–6, 68, 118 see account matter 38, 48, 60, 64, 66, 86, 100, 169 proximate/ultimate 22, 39 McKirahan, Richard 127, 175, 177 Mignucci, Mario 34 Moser, Paul 5, 116

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Index nature 98–9, 121–2 necessity 65, Ch. 9 passim, Ch. 11 passim, 134, 163 axiomatic 93–4, 99–100, 167 compositional 94–6, 99–100 see kath’hauto non–primary 133 nous 44, 49–51, 173–4 number 31, 37–8, 162, 169 order 18 part 20–1, 23–5, 39–40, 44 array of 24, 35 particular 108, 112, 138, 140 see individual phthartos 56–8 see contingent potential 19–20, 23–5, 35, 37–8, 40, 68–9 perception 30, 32–3, 49–50, 51, 67, 108–9 place 36, 68 primary 77–9, 93, 133 proof 58–60, 73–4, 78, 112, 129–30, 134, 170–1 Protagoras 30–3, 40, 109–10 prudence 45–7, 113, 124 psyche 35–6, 43, 52, 66, 67, 116–17 qualification 36–7 Quine, W.V.O. 64 reality 98, 149, 165 reckoning 45, 99 recognition 30, 36, 75–7, 81–2, Ch. 12 passim, 172 ‘more than’ Ch. 12 passim regress argument Ch. 14 passim relation Ch. 2 passim container-contained 20–2 donor-recipient 20–2 dynamic 28, 30 hexical 28ff., 42–3 modality of 29 proportional 28, 30

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239

Index relative 28–9, 35 symmetry/asymmetry 29 relevance 85–7, 171 reliability 18 reveal 56, 90, 105, 112–14 Ross, W.D. 95–6, 127 seeing 112, 113 self-evidence 106–7, 122–3 separate 42, 141, 159, 165 skepticism 64–5, 76, 102, 127, 153–5, 172–3 skill 45–7, 124 Sommers, Fred 135 Sosa, Ernest 5 specification 94, 142–3, 150, 153–5, 159–66 starting point 19–20, Ch. 7 passim, 112, 114, 118, 129, 131, 160, 171 see cause, foundation statement 59, 133 syllogism 134 term 133, 135, 152 testimony 65 theory 64–8

thought 44, 51–2 see hypolêpsis truth 83 unconditional 56–8, 60, 93 underlying thing 38, 48, 86, 97–8, 147–8, 151, 162, 167, 169 understanding 4–6 unique property 142–3, 161 unity 84–5 universal 23, 25, 89–92, 102, 108–9, 137, 140–1, 145–6 unpersuadability 119–22 unqualified 150 upwards 135, 136–8, 145, 154, 168–9 virtue 18–19, 27 virtue epistemology 6 whole 20–1, 23–5, 48 without qualification 59, 84, 93–4, 107, 110, 112, 143, 148 see for us vs. by itself Zagzebski, Linda 6