Formal and Informal Methods in Philosophy 2019055385, 9789004420496, 9789004420502

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Formal and Informal Methods in Philosophy

Poznań Studies in the Philosophy of the Sciences and the Humanities Founding Editor Leszek Nowak (1943–​2009) Editor-​in-​Chief Katarzyna Paprzycka-Hausman (University of Warsaw) Editors Tomasz Bigaj (University of Warsaw) –​Krzysztof Brzechczyn (Adam Mickiewicz University) –​Jerzy Brzeziński (Adam Mickiewicz University) –​Krzysztof Łastowski (Adam Mickiewicz University) –​Joanna Odrowąż-​Sypniewska (University of Warsaw) –​Piotr Przybysz (Adam Mickiewicz University) –​Mieszko Tałasiewicz (University of Warsaw) –​Krzysztof Wójtowicz (University of Warsaw) Advisory Committee Joseph Agassi (Tel-​Aviv) –​Wolfgang Balzer (München) –​Mario Bunge (Montreal) –​ Robert S. Cohen✝ (Boston) –​Francesco Coniglione (Catania) –​Dagfinn Follesdal (Oslo, Stanford) –​Jacek J. Jadacki (Warszawa) –​Andrzej Klawiter (Poznań) –​Theo A.F. Kuipers (Groningen) –​Witold Marciszewski (Warszawa) –​ Thomas Müller (Konstanz) –​Ilkka Niiniluoto (Helsinki) –​Jacek Paśniczek (Lublin) –​ David Pearce (Madrid) –​Jan Such (Poznań) –​Max Urchs (Wiesbaden) –​ Jan Woleński (Kraków) –​Ryszard Wójcicki (Warszawa) volume 113

Polish Analytical Philosophy Editor-​in-​Chief Jacek Juliusz Jadacki (University of Warsaw) Editors Jacek Paśniczek (Maria Curie-​Skłodowska University, Lublin) –​Jan Woleński (Professor Emeritus, Jagiellonian University, Kraków) –​Ryszard Wójcicki (Professor Emeritus, Polish Academy of Sciences)

The titles published in this series are listed at brill.com/​paph

Formal and Informal Methods in Philosophy Edited by

Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski

LEIDEN | BOSTON

This volume was prepared within the project “Philosophy from the Methodological Point of View” (2015/​18/​ E/​HS1/​00487), financed by the National Science Center (Poland). Cover illustrations: From the Private Archive of Jacek Jadacki, Warsaw. Used with permission. Library of Congress Cataloging-in-Publication Data Names: Będkowski, Marcin, editor. Title: Formal and informal methods in philosophy / edited by Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski. Description: Leiden ; Boston : Brill | Rodopi, 2020. | Series: Poznań studies in the philosophy of the sciences and the humanities, 1389-6768 ; volume 113 | Includes bibliographical references and index. Identifiers: LCCN 2019055385 | ISBN 9789004420496 (hardback : acid-free paper) | ISBN 9789004420502 (ebook) Subjects: LCSH: Methodology. | Logic. | Analysis (Philosophy) Classification: LCC BD241 .F645 2020 | DDC 101–dc23 LC record available at https://lccn.loc.gov/2019055385

Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/​brill-​typeface. issn 1389-​6 768  isbn 978-​9 0-​0 4-​4 2049-​6 (hardback) isbn 978-​9 0-​0 4-​4 2050-​2 (e-​book) Copyright 2020 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Brill Hes & De Graaf, Brill Nijhoff, Brill Rodopi, Brill Sense, Hotei Publishing, mentis Verlag, Verlag Ferdinand Schöningh and Wilhelm Fink Verlag. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Authorization to photocopy items for internal or personal use is granted by Koninklijke Brill NV provided that the appropriate fees are paid directly to The Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, USA. Fees are subject to change. This book is printed on acid-​free paper and produced in a sustainable manner.

Contents

Illustrations, Figures, and Diagrams viii



Introduction 1 Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski

part 1 Philosophy from the Methodological Point of View 1

Metareflection: a Method for Philosophy 9 Mieszko Tałasiewicz

2

Semi-​Formal Analysis of the Formality-​Informality Opposition in the Spirit of the Lvov-​Warsaw School 41 Jacek Jadacki

3

Analysis –​Paraphrase –​Axiomatization: Philosophical Methods in the Lvov-​Warsaw School 56 Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski

part 2 Historical Research and Its Methods 4

From Methodenstreit to the “Science Wars” –​an Overview on Methodological Disputes between the Natural, Social, and Cultural Sciences 77 Friedrich Stadler

5

Periodization as a Disguised Conceptualization of Historical Development: a Case Study of a Theory of the Historical Process Developed in the Poznań School of Methodology 101 Krzysztof Brzechczyn

vi Contents 6

Władysław Tatarkiewicz: Metaphilosophical Notes 126 Ryszard Kleszcz

7

Casimir Lewy and the Lvov-​Warsaw School 150 Tadeusz Szubka

part 3 On Formal Methods in Philosophy 8

Remarks on the Origin and Foundations of Formalisation 163 Srećko Kovač

9

The Status of Mathematical Proofs and the Enhanced Indispensability Argument 180 Krzysztof Wójtowicz

10

A Case of Metalogical Explanation of Logical Normativity 195 Kordula Świętorzecka

11

Leśniewski’s Intuitive Formalism 206 Sébastien Richard

12

The Case of Logic: Łukasiewicz-​Prior’s Discussion on Logic 229 Zuzana Rybaříková

part 4 On Informal Methods in Philosophy 13

The Semiotic Method in Art Theory and Aesthetics in the Lvov-​Warsaw School 241 Aleksandra Horecka

14

From Concepts and Contents to Connotations: Łukasiewicz’s Theory of Conceptual Analysis and Its Further Evolution 257 Marcin Będkowski

Contents

vii

15

Kotarbiński’s Methodological Reism: Framework and Inspirations 278 Alicja Chybińska

16

Interdisciplinarity: Analysis of the Concept and Some Examplifications in the Lvov-​Warsaw School 297 Anna Brożek



Index of Names 315

enprepdf

Illustrations, Figures, and Diagrams Illustrations 13.1 Biforium in Cistercian monastery in Wąchock (Poland) and the capital of column (Phot. A. Horecka) 251 13.2 Different forms of claws in romanesque columns in Cistercian monastery in Wąchock (Poland) (Phot. A. Horecka) 253

Figures 5.1 5.2 5.3

Transitions between epochs and formations 108 Stages and formations in the adaptive interpretation of historical materialism 113 The structure of the theory of the historical process in non-​Marxian historical materialism 120

Diagrams The structure of a class formation 105 The essential structure of the socio-​ancestral formation 107 The structure of the socio-​ancestral formation 107 The essential structure of the last formation of the social-​ancestral epoch and of the first formation of the class epoch 109 5.5 The structure of the political momentum 116 5.6 The structure of the cultural momentum 116

5.1 5.2 5.3 5.4

Introduction Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski 1. Reflection over methods of achieving knowledge has been present in philosophy from the very beginning. However, in the process of emancipating particular disciplines from the body of philosophy, many questions have arisen concerning the ways of achieving knowledge in the domain of philosophy itself. Do any particular philosophical methods or philosophers resolve problems in the same way as representatives of other disciplines? Is there any reliable method of dealing with philosophical questions? Are philosophical investigations discursive and possible to control? These questions express the main problems of the methodology of philosophy, or metaphilosophy. Over one hundred years ago, independently in several countries including England, Poland and Austria, a kind of philosophical thinking emerged which is referred to today as “analytical philosophy.” This term comes from the fact that analytic philosophers concentrate on small problems rather than constructing all-​embracing syntheses. However, it is easy to note that analysis, especially conceptual analysis, was present in philosophy much earlier, at least from Socrates’s times. So, what are the distinctive features of 20th century analytic philosophy? There are a few keywords that characterize it. The first is “language”:  contemporary analytic procedures are accompanied by the conviction that the words we use play an important role in cognition. The second is “obiectivity”: there is an intersubjective reality to which philosophical investigations refer; in consequence, philosophy has to take into consideration the results of sciences which refer to that same reality. The third is “logic”: an assumption that logical tools are useful in dealing with philosophical problems. The presence of the latter element in 20th century analytic philosophy was accompanied by the rise and enormous development of formal logic. This “marriage” of logic and philosophy bore various fruits. On the one hand, serious criticism appeared of traditional philosophy which stroke first of all in loosely formulated and poorly justified philosophical fantasies. On the other hand, optimistic views emerged from those who believed that logic could rescue philosophy, that it could become a tool which would help philosophers free themselves from deadlock. Many successes of applications of logic proved that analytic philosophy was solidly grounded in formal methods. However, analytical philosophy does not rely only on formal methods. Firstly, it also makes

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use of elements taken from broadly understood informal logic, namely from the logical theory of language (or logical semiotics) and general methodology. Secondly, the necessary, irremovable presence of various kinds of intuition in philosophy is often also emphasized by analytic philosophers. 2. The title of the present volume refers to the tension between formal and informal elements in the ways of practicing analytical philosophy. It gives partial answers to the question of the scopes and limits of both kinds of methods and how they are connected in philosophical investigations. The opposition of formality-​informality and the characteristics of both arguments of this opposition is not the only one discussed in this volume. Another problem concerns the status of philosophical methods. Are they unique or are they just identical to the methods of other sciences? And if so, are the methods applied in formal and natural sciences sufficient in philosophy or does it need a kind of reflection, as applied in the social sciences and humanities? Finally, in connection with the essential role of historical research in philosophy, what are the methods of the history of philosophy? That is why this volume is composed of four parts entitled: “Philosophy from the Methodological Point of view”, “Historical Research and Its methods”, “On Formal Methods in Philosophy” and “On Informal Methods in Philosophy”. 3. Part one deals with some general problems of metaphilosophy. The opening study by Mieszko Tałasiewicz, “Metareflection. A Method for Philosophy,” presents an approach to the old question of conceptual analysis, which, according to him, usually contains some constructive elements. Tałasiewicz’s hypothesis is that philosophical investigations are based on the interrelations between two kinds or concepts: psychological and logical. The author also discusses the cognitive tools necessary to prosecute this kind of analysis. The most important skill here is the ability of metareflection, namely the ability to consciously reflect on the results of introspection. Jacek Jadacki’s study, entitled “Semi-​Formal Analysis of the Formality-​ Informality Opposition in the Spirit of the Lvov-​Warsaw School,” explores the concepts of formality and informality. The author states that it is not possible to draw a strict line between formal and informal theories and languages: a given logical theory is not simply formal or informal but is more or less formal in comparison to another. Jadacki also discussed the aims and tasks of so-​called informal logic as opposed and complementary to formal logic. The last study of the first part, “Analysis –​Paraphfase –​Axiomatization. Philosophical Methods in the Lvov-​Warsaw School,” co-​authored by Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski, sketches three methods of analytic philosophy as they were practiced in the Lvov-​Warsaw School, being one of the main trends of 20th-​century

Introduction

3

analytic philosophy. The methods are:  analysis of concepts, semantic paraphrases of statements and axiomatization of theories. The authors reconstruct the assumptions, successive steps and conceptual tools of these procedures. A general analysis of the concept of method is also provided. 4. The second part of the volume deals with some problems of the history of philosophy and the methods involved in it. The study “From Methodenstreit to the “Science Wars”  –​An Overview on Methodological Disputes between the Natural, Social, and Cultural Sciences” by Friedrich Stadler recounts the history of the debates between different visions of sciences from the methodological point of view. The debate is generally concentrated on the question of whether there is one method (or one set of methods) applied in all sciences or whether there are various methods (or set of methods), depending on the areas of reality examined, or kinds of knowledge achieved, the assumptions accepted etc. The author indicates the Methodenstreit in economics as the first occurrence of the debate and discusses various variants of the controversy, the newest being the “science wars” in the philosophy of science. One of the problems of historical research is the periodization of history and its criteria. The study by Krzysztof Brzechczyn, “Periodization as a Disguised Conceptualization of Historical Development. A Case Study of a Theory of the Historical Process Developed in the Poznań School of Methodology,” reconstructs the tools of periodization proposed in the so-​called idealizational-​ adaptive reconstruction of historical materialism. This paper reflects the point of view of a group of methodologists centered around Leszek Nowak –​a philosopher who, starting in the 1970s, put a lot of effort into the reformulation of generalized materialistic historiosophy in the spirit of analytic philosophy. The main idea of this approach –​as applied to philosophical historiosophy –​is, as we can imagine, that the phases of philosophy are determined by changing economic conditions in such a way that the systems of philosophical ideas are dominant in those phases that ensure the highest stability of the cultural superstructure coupled with these conditions. The study “Władysław Tatarkiewicz. Metaphilosophical notes” by Ryszard Kleszcz presents the methodological views of Władysław Tatarkiewicz  –​a leading Polish historian of philosophy and aesthetics. Tatarkiewicz’s minimalist, analytic position is characterized, his attitude towards the role of logic in philosophy is reconstructed, and the problem of the division of sciences and its criteria is recalled. Kleszcz also discusses Tatarkiewicz’s view on the methodological status of philosophy: according to him, philosophy may be called “a science” only if we understand “science” broadly enough. The last study in this part, “Casimir Lewy and the Lvov-​Warsaw School,” by Tadeusz Szubka, is a certain historical case study. It concerns the personality

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of Casimir (also:  Kazimierz) Lewy, a Polish born British scholar. The author analyzes the Lvov-​Warsaw School’s influences on Lewy who was a student of Tadeusz Kotarbiński and points to the fact that the first did not accept the ontological positions of the latter. Szubka presentes also Lewy’s methodological position, including his ambivalent attitude towards formal methods and his conception of analysis. 5. The next two parts of the volume are devoted to applications of, respectively, formal and informal methods in philosophy. Part three is opened with the study of Srećko Kovač, “Remarks on the Origin and Foundations of Formalization.” In the first part of the paper, Kovač characterizes the origin and the structure of the formal system. He points to the fact that in formalism, logical forms and abstract concepts are projected and represented as perceptive signs which may be operated on. Also, the definition of formal system as a Turing machine is discussed. In the second part of the paper, the author expresses the conviction that the probative procedures in formal systems, being sequences of mechanical transformations, can be treated as deterministic series –​and thus these procedures fall under the general characteristics of deterministic structures. This conviction is confirmed by a detailed analysis of Jan Łukasiewicz’s three-​valued logic system, Ł3, which otherwise grew out of the discussions concerning determinism-​indeterminism and necessity-​contingency. The second –​after logic –​paradigmatic example of a formal system is mathematics. Krzysztof Wójtowicz in the study “The Status of Mathematical Proofs and the Enhanced Indispensability Argument,” performs a philosophical analysis of informal and formal probative procedures as possible explanatory procedures. This analysis decisively influences the answer to the questions of whether and in what sense one can speak of mathematical explanations of empirical phenomena, as studied in such sciences as physics or biology. In turn, the answer to this question is decisive for resolving the dispute over the realistic nature of mathematics itself. Returning to logic –​one of the non-​realistic approaches of its metaphysical status is to recognize the rules of inference as rules of a normative character. Unfortunately, the normativity of logic is generally characterized in terms of unspecified philosophical associations. In the article “A Case of Metalogical Explanation of Logical Normativity”, Kordula Świętorzecka tries to give the concept of normativity an operational sense. She relativizes it, in particular, to the norms of a given logical system –​in such a way that the system may be considered normative due to given norms (defining criteria of being valid or generally verifiable), when this system respects these norms.

Introduction

5

The study by Sébastien Richard, “Leśniewski’s Intuitive Formalism,” contains an analysis of the role of intuition in constructing formal systems. The author elaborates on Stanisław Leśniewski’s systems (Prototetics, Ontology, Mereology) which were constructed based on intuitions and –​in this sense –​not “purely formal.” Richard explicates various relations between intuitions and logic. Formal methods are often considered a rescue for philosophy. However, they have some limitations. Zuzana Rybařiková in the study “The Case of Logic: Łukasiewicz-​Prior’s Discussion on Logic,” shows that the shape of formal systems may be different depending on the philosophical intuitions of logicians. This is shown by an analysis of the similarities and differences between Jan Łukasiewicz and Arthur Prior. They were both adherents of the use of mathematical logic in philosophy but the first was a platonic and an extentionalist while the latter was a nominalist and a supporter of intentional logic. 6. The title of the study initiating the fourth part is “The Semiotic Method in Art Theory and Eesthetics in the Lvov-​Warsaw School,” authored by Aleksandra Horecka. She sketches out the semiotic approach to the analysis of art and its history. This approach makes use of the conceptual scheme of semiotics and thus is called the “semiotic method.” Horecka mentions Władysław Witwicki, Stanisław Ossowski, and Mieczysław Wallis as philosophers that used the semiotic method in aesthetic investigations. Kazimierz Twarowski is indicated as the founder of this approach. Marcin Będkowski, in the study “From Concepts and Contents to Connotations. Łukasiewicz’s Theory of Conceptual Analysis and Its Further Evolution,” reconstructs Jan Łukasiewicz’s method of conceptual analysis, stating that it is the second (after the Moorean one) early conception of analysis that appeared in analytic philosophy. The study presents the background of Łukasiewicz’s conception, its advantages and disadvantages, as well as future developments. In the study, “Kotarbiński’s Methodological Reism: Framework and Inspirations,” Alicja Chybińska reconstructs and discusses the methodological aspect of Tadeusz Kotarbiński’s reism. Reism thus understood is a postulate to use concrete names whenever possible in order to make our statements clear. The author indicates the source of Kotarbiński’s conception in his teacher’s, Kazimierz Twardowski’s, thought. Similarly to Twardowski, Kotarbiński accepted and consequently realized the postulate of precision and looked for tools to realize it. Contrary to Twardowski, Kotarbiński had simple ontological assumptions and postulated simplified language as well. The closing study, “Interdisciplinarity. Analysis of the Concept and Some Exemplifications in the Lvov-​Warsaw School” by Anna Brożek, starts with an analysis of the concept of interdisciplinary research. Some essential senses

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of the term “interdisciplinary” are described. In the first of the essential senses, interdisciplinary research takes place when two disciplines with the same material object and different formal objects interact. In the second essential sense, interdisciplinarity occurs when formal objects are the same while material objects are distant. Some methodological problems, like the need for a special language and for integrating theses, are discussed. Kazimierz Twardowski’s philosophy is given as an example of interdisciplinary research in philosophy. 7. The studies that make up this volume are connected  –​apart from the fact that they belong to philosophical methodology as broadly understood –​by three links. Firstly, all the studies published here not only refer to the methods used in analytical philosophy, but are also exemplifications of the analytical method –​ in either the more or less formal version. Thanks to this, this volume will find recipients both among “informalists” and “formalists”. Secondly, the authors of almost all these studies refer to the tradition of Polish analytical philosophy, and especially to the Lvov-​Warsaw School. However, they do this in different ways. Some simply reconstruct the methodological standpoint prevailing in the School as a whole (cf. (1c)); others analyze the positions of individual representatives of the School: Łukasiewicz (cf. Będkowski, Rybařikova), Leśniewski (cf. Richard), Kotarbiński (cf. Chybińska), Wallis (cf. Horecka) and Tatarkiewicz (cf. Kleszcz). Almost everyone reports, more or less extensively, the views of the first generation of the School –​or at least the views of students of representatives of this generation, e.g., Lewy’s views, who was Kotarbiński’s student (cf. Szubka), or the views of Nowak, who was Janina Kotarbińska’s student (cf. Brzechczyn); some also declare in their texts an acceptance of these views, or indicate in the title their general affinity with the ideas of the School (cf. Będkowski et al., Brożek, Jadacki). Thirdly, the majority of the authors of the presented volume are genetically connected with the Lvov-​Warsaw School, namely being indirect students and followers of members of the first generations of this formation. Thus, making an allusion to the title of the book, The Lvov-​Warsaw School. The New Generation (Rodopi 2006), edited by Jacek Jadacki and Jacek Paśniczek, one may say they belong to the newest generation of the School. This volume was prepared within the project “Philosophy from the Methodological Point of View” (2015/​18/​E/​HS1/​00487), financed by the National Science Center (Poland).

pa rt 1 Philosophy from the Methodological Point of View

∵

­c hapter 1

Metareflection: a Method for Philosophy Mieszko Tałasiewicz Abstract This paper presents a method of philosophical investigation rooted in the interrelations between psychological concepts and logical concepts. The proposed account describes philosophical method as a first-​person introspective analysis of psychological concepts and a further synthesis of logical concepts on the grounds of the content of psychological concepts, guided by various theoretical objectives. What is needed for the use of this method, as its cognitive prerequisite, is first-​person access to the content of concepts in both senses, which takes the form of a multi-​level hierarchy of rational metareflection. The notions of philosophical intuition and thought experiment are discussed within the proposed framework. So is experimental philosophy.

Keywords analysis  –​experimental philosophy  –​metareflection  –​philosophical method  –​ ­philosophical intuition –​thought experiment

1 Introduction1 The rapid development of experimental philosophy in recent years has not resulted in unquestionable breakthroughs in philosophy. What it certainly has done though, and for which the researchers involved in the experimental movement must take full credit, is to reinvigorate the metaphilosophical debate on the closer identification of the methods and sources of philosophical cognition.

1 This paper elaborates further some ideas originally presented in an article published in Polish as “Skąd się bierze filozofia? O analizie pojęć, intuicji i eksperymentach filozoficznych” [What Is the Origin of Philosophy? On Conceptual Analysis, Intuition and Philosophical Experiments] (forthcoming).

10 Tałasiewicz There is broad agreement that conceptual analysis is a method of philosophical cognition while the cognitive ability which provides relevant data and thus makes the use of this method possible is what is known as philosophical intuition, which can be stimulated through thought experiments. In the bulk of philosophical discourse inspired by experimental philosophy today, conceptual analysis is taken to be the analysis of the meanings of words in a given ethnic language (mainly English), while philosophical intuition is practically tantamount to linguistic competence, which helps capture such meanings.2 The difference between a philosopher and someone without a philosopher’s tool kit lies, if at all, in that the former, thanks to rigorous professional training (involving the ability to conduct thought experiments) can deploy this linguistic competence explicitly, whereas, with non-​philosophers, linguistic competence resides in some latent state and manifests itself in the ability to adopt certain linguistic behaviours rather than formulating clear content relationships.3 The supposition that something of this kind is at the heart of philosophy stems from the popular practice, dating back to Socrates, of citing what supposedly “everyone has accepted,” what they “would all agree with,” or what “most people would say.” If we award such methods of argumentation the status of empirical hypotheses with regard to common linguistic intuitions, it follows readily that so called experimental philosophy is not only a legitimate but also the most efficient form of practicing philosophy. If philosophy was an argumentation method built on the common meaning of common terms, and the oft-​cited “conceptual analysis” was the science of reporting the actual meanings in the language spoken by a given community, then the traditional methods harnessed for its needs might have heuristic benefits at most. Getting to true, evidence-​supported knowledge would call for empirical studies into how concepts are in fact used by competent speakers of a language. It would call for checking the extent to which the heuristic intuition of one philosopher or another correctly reflects “what everybody would agree with” or “what everybody would say.” This naturally would lead to revisionist tendencies, which are typical in experimental studies. It often appears that the actual experiments do not confirm prior assumptions as to the common agreement on this or that question. The result is that professional philosophers’ intuitions sound seriously suspect. Armchair philosophy begins to look not like a path to conceptual knowledge but one that meanders to a 2 This view is shared by experimental philosophers and their critics alike: “It is our shared, ordinary concepts that we talk about when we do conceptual analysis” (Kauppinen 2006, 96). See also (Ludwig 2007), (Cappelen 2012). 3 The role of the philosopher as proposed in (Gopnik and Schwitzgebel 1998, 79).

Metareflection: A Method for Philosophy

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dead end. Experimental philosophers therefore seek to trim away from natural conceptual intuitions any accretions caused by philosophical training by examining the linguistic competence of the ordinary speakers of a given language –​people who have not undergone rigorous philosophical training.4 Such an understanding of the role of philosophy in general, including the role of experimental philosophy, is false however, whether it be the final picture of philosophy it paints or the motivation that has given rise to it. Philosophy, simply put, is not about what people think, explicitly or implicitly, about the meaning of one word or another in their language. Nor is philosophy about what the meanings of particular words in a particular language actually are. Two and a half thousand years of the evolution of philosophy stand in stark contrast to the view of philosophy described above. This concept simply does not fit our understanding of what we call “philosophy.” We can hazard a claim, somewhat paradoxically, that it is a view which is empirically highly inadequate.5 What philosophers do does not boil down to analysing concepts understood in this way, or using their linguistic competence in the manner described. The practice of invoking what “everyone [supposedly] agrees with” does not have to and should not in itself be interpreted as an empirical hypothesis on the wide-​spread acceptance of a particular view or semantic intuition. As Joanna Komorowska-​Mach aptly puts it: The intuitions invoked by Plato, Gettier or Putnam are neither empirical hypotheses nor a smokescreen designed to conceal weaknesses in argumentation. Invoking them is rather an attempt to guess at, propose or nail down a point at which the intuitions of the author can be squared with those of the reader –​a point where further explanation appears to be unnecessary. It is an attempt whose failure does not result in rejecting the argument but which compels the author to produce additional ­explanations.6 komorowska-​m ach 2013, 163

4 The studies carried out by Edouard Machery and his colleagues on the intuitions about proper names were of this nature. See in particular (Machery et al. 2004). Volumes have been written in that spirit. Some recent examples, commendable for their methodological rigour, include (Ziółkowski 2016, 2017). A critical account of experimental philosophers’ claims can be found in (Deutsch 2015). 5 Some empirical research showing that major philosophical works do not conform to this picture has been done by Herman Cappelen in (Cappelen 2012). 6 The dialectical role of “intuitively” as the outset of an inquiry is noted also in (Cappelen 2012, 11).

12 Tałasiewicz Since no explanation can go on ad infinitum, all philosophical arguments must start at some point –​a point which is, in a sense, arbitrary. Socratic practice is no more than a way of signalling such a point. It provides no hints as to what kind of assumption the starting point must be.7 If the picture of philosophy sketched above is wrong, the question arises: What picture would be right? What is the nature of philosophical cognition? How does it work? What cognitive abilities does it engage? What makes it credible? Should we try to pin down the superficial claim about conceptual analysis and philosophical intuition in a different way than that proposed by experimental philosophers, we would get caught in a web of misunderstandings. Intuitions tend to be defined in contradictory terms (Edward J. Wisniewski maintains that “intuition is fundamentally a conscious enterprise” (Wisniewski 1998, 45) while Alison Gopnik and Eric Schwitzgebel would “call any judgment […] an intuition, just in case that judgment is not made on the basis of some kind of explicit reasoning process that a person can consciously observe” (Gopnik and Schwitzgebel 1998, 77), or are not defined at all (the “no-​theory theory of intuitions” in (Deutsch, 2015)). Some researchers attempt to bring some order into this chaos and classify the different uses of the term “intuition” (Cappelen 2012, Jenkins 2014). Others take a strong dislike to the term altogether: Philosophers might be better off not using the word “intuition” and its cognates. Their main current function is not to answer questions about the nature of the evidence on offer but to fudge them, by appearing to provide answers without really doing so. williamson 2007, 220

In this paper, I am not resorting to any more definitions of these terms at the starting point. Instead, I shall have a stab at a phenomenological description of a way in which one can practice philosophy. I don’t claim that it is the only worthwhile method of practicing philosophy but certainly it is one in which philosophy has not infrequently been practiced with quite spectacular results. In particular, I seek to present some philosophical methods and the cognitive

7 According to Max Deutsch, such assumptions can take on a different character, depending on the particular case:  “[I]‌n philosophy, nothing unifies the claims that get taken for granted […]. Philosophical starting points –​the un-​argued-​for premises in a philosophical argument –​need have no special phenomenological or epistemological features […]. Given this extreme heterogeneity, it would be strange to ascribe a special, evidential function to philosophical starting points, beyond the fact that they are argumentative starting points” (Deutsch 2015, 124).

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abilities which the former rely on, and to evaluate the credibility of their results. If, in the end, the reader accepts the use of such phrases as “conceptual analysis,” “thought experiment” or “philosophical intuition” within this description, we will have arrived at some sort of definition of these traditional terms at the endpoint of the process. The main aim of the paper though is an answer to the underlying question about the sources of philosophical cognition rather than resolving the problems of terminology. 2

Conceptual Analysis or Conceptual Synthesis?

Philosophy provides us with conceptual knowledge. This does not mean though that philosophy equals to a knowledge of concepts, at any rate, not only of concepts. Philosophy can consist in a knowledge of concepts in so far as concepts are an interesting element of reality being studied by the philosopher. Philosophers examine the nature of good and evil, necessity and possibility, rationality, knowledge, justification, consciousness and free will; they can also examine the nature of concepts. Philosophers of language or philosophers of mind examine the nature of concepts quite often. Be that as it may, knowledge of concepts is not a marked off kind of philosophy tout court. The concept of a concept is key to metaphilosophy, though. The concept of a concept covers two different categories of entities: concepts in the psychological sense and concepts in the logical sense. From the psychological perspective, concepts are subjective mental entities which encode information we have acquired, which comes from both external stimuli (of which we are not always conscious) and from advanced integrating processes (including automatic processes of which we are not always conscious). Thanks to external information, conceptual knowledge can thus be knowledge about external objects. This is why it is possible that, in the words of Hilary Kornblith, “by looking inward, I answer a question about an external phenomenon” (Kornblith 1998, 135). Concepts understood logically are the objective properties of objects and relations between objects, capable of playing the role of logical senses. Frege urged that on no account should we identify the former category with the latter. And indeed, we shouldn’t. Different as they are though, they are related with one another in certain ways. Tadeusz Czeżowski sums up this relationship as follows: The act of thinking is unrepeatable […]; the content, on the other hand, may be […] repeated successively in invoked presentations and may be the same in the presentations of different subjects. The content[s]‌[are]

14 Tałasiewicz evoked as results of psychic actions as [their] product[s] […][however] we may separate these contents from subjective and inner experience […][and] de-​subjectivize, externalize and preserve them in the expressions of language or in other signs. czeżowski 2000, 30–​31

It could be argued then that concepts understood psychologically are the source of content for concepts in the logical sense. Since the two categories are interrelated, they shed some light on each other. In the past, logical concepts were practically the only path leading to psychological concepts. The result was –​as we now know –​a fairly naïve form of psychology. Today, thanks to developments in cognitive science, we know a lot about concepts in the psychological sense, about their formation mechanisms, their innate components, and what makes them credible in general. But, to an extent not greater than in the past, however, today’s state of knowledge of psychology can be a path to concepts in the logical sense. This would make a philosophy just as naïve as the psychology of the past. As it happens, philosophy, or at least the philosophical variety I  seek to explicate here8, is the discipline which is rooted in this interrelatedness and prompts the transition from private concepts to logical senses. This transition –​a transition from the order of cause and effect to the order of reason and consequence  –​could be referred to, perhaps overstating the case a bit, as a transition from what we “know” as animals to what we know as rational subjects (could the pineal gland be involved in this perhaps?). The method of philosophy understood this way could be called conceptual analysis, but such use of this term would convey a completely different sense than is customary in the majority of today’s philosophical discourse. The method involves grasping the content of psychological cognitive concepts in order to extract from 8 This understanding of philosophy is typical, in particular, of philosophers endorsing Franz Brentano’s philosophical legacy. More specifically, it was championed by philosophers from the circle of Kazimierz Twardowski, who studied under Brentano (Twardowski 1977). Some similarities to the approach discussed here can also be traced to phenomenology pioneered by another of Brentano’s students and a colleague and correspondent of Twardowski –​Edmund Husserl (see in particular (Husserl 1973)). A detailed account of the development of the notion of conceptual analysis in Twardowski’s Lvov-​Warsaw School is given by Anna Brożek (Brożek 2019). The key element, common to both traditions, appears to be the distinction between the state of mind as a mental entity (subject potentially to empirical examination from a third-​person perspective) and its introspectively accessible content. Incidentally, this state/​content distinction is widely held beyond these traditions, too. It is heavily exploited for instance in (Deutsch 2015, 35–​39).

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them the (representations of) properties and relations inherent in the objects being studied, followed by the grouping of such properties and relations into appropriate sets, which ultimately make it possible to systematize the information we have gathered. Conceptual analysis is thus an analysis of concepts in the psychological sense, but it is a synthesis of concepts in the logical sense.9 The philosopher’s task is to construe concepts as senses, not to analyse them. The concepts thus do not have to be connected with meanings of words in natural languages. Often, their synthesis involves having to introduce new technical terms or attaching a new technical sense to previous everyday expressions. The criterion of success is rather compound. It is not just a good correspondence between the source psychological concepts and the resulting logical concepts.10 It is also important that the new concepts (in the logical sense) be more ordered and more capable of further development by the intellect than could be achieved by examining the word meanings in natural languages. Further development involves various theory-​making processes, based on sophisticated argumentation, which are designed to structure a conceptual framework and formulate new material theorems.11 The so called reflective equilibrium method, as described in (DePaul 1998), consisting in making one’s beliefs, concepts and theories coherent, might be regarded as a partial account of this stage of conceptual analysis. An important role among these processes is reserved for giving certain descriptions the status of definition and for establishing logical relationships between concepts in all those places where we discern material relationships between the referents of these concepts. In the process, a part of our knowledge acquires the status of analytical truths, which does not conflict with the fact that the primary source of this knowledge is experience gained in the course 9

10

11

Jan Łukasiewicz’s reference to this constructive component of conceptual analysis in his “Analiza i konstrukcja pojęcia przyczyny” [Analysis and Construction of the Concept of Cause] (Łukasiewicz 1906) is a rare example in the literature of attention given to the problem. An exemplary account of how to establish any kind of correspondence between subjective experiences and objective properties is given in (Searle 2015), esp. on pages 100–​ 134. I will refer to this work extensively further in this paper, where a certain amount of relevant terminology is introduced; let me include just one quotation here, for the air of the enterprise: “The non-​intentional characterization of the visual experience is simply that it has [a certain] sort of qualitative character. That qualitative character fixes red as the conditions of satisfaction because (in part) the essence of redness is the ability to cause experiences that have this character, and any perceptual experience is experienced as having its cause as its object” (Searle 2015, 124). The role of argumentation in philosophy is given the attention it deserves by, in particular, Max Deutsch (Deutsch 2015), where numerous examples are to be found.

16 Tałasiewicz of our cognitive development. Truths that have attained this status are apodeictic, but the process itself is not. Rather it is a result of a tentative conceptual ordering, which can be and often is criticized, improved or changed completely under the pressure of the view that it is not as good as expected in clarifying the given set of facts and conditions and preparing the ground for further theory-​making processes. Consequently, the fundamental opposition of a priori and a posteriori becomes hardly possible, as many philosophers, from Quine to Williamson aptly observed.12 3

Introspection and Metareflection

Let us consider now what cognitive abilities would be needed for the conceptual analysis just described. Most definitely, we need to be able to consciously apprehend and process the components of primary conceptual knowledge (in the psychological sense). As Richard Fumerton said: Indeed, if we couldn’t rely on a relatively unproblematic access to mind of a sort that we have been presupposing for thousands of years, it’s hard to see how we could even get started in the study of the mind that ­interests us. fumerton 2007, 59

Let us call it the elementary introspection ability (EI). The primary observation whereby object P has some property W can be isolated and compared with others, noting that object Q also has property W, while object S doesn’t. This way, our mind can recognize the relation of similarity between P and Q with respect to W by way of introspection (just as much can be said about the relation of difference between P and Q on the one hand and S on the other). However, the statement that these are relations of similarity and difference between extraneous objects rather than between states of mind still holds. EI does not involve a comparison between the states of mind which constitute our knowledge as such but rather, a comparison of the content of these states –​a comparison of the situations represented in these states. In order to be able to use conceptual analysis in the sense introduced above, we must also be able to represent logical relations, including entailment. 12

Sed contra (Ludwig 2007).

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Discussion of all determinants of logical competence calls for a separate elaboration, but it will suffice to say at this point that this competence relies at least on the ability to compare the truth-​conditions of logical propositions. Such an ability is at any rate used explicitly in the teaching of logic.13 This runs counter to George Bealer’s view that the sources of logical knowledge are seemings –​ irreducible rational intuitions that certain sentences are logically true (Bealer 1998). It does fit though with Williamson’s view that logical truths are not derived from the understanding of the meanings of the words involved.14 The correct mechanism is rather an introspective perception and comparison of representations of certain objective relations between situations which determine the truth conditions of the propositions expressed. Elementary introspection is not all, though. More advanced procedures employed by conceptual analysis require further resources, in particular, the ability to reflect, consciously, on the results of the operation of elementary introspection. Let us call this ability Refined Metareflection (RM), and have a closer look at it. Refined metareflection is a conscious apprehension of the content of cognitive states and the states themselves, the procedures employed to organize and modify content, and of the rules of evaluation of these procedures etc., the sum total of which makes a multilevel structure. In order to explain this 13

14

In a typical course e.g. logical validity would be defined thus: A logically valid formula of predicate calculus is any and only such an expression of this calculus which is true in every model. Thus, the formula: ∀xP(x) → ~∃x~P(x) is logically valid because it is not the case that there is a kind of object and a property pertaining to object of this kind such that it is true that every object has the stated property, and false that there is no object that does not have the stated property. Similarly, the formula: ∃x∀yR(x,y) → ∀y∃xR(x,y) is logically valid because it is not the case that there is a kind of object and a relation holding between object of this kind such that it is true that there is an object standing in this relation to every object, and false that for every object there is an object standing in this relation to the former. However, the formula: ∀x[P(x) ∨ Q(x)] → (∀xP(x) ∨ ∀xQ(x)), is not logically valid because there is such a kind of object and two such properties pertaining to object of this kind that it is true to say that each object has either the first or the second property and false to say that each object has the first or each has the second property. An example of this kind of object is the set of natural numbers, of which every number is either even or odd, while it is not true that every natural number is even or every natural number is odd. Williamson gives an example of some Peter who might not assent to a sentence “Every vixen is a vixen,” although he knows English perfectly well and fully understands this sentence –​just because this Peter nourishes a kind of weird combination of logico-​empirical views. Namely Peter takes universal quantification to be existentially committing and –​ simultaneously –​he believes in a conspiracy theory that there are no foxes, and consequently no vixens (Williamson 2007, 86–​87).

18 Tałasiewicz metareflective hierarchy, it would be best to refer to some conception of intentional states sufficiently complex to show clearly the relevant distinctions. In this paper, I shall focus on the conception of John Searle (Searle 1983, 2015).15 According to this conception, an intentional state is a state of mind that can be satisfied as well as not. Besides other components, its structure incorporates content which is made up of the conditions of satisfaction of this state. An important part of this content can be an explicit link between this state and other states, which together make the so-​called Network. 16 Besides the content, an intentional state can also have its object, which is the actual fulfilment of the conditions of satisfaction. This is a classic Husserlian distinction between an intentional state, its content, and its object. The object is distinct from the intentional state it is the object of and from the content of this state, and can be an entity or a state of affairs,17 extraneous to the subject or not, which must exist or hold in order for the intentional state to be satisfied. In particular, the object of one intentional state can be another intentional state at which the former is directed, and, more importantly, the object of one intentional state can be the content of another intentional state. (Objectless intentional states are also possible –​the essence of intentionality is the existence of content, not an object.18) An important component of the content of states of perception can be the condition that these states be caused by external objects of perception. To Searle, this means that intentionality can rely on certain forms of self-​ reference (the conditions of satisfaction of a state refer to, among other things, 15

16

17

18

Invoking Searle’s conception at this point is by way of illustration only –​another conception of intentional states that has been given sufficient refinement would do just as well. The key thing is that the adopted conception accounts for an introspective insight into the content of the mental states of the subject rather than for merely experiencing of such states. Apart from that, intentional states, being mental particulars, are bound together by a web of causal relationships which, if not part of the content, need not be experienced consciously. Empirical psychology rather than introspection might perhaps tell us more about such ties. For some parts of the theory of intentionality an important distinction would be: whether the objects of intentional states are something we can state or rather refer to. This gives rise to the problems of reference/​predication distinction, nominal/​propositional intentionality and so on. See e.g. (Searle 1983, 6–​11), Husserl 2001, vol. 2, 152–​158). In the present paper I will treat these cases jointly, though. Cf. (Husserl 2001, vol. 2, 98–​99), (Searle 1983, 17). The earlier views, whether those of Brentano or Twardowski (Twardowski 1977), postulating purely intentional objects (respectively, rejecting objectless acts) do not accord with Searle’s, Husserl’s or my own beliefs that, if the intentional object does not exist in the real world, then it does not exist at all.

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the state in question), and on the fact that certain forms of causation –​Searle calls them intentional causation –​are perceived directly: the fact that something is a cause/​effect of something else can be a primary empirical input.19 Another component of the intentional system as proposed by Searle is the so-​called Background. The Background is a system of involuntary, automatic cognitive mechanisms which, without our conscious interference, organize raw empirical data to the extent that they can become the object of rational reflection. A number of such innate mechanisms have been postulated by theorists in developmental psychology and cognitive linguistics (Carey 2011; Clark 2003). Let us highlight one particularly relevant here. Williamson calls our attention to a procedure which employs counterfactual reasoning to derive results or consequences from the given set of data (“on-​ line” if experienced, “off-​line” if imagined) on the basis of accepted relationships (causal or logical). In particular, according to Williamson, philosophical reasoning about metaphysical modalities is a special type of counterfactual reasoning: A is necessary if a counterfactual development of non-​A entails a contradiction (Williamson 2007). This procedure requires a whole range of cognitive resources (expectation-​forming capacities, propensities to form expectations) operating, typically, on the basis of what we perceive and enabling us to anticipate a further course of events. An example of such a mechanism is a mechanism which allows us to predict the trajectory of a falling stone (whose primary purpose is to help us avoid danger). The first stage of using such automatic mechanisms in rational reflection –​as we are told by Williamson –​is to trigger these mechanisms “off-​line”, without access to the data of actual experience. Within Searle’s framework, this would mean that, informed by the metareflection of a higher order, we would purposely substitute the imagined data for perceived data as the primary inputs for these expectation-​forming capacities. “Off-​line” operation of this mechanism, which at this stage is still part of the involuntary Background, is the basis for asserting counterfactual sentences of the kind: “If the bush had not been there, the rock would have ended in the lake” (Williamson 2007, 142).

19

I don’t mean to say that causation is a “perceptual primitive” in that sense in which perceptual primitives oppose internal mechanisms. Indeed, in my view, Searle’s position accords with that of Susan Carey whereby the concept of causation cannot be reached but with the aid of some innate mechanism of core cognition (Carey 2011). Searle just conceptualizes these mechanisms as the forms or structures (plausibly innate) of certain intentional states. What is important is that both for Carey and Searle causality need not be inferred through some logical reasoning but can be given as a cognitive primitive (a product of interaction of our internal cognitive apparatus with some external stimuli).

20 Tałasiewicz It is not, of course, a source of infallible knowledge, but it is not useless. Its reliability derives from the reliability of the automatic mechanism itself, which is calibrated in numerous “on-​line” situations, where experience verifies its operation directly. The second stage of rational emancipation of counterfactual reasoning involves replacing involuntary mechanisms with explicit knowledge about law-​ like relations (causal or logical) which allows us to derive counterfactually the consequences from imagined inputs in a fully conscious manner.20 As is well known, such reasoning requires at the outset law-​like, and in particular, causal grounds for deriving consequences from counterfactual antecedents.21 In order to avoid being caught up in a vicious circle, we must not derive these grounds from our counterfactual reasoning, we have to obtain them independently. As an input in direct experience, intentional causation is a rich source of such independent grounds for further counterfactual reasoning. 4

Philosophical Intuition: First-​Person Perspective and Autonomy of Philosophy

The cognitive procedures just discussed and the attendant abilities are commonly relied on by all branches of science, not only by philosophy.22 This has led some theorists, for example Williamson, to claim that philosophical cognition does not differ at all from scientific cognition and that it is in fact an overarching and highly-​specialised form of the latter.23 Although it may well 20 21

22 23

“Far from being sui generis, the capacity to handle modality is an »accidental« byproduct of the cognitive mechanisms that provide our capacity to handle counterfactual conditionals” (Williamson 2007, 162). This is because “counterfactual reasoning” and “causal reasoning” are interconnected (Williamson 2007, 141). The sentence “All butterflies are white,” when used with reference to a certain observed population, rendered simply as a general statement, does not allow us to make predictions about the colour of the next observed butterfly, while the same sentence rendered as a law/​rule permits us to accept the counterfactual sentence, “If another butterfly suddenly appeared, it would be white.” Generally, whenever we go beyond the co-​occurrence between two things or a simple correlation, we must be prepared to accept certain counterfactual conditional statements; or conversely: acceptance of counterfactual conditional statements requires that we invoke some generally accepted rules which go further than merely establish a simple correlation. See e.g., (Lewis 2001). Many examples are given in (Czeżowski 2000). “The common assumption of philosophical exceptionalism is false” (Williamson 2007, 30). Herman Cappelen would go further and even deny the internal coherence of philosophy: “The various activities that get classified together as »philosophy« today are so classified as the result of complex historical and institutional contingencies, not because

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be the case that philosophy does not require recourse to a completely new cognitive ability that is extrinsic to scientific cognition, there is a considerable difference in degree to which metareflection is used in philosophy and the level of metareflection that is achieved therein. This is not supposed to mean that philosophy achieves a higher level of methodological sophistication than the sciences (the opposite is more likely true). It means only that the introspective part of the inquiry is more heavily exploited in philosophy.24 It’s worth noting that, even in scientific cognition, the first-​person component is not entirely disregarded. As Richard Fumerton aptly puts it: “the fact is that we know the physical world through our five senses only as the potential cause of various sensations and connections between sensations” (Fumerton 2007, 63). However, “from a naturalistic perspective, there are substantial advantages to looking outward at the phenomena under investigation rather than inward at our intuitions about them” –​says Kornblith (Kornblith 1998, 136). If we take “naturalistic” in this quotation to mean “scientific” as opposed to “philosophical,” we will be able to see clearly the difference in perspective we are after. Every science starts with looking “inward” in order to later distance itself from this perspective and look outward, while philosophy stays focused on the fact that in the core of the matter every conscious and rationally controlled instance of

24

philosophy has an essence that ties it all together as a natural kind […] There is literally nothing interesting to be said in general about the common »evidential sources« of applied ethics, formal semantics, theories of perception, philosophy of quantum mechanics, etc.” (Cappelen 2012, 21). Although my attitude towards Cappelen’s book is generally very sympathetic, in this point I disagree. Well, some sorts of applied ethics, semantics or theory of perception perhaps just aren’t philosophy but rather economics or political sciences, linguistics or psychology. However, as long as these disciplines are subdisciplines of philosophy, they have something in common, something in their methodological core. This core I am trying to describe reaches even the philosophy of quantum mechanics, which –​in contrast to quantum mechanics per se –​is driven by the struggle to square the outcome of the mathematical apparatus of the physical theory with our reflective ways of thinking about the world (including our notions of objectivity, probability, causal connection, interaction, localization, simultaneity etc.). The ability to apply higher-​order metareflection may be correlated with so-​called higher-​ order intentionality –​a term used by cognitive psychologists for a constituent of the so-​ called theory of mind, which we rely on when we attribute thoughts to other people: “I believe that John thinks that Olga said that Tony was convinced that Sophie saw that Alice has a cat.” Empirical research shows that most people reach order five to six; above that level, the ability to reason in this way declines rapidly. Interestingly, this ability is not correlated with the level of intelligence (Dunbar 2004). If we were to postulate some special cognitive ability, available to the select few, and useful in practicing philosophy, then the ability to use metareflection of a higher order would claim this place, I think.

22 Tałasiewicz looking outward is de facto an instance of looking inward, at the content of our concepts, containing information about the outer world. The most important thing in affirming the autonomy of philosophy is that metareflection, heavily exploited in philosophy while being a rather subsidiary ability in scientific cognition, is the first-​person ability par excellence. This is the determining factor in why third-​person sciences such as experimental philosophy, linguistics or psychology (not to mention neurophysiology) are not capable of accomplishing the goals which philosophy sets for itself.25 Although psychology, or broadly speaking, cognitive science, can study, from an external perspective as it were, the nature of the ability that we have called metareflection, as well as the mental states which are the carrier of our knowledge, in terms of their causal connections, it cannot replace first-​person metareflection in seeking to understand the content of our beliefs and in processing them.26 This does not mean however that philosophy departs radically from the requirements of scientific rationality. The methodological criticism that can be raised against first-​person introspective cognition revolves around the recognition that mental states are “private” and, as such, inaccessible to anyone except the subject of those states. Allegedly, this rules out the ability to communicate such states to others and calibrate any beliefs their owners may have about those states. In line with this criticism, introspective knowledge has the appearance of being absolutely certain, and if in fact it is faulty, there is no hope of ever correcting or improving it. Such criticism does not apply to the proposed model of metareflection, though, because important features of this model build on the fact that not only the cognitive states themselves but also the intentional content of such 25

“We must ultimately return to the first person approach to achieve the goals we set ourselves in philosophy” (Ludwig 2007, 154). “It might be that the ultimate physical reality theorized in our speculation about the brain includes as constituents the very phenomenal properties that are the objects of introspection” (Fumerton 2007, 63). Another barrier for the sciences, apart from their third-​person perspective, is the normative character of some key concepts in philosophy, which frequently manifests itself in numerous disputes about the naturalisation of such-​and-​such areas of philosophy (see, e.g., Kim 1988). This aspect, which is otherwise very important in order to reflect the full spectrum of philosophical inquiry, has been left out of account here. 26 Admittedly, the reverse relationship between philosophy and the sciences is not extremely fruitful either. Philosophy is not entirely useless in science, for as Gopnik and Schwitzgebel point out: “philosophically-​informed intuition can contribute to [for example] empirical psychology” (Gopnik and Schwitzgebel 1998, 78). This contribution is however rather limited. It is not the job of philosophy to support empirical research, let alone replace it. As a rule, philosophy answers other cognitive needs than empirical sciences.

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states can be the subject of further reflection. The privacy and uniqueness of cognitive states does not entail the privacy and uniqueness of the content of these states. If two people are looking at the same thing, their states of perception are different, while the intentional content of these states is, or can be, identical or at least systematically similar. Having grasped such content in metareflection (as intentional object of meta-​states), viewers can express them through concepts in the logical sense and this way “exchange their experiences,” even if it is only a small part of their overall experience. This experience is not served on a platter. Philosophical methods must be very rigorous. Just as physical experience will be more meaningful to someone who has the relevant theoretical background to understand and interpret it, so will metareflection be more useful to someone who, thanks to their professional knowledge and relevant training, will be in a better position to separate what is important from what is unimportant, register a relatively large part of their states and discern interesting relations in them.27 The philosopher is interested in a perspective that guarantees the best possible knowledge, including philosophical knowledge (but not exclusively): the better trained the philosopher is, the bigger part of this knowledge is represented in his cognitive states and the more he is aware of factors that interfere with sound judgment; the philosopher’s task meanwhile is to concentrate his efforts on identifying and mentally removing any such interference (see, e.g., Ludwig 2007, 149). The “intuitions” of laymen and novices are, relatively, less reliable and less convincing for other philosophers (even if they are wide-​spread): We should not regard philosophical training as an illegitimate contamination of the data, any more than training natural scientists […] is a ­contamination of their data.28 Williamson 2007, 191

27

28

In short, this training involves, among other things, potentially as close as possible integration of acquired knowledge with the system of former beliefs (“reflective equilibrium”), and secondly, clearing the paths for quick access to a relevant part of this knowledge (still another objective of philosophical training is mentioned at the end of this section). One of the more common senses of the term “philosophical intuition” used in the literature is precisely the ability to follow these paths (Sorensen 2014). This sense, taken literally, is quite trivial. The quick access procedure, in and of itself, can however be a source of metaphilosophical misunderstanding; in particular, the belief that things such as phenomenologically instant recognition of the truth of advanced mathematical or logical propositions are the instances of operation of some mysterious sui generis mental capacity such as “rational intuition” or “a priori intuition.” See also (Sorensen 2914).

24 Tałasiewicz In this regard, philosophical metareflection can successfully be compared to a scientific method:  it is a systematic, in-​depth, dispassionate and rational consideration of the key aspects of cognition, allowing for error and compelling the philosopher to subject her findings to the critical analyses of the others. The difference is that critical rigour is applied here to the first-​person ­perspective. We have thus come very close –​I believe –​to what lies behind the idea of philosophical intuition in its relevant sense:  intuition is taken to be First- ​ Person- ​ M ethodical- ​ Reflection- ​ O n-​ T he- ​ C ontents- ​ O f-​ A- ​ S ubject’s-​ Intentional-​States-​And-​Their-​Interrelations. Ergo it is made on the basis of explicit reasoning, in contrast with the notion of intuition adopted in (Gopnik and Schwitzgebel 1998, 77), is not spontaneous, contra (Goldman and Pust, 1998, 179), is an instance of introspection in the general sense, contra (Sosa 1998, 258). The result of the operation of intuition so understood is, in particular, our internal observations as to what the determinants and mechanisms are of a rational interpretation of the reality which we are trying to understand. For example, as early as the dawn of philosophy, a certain observation was conceptualised –​which we can replicate through our own introspection today –​whereby we hold beliefs in different ways, and, depending on the way in which we hold them, such beliefs are either more or less valuable. This gave rise to a distinction between doxa and episteme, and subsequent attempts were focused on defining those terms in such a way as to best capture the difference between the two, and explain why beliefs coming under the latter were more valuable than those coming under the former. Through these attempts, a variety of parameters of beliefs have been identified and studied: truth and probability, objective justification and subjective reassurance, and many more. The result was a development of the concept of knowledge and formulation of the classical theory of knowledge best summed up as justified true belief (jtb). This didn’t put a stop to further efforts in the area of belief evaluation because the jtb theory did not capture all the nuances which we can observe in our internal classification procedures regarding our beliefs. As Edmund Gettier (Gettier 1963) pointed out, and as was reaffirmed by many of his followers, the holding of justified true beliefs gives rise to further distinctions:  some beliefs are held with even higher rank and meet some additional condition than just truth and justification (for example, the condition that the truth of a belief must obtain in virtue of the facts constituting the justification). This problem has nothing to do with ascertaining, in a supposedly “intuitive” way, whether the linguistic concept of “knowledge” applies or does not apply to Gettier-​cases, contra (Bealer 1998,k 207). It is an open question as to the

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word “knowledge” can be used to refer only to this deeper/​better way of holding beliefs or whether it could be left with the traditional definition, which comprises both ways and is only subdivided further into (better and worse) kinds of knowledge. In the end, any such question will in fact come down to the use of terminology. If we are determined to answer it, we can try and find some arguments citing, for example, the economy principle for a conceptual framework or the consistency with how the term “knowledge” is applied in common usage. We can also simply ask people about their preferences as regards the use of the word “knowledge,”29 although this particular method would not enjoy special philosophical relevance, just as there isn’t much relevance in considering the everyday meaning of this word. From the philosophical perspective, the relevant point in Gettier’s work, which once introduced to the philosophical community was widely embraced, is that some of our beliefs can be ranked higher than only as true and justified. What we propose to do with this constatation is also philosophically important: how would we account for the difference that is perceived by all competent disputants? Perhaps we will say that this additional “depth” is in the justification of the belief being relevant to the truth of the belief, or in the truth of the belief being the source of the justification, and whatever else we do to further pin down the metaphor of source. Suggestions vary and are questioned in different ways. All are aimed, however, at making sense of Gettier’s unquestionable discovery30. There are further distinctions made in subsequent development of this topic, like accidental vs. non-​accidental truth which establishes the problem of epistemic luck or misfortune, or qualitative vs. numerical identity of truthmakers relevant to the truth of the beliefs, etc. I take the view that intuition understood in the way just described was a source of many other great philosophical achievements. Take for example the distinction between intentional and unintentional states in Brentano; the distinction between the act, content and subject of presentation in Twardowski; the differentiation between positing and non-​positing intentional acts or nominal and propositional semantic categories in Husserl, referring and ascriptive use in Strawson (syntactic distinction); referential and attributive use in Donnellan (semantic distinction) and more generally, singular and descriptive thoughts in a number of authors, beginning with Russell, through Kripke, up 29 30

Such surveys were actually carried out, as noted by (Deutsch 2015). “Gettier’s” here is meant rather loosely: the point of my claim is not that it was precisely Edmund Gettier and no one else who unquestionably made this discovery. The point is that the discovery of beliefs-​deeper-​than-​just-​justified & true (commonly but perhaps not unquestionably attributed to Gettier) is unquestionable (in the sense elicited above).

26 Tałasiewicz to recent works of François Recanati; distinction of referring and denoting in Evans (pragmatic distinction); distinction between illocution and perlocution in Searle; distinction between the context of utterance and the context of evaluation in Kaplan, distinction between “wordly facts” and “propositional facts” in situation semantics –​and many many others.31 All these discoveries can be conceptualised as observations made in the “empirical material” of observers’ metareflection; as results of their introspective experience of their own mechanisms for referring to reality (including their explanatory needs and their standards for concept comprehension and theoretical usefulness). It would be good to elaborate this point further, case by case –​but that would require a book, not a paper. Here I must constrain myself to giving just these hints of how we can conceptualize philosophical findings. Certainly, we have departed here a long way from the analysis of linguistic concepts. Conceptual work on experience understood in this way is of a synthetic rather than analytic kind. We seek to lock in our concepts what we have observed so that others could learn about it and compare it with their own inner experience. This work in theory-​building on the grounds of introspective observations can be very troublesome and lead to long-​lasting philosophical controversies32; yet the observations themselves seem relatively unproblematic, once made. The distinctions mentioned above, as such, are rarely questioned and the ability to see them, I daresay, is one of the major objectives of philosophical training.33 31

32 33

The above examples are taken mainly from the philosophy of language; but in all other fields of philosophy one can find analogous ones: the distinction between good and nice/​ pleasant/​sympathetic on one side and between good and profitable on the other  –​in ethics; the distinction between what we do intentionally and unintentionally, and what we don’t do at all but what is just the effect of the impact of our body as a link in a physical causal chain –​in the philosophy of action; the distinction between universals and tropes (Armstrong), or minimal and non-​minimal truthmakers, or between qualitative and numerical identity –​in metaphysics. “Philosophical cases are puzzling. They are difficult and challenging and so we hardly ever conclusively settle on one answer to the various questions raised by a case” (Cappelen 2012, 189). It is rather obvious that philosophers’ declarations as to the sources of their conceptions tend to be deceptive. Even Williamson, whose work is concentrated on metaphilosophical rather than semantic questions appears to be trying to “cover up” the fact he had used introspection. Ostensibly, he appears to distance himself from introspection as a philosophical tool, as we can gather from the following excerpt:  “Of course, dwelling introspectively for long on any belief […] has its characteristic phenomenology, but that is the phenomenology of the dwelling, not of what is dwelt upon” (Williamson 2007, 217). When, however, he needs to ground his arguments on the issue of Gettier’s cases (claiming that they lack a certain regress), he does not hesitate to reach for introspective

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27

Calibration Problem

Let us look more closely at how it is possible that metareflection, which is an introspective mechanism and, as such, a rather “private” one, is subject to calibration and correction after all. Indeed, it can be calibrated and corrected in two ways. First, calibration can involve setting our own experience against third-​ person knowledge of the world we are thinking about and of human cognitive states involved in such thinking, when we “learn to look at ourselves the way one looks at distant things.” This particular method can be something of a surprise after we have said that an analysis of the cognitive states we are interested in within a third-​person perspective is insufficient for philosophy. This does not mean, however, that a third-​person perspective has no value at all. Scientific research, including research carried out under the aegis of so called experimental philosophy, remains an important supporting tool for philosophers. I share Sorensen’s views whereby: As an epistemologist, I follow developments in the psychology of reasoning and the psychology of perception. I read experimental philosophy in the same interdisciplinary spirit. sorensen 2014, 136

Bealer’s claim, on the other hand, seems to me too strong. He argued that: Among the central questions of philosophy […] most can in principle be answered by philosophical investigation and argument without relying substantively on the sciences. bealer 1998, 201

I hold that among the central questions of philosophy most cannot be answered relying solely on the sciences, without specific philosophical investigation and argument. On my account it might well be, in certain cases, that relying on the sciences, while far from being sufficient, proves to be necessary for development in philosophy.34 Science teaches us about many aspects of

34

data: “Plainly, no such infinite regress of inferences occurs in us. At some point, we simply apply our concepts to what confronts us, without relying on an inference from further premises” (ibidem, 194). I think that is why philosophy has for thousands of years been the inspiration for new sciences. When philosophy needs the support of science but can’t find it in the existing disciplines, it gives birth to and nurtures a new science. For a while, it tells this new science

28 Tałasiewicz the world we would not be aware of unless thus taught –​for instance, acquaintance with the theory of relativity is essential in philosophizing about space and time –​and teaches us about determinants of cognitive behaviour from a third-​person perspective. We must take this into account in our first-​person reasoning. Philosophers can speculate about matters that do not lend themselves to empirical verification, but they can’t spout nonsense about matters thus verifiable. The philosopher must be interested in the results of empirical sciences in so far, too, as they are useful in showing her yet another way of successfully controlling her own cognitive limitations and more effectively “bracketing” irrelevant factors. An account of control procedures, stemming from empirical findings about the flaws in human reasoning, and applied to first-​person thinking, is given by Richard Foley, who summarizes it saying: I am not entitled simply to dismiss […] empirical challenges […] I must […] reexamine as best I  can my way of thinking about the issues and monitor myself in light of these empirical challenges. However, I have to do this, and I am entitled to do this, from my own perspective, using the faculties, procedures, opinions, and so forth I have confidence in, even if these faculties, procedures and opinions are precisely the ones the empirical studies are challenging. foley 1998, 256

That first-​person reflection devoid of such controlling impulse leads sometimes to a dead-​end is amply showed by (Wisniewski 1998), (Shafir 1998), (Ramsey 1998) and many others. We have stated that, in many cases, the philosophical conceptual framework does not have to, or perhaps even should not, mirror the semantic framework of everyday language. Admittedly, it could be argued that even very advanced conceptual structures in science or philosophy must ultimately be rooted in one way or another in concepts thrown up by everyday practice.35 Yet, in so

35

what to do, what time to come back home, etc. After some time, the new science matures, gets cross with mother philosophy and moves out of home, broadcasting to the whole world that philosophy is good for nothing. Some time passes again, and the ill-​feeling abates. It may be possible again to have family dinner and relax a bit the more willingly we accept that each generation has its own home and its own house-​rules. “Philosophy is not itself a science, but it cannot afford to be positively antiscientific by ignoring the results of scientific investigations of its subject matter” (Deutsch 2015, 158). “The acquisition of the theoretical concepts of the special disciplines presupposes and rests upon the possession of the pre-​theoretical concepts of ordinary life” (Strawson 1992, 21).

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far as philosophy is an analysis of everyday concepts at all, it is an analysis of these concepts outside the scope of their everyday usage. It is an analysis of concepts in borderline situations in which the everyday meaning simply fails to deliver.36 On the other hand, where the ordinary linguistic competence holds up, the philosopher should, in some cases, take it into account, at least as one of the factors. On this point then, I hold a different view than Ernest Sosa, who maintains that appealing to philosophical intuitions can be problematic if surveys point to a considerable difference of opinion among the respondents (Sosa 2007, 102). I believe that it is the universal agreement among members of the language community on the use of certain terms in certain circumstances that can act as a bar for the philosopher stopping her from straying beyond this consensus in her analyses –​this is the calibrating function of linguistic competence. As Kornblith would say, the intuitions of the majority are not definitive, but they do carry substantial epistemic weight, at least in comparison with the intuitions of any single individual, even oneself. kornblith 1998, 133

The “considerable difference of opinion” suggests precisely that linguistic competence fades away while the philosopher can confidently get on with using more refined advanced philosophical methods. The concepts of justice and responsibility are particularly clear examples of philosophical cases that should be kept close to the common conceptual framework. The two concepts should be easy to grasp for the wider public, in particular for anyone engaged with justice as dispensed by the courts. It is natural to expect that the philosophical constructs involved in these concepts will not depart significantly from common semantic intuitions to the extent that such intuitions are relatively coherent and recognizable; otherwise the justice system which relies on these concepts in its verdicts would alienate itself from the society it is meant to serve. In such areas, faithful correspondence to the meanings in everyday language, besides their theoretical usefulness, is an important criterion for practical acceptability of the philosophical conceptual framework. This doesn’t mean that ordinary speakers’ linguistic intuitions act as arbiters here, but it does mean that, in these areas of philosophy, it is important to have explanatory structures clarifying the difference between 36

“The analytical philosopher uses words which belong to common discourse in senses rather different from, and wider than, those that they ordinarily possess” (Strawson 1992, 23).

30 Tałasiewicz theoretically motivated philosophical concepts and the practically important intuitions of ordinary speakers of the language.37 As Max Deutsch observed, Data about people’s philosophical beliefs and intuitions are relevant to philosophy in a broadly ethical way; that is, such data are relevant to how we should treat others and how, more fundamentally, we should understand the social practices of different groups of people. deutsch 2015, 160

The other method of calibrating our metareflection involves setting it against the results of other people’s metareflection (expressed, for example, in philosophical dissertations). We can fail to spot something in introspectively analysing our representation of a particular situation, while another person can point out the omission to us availing herself of her own representation of the same situation. A particular type of such an omission is our failure to spot something in a given situation despite it featuring in our representation because a certain level of our metareflection malfunctions: in analysing our representation of this situation we disregard a detail which this representation actually includes. What metareflection (introspection) has in common with perception (extraspection) is that it can be more or less accurate, or even faulty: the intentional contents of the states of mind, which are the objects of our metareflection, in reality (that is in our mind) are richer than it would appear from the content of this metareflection. We could have just the right concepts but be completely wrong in our intuitive beliefs, if we are insensitive to the structure that our concepts (and the world) actually have. jenkins 2014, 110

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An example of this kind of contribution to philosophy is an explanation of experimentally determined conceptual entanglement between intentional action and moral value, characteristic to the Knobe effect or the Butler effect. As such, these effects are not a sufficient reason to reject whatever theories of action, consciousness or value there might be, but are a good enough reason to supplement the preferred concepts with explanations, or at least a model of a possible explanation, about why a conceptual entanglement of one kind rather than another becomes prevalent in the given circumstances. The challenge of building a bridge between a particular philosophical conception and the results of experiments is taken on by Katarzyna Paprzycka (Paprzycka 2015), who seeks to explain the above effects.

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If alerted to it by another person, we simply notice an aspect we have failed to notice before. We can say: “Oh, I can see this now,” or something to this effect. The whole argumentation takes the form of “Look –​I can see now,” and there is nothing unusual about it. It is as if each person was looking at their own copy of a particular painting and one said to the other: “Look, a string on the lute has snapped.” The other person, looking at her painting, would then say in turn: “You’re right! I didn’t notice that at first, but I can see it now.” Philosophy often takes this role for itself: to show people what they can’t see yet but will when it’s pointed out to them.38 A nice example of this kind of persuasion in philosophy is Kripke’s argument that in using the name “Gödel,” in a familiar scenario, we are not referring to Schmidt: “It seems to me that we are not. We simply are not” (Kripke 1980, 84). Having given some thought to their own way of using names, those at whom the “argument” is directed admit as one that he is right because they can see in them what Kripke is showing on his copy of the picture.39 Some sort of shared experience is all that is needed to put the foundations under this kind of calibration of introspective knowledge and the best explanation for this shared experience is an assumption of the existence of the same external world and a relative similarity between people’s cognitive mechanisms. In fact, such an assumption seems necessary for us to be able to think at all about our own states of mind in a verbalized manner, given the social nature of language acquisition. It could very well be too, however, that our representation of a given situation does not include whatever it is that has been pointed out to us (for our original experience was too limited) and no refinement of our metareflection will be of any use. In this scenario, if we can’t find in our experience what is 38

39

That “the method of cases” is drawing attention to philosophically interesting features of the world and noticing important connections therein is highlighted in (Cappelen 2012), where the cases are described as “fact focusers” (ibidem, 133). The author points to the focus on the relation between mental content and social environment in Burge (ibidem, 190); to the distinction of eight sorts of conceivability in Chalmers (ibidem, 185) etc. I don’t mean that Kripke marshals no arguments to support his claim at all. Certainly he does, as is convincingly shown in (Deutsch 2015). What I do mean though is that, besides different forms of argumentation, we are dealing here with a simple demonstration of a certain difference in ways of referring to the objects of our thoughts, discernible in our inner experience. Incidentally, the obviousness of the Gödel case does not extend to the theory which Kripke attempts to argue for on the basis of this case. Recognition of the difference between direct or singular versus descriptive reference turned out to be widespread and long-​lasting, while Kripke’s positive conception in its own right earned him criticism from e.g., (Evans 2002) and (Searle 1983). (But there are its advocates as well, e.g. (Devitt 2011).) The current version of singularism is more likely to be represented by the mental files approach (Récanati 2012).

32 Tałasiewicz expected of us, we must have some additional reasons to correct this experience. Notably, such reasons can include inadequacy of our conceptual framework, which we have identified ourselves or which has been pointed out to us. If that is the case, we need a new, specially-​designed experiment. This scenario requires not so much that we correct our metareflection as revise the original representation or indeed revise our original experience. In this way, we have reached a certain account of the thought experiment. 6

Thought Experiments

Under this account, thought experiments are designed to bring to the fore the differences which did not become sufficiently apparent in the conceptual material gathered before but which should be made clear, in light of the theoretical difficulties which compel us to make a correction in our conceptual system. Illuminating certain philosophically relevant distinctions may be connected with our having to imagine counterfactual situations which allow us to separate aspects of reality which typically go together in any real-​life experiment.40 As should be apparent, this is an endorsement of Williamson’s view that “Paradigm thought experiments in philosophy are simply valid arguments about counterfactual possibilities” (Williamson 2007, 207). It seems though that at least some thought experiments are more than just a model of argumentation. In some respects, they resemble real-​life experiments. On our account, analysis of counterfactual possibilities involves creating of states of imagination bearing characteristics required by the purpose of the experiment, and subsequently producing states of quasi-​perception whose intentional objects would be those imagined situations (that is, the content of those imagined states) and subjecting those states of quasi-​perception to a metareflective analysis driven by theories that informed the entire exercise. In metareflection, these states appear to be similar or analogical, in many respects, to the states of perception.41 Although the intentional objects of states of imagination understood 40

41

This function of reduction –​mental bracketing of factors irreplaceable in a real-​life experience –​brings to mind again the original similarity between the analytical method (the subject of this study) and the phenomenological method referred to earlier in this paper. A clear distinction between these two philosophical traditions lies rather in their attitude to certainty: phenomenology prioritises a Cartesian quest for certainty. Analytical philosophy does not set itself such an unrealistic, I believe, goal. The method of reduction they have in common, though. Of course, another level of metareflection will throw up serious differences between them: the satisfaction condition for an actual state of perception is the existence (in the

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in this way do not in fact exist, the states themselves do exist and have their own content. The role of this content exceeds just being the reservoir of antecedents in counterfactual reasoning because the content as such can be an intentional object of cognitive acts in a metareflection of a higher order, just as the content of ordinary states of perception. Thus, states of imagination expand the raw data base to which we can return even if the original arguments constructed with their aid turn out to be invalid. A good example is the famous trolley thought experiment (Thomson 1985). The experiment separates the moral factors and consequences of either acting or refraining from acting from any other factors and consequences which, in real life, would influence decision-​making: emotional, legal, cultural or epistemological ones. Thomson presents a scenario where a run-​away trolley could be sent down a spur killing one person or allowed to continue along its path where it will kill five people. And another one, in which a surgeon is able to save five people in need of transplantation of different organs by killing one healthy person and taking the organs from this person’s body. The experiment does not assume –​and should not assume –​the operation of any other factors influencing decision-​making. In reflecting on these scenarios (our thoughts being the more valuable the more we refrain from adding to our initial data set information we would expect to be given if these were real-​life situations), we have the opportunity to spot a distinction we would never encounter in real life and thus refine our concept of moral duty. Just what sort of refinement the concept of moral duty receives depends on the perspicacity of the philosopher turning over these dilemmas, on a whole range of her wider beliefs, and on the larger conceptual framework at her disposal. Philosophical literature is replete with a variety of reactions and arguments in the area of “trolley science”. Our insight into the problem at hand, courtesy of such experiments, can be the basis of totally different conceptualisations, depending on the larger conceptual framework or the hierarchy of acceptable rules which govern our inner experience. Still, such experiments can give us a genuine enrichment of the range of our initial data. The trolley experiment is a perfect opportunity to compare the role of experiments from a first –​and third-​person perspective. It was frequently “replayed” as a realistic experiment testing the reaction of the participants who were told world) of the state of things perceived, whereas the satisfaction condition for a quasi-​ state of perception is the actual existence of the relevant state of imagination (in our mind) whose content, from the phenomenological perspective, corresponds to some possible state of affairs, without the requirement, however, of the actual existence of such a state of affairs.

34 Tałasiewicz the trolley story. A classical experiment –​a first-​person experiment –​allows the philosopher to refine her beliefs about the nature of moral judgments by placing her in an imaginary situation where she has to pass judgment on the basis of all the philosophical knowledge she has at her disposal, using the best conceptual apparatus she is capable of bringing into it. And if she is in trouble at this stage, it means she must try harder, that her best knowledge and her best conceptual apparatus are not yet sufficient –​a part of moral reality still remains unexplored. By contrast, survey “replays” test the distribution of common beliefs as to how to react in the situation described. These “replays” are in fact different experiments, providing completely different data. I disregard the fact here that, in many cases, the original story has often been modified. 42 The point is that, even if the participants had been exposed to precisely the same story, their collected opinions are a completely different set of data than the results of a first-​person analysis carried out by a philosopher: The first person perspective in thought experiments is […] methodologically primary, as it is the only perspective from which we can attain the goals of philosophical inquiry. ludwig 2007. 15743

Thus, a thought experiment is not a cheap substitute for a real-​life experiment –​ it is a completely different tool, capable of reaching out to areas which are out of range to a real-​life experiment. It is intended to create artificial cognitive states in our minds, usually unavailable in ordinary cognition, in order to help the philosopher, using metareflection, spot interrelations or patterns in such states, which in real-​life are not so easily detectable or are otherwise distorted. Imagination cannot furnish knowledge about the external states of affairs, but it can give us new insights into the process of conscious apprehension and organisation of our inner cognitive states and overall picture of our knowledge-​ forming processes. Knowledge about conscious apprehension and organisation of our inner states is vitally important in philosophy:  philosophical 42

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Such tiny modifications, by the way, create significant problems within the third-​person-​ style of research itself. As psychologists notice, “by presenting content in a suitably concrete or abstract way, thought experiments may recruit representational schemas that were previously inactive. As a result, they can be expected to evoke responses that run counter to those evoked by alternative presentations of relevantly similar content” (Szabó Gendler 2007, 86). Many examples of actual troubles with modifications of scenarios and resulting incommensurability of survey answers are discussed in (Ziółkowski 2015, 2016, 2017). This point is highlighted in (Zawiła-​Niedźwiecki 2015), too.

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cognition, even when oriented towards external objects, has the philosopher considering the routes in which information from external objects reaches the conscious level and connects with concepts in the logical sense. 7

Summary

Summing up, I have presented a certain way of practicing philosophy –​with no pretence of it being complete (the normative aspect of philosophical theory in particular has been left out of account)  –​described its methods and considered the cognitive abilities likely to be needed in pursuing its objectives. By the way I have introduced certain reading of “conceptual analysis” and “intuition,” under which conceptual analysis and intuition are important (or even crucial) for philosophy, which, however, does not contradict Cappelen’s claim that conceptual analysis and intuition are marginal or even non-​existent –​under his reading of the terms (Cappelen 2012, 206). Conceptual analysis under proposed reading is not concerned with analysing the meanings of the words in natural languages but with examining the situations accessible through the content of cognitive acts and building a relevant conceptual framework (sometimes full of technical jargon the likes of which is never used in everyday speech). Strictly speaking, the term we should be using here is “synthesis” rather than “analysis.” Only in some cases, where the philosophical concepts refer to vital social practices (e.g., the workings of the justice system), can the analysis of the common meanings of words used in connection with such practices be an element (never sufficient on its own) of such philosophical synthesis. Philosophy practiced in this way is grounded in first-​person metareflection on a philosopher’s own cognitive states as analysed through introspection, including, most importantly, the contents of such states and the interrelatedness between the contents of such states. Metareflection is a bridge between concepts in the psychological and logical sense, making it possible to convert the information in our minds into rational knowledge. This knowledge can refer to both external reality44 and to our own cognitive mechanisms (e.g. conditions of semantic reference). That is why it is correct to say that conceptual knowledge can be regarded as knowledge about the world rather than about the concepts themselves (Williamson 2007, 18), (Jenkins 2014, 103), (Sosa 2007, 100), and that the role of philosophy, at least one of its key roles, can also be thought

44

“Basic categories are […] the categories that mirror the correlational structure of the world” (Rosch and Mervis 1998, 43).

36 Tałasiewicz of as gaining knowledge about reality as represented by some of the concepts (Ludwig 2007). In particular, many of the concepts we lay claim to: truth, good, beauty, justice, knowledge, cause, purpose, action, consciousness, causation, values, virtue, rationalisation, comprehension, sense, free will, are regared as being especially important to philosophy. They also represent some aspects of reality in which we operate and encapsulate some of our cognitive processes applied in the course of cognitive development thanks to which we were able to experience this reality and communicate with each other about it.45 Empirical knowledge can open an interesting insight into our cognitive mechanisms by pointing up the contrast between a third –​and first-​person perspective. Reflecting on this contrast can be a valuable philosophical experience. In order for such reflection to be possible, the philosopher must have some idea about what “ordinary” science has to say about the things that interest her. And if the science in question says nothing, because, for example, it finds little merit in exploring such things, the philosopher can successfully find out for herself about the things she is after, in particular by carrying out empirical research which is driven by her philosophical agenda.46 First-​person introspective knowledge is thus capable of being corrected –​ both by comparison with that of other people and by comparison with third-​ person empirical knowledge about the same object. The possibility of calibrating intuition and the requirement for critical examination of the solutions being adopted ensure that the minimum rudimentary conditions of scientific rationality are satisfied. Cognitive abilities relied upon by the philosopher do not differ markedly from the abilities required in any intellectual activity. Yet philosophy is autonomous and distinct among the sciences. It is the most general of sciences 45

46

An important but separate problem is the status of mathematical knowledge. There is a diverse range of views on the sources of this kind of knowledge: starting from a belief that mathematical objects are like Plato’s ideas and a special insight is needed to say anything about them, and terminating in a belief that mathematics is a generalisation of mental experience filtered through the complex cognitive structures of our mind. The empirical foundations of mathematics are discussed by (Jenkins, 2014). At any rate, the nature of mathematical knowledge is as perplexing as the nature of philosophical knowledge. Equally perplexing is the position of the nature of mathematical knowledge vis-​a-​ vis the nature of philosophical knowledge. It wouldn’t do to get bogged down in these complexities here, which is why I have left out of my account discussion of the relationship between mathematical and philosophical knowledge (including the philosophy of mathematics). Such is the role –​limited but useful –​for experimental philosophy as one of the tools for “calibrating” first-​person metareflection. Thus, I wouldn’t follow Cappelen in calling x-​phi “a big mistake,” cf. (Cappelen 2912, 219).

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studying the natural world –​as described earlier –​but it is actually a lot more than that. Philosophy stands “before” and “above” other sciences. Owing to the nature of the first-​person perspective, philosophical reflection is primary to all science, as it is the first-​person perspective that is the guiding light of any scientific agenda. Science explains the world and the mechanisms by which it is governed, but what we take to be a suitable explanation and how we divide the world into interesting aspects that need explaining must be approached from a first-​person perspective. Philosophy is a source that inspires scientific inquiry and the highest-​level platform that integrates scientific findings in a way that makes them intelligible. This special status of philosophy is a reason for a considerable divergence within it, indeed, it perhaps accounts for philosophical diversity more than anything else, for it makes the room for the pursuit of fundamentally different cognitive objectives. One of such fundamental divisions, I believe, lies between a philosophy that is preoccupied with seeking certainty and a philosophy that is not so preoccupied. Another reason for such divergence is that differences of opinion concern complex conceptual-​argumentative structures, while individual experiences, distinctions or logical relations are often commonly accepted. Unlike other sciences where even highly refined theories remain on fairly elementary levels of introspective metareflection (compared e.g. to great sophistication of their mathematical structure), philosophical paradigms engage metareflection of much higher order, which in turn weakens the link between such paradigms and direct experiences shared by all. To this extent, if we take into account that the routes of cognitive development vary from person to person, we will soon discover that, given the same inputs in a given situation, different philosophers find different conceptualisations of the same problem plausible. Philosophical way of pursuing knowledge explains an apparent paradox to which Williamson draws our attention: “The questions about the structure of thought and language become central to the debate, even when it is not primarily a debate about thought or language” (Williamson 2007, 45). The primacy of thought and language in philosophy is brilliantly highlighted by Strawson, who captured this feature by way of writing about the subject-​predicate distinction he had studied: “We assume that the subject-​predicate duality […] reflects some fundamental features of our thought about the world” (Strawson 1974, 11). “We are dealing here with something that conditions our whole way of talking and thinking, and it is for this reason that we feel it to be non-​ contingent” (Strawson 1959, 29). I  should like to add that it is not just the subject-​predicate distinction but a large part of valuable philosophical cognition that deals with something that conditions our way of talking and thinking

38 Tałasiewicz and reflects fundamental features of our thought about the world. For there is something more in our cognition than just gathering, storing and processing information about the world we live in. We are animals and our cognitive system does all these things, just like the cognitive systems of all animals do, according to the level of their development. How it is done is the job of cognitive science to find out. But we do more than that. We make sense of the world, literally, by transforming information into logical senses, in the way cats or dogs, or apes, do not. Philosophy is about making sense.

References

Bealer, G. 1998. Intuition and the Autonomy of Philosophy. In: Rethinking Intuition … 1998, 201–​239. Brożek, A. 2019. Franz Brentano and the Lvov-​Warsaw School. In: Franz Brentano in Vienna. The Vienna Circle Collection. Edited by D. Fisette, G. Fréchette and F. Stadler. Dordrecht, Heidelberg: Springer (in press). Cappelen, H. 2012. Philosophy without Intuitions. 1st ed. Oxford: Oxford University Press. Carey, S. 2011. The Origin of Concepts. Oxford Univ. paperback ed. Oxford Series in Cognitive Development. Oxford: Oxford Univ. Press. Clark, E.V. 2003. First Language Acquisition. Cambridge: Cambridge University Press. Czeżowski, T. 2000. Knowledge, Science, and Values: A Program for Scientific Philosophy. Poznań Studies in the Philosophy of the Sciences and the Humanities. Amsterdam, Atlanta (GA): Rodopi. DePaul, M.R. 1998. Why Bother with Reflective Equilibrium. In: Rethinking Intuition… 1998, 293–​309. Deutsch, M. 2015. The Myth of the Intuitive: Experimental Philosophy and Philosophical Method. Cambridge (MA): The mit Press. Devitt, M. 2011. Experimental Semantics. Philosophy and Phenomenological Research 82(2): 418–​435. Dunbar, R.I.M. 2004. The Human Story: a New History of Mankind’s Evolution. London: Faber and Faber. Evans, G. 2002. The Causal Theory of Names. In: G. Evans. Collected Papers. Reprint. Oxford: Oxford Univ. Press [u.a.], 1–​24. Foley, R. 1998. Rationality and Intellectual Self-​Trust. In:  Rethinking Intuition… 1998, 241–​256. Fumerton, R. 2007. Render Unto Philosophy that Which Is Philosophy’s. Midwest Studies in Philosophy 31: 56–​67. Gettier, E. 1963. Is Justified True Belief Knowledge? Analysis 23: 123–​123.

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Goldman, A. and J. Pust. 1998. Philosophical Theory and Intuitional Evidence. In: ­Rethinking Intuition… 1998, 179–​197. Gopnik, A. and E. Schwitzgebel. 1998. Whose Concepts Are They, Anyway? The Role of Philosophical Intuition in Empirical Psychology. In: Rethinking Intuition… 1998, 75–​91. Husserl, E. 1973. Experience and Judgment. Investigations in the Genealogy of Logic. Evanston: Northwestern University Press. Husserl, E. 2001. Logical investigations. International Library of Philosophy. London, New York: Routledge. Intuitions. First edition. 2014. Edited by R. Booth and D.P. Rowbottom. Oxford (UK): Oxford University Press. Jenkins, C.S.I. 2014. Intuition, ‘Intuition’, Concepts and the A Priori. In: Intuitions. 2014, 91–​115. Kauppinen, A. 2006. The Rise and Fall of Experimental Philosophy. Philosophical Explorations 10(2): 95–​118. Kim, J. 1988. What is ‘Naturalized Epistemology’? Philosophical Perspectives 2: 381–​405. Komorowska-​Mach, J. 2013. Negatywny program filozofii eksperymentalnej a odwołania do intuicji w argumentacji filozoficznej” [Negative Program of Experimental Philosophy and Referring to Philosophical Argumentation]. Filozofia Nauki 83(3): 157–​165. Kornblith, H. 1998. The Role of Intuition in Philosophical Inquiry: An Account with No Unnatural Ingredients. In: Rethinking Intuition… 1998, 129–​141. Kripke, S. 1980. Naming and Necessity. Cambridge (MA): Harvard University Press. Lewis, D.K. 2001. Counterfactuals. Rev. ed. Malden (MA): Blackwell Publishers. Ludwig, K. 2007. The Epistemology of Thought Experiments. Midwest Studies in Philosophy 31: 128–​159. Łukasiewicz, J.L. 1906. Analiza i konstrukcja pojęcia przyczyny [Analysis and Construction of the Concept of Cause]. Przegląd Filozoficzny 9(2–​3): 105–​179. Machery, E., R. Mallon, S. Nichols and S. Stich. 2004. Semantics, Cross-​Cultural Style. Cognition 92: B1-​B12. Paprzycka, K. 2015. The Omissions Account of the Knobe Effect and the Asymmetry Challenge. Mind and Language 30(5): 550–​571. Ramsey, W.M. 1998. Prototypes and Conceptual Analysis. In:  Rethinking Intuition… 1998, 161–​177. Récanati, F. 2012. Mental Files. 1st ed. Oxford: Oxford University Press. Rethinking Intuition:  the Psychology of Intuition and Its Role in Philosophical Inquiry. Studies in Epistemology and Cognitive Theory. 1998. Edited by M.R. DePaul and W.M. Ramsey. Lanham (MA): Rowman & Littlefield. Rosch, E. and C.B. Mervis. Family Resemblances: Studies in the Internal Structure of Categories. In: Rethinking Intuition… 1998, 17–​44.

40 Tałasiewicz Searle, J.R. 1983. Intentionality. An Essay in the Philosophy of Mind. Cambridge, New York: Cambridge University Press. Searle, J.R. 2015. Seeing Things as They Are: a Theory of Perception. Oxford, New York: Oxford University Press. Shafir, E. 1998. Philosophical Intuitions and Cognitive Mechanisms. In: Rethinking Intuition… 1998, 59–​73. Sorensen, R. 2014. Novice Thought Experiments. In: Intuitions. 2014, 135–​147. Sosa, E. 1998. Minimal Intuition. In: Rethinking intuition… 1998, 257–​269. Sosa, E. 2007. Experimental Philosophy and Philosophical Intuition. Philosophical Studies 132, 99–​107. Strawson, P.F. 1959. Individuals: An Essay in Descriptive Metaphysics. London: Routledge. Strawson, P.F. 1974. Subject and Predicate in Logic and Grammar. University paperbacks 538. London: Methuen. Strawson, P.F. 1992. Analysis and Metaphysics: An Introduction to Philosophy. Oxford, New York: Oxford University Press. Szabó Gendler, T. 2007. Philosophical Thought Experiments, Intuitions, and Cognitive Equilibrium. Midwest Studies in Philosophy 31: 68–​89. Thomson, J.J. 1985. The Trolley Problem. Yale Law Journal: 94: 1395–​1415. Twardowski, K. 1977. On the Content and Object of Presentations: A Psychological Investigation. Melbourne International Philosophy Series. The Hauge: Nijhoff. Williamson, T. 2007. The Philosophy of Philosophy. The Blackwell/​Brown Lectures in Philosophy. Malden (MA): Blackwell Pub. Wisniewski, E.J. 1998. The Psychology of Intuition. In: Rethinking Intuition… 1998, 45–​58. Zawiła-​Niedźwiecki, J. 2015. Czy badania eksperymentalne mogą coś rozstrzygnąć na gruncie filozofii moralności? Rzecz o wagonikologii [Can Experimental Research Resolve Anything in Philosophy of Morality?]. Lecture delivered during 10th Polish Philosophical Congress in Poznań. Ziółkowski, A. 2015. Analiza metod filozofii eksperymentalnej na wybranych przykładach [Analysis of Methods of Experimental Philosophy: Selected Examples]. Doctoral dissertation. University of Warsaw. Ziółkowski, A. 2016. Folk Intuitions and the No-​Luck-​Thesis. Episteme 13(3): 343–​358. Ziółkowski, A. 2017. Experimenting on Contextualism: Between-​Subjects vs. Within-​ Subjects. Teorema: International Journal of Philosophy 36(3): 139–​162.

­c hapter 2

Semi-​Formal Analysis of the Formality-​Informality Opposition in the Spirit of the Lvov-​Warsaw School Jacek Jadacki Abstract The starting point of this paper is conceptual-​terminological specification within the class of transformations performed on language formulas. The following types of transformations are distinguished: enlargement, generalization, extrapolation and variabilization –​as well as standardization, schematization and clarification. The term “formalization” is sometimes used as a synonym for “variabilization,” “schematization” (that is, its basic sense), or “axiomatization.” Each theory is inherently a formal theory (in the basic sense); therefore, the opposition of formal theories to informal theories, and in particular of formal logic to informal logic, has no reason for existence; instead of the formality vel informality of some theories, e.g., logic, one should say that one theory, in particular a logical theory, is more (or less) formal than another. The motive for postulating informal logic is the charge of inadequacy against traditional formal logic. In practice, what is practiced under the banner of “informal logic” is sometimes the result of operations that have been called “clarification” here, or such an extension of classical logic that would be a theory of argumentation more adequate than the latter.

Keywords axiomatization  –​ clarification  –​ classical logic  –​ formalization  –​ Formal Theory  –​ ­Informal Theory –​schematization –​theory of argumentation –​transformation

1

Introduction: the Need to Clarify the Title Opposition1

In 1978, the first issue of the journal Informal Logic appeared. Ralph Henry Johnson and John Anthony Blair wrote in their introduction “From the E ­ ditors:” 1 The text was created as part of the project “Kazimierz Twardowski’s Place in Polish Culture and European Philosophy” (2016/23/B/HS1/00684), financed by the National Science Centre (Poland).

42 Jadacki Informal logic means many things to many people. Let us then declare our conception of it. For the time being, we shall use this term to denote a wide spectrum of interests and questions, whose only common link may appear to be that they do not readily lend themselves to treatment in the pages of The Journal of Symbolic Logic. More positively, we think of informal logic as covering the gamut of theoretical and practical issues that come into focus when one examines closely, from a normative viewpoint, the reasoning that people actually engage in. Subtract from this the exclusively formal issues and what remains is informal logic. Thus our conception is very broad and liberal, and covers everything from theoretical issues (theory of fallacy and argument) to practical ones (such as how best to display the structure of ordinary arguments) to pedagogical questions (how to design critical thinking courses; what sorts of material to use). johnson & blair 1978: 1

This ‘broad and liberal conception’ has been characterized by the editors “negatively” and “positively:”  negatively  –​by contrasting the informal logic with formal (“symbolic”) one; positively –​by indicating what (“the reasoning that people actually engage in”) and how (“from a normative viewpoint”) the informal logic “covers.” The editors’ very imprecise characterization was probably dictated by their desire to attract as many people as possible to their journal, whose “logical” aspirations could not be satisfied by The Journal of Symbolic Logic. However, reading texts from later years, included in the field of informal logic –​as well as considerations about the informality-​formality opposition justifies the analysis of this opposition presented here. This analysis will be “semi-​formal.” What means “semi-​formal” can only be specified at the end of the paper, after making the necessary conceptual distinctions. 2

Operations on Formulas

The language in which one speaks of various transformations made on language formulas is unfortunately far from being precise  –​and without sufficient precision in this respect, the characteristics of the title opposition will always leave much to be desired. Let’s start with the appropriate conceptual-​terminological specification. It will not do without neologisms and ­neosemantisms.

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2.1 Enlargement Let’s compare the following formulas: (1) Jack likes Aggie. (2) A certain boy likes a certain girl. (3) A certain man likes a certain man. (4) A certain object likes a certain object. (5) A certain object remains in relation to a certain object. (6) There is a certain state of affairs. We will say about formulas (2)–​(6) that they are, in turn, more and more far-​ reaching enlargement of formula (1). What is the transition from (1) to (2), from (2) to (3) etc.? This transition consists in the fact that these or other members of subsequent formulas are replaced by more and more extensive members in comparison to the first ones (i.e.: “Jack”/​“Aggie”, “a boy”/​“a girl”, “a man”, “an object”). 2.2 Generalization, Extrapolation and Variabilization Enlargement should be distinguished from generalization, extrapolation and variabilization. Generalization consists in giving a formula containing a certain quantifier such a form, that if this quantifier is a particularizer, it is replaced by a generalizer, and if it is a generalizer with a certain range, it is replaced with a generalizer with a range that extends beyond the output range. For example, the generalization of formula (2) is the formula: (7) Every boy likes a certain girl. The generalization of formula (7) is, for example, the formula: (8) Every man likes a certain man. In turn, extrapolation consists in giving a formula containing a certain quantifier with a specific range such a form that this quantifier is replaced with a quantifier with a range that is excluded with the range of the output quantifier. For example: the extrapolation of formula (7) is the formula: (9) Every girl likes a certain girl. Finally, variabilization consists in replacing a constant term of a certain expression –​a variable member (scil. a variable) with a range of variability, the subset of which is the denotation of an altered fixed member.2 For example, 2 An example of the operation of variabilization meant by Kotarbiński is when he speaks of the formula “x × (3 + x)” arising, e.g., from the expression “2 × (3 + 2)” by removing “2’s from that expression and filling the blanks with x’s” (Kotarbiński 1929/​1966, 130). However, I would not agree with Kotarbiński that –​contrary to the expression “2 × (3 + 2),” having “a certain meaning” –​the formula “x × (3 + x)” “does not mean anything” (ibidem). Incidentally, the operation reverse to variabilization is what some call “verbalization.”

44 Jadacki the result of the variabilization of formulas (1) and (6) are, for example, successively: (10) x likes y. (11) p. 2.3 Standardization Consider language L* such that structural rules defining the construction of expressions of language L* are indicated. Let us further consider language L such that the structural rules are not indicated for language L or that the structural rules of language L are different from the structural rules of language L*. Standardization of utterance U of language L due to language L* is a reformulation of utterance U in the form of utterance U* such that: (i) utterance U* is a translation of utterance U; (ii) utterance U* is built in accordance with the structural rules of language L*. Of course, more or less restrictive conditions may be imposed on the translation referred to in (i). And so: each and only such expression, which is synonymous to E, equivalent to E, etc., is considered as a translation of expression E. 2.4 Schematization Schematization of a given statement formulated in a given natural language consists in replacing elements of a defined order of this expression with individual symbols. And so formula (1) would be after schematization: (11) Pja. Making schematization understood in such a way –​must be accompanied by an interpretative preamble, explaining the assignment of individual members of natural language elements to defined symbols. In our example, this preamble would be: Let: (i) the symbol ‘Pxy’ replaces the expression “x likes y;” (ii) the symbol ‘j’ replaces the word “Jack:” (iii) the symbol ‘a’ replaces the expression “Aggie.” Sometimes, the schematization of a given formula requires the standardization of this formula –​especially when a language whose symbols are to replace expressions of a formalized language has a definite and also a different structure than the formalized language. Consider, for example, the first of Newton’s classical principles of dynamics. In the original version it reads: (12) Corpus omne perseverare in statu suo quie scendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statumi llummutare. (Newton 1687a, 20).

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In English: (13) Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it (Newton 1687b/​1934, 13). Let’s standardize principle (13) in respect to the structure of the language of predicate calculus: (13*) For each body for which there is no force that would act on this body, then the body remains at rest or moves in a uniformly rectilinear motion. Let us now accept the following preamble: b –​ body; f –​ force; Axy –​ x acts upon y; Mx –​ x moves uniformly rectilinearly; Rx –​ x remains at rest. In this case ‘b’ and ‘f’ are variables with limited scopes, and ‘A’, ‘M’ and ‘R’ are constants. The effect of schematization of rule (13*) using these symbols  –​and the specific symbols of the language of predicate calculus –​will be the formula: (13 **) ∀b [~ ∃f ( Afb ) → ( Mb ∨ � Rb)]. As Ajdukiewicz aptly notes –​the function of schematization is to ensure schematized formulas “much more clarity” (Ajdukiewicz 1965b/​1974, 98/​98). 2.5 Clarification Natural language has certain features that make use of logic tools for its analysis which must be preceded by deprivation (or at least registration) of these features.  It includes, among others, ellipticity, amphibolicity, polysemia, occasionality and approximation.  Let’s name the operation of removing these cognitively undesirable attributes –​as well as revealing presuppositions and enthymemes –​“language clarification.” Otherwise, clarification is coupled with standardization in such a way that, on the one hand, standardization must sometimes be preceded by clarification, and, on the other hand, clarification can sometimes be achieved more easily by standardization in respect to the language free from the defects mentioned above.3  In addition, both standardization and clarification must 3 Some aspects of clarification are discussed in the chapter “Semiotic anomalies” of “Spór o granice języka” [Controversy Concerning the Limits of Language]. Cf. (Jadacki 2002, 161–​187).

46 Jadacki ultimately be based on non-​algorithmic semantic intuitions. In the choice of such intuitions, we can be guided, at best, by ad hoc rules –​such as the principle of charity, according to which one should look for such hidden elements of argumentation that ensure its greatest deductive power, or the principle of logical minimum, according to which the given enthymematical argumentation should complement the weakest premise among the premises guaranteeing the conclusiveness of this argument. 3

Theory

3.1 Deductive Theory The deductive theory is a set of sentences such that every sentence belonging to it is an axiom, a theorem or a definition in this theory. An axiom is a sentence in deductive theory which has no proof in this system; while a theorem is a sentence which has proof in this theory. At the same time: a given sentence has proof in a certain deductive theory, when this sentence was derived from the axioms of this theory by applying the adopted inference rule. The primitive term of the language of a given deductive theory is a term that has no definition in this theory; whereas the derivative term is a term that has such a definition. In turn, a simple term is a term that does not have members that are terms; whereas a complex term is a term that has such members. The deductive theory is in opposition to the empirical theory, which is a set of sentences for which every sentence belonging to it is an observational thesis, an explanatory hypothesis or a definition. 3.2 Axiomatized Theory Generally, one can say that the axiomatization of deductive theory T consists in a clear indication of: (i) primitive terms of the language of theory T; (ii) derived terms of the language of theory T –​together with their definitions; (iii) rules for forming the complex terms of the language of theory T; (iv) axioms of theory T; (v) rules of inference accepted in theory T. In 1928, Łukasiewicz explicitly formulated a program for conferring the philosophy of the form of the axiomatized deductive theory: Scientific philosophy should start its construction from the very beginning, from the foundations. To start from the foundations means here to take

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in the first place a survey of philosophical problems and to choose from among them only these problems which can be formulated intelligibly, rejecting all the others. Mathematical logic can be already useful in this preliminary work, for it has fixed the meaning of many expressions belonging to philosophy. Then we ought to start trying to solve the philosophical problems which can be intelligibly formulated. The most useful method of realizing such a task seems to be again a method of mathematical logic:  the deductive, axiomatic method. We need to base our work on sentences which are as intuitively clear and undoubted as possible; such sentences should be taken as axioms. As primary or undefined notions we need to choose such expressions that their sense can be universally explained by cases.4 […] The results obtained in this way should be constantly controlled with the data of intuition and experience and the results of other sciences, especially natural sciences. In the event of non-​compliance, the system should be improved by formulating new axioms and selecting new primitive concepts. It is necessary to take care of contact with reality constantly, not to create mythological beings, […] but to understand the essence and construction of this real world in which we live and act, and which we want to somehow transform into a better and more perfect one. Łukasiewicz 1928, 42

3.3 Formal Theory and Informal Theory The term “formalization” is used in three main senses, namely as a synonym of (i) variabilization,5 (ii) schematization,6 or (iii) axiomatization.7 Next, we will only talk about formalization-​schematization.

4 The translation to this place comes from (Jadacki 2017, 114). 5 Among the logicians associated with the Lvov-​Warsaw School, Bocheński, among others, puts the matter in such a way; according to him, formal logic is the theory of “logical sentences,” i.e., “formulas which exhibit variables in place of words with total meaning; an example is ‘B belongs to all A’.” In particular, formal logic studies, “the formulas of the prescribed type for which, when they are determined by the constants, the state of affairs must be admitted” (Bocheński 1961, 2–​3). 6 Bocheński calls the formalization-​schematization the “abstractive method” of creating logic, which consists in the fact that “the logical theorems are gained by abstraction from ordinary language” (Bocheński 1961, 266). 7 It is captured in such a way, among others, by Ajdukiewicz, describing the developmental stages of deductive theories. The last stage, consisting in the axiomatization of the theory, is called by him just “the stage of formalization” (Ajdukiewicz 1965b/​1974, 218 ff).

48 Jadacki For those who, like me, think that there is no theory that does not contain laws, and so general statements, it is clear that the presence of these laws determines that every theory is formalized. Consider any thesis of (first-​order)predicate calculus. Let it be, for example, one of the versions of De Morgan’s law: (14) ~ ∀x ( Px ) ↔ ∃x ~ ( Px ). It is said about such a law that it is a formal law, because it concerns only the shapes-​forms of symbols that occur in it, and omits the content of these symbols (this content is abstracted). This is, of course, a simplification, because: (i) The symbols of constants in this calculus have after all a definite content, designated in the case of the functors of negation and equivalence by the axioms of propositional calculus or by logical matrices, and in the case of quantifier symbols by predicate calculus axioms. (ii) Variables in law (14) are also provided with content by limiting the range of their variability: ‘x’ –​e.g. to the class of things, and ‘P’ –​to the class of attributes. What is the difference between laws (14) and (13**)? The difference is that the domain of theory to which (14) belongs is larger than the domain of theory to which (13**) belongs. Therefore, opposing formal theories to informal theories, in particular formal logic to informal logic, has no rational basis –​and instead of the formality vel informality of some theories, e.g., logic, one should say that one theory, in particular a logical theory, is more (or less) formal than another. I cannot give the general characteristics of a more-​formal-​than relationship. I will limit myself to the following illustration only. Well, law (14) is more formal than rule (13**), because the ranges of variability of variables from (14) are supersets of the ranges of variability of the respective variables from (13**). In particular, the range of the variable ‘x’ –​is a set of all objects (of a certain universe); while the ranges of variables ‘b’ and ‘f’ –​ are sets of bodies and forces respectively (and thus only of certain objects, while the range of variable ‘P’ is a set of all properties, while the ranges of variables ‘M’ and ‘R’ are only certain definite («active») properties. However, the image is darkened by the presence of variable ‘A’, whose scope is the specified two-​ argument relationship; there is no generalized equivalent for this relation in (14) in the form of a variable whose range would be any two-​argument relation. It is worth noting that there is no formula that would be fully formal. Certainly, law (14) is not such a formula. The impression that it is quite different

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comes from the fact that in the calculus of predicates, to which law (14) belongs, the content elements (ranges of appropriate variables and interpretations of constants) are specified in the preamble excluded outside tautologies in the form of a meta-​language description. 4

Adequacy of Theory

Consider set of objects S and theory T. If every object belonging to set S satisfies every thesis of theory T, then: (i) set S is a model of theory T; (ii) theory T is adequate to set S.8 This is the case, for example, when S* is the set of states of affairs, and T* is classical propositional calculus.  Suppose, however, that set S** is a set of things. Well, set S** is not a model of theory T*, and theory T* is not adequate to set S**. For in theory T*, the only variables are propositional variables, and the denotations of sentences (scil. the elements of set S**) are just only states of things –​not things. When a set of objects, in relation to which a certain theory is adequate, is a real field, then the theory, as Ajdukiewicz puts it, “fulfills an extremely important though only service role in the scientific cognition of reality:” For if a researcher who is studying real facts succeeds in finding out that the fact he is concerned with satisfies the axioms of a given abstract deductive theory (i.e., if the sphere of those facts is a model of that theory), then owing to the work done earlier by the scientist who studied that abstract theory by deducing derived theorems from axioms, the student of facts can learn, without any extra effort on his part, that the domain he is concerned with also satisfies the derived theorems of that theory; he thus significantly broadens his knowledge of the sphere of facts he is studying. ajdukiewicz 1965b/​1974, 206

8 Theses (i) and (ii) are basically equivalent, but thesis (i) better suits the procedure in which we search for a model for the constructed theory, and thesis (ii) –​for the procedure in which we construct a theory for the previously specified set of objects. Bocheński links the first procedure with “mathematical logic (logistic, symbolic logic etc.). […] Mathematical logicians proceed in […] [such a] way: first construct purely formal systems, and later look for an interpretation in every-​day speech” (Bocheński 1961, 266). Bocheński, very rightly, emphasizes that “this process is not indeed always quite purely applied; and it would not be impossible to find something corresponding to it elsewhere. But at least since Boole, the principle of such construction is consciously and openly laid down, and holds sway throughout the realm of mathematical logic” (ibidem).

50 Jadacki The elements of set S, which theory T deals with, and the relations between these elements must obviously be identified by a certain language –​let’s say: L. If language L is different from the language of theory T, then to assess the adequacy of theory T, we need that the statements about set S formulated in language L be standardized in respect to the language of theory T. Sometimes, the adequacy assessment may be wrong just due to incorrect (unsuccessful) standardization. Sometimes, however, the reasons may be deeper. 4.1 Inadequacy of Classical Logic Critics of classical logic generally identify classical logic with (assertive) syllogistic logic, propositional calculus, and predicate calculus (usually first-order one), and this logic is considered an inadequate in respect to argumentative operations (in particular: reasoning). It can be briefly said that they deny the adequacy of this logic as the theory of argumentation.9 They think, namely, that: (i) arguments in natural language are rarely fully standardized in respect to the language of classical logic; (ii) this logic applies only to declarative sentences (i.e. so-​called sentences in the logical sense), while non-​declarative sentences are also members of real argumentation; (iii) this logic is not suitable as a tool to assess the correctness of real argumentation (“real life [everyday] arguing” (Groarke 2017)), because it can only be used to examine whether the members of this argumentation remain one to another in relation to the logical consequence; meanwhile, in real argumentation, it is often about other things. Well –​it is true that the inadequacy ascribed to classical logic actually takes place. However, classical logic does not simply have the aspirations referred to in (i)-​(iii). This should be by no means equated with the fact that classical logic is at most a theory of some “concocted arguments.” Many representatives of the Lvov-​Warsaw School believed that the axiomatization of a theory is a means not to eliminate semantic intuitions, but to “give precision” to them (Ajdukiewicz 1965b/​1974, 215). The usual way of dealing with a certain inadequacy is to construct a theory that removes this inadequacy.

9 It must be admitted that some formulations of the logicians themselves give rise to such criticism. Kotarbiński, for example, writes about the formal logic as the science of forms of reasoning (Kotarbiński 1929/​1966, 129), which could suggest that it concerns all forms of reasoning.

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A good example of this is the criticism directed by Ajdukiewicz towards the reconstruction of concepts associated with the terms: “inference,” “proof,” “verification,” “explanation,” “deduction,” “reduction” and “reasoning” made by Łukasiewicz (and modified by Czeżowski). Ajdukiewicz considered these reconstructions to be inadequate in respect to the concepts as commonly referred to. Therefore, the conceptions of Łukasiewicz and Czeżowski would deprive us of certain concepts “needed” in methodology. Ajdukiewicz suggested that they should be suitably modified, and in particular “extended in [their] concept of reasoning so that it would cover solving all kinds of problems, and even more broadly: all kinds of mental tasks, if we solve them using inference or even just drawing sentences from others” (Ajdukiewicz 1955, 220–​221), wherein one infers a certain sentence from an accepted sentence, and one draws it from a “conceivable,” assumed sentence. 4.2 Postulate for Adequate Logic The problem of the adequacy of classical logic –​and in general: of logic –​was posed in the Lvov-​Warsaw School by its founder in the work “Logical Symbolism and Thinking” unpublished up to now (Twardowski 1917). Twardowski put in this work a thesis that both traditional logic (syllogistics) and its modernized nineteenth-century versions are not adequate theories of argumentation. It avoids here the logical formalism, wanting to capture immeasurable wealth and immense diversity of forms of thinking into several formulas. Thus, these theories cannot only be regarded as an exhaustive picture of reasoning, but also, in practice, expose us to numerous difficulties. And indeed: Does anyone really resort to these forms to show the inaccuracy of reasoning? Probably only philosophers, when they want to show an illogicality to their opponents. Twardowski gave three conditions that a logical system should fulfill to be an adequate theory: (A) [An adequate system] should not prejudge what categories of judgments are or force all judgments to take only certain definite forms. Each judgment must be part of the reasoning as closely as possible, but at the same time it can be expressed in the closest accordance with the spirit of the appropriate language. Language buffs make it difficult to investigate reasoning. (B) [An adequate system] must be free from rules and regulations, whose learning and application requires a separate skill. […] (C) [An adequate system] must correspond to the essence of reasoning, and not substitute for it any other operations that are at best only a certain isolated form of reasoning.

52 Jadacki The following system fulfills these criteria: Reasoning is to see what judgments result from others. […] At the bottom of […] reasoning, there is […] the conviction […] that: If [the reason] is true, then [the consequence] must be also true. This general principle of reasoning breaks down in practice into thousands of concrete forms. Twardowski formulated two exemplary detailed rules: If it is true that object A never has certain property P, then it must also be true that objects B which have this property P are not objects A. If [it is] true that objects A have property P, and objects B do not have property C, then it must also be true that objects B are not objects A. Twardowski’s conclusion was: The theory of logic is to search for all these properties in a possible assembly and group them. But before this happens, we can check the correctness of reasoning. Namely, [we can] always be aware of what principles [lie at the basis of this reasoning]. 4.3 Non-​Classical Logic The answer to the observation that the conjunction “or” of natural language does not usually behave as an ordinary alternative of propositional calculus (‘∨’), was to enrich the repertoire of the conjunctions of this account with the disjoint alternative “either-​or.” The answer to the observation that it is impossible to standardize the utterances of natural language containing the conjunction “and” with the aid of the conjunction of propositional calculus (‘∧’) because, at least in some contexts, this conjunction is an abbreviation of the temporal conjunction “and then”, is to construct a system enriched with an appropriate temporal operator. The fact that the “if-​then” conjunction is used in natural language is not only to exclude the situation in which the predecessor’s event is accompanied by a successor, but also to express the fact that the user of this conjunction does not know whether the predecessor is real or not –​this gave impetus to research on the expressive function of utterances. The inadequacy of assertive syllogistics consisted, on the one hand, in the failure to account for relations, and on the other –​alethic modalities; the remedy was the logic of predicates (with predicates of any number of arguments) and different versions of modal logic –​starting from modal syllogistics. The genesis of Łukasiewicz’s multivalued logic and Leśniewski’s mereology was similar.  The first was brought to life to meet indeterministic intuitions, according to which, for some sentences about the future, the principle of excluded middle does not apply. In turn, the second was to capture the specific

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properties of the natural language conjunction “is an element of” (resp.“is part of”), which does not belong to the conjunction “is part of” of standard set ­theory. 4.4 So-​Called Informal Logic In connection with the alleged inadequacy of classical formal logic, it is postulated that an adequate theory of argumentation be constructed, which –​very unfortunately –​is called “informal logic.”10 This is an unfortunate term for two reasons. First, classical logic  –​although it is generally a formalized theory (in the above-​mentioned sense) –​can also be formulated in non-​formal language. Secondly, the theory of argumentation –​taking into account the areas postulated by critics of the adequacy of the classical logic –​can also be both formal and informal (and also –​otherwise –​axiomatized or not). In practice, what is practiced under the banner of “informal logic” is sometimes the result of operations that have been called “clarification” here, or such an extension of classical logic that would be more adequate theory of argumentation than the latter, i.e.: (i) argumentations whose elements are not only declaratives (sentences in the logical sense), but also, for example, interrogatives and imperatives; (ii) argumentations in which it is not about a deductive force of premises, i.e., a degree of justification that they give the conclusion in terms of logical value (truth or probability) or assertive value (certainty or admissibility), but about their persuasive force, i.e., about to what extent they contribute to the change of the convictions of the addressee’s argumentation, which is desired by the person using this argumentation. 5

Conclusion: Semi-​Formal Analysis

As announced, in the conclusion I will present my explanation of the neologism “semi-​formal.”

10

It is worth noting that people practicing this so-​called informal logic admit their affinity with Ajdukiewicz’s idea of pragmatic logic. For example, we read in (Groarke 2017): “Outside of the English speaking world, the goals of informal logic have been pursued in the Polish tradition of “pragmatic logic,” which promotes the tools of logic as a component of general education which can ensure that students think more clearly and consistently; express their thoughts and ideas systematically and precisely; and justify their claims with proper inferences.”

54 Jadacki Well, I  consider “semi-​formal analysis” an analysis, the effects of which are grasped in formal formulas, such that the content of their interpretative preambles are incorporated into these formulas themselves. For formula (14), such a semi-​formal counterpart would read, for example, as follows: (15) It is not true that for each individual x we have that property P belongs to individual x –​always and only when –​for an individual x we have that it is not true that property P belongs to individual x. Many representatives of the Lvov-​Warsaw School used just such semi-​formal formulations in their analyses. A formal analysis –​or rather (in the spirit of § 3.3) more formal than my analysis presented here –​of the title opposition is waiting for its creator.

References

Ajdukiewicz, K. 1955. Klasyfikacja rozumowań [Classification of Reasoning]. In:  Ajdukiewicz 1965a, 206–​225. Ajdukiewicz, K. 1965a. Język i poznanie [Language and Cognition]. Warszawa: pwn. Ajdukiewicz, K. 1965b/​1974. Pragmatic Logic. Warszawa, Dordrecht: pwn, Reidel. Blair, John Antony & Ralph Henry Johnson 1978 From the Editors. Informal Logic vol. I, no. 1, pp. 1–​3. Bocheński, J. M. 1961. A History of Formal Logic. Notre Dame (IN): University of Notre Dame Press. Groarke, L. 2017. Informal Logic. In Stanford Encyclopedia of Philosophy. https ://​plato. stanford.edu/​entries/​logic-informal/​. Jadacki, J. 2002. Spór o granice języka [Controversy Concerning the Limits of Language]. Warszawa: Wydawnictwo Naukowe Semper. Jadacki, J. 2017. The Lvov-​Warsaw School and Austro-​German Philosophers. Two Cases. In: The Significance… 2017, 93–​131. Kotarbiński, T. 1929/​1966. Gnosiology. The Scientific Approach to the Theory of Knowledge. Oxford, Wrocław: Pergamon Press, Ossolineum. Łukasiewicz, J. 1928. O metodę w filozofii [For a Method in Philosophy]. In:  J. Łukasiewicz. 1998. Logika i metafizyka [Logic and Metaphysics]. Miscellanea. Warszawa: Wydział Filozofiii Socjologii UW, 41–​42. Newton, I. 1687a. Philosophiae naturalis principia mathematica. Tomus primus. Geneve 1739. Typis Barrillot, Filii Bibliop, Typogr. Newton, I. 1687b/​1934. Mathematical Principles of Natural Philosophy. Berkeley: University of California Press. English translation of (Newton 1687a).

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The Significance of the Lvov-​Warsaw School in the European Culture. 2017. Edited by A. Brożek, F. Stadler and J. Woleński. Wien: Springer. Twardowski, K. 1901. Zasadnicze pojęcia dydaktyki i logiki [The Main Notions of Didactics and Logic]. Lwów: Towarzystwo Pedagogiczne. Twardowski, K. 1917. Logical Symbolism and Thinking (ineditum).

­c hapter 3

Analysis –​ Paraphrase –​ Axiomatization: Philosophical Methods in the Lvov-​Warsaw School Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk and Dominik Traczykowski Abstract The aim of this paper is to sketch out three methods of dealing with philosophical questions used by members of the Lvov-​Warsaw School. These methods are: analysis of concepts, paraphrase of theses, and axiomatization of theories. In the first part of the paper, we provide a rudimentary analysis of the concept of method. We point to the fact that in order to characterize a certain research method, one has to indicate the aim of applying it, list its stages, and reconstruct its underlying conceptual scheme. In the second part of the paper, we describe analysis, paraphrase and axiomatization in terms of aims, steps, and conceptual tools. We also present some examples of applications of these methods in works by Kazimierz Twardowski, Jan Łukasiewicz, Tadeusz Kotarbiński, Tadeusz Czeżowski, and Kazimierz Ajdukiewicz.

Keywords analysis –​axiomatization –​conceptual scheme –​Lvov-​Warsaw School –​paraphrase

1 Introduction1 The Lvov-​Warsaw School (in brief: lws) is a group of scholars connected by common roots, sets of problems and methodological standards. The common roots lay in the University of Lvov and Kazimierz Twardowski’s lectures and seminars in philosophy.

1 The text was created as part of the project „Philosophy from the Methodological Point of View” (2015/18/E/HS1/00487), financed by the National Science Centre (Poland).

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The problems discussed in Lvov and then in Warsaw may be characterized by three keywords: object, truth and action (cf. Jadacki 1997). Of course, this defines the scope of investigations very broadly (object:  ontology, truth: epistemology, action: axiology). However, the basic analyses of these three areas and the borders between them were something typical for members of the LWS. The fact that a group of thinkers analyze similar problems does not mean that they propose the same solutions for these problems. Members of Twardowski’s school did not share any common worldview or any philosophical views. Sometimes, even clearly opposite ­results were ­issued. The third junction of the members of the LWS, often referenced as the most important, was methodological. It is said that Twardowski did not force on his students any worldview or even any philosophical standpoint; that he only taught them how to analyze philosophical problems methodically, how to express thoughts clearly, and how to justify their views responsibly. There were two disciplines considered by the members of lws as a methodological basis for philosophy:  psychology and logic. Twardowski started from a psychologistic position. However, in his own studies and, to the greatest degree, in works of his students there was a move from psychology to logical semiotics. In turn, Jan Łukasiewicz proposed a program of the “logicization” of philosophy, having in mind a program of presenting philosophical theories as axiomatic systems. Generally speaking, in the development of the LWS, it turned out that logical tools best serve the realization of the postulates. The methodological basis of the lws is usually presented only generally. That is why a person that would like to follow in the footsteps of the members of the lws cannot find any clear rules of how to deal with philosophical problems in a “Lvovian-​Warsawian” way. However, these methodological procedures and tools may be reconstructed both in explicit statements about methodological procedures and in papers that present the results of the application of these procedures, i.e., implicitly. In this paper, rudimentarily but explicitly, we give a characterization of three methods applied in the lws in solving philosophical questions. This paper consists in three main parts. In the first, we present some terminological distinctions concerning the concept of method. In the second, we move on to a description of the selected methods formulated and applied in the lws, namely: analysis, paraphrase, and axiomatization. In the third, closing part, we formulate some general comments concerning the methodological background of the lws and we point to some methodological peculiarities of the lws as a branch of the analytic movement.

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Concept of Method

There are various standpoints concerning the status of methods in philosophy. Sometimes it is assumed that there is no place for any methods in philosophy, since the research method is, in any case, a systematic way of proceeding, and philosophical considerations are not systematic. In turn, it is sometimes thought that there is no such thing as philosophy as a scientific discipline: that one can only speak about a philosophical kind of thinking  –​that is, about “philosophizing.” We reject both of these extremes. We share the view of the members of the lws that philosophy is a science in a broad sense, and that various methods are used in it. The demarcation line between science and non-​science is determined by the degree of fulfilling criteria of clarity of expression and due justification. 2.1 Definition of Method Despite the fact that in recent years the problems of metaphilosophy or methodology of philosophy have become more and more important, the concept of method has hardly been analyzed by philosophers. That is why we start from some basic terminological distinctions concerning the concept of method and different kinds of methods. These distinctions will be then used in the description of particular methodological procedures in § 3. The term “method” is ambiguous. In our opinion, when applied to scientific research, the most useful definition of “method” is the one relativized to the aim. There are various aims in research and there are various methods applied to achieve them. The aim of a philosopher is usually to resolve a certain philosophical problem, to answer a certain philosophical question. However, sometimes better formulating an old problem or eliminating an improperly posed question is also a serious aim for a philosopher. As philosophy is often considered by its critics as a discipline which is stocked in old and senseless debates, which does not make any progress, even a small step forward towards the improvement of a conceptual scheme is worth of making an effort. Suppose that our aim is to answer a given philosophical question. To apply a certain method in solving this question is to prosecute a certain planned sequence of actions in order to answer satisfactorily this question. A method is just this sequence of actions designed as leading to the answer. Based on these intuitions, let us introduce a following contextual and stipulative definition of the term “method:” Assume that A1, …, An are action-​types, and a1, …, an are action-​tokens falling under types A1, …, An respectively. A procedure-​type P = {A1, …, Ak} is a method

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of achieving the goal-​type G iff a certain procedure-​token {a1, …, ak} is consciously used (or planned to be used) to achieve the goal-​type G. To put it shortly: (met) Method of achieving a given goal is a procedure applied consciously to achieve this goal. Without going into details, we shall just point out that there is a need to differentiate between mere method, i.e., the configuration of actions, and some sentences concerning these actions. Among these sentences, one may identify “description of a method” (a set of sentences stating what actions are/​were/​will be taken in order to achieve a given goal) and “instruction of method” (a set of directives, or sentences expressing some obligations, stating what actions should be taken in order to achieve a given goal). In § 3, we provide some descriptions of methods which may be easily transformed into instructions. 2.2 Reliable and Infallible Methods There are various kinds of methods and various criteria of evaluating them. We focus here only on the aspect of reliability. To start with, we should differentiate between a goal and a result of action. We would like to say that method is applied effectively when the factual result achieved is identical with the intended goal; otherwise it is used ineffectively. Loosely speaking, a reliable method is a method whose applications are “usually” effective. It is useful to define this concept in a comparative way. From among two methods of achieving the same goal, the method which allows one to achieve a given goal more often (or with a higher probability) is more ­reliable. A border case of effective method is an infallible method, namely a method that always results in achieving the planned goal. In particular, one may say that: The method {A1, …, Ak} of achieving the goal (of the type) G is infallible (i.e., fully reliable) iff whenever the procedures of type A1, …, Ak are carried out, goal G is reached. A question arises of whether there are any reliable methods in philosophy. At first glance, it seems that a good candidate for a reliable method is an axiomatic method, which is also applied in philosophy. We will discuss this problem in § 4. Notice that in our initial definition of method, we do not require a configuration of action, being a method, to be reliable. Of course, reliable methods are especially valuable (both in philosophy and other disciplines), but reliability/​ infallibility is not the necessary condition for being a method in general.

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2.3 Local and Global Methods Methods may be divided in various ways. For our sake, it is important to divide methods into (a) global and (b) local.2 How does this work? Let us assume that in order to achieve a main goal G, some partial goals, let us say G1, G2, should be achieved. Moreover, let us assume that we have a method of achieving G1. Then, we will say that the method of achieving G1 is local regarding to the global method of achieving G. The method of achieving G1 could be a global method regarding the goal of achieving G1. Let us look at examples. Suppose we study the problem of whether the world is deterministic or not. Then, the analysis of the concept of determinism is a global method of determining what the term “determinism” means, but it is only a local method in the process of answering the question of whether the world is deterministic. Or suppose we want to know whether a certain sentence S1 follows from a sentence S2. In order to establish that, we have to construct schemes of S1 and S2 in a language of a certain logical calculus. Methods of constructing such schemes are only local methods with respect to the method of answering our question. On the one hand, it is not enough to know what the term “determinism” means in order to solve the problem of whether the world is deterministic or not; on the other hand, we cannot solve this problem unless the meaning of the term “determinism” is established. That is why elaborating local methods is an important part of creating the methodology of any discipline. 2.4 Methods and Tools Another concept related to the problem of method is the concept of methodological tool. Speaking loosely, a methodological tool is something used in the methodological procedure. Methodological tools can be divided into (a) tool-​things (physical ones) and (b) conceptual tools (mental ones). The latter appear in all disciplines of knowledge, in particular in philosophy, in which basically there are no technological tools (tool-​things such as microscopes, computers, questionnaires).3 These conceptual tools are usually a part of a theory which serves as a basis of the research.

2 Surely, methods could be divided into simple and complex ones, but the criterion of simplicity is problematic. The criterion of complexity seems to be more useful. As was indicated before, methods are relativized to goals (there is no absolute method). 3 However, there are some fields of philosophy in which tool-​things are used, e.g., in so-​called experimental philosophy (where researchers use questionnaires etc.).

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Anyway, conceptual tools should not be confused with a mere method. Concepts themselves are not yet configurations of actions. However, it happens that some methods are named after the conceptual tools applied in them. 2.5 The Concept of Method: Summary The distinctions presented above have the following practical implications for methodologists. In order to characterize philosophical method M, one should clearly indicate: (a) the aim of the application of method M, i.e., a (type of) philosophical question which is answered by means of method M (we assume that the purpose of philosophical investigation is usually answering a question stating a certain problem); (b) the stages of method M, or actions that are performed by achieving the goal mentioned in (a); (c) the conceptual or technological tools applied in M; (d) the methodological status of M (this concerns, above all, the question of whether the method is reliable). Someone who is going to characterize or reconstruct a given method which is already being used in given investigations may face some problems. Firstly, sometimes the purpose of the method is not clearly indicated by the people who use this method. It may also happen that the intended result is not identical with the real result. Secondly, it happens that the person using this method skips the description of the method steps and presents only the results. Thirdly, conceptual tools may not be clearly indicated. In general, the methodological reflection is not always presented in works of philosophers. It happens that some preliminary distinctions are made but this is not a rule (there are usually no methodological distinctions).Therefore, the method applied by a given philosopher often requires reconstruction. Now, let us move on to the next point –​the philosophical methods used in the lws. 3

Three Methods of Philosophy

In this paragraph, we would like to consider three methods, namely: analysis (broadly understood as a decomposition, construction and/​or reconstruction) of concepts, paraphrase of theses, and the axiomatization of theories as they were presented and practiced in the lws. To describe these methods, we will indicate their goal, their assumed conceptual tools, and their stages. We will also give some examples of applying these methods for each of them.

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3.1 Analysis of Concepts 3.1.1 Sources Probably all analytic philosophers propose some conceptual analyses. Moreover, analysis of concepts has been present in philosophy from the very beginning and even in the works of philosophers that are no keen to be included in the analytic tradition. Analysis of concepts is present also in the works of every member of the lws. However, in this short and limited paper, we will focus only on some representative examples. Our reconstruction of the steps of conceptual analysis is based on works of (Łukasiewicz 1906) and (Czeżowski 1953), in which this method is described explicitly. Despite some differences in the approaches of these two authors, we are convinced that there are essential similarities in their visions of the analysis of concepts. And the fact that Łukasiewicz’s paper was published at the beginning of the existence of the lws and Tadeusz Czeżowski elaborated on the problem almost 50 years later, shows somehow the continuity of the methodological approach. Two analyses of concepts:  Łukasiewicz’s analysis of the concept of cause and Twardowski’s analysis of the concept of concept (sic!) will serve as examples of the application of the presented method. 3.1.2 Analysis and (Re)Construction of Notions: Description Let us assume that concepts are senses (connotations) of names and that they may be represented as sets of properties. You do not have to accept this claim to understand what follows but there are some advantages of accepting this assumption: the theory of concepts may be considered an analogue of the theory of meaning and the theory of analysis as corresponding to the theory of definitions. For instance: the concept of square or the connotation of the name “square” is composed of two properties: being-​rectangle and being-​equilateral. You may state it in a sentence “Being-​rectangle and being-​equilateral are essential properties of squares” or in a definition: “»Square« means the same as »equilateral rectangle«.” The goal of the analysis of a given concept (or the meaning of a given expression) is to indicate the content of this concept (or the definition of this expression). Sometimes, an indirect goal is to design a conceptual framework such that the analyzed concept is a part of this framework. There are many possible conceptual tools used in this method. In the lws they were as follows: the theory of the semiotic functions of expressions (e.g., the connotation/​denotation or extension/​intension distinction), the theory of concepts, the theory of objects (e.g., the distinction between constitutive and consecutive properties of objects); in more sophisticated or more developed

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versions of this method some elements of set theory and the elements of logical calculi may be also applied. In the analytic procedures described by Łukasiewicz and Czeżowski, we are inclined to distinguish the following four main stages: Stage i. Selection of corpus. Every conceptual analysis needs a corpus. However, various kinds of corpuses may be used here. Suppose we analyze the concept of A (or the meaning of “A”). If only they are accessible, we may examine some As (designates of “A”) in order to determine their properties. This is how it usually happens in empirical sciences: if you want to establish the concept of sparrow, you examine various sparrows; in order to analyze the concept of water, you examine some instances of water. However, the corpus of analysis may also be indirect, only –​so to speak –​ verbal. Instead of examining “real” As, one may examine texts in which the term “A” is used, to establish what properties are ascribed to As by the users of this term. This happens when one, for instance, analyzes the concept of essence by Aristotle or the concept of force in classical mechanics. A biologist, by analyzing the concept of sparrow, may also rest on what other biologists (and ordinary people) speak of sparrows. In the case of philosophical concepts, corpuses may be very various:  real instances of concepts, everyday language or scientific language expressions. Finally, we may also base the analyses on our own real or imagined expressions (our own intuitions). Let us add that the choice of corpus is to some degree dictated by the conceptual scheme (theory, paradigm) accepted by the analysts. Stage ii. Collecting and examining the corpus data. The corpus data are gathered and then compared, compiled, juxtaposed. In this process, one aims at listing the common properties of As (designates of “A”) and differentiating As from other objects. The reasoning used at stage ii is usually enumerative and eliminative induction. Stage iii. Definitional hypothesis (often stipulative in nature). In stage iii, one puts forward a hypothesis about essential properties of As. In other words, one answers the question of regarding the content of the concept of A (or what components of connotation of “A” are). This result is expressed in an analytic description of A (listing its essential properties) or in a definition of “A.” It is especially important to point out two features of stage iii. Firstly, this stage (as is emphasized especially by Czeżowski) is executed with the use of a certain kind of intuition. Sometimes, we need intuition to see which common features of As are essential properties of them. Sometimes,

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it is said that we have to intuitively see what is general in a certain particular object. Secondly, it often happens that this hypothesis is and even has to be somehow stipulative and constructive. It often happens that the proposed definition does not cover all corpus data either because the data are contradictory or because its seems that it is better to exclude some data from a theoretical point of view. Such stipulative or regulative conceptual changes are widespread in the natural sciences. (Consider the evolution of the concept of mammal, of acid, etc.) They may obviously also occur in philosophical reflection. Stage iv. Testing the consequences of the definitional hypothesis. At this stage, one draws consequences from the definition proposed in stage iii. These consequences may concern the objects from inside or from outside of the initial corpus. One also confronts the (re)constructed concept with other concepts in our conceptual scheme. This kind of investigation may lead to the conclusion that the hypothesis formulated in stage iii is somehow incorrect and has to be changed. For instance, it may turn out that the proposed definition does not cover some objects that we want to fall under the analyzed concept or vice versa: that some objects fall under the constructed concept but we do not want to have them in the scope of this concept. In such a situation, the whole procedure, or some stages of it, has to be repeated. It is easy to notice that this procedure falls under the hypothetico-​deductive model of reasoning in empirical sciences. Czeżowski was fully aware of this fact and indicated Galileo as the first who applied it; he also stressed that this method was commonly applied in Franz Brentano’s school (however with different problems). Now, let us shortly consider two examples showing how this method was applied in practice. 3.1.3 Example i: Łukasiewicz’s Analysis of the Concept of Cause Łukasiewicz’s goal (Łukasiewicz 1906) is to provide an analysis of the concept of cause. In the first part of the paper, he presents methodological remarks on the nature and analysis of concepts. What are Łukasiewicz’s conceptual tools? They are:  the theory of objects (consecutive and constitutive properties) and the theory of relations (as he considers causes and effects as arguments of some relations). He declares that he uses inductive and deductive reasoning. His inquiry may be structured in the following stages: Stage i. Łukasiewicz takes into considerations various statements or definitions of “cause” that occur in papers of philosophers and physicists. However, he

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also stresses that the concept he analyses is real and in every empirical discipline one has to rely on some real examples. (He gives three such examples: the flow of electricity is the cause of platinum wire heating, an impact on the heart of a man is the cause of his death, political disturbances are the cause of decline in the value of securities.) Stage ii. Łukasiewicz seeks common features of objects called “causes.” He compares the statements about and definitions of cause proposed by various scholars. He states that these formulas are contradictory. So, it would not be possible to formulate a definition of cause which embraces all gathered corpus data. Stage iii. The results of the stage ii lead Łukasiewicz to the conclusion that he should construct the concept of cause. His constructive definition reads: The cause is the first part of the relation of simple dependency, connecting real objects. Stage iv. Łukasiewicz indicates two criteria of correctness of the analysis of real concepts: their adequacy with reality and logical consistency. He states that the concept constructed by him satisfies these criteria. However, Łukasiewicz announces at the beginning: If such a discrepancy appears (scil. between the definition proposed and the current use of the word “cause”), I will not be able to remedy it. You just have to give up the habitof naming with the word “cause” something that does not fall under the concept of cause, just as you should give up the habit of naming with the word “carbonic acid” a chemical compound signified by “CO2,” which is not an acid, but an acid anhydride. łukasiewicz 1906, 16

Łukasiewicz was fully aware that his proposal had some counterintuitive consequences. We do not have space here to discuss it in detail but the discussion over Łukasiewicz’s proposal that took place in literature may serve as a kind of test of his definition. 3.1.4 Example ii: Twardowski on the Essence of Concepts We chose Twardowski’s paper “The Essence of Concepts” (Twardowski 1903/​ 1924) as a second example because, first of all, Czeżowski mentions Twardowski’s proposal as a paradigmatic example of analysis (in Czeżowski’s terms –​of analytic description, cf. Czeżowski 1953, 43). The paper was published in Polish in 1924 but it is based on a lecture delivered in German by Twardowski in Vienna, in 1903.

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Twardowski’s goal is to provide the definition of concept. His conceptual tools are: his theory of presentations and judgments, his conception of inductive and deductive reasoning, and his theory of introspection. The stages of the Twardowski’s analyses are as follows: Stage i. Twardowski accepts a broad concept of experience which covered both extraspection and introspection. The corpus for his analysis of the concept of concept is based in introspection. He takes into account two examples of concepts: the concept of a pentagonal lawn and the concept of a hectogon (a hundred-​sided polygon). However, Twardowski also makes use of existing definitions and conceptions of concepts as indirect data. Stage ii. The corpus data are –​at this stage –​gathered and then compared, compiled and juxtaposed in detail. Stage iii. Twardowski’s definitional hypothesis is: The concept is a whole consisting of two presentations: a background presentation and a presentation of a modifying judgment. Stage iv. At this stage, Twardowski points out the following advantages of his proposal: The theory that we are here advocating is recommended not only by the fact that it enables us to explain by means of a uniform principle all of the (abstract parts of) mental phenomena that ought to be regarded as concepts, but also by the fact that it receives unsolicited confirmation from the side of related but different views whose genesis it at the same time illuminates. twardowski 1903/​1924, 312

3.2 Method of Semantic Paraphrases 3.2.1 Sources The term “method of paraphrases” exists in the methodological reflection of the LWS first of all thanks to Jan Woleński’s monograph concerning it (Woleński 1985/​1989), where he uses this term4 in reference to some of Ajdukiewicz’s works. We would prefer to understand this concept more broadly in order to

4 NB, both in the Polish version of his book and in its English version, Woleński hesitates between using the terms “method of paraphrasis” (Woleński 1985/​1989, 64, 67), “method of paraphrasing” (Woleński 1985/​1989, 66), or “paraphrase method” (Woleński 1985/​1989, 77). We have decided to use here the term “method of paraphrases” consistently. Woleński applied this term to the characteristics of the lws; the term itself was in use earlier –​cf. eg. (Routley and Sylvan 1980, 552–​555); we omit of course the long history of the term “paraphrase method” in reference to biblical studies.

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incorporate into the scope of this concept also some other procedures applied in analytic philosophy, including Kotarbiński’s reistic paraphrases. To sketch out what this method consists of, we shall use Ajdukiewicz’s paper entitled “A Semantical Version of the Problem of Transcendental Idealism” (Ajdukiewicz 1937) as well as some of Kotarbiński’s investigations as examples. 3.2.2 Paraphrases: Description The aim of applying the method of paraphrases is to establish the value of some philosophical theses. An essential element of the method of paraphrases is providing a paraphrase, namely a certain equivalent, of the theses in question. The conceptual tools are theory of language, semantics, and metalogic. In particular, the stages of the method of paraphrases are the following: Stage i. Formulation of initial thesis T in language L. At this stage, thesis T is formulated and sometimes preliminarily specified in the original language (ordinary language or the language of a given philosophical investigation). Stage ii. The choice of language L’ for paraphrasing. In order for the paraphrase to be an improving procedure, the language L’ should be more perfect in a definite respect than language L. In particular, the dictionary or the syntactic rules of language L’ should be more precise than those of language L. Stage iii. Transforming thesis T to thesis T’ expressed in language L’. Thesis T’ is to be (intuitively?) equivalent to thesis T. Stage iv. Finding the theses formulated in language L’ which could be the basis for evaluating thesis T’. Stage v. Evaluation of thesis T’ by giving its justification, drawing consequences from it and testing these consequences, etc., based on the results of stage iv. 3.2.3 Example i: Ajdukiewicz’s Paraphrase of Transcendental Idealism Ajdukiewicz’s goal is to evaluate the thesis of transcendental idealism. His conceptual tools are some results of metalogic (its theorems and concepts). Stage i. The paraphrased thesis states: Reality is nothing but a correlate of the transcendental subject. This thesis is formulated in the language of transcendental idealism. It is initially specified by Ajdukiewicz as: All theses about reality are dictated by transcendental norms. Stage ii. Ajdukiewicz chooses the language of metalogic as the language of the paraphrase of the thesis established in stage I.

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Stage iii. He proposes the following paraphrase of the thesis from stage I: All true theses of natural sciences are logical consequences of the axioms adopted in these sciences. Stage iv. Ajdukiewicz uses some metalogical theorems to evaluate it. The theorems are: (1) The axiomatic system of arithmetic is incomplete, i.e., not all true sentences about objects of the domain of arithmetic are logical consequences of the axioms adopted in this system. (2) Arithmetic is part of every theory of the natural sciences. Thus (3) Every axiomatized theory of the natural sciences is incomplete. Stage V. In consequence, some true theses of the natural sciences are not logical consequences of the axioms adopted in these sciences. Therefore, the thesis of transcendental idealism –​as contradictory to the above consequence –​ is false. 3.2.4 Example ii: Kotarbiński’s Reistic Paraphrase Kotarbiński’s reistic paraphrases may be connected to the method of paraphrases in various contexts. What we would like to show is that the mere conception of reism may be interpreted in this framework. The first impulse that led Kotarbiński to the reistic position was included in his paper “The Question of the Existence of Ideal Objects” (Kotarbiński 1920), but he presented his reism as a doctrine for the first time in Gnoseology (Kotarbiński 1929/​1966). In a review of this book, Ajdukiewicz pointed out the fact that Kotarbiński had formulated two different versions of reism: ontological and semantic. The ontological thesis is: (RO) Only things exist. While the semantic one (in some interpretations) reads: (RS) Every senseful sentence is either a sentence in which all names are names of things or one which may be paraphrased into a sentence in which all names are names of things. Kotarbiński and his followers accepted the distinction between ontological and semantic aspects of reism. However, Kotarbiński hesitated about the relation between (RS) and (RO), and in particular, whether (RO) justifies (RS) or vice versa. In our opinion, (RS) can be considered a kind of paraphrase of (RO), and using (RS) for justifying (RO) falls under the scheme of the method of paraphrases. Let us look at it. Stage i. Formulation of initial thesis T in language L. The initial (ontological) thesis of reism is RO.

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Stage ii. Kotarbiński chooses the language of semantics (or logical semiotics) as the language of paraphrasing the original formula. Stage iii. The ontological thesis of reism takes the (semantic) form: RS. Stage iv. The key question here is, of course, whether a given non-​reistic sentence can be paraphrased to an equivalent reistic sentence. Kotarbiński gives some examples of sentences containing abstract names which are transformed by him into sentences with concrete names only: Whiteness is a property of snow. The love of Romeo and Juliet was passionate. The eruption of the Vesuvius was sudden.

Snow is white. Romeo and Juliet loved each other passionately. Vesuvius erupted suddenly.

Of course, these are only some examples which do not justify the general thesis RS. In fact, Kotarbiński’s critics pointed to the existence of many sentences that cannot be transformed into reistic ones (for instance, some mathematical sentences or sentences about social facts). However, at that point, Kotarbiński claimed that his examples justify T’ sufficiently. Stage v. According to Kotarbiński (in some interpretations of reism), the thesis RS which he thought to be true, justifies Ro. Against Kotarbiński, the examples given in stage iv do not prove the truthfulness of RS. The other problem of reism is the lack of criteria for correct paraphrasing one sentence with another. Moreover, in order for this conception to be useful, one needs the criteria of sensefulness to be formulated outside the doctrine of reism. 3.3 Axiomatization 3.3.1 The Description of Method Let us quote Łukasiewicz who gave an extensive description of axiomatization as a philosophical method in his paper “For a Method in Philosophy”: The future scientific philosophy must derive its construction from foundations. To start with the foundations means to carry out a review of philosophical issues and choose from them only those issues that can be formulated in a comprehensible way and reject all others. […] Then one has to attempt to solve these philosophical issues that can be formulated comprehensibly. The most appropriate method that should be used for this purpose seems to be the […] method of mathematical logic: the

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deductive method, the axiomatic method. One must rely on sentences, as intuitively clear and certain as possible, and accept such sentences as axioms. As a primary or undefined concept, one should choose such expressions, the meaning of which can be comprehensively explained by examples. It is necessary to try to make as few axioms and original notions as possible and to enumerate them all exactly. All other concepts must be unconditionally defined on the basis of original notions, and all other theorems unconditionally proved on the basis of axioms with the help of the rules of proof adopted in logic. The results obtained in this way should be constantly checked against the data of intuition and experience and with the results of other disciplines, especially the natural sciences. Łukasiewicz 1928, 42

The goal of axiomatization (in philosophical investigations) is to provide a mature form for philosophical theories, to scrutinize reasonings, and to draw consequences from accepted theses. Conceptual tools are the tools of mathematical logic, metalogics, semantics, etc. The stages of axiomatization are: Stage i. Choosing primitive terms. Stage ii. Searching for axioms. Stage iii. Defining derived terms on the basis of primitive ones. Stage iv. Deriving some theorems from axioms. Stage v. Comparing the results with the data received thanks to intuition, experience, empirical sciences. 3.3.2 Example i: Łukasiewicz’s Three-​Valued Logic Łukasiewicz’s three-​valued logic may be examined as a purely logical result without any philosophical interpretation. However, Łukasiewicz admitted that his system had strong philosophical inspirations. In fact, he would like to provide a system of logic which would support his indeterministic intuitions, according to which there are some sentences with indeterminate logical value. Łukasiewicz’s tools are:  concepts, principles, directives of mathematical logic and logical matrices. Stages: as indicated above. The difference between the two-​valued logic and the three-​valued logic lies in the choice of axioms, and also in the interpretation (semantics) of the calculus defined by the truth matrices; in addition to the values 0 and 1,there is also the value ½. For example: On the ground of two-​ valued logic, the formula “p iff not-​p” is a contradiction. However, on the basis

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of three-​valued logic, it is not a contradiction, because if “p” has the third value (½), then “not-​p” has also third value (½). Regarding the stage of comparing the results with the data (V), Łukasiewicz shows that his three-​valued logical system corresponds with indeterministic intuitions. The value ½ is ascribed to the sentences which, intuitively speaking, are determined neither as true nor as false. 3.3.3 Example ii: Leśniewski’s Mereology Leśniewski’s goal is to present the theory of part and whole in a formalized way. As in the previous case, concepts, principles, and directives of mathematical logic are his tools. Stages: as indicated above. Regarding the stage of comparing the results with the data (V), Leśniewski demonstrates that his system corresponds with nominalistic conceptions and does not expose itself to the paradoxes of set theory. 4

General Comments on the Methods of Philosophy in the lws

4.1 Relations between Methods In the previous sections, three methods of dealing with philosophical problems that were used in the LWS are presented. These are: the analysis of concepts, the paraphrase of sentences and the axiomatization of theorems. Now, let us add some comments on relations between these methods and their peculiarities. There are some obvious connections between the methods described in § 3. For instance, it occurs that the method of analysis of concepts is a local method with respect to paraphrase or axiomatization. On the other hand, paraphrasing some theses from one language into another may sometimes be applied as a step of comparing the corpus data of analysis. Analysis, paraphrase and axiomatization also have some important common methodological features. Firstly, in each of them an important role –​at some stage –​is played by intuition. In the analysis, while trying to formulate a definitional hypothesis –​one needs the intuition of generality to assign some entities to the same category. In the paraphrase, intuition is necessary to deliver the justification of the paraphrase. In axiomatization, intuition plays an important role in the choice and control of axioms. Secondly, none of described methods is an infallible method of solving philosophical problems. Analysis of concepts may serve to make vague problems clearer and to deliver a conceptual scheme. Paraphrase may help to express old

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problems better. But the results of analysis are only hypothetical and there are no strict ways of evaluating paraphrases. Concerning axiomatization, it seems that Łukasiewicz was too optimistic in evaluation of this procedure. Given a complete system of axioms and rules of inference, we may state infallibly whether a given thesis follows from these axioms or not. However, we do not establish axioms in any infallible way. Łukasiewicz was fully aware of that and that the consequences of axioms inherit this feature –​and that is why they need to be controlled with other data. 4.2 Methodological Peculiarities of the lws In the LWS, traditional problems of philosophy were not refused or treated as senseless. On the contrary, they were analyzed seriously and resolved or at least clarified. Certainly, analysis of concepts, paraphrase of theses and axiomatization/​ formalization of theories serve the main and general postulates of the lws: the postulate of precision and justification. Moreover, it is easy to notice the linguistic approach to problems and the trust in the instruments of logic (broadly understood). These are elements common to the members of the lws and other groups of early twentieth-​century analytic philosophy, especially those of Cambridge and Vienna. However, let us now consider whether the analyses presented above add something to the question of the methodological peculiarities in the lws. A distinctive property of conceptual analysis in the LWS was its (re)constructive character. While George E. Moore’s analysis required that analysans be equivalent to analysandum, Łukasiewicz’ requirements were different: the concept constructed must be adequate to some part of experience and has to fulfill logical criteria but do not have to be, and sometimes even cannot be, simply reporting. The scheme of reconstructive analysis reminds one of Carnap’s rational reconstruction and his conception of explication; however, Carnap’s ideas were formulated much later. A distinctive feature of the method of paraphrases is its semantic character. Let us stress that the investigation here aims not (only) at establishing the logical form of initial expressions –​at least not in the sense in which Barbara Stanosz and Adam Nowaczyk talk about the logical form: In practice, the logical reconstruction of a language (e.g., of a certain scientific theory) consists in giving it the form of the language of functional calculus. The logical form (structure) of a given sentence then is represented by a logical scheme corresponding to the translation of this sentence into the language of functional calculus. The condition for the

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adequacy of the translation is the preservation of inferential relationships, which in the language of functional calculus are governed by the formally defined relations of the (logical) consequence. Stanosz and Nowaczyk 1976, 110

Paraphrases are not just syntactic schemas of paraphrased sentences; the former are semantic analogues of the latter. Finally, the program of axiomatization of philosophy was something unique and typical for the lws. Of course, this program was not completed by the early generations of the lws (in fact, Łukasiewicz was aware that this was a project for many generations). However, the history of logic and its applications in the 20th century shows that this program has partially achieved many successes (even if not always in a direction of which Łukasiewicz would have approved).

References

Ajdukiewicz, K. 1937. A Semantical Version of the Problem of Transcendental Idealism. In: K. Ajdukiewicz. 1978. The Scientific World-​Perspective and Other Essays. 1931–​1963. Dordrecht: D. Reidel Publishing Company, 140–​154. Czeżowski, T. 1953. On the Method of Analytic Description. In:  T. Czeżowski. 2000. Knowledge, Science, and Values. Amsterdam, Atlanta: Rodopi, 42–​51. Jadacki, J. 1997. The Conceptual System of the Lvov-​Warsaw School. In: J. Jadacki. 2009. Polish Analytical Philosophy. Studies on its Heritage. Warszawa: Wydawnictwo Naukowe Semper, 68–​76. Kotarbiński, T. 1920. Sprawa istnienia przedmiotów idealnych[The Question of the Existence of Ideal Objects]. In: T. Kotarbiński. 1958. Wybór pism [Selected Writings]. Vol. ii. Myśli o myśleniu [Thoughts of Thinking]. Warszawa: pwn, 7–​39. Kotarbiński, T. 1929/​1966. Gnosiology: The Scientific Approach to the Theory of Knowledge. Wrocław, Oxford: Ossolineum, Pergamon Press. Łukasiewicz, J. 1906. Analiza i konstrukcja pojęcia przyczyny [Analysis and Construction of the Concept of Cause]. In:  Łukasiewicz 1961, Z zagadnień logiki i filozofii [Some Problems of Logic and Philosophy]. Warszawa: PWN, 9–​62. Łukasiewicz, J. 1928. O metodę w filozofii [For a Method in Philosophy]. In: Łukasiewicz 1998, 41–​42. Łukasiewicz, J. 1998. Logika i metafizyka [Logic and Metaphysics]. Miscellanea. Warszawa: Wydział Filozofii i Socjologii UW. Routley, R. and R. Sylvan. 1980. Exploring Meinong’s Jungle and Beyond: an Investigation of Noneism and the Theory of Items. Canberra: Australian National University.

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Stanosz, B. and A. Nowaczyk. 1976. Logiczne podstawy języka [Logical Foundations of Language). Wrocław: Ossolineum. Twardowski, K. 1903/​1924. “The Essence of Concepts”. In: K. Twardowski. 1999. On Actions, Products and Other Topics in Philosophy. Amsterdam, Atlanta:  Rodopi, 73–​97. Woleński, J. 1985/​1989. Logic and Philosophy in the Lvov-​Warsaw School. Dordrecht: ­Kluwer Academic Publishers.

pa rt 2 Historical Research and Its Methods

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­c hapter 4

From Methodenstreit to the “Science Wars” –​ an Overview on Methodological Disputes between the Natural, Social, and Cultural Sciences Friedrich Stadler Abstract The so-​called classical “Methodenstreit,” which originated in economics with Carl Menger and Gustav Schmoller in 1883 was followed by several variants beginning with the historical sciences in the last decade of the 19th century. One highly contested question in terms of methodology was the existence, role and function of laws in history and the cultural sciences as necessary elements of any possible historical (causal) explanation –​an alternative methodology to an exclusively intuitive understanding (Verstehen) claimed by the proponents of German historicism (Historismus) and the humanities (Geisteswissenschaften). Throughout further methodological debates during the last century we can see the recurrence of similar topics in the sciences as well as in the philosophy of science in different contexts without any consensus about the basic dispute. The following article is an attempt to reconstruct this ongoing debate in more detail and to provide a first overview of the several variants of Methodenstreit with the continuous central question, whether there is one unified science as a regulative conception covering humanities with one scientific method or not. To date, the research literature is dealing only with specific manifestations of this issue. My argument is that the main issues recurring in the history and philosophy of science of the 20th century are manifestations of central, still unresolved methodological and epistemological problems which can be investigated from a meta-​theoretical as well as a contextual point of view.

Keywords Methodenstreit  –​methodological debates  –​positivism dispute  –​historism  –​ ­historicism  –​scientific explanation and understanding  –​science and humanities  –​ history and philosophy of science –​cultures of science –​“Science Wars”

78 Stadler 1

Preview

The so-​called classical “Methodenstreit,” which originated in economics with Carl Menger and Gustav Schmoller in 1883, was followed by several offshoots beginning with the historical sciences in the last decade of the 19th century. The contested methodological question was the existence, role and function of laws in history and the cultural sciences as necessary elements of any possible historical (causal) explanation –​an alternative methodology to the exclusively intuitive understanding (Verstehen) championed by the proponents of German historicism (Historismus) and the humanities (Geisteswissenschaften). Max Weber can be seen as the first to mediate between the two currents arguing in favor of a unification of the cultural and social sciences. This still unresolved dispute will be reconstructed and evaluated in the context of scientific explanation in 20th century philosophy of science. Throughout the following methodological debates during the last century we can see similar topics reappearing in the sciences as well as in the philosophy of science in different contexts without any consensus so far. The following article is an attempt to trace this ongoing debate as a preliminary study and sketch for further investigations. Without doubt, each manifestation of the Methodenstreit would deserve a separate closer investigation, hopefully to be elaborated in the near future within the interdisciplinary research field of history and philosophy of science. 2

Overview on the Variants of Methodenstreit

The Methodenstreit in economics between the Austrian School and the Historical School in the German Empire commenced in 1883. The main opposing figures were Carl Menger and Gustav Schmoller, who was a proponent of the then dominant historicism (Historismus) in historiography and the historical studies. Its research program was accompanied by the philosophical input of Gustav Droysen, Wilhelm Dilthey, Wilhelm Windelband and Heinrich Rickert. The subsequent controversies in historical studies between 1891 and 1899 became manifest in the dichotomy of understanding and explaining –​with Georg von Below and Friedrich Meinecke vs. Karl Lamprecht and Ludo Moritz Hartmann as the conflicting historians, and continued with Max Weber who took a mediating stance regarding the question of a dualism or unification of the social and cultural sciences. We find these dualisms again in recent research literature (Ute Gerhardt and Fritz Ringer) on the role and function of Weber’s ideal

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type as a methodological and epistemological model (Gerhardt 2001; Ringer 1997). The discussion can be seen as transcending disciplinary boundaries if we focus on the philosophical assessments of Moritz Schlick, Felix Kaufmann, Richard von Mises and Karl Popper. Again, after WW II, there was a dispute on historical explanation in connection with the Hempel-​Oppenheim-​Scheme (Covering Law Model), which was dealt with critically by Wesley Salmon’s re-​ consideration in the philosophy of science. The reflection on these issues in philosophy of science led up to the Methodenstreit of the “Science Wars,” to be described later on. Let us take a closer look at these controversies and their overlapping topics: In economics we already see the alternatives of a historicization (history of economics equates political economics as a scientific discipline) or axiomatization, induction or deduction vis-​à-​vis the priority of history in economics. And there seemed to be a recurrence of this topic in jurisprudence and legal studies from the 19th to the 20th century with the opponents Rudolf Stammler and E.I. Bekker from 1888 onwards, with a second round unfolding with Carl Schmitt vs. Hans Kelsen since 1933. Even after WW II a fictitious controversy re-​appeared between Johannes Messner and Hans Kelsen with reference to the tension between a historical description vs. normative justification, (Christian) natural law vs. pure theory of law (including the dualism of “is” and “ought”). (Topitsch/​Messner 1966). These case studies prove very instructive for today’s methodological discussions: in the historical sciences and historiography at the end of the 19th century (Georg von Below vs. Karl Lamprecht) we recognize the limits of historicism as compared to the “Culturgeschichte” (actually, a social and cultural history). The two worlds of understanding (intuition) vs. causal explanation with historical laws emerged parallel to the formation of the Geisteswissenschaften opposing the emerging field of materialism, positivism and ­evolutionary theory. It is the old story of the dualism between idiographic humanities and nomothetic sciences as a manifestation of two exclusive worlds and methodologies. Therefore, it is not really surprising that this alternative also became manifest in the value dispute (Werturteilsstreit) in German sociology, 1909–​1914. Here, Max Weber defended, against Gustav Schmoller, scholarship without values (Wertfreiheit) aiming at objectivism, although values are inevitable in this procedure. The oppositions of facts and norms, is and ought, sciences and Weltanschauung (ideology), knowledge and action, were linked to the concept of the ideal-​type (Idealtypus) as a methodological instrument, at least for the cultural and social sciences. This debate without an agreement between the competing camps was partly present again after WW I in the dispute regarding sociology of knowledge in 1928 ff., when Max

80 Stadler Scheler and Karl Mannheim provoked heated replies by Austro-​Marxists (e.g., Otto Neurath) on the one side, and philosophers of the humanities, on the other. Herein we can identify well known elements like historicism and relativism, skepticism, and cultural pessimism as targets of an objective and foundational claim in the sciences. A special story is related to the three variants of disputes regarding “positivism” in the 20th century, which is more or less a misnomer regarding the contents of their direct and indirect discussions because the term “positivism” was used as a contested cultural label in an ideological context –​with attributions or rejections of the addressed proponents and “schools.” In the first variation with the attack of W.I. Lenin on Ernst Mach’s alleged positivism entitled Materialism and Empirio-​Criticism. Critical Remarks on a Reactionary Philosophy (in Russian 1909) we already see the politics-​driven argumentation of a crude dualistic scheme between Marxism-​Leninism and Austro-​Marxism (including Friedrich Adler and Otto Neurath), as well as the proletariat and bourgeoisie, and (historical and dialectical) materialism/​realism and positivism/​idealism. This was an attack on the strong Avenarius-​Machian movement in pre-​ revolutionary Russia represented by Mensheviks and Bolsheviks. According to Philipp Frank, this claim was anachronistic, because it adhered to traditional metaphysical “school philosophy” beyond any contemporary research in the sciences like quantum physics or relativity theory. One generation later this opposition between dialectical materialism and a logical-​empirical approach towards modern sciences was revived by Max Horkheimer’s attack on Otto Neurath in exile in 1935. Here again we can detect the split between a dialectical metaphysical-​realist philosophy (“critical theory”) and an anti-​metaphysical unified science, which also included the historical and social sciences (as a publication project, the International Encyclopedia of Unified Science)  –​conceived of in the tradition of the French Encyclopédie. Despite an earlier communication on joint future projects, this interaction ended abruptly with Horkheimer’s article “The Most Recent Attack on Metaphysics” in 1937 (written in German as “Der neueste Angriff auf die Metaphysik”), in spite of the fact that Neurath provided a reply (“Einheitswissenschaft und logischer Empirismus”) as an invitation to continue with a cooperation of the two “schools” –​which Horkheimer refused to publish in the same journal Zeitschrift für Sozialforschung (Dahms 1994). Only in US exile did both camps come together, e.g., with Edgar Zilsel’s projects on the origins of modern science (Stadler 2018). The issue of the unity and diversity of the sciences and humanities still appeared on the agenda after WW II and culminated after the publication of P.C. Snow’s lecture on The Two Cultures in 1959 (Snow 1959/​1964). This fervent

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appeal for the acknowledgment of modern science and technology in the camp of British-​American writers and intellectuals triggered off a heated debate on the role and function of literary criticism and the humanities vis-​à-​vis the dynamic natural sciences, covering quantum physics and relativity theory. It was also a manifestation of an ideological dispute in the Cold War period with the socio-​cultural decline being lamented given the alleged widespread ignorance of scientific-​technological achievements on the side of literary scholars and journalists. This transatlantic controversy continued until the 1960s and was echoed in the book of the German sociologist Wolf Lepenies who dealt with “Three Cultures” of natural science, social science, and the humanities/​literature by comparing the UK, France and Germany (Lepenies 1985). In each of these scholarly cultures the author identified progressive and conservative tendencies, with positive or negative attitudes towards the Enlightenment reflecting national thought styles. In German sociology, at the beginning of the roaring 1960s, the third, so-​ called “positivism dispute” emerged as a confrontation between the last generation of the Frankfurt School (Adorno and Habermas) and proponents of Critical Rationalism (Karl Popper and Hans Albert). This took place during a conference in 1961, followed by the notably expanded proceedings published only eight years later in the context of the international 1968 movement (Adorno et al. 1969). This book was translated into English, resulting in an enormous polarization between the left-​wing student generation and the traditional conservative philosophy as a legitimation of a liberal “capitalist reasoning” (1976). The political context blurred the real commonalities and differences to be found in the application of scientific methods in the social sciences and the limits of a “bourgeois” non-​dialectic methodology. Again, the (dis)unity of the sciences in terms of methods was on the agenda of this unresolved controversy between neo-​Marxists and social-​liberal philosophers which ended up without any agreement. The two options of a “critical theory” and a “critical rationalism” certainly did not address any topic of the labelled “positivism” dispute. But it was the focus of Paul Feyerabend’s best-​selling book, Against Method (1970), originally planned as a joint book project together with Imre Lakatos who died unexpectedly during the publication process. Feyerabend’s criticism of a merely abstract and normative philosophy of science as represented by Karl Popper had already begun in the famous London conference at the lse in 1965, when Thomas Kuhn, Imre Lakatos, Paul Feyerabend, Rudolf Carnap and Karl Popper addressed the tension between the context of discovery and the context of justification –​a distinction going back to Hans Reichenbach`s book Experience and Prediction (1938). It was the question of a linear progress

82 Stadler with rationality vs. a historical conception of science and philosophy of science with a relativistic and sociological approach to scientific enterprise, and last not least, unity or plurality of methods. A late reverberation and renaissance of all these disputes emerged at the end of the 1990s under the martial label of “science wars,” when the natural scientists Alan Sokal and Jean Bricmont in their book Fashionable Nonsense. Postmodern Intellectuals’ Abuse of Science (1998) accused British and American postmodernist philosophers, French intellectuals, proponents of post-​ structuralism, and feminist philosophers of science (e.g., J. Lacan, B. Latour, J.  Baudrillard, G.  Deleuze, P.  Virilio) of ignorance and misuse of science in philosophy and the humanities. This was initiated by the preceding so-​called “Sokal hoax” (1996), when Sokal submitted a fictitious text written in postmodern rhetoric to a journal which was accepted for publication. The book mainly addressed the alternatives between rationality and constructivism, objectivity and relativism, truth and convention, science and literature, and the narrative turn vs. scientific explanation (rational reconstruction). This new variation on another Methodenstreit allowed one to question the differences and common elements of all these past controversies. The need for an explicit theory of truth was postulated, provoked by an avalanche of titles such as On Bullshit and On Truth (booklets by Harry Frankfurt, 2005 and 2006). It seems that these controversies were not manifestations of a trivial power politics but rather the need for a “science in context” (covering epistemology and methodology), to be illustrated by concrete case studies in the history of philosophy and science. Let us delve deeper into the specific disputes, which to date are mostly still unresolved. 3

Some Variants of the Methodenstreit

Methodenstreit in Economics 1883 ff.: the “Austrian School” vs. the German “Historical School” The founder of the Austrian school of economics, Carl Menger (1840–​1921), followed by Ludwig von Mises and Friedrich A. von Hayek, presented a subjective marginal utility theory, based on methodological individualism, self-​ organization and market liberalism. This theory of subjective value towards economic commodities was also directed against the Marxist value and exploitation theory in the sense that it advocated an axiomatic and deductive methodology as opposed to any historical explanation and empirical inductivism, as was on the agenda of the German school represented by Gustav Schmoller (1838–​1917). Menger’s position was mainly directed against the 3.1

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dominant paradigm of historicism (Historismus), also seen as a manifestation of German nationalism before WW I. But in the second generation of the “Austrians” with Hayek’s criticism of “scientism” as an absolute norm of the natural sciences, there was another argument claim for the division of science and humanities, at least regarding two different scientific methods. In this quarrel Hayek’s good friend Karl Popper did not share the Austrians’ view, since he defended one method for all sciences (except history and historical studies), namely his hypothetico-​deductive falsificationism as one element of critical rationalism (claiming a modest state policy in favor of a social welfare state). Ludwig von Mises, who strongly attacked any form of socialist planning theory and practice, arguing against Otto Neurath, concluded later on in his “The Historical Setting of the Austrian School of Economics” (1969, 12) that: The term “Methodenstreit” is, of course, misleading. For the issue was not to discover the most appropriate procedure for the treatment of the problems commonly considered economic problems. The matter in dispute was essentially whether there could be such a thing as a science, other than history, dealing with aspects of human action (https://​mises. org/​library/​historical-​setting-​austrian-​school-​economics). Just this aspect of human action, with the contested assumption that each action is by itself rational, can be interpreted in the frame of a conventionalist conception, even if it is axiomatic in essence (Linsbichler 2017). This would make it possible to see a closer family resemblance between the two camps in historical context beyond rigid school historiographies. As for the historical dispute, the differences may be reconstructed, as proposed by Backhaus and Hansen who claim that: For Schmoller, two issues were central: to use economics […] as an instrument for economic policy; and to base the science empirically with all the methods available. In contrast, the Austrian position had a different view of economics as a science, seeing it more as a system of ideas, which implies a radically different use of empirical evidence. backhaus and hansen 2000, 307

We get a better understanding of this clash if we describe the related paradigm and research program of German historicism (Wittkau 1992). Its main characteristic features were the principal historicization of knowledge (any knowledge is embedded in the historical context), the concept of man and society

84 Stadler as a counterpart to nature and therefore naturalism with the framing thematic triangle of development, temporality, and individuality. An underlying relativism resulted from history being conceived as scale and frame for truth and falsity in general, which became manifest in the articles of the (still existing) journal Historische Zeitschrift (HZ). Methodologically, history was presented as a scientific discipline aiming at objective knowledge, employing hermeneutics and philology with intuitive understanding/​description (as counterparts to causal explanation). The method of understanding is closely linked to the rise of hermeneutics in the humanities (Geisteswissenschaften). It is aiming at the meaning of a text via interpretation or the meaning of an individual’s action via intuition and introspection by the interpreter. The intended result of such a procedure was the individual understanding (not causal explaining) of a single historical event or fact. The underlying dualism of facts and laws corresponded to that of induction and deduction. In order to make history scientific vis-​à-​vis the natural sciences, auxiliary subdisciplines (historical Hilfswissenschaften) were established in the historical seminars at German universities with a distinct research program: the main topics referred to covered elites and “great men,” individuals, power politics, nations and states, ideas, and Euro-​centric diplomatic and political history, written on a web of historical facts as single events. The problems of this ambitious program became apparent at the dawn of wwi in the German nationalist context. It stimulated the question of a unique “German way” (Deutscher Sonderweg), according to Georg Iggers (1996), or of still being capable of a modernized historical science, according to Jörn Rüsen (1992). Despite these differing interpretations the unresolved issues are still also being discussed in other fields of scientific disciplines. The fortunes and limits of relativism is on the agenda as is the tension of theory and practice already introduced by Max Weber with his value-​freedom postulate. The methodological and epistemological unity or plurality of all sciences was addressed especially in the historical sciences, where the alternative of a nomothetic structural and social history (Karl Lamprecht) emerged as a counter-​narrative to German historicism, partly mediated by Max Weber. In contemporary discourse these positions can be identified in the field of history among neo-​Marxist proponents (Hobsbawm 2001), the Annales-​school (Bloch 2002) and Social History (Hans Ulrich Wehler and Jürgen Kocka). But there was also a genuine philosophical background to all of these disciplinary controversies, so that we can speak of a more general theoretical grounding of these phenomena.

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Methodenstreit in the Historical Sciences 1891–​1899: Understanding vs. Explaining We also see a sort of recurrence of this philosophical divergence in historiography and the historical studies of this time, as can be exemplified by the “cultural historian” Karl Lamprecht (1856–​1915), who was Professor of History in Leipzig, 1891–​1915, and provoked the rage of the community of German historians of historicism. His books on German History comprising 12 volumes (Deutsche Geschichte 1891–​1909), were the starting point of the historical Methodenstreit (1891–​1899), also called the Lamprecht dispute (“Lamprecht-​Streit”). In addition, titles like “What is Cultural History? Contribution to an Empirical History” (“Was ist Kulturgeschichte? Beitrag zu einer empirischen Historik,” 1896/​ 97), or Modern Historical Science (Moderne Geschichtswissenschaft, 1905) reinforced the heated reaction of his dominant colleagues. Politically of a national-​ liberal attitude, Lamprecht conceived his “Culturgeschichte” as incorporating the totality of social, economic, political and mental phenomena. This historiography was a prototype of socio-​economic historiography (regional studies), introducing explanations with social-​psychic regularities (influenced by W. Wundt’s ethno-​psychology) and laws. It is not surprising that Lamprecht found followers and adherents in the US, the UK, and in France, especially in the school of the Annales (Chickering 1993; Burke 1991). The counter-​community was led by the historian Georg von Below (1858–​1927), who accused Lamprecht of adhering to Darwinism, positivism, naturalism and historical materialism. As a conservative historian he privileged the political and individual factor in history, against any developmental and lawlike historical explanation, and distanced it from Enlightenment and sociological thinking. He was supported by the national-​republican historian Friedrich Meinecke (1862–​1954), the founder of the history of political ideas and editor of the most influential periodical Historische Zeitschrift. In his book on the genesis of historicism (Die Entstehung des Historismus, 1936), Meinecke focused on the discovery of the individual as directed to collective entities in history. It is worth mentioning here that an “Austrian Lamprecht” existed in parallel, the historian and (German-​republican) politician Ludo Moritz Hartmann (1865–​1924): as a representative of Social Democracy he worked mainly outside the university as an historian, sociologist, politician, and adult educationist. He was a private lecturer (Privatdozent) of Roman History and History of the Middle Ages, becoming an extra-​ordinary professor at the University of Vienna only in 1918, and in the last year of his life he was appointed professor at the University of Vienna. In the republican era he served as an ambassador in Berlin 1918–​1920 with the aim of the unification of Germany and Austria. His research fields cover Italian history (of the Middle Ages) and global history 3.2

86 Stadler embedded in a monistic world view with a unity of method, and claiming the methodological principle of economy as a convinced adherent of Ernst Mach. This historical method, as a clear alternative to German historicism, strived for an explanation based on historical materialism and evolutionary theory, typological comparison, and interdisciplinarity as a methodological innovation. This was the birth of historical sociology, socio-​economic history, and social history, offering explanations based on laws and law-​like trends. Hartmann preferred the collective over the individual in his global history and practiced a bottom up popularization of science between enlightenment and democracy, nevertheless claiming objective knowledge following his role models Darwin, Marx, and Mach. In Austria, he was certainly one of the pioneers of social and economic history (Fellner 1985). The Renaissance of Historical Explanation: the Hempel-​ Oppenheim-​Scheme Revisited Carl G. Hempel, in his “The Function of General Laws in History” (1942), reprinted in Aspects of Scientific Explanation and other Essays in the Philosophy of Science (1965), presented a model of explanation which became known as the Hempel-​Oppenheim-​Scheme, or the Covering-​Law-​Model (clm), in which he extended Max Weber‘s methodical unification efforts: 3.3

First, the separation of ‘pure description’ and ‘hypothetical generalization and theory-​construction’ in empirical science is unwarranted; In the building of scientific knowledge the two are inseparably linked. And, second, it is similarly unwarranted and futile to attempt the demarcation of sharp boundary lines between different fields of scientific research, and an autonomous development of each of the fields. The necessity, in historical inquiry, to make extensive use of universal hypotheses of which at least the overwhelming majority come from fields of research traditionally distinguished from history is just one of the aspects of what may be called the methodological unity of empirical science. hempel 1965, 243

The subsequent refinements with deductive-​ nomological and inductive-​ statistical explanations, etc. did not prevent historians and philosophers of the humanities from rejecting this basic unifying option. The historical explanation within the framework of the clm was subsequently elaborated and diversified:  as causal explanation with functional and intentional-​teleological sub-​categories, and as historical-​genetic explanation. Hempel himself offered the concept of rational explanation as a type

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of dispositional explanation. Nevertheless, the criticism continued with some variations and adaptions. The controversy ended up in the long run because historians did not use the clm and their historiography contradicted the methodology of the philosophy of science. Last not least, there was the question as to what should be explained (facts, mass data, trends, laws etc.), or understanding all as a pro/​con game vis-​à-​vis hermeneutics and interpretation. In 1989 Wesley Salmon reconstructed and further described “Four Decades of Scientific Explanation” since 1948 (in memory of Carl Hempel and Herbert Feigl): –​ He characterized the first decade as “Peace in the Valley,” including explanation in history and prehistory (11). –​ The second decade is described as an expansion and conflict regarding statistical explanation with objections to the Deductive-​Statistical-​Model and the Inductive-​Statistical-​Model (33). –​ The third decade is presented as deepening the differences, followed by the fourth decade, described as “a time of maturation” (61 and 117). Five years earlier, Salmon had already reconstructed a development from statistical relevance (SR) to the causal-​mechanical model (CM). Philipp Kitcher (1989) argued in favor of an unificationist model via “Explanatory Unification and the Causal Structure of the World” (410–​505). –​ As the topic for the fifth decade Salmon draws on the open problem of law-​like statements with purely qualitative predicates and probabilistic ­causality. With regard to the problems raised by the Einstein-Podolski-Rosen (epr) ­paper regarding explanation in quantum physics Salmon concedes: “To provide a satisfactory treatment of microphysical explanation constitutes a premier challenge to contemporary philosophy of science” (Salmon 1989, 186). Independently, there was once again the issue concerning history and explanation in the historical sciences after the linguistic, pragmatic, historical and narrative turns (if history is a science like New Archaeology according to Salmon’s judgment). The Philosophical Background of the Methodenstreit: Mach, Vienna Circle, Feyerabend One of the main German philosophers of the 19th century, Wilhelm Windelband (1848–​1915), postulated the unity of reality, while also claiming an absolute (a priori logical) distinction of the methods of the natural and social/​ cultural sciences. Whereas the former stick to a nomothetic and generalizing method dealing with laws and general relations, the latter are committed to an ideographic method via intuitive understanding. This dualism was specified 3.4

88 Stadler by Wilhelm Dilthey (1833–​1911), who divided reality by means of a corresponding dualism of science (Naturwissenschaften) and the humanities (Geisteswissenschaften), dealing with the exclusive research-​subjects of nature and mind (with the opposition Natur vs. Geist). Accordingly, the neo-​Kantian philosopher Heinrich Rickert (1863–​1936) presented a conception of the historical-​cultural sciences in his seminal book The Limits of Concept Formation in Natural Science (Die Grenzen der naturwissenschaftlichen Begriffsbildung. Eine logische Einleitung in die historischen Wissenschaften, 1902), which influenced Max Weber’s methodology of ideal-​types. This programmatic book with its dualistic conception of the sciences prompted Moritz Schlick, the later founder of the Vienna Circle, to adopt a critical position. Schlick, who attended lectures of Dilthey in Berlin, criticized Windelband and Rickert in his article “Die Grenzen der naturwissenschaftlichen und philosophischen Begriffsbildung” (The Boundaries of Scientific and Philosophical Concept-​Formation, 1910/​11) by combining understanding and explaining and by separating quantitative and qualitative relations as follows: 1. The boundaries between the sciences are mobile, and tend towards a fixed end-​state, which ought to be defined. –​Science consists not in establishing and knowing facts, but in conjoining the latter by means of laws. 2. The method of exact science consists in reducing all regularities to purely quantitative spatio-​temporal relationships, while eliminating qualities so far as possible. 3. This method is applicable to all natural happenings, up to the point at which it encounters irreducible qualities. 4. Philosophy is the doctrine of qualities. 5. Psychology, despite experimental methods, can never be made subject to the scientific type of concept-​formation. 6. Comparison of the present definition of philosophy with other ­definitions. And finally, he concludes that: 7. Scientific and philosophical concept-​formation do not constitute an irreconcilable opposition:  the former is reducible to the latter (Schlick 1910, 25). With regard to Rickert’s distinction, Schlick rejects the separation of the historical from the natural sciences based on the dualism of facts and laws. Mach (1838–​1916) was as a pioneer and reformer of the history and philosophy of science, since he stressed the historical and pragmatic dimension of all sciences. He worked as a physicist (where he influenced Einstein’s relativity theory with his relativistic “Mach principle”), a psychologist, a historian of

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science and a “scholar of nature” (Naturforscher) against academic metaphysical philosophy with the early declaration that Classical education is essentially historical education. […] Yes, there is a special cultural education for the natural scholar, which consists in the knowledge of the development of the history of his science. Let us not let go of history‘s guiding hand. History has made all, history can alter all. Let us expect from history all. mach 1872/​1911, 18

Regarding the methodological dispute, Mach defended a methodological strategy covering induction, abduction, and deduction, but he showed skepticism towards a naïve induction, as expressed in his Knowledge and Error: From all this, it emerges that the mental operation by which new insights are gained, which is usually called by the unsuitable name “induction,” is not a simple process but a rather complex one. Above all it is not a logical process, although logical processes may figure as auxiliary intermediate links. Abstraction and the activity of phantasy does the main work in the finding of new knowledge. mach 1905/​1976, 329

And he argued: Since there is no adequate method to guide us towards scientific discovery, successful discoveries appear in the light of artistic achievement as was well known to Johannes Müller, Liebig and others. mach 1905/​1976, 236

Mach concluded consistently that the use of the label “inductive sciences” for the natural sciences is thus not justified because it is rather the combination of poetical imagination and the principle of economy (according to Occam’s razor). He favored description over explanation, as well as functionalism instead of causality. Here we also recognize that heuristics is given the same meaning as justification of propositions and theories, thus bridging the dualism of the context of discovery and the context of justification. Given this methodological episode we may conclude with the remarkable renaissance of Mach’s theory of research by Paul Feyerabend, when he referred to Mach’s historical-​pragmatic tradition as an antidote to the dominant abstract-​theoretical one in modern philosophy of science, as follows:

90 Stadler The Machian critique was part of a reform of the sciences; it linked critique with new findings; the positivists, however, and their untiring opponents, the “critical rationalists,” began with several frozen components of the sciences that were no longer accessible to research and reinforced them with the help of philosophical arguments (Popper‘s “contributions”  to realism). Mach’s critique was dialectic and useful, the critique of philosophers is dogmatic and without results. feyerabend 1980, 373f.

And in his “Mach’s Theory of Research and its Relationship to Einstein” (1988) Feyerabend argued that Mach criticized the mechanistic physics of his time and provided a theory of research, employing an historical-​critical method. With the word “dialectic” Feyerabend was most likely alluding to Mach’s epistemological balance between Knowledge and Error (Mach 1905) or the interplay between abstraction and phantasy in the generation of knowledge. He concludes with the following methodological plea as an upshot of this reconstruction: –​ oppose established views in the history of science; –​ advocate a return to texts and sources; –​ be critical of simplified established accounts; –​ avoid pseudo-​disputes and pseudo-​problems such as: positivism vs. realism; –​ avoid pure philosophical solutions; –​ reject overly simple philosophical approaches to complex historical ­processes; –​ be cautious vis-​à-​vis philosophical “fairy-​tales.” After emigrating to the U.S., Philipp Frank (1884–​1966), Einstein’s successor in Prague 1912, founded, the Institute for the Unity of Science and established Science Education in Harvard. Before that he had edited the book series “Schriften zur wissenschaftlichen Weltauffassung” (together with Moritz Schlick). In his collection of articles published in Modern Science and its Philosophy (1949) he reconstructed the origins and development of Logical Empiricism since its beginnings in Vienna with Nietzsche and Mach vs. Kant’s so-​called “school philosophy” (“Schulphilosophie”). He succeeded in theoretically bridging the gap between modern empiricism (Berkeley, Hume, Mach) and symbolic logic (Abel Rey, Henri Poincaré und Pierre Duhem). As a formal tool he introduced Hilbert’s axiomatics of geometry: it served as a conventionalist system of implicit and operational definitions (P.W. Bridgman), plus Einstein and Russell towards an anti-​idealist turn without absolute foundationalism:

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according to Mach the general principles of science are abbreviated economical descriptions of observed facts; according to Poincaré they are free creations of the human mind which do not say anything about observed facts. The attempt to integrate the two concepts into one coherent system was the origin of what was later called logical empiricism. frank 1949, 11 f.

No physical theory does describe the “world-​in-​itself,” but only its structural connectivity (according to Schlick‘s Allgemeine Erkenntnislehre/​General Theory of Knowledge). Again, there is only a quantitative access to the external world, which cannot be conceived of by its content in the language of philosophy and science. This is the consequence of the distinction between metaphysical experience and epistemic cognition according to Schlick’s “consistent empiricism” (1950, 462 f.): Thus, knowledge is essentially a reproduction of the order, the structure of the world; the material content belonging to this structure cannot enter it; for the expression is, after all, not the thing in itself which is being expressed. Therefore, it would be senseless to attempt to express the ‘content’ itself. Herein lays the condemnation of ever y variety of metaphysics. In his book Das Kausalgesetz und seine Grenzen (The Law of Causality and its Limits, 1932/​1988) Frank had confirmed this way of reforming philosophy, e.g., by rejecting Lenin’s attack on Mach (1909), who falsely characterized Frank as an idealist Neo-​Kantian. On Poincaré, Kant and Lenin he wrote that “it is important above all to stress our opposition to Kant‘s conception of the law of causality […] set forth by Hans Reichenbach for the example of statements about space and time in his publication The Theory of Relativity and A Priori Knowledge” (Frank 1932/​1988, 231). Richard von Mises, the pioneer of applied mathematics, published a comprehensive book entitled Kleines Lehrbuch des Positivismus. Einführung in die empiristische Wissenschaftsauffassung (1939), which appeared in English twelve years later as Positivism. A Study in Human Understanding (1951). Herein, he concluded that “the modern catchword ‘historicism’ indicates a situation that is hardly peculiar to the historical sciences” (225) and summarized in part vii on human behavior, that The whole of science can be resolved (in a vague way) into separate sciences, according to the phenomena that each treat. The idea that there

92 Stadler is a fundamental unbridgeable difference in method, or even in the kind of “understanding” between the natural sciences and the humanities is untenable. In history and the social sciences, too, one deals with observation and inductive generalizations, hence theories, and with the first approaches to tautological systems, every result is, in the last analysis, a proposition verifiable in experience. Physics and the branches of knowledge bordering on it are characterized by the fact that they deal with the simplest phenomena, e.g., with those which can be better isolated than all others, and this accounts for the fact that these sciences are more advanced with respect to the accumulation of experiences and to their epistemological elaboration. von mises 1951, 369 f.

This regulative idea of a methodological unity of the sciences rests on the assumption of different degrees of complexity in the individual sciences, which do not justify a dualism or a triad of the natural sciences, social sciences, and humanities. This view was shared mainly by the phenomenologist and philosopher of law, Felix Kaufmann, another member of the Vienna Circle, who elaborated on the Methodenstreit historically and systematically in his Methodenlehre der Sozialwissenschaften (1936). After his forced migration to the usa (New School for Social Research, n.y.c.) he tried to accommodate American pragmatism, especially John Dewey, and rewrote his former book as Methodology of the Social Sciences (1944). The first book was translated and edited with a long and informative introduction by Ingeborg Helling in 2014. Its second part deals with the Methodenstreit in the social sciences, and is dedicated to Hans Kelsen and Ludwig von Mises. Kaufmann compares the naturalist and anti-​naturalist theses (later adopted by Karl Popper in his The Poverty of Historicism) and argues against an exaggeration of the methodological differences between the cultural and social sciences from a philosophy of science standpoint. Despite all existing differences between scientific disciplines we have to establish a meta-​ level of rules to be employed without making any essentialist claim to different research fields and methodologies. In short, Kaufmann argues against an exclusive purity of method and the a priori nature of principles so as to overcome the methodological dispute by way of rational reconstruction. 3.5 Max Weber as a Mediator Max Weber (1864–​ 1920), the famous German historian, sociologist and economist paved the way for the research topos of cultural history

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(Kulturgeschichte): Man is culturally defined via interpretation and the usage of values and meaning (“Sinn”). He argued for value relations without an absolute value legitimation as a manifestation of the formation of “culture.” In this regard Weber also postulated the contested value-​freedom for the cultural and social sciences, which caused the value dispute in German sociology (“Werturteilsstreit”), another variant of the Methodenstreit (Weber 1991,1995; Schurz/​ Carrier 2013). Weber‘s methodology emerged from the insight that there is no science without presuppositions. Nevertheless, the value freedom thesis is possible and necessary with the methodological tool of ideal-​types (“Idealtypus”) in a neo-​Kantian context. According to Weber we are faced with a dualism of factual judgments vs. value judgments, and respectively with the nomological vs. historical method (viz., explanation and understanding). The structuring ideal-​ type concept formation is done with a methodological individualism against any form of holistic explanations with collective entities like working class or capitalists. According to his Kantian background Weber developed social science as a science of reality (“Wirklichkeitwissenschaft”): both explanation with subsumption and understanding with interpretation, as well as a method of counter-​factual judgments (employing thought experiments), are viable tools for generating knowledge. This complex and transcending position raised the question of whether Max Weber is the godfather of a dualism or a pioneer for the unification of the social and cultural sciences. Here again, the divergence of the scientific community re-​appears in contemporary historiography:  on the one side, the German sociologist Uta Gerhardt represents the branch of the humanities with a phenomenological impetus, and, on the other, the historian Fritz Ringer aims at a unification of the cultural and social sciences, both referring to Max Weber as their main scholar of reference: Gerhardt, in her Idealtypus. Zur methodischen Begründung der modernen Soziologie (2001) places Weber in the context of Georg Simmel and Heinrich Rickert as proponents of a non-​positivist foundation of sociology, later on represented by Alfred Schütz and Talcott Parsons. Her conception of ideal-​type presupposes the separation between science and world, and conceives culture as a precondition for understanding the other, as a frame for analytic and ­historical understanding. By contrast, Ringer, in his book Max Weber‘s Methodology. The Unification of the Cultural and Social Sciences (1997), places Weber in the context of historicism/​positivism, confirming Weber’s programmatic essay “Wissenschaft als Beruf” (Scholarship as a Profession, 1919) as opposed to ideology and a Weltanschauung linked to practical intentions. Departing from Rickert, he makes a plea against naturalism, holism and irrationalism, in favor of a singular causal

94 Stadler analysis of human actions. In this line the ideal-​type combines interpretation and explanation, theory and practice, with the following claims: 1. Singular causal analysis posits the individual as the research subject based on “rules of experience.” 2. The Historical School of Economy presents the “economic man” as ideal-​type, therefore synthesis of the German and Austrian schools seems possible. Furthermore, causalities as intervening factors enable a counterfactual and comparative historiography also employing thought experiments in historical studies. The method of interpretation is presented as a special case of singular causal analysis leading up to a unification of cultural and social sciences: interpretation and causal explanation are compatible, but no exclusive deductive-​nomological model as proposed by the “Austrians” exists. Recently, such a singular causal explanation was continued by Donald Davidson, Alasdair MacIntyre, and Wesley Salmon. Generally, Ringer argues against any artificial dualisms like understanding and explanation, or induction and deduction. Given Weber’s specific interpretation here, Fritz Ringer appears as a marginalized outsider in the Weber community, maybe like Lamprecht in the historical school some 100 years earlier. This has to do with Ringer bringing together modern philosophy of science and the cultural-​historical studies, claiming their principal (methodological) unity. Independently of this continuation of methodological controversy we can also identify this subject in the field of philosophy of science proper. 3.6 Methodenstreit and Philosophy of Science Revisited We have seen the following in the previous sections: –​ The Methodenstreit in general is still relevant in the philosophy of science, situated between unity and disunity. –​ The Methodenstreit in the historical sciences is still unresolved and contested, with the question as to whether there is a (dis-​)unity of methods. –​ As a desideratum, we may conclude that historical explanations in the Methodenstreit of the historians have yet to be reconstructed and researched by today’s philosophy of science: the range between narration, description or explanation remains to be specified. –​ Recent philosophy of science deals mostly with the natural sciences, partly with the social sciences, and scarcely with the cultural sciences and humanities (as becomes manifest in most of the textbooks of the philosophy of science). –​ Precisely this issue was on the agenda until World War ii, as we have seen exemplified by F. Kaufmann, O. Neurath, R. v. Mises, V. Kraft, K. Popper and others.

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–​ After 1945 the problem of historical explanation was addressed only occasionally by professional historians (e.g., by Th. Haussmann 1991) interested in theoretical approaches –​but with the exception of C.G. Hempel, W. Stegmüller, and G.H.  von Wright (Explanation and Understanding, 1971), and hardly by philosophers and (analytic) philosophers of science. –​ The reason for this decline of interest and research is related to poststructuralism and postmodernism:  the emergence of narrative turns and anti-​ enlightened motifs accompanied by an ahistorical philosophy of science, and at the same time ignorance of the rich and creative tradition of history and philosophy of all sciences from 1900 up to wwii, recurring again with the History and Philosophy of Science (hps) and History of Philosophy of Science (hopos) after 1989/​90. Some of the most polarizing issues were, and still are, the alternatives/​options between induction and/​or deduction, or: context of discovery (CD) and context of justification (CJ). Since Aristotle’s unified inductive-​deductive methodology, and the overcoming of skepticism by a priori-​conception after Hume and Kant, induction was dealt with by J. St. Mill as correlated to the CD and CJ distinction. Then, the big issue was: is there subjective or objective knowledge as a corresponding epistemology? Mach’s doctrine of a co-​existence and balance of induction, abduction, and deduction in his Knowledge and Error (1905/​1976) prompted the choice of one particular method, e.g., in Popper’s Logic of Scientific Discovery (Logik der Forschung, 1934): his claim was the practical and theoretical impossibility of any induction. That same year, Herbert Feigl combined induction and frequency theory of probability, with a justification for inductive extrapolations (and interpolations) beyond Hume and skepticism in general. And Carnap (Logische Syntax of Language, 1934) claimed the unity of syntax, semantics and pragmatics in the philosophy of science with the methodological principle of tolerance. As an indirect response Hans Reichenbach (Experience and Prediction, 1938) introduced the dualism of CD and CJ, with epistemology as exclusively CJ. In his Rise of Scientific Philosophy (1951/​1954, 231) he wrote: “justification of a theory in terms of observational data is the subject of induction.” It is no surprise that at the same time John Dewey postulated the need for a coherent doctrine of the nature of induction and deduction in his Logic. The Theory of Inquiry (1938). 3.7 The “Science Wars” –​a Last Stage of the Methodenstreit? A sort of recurrence and reconfiguration of the Methodenstreit with reference to the controversial notion of relativism can be observed at the end of the 20th century. Sokal and Bricmont (1998) accused Duhem/​Quine, Popper, Kuhn and Feyerabend of adhering to an epistemic relativism and irrationalism, and at the

96 Stadler same time argued against the skeptic consequences of a formalized scientific method according to the Vienna Circle. Although we know of historical counter examples such as Neurath, Frank (vs. Popper and Hayek since 1934) in the context of Methodenstreit, scientific realism and objectivism are presented as uncontested options for scientific knowledge. The “Neurath Boat” was already an option advocating a nonreductive naturalism, methodological holism, and reflexive social epistemology employing the holistic Duhem-​Neurath-​Quine thesis. But Noretta Koertge, in A House Built on Sand. Exposing Postmodernist Myths About Science (1998), in Popper’s sense attacks “relativism” as a threat to rationality and objective knowledge. As a counter example already the Vienna Circle endorsed a clear critique of Cartesian “certism” (or “scientism”) and a turn towards a (non-​foundationalist) epistemology and (methodological) relativism, e.g., by Philipp Frank (and Einstein) with his defense of relativism in the tradition of Mach, Poincaré, Duhem, Bridgman, etc. as a “Link between Science and Philosophy” (1949). Frank’s Relativity –​ A Richer Truth (1952) expresses the fate of the philosophy of science in the context of the Cold War period (G. Reisch 2005), when European relativism was attacked as being responsible for the rise of Fascism and National Socialism by US philosophers. In the long run, the compatibility of relativity and objectivity of truth (against naive realism) following the pragmatic turn became a serious position, e.g., in the International Encyclopedia of Unified Science (1938 ff.), which included articles by John Dewey (Theory of Valuation, 1951) and Thomas Kuhn (Structure of Scientific Revolutions, 1962), or the Minnesota Studies in the Philosophy of Science with the first publication of Paul Feyerabend’s “Against ­Method” (1970). 4

Concluding Remarks

The main issues recurring in the history and philosophy of science in the 20thcentury are manifestations of central, still open methodological and foundational problems which can be investigated from a meta-​theoretical as well as contextual point of view. These include: unity and plurality of the sciences, two or three cultures of the sciences (Humanities/​Geisteswissenschaften, natural sciences and social sciences, between understanding and explanation), inductive or deductive reasoning, relativism and objectivism, the dualism of facts and values (is –​ought) etc. A special case seems to be a reconstruction and analysis of the “Science Wars” in the late 1990s, where some of the already cited topics and problems were addressed again in different cognitive and cultural contexts of

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postmodernism (incl. feminist philosophies of science) between relativism and objectivism/​realism. But the challenge of an empiricist/​naturalist or rationalist version of science and its philosophy (with reference to convention and construction, description and explanation) remains. In any case, a historical and rational reconstruction enables a closer understanding of these ongoing disputes. The focus on methods in philosophy and philosophy of science reveals the still existing split between informal and formal methods, which had already separated two main figures of the Vienna Circle, namely Otto Neurath (who criticized symbolic logic in danger of producing a new metaphysics) and Rudolf Carnap (who made the journey from the logic of science, via syntax to formal semantics). This divergence can be identified again in contemporary philosophy as an unresolved problem. But the history of the Methodenstreit facilitates a better understanding and provides good arguments for both sides, in addition to helping to prevent a mere repetition of the good old debates. This is also a plea for historicizing methodological and epistemological debates today (e.g., with Martin Kusch’s erc project “The Emergence of Relativism”). These trends are reminiscent of Philipp Kitcher’s recommendation to reconcile the “realist-​rationalist cluster” and the “socio-​historical cluster” in ­science studies (Kitcher 1998) with reference to theory-​ladenness, underdetermination, variety of beliefs, and “actor” categories. A different reaction was Stephen Weinberg’s rejection of “epistemological relativism” in history and/​or philosophy of science, and the defense of Popper by his follower N. Koertge. But, in 1934, Popper himself had referred to the image of the sciences without an absolute, secure empirical basis, alluding to Hermann Weyl, who –​much in the sense of Neurath and Frank –​employed two alternative pairs of concepts, namely “subjective-​absolute” and “objective-​relative.” This already clarified that the alternative option to epistemological relativism is philosophical absolutism and that relativism is compatible with objectivism. A possible equivalent to this relativism seems to be a methodological fallibilism, by means of which any foundationalist conception of science can be avoided. In addition, the distinction of context of discovery and context of justification correlates with inductive-​deductive reasoning, either as dualism or a unified position. And such an approach calls for an integrated history, sociology and philosophy of science. (Stadler 2012, 2014, 2018).

References

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100 Stadler Scientific Explanation. 1989. Edited by P. Kitcher and W. Salmon. Minnesota Studies in the Philosophy of Science. Vol. xiii. Minneapolis: University of Minnesota Press. Snow, C.P. 1959/​1964. The Two Cultures. And a Second Look. An Expanded Version of the Two Cultures and the Scientific Revolution. Cambridge (UK):  Cambridge University Press. Sokal, A. 1996. Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity. Social Text 46/​47: 217–​252. Sokal, A. and J. Bricmont. 1998. Fashionable Nonsense: Postmodern Philosophers’ Abuse of Science. New York: Picador. Sokal, A. 2008. Beyond the Hoax. Science, Philosophy and Culture. Oxford: Oxford University Press. Stadler, F. 2004. Induction and Deduction in the Philosophy of Science: A Critical Account Since the Methodenstreit. In: Induction and Deduction in the Sciences. Edited by F. Stadler. Dordrecht, Boston, London: Kluwer, 1–​16. Stadler, F. 2012. History and Philosophy of Science. Zwischen Deskription und Konstruktion. Berichte zur Wissenschaftsgeschichte 3: 217–​238. Stadler, F. 2004. History and Philosophy of Science:  Between Description and Construction. In: New Directions in the Philosophy of Science. Edited by M.C. Galavotti et al. Cham, Heidelberg, New York, Dordrecht, London: Springer, 747–​768. Stadler, F. 2010. History and Philosophy of Science. From Wissenschaftslogik (Logic of Science) to Philosophy of Science: Europe and America, 1930–​1960. In: Vertreibung, Transformation und Rückkehr der Wissenschaftstheorie. Am Beispiel von Rudolf Carnap und Wolfgang Stegmüller. Edited by F. Stadler. Wien, Berlin: lit Verlag, 9–​84. Stadler, F. 2018. George Sarton, Ernst Mach, and the Unity of Science Movement. A Case Study in History and Philosophy of Science. Sartoniana 31/​2018. Edited by R. Rubens and M. van Dyck. Ghent: Ghent University. Topitsch, E., Messner J. 1966. Atheismus und Naturrecht /​Ein Streitgespräch. In: Neues Forum a. 13: 457–​478, 607–​611, 698–​702. Von Mises R. 1951. Positivism. A Study in Human Understanding. New York: Dover Publications. 2nd German edition: Kleines Lehrbuch des Positivismus. Einführung in die empiristische Wissenschaftsauffassung. 1990. Edited by Friedrich Stadler. Frankfurt/​ M.: Suhrkamp. Von Mises, L. 1969. The Historical Setting of the Austrian School of Economics. Online Edition. New Rochelle: Arlington House, Ludwig von Mises Institute. Weber, M. 1995. Schriften zur Soziologie. Edited by M. Sukale. Stuttgart: Reclam. Weber, M. 1991. Schriften zur Wissenschaftslehre. Edited by M. Sukale. Stuttgart: Reclam. Werte in den Wissenschaften. Neue Ansätze zum Werturteilsstreit. 2013. Edited by G. Schurz and M. Carrier. Berlin: Suhrkamp. Wittkau, A. 1992. Historismus:  zur Geschichte des Begriffs und des Problems. Göttingen: Vandenhoeck, Ruprecht. Von Wright, G.H. 1971. Explanation and Understanding. Ithaca: Cornell University Press.

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Periodization as a Disguised Conceptualization of Historical Development: a Case Study of a Theory of the Historical Process Developed in the Poznań School of Methodology Krzysztof Brzechczyn Abstract The aim of this article is to outline the theory of the historical process developed within the framework of the Poznań School of Methodology, mainly by Leszek Nowak and a team of his co-​workers. The main interpretative key used in this reconstruction is the vision of the periodization of the historical process accepted in the adaptive reconstruction of historical materialism and in non-​Marxian historical materialism. In the adaptive interpretation of historical materialism, the basic mechanism of historical development was the adjustment of property relations to the growth of productive forces, which decided the way of the periodization of the historical process. In non-​ Marxian historical materialism, the main mechanism of the motion of society was the class struggle between the classes which emerged in the political and economic spheres of social life and the supra-​class competition between rulers and owners which led to a new periodization of the historical process: into economic and political epochs.

Keywords adaptive reconstruction –​historical materialismn –​historical process –​­periodization –​ Poznań School of Methodology

1

Foreword

In this article, I attempt to present the theory of the historical process deve­ loped within the framework of the Poznań School of Methodology, mainly by Leszek Nowak and his co-​workers. Since it is hardly possible to present all the

102 Brzechczyn main theses of substantial philosophy of history (that term will be used interchangeably with the theory of the historical process), including its deve­ lopments and applications, in one article, I would like to focus on only one dimension of the theory of the historical process developed within the Poznań School of Methodology –​one that does give, to an extent, a picture of the substantial philosophy of history of that school. The issue I have selected for that purpose is the problem of the periodization of historical development, which makes it possible to present the philosophy of history of the Poznań School of Methodology in the form of a synthetic summary and reveal sometimes hidden links between theoretical assumptions and division of past into epochs and formation. I have made that choice because time is one of the basic categories which constitute historical narration. We should distinguish between periodization and chronology, that is, the division of time into equal sections, for example, years, decades, or centuries (Sato 2015; Lorenz 2017, 122). According to Jerzy Topolski, the basis of periodization is the use of theoretical concepts, such as feudalism, revolution, modernization, or crisis, which are ascribed a temporal scope of application. He claims: Periodization is one of the most important tools in the process of the creation of historiographical concepts which construct past reality, and it is one of the most important –​or most active –​factors which create historical images in the social consciousness. topolski 1996, 133

To determine a separate historical period means, in a way, to synthetically report on the evaluation of the place and role of that period in the course of history (nation, state, part of the world, the world, etc.) topolski 1996, 135

Therefore, it seems that periodization arguments about the length of particular epochs are theoretical discussions in disguise (Griesemer 1996, 20). The laws/​dependencies/​models/​ideal types assumed by historians are rarely formed explicite. Historians distinguish historical periods on the basis of the laws or development mechanisms which they assume to have had significant influence on the past of particular societies at a particular time, and they do not have to be conscious of that basis. In Chris Lorenz’s words: Historians always periodize time because the differentiation between past and present is already a form of periodization. Periodization presupposes

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principles of selection and ideas about coherence –​about continuity and discontinuity –​because periodizing is as much about what to leave out as what to keep in. Periodization therefore requires systematic abstraction  –​which may explain why most historians have avoided the topic altogether and why many tend to conflate periodization and chronology, even some of the theoretically minded historians. … lorenz 2017, 120

Periodization discussions held in Poznań School of Methodology are rare example of analyzes where conscious accepted methodological assumptions and theoretical principles decide about the way of division of human history, not reverse: periodization disputes are, as often happened, disguised and hidden form of discussion over the rules of theoretical conceptualization of historical development. Therefore, it is one of the reasons why the scientific output of Poznań School is still worth of study. 2

The Main Ideas of the Adaptive Interpretation of Historical Materialism

The problem situation which generated the creation of the adaptive interpretation of historical materialism was how consciousness was determined by being.1 When Marxism is interpreted, it is commonly understood as saying that there are cause and effect relationships between global productive forces and relations of production, a social base and a legal and political superstructure, social and economic conditions and particular states of social consciousness. That gives rise to well-​known interpretive difficulties as it has not been clear how productive forces can lead to the emergence of particular relations of production, a social base –​of a legal and political superstructure, and social and economic conditions –​of particular states of social consciousness. One solution to that problem was the adaptive understanding of those dependencies proposed by Leszek Nowak (1973, 1982). He assumed that there are two sets of states of affairs: set α, also called a set of varieties, and set β, termed a set of conditions. Let elements of set α possess certain property k in various degree. If elements of set α occur together with an element B of set β (state of affairs B is the conditions for members of set α), then only those elements of

1 In this chapter, I use fragments –​adapted to the purposes of this work –​of my article from (Brzechczyn 2017).

104 Brzechczyn set α will become widespread which possess property k in a highest degree.2 The adaptive dependency of set α in conditions B of set β with respect to property k is presented by means of formula: Aopt = ad k (α , B ) which is read as follows: from the set of states of affairs α, that one becomes widespread which under conditions B will lead to a result characterized by property k in the highest degree; that state of things from set α is denoted by Aopt. The property k is named a criterion of adaptation and function ad is termed an adaptation function. The author illustrated his interpretive suggestion with the example given below. Let us assume that a person has invented a new device which improves work efficiency and, consequently, makes it possible to increase the surplus product. As they compare various systems of the organization of production (traditional, invented by specialists, etc.), owners select the one which they believe to be capable of ensuring the greatest surplus product. However, if the expected increase does not take place, the owners –​thinking that they have made the wrong choice –​will continue looking for an appropriate system of the organization of production. If any of them delays the reorganization of production, that owner’s profits from the surplus product will shrink and, in the end, he or she will go bankrupt. After a sufficiently long time, by trial and error, and the elimination of those who do not learn fast enough, an optimal system of the organization of production, with respect to the used tool, will become common in the observed economic sector. The mechanism of the adaptation of systems of production to the level of productive forces, which operates in the way described above, has been formulated as follows: (i) that system of the organization of production, from a set of historically given systems of the organizations of production, is adopted on the mass scale in a given society, which at a given level of productive forces, ensures the highest surplus product for the owners of the means of ­production. There is an analogous adaptive dependency between the superstructure and the economic base. On a mass scale, those systems, from among the various legal and political systems (traditional or invented by philosophers), become common which ensure the most effective introduction of the optimal system 2 Łastowski introduced the notion of the threshold level of intensity of adaptation property. According to him, states of affairs from a set α become widespread if they possess the property k sufficiently close to its highest degree that is: “they exceed the definite threshold value (intensity) of the criterion of adaptation” (Łastowski 1982, 123).

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of the organization of production, from the point of view of the owners’ class, given a particular state of the base. That dependency is formulated as follows: (ii) that political system, from a set of historically given politico-​legal systems, is adopted on a mass scale in a given society, which ensures an introduction of the most optimal organization of production at a given level of the economic base. The dependency of social consciousness on social being is similarly adaptive in nature. In this case, the interests of the owners’ classes, guaranteed by the legal and political system, function as a selector of individual ideas. On a mass scale, such ideas become common as, in given social and economic conditions, ensure the durability of a political system. That is expressed by way of the following dependency: (iii) those ideas, from a historically given set of ideas, are adopted on a mass scale in a given society, which ensure the highest stability of the legal and political system at given social and economic conditions. Dependency (I)  describes the adaptation of systems of the organization of production to the level of productive forces. Together, the level of productive forces and the optimal system of production (relations of production) constitute an economic base. Dependency (ii) describes the adaptation of legal and political systems to the economic base. The optimal political and legal system is called a legal and political superstructure. Together, an economic base and a legal and political superstructure form social and economic conditions. Social consciousness adapts to them (which is described as dependency iii). The adaptation statements obtained in that way and binding for numerous idealizational assumptions constitute the initial model of the socio-​economic formation. Later (in 1970s and at the beginning of 1980s), their gradual cancelation (one of the key assumptions was that of the stability of productive forces) became the basis for the development of the adaptive interpretation of historical materialism. Graphically, the system of dependencies in a socio-​ economic formation can be presented as follows: The means of production

The system of the organization of production

Economic base Economic and social conditions (being)

diagram 5.1 The structure of a class formation

Political and legal system (superstructure) Economic consciousness

106 Brzechczyn 3

Inter-​Epoch and Inter-​Formation Transitions. The Periodization of Historical Development in the Adaptive Interpretation of Historical Materialism

3.1 The Paradox of Historicism There were two concepts which were assumed by the adaptive interpretation of historical materialism, namely: the categorial interpretation of Marxian dialectics (Nowak 1977c) and the idealizational theory of science (Nowak 1970, 1971, 1974, 1977b, 1980; Nowak and Nowakowa 2000). The categorial interpretation of dialectics made it possible to characterize the nature of historical reality –​described by the adaptive interpretation of historical materialism –​in ontological terms, while the idealizational theory of science determined the methodological status of the statements which were put forth and the manner of their concretization. The categorial reconstruction of Marxian dialectics presupposes the variability of the main factors of studied phenomena (Nowak 1977c, 89–​90), while Mar­ xian historical materialism presupposes that productive forces and the relations of production are set once and for all and are the main determining factors in social life, in all societies and in all historical periods. That paradox gives rise to the question of whether the repertoire of main factors is or is not subject to change in historical development. If the answer is yes, it is, then another question arises about the nature of those non-​economic but still m ­ aterial factors. 3.2 Epochs and Formations Within the framework of aimh, researchers have been trying to deal with the aforementioned paradox of historicism by creating an idealizational-​adaptive interpretation of historical materialism in which the basic periodizing units were epochs and formation. This approach –​developed mainly by Jolanta Burbelka (1980, 1982) –​was inspired primarily by Frederick Engels’s Origins of the Family, Private Property and the State based on research done by American anthropologist Lewis Morgan; the important point of departure were Karl Kautski’s (1909) and Ludwik Krzywicki’s (1960) works on ancestral societies. In Burbelka’s interpretation, the main factor in ancestral societies is the reproduction of immediate life and not economic production. She claims that the production of goods only becomes the main factor in the epoch of class societies. According to the reconstruction of the basic concepts of Engels’s historical materialism (Burbelka 1980, 38–​39), the factor of the reproduction of immediate life and of kinship relationships is an element of an “ancestral base.” The economic and political superstructure and the “ancestral base” constitute, together, an “ancestral being” (socio-​ancestral conditions). Socio-​ancestral conditions, understood in that way, determine the tribal consciousness prevalent

107

Periodization as a Disguised Conceptualization

in the whole society. As the above considerations concern a pre-​class society, that consciousness is a tribal consciousness and not the consciousness of the dominant social class. Therefore, the essential structure of a typical formation of the ancestral epoch looks as follows: R, Kr R, Kr, E-​PS R, Kr, E-​PS, TrC diagram 5.2 The essential structure of the socio-​ancestral formation; Abbreviations used: R – reproduction of immediate life, Kr – kinship relationships, E-PS – economic and political superstructure, TrC – tribal consciousness.

Burbelka also reconstructed the basic laws of the theory of the ancestral formation: (i. A) That type of a kinship relationship, from a set of historical types of kinship relationships, is adopted on a mass scale which ensures the highest survival ratio, in given conditions of the reproduction of life. (ii. A) That economic and political system, from a set of economic and political systems, is widespread which ensures the most effective augmentation of the optimal kinship relationships, in a given ancestral base. (iii. A) That system of ideas, from a set of historical systems of ideas, is adopted on a mass scale which ensures the highest stability of an optimal economic and political superstructure, in given socio-​ancestral ­conditions. The structure of the socio-​ancestral formation was analogous to that of the socio-​economic formation:

The reproduction of Immediate life

Kinship relationships

Ancestral base

Economic and political system

Socio-​ancestral conditions diagram 5.3 The structure of the socio-​ancestral formation

Tribal consciousness

108 Brzechczyn Burbelka distinguished three socio-​ancestral formations on the basis of kinship relationships (the form of marriage): As regards the first social-​ancestral formation, group marriage of the first degree was common there, which precluded sexual relationships of, first, parents with children and, later, of siblings. Group marriage of the second degree became popular in the next ancestral formation; it precluded sexual contacts between close and more distant relatives. The monogamous marriage became more common in the third ancestral kinship formation. It constituted a further restriction on people’s sexual relationships. The aim of that diachronic evolution of the forms of marriage was, according to the interpretation presented above, to produce the healthiest possible offspring. The author also postulated that the history of the development of humanity could be divided into two principal epochs: the tribal one and the class one. Within those two eras, we could distinguish the

­f igure 5.1  Transitions between epochs and formations Explanations: the curved lines represent formations; the dashed curved line –​ formations in the socio-​ancestral epoch; the continuous curved line –​formations in the socio-​economic epoch; the first arrow from the bottom signifies the need for the reproduction of the immediate life in the socio-​ancestral epoch (continuous line), which was a fundamental need in this epoch and was also present in the socio-​economic epoch (broken line); the second arrow from the bottom represents the need for material production in the socio-​ ancestral epoch (the broken line), which was present in that epoch but was not fundamental then, and in the socio-​economic epoch this need is represented (as a fundamental one) by a continuous line (Burbelka 1982, 224–​225).

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socio-​ancestral formation and the socio-​economic formation. That is illustrated in the f­ ollowing image. The author also defined the principles of transitions between the epochs. The main factor for the development of societies in the kinship epoch was the reproduction of life, while in the class epoch it was production. Let us once more recall the essential structures of the socio-​ancestral formation and the class-​economic one. According to Burbelka, the transitions between epochs happen as follows: 1. In the last formation of the previous epoch, the main factor from the next epoch occurs above the surface essentiality level. 2. In the first formation of the new epoch, the main factor from the previous epoch occurs above the surface essentiality level. 3. In the new epoch, the main factor from the previous one cannot occupy a position at the lowest essentiality level (Burbelka 1980, 127). Consequently, the essential structure of the last formation of the social-​ancestral epoch and of the first formation of the class epoch, then, looks as follows: The essential structure of the last formation of the ancestral epoch: R, Kr R, Kr, P R, Kr, P, E-​PS R, Kr, P, E-​PS, TrC

The essential structure of the first formation of the class epoch: P, SOP P, SOP, R P, SOP, R, PLS P, SOP, R, PLS, EC

diagram 5.4 T  he essential structure of the last formation of the social-​ancestral epoch and of the first formation of the class epoch. Abbreviations used: R – reproduction of immediate life, Kr – kinship relationships, E-PS – economic and political superstructure, TrC – tribal consciousness, P – production, SOP – system of the organization of production, PLS – political and legal superstructure, EC – economic consciousness.

3.3 On Two Visions of the Development of Productive Forces The researchers from the Poznań School were more interested in the nature of the transitions between the formations in the class epoch. Alternative periodizations of that epoch were presented by Krzysztof Łastowski (1981, 1982) and Piotr Buczkowki (1978, 1981, 1982). Both authors rejected the assumption about the stability of productive forces, but they conceptualized their growth differently.

110 Brzechczyn Krzysztof Łastowski, with the use of analogies between the development of biological and human societies, introduced the concept of the directional, stabilizing, and differentiating growth of productive forces. The stabilizing development of productive forces occurs in every formation. It is quantitative in nature and consists in gradual improvements of the existing working tools. That type of increase of productive forces does not lead to a holistic transformation of the existing systems of the organization of production, the political-​legal system, and social consciousness. Those systems may, at best, gradually and slightly become more efficient –​from the owners’ point of view –​with respect to the creation of the surplus product. Things change with the appearance of the directional development of productive forces which is related to the implementation of a new kind of production (for example, industry in an agrarian society). At such a time, there emerges a new class of owners which maximizes the new kind of surplus product. Consequently, the criterion of adaptation is changed. If the new productive forces dominate economic production, then, by way of adaptation, there appear and become prevalent: a new manner of the organization of production, a new legal and political superstructure, and a new social ­consciousness. Łastowski also admitted the possibility of the appearance of a new type of productive force which would be separate from the existing one but not more productive. In such a case, the development of productive forces would be variegated: there would be two (or more) classes of owners of the means of production, and each such class would maximize a different kind of the surplus product. There are two (or more) criteria of adaptation. Once more, new manners of the organization of production, the legal and political superstructure, and social consciousness adjust, by way of an adaptive dependency, to the level of productive forces. In Łastowski’s view: This is, as may be seen, the picture of multitrack development. It makes provision for not all the societies undergoing the same formations, i.e. for the development not to run on one track. It seems that in particular the question of the so –​called Asiatic formation, though controversial until the present time, supplies a certain foundation for the multi-​track picture of the development of societies. łastowski 1982, 153

Having reached that conclusion, Łastowski does not characterize said paths of the development of productive forces –​or their social ramifications –​in greater, historical and empirical, detail.

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Piotr Buczkowski (1978, 1981, 1982; a presentation of his concept:  Brzechczyn 2005) elaborated alternative vision of transitions between formations in the class epoch. He also introduced a distinction between relations of property and the system of the organization of production. In Buczkowski’s words: If someone is an owner of object P, than he takes decisions concerning its use, or he delegates someone else to make these decisions. Moreover, other social roles resulting from the relation to a given object must be performed by other members of society. E. gr. in the basic for us case of property of the means of production first of all the social roles of the direct producers must be performed. One should emphasize here that the readiness to perform any role does not at all mean voluntary acceptance but it may result from the awareness of sanctions which may be applied for insubordination to this requirement. buczkowski 1982, 160–​161

A system of the organization of production includes those sociological principles of behavior applicable to the process of production which do not belong to relations of property, for example, the division of labor, cooperation among employees, the organization of work processes and the resulting subordination relations, professional qualifications, etc. From the set of systems of the organization of production available at a given time, the relations of property select that subset which is compatible with them, that is, they strengthen the owner’s role in the production process (Buczkowski 1978, 162). That system, from the subset of systems of the organization of production which is compatible with the relations of property, becomes common which, at a given level of productive forces, ensures the owners’ class the highest surplus product. The author concretizes the initial model which assumes that productive forces are stable. He rejects that assumption by assuming that: –​ the level of productive forces changes in subsequent periods of time; –​ there are two types of productive forces, and initially the existing productive powers dominate the new ones; and –​ the dominant productive forces are compatible with the prevalent property relations. In the considered society, most owners of the existing means of production of type A introduce those organizational systems from a set of the systems of the organization of production compatible with relations of property PrA which bring the dominant owners’ class the highest surplus product. The owners of the new means of production of type B introduce those organizational systems, from a set of the systems of the organization of production compatible with

112 Brzechczyn relations of property PrB, which bring them the highest surplus product. The new systems of the organization of production are compatible with relations of property PrB but incompatible with the prevalent relations of property PrA. There are, then, two types of productive forces in the society. Their owners introduce such systems of the organization of production as are optimal with respect to the level of productive forces of type A and B. Since the old productive forces dominate, and the new type remains, so to speak, marginal, the economically stronger class, that is, the owners of type A productive forces, has a monopoly on the introduction, on a global scale, of legal, political, ideological, and other systems which augment their position in society. The situation changes when the new productive forces start becoming more common in the society and producing a greater part of the national income than the pre-​existing productive forces A. That leads to a conflict of productive forces B with prevalent relations of property PrA. At that point, relations of property PrB start becoming common on a global scale; at a given level of productive forces B, they ensure the new class of owners of the means of production the maximization of the surplus product on the basis of the use of the optimal system of the organization of production. What follows in the subsequent periods, from a set of the historical systems of the organization of production compatible with new relations of property PrB, is that those organizational systems become prevalent in the society which ensure the class of the owners of type B means of production increasing levels of the surplus product, as the level of productive forces B changes. Next, that movement of adjustment to the new productive forces encompasses the remaining layers of the organization of social life: the legal and political superstructure and social consciousness, which adapt to the new type of productive forces. The image of a transition between formations obtained in that way is based on the coming into existence of a new type of productive forces and on a transformation of property relations. Within the framework of the adaptive interpretation of historical materialism, Buczkowski suggested a new periodization of social development. The class epoch consists of two stages. At each of them, a different –​ ­agrarian or industrial –​type of productive forces was dominant. The transition from one stage to the other happened by way of a macro –​revolution. During that revolution, the classes connected with the more efficient productive forces subdued the other social classes and fields of production. Socio-​economic formations can only be distinguished within those stages. For each stage, Buczkowski found two separate formations: slavery and feudalism in the agrarian phase, and free-​market capitalism and monopolistic capitalism (imperialism) in the industrial phase. Here is a graphic representation of historical development according to this author:

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­f igure 5.2  Stages and formations in the adaptive interpretation of historical materialism. Abbreviations used: PF –​productive forces; t –​ time; mA, mB –​the curve of the maximization of the surplus product of type A and B means of production; S, F, C, I –​respectively: the slavery, feudal, capitalist, and imperialist formations; AS, IS –​respectively: the agrarian and industrial stages; R –​the revolution related to the change of relations of property; MR –​the macro-​revolution related to the change of productive forces; AE, CE –​respectively: the socio-​ancestral epoch and the class epoch, t –​ time (Buczkowski 1982, 186).

4

Political Momentum in the Adaptive Interpretation of Historical Materialism

When two forms of ancestral (evolutionistic) and class (economic) materialism were distinguished, a problem appeared regarding the definition of the materialness of factors of social development. According to Andrzej Klawiter: “in a formation, the same material factor changes whereas within epochs a change of the type of material factors occurs” (Klawiter 1982, 284–​ 285). Klawiter proposed that the materialness of factors of social development should be determined methodologically, that is:  in a given historical

114 Brzechczyn period, those factors should be viewed as material, which fulfill the role of main factors. According to Nowak, three conditions must be met for the explication of the concept of materialness: –​ economic relations are to be material relations, –​ kinship relations are to be material relations, and –​ it cannot follow from the mere concept of a material relation that material relations are either economic or kinship relations. An appropriate definition of the concept of materialness includes a class of material relations which is broader than the two-​element class consisting of economic and kinship relations (Nowak 1977a, 252). In Nowak’s view, in  a socialist society, political relations aspire to the status of material ­factors: It is not impossible that socialist societies are governed by regularities noted by the third historical materialism, not ancestral or economic historical materialism but one that would be analogous to both of them and would have some factors of a third kind –​other than kinship or economic factors –​as the main factors. nowak 1977a, 252

Arguments for that thesis were –​according to Nowak –​discussions about the boundary between the base and the superstructure in the socialist economy or the role of an economic plan in economic activity held in socialist societies. Another issue was the status of social momentum, which was perceived as a relatively autonomous sphere of social life (Buczkowski, Klawiter and Nowak 1982, 241–​242). Here are the postulates satisfied by the definition of social momentum: –​ it reflects, in its internal structure, the global structure of social life which has three levels: the material one, consisting of means of a certain type and of a set of social relations among the people who use those means, a system of institutions which augment that state of interpersonal relations, and consciousness (knowledge) which motivates people to perform the social roles ascribed to them; –​ there are relations of adaptive dependency in it, characteristic of the global structure of social life: interpersonal relationships are adjusted to material means of a given type, an institutional system adjusts to the level of material means and social relations, etc.;

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–​ in the “final instance”, the material level decides about other levels of social life; –​ there is a division into those who decide about the use of material means and those who do not have such influence. The condition for the emergence of new social momentums is the appearance of new work tools. The concept of a work tool was used in a broader sense, encompassing not only production tools in the economic meaning of the term but also the means of coercion and of knowledge production. The condition for the diffusion of the new forms of the division of labor is, apart from the appearance of new tools, the ensuring of the maximization of the social interest of the new group which has those tools at its disposal, to at least the same degree as in the existing fields of the social division of labor (Buczkowski and Nowak 1979, 77; for an alternative conceptualization which points to the condition of the reproduction of the social being as the criterion of the adopting of the new tools on the mass scale and the resulting division of labor, see: Bartoszek, Bogalska –​Czajkowska, Czajkowski and Małkiewicz 1989; Czaj­ kowski 1993). Piotr Buczkowski, Andrzej Klawiter and Leszek Nowak (1982) made an attempt to create a third version of materialism, which should explain the development of socialist societies. The authors assumed that the internal structures of the political and cultural spheres were analogous to that of the economic sphere. In the political sphere, we could distinguish the means of coercion and a system of the organization of power which constituted a political base; the political base and the system of political institutions combined to produce social and political conditions, and there was also political consciousness. Those elements of the political momentum were linked by means of adaptive dependencies described with the following formulas: (i. P) That system, from a set of historically given systems of the organization of power, is adopted on mass scale in a society which ensures the highest sphere of regulation to the class of rulers, at a given level of the means of coercion. (ii. P) That system of political institutions, from a set of historical systems of political institutions, becomes widespread in a society which ensures the introduction of the most optimal system of the organization of power, at a given state of the political base. (iii. P) That system of ideas, from a set of historical systems of ideas, is adopted on the mass scale in a society which is the most effective tool for legitimizing the optimal system of political institutions, at a given level of social and political conditions.

116 Brzechczyn The means of coercion

The system of the organization of power

Political base

The system of political institutions

Political and social conditions

Political consciousness

diagram 5.5 The structure of the political momentum

The cultural momentum of a society was reconstructed in a similar way, by distinguishing the means of knowledge production and a system of the organization of knowledge production making up the cognitive base of a society. The cognitive base with the system of the organization of knowledge created cognitive and social conditions with an impact on meta-​cognitive consciousness. The adaptive dependency also linked the distinguished elements of the structure of the cultural momentum. This was expressed with the following formulas. (i. C) That system out of a set of historically given systems of the organization of knowledge production, is adopted on the mass scale in a society, at a given level of the means of knowledge production which is the most effective for increasing the number of the proponents of the ideas introduced by the people who have at their disposal the means of knowledge production,. (ii. C) That system out of a set of historically given systems of the organization of knowledge, is adopted on the mass scale in a society which ensures the introduction of the most optimal system of producing knowledge at a given state of the cognitive base. (iii. C) That system out of a set of historically given systems of meta-​cognitive consciousness, is adopted on the mass scale in a society which best The means of knowledge production

The system of the organization of knowledge production

Cognitive base

The system of the organization of knowledge

Cognitive and social conditions

diagram 5.6 The structure of the cultural momentum

Meta-​cognitive consciousness

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legitimizes the most optimal system of the cognitive organization at a given social-​cognitive conditions in the society. The authors assumed that the dominance of the economic momentum over the remaining momentums meant that the level of technological development directly, i.e. in a causal manner, decided about the effectiveness of the means of coercion and of the means of the propagation of knowledge. Moreover, when the assumption about the independence of the political momentum from the economic momentum was canceled, then the acceptance of the optimal system of power depended, in an adaptive way, on the level of the means of production and coercive measures. Those systems, from a set of historical systems of the organization of power, become common as they ensure the preservation of the most optimal system of the organization of production. That power system, from a set of power systems compliant with the optimal system of the organization of production, becomes prevalent which ensures the greatest sphere of power regulation. There are analogous relations on other levels of social life. The same relations occur between the economic and cultural momentums. The authors considered a situation in which the economic momentum lo­ ses its distinguished position (Buczkowski, Klawiter and Nowak 1982, 268). That happens when this momentum is not capable of maximizing its criterion of adaptation (the surplus product). Then, one of the subjugated momentums begins to dominate social life and ensures, through its domination, the survival of the society as a whole, as well as maximizing its own criterion of adaptation (in the case of the political momentum that criterion will be the increase of power regulation). According to the authors, the so-​called Asiatic social formation resulted from the dominance of the political momentum. Consequently, in the adaptive interpretation of historical materialism, the Asiatic social formation has been conceptualized in three ways:  Łastowski claimed that it to be a result of a variegated development of productive forces, and Buczkowski, Klawiter and Nowak –​a result of the dominance of the politi­ cal momentum. Moreover, Andrzej Klawiter (Klawiter 1989) analyzed in more detailed way the conditions of emergence of the Asiatic social formation and its theoretical status. According to his interpretation: General historical materialism would have to be not only the theory of formation but the theory of epochs and formations. The social epoch becomes the principle unit of periodization and social formation are social systems relative to the given social epoch. According to this approach the crucial points in human development are not inter-​formational transitions, but inter-​epochal transition. klawiter 1989, 30

118 Brzechczyn During the inter-​epochal transitions took place systematic bifurcations. The result of decline of the kinship epoch was an emergence of two formations: Asiatic and ancient formation based on slavery labor. The second inter-​epochal transition was transformation of the economical epoch into ‘institutionalized’ one where the political factors became the main determinants of social life. In the East the socialist economy emerged where the apparatus of Communist party became the collective owner of the means of production. Whereas in the West, the free-​competition capitalism was transformed into ‘managerial’ capitalism where the role of individual owners was gradually diminishing in favor of the rise of corporations connected with the state ­apparatus. 5

Class and Supra –​Class Societies. On the Rules of Periodization in Non-​Marxian Historical Materialism

For Nowak, attempts at applying the generalized form of the adaptive interpretation of historical materialism to the construction of a theory of socialism appeared to be unconvincing, which inspired him to construct non-​Marxian historical materialism (Nowak 1998, 228–​229). The new theory overtakes the adaptive interpretation of historical materialism’s view of the isomorphic structures of three realms of social life: politics, culture, and economy, and it strengthens the antagonistic nature of historical materialism. Consequently, the concept of social class is generalized. Nowak assumes that social classes exist not only in economy but also in politics and culture. In political life, the rulers’ class, which has at its disposal the means of coercion, increases the global sphere of influence and restricts citizens’ autonomy. In economic life, the owners’ class, which has at its disposal the means of production, maximizes its surplus product at the cost of producers’ direct income. In culture, the monopoly of the means of spiritual production allows the priests’ caste to augment their spiritual authority and restrict believers’ autonomy. The social antagonisms based on unequal access to material social means (means of coercion, production, and indoctrination) in each of the three realms of social life are, then, autonomous. Class divisions from the adjacent spheres of social life can only strengthen or weaken social antagonisms in a given social sphere. Class divisions can also cumulate and, for example, one social class, in order to boost its social power, can overtake the means of coercion and of production or the means of coercion and of indoctrination, etc. Nowak notes that the phenomenon described above leads to a situation in which: the economic momentum loses its exceptionality in a more general perspective. It turns out to be one of the three material momentums of society

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with the same internal structure […]. Now, when it is known that not only economic momentum is marked by the fact that the dominant role is played in it by the disposal of the material means of society and the needs of the masses, when it is known that not only the economic sphere of society generates the class division, then the role played in society by economy ceases to be self-​evident and requires an explanation. […] Now, there appears the possibility of taking into account –​within the materialist, not the idealist, and class, not the individualist perspective –​that there are at least theoretically admissible types of societies where not the economy but, e.g. politics plays the dominant role […]. Now this has become, not a matter of speculative considerations, but simply a matter of facts. […] in fact, such speculations are without any relevance  –​no society is possible without the working of gravity, an appropriate interval of temperature, appropriate rules of heredity and thousands of factors of a similar kind. nowak 1983, 177–​178

In light of Nowak’s materialist theory of power, then, real socialism turns out to be a system which evolves according to political and not economic development mechanisms. In that theory, economy is subordinated to the social interest of the political power. In Nowak’s words: social history comprises three development lines: on the one hand, the line of ancestral societies, from which the line of non-​European civilizations (for example, Inca or Chinese) derives, and, on the other hand, the line of the Western civilization. nowak 1997b, 12

The most substantial share of the philosophy of history traditionally divides the history of the societies of the world into the oriental and occidental lines of development. I would like to argue that that division is too rough to grasp the developmental diversity of non-​European societies. Furthermore, the criterion of this division is unknown –​there is only the reference to the geographical characteristics of the “West” and “Orient”. The significant feature of the societies belonging to the occidental line of development (European civilization) was the separation of class divisions. In the history of non-​European civilizations, different configurations of accumulated class divisions appeared (Brzechczyn 2007). If, then, we limit our reflections to the history of European societies, we could say that there have been three historical epochs: –​ ancestral societies, –​ economic societies (classical Western civilization), and –​ political societies (real socialist societies).

120 Brzechczyn That can be illustrated in the following way.

­f igure 5.3  The structure of the theory of the historical process in non-​Marxian historical materialism A single arrow means the relation of concretization, a short arrow –​a transition between formations, and a double arrow –​a transition between epochs; epoch A, B, and C, respectively, represent the ancestral, economic and political epochs (based on: Nowak 1981, 57).

In non-​Mhm, the mechanism of the motion of an economic society was also changed in comparison with the mechanism of development in the adaptive interpretation of historical materialism. In the latter conceptual framework, the basic mechanism of historical development was the adjustment of property relations to the growth of productive forces. Whereas, in the theory of economic societies in non-​Mhm, the main mechanism of motion was economic class struggle between owners and direct producers, which enforced the evolution of property relations. The tendency of the development of Western societies  –​from slavery through feudalism to capitalism  –​was growing liberation of labor. In fact, serf was more liberated than a slave, and a worker in a capitalist factory was more liberated than a serf. However, in socialist societies those mechanisms of development changed because the main social contradictions occurred in the political realm. The interest of the rulers’ class was the maximization of political control over of activity of citizens. Generally speaking, the development of a purely political society involves the stages of the increasing, stabilization and reduction of power regulation. Another source of social antagonism was the supra-​class competition between rulers and owners. The domination of a class of rulers over a class of owners may lead to taking over control of the means of production and building of a totalitarian society. The domination of owners over the class of rulers may lead to taking over control over the means of coercion by owners (Nowak 1983, 189–​210).

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The periodization of the historical process assumed in n-​Mhm is ambiguous because of the conceptualization of the socio-​ancestral epoch. According to adaptive interpretation of historical materialism, the developmental regularities of ancestral societies relied on the mechanism of adaptation of kinship relations to the need of reproduction of immediate life. Whereas, in the economic and political epochs, developmental regularities are based on the  mechanism of class struggles (of economic and political types), which are the basis for the refutation of historical materialism in adaptive version. Therefore, n-​Mhm in its present shape is compounded both from solidaristic part (inherited from adaptive interpretation of materialism) in regard to ancestral epoch and antagonistic part in regard to economic and political epochs. Therefore the most important deficiencies of the periodization are: –​ the nature of ancestral societies: in the adaptive interpretation of historical materialism, it is believed to be a non-​antagonistic formation because class divisions appeared in class societies; however, if non-​Marxian historical materialism is an antagonistic theory, then it should, as it distinguished the line of ancestral societies, also determine the type of social antagonism characteristic of that type of societies (such an attempt was made in Buchowski 2003); –​ in that theory, socio-​economic formations (slavery, feudalism, capitalism) are distinguished, but analogous socio-​political or socio-​cultural formations are not, so we should either give up socio-​economic formations or introduce socio-​political and socio-​spiritual formations (Brzechczyn 2004, 107–​109); –​ the social systems in non-​European societies represent different configurations of cumulated class divisions (Brzechczyn 2007, 250–​252), 6

Conclusions

Periodization always assumes a theory of the historical process that is connected with its spatialization, understood as the setting up of a geographical range of the influence of factors recognized as principal ones in a given theoretical approach (e.g. Griesemer 1996, 20–​21). Periodization proposed in theory of historical process developed in Poznań School of Methodology resulted from conscious accepted methodological assumptions and theoretical view on importance of the selected factors of historical development. Leszek Nowak proposed an idealizational and essentialist interpretation of Marxian historical materialism what allowed him to show that Marx’s (and especially his interpretators) periodization of history is obscure. Nowak argued that new, adaptive reinterpretation of Marx’s famous formulae (social being

122 Brzechczyn determines social consciousness; base determines superstructure; material productive forces determine existing relations of production) reveals that the division of human history into two epochs: ancestral and economic societies. The epoch of economic societies consisted from three economic formations (slavery, feudalism, capitalism) reflects essential changes in economic regularities. Adaptive interpretation of historical materialism allowed also to i­ nterpret conditions of systematic bifurcation during the transition from ancestral to economic epoch. At that inter-​epochal transition there emerged two separate lines of development: Asiatic (Oriental) and the classical (Western) three-​formation line of development. However, in adaptive interpretation of historical materialism the status of the political momentum was unclear and interpreted in various way. In his later works Nowak presented new theory, non-​Marxian historical materialism where the sphere of politics was fully conceptualized. This theory resulted in an expanded, much more complex, multidimensional periodization of human history. However, some ambiguities of non-​Marxian historical materialism in that regard –​as I have argued elsewhere (Brzechczyn 2004, 66–​86; Brzechczyn 2007) –​indicate that this theory is still not, in its current form, a theory capable of encompassing the whole of historical development, including the history of non-​European societies. One research problem, which has yet to be solved within the framework of non-​Marxian historical materialism, is how to approach the development of societies which belong to both the European and non-​European developmental lines and how to create a consistent periodization of the historical process on that basis.

References

Bartoszek, A., E. Bogalska-​Czajkowska, W. Czajkowski, and A. Małkiewicz. 1989. The Social Division of Labour. In Dimensions of the Historical Process. Edited by L. Nowak. Poznań Studies in the Philosophy of the Sciences and the Humanities. Vol. 13. Amsterdam: Rodopi, 103–​118. Brzechczyn, K. 2004. O wielości linii rozwojowych w procesie historycznym. Próba interpretacji ewolucji społeczeństwa meksykańskiego [On the Multitude of the Lines of Development in the Historical Process. An Attempt at Interpretation of Evolution of Mexican Society]. Poznań: Wyd. Naukowe uam. Brzechczyn, K. 2005. Dynamika formacji. O Piotra Buczkowskiego koncepcji marksizmu analitycznego [The Dynamics of a Formation. On Piotr Buczkowski’s Concept of Analytical Marxism]. In:  Państwo, samorząd i społeczności lokalne. [The State, Local Government and Local Communities] Edited by K. Bondyra, M. S. Szczepański and P. Śliwa. Poznań: Wydawnictwo wsb, 389–​415.

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Brzechczyn, K. 2007. On the Application of non-​Marxian Historical Materialism to Development of non-​European Societies. In The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak. Edited by J. Brzeziński, A. Klawiter, T. A. F. Kuipers, K. Łastowski, K. Paprzycka, and P. Przybysz. Amsterdam, New York (NY): Rodopi, 235–​254. Brzechczyn, K. 2017. From Interpretation to Refutation of Marxism. On Leszek Nowak’s non-​Marxian Historical Materialism. Hybris 37: 141–​178. Buchowski, M. 2003. Społeczeństwo pre-​ momentowe. Próba uzupełnienia nie-​ Marksowskiego materializmu historycznego [Pre-​Momentum Society. An Attempt at Complementing Non-​Marxian Historical Materialism]. In: Ścieżki transformacji. Ujęcia teoretyczne i opisy empiryczne. [Transformation Paths. Theoretical Approaches and Empirical Descriptions] Edited by K. Brzechczyn. Poznańskie Studia z Filozofii Humanistyki. Vol. 19. Poznań: Zysk i S-​ka, 295–​316. Buczkowski, P. 1978. Teoria ruchu formacji społeczno-​ekonomicznej. Próba interpretacji adaptacyjnej [The Theory of the Motion of the Socio-​Economic Formation. An Attempt at an Adaptive Interpretation]. In: Założenia materializmu historycznego [Presuppositions of Historical Marxism]. Edited by L. Nowak. Vol. 3. Poznań, Warszawa: pwn, 157–​199. Buczkowski, P. 1981. Z problematyki teorii społeczeństw ekonomicznych [On the Problems of the Theory of Economic Societies). Szczecin: pam. Buczkowski, P. 1982. Toward a Theory of Economic Society, An Attempt at the Adaptive Interpretation. In: Social Classes…, 158–​210. Buczkowski, P., A. Klawiter, and L. Nowak. 1982. Historical Materialism as a Theory of Social Whole. In: Social Classes…, 236–​280. Buczkowski, P., and L. Nowak. 1979. Idealizacja a istotność. Studium przypadku: ­Marksowska teoria klas społecznych [Idealization and Essentiality. Case Study: Marxian Theory of Social Classes]. In: Odkrycie, abstrakcja, prawda, empiria historia a ­idealizacja. [Discovery, Abstraction, Truth, Historical Empiricism and Idealization] Edited by A. Klawiter and L. Nowak. Warszawa, Poznań: pwn, 59–​86. Burbelka, J. 1980. Epoki i formacje. Próba rekonstrukcji adaptacyjnej [Epochs and Formations. An Attempt at an Adaptive Interpretation]. Kraków: Ossolineum –​ pan. Burbelka, J. 1982. Historical Materialism. General Theory and Forms. In: Social Classes…, 211–​235. Czajkowski, W. 1993. Social Being and its Reproduction. In Social System, Rationality and Revolution. Edited by L. Nowak and M. Paprzycki. Poznań Studies in the Philosophy of the Sciences and the Humanities. Vol. 33. Amsterdam: Rodopi, 153–​176. Griesemer, J.R. 1996. Periodization and Models in Historical Biology. In: New Perspectives on the History of Life. Edited by M.T. Ghiselin and G. Pinna. Los Angeles: The California Academy of Science, 19–​30. Kautsky, Karl. 1909. Ethics and the Materialist Conception of History. Chicago: Charles H. Kerr & Co.

124 Brzechczyn Klawiter, A. 1982. The Theory of Social Formation in Historical Materialism. In: Social Classes…, 281–​294. Klawiter, A. 1989. Historical Materialism and the Visions of Social Development. A Study of Transformation of Marxian Periodization Formula. In Dimensions of The Historical Process. Edited by L. Nowak. Poznań Studies in the Philosophy of the Sciences and the Humanities. Vol. 13. Amsterdam: Rodopi, 9–​37. Krzywicki, L. 1960. Dzieła [Works]. Vol. 4. Warsaw: pwn. Lorenz, Ch. 2017. ‘The Times They Are a-​Changin’. On Time, Space and Periodization in History. In: Palgrave Handbook of Research in Historical Culture and Education. Edited by M. Carretero, St. Berger and M. Grever. London: Palgrave, 109–​130. Łastowski, K. 1981. Problem analogii teorii ewolucji i teorii formacji społeczno-​ ekonomicznej [The Problem of the Analogy of the Theory of Evolution and the Theory of the Socio-​Economic Formation]. Warszawa, Poznań: pwn. Łastowski, K. 1982. The Theory of Development of Species and the Theory of Motion of Socio Economic Formation. Social Classes…, 122–​157. Nowak, L. 1970. O zasadzie abstrakcji i stopniowej konkretyzacji [On the Principle of Abstraction and Gradual Concretization]. In Założenia metodologiczne “Kapitału” Marksa [Methodological Presuppositions of Marx’s “Capital”]. Edited by J. Topolski. Warszawa: KiW, 123–​218. Nowak, L. 1971. U podstaw Marksowskiej metodologii nauk [The Foundations of the Marxian Methodology of Science]. Warszawa: pwn. Nowak, L. 1973. Teoria formacji społeczno-​ekonomicznej jako teoria adaptacyjna [The Theory of a Socio-​Economic Formation as an Adaptive Theory]. Studia Socjolo­ giczne 4: 5–​21. Nowak, L. 1974. Zasady marksistowskiej filozofii nauki. Próba systematycznej rekonstrukcji [The Principles of the Marxist Philosophy of Science. An Attempt at a Systematic Reconstruction]. Warszawa: pwn. Nowak, L. 1977a. O wielości materializmów historycznych [On the Plurality of Historical Materialisms]. In: Założenia teoretyczne badań nad rozwojem historycznym [Theoretical Presuppositions of the Study on Historical Development]. Edited by J. Kmita. Warszawa: pwn, 250–​256. Nowak, L. 1977b. Wstęp do idealizacyjnej teorii nauki [The Introduction to the Idealizational Theory of Science]. Warsaw: pwn. Nowak, L. 1977c. U podstaw dialektyki marksowskiej. Próba interpretacji kategorialnej [The Foundations of Marxian Dialectics. Towards a Categorial Interpretation]. Warszawa: pwn. Nowak, L. 1980. The Structure of Idealization. Towards a Systematic Interpretation of the Marxian Idea of Science. (Synthese Library, vol. 139). Dordrecht, Boston, London: Reidel.

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Nowak, L. 1981. Wolność i władza. Przyczynek do nie-​Marksowskiego materializmu historycznego [Freedom and Power. Towards a non-​Marxian Historical Materialism]. Poznań: NZS AR. Nowak, L. 1982. The Theory of Socio-​Economic Formation as a Theory of Adaptation Process. In: Social Classes…, 110–​121. Nowak, L. 1983. Property and Power. Towards a non-​Marxian Historical Materialism (Theory and Decision Library, vol. 27). Dordrecht, Boston, Lancaster: Reidel. Nowak, L. 1998. The Adaptive Interpretation of Historical Materialism: A Survey. On a Contribution to Polish Analytical Marxism. In: Marx’s Theories Today. Edited by L. Nowak and R. Panasiuk. Poznań Studies in the Philosophy of the Sciences and the Humanities. Vol. 60. Amsterdam, Atlanta: Rodopi, 201–​236. Nowak, L. 1997. Marksizm versus liberalizm. Pewien paradoks [Marxism Versus Liberalism. A Paradox]. In: Marksizm, liberalizm: próby wyjścia [Marxism, liberalism: Attempt of Overcoming]. Edited by L. Nowak and P. Przybysz. Poznańskie Studia z Filozofii Humanistyki. Vol. 17. Poznań: Zysk i S-​ka, 7–​21. Nowak, L., and I. Nowakowa. 2000. Idealization X: The Richness of Idealization. Poznań Studies in the Philosophy of the Sciences and the Humanities. Vol. 69. Amsterdam, Atlanta: Rodopi. Sato, M. 2015. Time, Chronology and Periodization in History. In: International Encyclopedia of the Social and Behavioral Sciences. Edited by J.D. Wright. Oxford: Elsevier, 409–​414. Social Classes Action and Historical Materialism. 1982. Edited by L. Nowak. Poznań Studies in the Philosophy of the Sciences and the Humanities. Vol. 6. Amsterdam: Rodopi. Topolski, J. (1996). Jak się pisze i rozumie historię. Tajemnice narracji historycznej [How to Write and Understand History. The secrets of Historical Narration]. Warszawa: Rytm.

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Władysław Tatarkiewicz: Metaphilosophical Notes Ryszard Kleszcz Abstract Władysław Tatarkiewicz was one of the most significant Polish historian of philosophy and historian of art and aesthetics. In reality, he was not only a historian but also a scholar of broad interest in area of systematic philosophy (aesthetics, general axiology, ethics and methodology of humanities). In this paper, I discuss his important methodological and metaphilosophical ideas. The article presents not only Tatarkiewicz’s metaphilosophical/​methodological opinions but also tries to reconstruct specificity of his philosophical position.

Keywords history of aesthetics  –​history of art  –​history of philosophy  –​metaphilosophy  –​ ­methodology –​ Władysław Tatarkiewicz –​ systematic philosophy

…

It is not the privilege of philosophy to “bring us closer to the truth.” All sciences do this in their own way, and so do everyday experience and thinking. They show us mental truths as well as quite general ones. But mostly only the truths with a small “t.” władysław tatarkiewicz

…

[Władysław Tatarkiewicz] is one of the most eminent citizens of this great supra-​territorial and timeless Republic of thinkers in which only one law governs: love and respect for the truth. izydora dąmbska

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Introduction

Władysław Tatarkiewicz, one of the great figures of Polish twentieth-​century philosophy, was a historian of philosophy, an aesthetist, a historian of aesthetics and also an art historian. These domains of his work are widely known and his achievements, especially in the field of aesthetics and its history, are held in high regard, including by the world’s leading aesthetists.1 His scholarly output further comprises many works in the field of systematic philosophy. This kind of output belongs mainly in the domain of axiology and ethics. However, some of his works are also methodological in nature or, as I will try to demonstrate, in part metaphilosophical. The achievements of this philosopher in the field of axiology and ethics seem to be relatively well known, at least in Poland.2 On the other hand, less attention has been devoted to the analysis of Tatarkiewicz’s views concerning, at least in part, the understanding of philosophy (its goals and functions)3, its methods, and the relation of philosophy to science and other areas of culture.4 That is, the issues which can be classified within the discipline of metaphilosophy.5 When attempting to reach reasonable conclusions in this regard, however, one faces a certain difficulty. In the scholar’s output, there is no concise system of views comprising a clear and complete whole constitutive of this field. Yet, in his monographs, articles, and reviews, or in interviews with Tatarkiewicz, we find a significant number of more or less extensive indicators, sometimes only loose remarks, which allow the reconstruction of at least some of the Tatarkiewicz’s metaphilosophical assumption. Such reconstruction requires the indicators to be extracted and arranged into a coherent whole. At the starting point, however, there is an uncertainty as to whether it will be possible to create a uniform, not to mention holistic, picture. For these reasons, I have decided to call this sketch of metaphilosophical views Metaphilosophical Notes. The final results of this project will reveal whether, and to what extent, it will be possible to construct even a partially concise whole from these notes, one could say crumbs.

1 Cf. on Tatarkiewicz’s aesthetic views:  (Dziemidok 1967), (1971); (Wiśniewski 1979); (Jaworska 1982). 2 Cf. (Wiśniewski 2013; 1978; 2001). 3 However, it cannot be argued that there are no such works at all. In this regard, see especially: (Pacuła 1976); (Dąmbska 1981); (Jadacki 1981); (Woleński 1987). 4 With regard to the methodological issues, cf. (Jadacki 2003). 5 Briefly, metaphilosophy can be understood as: “The theory of the nature of philosophy, especially its goals, methods, and fundamental assumptions” (The Cambridge Dictionary of Philosophy, 487). Cf. also (Kleszcz 2011, 31–​44); (Overgaard, Gilbert, Burwood 2013, 1–​16).

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Intellectual Environment

When attempting to reconstruct a general outline of the views of the scholar in question, including his metaphilosophy, initial consideration needs to be given to the intellectual environment which constituted his intellectual background and to the intellectual currents which influenced him and/​or were close to him. The first lecturer of philosophy that Tatarkiewicz encountered was Adam Mahrburg, a Warsaw philosopher educated in Russia (St. Petersburg) and Germany (Leipzig, Wundt’s laboratory). During law studies at the imperial Russian-​language Warsaw University, Tatarkiewicz also attended secret lectures led by Mahrburg. After many years, he regarded the philosophical qualities of this scholar very highly. This is what he writes in Zapiski do autobiografii [Notes for an Autobiography]: I was not interested in university lectures, but I attended the secret, mostly philosophy and psychology lectures by Adam Mahrburg. These conspiratorial lectures were probably the best I ever attended in my life. But I would go to them for pleasure, just like going to a concert or theatre, and it never occurred to me that I would one day lecture on philosophy.6 tatarkiewicz 1979, 122–​123

The first philosophical community, or school of philosophy, which influenced Tatarkiewicz were the Marburgian neo-​Kantians.7 He met them, in particular, professors Herman Cohen and Paul Natorp, as a student of philosophy in Marburg. He was influenced by these scholars to some extent (Tatarkiewicz 1978b, Przedmowa, 9). However, this influence was limited. Władysław Tatarkiewicz, as he himself says, adopted from his Marburg teachers a general framework of philosophizing and expression, as well as the courage to analyze great philosophers in order to look for the essence of their views. This influence was not insignificant for someone dealing with the history of philosophy. However, neither his sympathy for Aristotle, the topic of his doctoral dissertation, nor his thesis about the pluralism of his views were adopted from them (Tatarkiewicz 1978b, “Przedmowa,” 12). This thesis, concerning Stagirite, supported by Tatarkiewicz in his doctoral dissertation, was completely unknown to the Marburgian neo-​Kantians. 6 Cf. also (Tatarkiewicz 1915, 206; Tatarkiewicz 1948, 7–​8). Tatarkiewicz, speaking about the philosophical celebrities he encountered in his life, lists the following Poles as: Kazimierz Twardowski, Fr. Konstanty Michalski and Adam Mahrburg (Tatarkiewicz 1979, 174). 7 W. Tatarkiewicz’s writings regarding the Marburg School are collected in the volume (Tatarkiewicz 2010, passim).

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The influence of Cohen and Natorp, though inspiring interest in the history of thought, can therefore be considered more formal than factual. This is what Tatarkiewicz himself says about his philosophical studies in Marburg: There were few classes: four times a week in the afternoon there were lectures by two professors. … I worked in my room in the mornings and evenings, in the first year I read Plato, in the second Kant, in the third the professor suggested Aristotle as the topic of my doctoral dissertation. I bought five great volumes of the old Prussian Academy edition of his works, and gradually remembered the Greek I had learned in grammar school. After a year, the dissertation was ready, I  did not think about whether it was good; I was thinking about getting a diploma, not about making philosophical discoveries; I showed it to the professors, they did not advise anything, did not criticize, they approved. … This is how my studies ended … I learned in their course how some philosophers do science, but none of them advised me how I should do it; nor did they suggest a topic for further work. I admired my Marburg masters, but I did not have the slightest desire to follow their path. tatarkiewicz 1979, 125

But even this influence ceased when in 1915 Tatarkiewicz took up the position of a lecturer in philosophy at the, by then, Polish University of Warsaw. Although the influence of the Marburg professors had ceased, the sympathy of the then young scholar to the author of Nicomachean Ethics, who did not have the recognition of the Marburgers, proved to be something permanent (Tatarkiewicz 1978, vol. 3, 244). This sympathy was already stable, although his concept of Aristotle’s views was subject to certain transformations. It is clearly different in his doctoral dissertation and in the first volume of Historia filozofii [History of Philosophy], and a bit more different in a later publication devoted to Aristotle’s ethics (Trzy etyki: studium z Arystotelesa [Three Ethics: A Study in Aristotle]). What made the greatest impression on Tatarkiewicz in this second period was the philosophical common sense characteristic of Stagirite (Tatarkiewicz 1978, vol. 1, 104–​120, especially 120). As emphasized in the preface to the Polish translation of the Die Disposition der Aristotelischen Prinzipien: This time, I saw Stagirite very differently, as the most reasonable of philosophers, as the one who found the golden mean, who was more cautious than all the classicists of caution. I  have maintained this second conception so far. It became more prominent when in the 1930s I  was involved in Aristotle’s ethics, the ethics of moderation and friendship. It

130 Kleszcz became even stronger in the 1950s when I studied his aesthetics, when I found (in Politics) the definition of art as a noble entertainment, and also when I found (in Eudemian Ethics) the analysis of aesthetic experience in all its complexity and (in Rhetoric) the theory of beauty in terms of observable phenomena. This confirmed for me the concept of Aristotle as a philosopher of common sense. I encountered such philosophy at least once in my times: in Kazimierz Twardowski.8 tatarkiewicz 1978b, 13

We have now come to the second environment which had a significant influence on Tatarkiewicz, which is the Lvov environment established by Twardowski. This will be discussed in the next section, which looks at his (Tatarkiewicz’s) attitude to analytic philosophy in general. 3

On Analytic Philosophy

The aforementioned affinity and respect for Aristotle are also evident in an interview he gave in 1974 to Stefan Kisielewski for Tygodnik Powszechny. In this interview, or rather in answers to previously prepared questions, Tatarkiewicz, showing some scepticism about the possibility of building a philosophical system, once again expresses his sympathy for the Aristotelian system, noting: I understand the need for a philosophical system, but this effort does not attract me. Sometimes I think that this is not a task for a human being; in any case it is not for me. If I were to associate myself with any system, it would be Aristotle’s.9 kisielewski 1974, 2

It can be seen, thus, that Tatarkiewicz’s attitude was moderately minimalistic, close to what we find in analytic approaches, as well as in the one preferred by 8 In his 1933 work devoted to the ethical views of Stagirite titled Trzy etyki: studium z Arystotelesa (first edition in French 1931, Polish edition 1933), Tatarkiewicz distinguishes three ethical positions evident in Aristotle, which can be found in the Nicomachean Ethics. These are: the ethics of contemplative life, the ethics of active life, based on the principle of justice, and the ethics of friendship. What is usually referred to as Aristotelian ethics is the ethics of active life outlined in books i-​i v of Nicomachean Ethics. Cf. (Tatarkiewicz 1971d, 324-​ 338). 9 At another place in this interview, Tatarkiewicz adds that in Aristotelianism he is fascinated by the attempt to conceptualize the multiplicity of things in simple terms. Cf. (Tatarkiewicz 1971d, 2).

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Kazimierz Twardowski. It is in his work that Tatarkiewicz finds the common sense that he values. As he notes, the work of the founder of the Lvov-​Warsaw School also began with Aristotle (Tatarkiewicz 1978b, Przedmowa, 13). In the case of Twardowski, Władysław Tatarkiewicz was attracted to the merits of his works and his pedagogical achievements. As stated in a brief description of his views in volume 3 of Historia filozofii [History of Philosophy]: The bright and sober thinker, and the teacher by God’s grace, he was, along with Mahrburg and Weryho, the most accomplished philosopher in Poland in the last half-​century. tatarkiewicz 1978, vol. 3, 360

As Tatarkiewicz notes, this eminent teacher and bright thinker: created a school that had not yet been created by any philosopher in Poland. He implemented Jan Śniadecki’s desire: to create a philosophy that would be adequate for educating scholars. tatarkiewicz 1978, vol. 3, 361

This high evaluation concerned the activity of the entire community in which Twardowski was active. As Tatarkiewicz observes, characterising the period after his return from studies in Germany: Having completed my doctoral studies, I  went to Lvov. I  wanted to know how the Poles work. Immediately I found out that they work differently and better: Twardowski’s school taught how to work scientifically. … .I managed to attend only two lectures and two seminars by the master. I do not remember what was being talked about, but I remember the method and it suited me more than that of other Western professors. tatarkiewicz 1979, 125

This acclaim for Twardowski and his school was expressed in recognition of the method of philosophizing, as well as in reckoning with Twardowski’s views. This is what Tatarkiewicz wrote in a letter to Twardowski, referring to his Historia filozofii [History of Philosophy], completed in 1929 (published by Ossolineum in 1930): I must admit that when writing it, I was wondering whether there was sufficient clarity and accuracy of thought, structure and expression, the

132 Kleszcz examples of which the Professor has provided and is therefore entitled to demand from Polish philosophical writers. quoted after: jadczak 1997, 190

It should be added that Twardowski also valued Tatarkiewicz. We find mutual recognition and respect in the letters they wrote to each other. Among other things, Twardowski warmly supported Tatarkiewicz’s candidacy for a position at the 3rd Philosophical Department at the University of Warsaw. He also contributed to Tatarkiewicz’s successful habilitation at the University of Lvov.10 In Dzienniki [Diaries], he noted his support for entrusting the department at the University of Wilno to Tatarkiewicz: I talked to Dr. Ziemacki […] about the opening at the department of philosophy in Wilno. I strongly recommended Tatarkiewicz. twardowski 1997, Part I, 114

In general, it may be argued that respect for common sense and for the postulate of clarity and precision meant that he was close to the trends of this nature. As far as analytic thinking is concerned, close to Tatarkiewicz’s heart was openness, which was greater than in positivism and not dogmatically decisive about the limits of research and cognition (Tatarkiewicz 1978, vol. 3, 368). Tatarkiewicz also valued the change that was taking place due to analytic philosophy, namely the move away from the specialist language, accessible to a small group of initiates, in favour of what he called ordinary and simple talk (Tatarkiewicz 1978, vol. 3, 372). It is also worth noting that in the interview given to Stefan Kisielewski, Władysław Tatarkiewicz clearly indicated that British analytic philosophy suited him best: I can say what “position” suits me in philosophy: British “analytic philosophy.” In “life,” but not in my academic work, I find Pascal helpful. kisielewski 1974, 2

This statement emphasizing an affinity for analytic philosophy, this time British philosophy specifically, touches upon two interesting issues.11 Tatarkiewicz 10 11

Cf. (Twardowski 1997, Część I: 1915–​1927, 96, 104 -​105). R. Jadczak writes more broadly about the relations between Tatarkiewicz and Twardowski (Jadczak 1997, 181–​192). When pointing out the closeness to British analytic philosophy, G.E. Moore seems to be of particular significance. Tatarkiewicz was the author of a review of his Polish edition of Principia Ethica (Polish title:  Zasady etyki). Cf. Ruch Filozoficzny V (3). 1919/​

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notes that on the theoretical level, British analytic reflection is close to him, whereas in the realm of life it is Pascal’s reflection.12 Regarding the first issue, let us note that Tatarkiewicz must have been close to the realist attitude of the British analytical philosophers, their focus on careful philosophizing, distrust in the aspirations to build a system and focus on the implementation of partial, somewhat preparatory tasks, scrupulous analysis of notions, and adjourning the (potential) construction of philosophical syntheses (Tatarkiewicz 1978, vol. 3, 224–​235). The distinction between theoretical and life (existential) cognitive realms is also interesting. Theoretical philosophy does not provide answers to existential dilemmas, hence they should be sought elsewhere. As Tatarkiewicz points out: In Pascal, I value the assertion of helplessness of rational methods in dealing with life’s most important issues. And the clear recognition of the “order of the heart” alongside the “order of reason,” I value the statement that “a man is always divided against and opposed to himself,” that “the heart has its reasons, which reason does not know,” that one must “have three qualities –​ those of the geometrician, of the Pyrrhonist and of the humble Christian.” tatarkiewicz 1978a, 136

If any clues concerning “life’s most important issues” can be found in a broadly understood philosophical reflection, they can only be found in Pascal’s thinking, which is unusual for a philosopher-​theoretician. Tatarkiewicz also wrote about Pascal in a text dedicated to Twardowski, titled: Porządek dóbr. Studium z Pascala [Order of Goods. A Study in Pascal] (Tatarkiewicz 1971e, 339–​365). This distinction is consistent with the general attitude of the Polish philosopher. This is because Tatarkiewicz was convinced that science and scientific cognition do not have a “monopoly on learning about and explaining the world.”13

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1920: 51a-​52a. It is also necessary to point out Moore’s influence on the solutions adopted by Tatarkiewicz in his work O bezwzględności dobra (cf. Wiśniewski 2013, 24, 26–​27, 41–​ 42, 47–​48, 57–​63, 79–​80, 96 et seq.). In a letter to Andrzej Nowicki (16 February 1974), when answering the question about his philosophical ancestors, Tatarkiewicz slightly widens his catalogue. In addition to Aristotle, Pascal, and British analytics, he adds scholastics (as to the order of presentation) and essays by Bacon, which he values higher than Hume’s essays, appreciating their literary elegance of presentation. He also adds that he is not fond of French or German style in scientific literature (Listy Władysława Tatarkiewicza z lat 1942–​1977 do Andrzeja Nowickiego (inedita) 1980, 8). In the preface to the collection of essays Droga do filozofii [Road to Philosophy] Tatarkiewicz recalls that he was once considered a positivist. He also notes that this

134 Kleszcz In terms of the consequences, this distinction is convergent with the distinction between great and close philosophers. Among philosophers (analogically among statesmen or creators of culture), we find people who are somehow objectively great and those who are close to certain people or communities.14 For Tatarkiewicz, such philosophers as Descartes, Spinoza, Saint Thomas or Leibniz are undoubtedly great, but they are not close to him. On the other hand, Aristotle and Pascal are close to him (Tatarkiewicz 1978a, 130-​136). The first was a philosopher of common sense, as discussed above, and the second one was close because he addressed existential issues which were important to Tatarkiewicz but which were not well represented in analytic philosophy, especially of that time. So, it can be argued that Tatarkiewicz, at least for his own use, proposes to go beyond analytical thought and to reach for reflection of the existential-​religious type. It is worth adding that Tatarkiewicz did not overestimate the possibility of using philosophical tools in the domain of religion. In the interview given to Kisielewski, he pointed out that in the case of religion, an element of mystery connected with faith must be preserved.15 4

Tatarkiewicz on the Role of Logic in Philosophy

The affinity for analytical thought naturally raises questions about the role that Tatarkiewicz ascribed to logic in philosophy. Logic in its modern form (what used to be called logistics, or mathematical logic) has played an important role in the analytic tradition since its dawn. The importance of this tool for

14

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label could be accepted, if positivism was considered an adequate theory of science and, at the same time, if it could be assumed that science has no cognitive monopoly, as already pointed out (Tatarkiewicz 1971, Przedmowa [Foreword], 8). As pointed out by J. J. Jadacki, in this respect we can discern the influence of his Wilno friend, Marian Massonius (Jadacki 1981, 42–​43). Of course, philosophers can be great and close at the same time. For many philosophers and historians of philosophy, such thinkers as Plato, Aristotle, Saint Thomas or Kant are both great and close. However, for others, some of them may be great but not close. Moreover, it must be remembered that a judgement of greatness may be corrected by the next generation. But, as Tatarkiewicz points out, some of the great have stood the test of time. “I am an advocate of dualism, delimitation, there must be mysteries of faith!” (Kisielewski 1974, 2). This dualism is also evidenced by a distinctive sentence from a letter to Professor Ryszard Wiśniewski: “One more thing: defining my ethics as secular is ambiguous, it is »secular« in an areligious sense (like physics or linguistics), but not in an anti-​religious sense (like materialistic philosophy). Thus, Tatarkiewicz, as a Catholic, seems to clearly separate various realms of culture and cognitive activity, without granting a monopoly to any them” (Listy Władysława Tatarkiewicza do Ryszarda Wiśniewskiego 2011, 717).

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philosophy, especially in this tradition, needs no explanation. The great contemporary English philosopher Michael Dummett was inclined to view Gottlob Frege, the founder of modern logic, as the father of analytic philosophy. Regardless of the validity of Dummett’s view, historical reliability requires us to recognize that since the beginning of philosophical analysis, apart from the approach which postulated an extensive application of logic in philosophy (B. Russell’s approach), there was also the approach represented by G. E. Moore, who did not use the tools of formal logic in his analysis of ordinary language. And to Tatarkiewicz, this second, that is informal attitude is closer. I have mentioned how important it was to him to organize the conceptual apparatus and bring clarity to the language used. This is clearly discernible in the content of his short letter constituting an answer to the Znak monthly questionnaire which asked the question: “What is the philosophy that you do?” That’s how Tatarkiewicz answered this question: My philosophy consists in organising concepts, nothing more. Namely, those which I use constantly, and which are so appealing that not only can one write books about them, but even publish them. […] I just want to clearly organize the concepts I use –​which is quite a task. tatarkiewicz 1977, 1334

Thus, he was an advocate of using widely understood logical tools in philosophy, especially when the goal was elucidation of the terms used and clarification of theorems. This attitude sheds light on the importance that Tatarkiewicz attached to semiotic tools (Pelc 2001, 33–​41).16 We encounter the processes of defining, determining meaning, extracting ambiguity and classifying at every step in his work.17 The importance attached to semiotic analysis and definition is confirmed by the content of the first four chapters of the treatise O szczęściu18

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17

18

This is clearly articulated by Pelc: “Even though Władysław Tatarkiewicz was not a semiotician, in almost every book and treatise, in every chapter of his Historia filozofii he wrote about words, and while lecturing he talked about words, revealing their ambiguity; he warned about its effects and showed interpretative possibilities of what seemed to be a single view” (Pelc 2001, 38). As pointed out by Tatarkiewicz, apart from gathering facts or determining their origin, classification activities, which allow for the emergence of characteristic types, play an important role in the work of a humanist, especially a historian of art or philosophy (Tatarkiewicz 1951, 103 et seq.). He indicates there that a definition can be a reconstruction of meaning, its construction or it can lie in the middle (Tatarkiewicz 1962, 38 et seq.).

136 Kleszcz [On Happiness]. The first chapter, entitled Cztery pojęcia szczęścia [Four Concepts of Happiness], begins with an unambiguous statement: Thinking about happiness must begin with a linguistic analysis: we must first explain what the word “happiness” means so that we can then talk meaningfully about happiness. tatarkiewicz 1962, 15

Such analyses of meaning are especially important and difficult when working in the realm of anthropological and axiological issues, which are the subject of the treatise O szczęściu [On Happiness]. However, as Tatarkiewicz’s work demonstrates, it is also possible to obtain the desired degree of clarity in this matter. Additionally, this text displays significant literary qualities, which is important in the case of a work intended not only for professional philosophers.19 Specifying the meanings used requires the process of defining. Each constructed definition assumes prior analytical processes. According to Tatarkiewicz, apart from constructing definitions, typological concepts also play an important role, especially in the humanities (Tatarkiewicz 1951, 113 et seq.). Jerzy Pelc provides the following general description of Tatarkiewicz’s methodological standpoint:  semiotism (along with classification processes), historicism and typologism (Pelc 2001, 39–​41). The attribution of key significance to semiotic analysis seems to be a particularly important tool which, together with historicism, becomes the “brandmark” of Tatarkiewicz. Tatarkiewicz, as a seasoned historian of philosophy, also pointed out that one cannot be a historian of philosophy without making certain methodological (metaphilosophical) decisions. A historian of philosophy must also be a philosopher because, as Tatarkiewicz notes: It is not enough for a historian of philosophy to know philosophy: they must also be a philosopher. This is due to the nature of this role, which involves constant intervention during the process of developing the material. And the right question is not whether the historian of

19

This is pointed out by J. Pelc, who argues that “Władysław Tatarkiewicz not only combined literary appeal with semantic discipline, but also achieved an important independent scientific result. He based the analysis of meanings on historical material. For a historian of philosophy, he provided valuable material for considerations other than terminological; simultaneously, for a semanticist he offered an overview of terms from a historical perspective, showing modifications, differentiation and development of concepts” (Pelc 2001, 35).

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philosophy must use philosophy in their research, but what philosophy they should use. tatarkiewicz 1971c, 85

Even though Władysław Tatarkiewicz highly valued logic in its broad sense (general logic), as supported by the above remarks, he was not inclined to accept the type of position which can be described as logicism in philosophy. An approach certainly alien to him was that taken by Jan Łukasiewicz, which the latter articulated emphatically in his paper “O metodę w filozofii” [On the Method in Philosophy] presented at the Philosophical Congress in Warsaw in 1927. In this paper Łukasiewicz expresses the view that the systems of modern philosophy constructed by Descartes, Spinoza, Kant, or the post-​Kantian idealists do not have scientific value (Łukasiewicz 1928, 3–​5). This is because, when analysing these systems, one finds vague notions, lack of justification of statements, and errors in reasoning. Even if one finds some value in these systems, this value is not scientific. The cause of these shortcomings should be identified, above all, in not using logical tools. Łukasiewicz, and later Bocheński too, is convinced that disregarding logic and preference for the theory of knowledge by modern philosophy lies at the root of the weakness of modern thought. According to Łukasiewicz, this weakness has been clearly demonstrated by the developments of mathematical logic in modern times. Thus, in his opinion, giving philosophy a scientific character requires, above all, the use of mathematical logic and, in essence, the axiomatization of philosophy. When: the axiomatic method, applied to philosophy, yields results, then it will be time to turn to the past and to look for the beginnings and traces of new achievements of thought in the history of philosophy. łukasiewicz 1928, 5

Such a position, presented in general terms by Łukasiewicz, seemed to be anti-​ philosophical to Tatarkiewicz. Such an anti-​philosophical attitude, however, would not characterize Kazimierz Twardowski himself, but some of his students. Łukasiewicz’s position was a representative expression of this attitude. Nevertheless, Tatarkiewicz highly valued Łukasewicz as a logician and a representative of mathematical logic. This is what Tatarkiewicz writes about his assessment of the anti-​philosophical trend in Historia filozofii [History of Philosophy]: Analytical philosophy in Poland has undergone evolution in the 1920s, taking a form much more extreme than found in Twardowski and

138 Kleszcz originally in his students. This was due to taking up mathematical logic: in the light of its demands, philosophical endeavours seemed unscientific. And so an anti-​philosophical attitude emerged among philosophers. Twardowski’s caution towards philosophy turned into dislike for philosophy … the peak moment of this anti-​philosophical attitude can be traced to a speech by Łukasiewicz at the Warsaw Congress in 1927. tatarkiewicz 1978, vol. 3, 369

In general, it can be said that respect for common sense and for the postulate of clarity and precision meant that Tatarkiewicz valued analytical thought, especially the Twardowski School. While appreciating the importance of broadly understood logic in philosophy, he did not share the postulate of what we would see today as logical philosophy. In this he did not, in fact, differ much from the creator of the Lvov-​Warsaw School (hereinafter lws).20 Pointing out in this text the important similarities and certain differences in the understanding of philosophy by Tatarkiewicz and the lws, I am prepared to recognize the issue of his affiliation to this school as a problem, to a certain extent, a conventional one. This is supported by substantive arguments and the opinion of the philosopher himself expressed in a letter to Prof. Ryszard Wiśniewski: I realize that it was particularly difficult to place me within some direction and school of thought. I did my studies at a university where there was indeed a philosophical school. But in my doctoral thesis I had already broken out of this school. And then I never entered any school (unless we could count my recognition for the methodological school in Lvov). I did not even wonder where my place was on the philosophical map of the 19th century. If anyone pushed me, I would probably say that I was close to Brentano and the British realists. My knowledge of the Baden School is negligible. For me Kant is a great thinker with whom I have little in common. listy 2011, 717

5

Philosophy and Lay (Common Sense) versus Scientific Knowledge

When presenting Tatarkiewicz’s views on this matter, firstly we need to pay attention to those of his considerations which touch upon the question of the 20

Regarding Władysław Tatarkiewicz’s affiliation with lws, cf. (Woleński 1985, 9, 17–​20, 28–​32, 75–​76, 287-​289, 294, 309 –​312); (Jadacki 1987, 306); (Zegzuła-​Nowak 2010, 93–​112, especially 95–​111).

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relationship between philosophy and science (exact sciences). This will allow us to see, at least in general terms, those features which, in his opinion, are important when considering the specifics of philosophical cognition. As Tatarkiewicz claims in his Droga do filozofii [Road to Philosophy], the reality that surrounds us is rich, diverse, and has various aspects. It can be cognized in a variety of ways and with the help of various tools. Philosophy is only one kind of human knowledge. Therefore, in order to capture its methodological specificity, it is advisable to compare it with other types of knowledge. He takes three types into consideration. In particular, he distinguished philosophical knowledge from two other kinds: natural knowledge and scientific knowledge. If, for a moment, we put aside philosophy and the type of knowledge adequate for it, then, on the one hand, we have the perspective of natural cognition and the natural perspective of the world which is derived from it. On the other hand, we have scientific knowledge and the scientific perspective of the world derived from it (Tatarkiewicz 1971f, 19–​51). Recognising the specificity of these two different types of knowledge (and the corresponding different perspectives of the world formed in their context) may allow one to capture the specificity of each of them and also shed light on the methodological specificity of philosophy, which is of particular interest here. The natural perspective of the world is experienced by every human being. Although only part of the world is available to a single individual, he/​she develops an opinion about its whole (Tatarkiewicz 1971f, 13 et seq.). From the natural perspective, the world is treated as a set of material things that are connected with each other and arranged in time and space. Things have various properties. Such a perspective of the world is thus a perspective typical of realism, which accepts the thesis of the existence of a world independent of us (Tatarkiewicz 1971f, 13–​14). Acquiring such a perspective of the world does not require any particular education or professional preparation. It is formed on the basis of sensory impressions and perception. In addition, internal experience and thinking participate in its formation. Its form depends not only on the characteristics of the world, but also on the characteristics of the person who is constructing this perspective of the world (Tatarkiewicz 1971f, 20). The natural perspective of the world is, generally speaking, common to all. So it is also the perspective of those who undermine it, including some scholars and philosophers.21 The natural perspective of the 21

Such a natural perspective of the world could be subject to various extensions (expansion) and analysis. We find such an interesting proposal, referring to Tatarkiewicz, in (Jadacki 2000, 107–​122).

140 Kleszcz world, regardless of its value, has some weaknesses. Its details are relative and variable, it changes depending on the state of our body and mind, and finally it is an incomplete perspective of the world. However, it is worth emphasizing that this perspective provides the basis of and a starting point in gaining knowledge and building a perspective that is different from the natural one. Science is what extends, improves and corrects, introduces evidence to what was only guesswork, specifies, and organizes, but at the same time limits the scope of interests in relation to lay (common sense) knowledge (Tatarkiewicz 1971f, 25 et seq.). Scientific cognition is to be:  complete, strict, responsible and impartial. These characteristics make it different from lay cognition. Scientific knowledge can be treated as an improvement of lay knowledge, due to the fact that it extends, improves, verifies and provides evidence as well as explanations for accepted theses. In addition, it clarifies and organizes the theses, which is achieved by their incorporation into larger systems. Importantly, at the same time, science limits its aspirations by putting aside certain issues which are outside its scope of competence. These issues concern goals, meanings (meaning of life or its purpose) and values. Modern science does not address such issues. For this reason, due to resignation from pursuing certain goals, the nature of scientific cognition may be methodological, as discussed earlier. It can be argued that the history of modern science shows that its remarkable successes in cognitive and technological applications were possible thanks to such cognitive asceticism. At the same time, this means that science does not aspire to gain knowledge about every realm of reality. This outline of the characteristics of scientific knowledge highlights its differences in relation to philosophical knowledge and philosophy itself. The latter does not apply such cognitive limitations on its scope. Science consists of various disciplines which can be distinguished based on various factual or practical criteria (Tatarkiewicz 1971a, 53 et seq.).22 The most important point to the differences that concern:  (1) the object of investigation (based on this criterion, we can distinguish natural sciences and humanities); (2) properties of the object of investigation (some properties are examined by physics and others by chemistry); (3) the method used (a priori and empirical sciences); (4) whether they seek individual truths or general truths (nomological sciences such as physics and idiographic sciences such as history). However, the last of these distinctions raises doubts in the 22

As Tatarkiewicz claims, the classification of sciences may concern two things. Firstly, it may concern the division of sciences into groups of sciences according to their similarity to each other. Secondly, it may concern the ordering of sciences according to a given principle.

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philosopher. He thinks that treating history as a purely idiographic science is not justified (Tatarkiewicz 1971a, 56). Tatarkiewicz doubts the existence of the latter at all, clearly stating: “There are no idiographic sciences” (Tatarkiewicz 1971a, 57). The science of history not only determines facts of an individual nature, but also characterizes these facts more generally by determining their adequate types or styles. Thus, Tatarkiewicz’s proposal is aimed at replacing the division of sciences into nomothetic and idiographic, as put forward by Windelband, with the division into nomological and typological sciences.23 And this division of science into typological and nomological seems to be crucial for Tatarkiewicz because what he takes into account is not the objects of the sciences but their various tasks (ibid.). Typological sciences determine various forms in which a given phenomenon occurs, whereas nomological determine what in a given field is common to all phenomena (Tatarkiewicz 1971a, 56 et seq.). Amongst typological sciences, he proposes distinguishing historical and typographic sciences. While the former determine how types of political regimes or artistic works were shaped throughout time, the latter examine the distribution of types in space (geographic sciences), or only the delineation of types of things, as happens, e.g., in descriptive botany (systematic sciences). Generally, it can be said that the humanities are typological and the natural sciences are nomological. However, there are some exceptions, as is the case with such sciences as historical geology, or the already mentioned descriptive botany. This is because they are both natural and typological sciences. The humanities and natural sciences, despite their differences, refer to experience, so they can be called empirical (Tatarkiewicz 1971f, 32). But there are also sciences that do not refer to experience and start with certainties. These are the a priori, deductive and formal sciences (Tatarkiewicz 1971f, 32–​33, Tatarkiewicz 1971a, 55). A priori and empirical sciences differ fundamentally in terms of the subject matter and accepted justification.24 Taking into consideration exact sciences of a purely cognitive approach, that is, pure sciences, the division proposed by Władysław Tatarkiewicz is as follows: 23

24

The name “nomological sciences” seems to Tatarkiewicz better suited because this name, in contrast to the name “nomothetic sciences”, does not prejudge whether the rules are discovered or established. Evident also in this matter is the philosopher’s caution and reluctance to prejudge choices, even terminological ones, in a situation where the issue itself is controversial. Another distinction would be that between pure sciences, the purpose of which is cognition, and applied sciences, the purpose of which is determining the ways of obtaining certain desirable states of affairs.

142 Kleszcz

What is usually called the scientific perspective of the world is provided by the natural sciences, that is, the disciplines which essentially belong to the nomological sciences. This picture differs fundamentally from the natural perspective of the world in being: (1) more uniform; (2) more systematic, due to generalizations contained in rules or types. This specificity of the scientific perspective of the world is most evident in advanced sciences, such as physics. Usually this perspective is considered to be superior to the natural perspective provided by lay cognition. But, as Tatarkiewicz observes, not always, and not every difference testifies to the superiority of the scientific perspective. Generally, the scientific perspective can be considered quantitative, whereas natural, qualitative. However, leaving qualities, which are considered subjective, out of the scientific perspective does not necessarily mean that there are no such qualities. This may be only due to the conviction that the sciences are not interested in what is qualitative (Tatarkiewicz 1971f, 44–​45). Another important difference between these perspectives of the world is the fact that in the natural perspective, the world is recognized as a set of things; whereas, in the scientific perspective, as a set of processes. However, things can be treated as objects of a subjective nature. But contrary to this, it can also be assumed that things in the scientific perspective are left out, not because they are not there, but because they are not needed for measurements and calculations. Each of these perspectives, the natural and the scientific, is deformed to some extent, but for each of them, the deforming factors are different. In the natural perspective, these factors are practical, whilst in the scientific perspective these factors consist in the

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need for calculation and measurement. So the choice of one of these perspectives always involves choosing a perspective of the world which is somehow already deformed. Then, when we want to build our view of the world, we have to choose between these two perspectives. If such a choice is to be made from an external, somehow neutral point of view, the role of arbitrator must be entrusted to philosophy. This, in turn, requires prior decisions of a philosophical nature, decisions in the field of metaphysics and the theory of cognition. In this approach, philosophy, especially the two above-​m entioned disciplines, becomes an arbitrator in the choice between the natural and scientific perspectives of reality. And this, in the philosopher’s opinion, is one of the important functions of philosophy. 6

The Specificity of Philosophy and Its Relation to Other Realms of Culture

The key issue, at this point in our deliberations, is the question of what philosophy is. However, this question and the possible answer require prior decisions. Determining the answer can be done on a descriptive level or on a normative level, where it is decreed what philosophy should be. Tatarkiewicz, being a historian of philosophy (and what is also important, a historian of aesthetics and art), usually positioned himself on the first level. This is because a historian of philosophy cannot narrow the subject of research, but should take into account all that is considered to be philosophy. Philosophy  –​ in his opinion –​ is different from all exact sciences in its status. Each of these sciences has a separate area of research interests. Meanwhile, philosophy would like to embrace in its scope all that exists. Therefore, it is the discipline with the widest scope and one that uses the most general concepts (Tatarkiewicz 1978, vol. 1, 13)  Thus, the scope of research interests distinguishes philosophy from the so-​c alled exact sciences. The question of whether philosophy can be regarded as a science is, in any case, a subject of dispute. Within the modern classifications of sciences, philosophy was often not included as a science, and sometimes it was even omitted from the proposed classifications.25 Is there any place for philosophy then? According to positivists, philosophy, unlike the philosophy of earlier eras, could strive 25

In particular, philosophy was left out of classifications originating from authors with a positivist attitude, such as the great classification of Auguste Comte. On the subject of classification of sciences in a historical context (cf. Piaget 1976).

144 Kleszcz to achieve one of two goals. It could, as wished for by, e.g., Comte or Spencer, strive to synthesize the output of exact sciences or, as J. S. Mill wanted, it could become a methodology of sciences (Tatarkiewicz 1978, vol. 3, 84–​85). In relation to philosophy, one can also acknowledge, as has been done at times, that it has no cognitive aspirations, but rather aspirations that bring it more in line with poetry. One can also see in it a tool for satisfying practical needs. But even if we acknowledge its cognitive qualities, it differs from the exact sciences. According to Tatarkiewicz, philosophy can be described as a science only if science is understood very broadly. In such a broad understanding, science is: “Methodological, technically improved acquisition of knowledge” (Tatarkiewicz 1971f, 47). So philosophy could be considered a science given such a broad definition of the latter. Philosophy so understood, however, is markedly different from the exact sciences. Philosophy does not only differ from other sciences in its scope. The difference also applies to research methods. For although it uses scientific methods, in some cases it goes beyond these methods. This is related to the fact that modern science involves knowledge that has been methodically acquired and that may be certain. However, such methodological requirements cannot be met by philosophy (Tatarkiewicz 1971a, 53–​54). The understanding of philosophy has been changing over the course of history, from antiquity to modern times. In the history of European philosophy, three basic periods can be distinguished: antiquity, the middle ages and modernity (Tatarkiewicz 1978, vol.1, 15–​16, Tatarkiewicz 1971c, 107). As parts of philosophy, three large groups of philosophical issues can be distinguished, forming three classical branches of philosophy. They are: metaphysics, which deals with being; the theory of knowledge, which looks at knowledge; and axiology (ethics in a broad sense), which focuses on values (Tatarkiewicz 1978, vol. 1, 14). Historically, the understanding of philosophy has evolved from philosophy understood as all knowledge to philosophy as limited to a narrower scope. A significant number of philosophers acknowledged, at some point, that such maximalist aspirations and the desire to build comprehensive knowledge go beyond the cognitive capacities available to people (Tatarkiewicz 1971f, 50 et seq.; Tatarkiewicz 1971c, 100 et seq.). As a result, philosophy (in any case, the dominant approaches) began to explore not being as such, but our thoughts about being. However, besides such a minimalist and cautious philosophy, the maximalist model which adheres to metaphysics has not vanished. As Tatarkiewicz argues, “one model always finds supporters among the brave, the second among the cautious” (Tatarkiewicz 1971f, 52). Tatarkiewicz himself was closer to this cautious, minimalistic understanding of philosophy, although this does not mean that he rejected,

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disregarded or excluded the maximalist approach. It can be assumed that he would agree with the statement that for philosophy, as a certain branch of culture, seen in the broad perspective, both approaches are necessary and adequate. But the specificity of philosophy also lies in the fact that it concerns what is the most important and most valuable for people and provides a view of the world (Tatarkiewicz 1978, vol. 1, 13). At this point, Tatarkiewicz moves away from the metaphilosophical attitude typical of the Lvov-​Warsaw School, in which philosophy and worldview issues were and should be separated. What belongs to philosophy in concreto and what is the object of philosophy is not constant but changes depending on the era. It depends on what we consider important from a research perspective. In different periods and for various philosophers or philosophical schools it can be the natural world, God, soul or morality. It also depends on the epistemological views adopted at a given time (various incompatible characteristics of the nature of knowledge sometimes reducing it to, e.g., psychology) and deciding on the object of knowledge and where its limits lie (it can be the real world, the phenomenological world, or our human thoughts about the world). 7

Tatarkiewicz’s Metaphilosophy –​a Synthetic Approach

In conclusion, let us synthesize the metaphilosophical notes found in the work of Władysław Tatarkiewicz as follows: (A) Tatarkiewicz’s thinking is characterized by: a sense of moderation and recognition for common sense, which he finds in Aristotle and ­Twardowski. (B) His perception of philosophy and its functions can be regarded as moderately minimalistic, but without positivist extremes. (C) The language of philosophy should be characterized by clarity and care for precision. Hence he values the lws’s maxim of semiotic analysis as well as the postulate of using the tools of general logic. (D) However, as much as he appreciates the role of logic, he does not share the postulates of logical philosophy, which he considers as leading to anti-​philosophical consequences. (E) As regards current trends, his attitude is close to analytic philosophy, which he values even though he considers it insufficient on the practical (existential) plane. (F) Tatarkiewicz distinguishes scientific, lay and philosophical knowledge and, analogically, three types of perspectives of the world. This can be considered a pluralistic vision of cognition, in which philosophy ought

146 Kleszcz to play the role of an arbitrator in disputes between the scientific and lay perspectives of the world. (G) This vision is close to certain trends in analytic philosophy, including the lws; however, at the same time, it contains certain distinct features which are specific to Tatarkiewicz. In his vision of human cognition, there is room for reflection of the worldview and existential type. However, even though Tatarkiewicz himself pointed to his methodological proximity to the lws, he did not want to be unequivocally associated with any philosophical school. (H) The analyses carried out above support the claim that the views expressed in Tatarkiewicz’s writings and extracted from his works, as regards the tasks of philosophy, its methods, and relation to other branches of culture, allow for a partial reconstruction of his metaphilosophical position. However, this does not give us a full and comprehensive picture. Since it is not possible to fully and systematically determine his position, and consequently, to build a comprehensive picture of Tatarkiewicz’s metaphilosophical views, the reference to Metaphilosophical notes in the title of this paper remains justified.

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148 Kleszcz Tatarkiewicz, W. 1962. O szczęściu [On Happiness]. Warszawa: pwn. Tatarkiewicz, W. 1971. „Droga do filozofii” i inne rozprawy filozoficzne [„Road to Philosophy” and Other Philosophical Writings]. Warszawa: pwn. Tatarkiewicz, W. 1971a. Nauki nomologiczne a typologiczne [Nomological and Typological Sciences]. In: Tatarkiewicz 1971, 53–​62. Tatarkiewicz, W. 1971b. O pisaniu historii filozofii [On Writing the History of Philosophy]. In: Tatarkiewicz 1971, 63–​86. Tatarkiewicz, W. 1971c. Okresy filozofii europejskiej [Periods of European Philosophy]. In: Tatarkiewicz 1971, 93–​108. Tatarkiewicz, W. 1971d. Trzy etyki:  studium z Arystotelesa [Three Ethics:  A Study in Aristotle]. In: Tatarkiewicz 1971, 324–​338. Tatarkiewicz, W. 1971e. Porządek dóbr. Studium z Pascala [Order of Goods. A Study in Pascal]. In: Tatarkiewicz 1971, 339–​365. Tatarkiewicz, W. 1971f. Droga do filozofii [Road to Philosophy]. In:  Tatarkiewicz 1971, 13–​52. Tatarkiewicz, W. 1977. Czym jest filozofia, którą uprawiam [What is Philosophy which I am Doing]. List do redaktora [Letter to the editor]. Znak 11–​12: 1334. Tatarkiewicz, W. 1978. Historia filozofii [History of Philosophy]. Vol. 1–​3. Warszawa: pwn. Tatarkiewicz, W. 1978a. Parerga. Warszawa: pwn. Tatarkiewicz, W. 1978b. Układ pojęć w filozofii Arystotelesa [Order of Concepts in Aristotle’s Philosophy]. Translated from German by I. Dąmbska. Warszawa: pwn. Tatarkiewicz, W. 1979. Zapiski do autobiografii [Notes to Autobiography]. In:  T.  and W. Tatarkiewiczowie. 1979. Wspomnienia [Memoirs]. Warszawa: piw, 115–​188. Tatarkiewicz, W. 2010. Szkoła marburska i jej idealizm [Marburg School and its Idealism]. Edited by P. Parszutowicz. Kęty: Wydawnictwo Marek Derewiecki. Twardowski, K. 1997. Dzienniki. Część I: 1915–​1927 [Diaries. Part I]. Toruń: Wydawnictwo Adam Marszałek. Wiśniewski, R. 1978. Porządek dóbr w etyce Władysława Tatarkiewicza [Order of Goods in Ethics of Władysław Tatarkiewicz]. Etyka 16, 131–​146. Wiśniewski, R. 1979. Podstawy teorii wartości estetycznych Władysława Tatarkiewicza”[Introduction to Theory of Aesthetical Values]. Studia Estetyczne 16: 151–​171. Wiśniewski, R. 2001. Aksjologia kluczem do filozofii Władysława Tatarkiewicza [Axiology as the Key to Philosophy of Władysław Tatarkiewicz]. Przegląd Filozoficzny. Nowa Seria 1: 43–​53. Wiśniewski, R. 2013. Dobro, moralność, szczęście i piękno. Studium aksjologii Władysława Tatarkiewicza [Good, Morality, Happiness and Beauty. Study on Axiologyy of Władysław Tatarkiewicz]. Bydgoszcz: Oficyna Wydawnicza Epigram. Woleński, J. 1985. Filozoficzna Szkoła Lwowsko-​ Warszawska [Philosophical Lvov-​ Warsaw School]. Warszawa: pwn.

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Woleński, J. 1987. Władysław Tatarkiewicz o filozofii [Władysław Tatarkiewicz on Philosophy]. Kultura, Oświata, Filozofia 9/​10: 142–​149. Zegzuła-​Nowak, J. 2010. Spór o tożsamość filozoficzną Władysława Tatarkiewicza”[Disputation about Philosophical Identity of Władysław Tatarkiewicz]. Edukacja Filozoficzna 49: 93–​112.

­c hapter 7

Casimir Lewy and the Lvov-​Warsaw School Tadeusz Szubka Abstract The Polish-​born British philosopher Kazimierz (known as Casimir) Lewy (1919–​1991) was an inspiring and influential lecturer and reader at the University of Cambridge who significantly contributed to the intellectual formation of a number of British philosophers in the second half of the twentieth century. He was a characteristically analytic philosopher along the lines of his Cambridge mentors, in particular G. E. Moore and John Wisdom. However, his philosophical interests arose in Warsaw through encounters with the writings and lectures of Tadeusz Kotarbiński. Even though Lewy was well acquainted with the tradition of Polish analytic philosophy, embodied in the Lvov-​ Warsaw School, and discussed it occasionally in his work, he was rather resistant to it. This paper provides an account of Lewy’s exposure to that school, and then suggests what the rationale of this resistance could be. Its sources are discerned in: (1) Lewy’s unrepentant affirmation of the existence of abstract objects, including concepts and propositions, and of modalities; (2) his flexible approach to logic and deference to the ordinary notion of entailment, and (3) his conception of philosophical analysis along the lines of G. E. Moore.

Keywords abstract objects –​analytic philosophy –​Casimir Lewy –​entailment –​Lvov-​Warsaw School –​ Tadeusz Kotarbiński

The Polish-​born British philosopher Kazimierz (known as Casimir) Lewy (1919–​1991) was an inspiring and influential university teacher. His passionate and inimitable lectures and tutorials at the University of Cambridge significantly contributed to the intellectual formation of a number of British philosophers in the second half of the twentieth century. He was a characteristically analytic philosopher along the lines of his Cambridge mentors, in particular G. E. Moore and –​at least to some extent –​John Wisdom. However, his philosophical interests arose in Warsaw through encounters with the writings and

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lectures of Tadeusz Kotarbiński. Even though Lewy was well acquainted with the tradition of Polish analytic philosophy, embodied in the Lvov-​Warsaw School, and discussed it occasionally in his work, he was rather resistant to it. In what follows, after an account of Lewy’s exposure to that school, I shall try to suggest, as succinctly as possible, what the rationale could be for his resistance. 1

Kotarbiński, Tarski, and Czeżowski

It has been claimed that Casimir Lewy was attracted to philosophy as a teenager while attending the Mikołaj Rej High School in Warsaw. According to a biographical note included in the collection of essays Exercises in Analysis, when Lewy was 15 years old “his interest in philosophy and logic was aroused by an article in a literary weekly about the philosophy of T. Kotarbiński. He thereupon bought a copy of Kotarbiński’s university textbook on the theory of knowledge, logic and the scientific method and found it of such absorbing interest that, besides continuing his reading in philosophy, he attended lectures at Warsaw University” (Exercises in Analysis…, ix). The editor of this collection, Ian Hacking, gives another account of those events in his biographical memoir of Casimir Lewy, published after a lapse of several years after Lewy’s death (Hacking 2006). He claims there that young Casimir was “passionate about poetry, but at the age of fifteen he came across a philosophical article in a literary magazine that changed the course of his life”. The author of this article, Hacking unambiguously states, was Tadeusz Kotarbiński, and Lewy was so impressed by its content that he “at once bought Kotarbiński’s 1929 textbook on methodology, logic and the theory of knowledge, and decided to attend his lectures at the university. This he did, missing (with permission) his regular school classes whenever necessary” (Hacking 2006, 172). The main discrepancy in these two accounts concerns the article that prompted Lewy’s interest in philosophy. The first account has it that it was an article in a literary weekly about Kotarbiński, while according to the second story it was a philosophical article in a literary magazine by Kotarbiński himself. Obviously, in the 1930s Kotarbiński was already a recognized public intellectual and his philosophical activity was widely appreciated (the first festschrift honouring his work was published in 1934). Hence it is quite likely that during those years a literary weekly in Poland paid some attention to his work. Nevertheless, it is very unlikely that such a presumably shallow piece of writing would be able to give rise to Lewy’s philosophical interests. Thus it seems that the second account must be correct: it was rather an essay by Kotarbiński in a literary or popular magazine that attracted Lewy to philosophy.

152 Szubka In 1930s Kotarbiński published a number of popular essays in two monthly magazines: Racjonalista [The Rationalist] and Wiedza i Życie [Knowledge and Life]. Racjonalista was a modest and short-​lived magazine of the Warsaw Intellectuals Circle of the Polish Association of Free Thought. Short essays by Kotarbiński on various philosophically relevant and social issues appeared there regularly. For Wiedza i Życie, a well-​established scholarly and scientific magazine for the general public, Kotarbiński wrote less frequently but his essays published there were more substantial and comprehensive. In 1934 a written version of his radio talks on selected ethical ideas, such as well-​being, victory, virtue, and duty, appeared there (Kotarbiński 1934/​1987), and a year later an essay on philosophical culture (Kotarbiński 1935/​1987). The latter paper was, as Kotarbiński himself acknowledged, a miniature introduction to philosophy. Kotarbiński emphasized there that philosophy as a university subject is in fact a loose collection of disciplines that consists of the history of metaphysical worldviews, ethics, psychology, and logic broadly construed. He argued that the most fruitful way of doing philosophy is to conceive of it as investigations concerning our knowledge of the world. This essay would certainly be a perfect encouragement to study philosophy in depth, and maybe reading it induced Lewy to study Kotarbiński’s rather demanding handbook (Kotarbiński 1929/​ 1961)1 and to attend philosophy lectures at the University of Warsaw. During his undergraduate and graduate studies at the University of Cambridge Lewy was under the very strong and formative influence of G. E. Moore and John Wisdom. He also interacted philosophically with C.  D. Broad and Ludwig Wittgenstein. The preface to his doctoral dissertation includes the following acknowledgement: I owe an enormous debt, which it would be difficult to exaggerate, to Professor G.E. Moore, to Mr John Wisdom, and to Professor L. Wittgenstein. I want to emphasize especially my debt to Mr Wisdom: for it was he who, as my supervisor, has taught me how to do philosophy, and who has taught me, if I may use the words of Cardinal Newman, not only to think, but to think for myself. Lewy 1942, iii.

1 This handbook, for many years crucial for Polish university education in philosophy, was translated into English and published under a rather unfortunate and idiosyncratic title Gnosiology (Kotarbiński 1966). Wolfgang Künne who draws on this translation in his comprehensive study of various conceptions of truth suggests that this title is simply “unappealing” (Künne 2003, 344). Presumably the bad terminological choice was partially responsible for the meagre interest in the book when it was published in English.

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His involvement with the tradition of Polish analytic philosophy was in those and subsequent years rather limited. In general there were four e­ pisodes of it. When Zbigniew Jordan (1911–​1977) was a soldier of the Polish Armoured Division in Scotland during World War Two, he made heroic attempts to continue his philosophical research and write for the English audience a general sketch of the pre-​war achievements of the Lvov-​Warsaw School. He was able to achieve this aim with the invaluable assistance of Casimir Lewy. At the beginning of his sketch, published as a separate booklet, Jordan wrote: Dr C. Lewy, of Trinity College, Cambridge, gave me much aid in collecting some not easily obtainable material, and has read through, corrected, and tried to make readable the English of this paper. Without his help it would never have been fit for publication. Jordan 1945, 7

Arguably, this service allowed Lewy to form early on in his academic career a synoptic picture of the development of the Lvov-​Warsaw School, though this picture was to some extent distorted, since Jordan was inclined to assimilate this movement to the Vienna Circle and Logical Positivism. Of course, this assimilation was unfortunate, especially for someone like Lewy who had no sympathy whatsoever for Logical Positivism.2 In 1944 Alfred Tarski published a revised and expanded English version of his logic textbook that originally appeared in Polish in 1936 under the title O logice matematycznej i metodzie dedukcyjnej [On Mathematical Logic and the Deductive Method]. Lewy reviewed it for “Mind” which at that time was the most prestigious philosophical journal in the Anglo-​Saxon World. He praised the book for being both clear and precise, and making explicit how to do mathematical logic. However, he found it defective and controversial in its philosophical facets. One could even justifiably say that Tarski, in this otherwise 2 Lewy was fond of alluding to the sarcastic saying of C. D. Broad that “Vienna contributed more notably to culture by its Schnitzel than by its Kreis” (Lewy 1976b, 45). He also wrote a critical notice (“actually, very critical notice” –​Kripke 2008, 186; 2011, 259) of Rudolf Carnap’s Meaning and Necessity (Lewy 1949), an important book that in many respects retained the spirit, if not the letter, of Logical Positivism. Lewy was also very sensitive (perhaps oversensitive) to positivist influences in translations of Tarski’s Polish works into German and English. For instance, he emphasizes that whereas in a certain Polish paper Tarski speaks about “ordinary intuitions,” these intuitions are turned into “ordinary usage” in the English version. Unfortunately, he points out, “this positivist metamorphosis occurs also in the German version of the paper” (Lewy 1976a, 31).

154 Szubka useful textbook, “completely neglects most of those problems and difficulties of logic which have the greatest philosophical interest” (Lewy 1944, 375). To begin with, Tarski is not very careful in his use of general terminology. Perhaps one can bear with his constant talk of true and false sentences, instead of true and false propositions, but what is more worrying, he simply does not care about the terminology in question, and tends to identify sentences sometimes with propositions, and sometimes with statements (or even, which sounds a bit awkward, with asserted statements). Lewy recommends that Tarski should sort out this mess and “ought to have given some discussion of the relation between sentences, propositions, and statements, and if he wishes to identify sentences with propositions (or with statements), he ought to have made an attempt to justify this” (Lewy 1944, 375). Lewy finds the major philosophical drawback of Tarski’s textbook to be his cavalier treatment of the differences between the meaning of logical constants and the meaning of corresponding ordinary expressions. For example Tarski claims that the material implication of propositional calculus is in principle simplification and clarification of the meaning of the ordinary conditional “if … then”, devoid of its psychological and, more generally, inessential features. For Lewy this claim is simply preposterous. It is true that material implication and ordinary conditionals are to some extent related, but one cannot say that the features of the latter not represented or implemented in the former are merely psychological or inessential. Lewy thinks that Dr. Tarski ought to have plainly said that the use of “⊃ ”, though not, of course, unrelated to the ordinary use of “if … then”, is yet quite different from it, but that logicians have found it useful and important to introduce this notion of material implication, and that no harm can result from reading “p ⊃ q” as “if p then q”, provided that it is clearly realized, and remembered that this is not (except, perhaps, in very special cases) what is ordinarily meant by the phrase. lewy 1944, 376

One can also argue along similar lines against Tarski’s suggestion that material equivalence is a precise logical counterpart to the ordinary phrases “if and only if” and “necessary and sufficient condition”. For Lewy this is a highly contentious claim. Unfortunately, Tarski’s textbook abounds in claims and statements of this kind. Another example of his philosophical carelessness is the assumption that definitions in deductive systems may be formulated as material equivalences. Lewy suggests that if this is indeed so, they must

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be material equivalences of a special sort, and Tarski should have “explained more clearly and fully what sort of material equivalences they are” (Lewy 1944, 376). The general outcome of Lewy’s scrutiny of Tarski’s textbook is that it is unsatisfactory in its philosophical underpinnings and comments, but excellent in an innovative exposition of mathematical logic and the application of its methods to arithmetic. Lewy came to a very similar conclusion a few decades later while briefly discussing Tarski’s semantic conception of truth in his only book Meaning and Modality. He found it philosophically wanting in its general approach, but at the same time insisted that it was not his intention to belittle Tarski’s construction “as a contribution to pure logic” (Lewy 1976a, 19). Lewy also wrote for Mind a brief review of Tadeusz Czeżowski’s logic textbook for philosophy students, published in Poland in 1949 (Lewy 1951). He judged it to be “competent, clearly written, and fairly comprehensive” (Lewy 1951, 426). However, as with Tarski’s textbook, he spotted some controversial philosophical claims made by Czeżowski. Primarily, Lewy strongly objects to Czeżowski’s suggestion that the sentence (1)  “John believes that today is Saturday” should be more precisely formulated as (2) “John has a belief the expression of which is the sentence ‘Today is Saturday’.” This suggestion is wrong since one may show that the proposition expressed by (1)  is different from the proposition expressed by (2), and the former neither entails nor is entailed by the latter. In order to realize this difference, and the lack of entailment, it is enough to translate these two sentences into some other language, for instance back into Polish or into German. In his brief review Lewy was unable to develop this objection, but he did so in his other publications (Lewy 1947, Lewy 1976a). Its bottom line is that (1) is different from (2) since the former expresses a proposition about the mental state of John, and presupposes nothing, unlike the latter, about the language in which this mental state is conveyed, and the meaning of its particular expressions. Moreover, Lewy is not fully convinced by Czeżowski’s idea (who seems to be following in this respect Stanisław Leśniewski and Alfred Tarski) that the advantage of the theory of semantical categories over the simple theory of types as a means of solving Russell’s paradox amounts to its naturalness and intuitive justification. Czeżowski also seems to overestimate both these theories, and “is misleading in talking as if the simple theory of types (or the theory of semantical categories) were universally acknowledged to provide a final solution of the paradox” (Lewy 1951, 427).

156 Szubka Lewy concluded his brief review of Czeżowski’s textbook with a comment on its bibliography in which, as he was surprised to find, no work of Leon Chwistek is listed.3 2

Diverging Philosophical Perspectives

The outlined account of Casimir Lewy’s exposure to the works and ideas of the Lvov-​Warsaw School shows that he had good grasp of its achievements and appreciated its contribution to formal logic. However, he had a more critical attitude towards its philosophical tenets and methodology. One can discern at least three main reasons for this critical attitude. First of all, Lewy was unrepentant in his affirmation of the existence of abstract objects, including concepts and propositions, and of modalities. These substantial ontological commitments distinguished him from Logical Positivism and W. V. Quine, as well as from the Lvov-​Warsaw School. The author of an informative entry on Lewy in The Dictionary of Twentieth-​Century British Philosophers puts it as follows: In sharp contrast to Quine, Lewy speaks of propositions almost as close family friends, readily identified as logically distinct from sentences and statements. Lewy has no hesitation in talking of concepts and meanings, of entailments and de re and de dicto necessities; and he resists all conventionalist attempts at analyses of these in terms of linguistic rules. cave 2005, 568

Thus Lewy would have no philosophical sympathy whatsoever with Kotarbiński’s reism and concretism, with its rejection of abstract entities, including concepts and propositions, as misleading figments of the imagination or intellectual projections, and even to a more moderate view, quite common in the Lvov-​Warsaw School, and in Polish analytic philosophy in general, that concepts and propositions are simply meanings of words and sentences, and should be individuated by means of linguistic rules governing the use of words and sentences. Moreover, concepts and propositions are explanatory prior to meaningful linguistic expression. This was the gist of his criticism of Tarski’s

3 This oversight was rectified in the second edition of the textbook in which two items by Chwistek are included in the bibliography (Czeżowski 1949/​1968, 258).

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semantic theory of truth. In the conclusion of his argument about this issue he characteristically wrote: The “semantic” conception of truth presupposes a “non-​semantic” conception of truth  –​i.e. a conception of truth in which “true” is applied directly to propositions, and not to sentences. In other words, we must recognize the distinction between “the proposition that … is true” and “the proposition expressed by the sentence “…” is true.” lewy 1976a, 21

Secondly, for Lewy logic was certainly an important tool for doing philosophy and he very often made extensive use of it. Peter Thomas Geach in his review of Lewy’s book emphasizes that it will be “inaccessible to readers who know no formal logic,” though “quite accessible to anyone who has mastered a good elementary textbook of logic, so long as that contains the elements of modal logic” (Geach 1977, 496). However, Lewy’s approach to logic was more flexible than the approach prevailing among the members of the Lvov-​School. For him classical extensional logic was not sacrosanct and he was aware of its various limitations and perhaps even of absurdities when its enthusiasts uncritically applied it to philosophical problems. For instance, there is no reason to stick to material implication in defining various crucial logical notions and to struggle with the paradoxes and counterintuitive consequences it generates. Instead of those futile efforts it would be much better to focus upon and elaborate the intuitive concept of entailment, even though Lewy was well aware that to make it workable would be an arduous task, and he himself failed to complete it. Thirdly, Lewy conceived of philosophical analysis very much in the spirt of G. E. Moore. Successful analysis has to establish an illuminating identity between the concept or proposition under investigation and the concept(s) or proposition(s) giving an account of its content. To put it briefly in technical jargon, the identity relation must hold between analysandum and analysans, otherwise analysis will be incorrect. It is no surprise then that Lewy devoted a lot of attention to resolving the paradox of analysis that haunted G. E. Moore. The standard and simplified form of the paradox in question is: if (1) the concept of being a vixen is identical with the concept of being a female fox, and (2) the concept of being a vixen is identical with the concept of being a vixen, then the paradoxical (i.e. counterintuitive) conclusion follows: “the proposition that the concept of being a vixen is identical with the concept of being a female fox is identical with the proposition that the concept of being a vixen is identical with the concept of being a vixen” (Lewy 1976a, 69). The

158 Szubka conclusion is paradoxical since the stated identity is between an informative proposition, namely “the proposition that the concept of being a vixen is identical with the concept of being a female fox” and a completely trivial one, namely “the proposition that the concept of being a vixen is identical with the concept of being a vixen.” The details of Lewy’s attempt to resolve this puzzle and the viability of his resolution4 are not especially relevant in the present context, and would require a separate paper. More relevant here is Lewy’s reluctance to weaken the relationship holding between analysandum and analysans in correct analysis, as manifested, for example, in Rudolf Carnap’s idea of explication. Commenting upon Carnap’s contention that “it is not required that an explicatum have, as nearly as possible, the same meaning as the explicandum; it should, however, correspond to the explicatum in such a way as that it can be used instead of the latter,” Lewy says that it is “exceedingly vague” and unhelpful (Lewy 1949, 232). Although general claims about the methods of philosophical analysis endorsed by the members of the Lvov-​Warsaw School are extremely risky, due to the diversity of that movement, one could nonetheless plausibly argue that those methods are more similar to Carnap’s idea of explication than to the conception of Moorean analysis patently endorsed by Lewy. 3

Conclusion

In the obituary published in the yearbook of the Polish Society of Arts and Sciences Abroad Irena Lachmanowa wrote: Although almost all of Casimir Lewy’s life passed in Great Britain, he cherished a strong attachment to and sentiment for his country of birth. He was deeply interested in the achievements of Polish logicians and philosophers, mainly from the Lvov-​Warsaw School, whose views on the task of philosophy, the role of logic, and stance on speculative philosophy were very close to his. He was proud of the outstanding, world-​famous achievements of Professor Tarski in the area of the theory of truth and logic. His views on this topic were substantiated in depth and published. He was interested in the works of Tadeusz Czeżowski, especially in logic and moral philosophy. lachmanowa 1989-​90, 17–​18

4 In addition to pertinent chapters of Lewy (1976a) see also Strawson (1977) and Urquhart (1978).

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Presumably Lachmanowa is right that Lewy was deeply attached to the country of his birth and upbringing, but she undoubtedly overstated his appreciation of Polish analytic philosophy. Lewy was aware of its achievements and admired formal results obtained by Polish logicians; yet his vision and crucial tenets of philosophical analysis were different from the metaphilosophy of the Lvov-​Warsaw School.

References

Cave, P. 2005. Lewy, Casimir (1919–​91). In: The Dictionary of Twentieth-​Century British Philosophers. Edited by S. Brown. Vol. 1: A-​L. Bristol: Thoemmes Continuum, 567–​571. Czeżowski, T. 1949/​1968. Logika: Podręcznik dla studiujących nauki filozoficzne [Logic: A Coursebook for Philosophy Students]. Revised 2nd ed. Warszawa: pwn. Geach, P.T. 1977. Victory over the Verbalists [Review of Meaning and Modality by Casimir Lewy]. The Times Literary Supplement, Friday April 22 (no. 3919), 496. Exercises in Analysis: Essays by Students of Casimir Lewy. 1985. Edited by I. Hacking. Cambridge (UK): Cambridge University Press. Hacking, I. 2006. Casimir Lewy 1919–​1991. Proceedings of the British Academy 138: 171–​ 177. Jordan, Z. 1945. The Development of Mathematical Logic and of Logical Positivism in Poland between the Two Wars. London: Oxford University Press. Kotarbiński, T. 1929/​1961. Elementy teorii poznania, logiki formalnej i metodologii nauk. Revised 2nd ed. Wrocław: Zakład Narodowy im. Ossolińskich. Kotarbiński, T. 1934/​1987. Ideały [Ideals]. Wiedza i Życie 9 (6): 449–​457; 7: 530–​537. Reprinted in: Kotarbiński 1987, 211–​227. Kotarbiński, T. 1935/​1987. Kultura filozoficzna [The Philosophical Culture]. Wiedza i Życie 10 (6): 440–​451. Reprinted in: T. Kotarbiński. 1987, 91–​103. Kotarbiński, T. 1966. Gnosiology: The Scientific Approach to the Theory of Knowledge. Translated by O. Wojtasiewicz. Edited by G. Bidwell and C. Pinder. Oxford: Pergamon Press. Kotarbiński, T. 1987. Pisma etyczne [Papers on Ethics]. Wrocław: Zakład Narodowy im. Ossolińskich, 91–​103. Kripke, S.A. 2008. Frege’s Theory of Sense and Reference: Some Exegetical Notes. Theoria 74 (3): 181–​218. Reprinted in: S.A. Kripke. 2011. Philosophical Troubles. Collected Papers. Vol. 1. Oxford: Oxford University Press, 254–​291. Künne, W. 2003. Conceptions of Truth. Oxford: Clarendon Press. Lachmanowa, I. 1989–​90. Kazimierz Lewy. Rocznik Polskiego Towarzystwa Naukowego na Obczyźnie [The Annual of the Polish Society of Arts and Sciences Abroad] 34: 17–​19.

160 Szubka Lewy, C. 1942. Some Philosophical Considerations About the Survival of Death. A  dissertation submitted for the degree of Doctor of Philosophy. Cambridge (typescript available at Cambridge University Library). Lewy, C. 1944. Review of Introduction to Logic and to the Methodology of Deductive Sciences by Alfred Tarski. Mind 53 (212): 375–​377. Lewy, C. 1947. Truth and Significance. Analysis 8 (2): 24–​27. Reprinted in: Philosophy and Analysis. 1954. Edited by M. Macdonald. Oxford: Basil Blackwell, 242–​245. Lewy, C. 1949. Critical Notice of Meaning and Necessity by Rudolf Carnap. Mind 58 (230): 228–​238. Lewy, C. 1951. Review of Logika by Tadeusz Czeżowski. Mind 60 (239): 426–​427. Lewy, C. 1976a. Meaning and Modality. Cambridge (UK): Cambridge University Press. Lewy, C. 1976b. Mind under G.E. Moore (1921–​1947). Mind 85 (337): 37–​46. Strawson, P.F. 1977. Review of Meaning and Modality by Casimir Lewy. Philosophy 52 (202): 486–​488. Urquhart, A. 1978. Review of Meaning and Modality by Casimir Lewy. The Journal of Philosophy 75 (8): 438–​446.

pa rt 3 On Formal Methods in Philosophy

∵

­c hapter 8

Remarks on the Origin and Foundations of Formalisation Srećko Kovač Abstract The Aristotelian origins of formal systems are outlined, together with Aristotle’s use of causal terms in describing a syllogism. The precision and exactness of a formalism being based on the projection of logical forms to perceptive signs is contrasted with foundational, abstract concepts, independent of any formalism, which are presupposed for the understanding of a formal language. The definition of a formal system by means of a Turing machine is put in the context of Wittgenstein’s general considerations of a machine understood as a sign. A modification of Łukasiewicz’s logic Ł3 with the inclusion of justification terms is proposed in order to formally analyze some features of formalistic reasoning as a mechanical, causal affair within a wider context of “indeterminacy.”

Keywords causal term –​formal system –​indeterminacy –​logical form –​logic Ł3 –​syllogism –​ ­Turing machine

1

The Formalisation and Historical Origins of Logic

According to modern standards of the certainty and exactness of knowledge, one cannot be fully satisfied with a given theory until it is formalised, that is, presented in the shape of a formal system. A  formalised theory should precisely define its language (a set S of sentences) and make explicit its axioms, especially its logic:  logical axioms and rules of inference (the relation ⊢ of the derivability of sentences from a set of sentences), and is thus definable as an ordered pair 〈S, ⊢〉.1 Such standards were established by the founders of 1 See, e.g., Tarski’s early account in (1983). Cf. Béziau (2005).

164 Kovač modern logic at the end of the 19th and beginning of the 20th centuries. In this context, Łukasiewicz remarked in 1922: We are no longer satisfied with ordinary mathematical deductions, which usually start somewhere “in the middle”, reveal frequent gaps, and constantly appeal to intuition. … We want to know the axioms on which each system is based, and the rules of inference of which it makes use. łukasiewicz 1967a, 20

Regarding the philosophy of his time, Łukasiewicz was even more critical: Philosophy must be reconstructed from its very foundations; it should take its inspiration from scientific method and be based on new logic. łukasiewicz 1967a, 21

He added: “This is a work for generations and for intellects much more powerful than those yet born” (p. 21). These standards have their origins in ancient times. Łukasiewicz and Bocheński showed that Aristotle developed a ­deductive system of “formal logic” and that he established a general theory of axiomatisation. Admittedly, they concluded that Aristotle did not arrive at a formalised theory of logic, implemented in rigorously defined language, deeming that this had been achieved by the Stoic logicians.2 However, they pointed out that Aristotle’s concept and construction of “formal logic” was primarily due to his employment of term letters (variables), which enabled him to abstract from the associated meaning of a sentence and pay exclusive attention to the form (of a sentence) relevant for deductive inference. As stressed, for instance, by Bocheński, Aristotle’s formal logic is characterised by the use of variables and deals with “formulas”, that is, with sentences (including laws) where descriptive (“constant”) terms are replaced by variables.3 Moreover, ­Bocheński continues, there is a “further groundbreaking contribution of Aristotle to logic”: the 2 Sometimes giving almost exclusive emphasis to the linguistic expression of logical forms, Łukasiewicz (1957) denies that Aristotle succeeded in establishing a logical formalism owing to what Łukasiewicz considers an incorrect way of substituting concrete terms into logical forms and to the synonymous use of logical terms (e.g., “belongs to” and “is predicated to”, Łukasiewicz 1957, 17–​18, see Bocheński 2002, 113, transl. in Bocheński 1961). He recognises that Aristotle developed an axiomatic system of syllogisms (e.g., Łukasiewicz 1957, pp. 44, 73; in particular, see Bocheński 2002, 74, 81, 84, 86), albeit without fulfilling modern “formalistic” standards. 3 “[T]‌he use of letters instead of constant words gave birth to formal logic” (Bocheński 2002, 80–​81).

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axiomatisation (“notwithstanding its weaknesses”) of syllogistic (“categorical”, restricted to subject-​predicate propositions) (Bocheński 2002, for example, pp. 3–​5, 74, 84–​87, cf. Bocheński 1961). According to Bocheński, Aristotle’s general theory of “categorical” syllogism, as presented in Prior Analytics, is a historical paradigm of what we should understand as formal logic. In spite of some shortcomings in Aristotle’s presentation and wording,4 it is evident that his establishment of formal logic and general theory of axiomatics aimed at rigorous norms (especially if we consider Aristotle’s time period) and constituted a significant step towards the attainment of a fully formalised formal logic. Although Aristotle claimed that syllogism is a matter of “internal speech” (ἔσω λόγος, An. Post. A 10, 76b 275), he intended to implement his theory of syllogism and axiomatic theories in general in an appropriate, artificial language, not only by using term letters (“variables”), but also by expressing the structure of sentences and inferences in an unambiguous way, even if this structure departs from ordinary ways of speaking.6 Thus, in his Analytics he clearly distinguished logical words (‘all’, ‘not’, ‘some’, ‘belongs’) and expressed a logical structure of sentences. He rendered the ordinary way of saying ‘All Bs are As’ (which he had used earlier, e.g., in De interpretatione, still without term letters) as ‘A belongs to each B’ (or, metatheoretically, ‘A is predicated to each B’), and similarly for other sentences of the so-​called “logical square”. He often expressed a syllogism in the form of a conditional statement. By these means, Aristotle could strictly express the necessary “following” of a conclusion from its premises (An. Pr. A 1, 24b 18–​21) so that it was possible to explicate all implicit assumptions (for example, conversion in the second and third figures of a syllogism) in order to reduce reasoning to “perfect” syllogisms, where no implicit assumptions of this kind are present (see, for example, An. Pr. A4 26b 28–​30, A5 27a 15–​18). The foundational principles of a syllogism (the principles of contradiction and of the excluded middle), beyond the “working” formal logic (the theory of syllogism), are addressed by Aristotle in Metaphysics (Aristotle 1973), especially in book Γ. Thus, Aristotle was not very far from strictly defining an artificial, formalistic language, which together with logical axioms and rules would provide a formal system of logic (or some other special theory).7 Despite using expressions of natural language along with term letters 4 See, e.g., in Łukasiewicz (1957, 16–​19). 5 For Analytica Priora et Posteriora and their translations, see (Aristotle 1964, 2002, 2010, 1994–​ 2000). 6 Aristotle’s “structural discrepancy between abstract and the concrete forms of the syllogisms”, stressed by Łukasiewicz (1957, 17), may be considered evidence of the artificiality of Aristotle’s idiom in order to more exactly express logical forms. 7 An intensional semantics of Aristotle’s syllogistic system is proposed in (Kovač 2013).

166 Kovač and artificial phrases, Aristotle’s approach resembled the requirements for a formal system as formulated by Frege:  (a) a formal language (“ideography,” Begriffsschrift) should express only what is relevant for reasoning, excluding any tacit connotations that may derive from natural language and discourse context (“ideography” contains only special symbols, not “words” of a natural language), and (b) reasoning should be described without any gaps (lückenlos), with all necessary axioms, inference rules and definitions made explicit (Frege 1988, X, 3; Frege 1998, v-​v ii). 2

Formalism between Sensible Perception and Concepts

A formal system (formalism), as conceived by Frege, seems to be essentially concerned with abstract, non-​sensible “entities” such as concepts, propositions, inferences and thoughts (cf. Frege’s “pure thought” or “pure concepts”). Nevertheless, a formal system is established only via a “mapping” of these abstract entities onto sensibly perceivable, written signs (“formal language”, “ideography”). For Frege, proofs of a formal system are presented “to the eye” as a sequence of formulas (Frege 1998, V).8 This indicates that the foundations of a formal system include the requirement of sensible givenness, which is something beyond logic if logic is understood strictly as an intellectual activity of formal reasoning.9 It should be noted that inscriptions in themselves, merely as objects of a sensible experience, do not need to reveal anything about what they are 8 The visual accessibility of a written language is a pre-​condition of the “strictness of proving” (Strenge der Beweisführung) and “sharpness of distinguishing” (Frege 1998, vi; Frege 1988, xi). See Kant’s reflection in footnote 11 below. 9 The sensible intuitive givenness of the expressions in a proof written in a formal language was especially highlighted by Hilbert, irrespective of all of the differences from Frege’s philosophical position: “If a logical inference is to be reliable, it must be possible to survey these objects completely in all their parts, and the fact that they occur, that they differ from one another, and that they follow each other, or are concatenated, is immediately given intuitively, together with the objects, as something that neither can be reduced to anything else nor requires reduction” (Hilbert 1967, 376, our emphasis). Kant plays here an essential philosophical role: “[W]‌e find ourselves in agreement with philosophers, especially with Kant. Kant already taught … that mathematics has at its disposal a content secured independently of all logic and hence can never be provided with a foundation by means of logic alone. … [S]omething must already be given to our faculty of representation, certain extralogical concrete objects that are intuitively present as immediate experience prior to all thought” (­Hilbert 1967, 376). Hilbert’s considerations about Kant’s role were further deepened by Gödel on the grounds of his incompleteness theorems (see the last two paragraphs of 1995b).

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inscribing. For only if we in advance know that a given inscription is associated with a certain expression, particularly with a certain occurrence of an expression (e.g., with the first occurrence of ‘A’ in ‘A v non-​A’), can we read and grammatically or proof-​theoretically check, say, given inscriptions of a proof. Moreover, we only logically understand an expression such as ‘A v ¬A’ if we understand that this is just one way we can choose a formal language to express some logical law (besides ‘p v ¬p’, ‘ApNp’, etc.) with which this expression has to have some structural similarity. Therefore, although exactness, strictness and (grammatical and proof-​) checkability in a formalism stems on the one hand from sensible evidence of written expressions, it presupposes on the other some abstract and “ideal” or “conceptual” pre-​understanding of expression-​ types and expressed “forms” themselves (cf., for example, Frege’s or Gödel’s “concepts” and “thoughts”, Aristotelian ἔσω λόγος). In connection with this “conceptual” component in the understanding of formalised inscriptions, there is also the question of the design and choice of a formal system (its axioms, definitions and rules). For the formalisation of empirical knowledge, it is clear that the design of the system should consider and be based on empirical results. On the other hand, a question may be posed regarding the criterion of our choice of logical principles that should be incorporated into a formal system and accepted without being formally proven. Regardless of how one may respond to this question, the decision should obviously be made at least partly by means of conceptual considerations and one’s (= logical agent’s) self-​evidence beyond proof procedures. As illustration, an example can be found in Łukasiewicz’s investigation of the laws of excluded middle and bivalence in the context of Aristotle’s discussion in De interpretatione (see Aristotle 1974). As Łukasiewicz emphasises, in the foundations of logic we should rely on personal “self-​evidence”: Because it [the principle of bivalence] lies at the very foundations of logic, the principle under discussion cannot be proved. One can only believe it, and he alone who considers it self-​evident believes it. To me, personally, the principle of bivalence does not appear to be self-​evident. Therefore, I am entitled not to recognize it, and to accept the view that besides truth and falsehood there exist other truth-​values, including at least one more, the third truth-​value. łukasiewicz 1967a, 36–​37, our emphasis10

10

See in his earlier text: “Yet in all reasoning there is inherent formal creative reasoning: a logical principle of reasoning. … Logic is an a priori science. Its theorems are true on the strength of definitions and axioms derived from reason and not from experience. This science is a

168 Kovač While on the one hand the sensible givenness of signs facilitates exactness, on the other hand, if taken literally, that is, without sufficient abstract consideration of the signs, it leads to antinomies involving not just apparent, non-​actual “entities” (such as Aristotle’s “goatstag”), but logically self-​denying “subjects” and sentences (cf. “this sentence” in the formulation of the Liar, and Curry’s paradox). 3

The Machine as a Symbol of a Formalism

The aforementioned Tarskian set-​theoretic general definition of a formal system takes the concepts of a sentence and derivability (“consequence” of early Tarski) as primitive and describes them axiomatically by using set-​theoretic notions; that is, it defines a formal system by means of a specially designed meta-​theoretical axiomatic system, which has, in turn, its own pre-​formal presuppositions (see Gödel 1990). The concept of a formal system can be rendered precise in its “abstract” (“absolute”) sense independently of any formalism (i.e., not defined in some given formal system), and at the same time, fully exact and strict. As is known, according to Gödel, who follows Turing (1965), the universal concept of a formal system is given independently of a particular formalism (but not informally, see Crocco 2017) by a clear and precise perception of the concept of a mechanical procedure, defined by a Turing machine which can write down all the theorems of a given formal system (Gödel 1995a, 308): a “formal system is a mechanical procedure for producing formulas”. For Gödel, the “essence” of a formal system “is that reasoning is completely replaced by mechanical operations on formulas” (1986a, 195; 1986c, 370), i.e., it is equivalent to a Turing machine (“mechanical procedure”, “algorithm”) for writing theorems of the system (Gödel 1995a, 308, see Crocco 2017, cf. Kennedy 2014).11

11

sphere of pure mental activity.” (Łukasiewicz 1970a, 11). And later, in the 1930s: “We are concerned with that meaning, with the thought and ideas expressed by signs, even if we do not know what these meanings are, and not with the signs as such” (Łukasiewicz 1970b, 241). Nevertheless, Łukasiewicz laid much stress on the linguistic expressions of logical laws (the “nominalistic guise” of logic, Łukasiewicz 1970c, 222)  and sometimes radically dispensed with “thinking” as the object of logic: “It is not true, however, that logic is the science of the laws of thought. It is not the object of logic to investigate how we are actually thinking or how we ought to think. The first task belongs to psychology, the second to a practical art of a similar kind to mnemonics” (Łukasiewicz 1957, 12, cf. also Łukasiewicz 1970c). Kant’s “fabric of syllogisms” is a sort of anticipation: “Von der fabric der Vernunftschlüsse. Man sucht jederzeit die Vernunft zuletzt technisch zu machen, damit, indem man sie der Behandlung der Sinne unterwirft, man wegen der Fehler gewiß sey” (Kant 1924, 742, refl. 3256). Kant outlined, to his standards, a provably complete “system” of formal logic

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In the definition of a formal system by means of a Turing machine, the concept of a formal system is reduced to mechanical (and thus causal) terms and rendered objective.12 Such a definition should not come as a surprise. We claim that a mechanical (or at least generally causal) perspective was essentially involved in devising and defining central logical concepts (not merely in the sense of helpful techniques and tools for drawing conclusions) from the beginnings of the history of logic. It can be shown, for example, that Aristotle’s u ­ nderstanding of syllogism was basically dependent on causal terms (e.g., premises as causes of a syllogism). A syllogistic inference (of a “perfect” syllogism), according to an Aristotelian approach, is nothing but a (mechanical) “computation” (συλλογίζειν) of the terms of a syllogism according to the quality of the major (universal) premise and the quantity of the minor (­affirmative) premise on the basis of the transitivity of predication.13 “Necessity” in Aristotle’s definition of a syllogism amounts to a mechanical causation of the conclusion by the premises as its “causes”. Although the conclusion might be understood as the end (τέλος) of a syllogism, the conclusion follows (συμβάινει) merely due to the premises, without any additional, external cause (“through the being of premises”, διὰ τὸ ταῦτα εἶναι). In addition, what is in accordance with a causal understanding of a syllogism are the non–​reflexivity, non-​monotonicity, and transitivity of syllogistic reasoning as well as the non-​validity of not-​P ⊨ P (see Kovač 2013). Furthermore, specifically contributing to a mechanistic “picture” of ­Aristotel’s syllogistic is his rule of ecthesis (“exposition”), presupposed in the foundational layer of his syllogistic. As pointed out by Hintikka (1967),14 this is similar to Euclid’s ecthesis accompanied by construction (κατασκευή, “preparation,” “machinery”). By means of Aristotelian ecthesis, a construction of an instantiating term (concept) X is initiated as a sort of artificial, mechanical device that instantiates the terms of the premises and then “automatically” shows whether it also has some property P in question.15 Given that the ecthetic term is “lower” than all of the terms of a considered syllogism, it could be understood as a singular term, intended at representing a singular object.

12 13 14 15

(including non-​Aristotelian hypothetical and disjunctive propositional forms) on which this “fabric” should have been founded (cf., for example, Kant 1968, B viii-​i x, 94–​101, 131–​142, 359–​361; Kant 1924). The objectivity of the inherent “mechanical” thought of logical formalism is stressed by J. Salamucha (2003). He also thinks that “logical ‘mechanization’ ”, cultivating clarity, precision and objectivity, is essential for the development of “sound individuality” (p. 68). On a specific “arithmetical interpretation of syllogistic” by Leibniz, cf. in Łukasiewicz (1957, 126–​129). See Hintikka’s discussion on ecthesis in connection with Euclidean construction as a preparation for a proof. On Aristotelian ecthesis, see, for example, Żarnecka-​Biały (1993).

170 Kovač It seems that in a possible reduction of syllogistic to its foundations  –​the principles of non-​contradiction and the excluded middle (Met. Γ, in Aristotle 1973) –​ecthesis should play an essential role (cf. the ecthetic style of Aristotle’s definition of universal propositions in An. Pr. 24b 28–​30), regardless of the fact that in his “working logic” Aristotle uses ecthesis only occasionally, such as in proving conversion and third figure syllogisms (Kovač 2013).16 A Turing machine or a constructed ecthetic entity have a very general, symbolic character. To better understand their essence, we refer to some of Wittgenstein’s striking reflections on machines. We use a machine, or the drawing of a machine, to symbolize a particular action of the machine. For instance, we give someone such a drawing and assume that he will derive the movement of the parts from it. Wittgenstein 1958, 78e

We might say that a machine, or the picture of it, is the first of the series of pictures which we have learnt to derive from this one.17 wittgenstein 1958, 78e

According to Wittgenstein, a machine (or picture of a machine) can be used as a symbol for a certain way of operation (causation) or motion (activity), in distinction to a real machine, which additionally includes accidental properties such as deformability. In the symbolic sense, a machine has its determinate way of operation, its possible motions (excluding its additional behaviour as a given real machine), “in itself.” Wittgenstein suggests that a symbolic (picture of a) machine, containing possible motions, does not just depict motions, but rather, as a symbol, has some closer, non-​empirical relation to them18 (in Tractatus, Wittgenstein 1976, the possibility of a motion, and thus a machine, would indeed be understood as a picture of motion). Wittgenstein’s symbolic machine shares its abstractness with a Turing machine. 16

17

18

The following Aristotelian causal analysis of a syllogism is proposed in (Kovač 2013): the premises as the material cause (Met. Δ2, 1013b 20–​21), the figure of a syllogism (position of the middle term) as its formal cause, ecthesis as the moving cause, and the conclusion as the final cause. “Wir gebrauchen eine Maschine, oder das Bild einer Maschine, als Symbol für eine bestimmte Wirkungsweise. Wir teilen z.B. Einem dieses Bild mit und setzen voraus, daß er die Erscheinungen der Bewegung der Teile aus ihm ableitet” (Wittgenstein 1958, 78). “Wir könnten sagen, die Maschine, oder ihr Bild, sei der Anfang einer Reihe von Bildern, die wir aus diesem Bild abzuleiten gelernt haben” (Wittgenstein 1958, 78). Cf. “[S]‌o the possibility of the movement stands in a unique relation to the movement itself; closer than that of a picture to its subject’; for it can be doubted whether a picture

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We can conceive of a Turing machine (or its picture, presenting its scanning/​ writing head, its tape, and its flowchart) as a symbol of the specific provability (possible steps in proofs) of the corresponding formal system (not just as a device doing an assigned job). A Turing machine symbolises this formal system, containing in “itself” all provability “moves” of the system. Machines and pictures of machines in themselves constitute a universal language, independent of given formalisms, but nonetheless fully exact and strict and thus able to directly evince the rigouristic nature of a formalism.19 Let us note that in a Wittgensteinian sense, an Aristotelian ecthetic (singular) term X can be understood as a symbol of the interrelations of the terms as proposed by the premises of a syllogism, where we abstract from any other “real” properties X might otherwise possess, i.e., we can understand X as symbolising this particular syllogism as well as the conversions and other syllogisms it logically includes. 4

Formalism, Determinism and Ł3

To better understand some aspects of the foundations of formal systems, we will briefly analyse Łukasiewicz’s three-​valued logic Ł3, which is well-​known for having been inspired by the discussion on determinism, causality and contingency. Given that formal reasoning (proofs in a formal system) is a mechanical and thus causal affair, it should possess general features of determinacy. Determinism is for Łukasiewicz “the belief” that: if A is b at instant t it is true at any instant earlier than t that A is b at instant t. łukasiewicz 1967a, p. 22

19

is the picture of this thing or that. … [B]ut we do not say “Experience will shew whether this gives the pin the possibility of this movement”…” (Wittgenstein 1958, 79e). Wittgenstein’s philosophical interest in machines can be naturally connected with his study of aeronautics and in particular with the books containing machine drawings that he possessed in his private library, including works by Leonardo da Vinci (Les manuscrits de Leonardo de la Bibliotheque de l’ Institut de France, six vols., Paris, 1881–​1891), Faust Vrančić (Faustus Verantius, Machinae novae, Venetiis, 1615/​16, see Vrančić 1993) and Georg Andreas Böckler (Theatrum machinarum novum, Nürnberg, 1661). See Spadoni (1985, 25–​ 45) and http://​digitalcollections.mcmaster.ca/​russell-​lib/​media/​machinae-​ novae-​fausti-​verantii-​siceni. These books may have played a significant role in inspiring Wittgenstein in his early “picture philosophy” (sign and machine as pictures), as well as in his later philosophy of language games. Wittgenstein probably did not know that Vrančić was also the author of a small logic (Vrančić 2018), containing in its second edition an argumentation against the possibility of metaphysics.

172 Kovač Since a TM is an idealized device (independent of any circumstances in the physical world), we can take that, ideally, a TM for a formal system S is available at any instant t’ (independently of the indeterminacies of the physical world) and thus, if a TM which starts working at t’ is to produce a theorem T of S at the moment t, then it is and was always true that the TM for S, starting at t’, will produce T at t. Łukasiewicz did not give a formal definition of formal provability, but rather, the definition of necessity (L) for Ł3 Lφ = ¬ ( φ → ¬φ ) , which truth-​functionally excludes indeterminacy and falsehood, and covers an essential feature of the work of a (deterministic) TM that produces theorems of S.20 Possibility is defined dually, Mϕ = ¬L¬ϕ = ¬ϕ → ϕ (Łukasiewicz 1967b, pp. 55, 57). Ł3 and its reformulations make it possible to study in general how the indeterminacy of events interacts with deterministic structures (including formalisms) and how particular deterministic conditions are embedded in a ­deterministic, causal structure as a whole. Deterministic justification and indeterminism in Ł3 can be made more explicit if Ł3 is reformulated by using explicit necessity and possibility, as in Minari’s (2002) W◻, a “modal” equivalent of Ł3 (i.e., of its axiomatisation W by Wajsberg). For convenience, we repeat Minari’s W◻ (2002, 172): W◻.1 W◻.2 W◻.3 W◻.4 W◻.5 (=T) W◻.6 (=B) W◻.7 W◻.8

ϕ → (ψ → ϕ) (ϕ → ψ) → ((ψ → χ) → (ϕ → χ)) (ϕ → (ψ → χ)) → (ψ → (ϕ → χ)) ϕ → ¬¬ϕ, Lϕ → ϕ ϕ → LMϕ (Lϕ → (Lϕ → ψ)) → (Lϕ → ψ) ϕ → (ϕ → Lϕ)

¬¬ϕ → ϕ

Rules: Modus ponens, Necessitation,

20

In Ł3, the negation of indeterminacy returns indeterminacy, and the valuation v of ϕ → ψ returns min(1, 1 –​v(ϕ) + v(ψ)) (a conditional between indeterminacies returns truth).

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where ϕ, ψ, and χ are metavariables for formulas of W◻.21 A set Γ is inconsistent iff Γ ⊢ ⊥, where ⊥ is short for ¬(ϕ → ϕ). The counterparts of modal formulas K, 4 and 5 are theorems. In distinction to modal system S5 (and S4, which is used in Gödel’s 1933 modal translation of ipc), we recall that in Ł3 and so in W◻) some classical tautologies are not valid (due to the possible indeterminacy of subformulas), for example, ϕ ∨ ¬ϕ, ¬(ϕ ∧ ¬ ϕ), (ϕ ∧ ¬ϕ) → ψ (although ϕ → (¬ϕ → ψ) is valid). At the same time, some S5 (and S4) non-​valid formulas become valid in Ł3. For example, (Mϕ ∧ Mψ) → M(ϕ ∧ ψ), which seems to be “counterintuitive” if we consider it from the viewpoint of possible world semantics. However, in one-​world semantics with indeterminacies (like truth-​functional semantics for Ł3 and W◻), it might be something quite natural: all possibilities (say, ϕ and ψ) are now “incorporated” in one and the same world as its indeterminacies or, as the case may be, truths. Technically, since in Ł3 Mχ = ¬χ → χ and the conditional between indeterminacies returns truth, then M(ϕ ∧ ψ) never decreases the value of Mϕ ∧ Mψ. On the other hand, ϕ → Lϕ (“modal collapse”) is classically valid under the aforementioned truth-​ functional definition of L in in Ł3, but is non-​valid in Ł3 due to the potential indeterminacy of ϕ, which falsifies Lϕ. To verify the “modal collapse,” Ł3 requires ϕ itself as a pre-​condition: ϕ → (ϕ → Lϕ), i.e., if ϕ is assumed, then its “modal collapse” results; indeed, indeterminate ϕ (truly) implies indeterminate ϕ → Lϕ. Let us also note that L¬L⊥ is a theorem of Ł3 (as well as of S4 and S5, in their original sense of ‘L’), indicating that ‘L’, if viewed from the standpoint of Ł3 (W◻), cannot substitute the formal provability concept (because of the second incompleteness theorem), but rather generally accounts for the causal impossibility of a deterministic (mechanical) system being in some self-​contradictory state. Łukasiewicz’s necessity should be distinguished from a universal concept of proof (Gödel’s “absolute proof,” “abstract proof,” see Gödel 1986b, 1995d), which is not reducible to formal provability or determinism, as well as from Gödel’s ontotheological concept of necessity (Gödel 1995c), which, despite its S5 propositional base, leads to “modal collapse” as a natural consequence due to the specific higher-​order (“abstract”) concepts and perspective involved. Besides necessity in general, a state s of a deterministic mechanical system (like a deterministic TM) is necessitated (caused, justified) by particular configurations that precede s. In order to be able to formally present particular deterministic necessitation, we sketch out logic WJ, where besides L: ϕ, where L is a term (justification by means of a whole causal structure or an unspecified part of it), we introduce the form t: ϕ to allow specific causal justifications (“t presently 21

W consists of the axioms W◻.1, W◻.2, (¬ψ → ¬ϕ) →(ϕ → ψ), ((ϕ → ¬ ϕ) → ϕ) → ϕ, and modus ponens.

174 Kovač necessarily justifies ϕ”, “t actually causally justifies ϕ”). In WJ, we partially apply tools of justification logic (e.g., Fitting 2005), without possible worlds semantics. Vocabulary consists of L, ei,:, +,⨯, pi, ¬, →, (,) (i is a positive integer); justification term t ⩴ L | ei | (t1+t2) | (t1⨯t2); formula ϕ ⩴ p | ¬ϕ | ϕ1 → ϕ2 | t: ϕ. WJ has axioms analogous to W◻.1–​4, while W◻.5–​8 are replaced by Wj.5–​8, respectively: Wj.5 (=WjT) Wj.6 (=WjB) Wj.7 Wj.8

t: ϕ → ϕ ¬ϕ → L: ¬t: ϕ (t: ϕ → (t: ϕ → ψ)) → (t: ϕ → ψ) ϕ → (ϕ → L: ϕ)

where t is an arbitrary causal justification (possibly ‘L’). ‘L: ϕ’, which could be read as ‘there is a cause that ϕ’, can be understood as referring to a whole actual causal structure (e.g., the causal structure of a Turing machine under consideration), within which we know that ϕ is the case (effectuated). Wj.8 expresses a weakened “modal collapse”. The additional propositional axioms (involving an interplay between distinct justification terms) of Wj are: Wj.9 Wj.10 WJ.11

t: ϕ → (t+u): ϕ, u: ϕ → (t+u): ϕ t: (ϕ → ψ) → (u: ϕ → (L: ψ → (t⨯u): ψ)) t: ϕ → L: ϕ

Term (t+u) is the sum of deterministic causal justifications t and u, whereas (t⨯u) is the application of t to u (corresponding to the evidence in justification logic). In Wj, for simplicity, the necessitation rule allows ‘L:’ to be prefixed in front of a proven formula. The following proposition shows in which way the WJ counterparts of K, 4 and 5 involve a deterministic combination of causes and their embedding in a whole causal structure (L). Proposition. WJK WJ4 WJ5

t: (ϕ → ψ) → (u: ϕ → (t×u): ψ) t: ϕ → ((L⨯t)⨯t): L: ϕ ¬L: ϕ → (L⨯L): ¬t: ϕ

Proof.

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(a) WJK is proven by adapting the sketch of the proof for K in Minari (2002), starting from t: (ϕ → ψ) → (ϕ → ψ) (Wj.T) and (u: ϕ → ϕ) → ((ϕ → ψ) → (u: ϕ → ψ)) (Wj.2) to get t: (ϕ → ψ) → (u: ϕ → ψ), and combining the use of Wj.8 with Wj.10 to obtain WJK. (b) Proof of WJ4 (cf. hints for 4 in Minari 2002): 1. ϕ → (ϕ → L: ϕ), 2. L: (ϕ → (ϕ → L: ϕ)), 3. L: (ϕ → (ϕ → L: ϕ)) → (t: ϕ → (L⨯t): (ϕ → L: ϕ)), 4. t: ϕ → (L⨯t): (ϕ → L: ϕ), 5. (L⨯t): (ϕ → L: ϕ) → (t: ϕ → ((L⨯t)⨯t): L: ϕ), 6. t: ϕ → (t: ϕ → ((L⨯t)⨯t): L: ϕ), 7. t: ϕ → ((L⨯t)⨯t): L: ϕ. (c) Proof of WJ5 (cf. hints for 5 (=E) in Minari 2002): 1. ¬L: ϕ → L: ¬((L⨯t)⨯t): L: ϕ (WJB), 2.  ¬((L⨯t)⨯t):  L:  ϕ → ¬t:  ϕ (WJ4), 3.  L:  (¬((L⨯t)⨯t):  L:  ϕ → ¬t:  ϕ), 4. L: ¬((L⨯t)⨯t): L: ϕ → (L⨯L): ¬t: ϕ, 5. ¬L: ϕ → (L⨯L): ¬t: ϕ (1,4). ◻ The WJ counterpart of modal formula 4 may be informally conceived of as the positive introspection of deterministic evidence, leading to deeper foundations of a deterministic chain within a holistic causal structure. We note that WJ5 avoids requiring one and the same particular justification of any ϕ not justified by t, and instead states necessity in general, (L⨯L), as being responsible for ¬t: ϕ (see the discussion on the problem with the axiom candidate ¬t: ϕ →?t: ¬t: ϕ in Artemov and Fitting 2016, but cf. also Artemov et al. 1999). Corollary. W◻ ⊂ WJ, W ⊂ WJ. Proof. Given that L is also a t, with WJ.11 the first part easily follows. The second part is obvious, because W and W◻ are equivalent (see Minari 2002, Theorem 2.6 ii). ◻ Semantics. The usual truth-​functional semantics for Ł3 is extended to define the semantic properties of justification terms and the formulas that include them. To this end, a special function of deterministic evidence, E, is added. Let 1, ½ and 0 be the values true, indeterminate and false, respectively. Then, a WJ model M = 〈V, D, v, E〉, where the set of values V = {1, ½, 0}, the set of designated values D = {1}, v(ϕ) ∈ V such that v(p) ∈ V, v(¬ϕ) = 1 –​v(ϕ), v(ϕ → ψ) = min(1, 1 –​v(ϕ) + v(ψ)), with the addition that v(t: ϕ) = 1 iff v(¬(ϕ → ¬ϕ)) = 1 and t ∈E(ϕ), otherwise v(t: ϕ) = 0, and where the following conditions for ∈ E(ϕ) hold: (1) if t ∈ E(ϕ), then (t+u) ∈ E(ϕ); if u ∈ E(ϕ), then (t+u) ∈E(ϕ), (2) if v(¬ϕ) = 1 or v(¬ϕ) = ½, then L ∈ E(¬t: ϕ) for any t, (3) if t ∈ E(ϕ → ψ) and u ∈E(ϕ), then (t⨯u) ∈ E(ψ), (4) if v(¬(ϕ → ¬ϕ)) = 1, then L ∈ E(ϕ), (5) if t ∈ E(ϕ), then L ∈ E(ϕ). Minari (2002) has proven that W◻ is equivalent to W (as mentioned above), and thus sound and complete with respect to the same models as W. For the soundness and completeness of Wj, we focus on the formulas that include subformulas of the shape t: ϕ. (a) Soundness. Let us take some examples. (a) Axiom Wj.5 is semantically obvious from the definition of the satisfaction of t:  ϕ. (b)  For Wj.6,

176 Kovač suppose that ¬ϕ is true in M and thus ϕ is false in M. It follows that for any t, t: ϕ is false, and thus ¬t: ϕ and ¬(¬t: ϕ → t: ϕ) are true in M. With the condition (2) for E, we obtain the truth of L: ¬t: ϕ, and thus the truth of Wj.6. Suppose, alternatively, that ¬ϕ, and so ϕ, are indeterminate in M. Hence ¬t: ϕ is true and, by condition (2) for E, L: ¬t: ϕ is true as well, which gives the truth of Wj.6. (c) For Wj.10, assume that t: (ϕ → ψ), u: ϕ and L: ψ of Wj.10 = t: (ϕ → ψ) → (u: ϕ → (L: ψ → (t⨯u): ψ)) are true in M. It follows that ψ, and thus ¬(ψ → ¬ ψ), are true in M as well. By the condition (3) for E, the truth of (t⨯u): ψ results. (b) Completeness. The proof can be adapted from Minari (2002, Section 4), with L generalised to any justification term t. Let us sketch out such an adaptation. We define that a set Γ is Wj-​maximal consistent iff Γ ⊬ ⊥ and for each formula ϕ and each justification t, either (a) Γ ⊢ t: ϕ, or (b) Γ ⊢ ¬t: ¬ϕ and Γ ⊢ ¬t: ϕ, or (c) Γ ⊢ t: ¬ϕ (MAX3J, cf. Minari’s Definition 4.1). A Wj consistent set Γ can be consistently extended, for each ϕ and t, with only one of the subsets {t: ϕ}, {¬t: ¬ϕ, ¬t: ϕ} and {t: ¬ϕ} (cf. Minari’s Lemma 4.2). In addition, it can be shown (cf. Minari, Lemma 4.3) that for a Wj consistent set Γ, Minari’s following rewritten conditions hold: (i) if Γ ⊢ t: (ϕ → ψ) for some t, then exclusively either (a) Γ ⊢ v: ψ for some v, or (b) Γ ⊢ u: ¬ϕ for some u, or (c) Γ ⊢ ¬u´: ¬ϕ, Γ ⊢ ¬u´: ϕ, Γ ⊢ ¬v´: ¬ψ, and Γ ⊢ ¬v´: ψ for any u´ and v´; (ii) if Γ ⊢ t: ¬(ϕ → ψ) for some t, then Γ ⊢ u: ϕ for some u and Γ ⊢ v: ¬ψ for some v; (iii) if Γ ⊢ ¬t: ¬(ϕ → ψ) and Γ ⊢ ¬t: (ϕ → ψ) for any t, then either (a) Γ ⊢ u: ϕ for some u, and Γ ⊢ ¬v: ψ and Γ ⊢ ¬v: ¬ψ for any v, or (b) Γ ⊢ ¬u: ϕ and Γ ⊢ ¬u: ¬ϕ for any u, and Γ ⊢ v: ¬ψ for some v. − For the proof, for instance, of (i), assume (1) Γ ⊢ t: (ϕ → ψ), but (2) Γ ⊬ v: ψ for any v, and (3) for each u, Γ ⊬ u: ¬ϕ. From (2) and MAX3J it follows: Γ ⊢ v: ¬ψ or both Γ ⊢ ¬v: ¬ψ and Γ ⊢ ¬v: ψ. Thus, Γ ⊬ v: ¬ψ, from (3), since {t: (ϕ → ψ), v: ¬ψ} ⊢ u: ¬ϕ for some u. Therefore, Γ ⊢ ¬v: ¬ψ and Γ ⊢ ¬v: ψ for each v. Also, from (3) and MAX3J, Γ ⊢ u: ϕ or both Γ ⊢ ¬u: ¬ϕ and Γ ⊢ ¬u: ϕ. But Γ ⊬ u: ϕ, from (1), (2) and WJK. Therefore, Γ ⊢ ¬u: ¬ϕ and Γ ⊢ ¬u: ϕ for each u. The remaining instances of (i) and cases (ii) and (iii) can be proven by similar reasoning. − Furthermore, in analogy to Lindenbaum’s lemma (cf. Lemma 4.4 in Minari 2002), it holds that the extension of Γ in some of the three mutually exclusive ways, i.e., by {t: ϕ}, {¬t: ¬ϕ, ¬t: ϕ} or {t: ¬ϕ}, is consistent. Finally (cf. Theorem 4.5 by Minari), a canonical valuation vc can be defined by associating values 1, ½, and 0 to an atomic formula p in correspondence with alternatives (a)-​(c) of MAX3J, respectively, and by the condition that in a canonical model Mc, t ∈ Ec(ϕ) iff Δmax ⊢ t: ϕ, where Δmax is a maximal extension of Δ. Using (i)-​(iii) above, the

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correspondence of the canonical valuation (values 1, ½, and 0 of ϕ) and the derivability (of t: ϕ, of both ¬t: ¬ϕ and ¬t: ϕ, or of t: ¬ϕ) from the related Wj-​maximal consistent set (“truth lemma”) can by proven by induction, with strong completeness following as a result.

Concluding Notes

Since ancient times, formal logic (including ancient formalisms or ancient incipient formalisms, as well as modern logical systems) has possessed a causal, mechanical sense, as only precisely stated by Turing and Gödel in the 20th century. Wittgenstein’s reflections reveal the symbolic character of a machine. Łukasiewicz’s philosophical views and formal analyses can be used to better understand the embedding of deterministic justifications in general in a broader causal context which includes indeterminacy and contingencies. Łukasiewicz’s viewpoint was strongly influenced by the considerations on logical and physical concepts of necessity in the context of the causality of human decisions. This concept of necessity should be distinguished from Gödel’s wider concepts of “abstract” provability and ontotheological necessity.

Acknowledgments

I am grateful to the reviewers, to Kordula Świętorzecka, and to the audience of the conference Formal and Informal Methods in Philosophy, Warsaw, 25–​27 June 2018, for their helpful remarks and comments.

References

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178 Kovač Aristotle. 2010. Prior Analytics, Book 1. Translated by G. Striker. Oxford: Oxford University Press. Artemov, S., and M. Fitting. 2016. Justification Logic. In: The Stanford Encyclopedia of Philosophy, ed. E. N. Zalta. http://​plato.stanford.edu/​archives/​win2016/​entries/​logic-​justification/​. Artemov, S., E. Kazakov and D. Shapiro. 1999. Logic of Knowledge with Justifications. Cornell University. Technical Report CFIS, 99–​12. Béziau, J.-​Y. 2005. From Consequence Operator to Universal Logic. In: Logica Universalis. Edited by J.-​Y. Béziau. Basel: Birkhäuser, 3–​17. Bocheński, I.M. 1961. A History of Formal Logic. Translated and edited by I. Thomas. Notre Dame (IN): University of Notre Dame Press. Bocheński, I.M. 2002. Formale Logik. Freiburg, München: Alber. Crocco, G. 2017. Informal and Absolute Proofs: Some Remarks from a Gödelian Perspective. Topoi, https://​doi.org/​10.1007/​s11245-​017-​9515-​3 (first online 11 November). Fitting, M. 2005. The Logic of Proofs, Semantically. Annals of Pure and Applied Logic 132, 1–​25. Frege, G. 1988. Begriffsschrift and andere Aufsätze. 2nd edition. Hildesheim etc.: Olms. Frege, G. 1998. Grundgesetze der Arithmetik. Hildesheim etc.: Olms. Gödel K. 1986–​2003. Collected Works. Ed. by S. Feferman et al. Oxford: Oxford University Press. Gödel, K. 1986a. Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I (1931). In: Gödel 1986–​2003, vol. 1, 144–​195. Gödel, K. 1986b. Eine Interpretation des intuitionistischen Aussagenkalküls (1933). In: Gödel 1986–​2003, vol. 1, 300–​303. Gödel, K. 1986c. On Undecidable Propositions of Formal Mathematical Systems (1934). In: Gödel 1986–​2003, vol. 1, 346–​371. (Postscriptum 1964.). Gödel, K. 1990.Remarks before the Princeton Bicentennial Conference on Problems in Mathematics (1946). In: Gödel 1986–​2003, vol. 2, 150–​153. Gödel, K. 1995a. Some Basic Theorems on the Foundations of Mathematics and their Implications. In: Gödel 1986–​2003, vol. 3, 304–​323. Gödel, K. 1995b. The Modern Development of the Foundations of Mathematics in the Light of Philosophy. In: Gödel 2003, vol. 3, 374–​387. Gödel, K. 1995c. Ontological Proof. In: Gödel 1986–​2003, vol. 3, 403–​404. Gödel, K. 1995d. Vortrag bei Zilsel. In: Gödel 1986–​2003, vol. 3, 86–​113. Hilbert, D. 1967. On the Infinite (1926). In: From Frege to Gödel. Edited by J. van Heijenoort. Cambridge (MA): Harvard University Press, 367–​392. Hintikka, J. 1967. Kant on the Mathematical Method. Monist 51, no. 3: 352–​375. Kant, I. 1924. Logik. In: Kant’s gesammelte Schriften, vol. 16. Berlin, Leipzig: de Gruyter. Kant, I. 1968. Kritik der reinen Vernunft. 2. Auflage 1787. Kants Werke, vol. 3. Berlin: de Gruyer.

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The Status of Mathematical Proofs and the Enhanced Indispensability Argument Krzysztof Wójtowicz Abstract One of the most important arguments for mathematical realism is Quine’s indispensability argument. In recent years, the original argument has been modified, and taken on the form of the Enhanced Indispensability Argument (eia), where the explanatory virtues of mathematics are of primary importance. In particular, the notion of mathematical explanation (in contrast to causal or mechanistic explanation) in science is crucial for the debate. The issue of the explanatory role of mathematics in science is closely related to the problem of the explanatory role of mathematical proofs within mathematics. It is reasonable to claim that the explanatory role of a mathematical theorem in physics depends on how it is proven (that is, in particular, on the intra-​mathematical explanatory role of the proof). But here we have to take into account the problem of the relationship between informal proofs known from practice and their formal counterparts. From the point of view of logical analysis (allowing to identify the logically necessary ontological commitments, for instance using the tools from Reverse Mathematics), the formal version is important. From the point of view of the eia, the “real,” explanatory version is crucial. This leads to a tension between these versions of the argument.

Keywords formal proof  –​indispensability argument  –​informal proof  –​logical analysis  –​ ­mathematical explanation –​mathematical realism –​reverse mathematics

1 Introduction1 One of the most important arguments for mathematical realism is Quine’s indispensability argument. In recent years, the original argument has been 1 The preparation of this paper was supported by an ncn grant: 2016/​21/​B/​HS1/​01955.

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modified, and has taken on the form of the Enhanced Indispensability Argument (eia), where the explanatory virtues of mathematics are of primary importance. In particular, the notion of mathematical explanation (in contrast to causal or mechanistic explanation) is central to the debate. The issue of the explanatory role of mathematics in science is closely related to the problem of the explanatory role of mathematical proofs within mathematics. But when discussing this issue, we have to take into account the relationships between informal proofs known from practice and their formal counterparts. From the point of view of logical analysis (allowing, in particular, the identification of the logically necessary ontological commitments, for instance using the results of Reverse Mathematics), the formal version is important. From the point of view of the eia, the “real” version is important, which leads to a certain tension between these versions of the argument. My aim is to point out this problem and give a preliminary discussion. The structure of the text is as follows. In part (1) “The indispensability argument,” Quine’s classical argumentation in favor of mathematical realism is shortly recapped –​some objections are presented, and the response in the form of the Enhanced Indispensability Argument is presented. In part (2)  “Mathematical explanations in physics,” it is argued that the notion of distinctively mathematical explanation in science is sound, and some examples are presented. In part (3) “The explanatory role of proofs,” it is argued that not only the theorem itself, but also its proof has an explanatory contribution, so it has to be taken into account when discussing the issue of mathematical explanation in science. In part (4) “Real versus ideal proofs,” the tension between ordinary, everyday mathematical proofs and their formalized counterparts is discussed in the context of the eia. Part (5) “Real/​ideal proofs and mathematical explanation”, discusses these issues in the context of Reverse Mathematics. A short (6) “Summary” follows. 2

The Indispensability Argument

The most widely-​debated argument in the realism-​antirealism debate in the philosophy of mathematics is the (pro-​realistic) indispensability argument in its various forms, originally proposed by Quine. It arises in a natural way from Quine’s metaphilosophical and philosophical claims –​naturalism, the rejection of the dogmas of empiricism, his views on the status of logic, and, in particular, his holism. According to Quine’s holistic doctrine: The totality of our so-​called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic

182 Wójtowicz physics or even of pure mathematics and logic, is a man-​made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.2 quine 1951, 42

This account had a profound impact on the discussions concerning the ontological status of scientific theories. In particular, if we accept a physical theory, it will not be justified to treat only some of the scientific notions as interpreted, while others as auxiliary devices, devoid of interpretation. Ontological commitments of a scientific theory should be taken seriously, so, in particular, it is necessary to identify the corresponding ontology. It does not always have to be of a well-​defined character, which is quite obvious in the case of common-​ sense ontology,3 but the same phenomenon applies to scientific theories. We need a precise criterion that will allow us to exhibit the underlying ontology. According to Quine, the indicator of existence is given by quantification (cf. e.g. Quine 1969), and this provides a clear criterion of ontological commitments.4 Quine’s criterion applies to all terms used in scientific theories, in particular to mathematical ones. Mathematics is an essential component of any (theoretically advanced) scientific theory, which means that mathematical terms and notions cannot be “paraphrased away”.5 Quine’s indispensability argument in favor of mathematical realism therefore rests on two premises: 1. Mathematics is indispensable in science: empirical theories must inevitably use mathematical tools, and refer to mathematical objects. 2. Since we interpret scientific theories in a realistic way, it is necessary to recognize the existence of all objects to which quantification in a given theory refers. Therefore, we should, in particular, recognize the existence of mathematical objects. According to the indispensability argument, mathematical existential sentences should be interpreted at face value, as should other existential sentences 2 For a presentation of Quine’s holistic doctrine (in the context of the philosophy of mathematics) see, e.g. Resnik 2005. 3 “The common man’s ontology is vague and untidy in two ways. It takes in many purported objects that are vaguely or inadequately defined. But also, what is more significant, it is vague in its scope; we cannot even tell in general which of these vague things to ascribe to a man’s ontology at all, which things to count him as assuming”(Quine 1981, 9). 4 Quine’s idea is based on the first-​order thesis, according to which elementary logic is “the genuine logic,” I will not discuss the problem here. 5 An attempt has been made in (Field 1980), but it is widely believed that it was not successful.

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of scientific theories. Of course, we can only formulate realistic theses –​on the basis of the indispensability argument –​in relation to those fragments of mathematics which are applied in empirical theories. So we are dealing with the problem of identifying the ontological basis for applied mathematics. Quine’s criterion allows for the identification of ontological commitments (in particular mathematical ones) for particular theories (provided they are formulated in a logically correct form). So, we could think of limiting ourselves to “local indispensability arguments”–​according to which different physical theories make use of different mathematical tools, and the realistic interpretation of a particular physical theory requires us to recognize the existence of mathematical objects appearing within the particular theory. Prima facie, these objects do not need to be treated as special cases “universal mathematical species”, described within one single theory. However, this would be unnatural, and clearly contrary to mathematical practice and to the fact that we have a sense of unity in mathematics as a discipline. We do not consider, for example, sequences of natural numbers and real-​valued functions to be objects from two fundamentally different ontological categories  –​we rather understand them to “live” in the same mathematical universe (one of the arguments in favor of this thesis is the possibility of reconstructing relevant fragments of mathematics in one system, such as zfc or Z2). Mathematical notions usually permeate many disciplines –​in differential equations we use probabilistic techniques (in combinatorics analytic techniques, etc.). Even if there are many mathematical disciplines, mathematics –​as a whole –​is a very coherent subject. Mathematics can be reconstructed for instance in zfc (this is the most standard formalization); however, applied mathematics does not require the full power of zfc. In Quine’s opinion, theories of pure mathematics can be used to simplify and unify the theory of applied mathematics, but what exceeds these needs has the status of uninterpreted systems. Therefore, it will not be justified to consider set theory an adequate ontological basis for applied mathematics because its existential assumptions definitely go beyond what is established by virtue of the indispensability argument. There are various types of objections to Quine’s indispensability argument. An important group of them is based on the thesis that the mere indispensability of mathematics in science is not a sufficient argument in favor of realism: it is necessary to prove that this indispensability is of a special character. The main line of defense against this kind of criticism consists in proving that mathematics is not only indispensable for science, but also that it plays an indispensable explanatory role –​and this makes the position of mathematics so special. This line of argumentation is known as the Enhanced Indispensability

184 Wójtowicz Argument (eia), forcefully advocated by Baker, e.g. (Baker 2005, 2009). eia is a form of reasoning to the best explanation –​if it is necessary to accept the existence of certain objects, in order to explain certain phenomena, then it is justified (and even obligatory) to recognize that they do exist. Important questions in this context are: 1. is the explanatory indispensability a sufficient condition for recognizing the existence of objects of a certain type? 2. are mathematical objects really indispensable from the point of view of reasoning to the best explanation? Problem (1) is of a general nature, while problem (2) is closely related to the question of whether mathematics actually makes an explanatory contribution to the natural sciences –​that is, whether there are genuine mathematical explanations of physical phenomena. 3

Mathematical Explanations in Physics

The classic causal accounts of scientific explanation do not seem to be satisfactory in many cases, and the notion of non-​causal, abstract explanation is receiving growing attention (for an introductory presentation see, e.g. Reutlinger and Andersen 2016; Pincock 2015 discusses concrete examples). This applies in particular to mathematical explanations in science (an important subcategory of non-​causal explanations), which have been the subject of lively debate in recent years. It is important for the discussion to distinguish between “explanation using mathematics” and “distinctively mathematical explanation”(cf. e.g. Lange 2013). Some scientific explanations merely make use of mathematical language –​but we are interested in explanations, where mathematics does the genuine explanatory work. In the latter case, mathematical theorems explain the phenomena by appealing to abstract, mathematical properties of the system in question –​not by describing the causal nexus or the detailed ­mechanisms.6 I can give only a few examples here, as the subject is vast. They differ in technical complexity, but all of them aim to illustrate a general phenomenon: when looking for an explanation of a physical fact, we do not focus on a network of causal relationships, the mechanism underlying it, or the particular course of 6 An important class is topological explanation, which “explains by a reference to structural or mathematical properties of the system (e.g. graph-​theoretical properties, topological features, or properties of mathematical structures in general), and abstracts away from the details of particular causal interactions or mechanisms” (Kostić 2018, 2).

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events –​but rather on the abstract, mathematical structure of the problem. (1) The Borsuk-​Ulam theorem offers a mathematical explanation of the fact that there are always two antipodal points on the surface of the Earth where two parameters are equal (Baker 2005, 2009; Baker and Colyvan 2011).7 (2) (Baron 2014) examines the behaviour of predators (in particular –​of sharks), where a mathematical explanation is offered by theorems on stochastic processes. (3) Lange examines the case of a double pendulum. It has exactly four equilibria, which is explained by a theorem concerning continuous functions on a torus (Lange 2013). (4) Similarly, the structure of honeycombs is explained by a mathematical theorem: hexagonal tiling minimizes the total perimeter length (Hales 2000, 2001). This means, that the bees do not waste wax, and gain an evolutionary advantage.8 (5) Another, much discussed topic is the example of the periodical life-​cycle of cicadas (two primes: 13 and 17 years), introduced in (Baker 2005). In order to explain this phenomenon, we have to take note of the properties of prime numbers, so the explanation has a mathematical, rather than biological character. (6) Probably the simplest, but most famous example is the case of the system of seven bridges in Königsberg: they cannot be crossed in such a way that each bridge is crossed exactly once. This is explained by a simple theorem in graph theory, and examining the physical properties of the bridges (for example, the material of which they are made, their size, their temperature, the mental processes that accompany the attempts, etc.) is neither necessary, nor relevant. Of course, the explanatory role of mathematics is questioned. According to some authors, mathematics is only an auxiliary tool for capturing and expressing relationships between physical phenomena. It cannot provide any genuine explanatory contribution. Even if the use of mathematics is necessary –​still, it is only a kind of map, with a merely representative role, so it is a mere expressive device. The problem is intricate: are there physical properties of physical objects that are not expressed in a purely physicalistic language? According to the doctrine of “abstract expressionism,” mathematics has a very specific function: it allows claims to be made about the physical world that could otherwise

7 According to the Borsuk-​Ulam theorem, if f is a continuous function from the sphere into R2, then there exist two antipodal points x and y, such that the f(x)=f(y). This theorem provides a straightforward explanation of the fact that there are always two antipodal points on the surface of the Earth where quantities (like temperature and air pressure) have the same value. This must happen, independently of the particular causal courses of events. (cf. Baker 2005, 2009; Baker and Colyvan 2011). 8 However, see the critique in (Räz 2013, 2017), who argues that this example rests on a misunderstanding.

186 Wójtowicz not be expressed.9 Discussing these skeptical remarks would take us too far afield. I assume here –​as a working hypothesis –​that the notion of mathematical explanation in science is sound. 4

The Explanatory Role of Proofs

The question arises of where the explanatory power of mathematical theorems within physics comes from. Is it the theorem itself as such (treated as a given fact, expressing some constraints of the system in question), or does its conceptual environment also play a role here? In particular:  is it important how the theorem is proven, and does the explanatory power of the theorem stem from the proof? The problem of the explanatory nature of proofs within mathematics is widely discussed.10 So, in the context of mathematical explanations within science we encounter the problem of whether the explanatory virtues of proofs are also transferred outside of mathematics. Assume that a theorem α is used to explain a physical phenomenon. What exactly is the source of the explanatory character of α and what is the status of its proof? Consider two opposing answers: (a) It is the theorem per se, which is explanatory (so its proof does not ­matter): Given that the proof justifies the theorem, we are then entitled to make use of the theorem, e.g., in applications to physical facts. (…) The role of the proof of that theorem is to justify the acceptance of that theorem. Daly and Langford 2009, 648

(b) It is the proof of α, which provides (at least a part of) the “explanatory input” of the theorem: Intra-​mathematical explanations may spill over into the empirical realm. The idea is that if, say, the Borsuk-​Ulam theorem is explained by its proof

9

10

“Numbers enable us to make claims which […] we […] would otherwise have trouble putting into words” (Yablo 2002, 230). “Let »abstract expressionism« be the doctrine that mathematics is useful in science because it helps us to say things about concrete objects which it would otherwise be more difficult, or perhaps impossible, for us to say” (Liggins 2014, 600). See for instance (Mancosu 2018) for an up-​to date introduction into the subject with an extensive bibliography.

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and the antipodal weather patterns are explained by the Borsuk-​Ulam theorem, it would seem that the proof of the theorem is at least part of the explanation of the antipodal weather patterns. Baker and Colyvan 2011, 327

If we accept (a), then the details of the proof become inessential: all that matters is the fact that a legitimate proof exists. In particular, the problem of necessary assumptions (axioms), and the particular proof methods will not be considered important for discussions concerning the role of mathematical explanations in science. But this is at odds with mathematical practice: that mathematicians do not really have the feeling of understanding the real meaning, the deep content of a theorem until they examine the proof. This point of view is also incoherent with the fact that there is a vast discussion in the philosophy of mathematics concerning the appropriate axiomatic (and even logical) framework. How the theorem is proved, and what resources are used for this aim is an important issue. I therefore consider (a) to be a vastly oversimplified point of view  –​and my claim is that proofs are essential for the discussion concerning mathematical explanation in science. Thus, when discussing the problem of ontological commitments in the context of eia, we are confronted with the question of the nature and status of mathematical proofs. In particular, this is a question about the relationship between a mathematical proof understood as an idealized object in a certain formal system (e.g. in formal set theory or arithmetic, for instance zfc, PA or Z2), and a real mathematical proof known from everyday practice. Real mathematical proofs (e.g. in analysis or topology) are obviously not formal –​they are formulated in a “mathematical natural language,” i.e. a natural language augmented with many symbols (and rules governing their use and interpretation). Which of them should be referred to in the discussion and what is the interplay between them? 5

Real versus Ideal Proofs

The logical notion of proof (as a string of symbols in a formal language) differs strongly from the notion of an ordinary mathematical proof –​which is rigorous and convincing, but not formalized. In mathematical practice, the understanding of mathematical concepts, the process of identifying relations between them and a specific “grasp” of their content is essential. Mathematics is a very sophisticated analysis of concepts, and proofs –​loosely speaking  –​express the results of this analysis; their role is to convey ideas in a

188 Wójtowicz comprehensible way. Consequently, giving proofs amounts to performing intellectual acts, and the key to understanding the nature of a mathematical proof is to explain the semantics of the notions of mathematical discourse. To make a proof acceptable is rather to make it rigorous and convincing –​not to present its formalized version. In particular, mathematicians distinguish between proofs which explain, and proofs which only show that a certain fact is true, in a way “forcing” us to accept it, leaving a feeling of cognitive insufficiency.11 It is not uncommon that a new proof of an already known theorem reveals some new phenomena, and allows us to understand new relations –​ so obviously, the role of the proof is not only to justify the claim, but also to elucidate the problem.12 On the other hand, however, an important feature of mathematical proofs is their formalizability. Proofs known from everyday mathematical practice are formulated in the “natural mathematical language,” being a mixture of natural and symbolic languages –​however, we are convinced that mathematical proofs can be formalized.13 The mathematical proof in its idealized version is simply a string of symbols, constructed according to certain formal rules. We therefore have two possible visions of the mathematical proof which can be the starting point for further analysis: (1) A mathematical proof is an intellectual activity which is not constrained by purely formal conditions. The formal (or even linguistic) layer itself is less important. The essence of proofs is to convey content, ideas, 11

12 13

“Even when a proof has been mastered, there may be a feeling of dissatisfaction with it, though it may be strictly logical and convincing: such as, for example, the proof of a proposition in Euclid. The reader may feel that something is missing. The argument may have been presented in such a way as to throw no light on the why and wherefore of the procedure or on the origin of the proof or why is succeeds” (Mordell 1959, 11) (quotation from Mancosu 2008, 142). I think that a particular good class of examples is given by computer-​assisted proofs (the four-​color theorem is the classic and most widely discussed case). It is even claimed, that “Mathematicians are on the lookout for an argument that will make all computer programs obsolete, an argument that will uncover the still hidden reasons for the truth of the conjecture”(Rota 1997, 186). For a discussion on computer-​assisted proofs, and also on hypothetical quantum-​computer assisted proofs, see (Wójtowicz 2018). (Wójtowicz: forthcoming) contains an analysis in the context of relativistic computation). In 1950, the Fields medal was awarded to Selberg for giving an elementary proof of the Prime Number Theorem. This illustrates the general phenomenon: providing an elementary proof of an already proven theorem can be an important result. We can use zfc, or (for parts of mathematics) much weaker systems, e.g. different versions of arithmetic, or we can give a direct formalization of the theory we are interested in. These details are not important here –​the very fact of formalization is important for our discussion.

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intuitions –​and not its formalization. A proof is a sequence of intellectual acts rather than formal transformations. From this point of view, a proof is an operation on concepts, and semantic aspects have a non-​ reducible character.14 So, finally, the real mathematical proofs are the informal ones. Their formal versions are artifacts of a formal system which is merely a tool for imitating mathematics.15 (2) A mathematical proof is a formal construct whose semantic aspects are insignificant –​only compliance with formal rules counts. The informal proofs are only a kind of abbreviations (indicators) for the formal proofs.16 The fact that mathematicians associate certain ideas with these proofs (and are perfectly happy with them) is a psychological phenomenon. It might be very interesting, but it has no impact on the philosophical discussion concerning the genuine status of proofs. We accept informal proofs only because we know that they can be (in principle) formalized, i.e. their real nature can be revealed. The second point of view seems to be rather extreme. The mathematical proofs we encounter in practice are rigorous, but not formalized. No mathematician (working in  –​say  –​probability theory or functional analysis) ever bothers about translating the proof into the formal language of zfc –​this would not

14

15

16

In recent years, more and more works have been published which address the problem of mathematical proofs from this point of view (and not from the point of view of the formal theory of proof), cf. e.g. (Panza 2003), (Bassler 2006), (Rav 1999), (Rav 2007), (Dawson 2006), (Fallis 2003). One of the precursors of this way of thinking is Lakatos and his classical Proofs and Refutations (Lakatos 1976). For a recent discussion see, e.g. (Kahle 2018), (Hamami 2018) and the references within. Barwise(1989) makes the following claim: “The idea that reasoning could somehow be reduced to syntactic form in a formal, artificially constructed language is a relatively recent idea in the history of mathematics. It arose from Hilbert’s formalist program. There were proofs for thousands of years before logicians came along with the mathematizations of the notion. […] I think it is clear that current formal models of proof are severely impoverished since there are many perfectly good proofs that are not modeled in any current deductive system. […]. Moreover, identifying proofs with formal proofs leads to what may be an even more serious mistake […]. While writing things out in complete logical notations can sometimes result in added clarity, all too often it merely obscures things, which is why practicing mathematicians almost never use such a language. And, it is not uncommon for an error to enter the picture in the translation from the English description to the formal specification” (quoted after: (Rav 2007)). Azzouni (2004) argues that what makes a real proof convincing is the formal derivation behind it, formulated in a particular algorithmic system. So what mathematicians really do is find some abbreviations of these proofs. From Azzouni’s “derivation indicator” point of view, the formal derivations are the truth makers. Our proofs are simply some indicators of them. For critical discussion see, e.g. (Rav 2007), (Tanswell 2015).

190 Wójtowicz give any new insights, any epistemological gain. Mathematicians are perfectly happy with the standard proofs, and are not interested in analyzing their ­formal counterparts.17 On the other hand, it is commonly believed that mathematical proofs can be formalized –​at least in principle. There must be a link between the (informal) proofs we know from seminars and textbooks, and the formal strings of symbols in (say) zfc. The problem of the relationship between the formal and informal elements of mathematical proofs, the “Hilbert bridge” between the informal proof and its formal counterpart, deserves our attention –​especially in the context of ontological analysis.18 6

Real/​Ideal Proofs and Mathematical Explanation

From the point of view of the mathematical realist, arguing along the lines of the indispensability argument, the identification of the necessary background assumptions is fundamental. These assumptions do not have an instrumental, purely formal character, but possess an ontological weight. The identification of the logical strength of (set-​existence) axioms necessary to prove theorems of ordinary mathematics is the subject of reverse mathematics. Ordinary mathematical notions are represented in the language of second-​order arithmetic, and then the strength of the set-​existence axioms necessary to prove a given theorem of ordinary mathematics is identified (so that a natural hierarchy of subsystems of Z2 emerges). Many important results concerning theorems from differential equations, algebra, complex analysis, combinatorics etc. have been obtained.19 Reverse Mathematics provides interesting insights because it allows us to identify the strength of assumptions

17 18 19

This remark does not apply to proof theorists –​but they are not interested prima facie in, say, probability theory, but rather in the formal counterparts of proofs within probability theory. For a discussion of the notion of “Hilbert’s bridge” see (Rav 1999); a presentation of “Hilbert’s thesis” is given in (Kahle 2019). The language L2 of second-​order arithmetic contains two sorts of variables: for numbers and for sets of natural numbers. The indented model for Z2 is (N, P(N)) (in the same sense, as N is the intended model for PA). Mathematical notions are “encoded” in L2; this allows for the translation of ordinary theorems into the language of L2 and investigation of their metatheoretical status, in particular the strength of the necessary assumptions. These are usually (not always) identified by the scope of the set existence axioms –​i.e. axioms stating that for a certain formula ϕ(x), the set of objects with property ϕ exists (cf. (Simpson 2009) for details).

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necessary to prove theorems. And in terms of ontological commitments –​it provides a tool for identifying them.20 But the proof of the theorem performed in (one of the subsystems of) Z2 ­differs significantly from the original proof. In order to reconstruct it, mathematical concepts (such as real numbers, continuous function, derivative –​and others) must be “translated” into the language of second-​order arithmetic, which from the point of view of everyday mathematics is a very artificial procedure. So it is very likely that the proof of a theorem within (a subsystem of) Z2 differs strongly in terms of explanatory virtues from the original proof. We might therefore encounter a situation of a theorem α (playing an explanatory role), such that: 1. There is a proof using weak assumptions (i.e. within a relatively weak subsystem S0 of Z2), but the proof is not explanatory. 2. There is a good explanatory “ordinary” proof using stronger assumptions S 1. There seems to be a tension between the two ways of identifying the ontological commitments, i.e. via the original indispensability argument (when only the logically necessary assumptions have to be identified) and via the eia –​ when identifying the assumptions necessary for the explanatory proof is crucial. Obviously, in the latter case they might be stronger –​not any proof of the theorem τ will do, we allow only proofs which are explanatory. This seems to be a drawback of the eia in comparison to Quine’s original version. In the original version, we have to identify the logically necessary resources. Using eia we rather have to identify the epistemologically necessary resources. Thus, if the explanatory value of the proof is taken into account (so the proof is not only a means of justifying the claim, but also of explaining its meaning), it may turn out that the ontological commitments identified by reverse mathematics are different from those accepted by virtue of the eia. 7

Summary

The indispensability argument in its original form is intimately connected with the issue of identifying the assumptions which are necessary to prove the 20

This is the general scheme: assume we need some mathematical tools T in our scientific theory –​and are curious about the ontological commitments of T. Let us reconstruct T within L2 (i.e. the notions of T are expressed in the language of L2, just like the notion of natural numbers can be expressed in zfc). This allows us to identify the weakest subsystem S of Z2, where the theorems of T can be proven. And we can consider S to identify the ontological commitments.

192 Wójtowicz needed theorem (or –​more generally –​to build up the mathematical “toolkit” for a physical theory). A precise identification can only take place once a “logically pure” version of the proof (and in particular the theory we use) has been presented. So, in order to identify the ontological commitments, we need to work with a formalized version of the proofs (and –​in general –​of the theory). A good example is the identification of the necessary assumptions (needed for standard mathematical theorems) in subsystems of second-​order arithmetic, which is the subject of Reverse Mathematics. From the point of view of eia, what is really important is the explanatory value of the mathematical theory in question, in particular –​the explanatory value of theorems we put into use in physics. Here we encounter the problem of whether it is only the very theorem, which counts as explanation, or whether its proof also has an explanatory contribution. The second solution is much more consistent with mathematical practice. Consequently, explanatory proofs are important for the ontological discussion. And here a tension arises between real, everyday proofs and their formalized versions (counterparts). Translating a proof into a formal language will (probably) deprive it of its explanatory value, as the proof becomes a purely formal construct, distant from mathematical practice. Many formal proofs from applied mathematics can be reconstructed within Z2, and they allow for a precise identification of ontological commitments, but they cannot be used in the premise of the eia, as these proofs do not have explanatory value in the ordinary sense. On the other hand, explanatory proofs might need more resources and assumptions. For instance, Reverse Mathematics identifies the weakest possible axioms  –​not the weakest axioms needed for reconstructing an explanatory proof. So, according to eia, we put some conditions on the proof of a theorem before we can give it a realistic interpretation. But in this case, the ontological commitments of mathematics might turn out to exceed those of the case of the original indispensability argument (where only the logical analysis counts).

References

Azzouni, J. 2004. The Derivation-​Indicator View of Mathematical Practice. Philosophia Mathematica 3 (12): 81–​105. Baker, A. 2005. Are there Genuine Mathematical Explanations of Physical Phenomena? Mind 114 (454): 223–​238. Baker, A. 2009. Mathematical Explanation in Science. British Journal for the Philosophy of Science 60 (3): 611–​633.

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Baker, A., and M. Colyvan. 2011. Indexing and Mathematical Explanation. Philosophia Mathematica 19: 232–​224. Baron, S. 2014. Optimization and Mathematical Explanation:  Doing the Levy Walk. Synthese 191: 459–​479. Barwise, J. 1989. Mathematical Proofs of Computer System Correctness. Notices of the American Mathematical Society 36: 844–​851. Bassler, O.B. 2006. The Surveyability of Mathematical Proof: a Historical Perspective. Synthese 148:99–​133. Daly, C., and S. Langford. 2009. Mathematical Explanation and Indispensability Arguments. The Philosophical Quarterly 59: 641–​658. Dawson, J.W., Jr. 2006. Why do Mathematicians Re-​prove Theorems. Philosophia Mathematica iii (14): 269–​286. Fallis, D. 2003. Intentional Gaps in Mathematical Proofs. Synthese 134: 45–​69. Field, H. 1980. Science Without Numbers. Oxford: Basil Blackwell. Hales, T.C. 2000. Cannonballs and Honeycombs. Notices of the American Mathematical Society 47(4): 440–​449. Hales, T.C. 2001. The Honeycomb Conjecture. Discrete and Computational Geometry 25: 1–​22. Hamami, Y. 2018. Mathematical Inference and Logical Inference. The Review of Symbolic Logic 11 (4): 665–​704. Kahle, R. 2019. Is There a ‘Hilbert’s Thesis’? Studia Logica. Special Issue: General Proof Theory. Edited by T. Piecha and P. Schroeder-​Heister 107, Issue 1, February 2019, 145–165. P.doi.org/​10.1007/​s11225-​017-​9776-​2 c. Kostić, D. 2018. Mechanistic and Topological Explanations: An Introduction. Synthese 195: 1–​10. Lakatos, I. 1976. Proofs and Refutations. Cambridge (UK): Cambridge University Press. Lange, M. 2013. What Makes a Scientific Explanation Distinctively Mathematical? British Journal for the Philosophy of Science 64(3): 485–​511. Liggins, D. 2014. Abstract Expressionism and the Communication Problem. British Journal of the Philosophy of Science 65: 599–​620. Mancosu, P. 2001. Mathematical Explanation: Problems and Prospects. Topoi 20: 97–​117. Mancosu, P. 2008. Explanation in Mathematics. Stanford Encyclopedia of Philosophy, http://​plato.stanford.edu/​entries/​mathematics-​explanation/​. Mancosu, P. 2018. Explanation in Mathematics. The Stanford Encyclopedia of Philosophy. Summer 2018 ed. Edited by E. N. Zalta. https://​plato.stanford.edu/​archives/​ sum2018/​entries/​mathematics-​explanation/​. Mordell, L. 1959. Reflections of a Mathematician. Montreal:  Canadian Mathematical Congress. Panza, M. 2003. Mathematical Proofs. Synthese 134, 119–​158.

194 Wójtowicz Pincock, C. 2015. Abstract Explanations in Science. British Journal for the Philosophy of Science 66: 857–​882. Quine, W.v.O. 1951. Two Dogmas of Empiricism. In: W.v.O. Quine. 1951. From a Logical Point of View. Cambridge: Harvard University Press, 20–​46. Quine, W.v.O. 1969. Existence and Quantification. In: W.v.O. Quine. “Ontological Relativity” and Other Essays. New York: Columbia University Press, 91–​113. Quine, W.v.O. 1981. Things and Their Place in Theories. In: W.v.O. Quine. Theories and Things. Cambridge: The Belknap Press of Harvard University Press, 1–​23. Rav, Y. 1999. Why Do We Prove Theorems? Philosophia Mathematica 7:5–​41. Rav, Y. 2007. A Critique of a Formalist-​Mechanist Version of the Justification of Arguments in Mathematicians’ Proof Practices. Philosophia Mathematica (iii) 15: 291–​320. Räz, T. 2013. On an Application of the Honeycomb Conjecture to the Bee’s Honeycomb. Philosophia Mathematica 10 (5): 322–​333. Räz, T. 2017. The Silent Hexagon: Explaining Comb Structures. Synthese 194: 1703–​1724. Resnik, M.D. 2005. Quine and the Web of Belief. In: The Oxford Handbook of Philosophy of Mathematics and Logic. Edited by S. Shapiro. Oxford:  Oxford University Press, 412–​436. Reutlinger, A., and H. Andersen. 2016. Abstract versus Causal Explanations? International Studies in the Philosophy of Science 30 (2): 129–​146. Rota, G.-​C. 1997. The Phenomenology of Mathematical Proof. Synthese 111: 183–​196. Simpson, S. 2009. Subsystems of Second Order Arithmetic. Cambridge: Cambridge University Press. Tanswell, F. 2015. A Problem with the Dependence of Informal Proofs on Formal Proofs. Philosophia Mathematica 23 (3): 295–​310. Wójtowicz, K. 2019. Theory of Quantum Computation and Philosophy of Mathematics. Part II. Logic and Logical Philosophy, 29 (1), 173–193. Wójtowicz, K. The Significance of Relativistic Computation for Philosophy of Mathematics. Forthcoming (submitted). Hajnal Andreka and Istvan Nemeti on Unity of Science: from Computing to Relativity Theory through Algebraic Logic, Outstanding Contributions to Logic, Szekely G, Madarasz J. (eds.), Springer-Verlag Yablo, S. 2002. Abstract Objects: A Case Study. Philosophical Issues 12: 220–​240.

­c hapter 10

A Case of Metalogical Explanation of Logical Normativity Kordula Świętorzecka Abstract The presented paper contains a justification for the view that the concept of the normative nature of logic can be reduced to certain well-​known metalogic properties of inference relation. We consider a class of propositional logics identified with corresponding consequence operation used to define an inference relation. An inference pair which is valid or generally verifiable guarantees the reliability of a given reasoning, which is an interpretation of this pair. To phrase the description of such reasonings in normative terms, we can say that they respect the norms of a given logic, or that the logic is normative with respect to them. Our approach gives quite a simple and clear meta-scientific explanation of the concept, which sometimes is a subject of misleading philosophical associations.

Keywords applied logic –​general verifability of inferences –​logical normativity –​logical rules of inference –​ normativity –​ validity

The following remarks are inspired by a number of J. MacFarlane’s writings, most notably his Ph.D. dissertation, “What does it mean to say logic is formal?” (2000) and subsequent works (2002, 2004), as well as by such papers as Hanna (2006), Steinberger (2013, 2017), Tolley (2006), and Lu-​Adler (2017). More specifically, what prompted me to take up the following considerations is the arbitrariness and lack of clarity in the received interpretations of the views of Kant, Frege, and Carnap on the matter of the normativity of logic. In the writings mentioned above there is a general agreement that these three eminent thinkers spoke significantly on the subject. However, in a surprising and incomprehensible way the discussions of Kant’s, Frege’s and Carnap’s views fluctuate between contradictory interpretations.

196 Świętorzecka MacFarlane (2002), Hanna, and Lu-​Adler consider Kant to be a logical normativist. Tolley, instead, suggests a plausible interpretation of the concept of normativity according to which Kant is not a normativist at all.1 What’s interesting is that these analyses fail to address a fundamental question, namely that Kant considered logic –​the canon of human thinking –​as a finite set of Aristotle’s inference rules (which constitute the so-​called pure general logic and provide forms of Vernunft in a wider sense and Verstand) and rules from his transcendental analytics (the canon of pure Verstand).2 Such a concept of logic is neither a historical nor a systematic predecessor of modern logic. It is actually a combination of a tiny fragment of Aristotelian logic and a specific component of Kant’s philosophical system. In this context, the question of normativity belongs to the metaphilosophy/​history of Kantianism rather than to the philosophy/​history of logic.3 Philosophical investigations on Frege’s logical normativism encounter other difficulties. Frege was one of the few logicians writing about the similarities between logic and ethics (as opposed to psychology) explicitly. His concept of logic was the perfect prototype of the modern idea of a logical system. Frege distinguished between two different meanings of the term “law”: law in the descriptive sense and law in the normative sense. Additionally, he claimed that normativity is a feature of every descriptive law and explained this as follows: “[any] law asserting what is, can be conceived as prescribing that one ought to think [my emphasis] in conformity with it, and is thus, in that sense, a law of thought. This holds for laws of geometry and physics no less than for laws of logic” (Frege 1893, xv). If laws of logic are to have any special status (“a special title to the name »laws of thought«”), then it is only because “we mean to assert that they are the most general laws which prescribe universally the way in which one ought to think if one is to think at all” (12, xv). Here, Frege’s claims about the normativity of laws of logic are perhaps just a 1 MacFarlane and Lu-​Adler claim that the normativity of Kantian logic has a deontic nature. Hanna stresses its imperative character. Tolley (2006) argues against the normativistic interpretation of Kant’s logic by relying on the concept of a constitutive norm. 2 Cf. Kant (1998, 193–​203), (1992, 253–​255). 3 It is worth recalling here Bocheński’s view that: “[…] modern philosophers such as Spinoza, the British empiricists, Wolff, Kant, Hegel, etc. could have no interest for the historian of formal logic. When compared with the logicians of the 4th century B.C., from the 13th the 20th centuries A.D. they were simply ignorant of what pertains to logic and for the most part only knew what they found in the Port Royal Logic” (Bocheński 1961, 258). This view is perhaps too simplistic compared to the contemporary analyses (e.g. Tiles (2004), Kovač (2018)). However, certainly the term “logic” was used by Kant in an ambiguous way and this issue is not taken into account in the works considered.

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way of saying that the scope of their validity is wider than the scope of the laws of other disciplines.4 Steinberger, however, is looking for a more specific and prescriptive sense of Fregean normativity, which he characterizes in such a way that the laws of logic are to imply, and thus provide, general and constitutive norms of thinking as such (Steinberger 2017, 151). The interpretation of Carnap’s views given by Steinberger (2013; 2017) is less ambiguous, but it is in contradiction with Carnap (1987). The alleged Carnapian “relative logical normativism” is expressed by Steinberger in the following so-​ called relativized constitutivity thesis:  “There is […] a multiplicity of prima facie acceptable systems that are disjunctively constitutive [my emphasis]:  the very possibility of properly truth-​evaluable claims presupposes that we should fix on exactly one such system.” (Steinberger 2017, 160). Steinberger goes on to claim that: “[…] Carnap’s relativized constitutive norms [my emphasis] set to the shared logico-​linguistic standards of correctness that make productive scientific theory possible in the first place” (160–​161). Carnap, however, outlined a clearly antinormativistic approach to logic in the ­following remarks: I wish to emphasize that not only pure syntax and pure semantics but also descriptive syntax and descriptive semantics, as I understand them and intend to construct them, do not contain any kind of PRESCRIPTIVE COMPONENTS [my emphasis]. It is certainly true that, when a mother teaches her child to speak, or when a reviewer criticizes the style of the book, norms of the use of language are applied either explicitly or implicitly, and therefore the metastatements occurring in these contexts often contain prescriptive components. But in syntax and semantics I deliberately leave aside all prescriptive factors. Descriptive syntax and semantics deal with certain features of languages investigated empirically. Even there, the statements about these features are descriptive. […] I use the word “rule” in this field only in order to conform to the customary usage of logic. The so-​called rules are meant only as partial conditions of a definition; e.g., as I have often said, the rules of formation for a language L together form the definition of “sentence in L,” and all the rules of L form the definition of “L.” It seems to me that in the development of modern logic it has become ever more evident that logic and likewise syntactical and semantical analyses of language are purely theoretical; the use of terms like “rules,” “permitted operations,” and “prohibited operations” is 4 This sense of generality is considered by MacFarlane (2002).

198 Świętorzecka here, just as in algebra, merely a psychologically useful way of speaking which should not be understood literally. carnap 1987, 923–​924

These mutually contradictory or opposite, and misleading interpretations motivate a reader to put the following question: what in fact is the normativity of logic? It is precisely my case. In answer to my question I present (certainly one of many) possible elucidations. What should be explicitly stressed is that my proposal is based on the following conviction: if philosophical creativity is to concern matters in the close vicinity of scientific considerations, then it should take into account as much as possible the subjects and the methods of the latter. Our approach is systematic, and so we do not have historical intentions, in particular intentions to give any reinterpretation of texts of Kant, Frege, and Carnap. We form a certain extensional way of understanding the concept of normativity, based on a theory of deductive systems, which is currently used to give a meta-​scientific description of logic. We assume at the outset that the normativity considered here concerns logic when logic is applied to somehow distinguished non-​logical reasonings. This means that we restrict the concept of normativity to a certain specific context. Moreover, we consider only a class of logics that can be normative for certain types of non-​logical reasonings expressed in a language morphologically similar to the language of these logics. The latter restriction is introduced in section (1) and it allows a fairly simple description of the concepts articulated in section (2). However, our view can also be extended to logics that are much more complex and richer than those we take into consideration in (1). 1

Useful Notions from the Contemporary Methodology of Deductive Systems

We consider a certain class of propositional logics that have an interpretation in the models of two logical values. A logic is understood as a set of formulas (propositional expressions) of a specific symbolic language, determined by an appropriately defined consequence operation. The logical consequence may be used to speak about the inference. The relation of inference is a set of pairs, in which the first element is a set of formulas and the second element is an individual formula. Inference pairs are considered to be formal representations of the thought processes that we are interested in:  simple

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reasonings. Simple reasonings are treated as interpretations of inference pairs in ­section (2). An inference pair (X, α), such that formula α belongs to the consequences of the set X of formulas, is a valid inference on the basis of a given logic. From a semantic point of view, the notion of consequence can be linked to the concepts of valuation and truth in a given model. For every valuation of the variables of the language of logic, the truth of any formula belonging to a semantically determined consequence of any set X of formulas is guaranteed by the truth of the formulas from set X. An inference pair which is valid on the ground of semantic consequence is also generally verifiable, that is, for every valuation, the truth of its first element is a sufficient condition for the truth of its second element. Our brief outline of these concepts follows their account in Wójcicki (1984). We consider a class of logics expressed in standard propositional language J, whose vocabulary includes propositional variables:  p, p’, p’’, …. (Var); logical constants: ¬ (negation), ∧ (conjunction), ∨ (disjunction), → (implication), and ↔ (equivalence); and parentheses. The set of formulas for is characterized in the usual way. We begin with the definition of the consequence operation: Definition 1. Assigning C: 2FOR → FOR is a consequence operation iff for any X, Y ⊆ FOR it fulfills the following conditions: (T1) X⊆C(X), (T2) C(C(X)) ⊆C(X), (T3) if X⊆Y, then C(X) ⊆C(Y). Let e(α) be any substitution of formula α. We take the following explanation of the notion of substitution: (i) function e assigns any formula to every propositional variable; (ii) if formula α contains a sequence of variables p1, p2, …., pn (expressions in this sequence may be repeated), then e assigns to it a formula which arises from α in such a way that we replace the subsequent variables in the sequence p1, p2, …., pn with any formula, and if any variable is repeated we replace it with the same formula. With e(X) we will mark set e containing all the substitutions of formulas belonging to X. Definition 2. C is a structural consequence operation when for any X⊆FOR: e(C(X)) ⊆C(e(X)). We now define the notion of logic as follows: Definition 3. C is a logic iff C is a structural consequence operation. It can be said that logical theses do not require any specific premises to justify them –​they are consequences of an empty set of premises: Definition 4. Formula α is a thesis of logic C iff α∈C(∅). Set C(∅) is a set of theses of logic C.

200 Świętorzecka In the set of formulas for we will consider inferences that are supposed to be formal representations of simple reasonings in focus. Inferences are ordered pairs belonging to the set 2For×For. Definition 5. X⊢α iff (X, α) ∈ 2For×For. (We express (∅, α) as: ⊢α.) Some inferences are valid on the basis of logic C: Definition 6. Inference X⊢α is valid on the basis of C iff α∈C(X). When X⊢α is valid on the ground of C, we will write: X ⊢C α. On the basis of the definitions introduced above, in any logic C, for any X,Y⊆FOR, α∈FOR we have: (1⊢) if α∈X, then X ⊢C α, (2⊢) if (X ⊢C α and X⊆Y), then Y ⊢C α, (3⊢) if (∀β (if β∈Y, then X ⊢C β) and Y ⊢C α), then X ⊢C α, (4⊢) if α∈e({β: X ⊢C β}), then e(X) ⊢C α. Sets containing valid inferences are called inference rules of logic C. Additionally, we take into account the notion of a well-​defined logic: Definition 7. Logic C is well-​defined iff for any α, β ∈ FOR: (i) C({α∧β}) = C({α, β}), (ii)α∈C({β}) iff (β → α) ∈C(∅). Well-​defined logics are unambiguously determined by the sets of their ­theses: (*) if C is a well-​defined logic, then C(∅) defines C. (Proof: cf. theorem 11.3, Wójcicki 1984, 61.) In our class of well-​defined logics there are, for instance, the classical propositional logic cls and the intuitionistic propositional logic. Not well-​defined logics are, for instance, Łukasiewicz’s three-​valued logic and the relevant logics E, R, and RM (cf. Wójcicki 1984, 60–​68, 72–​73). Being well-​defined is connected to the fact that when we have the set of theses C(∅), then every consequence related to the same set of theses is indiscriminable with reference to C. Meanwhile, when C is not well-​defined, then it is possible to have a situation, in which there is consequence operation C’, different from C, and such that C’(∅) = C(∅). We will now describe consequence operations and inference pairs in a specific semantic context. To this end we will take into account Boolean algebra, which has two logical values AB=({0,1}, −, ∧, ∨, →, ↔), and we will determine the valuation function v of propositional variables Var in {0,1}, extended on any α, β ∈ FOR in such a way that: v(¬α) = −v(α); v(α ∧ β) = v(α) ∧ v(β); v(α ∨ β) = v(α) ∨ v(β); v(α → β) = v(α) → v(β); v(α ↔ β) = v(α) ↔ v(β). We use V to name the set of all possible valuations of the formulas of ­language J.

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Next, we say that: Definition 8. CV is a consequence operation that keeps its truth iff: (i) CV is a consequence operation and (ii)∀α (α∈CV(X) iff ∀v∈V (if ∀β∈Xv(β)=1, then v(α)=1). Definition 9. Logic C is complete in (AB,V) iff CV is a structural consequence operation that keeps its truth. In our semantics (AB,V) there is only one logic that is complete: classical propositional logic. The other logical consequence operations fulfill the right-​ hand side implication of condition (ii) from Def 8, but not the inverse. There are semantics in which intuitionistic logic, Łukasiewicz’s systems, and relevance systems are complete. Some inference pairs (X, α) are such that the truth of the formulas belonging to X implicates the truth of formula α. If that happens for every valuation, we say that a given inference pair is generally verifiable: Definition 10. Inference X⊢α is generally verifiable by V iff ∀v∈V (if ∀β∈Xv(β)=1, then v(α)=1). In light of the above definitions, we can also say that: (**) ∀α (X⊢CLS α iff X⊢α is generally verifiable by V). 2

The Connection between Normativity and Validity and the General Verifiability of Inferences

Let us now consider a specific propositional language of non-​logical constants, morphologically similar to J. Its vocabulary includes propositions: c, c’, c’’, … (Cs); connectors:  it is not the case that, and, or, if then, if and only if, that have the same signatures as accordingly: ¬, ∧, ∨, →, ↔; and we also use parentheses. (We do not have to decide whether Cs is a finite or infinite set). We will label such a language JCs. The set Sent of propositions of language JC is defined with the use of the same analogue inductive conditions as the set for. We take: S ⊆ Sent and s∈ Sent. Pairs (S, s) ∈ 2Sent×Sent are called simple reasonings. When the epistemic subject wants to confront any reasoning (S, s) with any logic, he formalizes (S, s). This procedure we can describe using a function f: Sent → For, such that: (i) ∀c, c’∈ Cs (if (f(c) ∈ V and f(c)=f(c’)), then c=c’), (ii) ∀s, s’∈ Sent: f(it is not the case, that s)= ¬f(s); f(s and s’)=f(s)∧f(s’); f(s or s’)= f(s)∨f(s’); f(if s, then s’)= f(s)→f(s’); f(s if and only if s’)= f(s)↔f(s’).

202 Świętorzecka We also use the notation f(S) for the set of f formalizations of all propositions from S⊆Sent. Function f retains the logical structure of the propositions from language JCs and its converse is called here the interpretation. We can now proceed to explain the normativity of logic. In the case of any interpretation of a valid inference pair, we say that its conclusion is a logical consequence of the assumed premises. On the semantical level, the interpretations of valid inferences are reasonings in which the truth of the conclusion is guaranteed by the truth of the premises. To phrase the description of such reasonings in normative terms, we can say that they respect norms of a given logic, or that the logic is normative with respect to them. Using this terminology, we can say that: (N1) for any logic C and language JCs: C is normative for (S, s) iff there exists an f: f (S) ⊢C  f (s). When C is a complete logic in a given semantics, the question of the normativity of any reasoning is reduced to the problem of the existence of a formalization that translates a reasoning into a generally verifiable inference. In connection to (**) and N1 above, we have: (N2) cls is normative for (S, s) iff there exists an f: f (S) ⊢f (s) and it is generally verifiable by V. For the other logics we have an implicational relation: (N3) if C≠CLS, then (if C is normative for (S, s), then there exists an f: f (S) ⊢C f (s) and it is generally verifiable by V). Our modest and simple approach reduces the concept of normativity to the validity or general verifiability of formalized reasonings. It should be stressed here that our account makes several initial pragmatic assumptions and demands further pragmatic additions. The first point would require a separate discussion. In brief, formalized language JCs is a far-​fetched idealization of many languages, which users can analyze by means of logic. The languages of traditional philosophical discourse and academic discourses fail to possess a formally determined structure. Reformulating such a language according to a syntactic and semantic categorization is a complex action that can also be considered normative in nature. Our approach does not address this problem and only deals with normativity in a narrow sense, that is, as referring to simple reasonings expressed in a specially designed language. The second point is about limiting the domain of formalized reasonings to comprise only reasonings that can be employed by users of language JCs. We must note here the possibility of restricting the number of reasonings to those that have a finite number of premises. If it is true that reasonings involve

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non-​logical applications of logic by the epistemic subject, who performs each time an act of accepting the subsequent premises, then such a restriction seems justified. Formally, it would be necessary to limit N1 to the class of logics to those that are compact. cls is compact. A further pragmatic limitation of the domain of reasonings could involve the elimination of the reasonings whose premises and conclusions are unrelated with respect to their content. At least some such reasonings would be excluded if we assume that we take any relevant or paraconsistent logic as a normative logic. We examine below some cases of reasonings for which cls is normative, but the relevant logics E, R, and RM, as well as Jaśkowski’s and da Costa’s logics considered in Wójcicki (1984, 9.4–​9.5) are not normative. Let us consider language JCs’ which contains only two propositional constants from Duns Scotus’s well-​known example:  Socrates is running and You are in Rome. Let us now consider the following reasonings: (P1) Socrates is running. So (if You are in Rome, then Socrates is running).5 (P2) Socrates is running and it is not the case that (Socrates is running), so You are in Rome. (P3) You are in Rome. So (Socrates is running or it is not the case that (Socrates is running)). (P4) If You are in Rome, then You are in Rome. So if Socrates is running, then Socrates is running. We note here that for any pi, pj ∈ Var: pj ⊢CLS pi→pj; pi∧¬pi ⊢CLS pj; pj ⊢CLS pi∨¬pi; (pi→pi) ⊢CLS pj→pj. These inferences are also generally verifiable. As a result of N1/​N2, we can say that classical propositional logic cls is normative for reasonings (P1)  –​ (P4). However, logics E, R, and RM are not normative for reasonings (P1)-​(P3) because their formalization, based on such logics, does not result in valid inferences (cf. N3). This is also the case with (P2) and (P3), assuming Jaśkowski’s or da Costa’s paraconsistent logics. For any different pi, pj ∈ Var: (pj, pi→pj) is not a valid inference in logics E, R, or RM (pj→(pi→pj) is not a thesis of these logics, although it is a thesis of stronger relevant logics TB and H). On the ground of no relevant logic or paraconsistent logic, inferences (pi∧¬pi, pj) and respectively (pj, pi ∨ ¬pi) are valid. Finally, it is worth noting that reasoning (P4) escapes the limitations resulting from a strong or weak rule of relevance that are supposed to model the pragmatic relationships between the content 5 Since we have a singleton in every example, to simplify the notation we omit the symbol of a set.

204 Świętorzecka of the two sides of the inferences. Logics E, R, and RM fulfill the strong rule of relevance: none of them contain an implicational function whose antecedent and consequent do not have common variables.6 We thus know that for any different pi, pj∈ Var: (pi→pi)→(pj→pj) is not their thesis. However, inferences (pi→pi, pj→pj) are valid on their grounds because p→p is one of their axioms. This is due to the fact that these logics are not well-​defined (cf. Def 7 and (*)): in our case above, the right-​hand side of the conditional implication (ii) from Def 7 is not fulfilled. Although our proposal probably faces further pragmatic problems, it also has obvious benefits. Our account shows that the normativity of logic can be given a meta-​scientific explanation, rather than just being the subject of unspecified philosophical associations.

Acknowledgments

I express my thanks to Professor J. Czermak and Professor S. Kovač for helpful and critical comments that contributed to improving the quality of the text. Any imperfections come only from the author himself.

References

Bocheński, J. M. 1961. A History of Formal Logic. Translated by I. Thomas. Notre Dame (IN): University of Notre Dame Press. Carnap, R. 1935. Philosophy and Logical Syntax. London: Kegan Paul, Trench, Trubner & Co. Ltd. Carnap, R. 1987. Wilfrid Sellars on Abstract Entities in Semantics. In: The Philosophy of Rudolf Carnap. The Library of Living Philosophers. Vol. xi. Edited by A. Schlipp. Illinois: La Salle, 923–​927. MacFarlane, J. 2000. What Does It Mean to Say Logic Is Formal? https://​johnmacfarlane.net/​dissertation.pdf [Accessed 1st February 2019]. MacFarlane, J. 2002. Frege, Kant, and the Logic in Logicism. The Philosophical Review 111: 25–​66.

6 The weak rule of relevance is fulfilled by a given collection of formulas when, if it contains expression α→β, such that α and β do not have common variables, then both ¬α and β belong to that set.

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MacFarlane, J. 2004. In What Sense (If Any) Is Logic Normative for Thought? Unpublished draft, https://​johnmacfarlane.net/​normativity_​of_​logic.pdf [Accessed 1st February 2019]. Frege, G. 1893. Grundgesetze der Arithmetik. Begriffsschriftlich abgeleitet. Vol. I, Jena, Verlag von Hermann Pohle. https://​archive.org/​details/​bub_​gb_​LZ5tAAAAMAAJ/​ page/​n5 [Accessed 25th June 2019]. Frege, G. 1879–​1891/​1979. Logic. In: Frege 1979, 1–​8. Frege, G. 1897/​1979. Logic. In: Frege 1979, 126–​151. Frege, G. 1979. Posthumous writings. Edited by H. Hermes, F. Kambartel and F. Kaulbach. Oxford: Basil Blackwell. Hanna, R. 2006. Rationality and the Ethics of Logic. The Journal of Philosophy 103: 67–​100. Kant, I. 1992. Lectures on Logic. Translated by J. M. Young. The Cambridge Edition of the Works of Immanuel Kant. Cambridge: Cambridge University Press. Kant, I. 1998. Critique of Pure Reason. Translated by P. Guyer and A. Wood. The Cambridge Edition of the Works of Immanuel Kant. Cambridge: Cambridge University Press. Kovač, S. 2018. Concepts, Space-​and-​Time, Metaphysics (Kant and the dialogue of John 4). In: God, Time, Infinity. 2018. Edited by M. Szatkowski. Berlin, Boston: De Gruyter, 61–​86. https://​doi.org/​10.1515/​9783110594164-​005. Lu-​Adler, H.2017. Kant and the Normativity of Logic. European Journal of Philosophy 25(2): 207–​230. Steinberger, F. 2013. How Tolerant Can You Be? Carnap on the Normativity of Logic. Philosophy and Phenomenological Research 92(3): 645–​668. Steinberger, F. 2017. Frege and Carnap on the Normativity of Logic. Synthese 194(1): 143–​162. Tiles, M. 2004. Kant:  form General to Transcendental Logic. In:  The Rise of Modern Logic: from Leibniz to Frege. Handbook of the history of logic. Vol. 3. 2004. Edited by D. Gabbay and J. Woods. Elsvier: N. Holland, 85–​130. Tolley, C. 2006. Kant on the Nature of Logical Laws. Philosophical Topics 34: 371–​401. Wójcicki, R. 1984. Lectures on Propositional Calculi. Wrocław: Ossolineum, pan.

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Leśniewski’s Intuitive Formalism Sébastien Richard Abstract When Stanisław Leśniewski read in 1911 Jan Łukasiewicz’s book The Principle of Contradiction in Aristotle he discovered modern symbolic logic and the Russellian antinomy of the classes, that do not contain themselves. He started then to look for a solution to this antinomy and elaborated his formal theory of wholes and parts. However, if he adopted the new formal tools of logistics, he refused to proceed in his building of formal systems as a “pure formalist”. In particular, for Leśniewski, a formal system must not be interpreted after having been built. An intuitive interpretation must be given from the beginning, the formal system being only a means to communicate the “logical intuitions” of the author. That is the reason why Leśniewski’s unconventional position has been called an “intuitive formalism” by Kearns or an “intuitionistic formalism” by Tarski. In this paper, I try to make these expressions more precise and explain how exactly the relation between intuition and formal systems must be understood according to Leśniewski.

Keywords antinomy of classes –​intuitionistic/​intuitive formalism –​formal system –​Mereology –​ Stanisław Leśniewski

In his 1929 “Grundzüge eines neuen Systems der Grundlagen der Mathematik,” Stanisław Leśniewski made the following claim: I see no contradiction […] in saying that I advocate a rather radical “formalism” in the construction of my system even though I am an obdurate “intuitionist.” leśniewski 1929, 78; 1992, 487

At the beginning of his paper on the “Fundamental Concepts of the Methodology of the Deductive Sciences,” Alfred Tarski claimed to be a disciple of

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Leśniewski. In particular he said that he adhered to the “intuitionistic formalism” of his former teacher:1 […] no particular philosophical standpoint regarding the foundations of mathematics is presupposed in the present work. Only incidentally, therefore I may mention that my personal attitude towards this question agreed in principle with that which has found emphatic expression in the writings of S. Leśniewski and which I would call intuitionistic formalism. tarski 1983, 62

It thus seems clear that Leśniewski maintained a particular philosophical position that can be called “intuitionistic formalism.” However, neither Leśniewski nor Tarski ever fully explained how this expression was to be understood. They only gave hints about what it could mean. What is certain is that for Leśniewski, and thus for the young Tarski, intuition had a major role to play in the building of formal systems. The aim of this paper is to explain what the Leśniewskian intuitionistic formalism was and how the Polish logician applied it. In this paper I will first gather several quotes from Leśniewski’s writings in order to get a better grasp of his intuitionistic formalism. I will then show how he criticized several aspects of the logistic systems developed by Russell and Whitehead with respect to his formal intuitions. Then I will highlight the role played by intuitionistic formalism in the building of Leśniewski’s own formal systems: Protothetic, Ontology and ­Mereology. 1

Leśniewski’s Intuitionism

I claim that Leśniewski’s intuitionistic formalism contains two parts: a critical and a constructive. The first part concerns some formal systems built by other logicians. It amounts to criticizing these systems from the point of view of their content –​ what they mean –​a content that is not in agreement with certain fundamental intuitions. The second part of Leśniewski’s 1 In a footnote added to the English translation of his paper in 1956, Tarski says that it was his position when he first published his paper in 1930, but that it now no longer reflects his present attitude. What this change of attitude means exactly is not easy to understand, because Tarski did not explain further what he meant by Leśniewski’s intuitionistic formalism. Most of the time, Tarski is very cautious when he gives clues about his own philosophical position. These are seldom and often elliptic.

208 Richard intuitionism concerns the construction of his three formal systems that are explicitly built to capture certain intuitions. The first part of Leśniewskian intuitionism can be found mainly in the early work (1910–​1913) of the Polish logician, that is, before he began to try to develop his own formal systems. Leśniewski was then mainly influenced by Mill’s logic, Brentano and Marty’s descriptive psychology, and Husserl’s general grammar. He discovered the new symbolic logic developed by Frege and Russell only in 1911, when he read Jan Łukasiewicz’s book on the principle of contradiction in Aristotle. This reading was a “revelation” (rewelacja) for the young philosopher. However, he did not start immediately using logistic tools. In fact he was even sceptical about such a use, because he could not understand the “sense” (sens) of the logical axioms and theorems that could be found in the examples of symbolic logic that he had at his disposal. What worried him more precisely was that he could not determine exactly “about what” (o czym) they were or “what” (co) they were trying to state. In this respect Leśniewski’s scepticism about logistic systems was “semantical” (semantyczny). Indeed Tarski, who borrowed his conception of semantics from his teacher, said that: Semantics is a discipline which, speaking loosely, deals with certain relations between expressions of a language and the objects (or “states of affairs”) “referred to” by those expressions. tarski 1944, 345

Leśniewski’s intuitionistic formalism could, as suggested by Jan Woleński, also be said to be “semantical” in this sense, since it claims that formal systems should be built in agreement with intuition: an intuition about what the linguistic expressions are about. The critical side of Leśniewski’s intuitionistic formalism, which ended in 1918–​1919, “prepared psychologically” (Leśniewski 1931, 154; 1992, 365) the way for its constructive part. As said before, this part concerns Leśniewski’s own formal systems which were built in agreement with some fundamental intuitions. He adopted the symbolism as a “tool” to convey “thoughts” (myśli) (Leśniewski 1931, 155; 1992, 365–​366), a tool that is more efficient and less ambiguous than ordinary language. The formalism thus comes after the intuition in order “to encode and communicate” it in a more precise way. In attempting to translate the theses of my “general theory of sets” as scrupulously as possible from the colloquial language into my new “symbolic language”, I have nevertheless constructed the proofs of the theorems of

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that theory in an intuitive way without in any way basing those proofs upon some clearly codified system of “mathematical logic.” leśniewski 1931, 155; 1992, 366

Formalization in this respect cannot come before the intuition or replace it. It only comes after in order to clarify it. Leśniewski built his formal systems as usual by positing axioms and definitions. It is these that should express a certain intuitive content: The psychic “source” of my axioms are my intuitions, which simply means that I believe in the truth of my axioms, but I am unable to say why I believe [them], since I am not acquainted with the theory of causality. My axioms do not have a logical “source,” which simply means that these axioms do not have proofs within my system, just as, in general no axioms, in the nature of things, have proofs in that system for which they are axioms. leśniewski 1916, 6; 1992, 130–​131

Leśniewski’s intuitionistic formalism does not only concern the content of the axioms of the formal systems to be built, but also the rules that allow us to deduce theorems from the axioms. These deduction rules should be formulated as precisely as possible –​ and Leśniewski was certainly one of the most precise logicians that ever existed –​but they should also be intuitive in some kind of way. More precisely the deduction rules should reflect the way the logicians and mathematicians naturally think  –​they should not be purely artificial. Leśniewski thus anticipated the natural deduction rules formulated later by Jaśkowski and Gentzen (Vernant 1997, 33). As interesting as this point is, I will, however, not examine it here. It must be said that from the point of view of the construction of formal systems the name “intuitionistic formalism” used by Tarski to qualify the philosophical doctrine of his teacher is a kind of contradictio in adjecto, since it seems to refer at the same time to Brouwer’s intuitionism and to Hilbert’s formalism.2 As Detlefsen puts it, the formalist mathematician “is free to stipulate of a concept she’s introducing that it [has] exclusively the properties provided for by the axioms she uses to introduce it. There is no content belonging to a concept introduced in this way except that which is provided for by the introducing axioms” (Detlefsen 2007, 294). The content of the concepts is 2 In what follows I relied on (Patterson 2012).

210 Richard constituted by the axioms that introduce them and is therefore identified with the “role” they play in the theory. They do not need to have “an intuitive content to be significant.” In other words, the axioms and rules of inference can be “chosen arbitrarily” (Carnap 2001, xv) –​ their meaning will be determined by their relations with the other logical symbols. The logical and mathematical symbols are just marks without meaning that are manipulated according to formal rules. Leśniewski’s approach to formal languages runs precisely in the opposite direction: in constructing a language, we first have to assign an intuitive meaning to the logical and mathematical symbols and then must consider the axioms and rules of inference that are in agreement with this meaning. For Leśniewski we need to discover what is, rather than trying to invent something that is not (Peeters 2000, 221). Therefore a formalized language is “always interpreted” (Woleński 2001, 72): its constants must have a meaning from the start. Leśniewskian formalism can thus rightly be said to be semantical, as suggested before: a formal system must possess a model. But Leśniewskian formalism is then semantic in a very specific way, since this model comes before the construction of the system. In the contemporary conception of formal systems inherited partly from Hilbert, the interpretation of a formal system is given by a model only after the formal system has been built. In this respect the Leśniewskian way of building formal languages is more traditional than Hilbert’s and is the one predominant today among logicians. If Leśniewski’s intuitionistic formalism is not formal in the formalist sense, it is not intuitionistic either in the sense of Brouwer. Brouwer’s and Leśniewski’s intuitionism share some common features, such as a critical nominalist position toward abstract entities and also a greater importance given to the construction of systems rather than to their pure formalization. However, Leśniewski cannot be said to be an intuitionist in the restricted sense of this term. For instance he does not reject the principle of the excluded middle. The term “intuitionistic” serves first of all to highlight the fact that intuition must come first when we are building formal systems. Therefore Leśniewskian intuitionistic formalism could be better called an “intuitive formalism,” as suggested by Kearns (1967, 62) and Woleński (2001, 72), or an “intuistic formalism,” as suggested by Jordan (1967, 487). I will adopt the first terminology. What exactly is the nature of the Leśniewskian intuition that should prevail in the construction of formal systems? It must be said that Leśniewski himself did not say much about it. Kearns (1967, 62–​64) offers us here some guiding reflections. First, we could ask if it is a common sense intuition. According to Jordan, Leśniewski used to believe in “the absolute truth of some assumptions” (Jordan 1967, 385). If intuition can reach absolute truths, it cannot pertain to the domain of common sense, which only gives us access to

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relative truths. However it must be some kind of “knowledge” (Kearns 1967, 62). Could we then say, with Kotarbiński, that, since the formal system called Ontology is an enquiry about “the general principles of being [zasady bytu]” (Kotarbiński 1986, 206; 1966, 210–​211), Leśniewskian intuition is an intuition about being? This suggestion is partly misleading. Ontology (in the Leśniewskian sense) cannot be characterized as a theory of being. It is rather a logical theory:  a theory about the ways to speak about reality. Consequently, Leśniewskian intuition seems to be an intuition of “how language must be if it is to adequately and efficiently represent the world” (Kearns 1967, 63). In other words, this intuition is not simply an intuition about the language or about the world, taken separately, but an intuition about both, in order for the first to adequately represent the second. First, it is not only an intuition about what exists in the world, because that would mean that we would only be able to speak about what exists, and not about what does not exist. Yet Leśniewskian Ontology is able to speak about non-​existing objects –​contradictory or fictional ones –​since it possesses names that can be empty. This does not mean that we have an intuition about what does not exist, because for Leśniewski this is precisely what we cannot have any intuition about. He says in particular that the expression “nothing” neither denotes nor connotes anything. Every singular proposition, that is a proposition of the form “a is one (of the) b(s)”, are always false when “a” or “b” is empty. However this does mean that we can talk about the nothing. For instance, we can say that nothing is something or that something is not nothing. From a general point of view, in Ontology, we can speak about what is and what is not, but without having to be ontologically committed toward what does not exist because we have no intuition about non-​existents. Ontology being a logical system, it is not directly founded on an intuition about how the world is, but about how to speak about the way the world is. This is also the case for Protothetic, which is a logical system:  an extended propositional calculus on which Ontology is founded. However this does not mean that there is no system that is founded directly on the intuition about how the world is. Leśniewski indeed developed a third formal system: Mereology. This formal system is not logical, but “extralogical” (Luschei 1962, 28). Syntactically this means that this formal system does not introduce any new semantic category. There are no grammar rules specific to Mereology. The grammar of Protothetic and Ontology is enough to formulate Mereology, whose they constitute the logical basis. The aim of Mereology is to express as precisely and clearly as possible the Leśniewskian intuitions about reality. Because these intuitions are about reality, Mereology should be built in a way that does not force us to admit existing objects that are only freely created by

212 Richard logicians. Extralogical formal systems should only be about a reality not created by their authors: I tried to write my work so that it would not concern exclusively some kind of “free creations” of various more or less Dedekindian creative souls; it follows hence, that I  cared more about the fact that my theorems, while possessing as exact a form as possible should harmonize with the “common sense” of the representatives of the “esprit laïque” who are engaged in investigating a reality not “created by them”, than I did about the fact that whatever I was saying should be in accordance with the “intuitions” of the professional set-​theoreticians whose intuitions emerge from a centrifuge of mathematical minds equipped with an apparatus of “free creativity” demoralized by “unreal” speculative constructions. leśniewski 1916, 5–​6; 1992, 130

Extralogical systems should not tempt us to admit fictitious objects. Leśniewski claims in another place that he has no predilection for “»mathematical games« that consist in writing out according to one or another conventional rule various more or less picturesque formulae which need not be meaningful or even –​as some of the »mathematical gamers« might prefer –​which should necessarily be meaningless” (Leśniewski 1929, 78; 1992, 487). The propositions of a formal system must have a meaning and the way we derive them has to “harmonize” in the way their author considered “intuitively binding.” In the following section of this paper I will set out how Leśniewski applied his intuitive formalism in the two parts explained above: the critical and the constructive parts. The first one concerns mainly the formalism set out by Russell and Whitehead in Principia mathematica. I will examine more precisely two criticisms raised by Leśniewski against Russell and Whitehead’s logical system: one concerning the assertion-​sign, the other concerning the status of levels of language. The second part of the intuitionistic formalism concerns Leśniewski’s own formal systems that have to be built in agreement with certain intuitions. In order to do this, I will examine the axiomatic basis of the three formal systems built by Leśniewski himself: Protothetic, Ontology and Mereology. 2

The Analysis of the Assertion-​Sign

Leśniewski’s first criticism of Russell and Whitehead’s Principia mathematica is about the expressions that contain the “assertion-​sign” “  ”. He finds the way

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these authors use the assertion-​sign rather confusing, and even contradictory. The first passage from the Principia mathematica that Leśniewski quotes is the following: The sign “”, called the “assertion-​sign”, means that what follows is asserted. It is required for distinguishing a complete proposition, which we assert, from any subordinate propositions contained in it but not ­asserted. russell and whitehead 1997, 8

Russell and Whitehead’s intention here is obvious: it is not because we assert, e.g. “ p ⊃ q”, that we can assert “q” alone. In order to do that we first need to also assert “p”. It is then clear, claims Leśniewski, that what is asserted in “  p ” is what follows the symbol “”. However this first interpretation seems to contradict another passage: On all occasions where, in Principia mathematica, we have an asserted proposition of the form “  . fx ” or “  . fp ”, this is to be taken as meaning “ .( x ). fx” or “ .( p ). fp” russell and whitehead 1997, xiii

This passage says that in “  .p ” what is asserted is not what follows the symbol “  ”, but the whole expression “  .p ”. This interpretation seems to be sustained by the following passage which Leśniewski does not quote: In symbols, if p is a proposition, p by itself will stand for the unasserted proposition, while the asserted proposition will be designated by “  .p ”. russell and whitehead 1997, 92

This is indeed not particularly clear. Leśniewski quotes a third passage from Principia mathematica regarding the meaning of the assertion-​sign: [The assertion-​sign] may be read “it is true that”. russell and whitehead 1997, 92

In other words, the expression “  .p ” would mean “it is true that p ”. But Leśniewski stresses that just after this passage Russell and Whitehead add: “­although philosophically this is not exactly what it means”. They do not explain further why this is so and Leśniewski thus puts it aside. I will show in the

214 Richard next section that the expressions “it is true that p” and “ p” cannot mean the same for Leśniewski because they belong to different levels of language. Leśniewski finds Russell and Whitehead’s explanations of the meaning of the assertion-​sign rather confusing. Since he can find no help from these authors, he tries to clarify himself what is expressed by “  .p ”. He uses three questions to classify its different possible interpretations: (i) if “ p ” is a proposition, is the expression“  .p ” also a proposition? (ii) if “  .p ” makes sense, does it mean the same thing as “p”? (iii) what should be considered as an axiom or a theorem, the expression following the symbol “  ” or the whole expression with the symbol included? These questions suggest three different conceptions: (a) The expressions “  .p ” and “p” are both propositions, but they do not mean the same, since “  .p ” means “we assert that p”. The assertion-​sign is thus part of what is expressed. The consequence of this reading seems to be that both expressions “  .p ” and “p” can belong to a logical theory, but only an expression prefixed with the assertion-​sign can be an axiom or a theorem of the theory. However this is clearly a mistake for Leśniewski. The reason is that the axioms and theorems of Principia Mathematica would then be “deductive confessions” (judgment-​acts) of the authors of the theory. They would only state what the authors assert and would therefore be about the authors’ thought. There would be confusion between the psychological and the logical. The second interpretation amounts to claiming that: (b) The expression “p”, but not the expression “  .p ”, is a proposition.3 Furthermore the two expressions do not mean the same and only “p” could be an axiom or a theorem. Since only the expression in the range of the assertion-​sign is a proposition, only this expression can be an axiom or a theorem of the logical theory. In this second conception, says Leśniewski, the assertion-​sign is used to distinguish the expressions that are propositions from those that are not. He thinks that this is superfluous: in ordinary language, thanks to the context, we are perfectly able to make a distinction between the expressions that are propositions and those that are not, without any use of a special symbol. If Russell and Whitehead cannot do that, then their formal language is defective and should be corrected. Leśniewski’s own formal languages are not defective in this respect,

3 Leśniewski adds that if “  .p” is not a proposition, the expression “” is a proposition which means “that which follows, is asserted”.

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because the inscriptional context is sufficient to determine to which semantic category a given expression belongs or if it is ill-​formed.4 The third conception is the following: (c) The expressions “p” and “  .p ” are propositions that mean the same. According to this third conception, we can read the expressions “  .p ” and “p” in the same way. The only use of the symbol “  ” is to indicate which propositions are asserted. This means that only the expressions prefixed with this symbol can be considered axioms or theorems. In this reading the symbol “  ” is part of what is expressed, but does not mean “we assert that”, such that a proposition such as “  .p ” is no longer a deductive confession of the authors. Against this reading, Leśniewski claims that if the assertion-​sign is used by Russell and Whitehead to indicate which expressions are asserted, the two logicians are not coherent. Indeed we can find in Principia mathematica expressions such as “⊢: ( y ) : ( ∃x ) . f ( x, y ) ”, which are not asserted by the authors. Leśniewski finds this “quite obvious”, but does not say why. What he seems to mean is that the expression “ ( y ) : ( ∃x ) . f ( x, y ) ” is not asserted by Russell and Whitehead, but rather deduced as a conclusion from a deduction (Vernant 2000, 318). There would be two uses of the assertion-​sign: one to assert a proposition and the other to mark the conclusion of a deduction. In fact this is precisely what Russell and Whitehead do, even if they do not say it specifically and if they are not always coherent with this use. For instance, the proposition “ ( y ) : ( ∃x ) . f ( x, y ) ” is deduced from the assertion “  . ( ∃x ) . f ( x, y ) ”, and thus written “ : ( y ) : ( ∃x ) . f ( x, y ) ” (see Russell and Whitehead 1997, xxiv). Finding the use of the assertion-​sign confusing, Leśniewski thinks that it should be omitted. The reading of the formulas that can be found in Principia mathematica become “intelligible” (Leśniewski 1927, 181; 1992, 195) only if we omit the assertion-​sign.5 Consistently Leśniewski does not use the assertion-​sign in his own formal systems. We can however find in Protothetic the functor of assertion “A ( p )”: (1) (∀p )[A(p) ≡ p] In other words, “A ( p )” has the same truth-​value as “p”: “A ( p )” is true when “p” is true and false when “p” is false. In this sense “A” is a truth-​function and 4 On this see (Richard 2018). 5 If this symbol is still sometimes used by logicians, it now has a different meaning since it is used to indicate a logical deduction. For instance, “Γ  ∆ ” will mean that “∆” can be deduced from the supposition of “Γ”.

216 Richard not a judgment-​act. With it Leśniewski makes explicit the “affirmative function”, which is most of the time implicit in formal languages (Vernant 1997, 31). “A” can then be assimilated into the Fregean “grasping of a thought” that the author of the Grundlagen used to symbolize “p”, and distinguish it from the simple thought “p” and its assertion “  p ” (Vernant 1997, 31). This functor plays an opposite role to the propositional negation that Leśniewski defines in the following way:6 (2) (∀p)[~(p) ≡ (p ≡ (∀q)(q))] The role played by the negation is the second semantical doubt raised by Leśniewski about the formalism used by Russell and Whitehead in Principia mathematica. I will now set it out. 3

Negation

Leśniewski examines the meaning that the authors of Principia mathematica give to expressions such as “~ p” which contain the negation symbol “ ~ ”. He quotes the following passage: If p is any proposition, the proposition “not-​p”, or “ p is false” will be represented by “~ p ”. russell and whitehead 1997, 93

According to Russell and Whitehead, the proposition “~ p” can thus be read as meaning “not-​p” (it is not the case that p) or “p is false”. But Leśniewski thinks that these two readings are not equivalent. When we say “p is false”, the proposition “p” is used in suppositio materialis. This is the use of the word “Socrates” in the sentence “Socrates is a height syllables word”. This is obviously not the same use of this word as the one made in “Socrates is a philosopher”. When we say “Socrates is a height syllables word” we have a proposition about a linguistic expression, and not about Socrates. To use Quine’s distinction, the word “Socrates” is then mentioned, and not used. To disambiguate this kind of use, we should use the quotation marks. In other words we should write “»Socrates« is a height syllables word”. The same applies to “p is false”: it is 6 The proposition “(∀q )(q )” is always false and thus represents the contradiction in ­Protothetic.

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a proposition about the proposition “p” that should be written “» p « is false”. In this last proposition, “p” is not itself a proposition but the name of a proposition. Again, Leśniewski’s criticism focuses on what formal expressions are about. As obvious as this may appear today, let me explain the argument that Leśniewski puts forward to show that “not-​p” and “» p « is false” cannot have the same meaning. Simply put, if these two readings were accepted as equivalent, we would be able to generate several interpretations of the same proposition containing a negation. Using the similar confusion that “ p ∨ q” could be read, according to Russell and Whitehead, as meaning “ p is true or q is true”, Leśniewski shows that the proposition “ ~ q. ∨ . p ∨ � r ” could be interpreted in at least eight different ways, which seems ridiculous to him. This may seem harmless, but Leśniewski shows that when we replace “ p”, “q” and “r ” with concrete sentences we obtain inadmissible results. For instance, we should accept that “not-​(Paris is situated on the Seine) or (Warsaw is situated on the Seine or Warsaw is situated on the Vistula)” means the same as “not-​(Paris is situated on the Seine) is true or (Warsaw is situated on the Seine or Warsaw is situated on the Vistula) is true”. But these two sentences do not have the same status, because they are not about the same things. The first one belongs to geography and is about the cities of Paris and Warsaw, while the other one is about the propositions “not-​(Paris is situated on the Seine)” and “Warsaw is situated on the Seine or Warsaw is situated on the Vistula”, and does not belong to geography. Geography, says Leśniewski, “does not concern itself at all with the truth about” such propositions (1927, 179; 1992, 193). Since the propositions “~ q. ∨ .� p � ∨ r ” and “~ q is true or p ∨� r is true” are not about the same things, they do not have the same meaning. The same applies to “~ p” and “p is false”. Leśniewski says that after four years of reflection he finally discovered that propositions such as “~ p” belong only to the calculus of propositions and should only be read as meaning “not-​p”. These sentences should in no case be read as meaning “» p « is false”. Today we would say that such a reading does not belong to the same level of language. While the proposition “~ p” belongs to the object-​language, the proposition “» p « is false” belongs to the metalanguage. As is well-​known, in his famous paper on the semantic conception of truth, Tarski made fruitful use of this important distinction, which Leśniewski is the first to have introduced. 4

Formal Systems

When he read Łukasiewicz’s book on the principle of contradiction in Aristotle, Leśniewski discovered modern logistics and, in particular, the antinomy

218 Richard of classes. This problem haunted him for years and, dissatisfied with Russell’s solution in terms of a hierarchy of classes, he tried to find a more “intuitive” solution to it. This research led in 1916 to the first formal theory of parts and wholes: mereology. This theory was formal, but it was not yet symbolized. It is only in 1920, under the influence of Leon Chwistek, that Leśniewski gave up his ambition to “tame” (Leśniewski 1927, 154; 1992, 364) the colloquial language. This change of attitude “was not accompanied by any far-​reaching parallel event in the domain” of his “ »logical« views” (Leśniewski 1931, 155; 1992, 366). The aim of formal mereology (Mereology) was then to capture certain intuitions about reality. However the logical theories available at this time on which Mereology could be based did not satisfy Leśniewski. They were not suited to frame a language that would adequately speak about the world. He thus devised two other formal systems symbolically formulated and hierarchically organized: Protothetic and Ontology. As stressed before, these two systems are logical and “present only general linguistic forms” (Kearns 1967, 68). Mereology is an extralogical system whose relations “are relations which hold between objects in the world” (Kearns 1967, 68). I will now show how Leśniewski’s intuitive formalism played a role in the construction of these systems, and more particularly in their basic principles. 4.1 Protothetic Protothetic is a powerful calculus of propositions in which it is possible to quantify over propositional and functorial variables. It admits only one basic semantic category:  the category of propositions (S ). It allows the formation of any propositional functor:  S / S , S / SS , S / ( S / S ), and so on. There is one primitive functor in this system: the equivalence symbol “ ≡ ”. Here is a possible axiomatization of Protothetic with three axioms:7 (AxProto1) (∀pqr)[((p ≡ r) ≡ (q ≡ p)) ≡ (r ≡ q)] (AxProto2) (∀pqr)[(p ≡ (q ≡ r)) ≡ ((p ≡ q) ≡ r)] (AxProto3) (∀gp)[[(∀f)g(pp) ≡ ((∀r)(f(rr) ≡ g(pp)) ≡ (∀r)(f(rr) ≡ g((p ≡ (∀q)(q))p)))] ≡ (∀q)(g(pq))]

7 Sobociński showed in 1955 that Protothetic could be formalized with a single (quite complicated) axiom.

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The first axiom states a kind of transitivity property for the equivalence functor. The second axiom concerns the associativity of equivalence. The third axiom is quite complicated, but it is also the most interesting one from the point of view of Leśniewski’s intuitionism. Sobociński explains that it contains: (a) The principle of bivalence expressed by equivalence and variable functors for two arguments. (b) Some forms of the law of extensionality for propositions which, together with [AxProto1] and [AxProto2], enable us to obtain a complete propositional calculus (Sobociński 1960, 56–​57). From this axiomatic basis, a principle of bivalence for binary functors can indeed be deduced. The principle of the excluded-​middle can also be obtained.8 As we can see, the Leśniewskian conception of what a propositional calculus should be from an intuitive point of view is quite traditional (except the quantification on functors). The first main intuition in this respect is that in a propositional calculus that enables us to speak about the world, we should only have two truth-​values: the true and the false. The second main intuition is that in a propositional calculus the truth-​value of a complex proposition should be a function of the truth-​values of the propositions it is made of. 4.2 Ontology To understand the role played by intuition in Ontology, let me consider the structure of singular propositions, i.e. propositions of the form “S is P”. Leśniewski’s intuition about such propositions, that is, about the way a formal system should be built in order to speak about individual objects, is mainly Aristotelian. Kotarbiński stresses that Ontology is: […] closely connected with traditional Aristotelian formal logic, of which it is an extension and an improvement, while on the other hand it is a terminal point in the attempt to construct a calculus of names in the area of logistics. leśniewski 1931, 162; 1992, 373

Therefore Leśniewski does not follow Frege and Russell in their rejection of the traditional predicative analysis of singular propositions. More technically, in Ontology, singular propositions look like the following ­symbolically: (1) a � ε b,

8 For the formal deduction of these principles see (Miéville 1984, 174–​185).

220 Richard where“a” and “b” are expressions belonging to the semantic category of names. “ε ” is called the “epsilon of Ontology” and is, intuitively, a formal representation of the copula “is” from ordinary language (Łukasiewicz 1953, 77). More specifically, the copula should be in agreement with the Polish “jest” (see Słupecki 1955, 13). A singular proposition belongs to the category of propositions (S ). It is obtained by joining “ε” with two expressions of the same category, i.e. names ( N ).9 Therefore “ε” is a functor that forms propositions and takes two names for arguments: its semantic category is S / NN . Thus, contrary to the set-​theoretic membership “∈,” the epsilon of Ontology does not make any distinction between the categories of its arguments. What about the truth values (true or false) of singular propositions “ a �� ε b ” now? What is the intuitive sense of the symbol “ε”? It is the sole primitive functor of Ontology and its meaning is captured by the sole axiom of Ontology. This axiom was first formulated by Leśniewski in 1920, and then successively simplified. It states the three conditions that a singular proposition has to fulfil in order to be true: ( a �� ε b ) ≡    (OntAx) ( ∀ab )  ( ∃c )( c �� ε a ) ∧ ( ∀dc ) (( d �� ε a ) ∧ � (� c ε � a )) ⊃ (� d ε � c )      ∧ ( ∀d ) ( d �� ε a ) ⊃ ( d �� ε b )       The three conjuncts express the three following conditions: (a) existensssce condition: “ ( ∃c )( c �� ε a ) ,” which means that there is at least one object denoted by the name “ a ;” (b) unicity condition:  “( ∀dc ) ( (d ε a ) ∧ (c ε a ) ) ⊃ (d ε c)”, which means that there is at most one object denoted by the name “ a ,” (c) inclusion condition:  “ ( ∀d ) ( d ε a ) ⊃ ( d ε b )  ,” which means that every object denoted by the name “a” is denoted by the name “b.” Let me illustrate how this works with an example. I will say that the name “a” is “Saint Augustin” and the name “b” is “the author of De civitate Dei.” They are both individual names, since they each denote one object, i.e. the same one. The obtained singular proposition of the form “a �� ε b ” means that Saint Augustin is the author of De civitate Dei. This sentence is true because the two names “Saint Augustin” and “the author of De civitate Dei” denote the same object. If 9 These names can be individual, general or empty.

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I replace “the author of De civitate Dei” with “a father of the Church,” I obtain the singular proposition “Saint Augustin is a Father of the Church” (or “Saint Augustin is one of the Fathers of the Church”), in which the functor “ ε ” joins an individual name with a general one. The new proposition is true, because the object denoted by “Saint Augustin” is one of the objects denoted by “Father of the Church.” In summary a singular proposition of the form “ a �� ε b ” is true only if the object denoted by “a” is the same object as the object denoted by “b” or is one of the objects denoted by “b.” In all the other cases, such a proposition is false. This includes the cases where “a” or “b” are empty names and the cases where “a” is a general name. 4.3 Mereology As mentioned earlier, when Leśniewski discovered modern logistics he also discovered the Russellian antinomy of classes. He could not stand purely technical solutions to this problem, such as the ones developed by Russell and Zermelo. These only “avoid” the antinomy by formulating rules that restrict the usage of the term “class” (Vernant 2000, 345). The aim of set theory for authors such as Russell and Zermelo is to give a secure foundation to mathematics. For Leśniewski it must be more than that, because mathematics cannot be a purely “non-​contradictory deductive system.” Deductive theories “serve to capture various realities of the world in the most exact laws possible” (Leśniewski 1927, 166; 1992, 177). It is because they moved away from this “intuitive basis,” because they lack “any connection with reality,” that the technical solutions developed by Russell or Zermelo cannot satisfy Leśniewski. The disease of which the antinomies are a symptom comes precisely from this remoteness from intuition. Therefore Leśniewski tried to find a solution to the set-​theoretic antinomy that would be more in agreement with his ontological intuitions. According to him it is the intuitive nature of the classical concept of class that is more specifically problematic. The meaning of this concept is captured by the axioms of classical set theory. Therefore they must be replaced by axioms more in accordance with our most robust intuitions about reality. Leśniewski’s criticism of naïve set theory is based on a distinction between two senses of the notion of class: “distributive” and “collective.” Sobociński defines distributive classes in the following way: The expression “ class ( a ) ” is in the distributive sense only an apparent name that replaces the well-​known term of classical logic “the extension of the objects a.” If we take the term class in this sense, the formula

222 Richard “ A�� ε Kl ( a )” means the same thing as “A is one of the elements of the extension of the objects a,” i.e. more shortly: “A is a.” sobociński 1949, 240

Distributive classes are here identified with sets as used in naïve set theory. Leśniewski’s conviction is that there are no abstract objects and in particular no classes in this sense. We should only accept classes in the collective sense. For Leśniewski, the notion of distributive class gives rise to antinomies because it is incoherent from an intuitive point of view. He claims that it is so in at least three respects: (a) There are empty classes. (b) The acceptance of the principle that every object belonging to a class is subsumed under the corresponding concept that defines this class. (c) A class whose concept only subsumes one element is not identical with this unique element. The negation of each of these theses gives us three characteristics of collective classes. The fact that the notion of distributive class is incoherent for Leśniewski does not mean that there is no place for it in his formal systems. It can be said that Ontology is, in some way, a theory of distributive classes, since it allows a treatment of the distributive sense of the notion of class. In order to do so the expression “is an element of the class of” in the distributive sense can be reduced to the ontological functor “ε .” For instance, if the expression “class of” in the proposition “Socrates is an element of the class of mortal beings” is understood in the distributive sense, then this proposition means the same thing as “Socrates is mortal,” where the copula is understood in the sense of the functor “ε ” (Sobociński 1954, 240). If there is no distributive class in Leśniewski’s formal systems, at least there is a “distributive predication” (Kearns 1967, 84). In the collective sense, the expression “class of” cannot be logically reduced in the way the distributive sense can be: the term “collective class” is a real name; we cannot eliminate it by using any other conception of logic. In the collective sense, the expression “class ( a )” indicates an object existing really, made out of all the objects in the domain of objects a. In other words, if we have any domain of objects a, we can, with the help of the term “ class ( a )” taken in the collective sense, obtain an object only made out of objects belonging to the domain indicated by the objects a. sobociński 1954,241

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The concept of collective class is not logical. It is extra-​logical and cannot be treated in Ontology, or either in Protothetic, on which Ontology is logically based. The axioms that rule the “real functor” “collective class of” cannot be reduced to those of Leśniewski’s logical systems and are external to them. They belong to a specific formal system: Mereology. As suggested by the last quote, a collective class is a concrete whole, an aggregate made out of its elements, and not an abstraction with respect to these. The relation that an object has with a collective class must be understood as a part-​whole relation, and not as a membership relation. Consequently, if in the expression “the class of British dominions,” the expression “the class of” is taken in the collective sense, then “the class of British dominions” designates an object made out of the different British dominions as parts, as for instance Canada, Australia, but also the parts of these parts, such as Alberta or Edmonton (Sobociński 1954, 218). In the distributive sense, Canada and Australia are elements of the class of British dominions, but it is not the case of Alberta or Edmonton, because they do not satisfy the classificatory concept of this class. Collective classes understood as aggregates of their elements are not different from these. They possess three fundamental characteristics which oppose those of distributive classes (Leśniewski 1927, 186–​187; 1992, 202–​203): (a) If any object is the class of objects a, then some object is a. (b) It happens frequently that a certain object is the class of such and such objects and at the same time, a class of entirely different objects. (c) If one and only one object is P, then P is the class of objects P. The first thesis rejects the possibility of any empty class, qualified by Leśniewski as a “theoretical monstrosity”: Being of the opinion that, if an object is the class of some a (e.g., people, points, square circles), then it actually consists of a, I always rejected […] the existence of theoretical monstrosities like the class of square circles, understanding only too well that nothing can consist of something which does not even exist. There has never been a time in my life which I would not have been in complete agreement with the lapidary remark of Frege à propos the theory of classes of Ernest Schroeder: “If”…“a class consists of objects, is an aggregate, a collective unity of them, then it must vanish when the objects vanish. If we burn all the trees in a forest, we thereby burn the forest. Thus there can be no empty class.” leśniewski 1927, 196; 1992, 214–​215

What indeed could be a concrete whole made out of no part? The collective conception of classes directly contradicts the distributive conception.

224 Richard In this last conception, when there is no object falling under a certain concept this concept defines an empty class. For instance, this is the case of the contradictory concept “square-​circle.” In the collective sense, a class always contains at least one element, i.e. itself. Therefore there is no empty collective class. The second characteristic thesis of collective classes rejects the traditional principle of extensionality according to which two identical classes are determined by formally equivalent functions. Therefore, if an object is the collective class of as and also the collective class of bs, then the class of as and the class of bs are the same object, but it is not necessarily the case that the objects a are the same objects as the objects b. Leśniewski illustrates this point with the following line AB:

This line can be considered the class of segments AC and CB and, at the same time, as the class of segments � AD and DB. If this consequence of the second characteristic of collective classes may seem acceptable, there are other ones that are more surprising. Indeed, according to the Leśniewskian conception of classes, we can say that the trees are the elements of the class of trees, but it is also the case of all the elements of trees, i.e. their parts. Therefore the leaves and the roots are also elements of the class of trees. It must be stressed that the second characteristic goes against the extensionality principle only in its classical sense, that is, the one captured by the theory of distributive classes. From this last point of view, we can consider the segment AD the distributive class { AC , CB} or the distributive class { AD,� DB} , but these will not be identical. From the point of view of collective classes, which are concrete wholes, the two classes { AC ,� CB} and { AD,� DB} are identical since they are made out of the same parts AC, CD and DB, for instance. There is thus an extensionality principle for collective classes: Axiom iii. If p is the class of objects a , and Q is the class of objects a, then p is Q. leśniewski 1928, 265; 1992, 232

This extensionality principle contradicts the second characteristic of collective classes only if we interpret extensionality in the classical sense. This difference may be seen as a consequence of Leśniewski’s nominalism, which is a stronger thesis than the classical extensionality thesis, as Goodman stressed it:

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Extensionalism precludes the composition of more than one entity out of exactly the same entities by membership; nominalism goes further, precluding the composition of more than one entity out of the same entities by any chain of membership. goodman 1956, 19

This explanation of the Leśniewskian nominalistic extensionalism in terms of composition of the same atomic elements would be satisfying if Mereology were explicitly atomistic, but Leśniewski never took a stand on this topic. However it has since been shown that an extensionality principle for Mereology can be formulated. In its strong version it simply states that two objects are identical if they have all their parts in common (see Simons 1987, 112 ff.). The third characteristic thesis about collective classes identifies every unary collective class with its unique element. Once more, this thesis opposes the classical conception of sets according to which every singleton is not identical to its unique element: “{a} ≠ a”. This distinction between a singleton and its unique element is necessary in classical set theory, because these two objects do not belong to the same logical type. Similarly the distinction between the membership of an object to a set and the inclusion of a set in another set forces us to make a distinction between a set and its elements, even when there is only one such element. Frege tried to show that the assimilation of a unary class to its sole element would lead to a contradiction (Frege 1895, 201–​202). Here is Russell’s version of this argument: If x be a term, we cannot identify x, as the extensional view requires, with the class whose only member is x; for suppose x to be a class having more than one member, and let y, z be two different members of x; then if x is identical with the class whose only member is x, y, and z will both be members of this class, and will therefore be identical with x and with each other, contrary to the hypothesis. russell 2010, 520

There is in classical set theory a primacy of the intensional over the extensional, of the concept associated with a class over the members of this class. This is not the case in Leśniewski’s conception of collective classes. However, the Fregean argument does not hold against it. If every individual can be viewed as a collective class of itself, that does not mean that this class is only “composed of” this individual. Indeed, all parts of this individual are elements of the collective class that it forms, unless this individual is a mereological atom (an

226 Richard object that has no part distinct from itself). It is only in this last case that an individual can be considered a class of which it is the sole element. Therefore, the Fregean argument is blocked: in the atomic case, because an atom cannot have two different elements and, in the non-​atomic case, because an individual is a collective class that may have elements, i.e. parts, that are not identical to it. For instance, a tree is the collective class composed of this tree, but it also has other elements, such as its leaves or its branches, since these are parts of the tree. That does not mean that the branches and the leaves are identical to the tree of which they are parts. They are only what is called today “proper parts,” while the tree itself is an “improper part” of itself. With these explanations of the formal characteristics of collective classes I set out how Leśniewski’s intuitions were captured in Mereology. They could also be examined in a more symbolic fashion from the axioms of Mereology,10 but I preferred here to avoid explanations of the formal peculiarities of this system to highlight the intuitions that gave rise to it.

References

Beets, Fr. and Gillet, E. (eds.) 2000, Logique en perspective. Mélanges offerts à Paul ­Gochet, Brussels: Ousia. Carnap, R. 2001. The Logical Syntax of Language. English transl. by A. Smeaton. L­ ondon: Routledge. Detlefsen, M. 2007. Formalism. In: The Oxford Handbook of Philosophy of Mathematics and Logic. Edited by S. Shapiro. Oxford: Oxford University Press, 236–​317. Frege, G. 1895. Kritische Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra der Logik. In: Kleine Schriften. Edited by I. Angelelli. Hidelsheim: Olms, 193–​210. Goodman, N. 1956. A World of Individuals. In: The Problem of Universals. Edited by I.M. Bocheński, A. Church, N. Goodman. Notre Dame (IN): University of Notre Dame Press, 15–​31. Jordan, Z.A. 1967. The Development of Mathematical Logic in Poland Between the Two Wars. In: St. McCall, Polish Logic. 1920–​1939. 1967. Oxford: Oxford University Press, 346–​397. 10 Leśniewski developped his first mereological axiomatic system in 1916. This system only contained the primitive functor “part of.” Then Leśniewski built three other mereological formal systems:  in 1918, 1920 and 1921. In 1948, Sobociński, on the basis of Grzegorczyk’s work, built a mereological system with only one axiom and one primitive functor (see Sobociński 1954, 221–​222).

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Kearns, J.T. 1967. The Contribution of Leśniewski. Notre Dame Journal of Formal Logic 8(1–​2): 61–​93. Kotarbiński, T. 1986. Elementy teorii poznania logiki formalnej i metodologii nauk. English transl. by O. Wojtasiewicz (1966. Gnosiology. The Scientific Approach to the Theory of Knowledge. Oxford and London: Pergamon Press). Kotarbiński, T. 1966. Gnosiology. The Scientific Approach to the The­ory of Knowledge. ­En­glish transl. by O. Wojtasiewicz. Oxford and London: Pergamon Press. Leśniewski, S. 1916. Podstawy ogólnej teoryi mnogości. In: Prace Polskiego Koła Naukowego w Moskwie 2, 5–​42. English trans. by D.I. Barnett (1992. Foundations of the General Theory of Sets. In: Leśniewski 1992. Vol. 1, 129–​173). Leśniewski, S. 1927. O podstawach matematyki I. Przegląd Filozoficzny 30: 164–​206. English trans. by D.I. Barnett (1992. On the Foundations of Mathematics. In: Leśniewski 1992. Vol. 1, 174–​226). Leśniewski, S. 1928. O podstawach matematyki II. Przegląd Filozoficzny 31: 261–​291. English trans. by D.I. Barnett (1992. On the Foundations of Mathematics. In: Leśniewski 1992. Vol. 1, 227–​263). Leśniewski, S. 1929. Grundzüge eines Systems der Grundlagen der Mathematik. Fundamenta Mathematicae 14: 1–​81. English trans. by M.P. O’Neil (1992. Fundamentals of a New System of the Foundations of Mathematics. In: Leśniewski 1992. Vol. 2, 410–​605). Leśniewski, S. 1931. O podstawach matematyki V. Przegląd Filozoficzny 33: 142–​170. English trans. by D.I. Barnett (1992. On the Foundations of Mathematics. In: Leśniewski 1992. Vol. 1, 350–​382). Leśniewski, S. 1992. Collected Works. 2 vols. Edited by S.J. Surma et  al. Dordrecht, ­Warsaw: Kluwer, Polish Scientific Publishers. Łukasiewicz, J. 1953. Symposium: The Principle of Individuation. Proceedings of the Aristotelian Society. Supplementary Volumes 27: 69–​82. Luschei, E. 1962. The Logical Systems of Lesniewski. Amsterdam: North-​Holland. Miéville, D. 1984. Un développement des systèmes logiques de Stanislaw Leśniewski. Protothétique –​ Ontologie –​ Méréologie. Bern: Peter Lang. Patterson, D. 2012. Alfred Tarski. Philosophy of Language and Logic. Basingstoke: Palgrave. Peeters, M. 2000. La ‘neutralité laïque’ de Leśniewski et ‘l’agnosticisme’ de Russell. In: Logique en perspective. 2000. 219–​248. Richard, S. 2018. Leśniewski on Metalogic and Definitions. Synthese 195(6): 2649–​2676. Russell, B. 2010. The Principles of Mathematics. London: Routledge. Russell, B., and A.N. Whitehead. 1997. Principia mathematica to *56. Cambridge (UK): Cambridge University Press. Simons, P. 1987. Parts. A Study in Ontology. Oxford: Oxford University Press. Słupecki, J. 1955. S. Leśniewski’s Calculus of Names. Studia Logica 3(1): 7–​71. Sobociński, B. 1949. L’analyse de l’antinomie russellienne par Leśniewski. Methodos 1(1): 94–​107; 1(2): 220–​228; 1(3): 308–​316; 2(6–​7): 237–​257.

228 Richard Sobociński, B. 1954. Studies in Leśniewski Mereology. In: Leśniewski’s Systems. Ontology and Mereology. Edited by J.T Srzednicki and V.F. Rickey. The Hague: Kluwer, 217–​227. Sobociński, B. 1960. On the Single Axioms of Protothetic. Notre Dame Journal of Formal Logic 1(1–​2): 52–​73. Tarski, A. 1944. The Semantic Conception of Truth. Philosophy and Phenomenological Research 4(3): 341–​376. Tarski, A. 1983. Fundamental Concepts of the Methodology of the Deductive Sciences. English trans. by J.H. Woodger (1983. Logic, Semantics, Metamathematics. 2nd ed. Edited by J. Corcoran. Indianapolis: Hackett, 60–​109). Vernant, D. 1997. Du discours à l’action. Paris: Presses Universitaires de France. Vernant, D. 2000. Sur les fondements de la mathématique de Stanislaw Lesniewski. In: Logique en perspective. 2000, 314-​248-​363. Woleński J. (2001). Théories de la vérité dans la philosophie autrichienne. French transl. by K. Mulligan and J. Plourde (2001. La philosophie autrichienne de Bolzano à Musil. Edited by J.-​P Cometti, K. Mulligan. Paris: Vrin, 43–​80).

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The Case of Logic: Łukasiewicz-​Prior’s Discussion on Logic Zuzana Rybaříková Abstract Although mathematical logic is considered a precise tool for solving philosophical issues, it has its own drawbacks. This paper illustrates one of these possible issues by drawing on the example of two philosophers, Jan L. Łukasiewicz and Arthur N. Prior. The two shared many similar views, as well as the conviction that mathematical logic should be used in philosophy. In addition, both were interested in the history of philosophy and both tried to deny determinism and formulate claims to support future contingency. For a certain time, Prior even adopted Łukasiewicz’s system of many-​valued logic and was a defender of it. However, after developing his system of temporal logic Prior was more reserved towards Łukasiewicz’s system and formulated several objections to it. While Prior was, in his later works, a proponent of intensional logic and nominalism, Łukasiewicz insisted that any decent system of modal logic had to be extensional. There are also hints that Łukasiewicz may have adopted a Platonist position, even though Łukasiewicz himself was not willing to discuss these philosophical questions in his work. In contrast, Prior was a nominalist. As a result, they postulated divergent systems of logic for solving similar philosophical issues.

Keywords Arthur Prior  –​determinism  –​intensional logic  –​Jan Łukasiewicz  –​many-​valued ­logic –​mathematical logic –​modal logic –​nominalism –​Platonism –​temporal logic

… You are an excellent logician, but I think that you are too much influenced by a bad philosophy. łukasiewicz 1956

…

230 Rybaříková …while I differed radically from the late Professor Łukasiewicz on the subject of modal logic, my debt to him will be obvious on almost every page. prior 1957, vii-​v iii

∵ The matter of an appropriate methodology for scientific philosophy was the subject of many debates at the end of the 19th century and beginning of the 20th century. A number of philosophers were aware that the success of natural sciences overshadowed that of philosophy, which had seen practically no progress. Therefore, they made several attempts to reverse this state and in doing so founded scientific philosophy. While the founder of the Lvov-​Warsaw School, Kazimierz Twardowski, prioritised psychology as the methodology, one of his earliest pupils, Jan L. Łukasiewicz, was convinced that the appropriate methodology was mathematical logic (Łukasiewicz 1957, 47). Mathematical logic was considered a precise tool for solving philosophical matters. However, the dispute between Łukasiewicz and Arthur N. Prior shows that choosing an appropriate system of logic within that was also crucial. There are several similarities between Łukasiewicz and Prior and their approach to philosophy. Both agreed that mathematical logic was an appropriate tool for solving philosophical problems, both were interested in the history of philosophy and both tried to deny determinism and formulate claims to support future contingency. Certain of these similarities might have been a result of the fact that both philosophers could be described as belonging more (in Łukasiewicz’s case) or less (in Prior’s case) to the Brentanian tradition; whereas Łukasiewicz was a pupil of Brentano’s student Kazimierz Twardowski and studied in Graz alongside Meinong, one of Prior’s professors, John Findlay, also visited Meinong and wrote an influential book about Meinong’s theory of object (Simons 2017; Copeland 2017). There is also no doubt that Prior was deeply affected by Łukasiewicz, as he admitted in the introductory quotation. Despite this closeness, Łukasiewicz’s letters and Prior’s writings express disagreement between them in the case of logic. In my paper, I would like to focus more closely on this disagreement and explain why neither of them was able to accept the arguments of his opponent. This paper points to the philosophical views of Prior that led to his criticism of Łukasiewicz’s many-​valued systems of logic, as well as to Łukasiewicz’s convictions that caused him to insist on his system of modal logic even though he was familiar with Prior’s remarks.

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Finally, I would like to suggest some consequences of this for the use of logic as a methodology of philosophy. 1

Łukasiewicz

Although Łukasiewicz started his career as a philosopher, he began to be critical of philosophy during his study of modern formal logic (Woleński 1999, 65–​66). Łukasiewicz (1961b, 114–​115) did not reject philosophy, but he claimed that philosophy was predominantly not a science because it lacked scientific method and its associated precision. To him, mathematical logic represented the model of accuracy that should be reached by philosophy too. Consequently, he claimed that philosophy could be refined by using the tools of mathematical logic. In contrast to philosophers from the Vienna Circle (and in accordance with many other philosophers from the Lvov-​Warsaw School), Łukasiewicz did not maintain that philosophy or metaphysics should be entirely denied. As he argued, although several issues remained unresolved, they were not unresolvable. In his paper “Logistic and Philosophy”, he pointed to several metaphysical topics which, according to him, could benefit from the application of mathematical logic. These included, for instance, finiteness and the infinity of the world, the problem of space and time, and causality (Łukasiewicz 1961c, 200–​203). Of these metaphysical issues, Łukasiewicz focused on determinism, which he dealt with, in accordance with his methodological agenda, using mathematical logic. Łukasiewicz (1961b, 115–​116) defined determinism as the belief that every instant that was, is or once will be true is true eternally. As he showed in his example that appeared in the paper “On Determinism,” determinists believe that if John met Paul yesterday in the Old Town Square in Warsaw, it was true even before John’s birth that he met Paul yesterday in the Old Town Square in Warsaw. Consequently, the future is not different from the past; it has just not passed yet. Nonetheless, the determinist’s situation is even worse, in Łukasiewicz’s view. For not only is time linear and everything true eternally in his or her conception, it also means that we have no free will and that we live our lives like puppets in accordance with a higher power that determines what we do. Such an interpretation was unacceptable to Łukasiewicz.1 1 From Łukasiewicz’s writing it follows that he favoured science and its methods, but his motivation to prefer indeterminism rather than determinism was not entirely scientific. Łukasiewicz revealed, in his “Farewell Lecture,” a great passion for science; but he had a greater passion for human freedom, which he believed should not be restricted even by science. Łukasiewicz (1970a, 85) claimed: “The creative mind revolts against this concept of science,

232 Rybaříková Łukasiewicz (1970a) could not accept this view because he was an ardent defender of free will. Nonetheless, there is a view that allows a combination of free will and determinism, namely compatibilism. Surma (2012, 96–​97) claimed that had Łukasiewicz accepted this view, he would not have had to deny determinism. However, Łukasiewicz (1961b, 115–​116) was in fact a proponent of incompatibilism. Therefore, to defend free will he had to reject ­determinism. According to Łukasiewicz (1970a), there are two coercions that support a deterministic view. These two coercions are causality and the law of bivalence. While the first coercion comes from natural science, the second originates in axiomatic disciplines. Łukasiewicz considered the second to be more serious. He claimed that natural laws could be avoided but the laws of axiomatic disciplines are inescapable. These coercions gave Łukasiewicz the opportunity to use mathematical logic and prove that determinism is not the only intelligible explanation. Łukasiewicz discussed causality twice: in the paper “Analiza i konstrukcja pojęcia przyczyny” [Analysis and Construction of the Concept of Cause] from 1907 and in the paper “On Determinism” from 1946. In both papers, a causal relation is described as being a logical relation of two facts. While in the first paper Łukasiewicz (1961a) defined several logical relations between cause and effect, in the second, more mature text, he described this relation as transitive (Riška 2004; Łukasiewicz 1961b, 119–​120). Every cause precedes its effect, and the cause A that caused the effect B is also the cause of the effect C which was caused by B. If time is considered, it could mean that any fact in the world is part of a long causal chain that started at the beginning of the world and will finish when the world ends. However, Łukasiewicz tried to deny this concept of the causal chain, maintaining that it is possible that there are infinitely long causal chains that belong entirely to the future. According to Łukasiewicz (1961b, 121–​123), there is a similarity between a causal chain and a time line. Time instants can be spotted along this line, as a present instant 0 and the instant 1 when something happened. If we decide that the cause of instant 1 lies in instant ½, then the first cause that will affect 1 is the first instant after ½. However, as the time line is dense, there is no such instant since there is always an instant between any two instants on the time line. This means that there are infinitively many instants between each time instant and consequently that there could be an infinitively long chain that lies entirely in the future.

the universe, and life. A brave individual, conscious of his value, does not want to be just a link in the chain of cause and effect but wants himself to affect the course of events.”

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The second coercion, Łukasiewicz found in Aristotle. In his book De Interpretatione, Aristotle (1959, 18a-​19b) discussed contradictory pairs of statements and argued that in such pairs exactly one of them had to be true and exactly one of them had to be false. However, Aristotle described a situation in the 9th chapter where this rule did not hold. If, he argued, we have a pair of contradictions –​“There will be a sea-​battle tomorrow” and “There will not be a sea-​ battle tomorrow” –​it is difficult to evaluate them as the current evaluation of truth-​values implies that the future is already settled. Łukasiewicz’s solution to this issue is well known. Since the law implies determinism, which is not desirable, to escape this consequence certain logical law must be sacrificed. Łukasiewicz was aware of this for a long time, but it took him a while to discover which law had to be denied. First, he focused on the law of excluded middle and the law of contradiction. In 1917, probably affected by the discussion between Kotarbiński and Leśniewski on the eternality and sempiternity of the truth, Łukasiewicz discovered that the meta-​logical law of bivalence was a more appropriate candidate for the law that caused determinism. This law states that every statement has to have one of two truth-​ values; true or false (Betti 2002). Consequently, Łukasiewicz argued that future contingent statements have a different truth-​value from truth (1) and falsehood (0). He introduced a third value, ½, to evaluate future contingent statements. This truth-​value, linked to the modal operator ◊, means “it is possible”. Hence, the truth-​values of the modal operator in Łukasiewicz’s three-​valued system of logic are as follows: ◊0 = 0 ◊½ = 1 ◊1 = 1

Łukasiewicz 1970b, 167

Introducing three-​valued logic, Łukasiewicz (1970a, 87) claimed to have developed the first system of non-​Aristotelian logic2 since the system violates Aristotle’s law of bivalence. It could be argued that it was not logical analysis exactly that helped Łukasiewicz to deal with the law of bivalence but rather the introduction of a new logic that showed that Aristotle’s laws of logic did not apply in all systems of mathematical logic. Łukasiewicz subsequently used this system of logic to solve Aristotle’s problem of possibilities and prove the independence of formulae (Łukasiewicz 1956). 2 Since the development of three-​valued logic was based on an analysis of Aristotle’s sea-​battle problem, Łukasiewicz later renamed the system “non-​Chrysippean” (1970b, 175).

234 Rybaříková Although Łukasiewicz’s three-​valued logic is his most renowned system, he also developed other systems of many-​valued logic. In 1922, he introduced an n-​valued system of logic during his talk at the University of Lvov (Simons 1989, 255). This system could have an infinite number of truth-​values, and was derived from his three-​valued logic, as Łukasiewicz (1961c, 159) admitted. Łukasiewicz (1961c, 159) preferred this system to three-​valued logic because, as he argued, the n-​valued system of logic was closer to his understanding of an indeterministic system of logic. After World War ii, Łukasiewicz (1970c, 358–​361) worked on Aristotle’s syllogistic on which he based his final system of many-​valued logic. This system was also influenced by a development of modal logic, in particular Quine’s criticism of modality (Łukasiewicz 1970d, 391–​392). It was presented in his “System of Modal Logic”, a paper published in 1953. As well as assigning four different truth-​values to this system, Łukasiewicz (1970c, 370)  differentiated between two different modalities which were represented by two functors for possibility: ∆ and ∇. In addition, he introduced the reversed turnstile ⊣ into the system. The use of the reversed turnstile before a formula means that the formula is not a thesis of the system. Conversely, where the classic turnstile precedes a formula in Łukasiewicz’s four-​valued logic, it means that the formula is a thesis of the system (Prior 1967, 77). In choosing many-​valued logic as an appropriate system for his analysis, Łukasiewicz had taken his philosophical views into account. They considerably affected the form of the final system. In addition to having a passion for a free will, Łukasiewicz was an opponent of psychologism and formulated several objections to this approach to logic. Simons (2017) claims that for Łukasiewicz the study of logic was primarily the study of calculi and truth-​values and not the study of linguistic meanings or psychological judgments. His rejection of psychologism might also have influenced the other feature of his system of logic; that is, Łukasiewicz was a keen proponent of extensional logic. In his letter to Prior, he claimed that any decent system of modal logic must be extensional (Łukasiewicz 1956). This is clearly apparent in his final system of modal logic –​ the system of four-​valued logic –​which contained the principle of extensionality (Łukasiewicz 1970c, 363–​364). In contrast to the philosophical views above, Łukasiewicz did not introduce any aspect of his philosophy of logic. During the period in which he dealt with mathematical logic he gave just a few hints on his philosophy, making his philosophy of logic even more opaque. There is an interesting issue concerning Łukasiewicz’s ontological position: that is, because of his inclination to extensional logic, it might seem that he was also a nominalist. Łukasiewicz (1961d, 213–​214) discussed nominalism and Platonism in logic in his paper “In Defense

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of Logistics,” in which he claimed that he was once sympathetic to nominalism. However, as this philosophical view contradicts certain needs of mathematics, he argued that he was no longer a proponent of nominalism. Furthermore, in a description of his personal understanding of logic, Łukasiewicz (1961d, 219) admitted that he considered systems of logic as a structure present in God’s mind. This claim appears to imply that Łukasiewicz was a proponent of Platonism, even though he did not state this directly. Murawski (2018, 646–​647) also listed Łukasiewicz among the Platonists. 2

Prior

Arthur Norman Prior was a philosopher, logician and theologian from New Zealand and is considered to be the founder of modern temporal logic. Before developing his main contribution to current logic, he was attracted to theology and published several theological writings. Although he studied philosophy under Findlay and graduated in the history of logic, he was attracted to Presbyterian theology as Grimshaw (2002, 483) reports. His theological career ended when he underwent a crisis of faith. However, certain theological issues, e.g. the issue of determinism and free will, occupied Prior’s mind until his death (Hasle 2012). After turning to philosophy, he was interested primarily in logic and ethics (which was also the title of his first book). It was through his interest in the history of logic and his teaching duties that he began to be aware of Łukasiewicz’s work (Copeland 2017). As Copeland (2017) points out, Prior was interested in the history of logic even during his studies at the University of Otago. He wrote a master’s thesis on the subject which was supervised by John Findlay. When he began teaching at Canterbury University College in Christchurch, Prior encountered Bocheński’s book A Precis of Mathematical Logic. Copeland claims that Prior was captivated by it, especially by Łukasiewicz’s Polish notation which Bocheński had used in the book. The precision of this philosophical work appealed to Prior and he adopted it as a textbook for his students, together with ancient and medieval logical texts. Consequently, Prior wrote to Bocheński and Łukasiewicz, and both logicians wrote back to him, pleased with his interest in their work. In his own work, Prior was, however, more influenced by Łukasiewicz. As both logicians shared similar interests, Prior (1952) valued Łukasiewicz’s work and adopted his system of logic. However, he soon discovered several controversial aspects in Łukasiewicz’s system, which he went on to criticise (Prior 1955). First, Prior (1967, 135) pointed out that Łukasiewicz’s systems of many-​valued logic contained unintuitive features. Specifically, he claimed that

236 Rybaříková in Łukasiewicz’s three-​valued logic, the law of contradiction and the law of excluded middle do not hold and therefore: (p ∨ ¬p) = ½, iff p = ½ (p ∧ ¬p) = ½, iff p = ½ Furthermore, Prior (1957, 2–​3) argued that Łukasiewicz’s system of four-​ valued logic was even more unintuitive. While Prior directly criticised the thesis ▫(p ⊃ q) ⊃ (p ⊃ ▫q), which is a thesis of Łukasiewicz’s system, Font and Hájek (2002, 160, 174–​177) went on to list more controversial theses that hold in Łukasiewicz’s four-​valued system of logic but which are not part of modern systems of modal logic. However, the most controversial feature of Łukasiewicz’s four-​valued logic is perhaps the fact that apodictic statements are not theses of the system. This means that the formula in the form ▫α is not a thesis of the system of logic (Łukasiewicz 1970c, 395–​396). In addition, Prior argued that Łukasiewicz’s systems of logic were still deterministic. Specifically, Prior (1955, 212) claimed that the conclusion of Diodoros’ Master Argument –​“what neither is nor will be the case is not possible” –​cannot be denied in Łukasiewicz’s three-​valued system of logic. As he proved: 1. (¬p ⊃ ¬q) ⊃ (q ⊃ p) axiom of 3VL 2. (¬p ∧ ¬Fp) ⊃ ¬◊p) 3. p ⊃ (p ∨ Fp) Finally, Prior differed from Łukasiewicz in terms of the philosophy of logic. As previously mentioned, Łukasiewicz insisted on an extensional system of logic. In contrast, Prior (1969, 35) argued that an extensional context could not express all the functions that systems of logic should have. Therefore, he preferred intensional logic. Prior was also more interested in the philosophy of logic than was Łukasiewicz. Although he developed several systems of logic, he was always curious about their ontological commitments. In several papers, he also formulated his own philosophical views on logic and metaphysics (e.g. Prior 1967, 137–​174). Prior was nominalist in his later papers. In Prior’s view, the combination of nominalism and intensional logic was not common in his time. He argued (1976, 190) that logicians who preferred extensional systems of logic were also inclined to nominalism, and that logicians who favoured intensional systems of logic were proponents of Platonism. In that respect, Prior called himself a deviant logician as he combined nominalism with a preference for intensional logic. Nonetheless, in the same vein Łukasiewicz could also be called a deviant logician, as he preferred extensional logic and probably also Platonism in exact contrast to Prior. It was primarily the philosophical convictions of both authors that gave rise to the differences in their views on logic. Objections to certain logical and

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metaphysical implications of Łukasiewicz’s system of many-​valued logic and his preference for intensional logic, led Prior to a rejection of Łukasiewicz’s many-​ valued logic. In contrast, as a result of his metaphysical views ­Łukasiewicz would not have approved of Prior’s intensional logic. Their interaction was, however, beneficial for both sides: because of Prior, Łukasiewicz’s work became better known. Łukasiewicz’s work had also an impact on Prior, because he used Polish notation and developed primarily propositional logic. In addition, Łukasiewicz was one of the founders of logical pluralism, from which Prior also benefited. This pluralism, however, raises an important question concerning the methodology of philosophy, namely: does it still mean that mathematical logic is a precise tool in philosophy, if the choice of the system of logic is affected by the philosophical preferences of each ­philosopher?

References

Aristotle. 1959. O vyjadřování. Translated by A. Kříž. Prague: Nakladatelství Československé Akademie Věd. Betti, A. 2002. The Incomplete Story of Łukasiewicz and Bivalence. In: The Logical Yearbook 2001. Edited by T. Childers and O. Majer. Prague: Filosofia, 21–​36. Copeland, B.J. 2017. Arthur Prior. In: The Stanford Encyclopedia of Philosophy. Summer 2017 ed. Edited by E. N. Zalta. https://​plato.stanford.edu/​archives/​sum2017/​entries/​ prior/​> [Accessed 11 September 2018]. Font, J.M., and P. Hájek. 2002. On Łukasiewicz’s Four-​Valued Modal Logic. Studia Logica 70 (2): 157–​182. doi:10.1023/​A:1015111314455. Grimshaw, M. 2002. The Prior Prior: Neglected Early Writings of Arthur N. Prior. Heythrop Journal  43 (4): 480–​495. doi:10.1111/​1468–​2265.00206. Hasle, P.F.V. 2012. The Problem of Predestination: As a Prelude to A. N. Prior’s Tense Logic. Synthese  188 (3): 331–​347. doi:10.1007/​s11229-​011-​9942-​4. Łukasiewicz, J. 1956. Łukasiewicz to Prior 20. 1. 1956. Unpublished manuscript stored in Prior’s Nachlass at the Bodleian Library in Oxford, Box 4. Łukasiewicz, J. 1957. Aristotle’s Syllogistic: From the Standpoint of Modern Formal Logic. 2nd ed. Oxford: Clarendon Press. Łukasiewicz, J. 1961. Z zagadnień logiki i filozofii. Pisma wybrane [Logic and Philosophy. Selected Papers]. Edited by J. Słupecki. Warszawa: Państwowe Wydawnictwo Naukowe. Łukasiewicz, J. 1961a. Analiza i konstrukcja pojęcia przyczyny [Analysis and Construction of the Concept of Cause]. In: Łukasiewicz 1961, 9–​62. Łukasiewicz, J. 1961b. O determinizmie [On Determinism]. In: Łukasiewicz 1961, 114–​26.

238 Rybaříková Łukasiewicz, J. 1961c. Logistyka i filozofia [Logistics and Philosophy]. In: Łukasiewicz 1961, 195–​209. Łukasiewicz, J. 1961d. W obronie logistyki [In Defence of Logistics]. In:  Łukasiewicz 1961, 210–​219. Łukasiewicz, J. 1970. Selected Works. Edited by L. Borkowski. Amsterdam, Warsaw: North Holland Publishing Company, Polish Scientific Publisher. Łukasiewicz, J. 1970a. Farewell Lecture by Professor Jan Łukasiewicz, Delivered in the Warsaw University Lecture Hall on March 7, 1918. In: Łukasiewicz 1970, 84–​86. Łukasiewicz, J. 1970b. Philosophical Remarks on Many-​Valued Systems of Propositional Logic. In: Łukasiewicz 1970, 153–​178. Łukasiewicz, J. 1970c A System of Modal Logic. In: Łukasiewicz 1970, 352–​390. Łukasiewicz, J. 1970d. Arithmetic and Modal Logic. In: Łukasiewicz 1970, 391–​400. Murawski, R. 2018. Ontology of Logic and Mathematics in Lvov-​Warsaw School. In: The Lvov-​Warsaw School. Past and Present. Studies in Universal Logic. Edited by Á. Garrido and U. Wybraniec-​Skardowska. Cham: Birkhäuser, 645–​661. Prior, A.N. 1952. In What Sense is Modal Logic Many-​Valued? Analysis 12 (6): 138–​143. oi:10.1093/​analys/​12.6.138. Prior, A.N. 1955. Diodoran Modalities. Philosophical Quarterly 5 (20):  205–​ 213. doi:10.2307/​2957434. Prior, A.N. 1957. Time and Modality. Oxford: Clarendon Press. Prior, A.N. 1967. Past, Present and Future. Oxford: Clarendon Press. Prior, A.N. 1969. Extensionality and Propositional Identity. Crítica:  Revista Hispanoamericana de Filosofía 3 (7/​8): 35–​60. Prior, A.N. 1976. Intentionality and Intensionality. In: A.N. Prior. Papers in Logic and Ethics. Edited by P. T. Geach and A. J. P. Kenny. London: Duckworth, 39–​55. Riška, A. 2004. Łukasiewicz on Causation. Organon F 11 (1): 1–​14. Simons, P. 1989. Łukasiewicz, Meinong and Many-​Valued Logic. In: The Vienna Circle and the Lvov-​Warsaw School. Edited by K. Szaniawski. Dordrecht: Kluwer Academic Publishers, 249–​291. Simons, P. 2017. Jan Łukasiewicz. In: The Stanford Encyclopedia of Philosophy. Spring 2017 ed. Edited by E. N. Zalta. https://​plato.stanford.edu/​archives/​spr2017/​entries/​ lukasiewicz/​> [Accessed 9th June 2017]. Surma, P. 2012. Poglądy filozoficzne Jana Łukasiewicza a logiki wielowartościowe [Jan Łukasiewicz’s Philosophical Views and Many-​Valued Logics]. Warszawa: Wydawnictwo Naukowe Semper. Woleński, J. 1999. Mathematical Logic in Poland 1900–​1939:  People, Circles, Institutions, Ideas. In:  J. Woleński. Essays in the History of Logic and Logical Philosophy. 1999. Kraków: Jagiellonian University Press, 59–​84.

pa rt 4 On Informal Methods in Philosophy

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­c hapter 13

The Semiotic Method in Art Theory and Aesthetics in the Lvov-​Warsaw School Aleksandra Horecka Abstract In 1937, Mieczysław Wallis –​a representative of the Lvov-​Warsaw School –​delivered a speech titled: “Art from a Semantic Point of View –​a New Method of Aesthetics” at a conference in Paris. After 1937, he published a number of articles in which he presented the application of this method. However, Wallis was not the only representative of the Lvov-​Warsaw school who used semantic categories to describe works of art. Władysław Witwicki and Stanisław Ossowski did as well. The foundations of that semantic method in the theory of art and aesthetics in the Lvov-​ Warsaw school were created by the founder of the School –​Kazimierz Twardowski, who defined a sign as an expressive object. The aim of this paper is to analyze the so-​called semiotic methods in aesthetics and the theory of art in the Lvov-​Warsaw school and to point out the basic assumptions of these methods and their variations and application.

Keywords Aesthetics –​Lvov-​Warsaw School –​semantic category –​semiotic method –​­theory of art

In 1937 Mieczysław Wallis gave a speech at a conference in Paris, “L’art au point de vuesé mantique –​un eméthode récente de l’esthétique” [Art from a Semantic Point of View –​a New Method of Aesthetics]. Wallis had previously dealt with issues in the domain of the semiotics of art: in 1934 he wrote an article “O rozumieniu pierwiastków przedstawiających w dziełach sztuki” [On the Understanding of Presenting Elements in Works of Art] but it was in anarticle published in 1937 that he called the semantic viewpoint on art –​“the aesthetic method.” In this article, he referred to the works of members of the Lvov-​ Warsaw School, inter alia: Władysław Witwicki’s Psychology (1963), Stanisław

242 Horecka Ossowski’s Analiza pojęcia znaku [Analysis of the Concept of the Sign] (1967) and U podstaw estetyki [At the Basis of Aesthetics] (1966), as well as the papers of Leopold Blaustein (Blaustein 2005a, Blaustein 2005b). Wallis also mentioned Jan Mukařowsky’s article “L’artcomme fait sémiologique” (Wallis 1968). The roots of the semiotics of art are probably in the German philosophy of the late nineteenth and early twentieth centuries. However it can be said that the Lvov-​Warsaw School developed its own method of art semiotics. This method was used in a narrower scope by:  Władysław Witwicki, Stanisław Ossowski, Leopold Blaustein, and Władysław Tatarkiewicz; and in a wide scope by Mieczysław Wallis and Prof. Jerzy Pelc who died last year. It is justified to talk about the art semiotics of the Lvov-​Warsaw School. What is the essence of this method? What are its assumptions? What are the variants of art semiotics in the Lvov-​Warsaw School? These are the questions that I would like to answer in this paper. 1

Basic Methodological Assumptions

1.1 Assumption as to the Identity of Certain Objects The semantic method of aesthetics and art theory mentioned in the Wallis’s article: “Art from a Semantic Point of View –​a New Method of Aesthetics” is a kind of semiotic method. It is often said that this method is generally based on the application of concepts developed on the basis of one domain –​semiotics –​to another domain –​aesthetics or the theory of art. Terms developed on the basis of semiotics (one philosophical field) are transferred to aesthetics (another philosophical field) or to the theory of art (another non-​philosophical field of the humanities). Such a transfer must, however, have reasonable grounds. It is based on the identity of at least some objects in both fields. We are dealing with the following absolutely basic assumptions: (T.1) The objects of science S1 are P objects –​The objects of semiotics are signs. (T.2) The objects of science S2 are Q objects –​The objects of art theory (aesthetics) are works of art. (T.3) Some Q objects (objects of science S2) are P objects (objects of science S1) or some Q objects (objects of science S2) are composed of P objects (objects of science S1) –​Some works of art are signs or are composed of signs. (T.4)  Q objects (objects of science S2), or parts of them which are P objects, are described in terms applied to P objects of science S1 –​Works of art (or parts of them) are described in semiotic terms. Recognition that certain objects of art theory (aesthetics) are signs depends, of course, on (1) the concept of a sign and (2) the ontic categories adopted.

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Assumptions as to the Ontic Category of the Semiotic Object and the Work of Art In every semiotic theory there are ontological assumptions regarding the ontic category of its objects, that is, assumptions concerning the ontic category of the sign. Depending on the ontological assumptions, different semiotic theories can be distinguished: (1) monocategorical (all signs are of the same ontic category, e.g. all are things (reism) or events (eventism)) and (2) polycategorial (signs can have different ontic categories (things, events, processes, states of affair etc.)). The necessary condition for the identity of objects of two domains is the categorical identity of these objects. It can be said that the representatives of the School  –​which I  mentioned above  –​agree on the ontic category of the sign. Twardowski –​and his disciples after him –​distinguished in 1912 the permanent products of man (things) from non-​permanent (processes, states of things, events) (Twardowski 1965, 235). A  semiotic object can be of any ontic category, it can be a thing, event, process, etc. Such a polycategorial semiotic conception perfectly suits works of art. Works of art are not only human products, but also have different ontic categories: they are, for example, things (sculpture, painting) or processes (dance). The semiotics of the majority of the School’s representatives (with some exceptions) is –​from the point of view of the ontic categories of the adopted objects –​ polycategorial. 1.2

1.3 Assumptions as to the Essence of the Sign and Semiotic Functions The basic concept that must be specified in semiotics as the method of ­aesthetics or the theory of art is the concept of a sign. A sign in the Lvov-​ Warsaw School is usually defined as an object that has a certain semiotic function. However, because different scholars accept different semiotic functions as sign functions, various groups of objects are considered signs. Let us assume, therefore, that an object that performs some semiotic function is a semiotic object. Kazimierz Twardowski distinguishes many kinds of semiotic functions and, as a consequence, he uses different concepts of the sign, including, inter alia: (1) x is sign1 of y if and only if x presents y, which do not fall under the senses (Twardowski, year unknown, 17), (2) x is sign2 of y if and only if x expresses y of the sender, (3) x is sign3 of y if and only if x evokes y in the recipient. One object can simultaneously perform several semiotic functions, and therefore fall into different concepts of the sign.

244 Horecka Mieczysław Wallis generally (in three different works of his) distinguishes three semiotic functions of the sign: (1) x is sign1 of y if and only if x represents y, (2) x is sign2 of y if and only if x expresses the sender’s thought y about the designatum of x, (3) x is sign3 of y if and only if x evokes in the recipient thought y about the designatum of x (Wallis 1983d, 33). Prof. Jerzy Pelc considers three semiotic functions: (1) designating, (2) meaning (connoting) and (3) expressing (Pelc 1960, 182). Leopold Blaustein, on the other hand, speaks of (1)  reproductive, (2)  schematic, (3)  symbolizing and (4) signifying signs (comp. Blaustein 2005b, 77). Depending on what character functions are adopted in a certain semiotic conception, various objects of aesthetics and art theory will be considered signs. Therefore, the scope of the applicability of semiotics to aesthetics or the theory of art will change. Semiotic functions can be of course divided into semantic (meaning and various types of representing (designating, reproducing etc.) and pragmatic (expressing and evoking). Hence we can talk about the semantics and pragmatics of art. Different scholars emphasize various functions; e.g. Twardowski and Witwicki concentrate on the function of expression, and Blaustein and Wallis on various forms of representation. Witwicki mainly cultivates the pragmatics of art, and Wallis and Blaustein –​semantics. Let us note, however, that the semiotic functions of expression adopted by representatives of the School are inconsistent with each other. Different scholars from the School’s circle define it differently. For example, Twardowski asserts that what is expressed is a certain mental object –​namely, a mental product or the mental action of a certain person. Each sign is an expression of some mental product, but not every expression of a mental product is a sign. That the psychophysical product of a certain person should be a sign of y, that x must also be a partial reason for the creation of some other y-​like mental product of recipient (comp. Twardowski 1965, 230). The function of expression in Twardowski’s conception thus also includes the functions of evocation and is built upon the latter. In Witwicki’s conception, a semiotic object expresses not only mental products and actions, but also human dispositions, which are the mental conditions for the emergence of mental experiences and unconscious mental objects. Wallis’s concept of expression is slightly different. At the beginning (in 1944 in an unpublished article “Art from the Semantic Point of View (Outlines and Fragments),” Wallis 1944) Wallis claims that signs can express any psychological individual experience of the creator. In subsequent semiotic papers,

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however, he adopted the function of representation as the basic semiotic function and claimed that the sign which represents another object expresses not any psychological state, but only the sender’s thought of the designatum of the sign. In this way, the function of expression is built on the representation function and somehow covers it. We have: x ––––––––––––––––––––––––––> y (semiotic object) (semiotic function of expression) (object expressed) The members of the Lvov-​Warsaw School represent different standpoints regarding the essence of the function of expression and about the scope of y. As to semiotic functions of representation, an attempt to classify them was undertaken by, among others, Wallis and Blaustein. Wallis distinguishes three types of representation: direct, indirect and symbolic (Wallis 1968, 85–​86). According to Wallis, we deal with a direct representation when it is based on the similarity of appearance, and with an indirect representation when it is based on a certain convention, as a result of a certain custom, and with symbolic representation –​when the representation “is based […] on certain objective properties of both terms and on certain conventions.” Hence we obtain three types of signs representing: iconic signs, conventional signs and symbols. For example, a photo of a cat directly represents a cat and is its iconic sign; the word “cat” indirectly represents a cat and is its conventional sign; and the black cat represents misfortune and is a symbol. According to Blaustein, we actually deal with four kinds of representation: one “visual”–​in the case of a reproducing sign–​and three “non-​visual” representations: (1) schematic (e.g. a schematic drawing of a cat as a cat’s sign), (2) symbolic (e.g. a black cat as a sign of misfortune) and (3) signitive (the word “cat” as a sign of a cat). It can be said that Blaustein’s signific objects correspond to Wallis’s conventional sign, reproducing and schematic together –​to Wallis’s iconic signs and Blaustein’s signitive sign –​to Wallis’s conventional sign. Leopold Blaustein

Mieczysław Wallis

signitive objects reproducing object Schematic object symbolic objects

conventional signs that represent objects indirectly iconic signs that represent directly symbolic signs

246 Horecka 1.4 Assumption as to the Field of Representation and Syntax Semiotics includes three domains: (a) semantics –​the relationship between the sign and reality and its designatum; (b)  pragmatics  –​relations between users and the sign; (c) syntax –​relations between signs. The semiotics of art also covers these three sections: semantics, syntax and pragmatics. In the Lvov-​Warsaw School the pragmatics of art was developed first, then semantics, and at the end –​syntax. We have already talked about semiotic and semantic functions. This, however, does not cover the essence of a sign. Signs combine into a unified whole. In the case of applying the semiotic method to the theory of art, it becomes necessary to develop a specific theory of the structure of semiotic objects and the theory of the combination of multiple parts into a unified harmonious whole –​it is necessary to develop the syntax of a work of art. The theory of syntax must be so general that it can be applied to semiotic objects of different types. Such a theory of syntax was worked out in the art semiotics of the Lvov-​Warsaw School. The concept of the field of representation is crucial in this theory. We first read about the field of representation at the Lvov-​Warsaw School in the lectures of Kazimierz Ajdukiewicz on logical semantics at the University of Jan Kazimierz in Lvov in the academic year 1930/​31. However, the issue of the relationship between a certain sign and its field of representation is not clear in Ajdukiewicz’s conception. In one instance, Ajdukiewicz writes that a certain object symbolizes something when it is considered to be in a certain relation to the field of representation, and another time, that the field of the representation is a component of the sign. The concept of the field of representation developed by Wallis in his unpublished work “Art from the Semantic Point of View (Outlines and Fragments)” (1944) and in the article “On the Semantic Field” (1983c) is inspired by Karl Bühler’s book Sprachtheorie: Die Darstellungsfunktion der Sprache published in 1934 (Bühler 1934) The field of representation, then called the “semantic field” is –​according to Wallis –​a spatial, temporal or other arrangement, such that the meaning of a given sign is co-​determined by its place in that arrangement. Wallis claims that “the sign acquires proper or full meaning only in a certain specific surrounding.” The sign’s surrounding determines the meaning of the sign. Wallis distinguishes three types of a sign’s surrounding: (1) semantic surrounding(composed of other signs, context), (2) pragmatic surrounding, or “a combination of matters and activities in which a given sign is involved, the situation in which it occurs” and (3) physical surrounding, or “elements of the physical environment in which the sign is located –​permanently or temporarily –​and which co-​ determine its meaning.”

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The semantic field is, according to Wallis, a special kind of semantic surrounding. It is “an arrangement –​spatial or temporal, or some other in which a certain sign has different meanings depending on the place that it or some of its elements occupy in this arrangement.” Let us note, however, that a semantic field defined in this way is not –​despite Wallis’ intentions –​a kind of a sign’s semantic surrounding. It is not a spatial or temporal arrangement of signs. A semantic field is conditio sine qua non for the semantic surrounding of a sign. Wallis gives many examples of semantic fields: the stave in note writing, the decimal system in arithmetic, the sentence scheme in analytical language, the field of a coat of arms in medieval heraldry, the fields of medieval painting, medieval sculpture and medieval architecture. But are such objects spatial or temporal? Rather, we would say that the semantic field is such an area or period that has at least two different parts such that the sign S1 placed in one of these parts has a different meaning than S2 (equiform with S1) placed in another part. A necessary condition for the existence of syntactic rules is the existence of a field of representation. Syntactic rules are rules for the placement of elements in the semantic field. Syntactic rules –​that is, syntax –​are not reserved only for language; such rules also apply to individual works of art. For example, Wallis writes that “heraldic figures would be […] somehow a »dictionary« of the language of medieval heraldry, and the rules of their arrangement in the semantic field of the coat of arms –​its »syntax«” (Wallis 1983c, 16). 2

Selected Applications of the Semiotic Method to the Problems of the Theory of Art and Aesthetics

Definition of Terms in the Field of Aesthetics and Art Theory by Means of Semiotic Concepts 2.1.1 Definition of a Work of Art Definitions of a work of art, in which there are semiotic terms, can be found, among other places in the works of Władysław Witwicki: 2.1

(Def.Witwicki-​Work-​of-​art) A  work of art is a product of artistic penchant, that is a product of permanent internal human need “to create a spectacles in which the author expresses himself meaningfully [that is intelligibly and beautifully –​A.H.] and the spectator finds an aesthetic experience.” witwicki 1963, 277

248 Horecka Each work of art is, according to Witwicki, a semiotic object, and strictly  –​ psychosemiotic, that is, a pragmatic function of expressing –​expressing the ­author’s mental states and dispositions. Władysław Tatarkiewicz also has a definition of a work of art containing semiotic terms: (Def. Tatarkiewicz-​Work-​of-​art) “A work of art is a reproduction of a thing or a construction of forms, or an expression of experiences, but only such a reconstruction, such a construction, such an expression that is able to delight, to move or to shake.” Tatarkiewicz 2005, 52

In this case, the category of reproduction appears (that is a kind of representation) and expression (let us note that Aristotelian mimesis is actually a semiotic term meaning a kind of representation). 2.1.2 Definition of Form and Content Professor Jerzy Pelc defines the form and content of a literary work: The form of a literary work is the language signs available for sensuous cognition, and the content is all that is meant, referred to and expressed by these signs. The sum of content and form is a literary work. Literary types and literary genres are specific formal-​content units (comp. Pelc 1947, 13–​21). This definition can be successfully extended to other works of art composed of different types of signs. 2.2 Division of Arts into Semantic and Asemantic This division of arts into semiotic and asemiotic or semantic and asemantic depends on the number and type of semiotic functions adopted. According to Witwicki, there are no asemiotic arts because all works of art express something; all are –​as we can say –​pragmatic. According to Wallis, who focuses on the semantic function of representation, the arts can be divided into semantic and asemantic ones. In works of semantic arts some elements could be asemantic and in works of asemantic arts –​some elements could be semantic. For example, literary works are semantic, and architectural works and musical works are usually asemantic, but they have semantic elements. Analysis of Parts of Works of Art Composed of Different Types of Signs (the Concept of a Semiotic Enclave) Wallis considers the issue of the so-​called semantic enclave, for example inscriptions in medieval art, or titles of works of art. The semantic enclave is a part of a work of art consisting of signs of a different kind than the work itself. 2.3

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A problem arises as parts of a work of art made up of signs of various types: conventional, symbolic and iconic combine with each other. Wallis analyzes subtitles and inscriptions in paintings from the Middle Ages to modern times, indicating how they combine with iconic signs (Wallis 1983j). Indication of Semantic Fields and Formulation of Syntactic Rules in the Case of Art Objects of a Certain Type Semioticians of art indicate appropriate semantic fields in painting and medieval sculpture, and then formulate syntax rules. For example, Wallis distinguishes the following semantic fields in medieval art: “top –​bottom,” “center –​ sides,” “right side –​left side” and formulate syntactic rules, e.g.: (1) The higher A stands in the hierarchy H than B, the higher the iconic sign of A is than the iconic sign of B in medieval painting. (2) The higher A stands in the hierarchy H than B, the closer to the middle of the painting the iconic sign of A is than the iconic sign of B (3) If Christ’s figure is in the middle of a painting and if A is good, the iconic sign of A is on the right side of Christ’s figure. (4) If Christ’s figure is in the middle of painting and if A is bad, the iconic sign of A is on the left side of Christ’s figure (Wallis 1983c, 16). 2.4

Analysis of a Work of Art or a Type of Work of Art in Semiotic Categories Analysis of specific works of art in semiotic categories consists in separating the parts constituting the signs of particular types and giving the syntactic rules of a given work of art. For example, Wallis analyzes the entire Christian church (Wallis 1983e, 170–​190) as an iconic sign and the symbol of Heaven understood as the abode of God, angels and saints and as a symbol of community. It also indicates individual symbolic, iconic and conventional elements that constitute parts of the church (e.g. presbytery, nave, vault, horizontal projection). Let us present semiotic analysis of a romanesque column (as an example of application of the semiotic method in domain of architecture). The column is an architectural vertical support. The romanesque column in the sacral building has semantic fields: up –​down. The current syntactic rule has the form: what is at the top is valuable positive (good), what is at the bottom –​it is valuable negatively (bad). The column is built of capital, shaft and base. The base rests on the plinth. Because the column as a whole is part of the house of God, it must be entirely good. The best is obviously what’s at the top –​ the capital. And that is why the artists devote the most attention to the capital –​they are the most carefully refined artistically. The iconic sign of the lily (Lilium candidum) is visible on the capital in the biforium. Lilies could grow 2.5

250 Horecka

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Illustration 13.1 Biforium in Cistercian monastery in Wąchock (Poland) and the capital of column (Phot. A. Horecka).

252 Horecka

…

…

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…

Illustration 13.2 Different forms of claws in romanesque columns in Cistercian monastery in Wąchock (Poland) (Phot. A. Horecka).

…

254 Horecka on nasty swamps and have beautiful, white, fragrant flowers –​some can find in this plant “semantic field” up –​down and rules –​what is high is beautiful, what is low –​it is ugly. A lily flower is a symbol of purity and perfection (often a symbol of the Mother of God). It is the iconic sign of this symbol that appears on the column’s capital. Where are “bad things” in the column? What’s bad is at the bottom –​it “slithers” from the plinth and “sits” on the base. These elements are called in architecture “claws” (in architecture “claw” is not a synonym for “crocket!”). Claws in the Cistercian monastery in Wąchock have different forms, which can be seen in the attached pictures. They are sculptures –​iconic signs of a snakes with a divided tongue, heads of some fantastic animals with bared fangs (devils) etc. What presented in sculptures are evil creatures symbolizing evil pressed by columns –​symbols of the power of the church –​to the floor. At the end, it is worth paying attention to the unique (in its shape) biforium with three arches –​the symbol of the Holy Trinity. Biforium itself, as a form of a window opening, is also a sign for medieval art semiotician –​a symbol of the passage of God –​light –​into the interior of a sacred space. The essence of the semiotic method developed in the Lvov-​Warsaw School is the application of semiotic terms (“sign,” “semiotic function,” “syntax rule” etc.) to (1) definitions of terms in the field of aesthetics and art theory (definitions of a work of art, form, cent etc.), (2) clasiffication of works of art and arts, (3) description of the individual works of art, (4) explanations of certain phenomena in art (eg historical variability of works of art, trends in art etc., according to, for example, the thesis that the history of art is a history of semantic structures). The transfer of terms from the field of semiotics to the theory of art and aesthetics is based on the assumption of at least a partial identity of objects in both fields: some works of art are signs or are built of signs). The transfer requires the “ontological” adaptation of the theory of art to a given sign theory or vice versa –​the theory of sign to the theory of art. Due to the diversity of ontological categories of works of art, the polycategorial concept of the sign is accepted by art semiotics from the Lvov-​Warsaw School. Due to the diversity of the sinus in arts, it becomes necessary to distinguish many semiotic functions and develop a general theory of the sign and the most general theory of syntax.

References

Ajdukiewicz, K. 2014. Wykłady Kazimierza Ajdukiewicza z semantyki logicznej w Uniwersytecie Jana Kazimierza we Lwowie w roku akademickiego 1930/​1931 [Lectures

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by Kazimierz Ajdukiewicz on Logical Semantics at the Jan Kazimierz University in Lvov in the Academic Year 1930/​1931]. Filozofia Nauki 1(85): 143–​158. Blaustein, L. 2005a. Przedstawienia imaginatywne. Studium z pogranicza psychologii i estetyki [Imaginative Notions. A Study from the Borderline of Psychology and Aesthetics]. In: Blaustein 2005c, 40–​68. Blaustein, L. 2005b. Przedstawienia schematyczne i symboliczne. Badania z pogranicza psychologii i estetyki [Schematic and Symbolic Notions. A Study from the Borderline of Psychology and Aesthetics]. In: Blaustein 2005c, 69–​91. Blaustein, L. 2005. Wybór pism estetycznych [Selected Aestetic Papers]. Kraków:  Towarzystwo Autorów i Wydawców Prac Naukowych Universitas. Bühler, K. 1934. Sprachtheorie:  Die Darstellungsfunktion der Sprache. Jena:  Gustav Fischer. Ossowski, S. 1966. U podstaw estetyki [At the Basis of Aestetics]. Warszawa: Państwowe Wydawnictwo Naukowe. Ossowski, S. 1967. Analiza pojęcia znaku [Analysis of the Concept of Sign]. In:  S. Ossowski. Dzieła, t.  4 (O nauce) [Collected Papers, Vol. 4:  On Science]. Warszawa: Państwowe Wydawnictwo Naukowe, 33–​59. Pelc, J. 1947. Zagadnienie treści i formy dzieła literackiego [Issue of Content and Form of Literary Work of Art]. Sprawozdania Towarzystwa Naukowego Warszawskiego. Wydział I Językoznawstwa i Historii Literatury 40: 13–​21. Pelc, J. 1960. Funkcje semantyczne a forma i treść w sztuce (Rozważania logiczne nad poglądami Władysława Tatarkiewicza na strukturę, oddziaływanie i rodzaje dzieł sztuki) [Semantic Functions and Form and Content in Art (Logical Considerations over Władysław Tatarkiewicz’s Views on the Structure, Influence and Types of Works of Art)]. In: Charisteria. Rozprawy filozoficzne złożone w darze Władysławowi Tatarkiewiczowi w 70-​tą rocznicę urodzin [Charisteria. Philosophical Dissertations Donated to Władysław Tatarkiewicz on the 70th Birthday Anniversary]. Edited by T. Czeżowski. Warszawa: Państwowe Wydawnictwo Naukowe, 173–​205. Tatarkiewicz, W. 2005. Dzieje sześciu pojęć [A History of Six [Aesthetic] Ideas]. Warszawa: Wydawnictwo Naukowe pwn. Twardowski, K. [year unknown]. Zarys logiki [The Introduction to logic] –​duplicated manustcript, handwriting of Twardowski’s wife, as Maria Ajdukiewicz declared on 9th June 1964. Twardowski, K. 1965. O czynnościach i wytworach. Kilka uwag z pogranicza psychologii, gramatyki i logiki. In:  K. Twardowski. Wybrane pisma filozoficzne [Selected Philosophical Papers]. Warszawa:  Państwowe Wydawnictwo Naukowe, 217–​240 (English translation: Actions and Products. Some Remarks from the Borderline of Psychology, Grammar and Logic. In: J. Brandl and J. Woleński (eds.), On Actions, Products and Other Topics in Philosophy. 1999. Amsterdam, Atlanta: Rodopi, 103–​132].

256 Horecka Wallis, M. 1944. Sztuka z punktu widzenia semantycznego (Zarysy i fragmenty) [Art from the Semantic Point of View (Outlines and fragments)]. Work written in oflag iic in Woldenberg. Located in Połączone Biblioteki WFiS UW i PAN in Warsaw, Rps PTF 21.3. Wallis, M. 1968. O rozumieniu pierwiastków przedstawiających w dziełach sztuki [On Understending of Presenting Elements in Works of Art]. In: M. Wallis. Przeżycie i wartość. Pisma z estetyki i nauki o sztuce 1931–​1949 [Experience and Value. Papers on Aesthetics and Science about Art 1931–​1949]. 1968. Kraków: Wydawnictwo Literackie, 80–​105. Wallis, M. 1983a. Dzieje sztuki jako dzieje struktur semantycznych [History of Art as the History of Semantic Structures]. In Wallis 1983i, 53–​70. Wallis, M. 1983b. Napisy w obrazach [Inscriptions in Pictures]. In Wallis 1983i, 191–​225. Wallis, M. 1983c. O polu semantycznym [On Semantic Field]. In Wallis 1983i, 12–​20. Wallis, M. 1983d. O znakach ikonicznych [On Iconic Signs]. In Wallis 1983i, 31–​52. Wallis, M. 1983e. Sztuka średniowieczna jako język [The Medieval Art as a Language]. In Wallis 1983i, 144–​149. Wallis, M. 1983f. Semantyczne i symboliczne pierwiastki architektury [Semantic and Symbolic Elements of Architecture]. In Wallis 1983i, 170–​190. Wallis, M. 1983g. Sztuka z punktu widzenia semantycznego –​nowa metoda estetyki [Art from Semantic Point of View –​New Method of Aestetics]. In: Wallis 1983i, 7–​11. Wallis, M. 1983i. Sztuki i znaki. Pisma semiotyczne [Arts and Signs. Semiotic Papers]. Warszawa: Państwowy Instytut Wydawniczy. Wallis, M. 1983j. O tytułach dzieł sztuki [On Titles of Works of Art]. In Wallis 1983i, 226–​271. Witwicki, W. 1963. Psychologia [Psychology]. Vol. 2. Warszawa: Państwowe Wydawnictwo Naukowe.

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From Concepts and Contents to Connotations: Łukasiewicz’s Theory of Conceptual Analysis and Its Further Evolution Marcin Będkowski Abstract We find pioneering conceptions of philosophical analysis in the works of George Edward Moore and Jan Łukasiewicz, the most eminent representatives of analytic philosophy. While the views of the first are widely known and have been repeatedly and extensively commented on, Łukasiewicz’s conception has unfortunately not provoked many comments or studies. In this article, I would like to reconstruct Łukasiewicz’s theory of conceptual analysis, present its motivation and weaknesses, and show its influence on the development of the semiotic method of analysis in the Lvov-​Warsaw School.

Keywords concept  –​conceptual analysis  –​connotation  –​content  –​Jan Łukasiewicz  –​ Lvov-​Warsaw School –​philosophical analisys –​semiotic method of analysis

1 Introduction1 The analytic approach to philosophy is characterized by a number of postulates addressed to the philosophical work, among others: striving for a clear and precise approach to problems and their formulation, searching for justification of theses, and generally, to making philosophy similar to science by ensuring the methodological correctness of its investigations. 1 The text was created as part of the project „Philosophy from the Methodological Point of View” (2015/18/E/HS1/00487), financed by the National Science Center (Poland). I would like to express my gratitude to Anna Brożek, Alicja Chybińska, Stepan Ivanyk, Agata Łukomska and Dominik Traczykowski. Their valuable comments and suggestions helped me to improve the previous version of this paper.

258 Będkowski Even considering analytic philosophy’s solicitude for methodological issues, the number of publications in the field of metaphilosophy or methodology in recent years testifies to a significant increase in interest in this subject. What is striking is the fact that, while analytic philosophers are strongly interested in the methodological aspects of philosophical work, there are hardly any in-​depth descriptions of the activities undertaken by philosophers: what exactly philosophers do, what methods they use, etc. Unfortunately, this fact casts a shadow over the whole of metaphilosophy and philosophical ­methodology. One of the valuable attempts to describe the various manifestations of philosophical analysis in historical and methodological perspective was presented by Michael Beaney in the entry “Analysis” in the Stanford Encyclopedia of Philosophy. This outstanding historian of analytic philosophy distinguished the three main conceptions of analysis:  decompositional, regressive and transformative analysis (Beaney 2014). In this article, I would like to follow Beaney’s distinction (and particularly his decompositional model) to see the first attempts of analytic philosophy to treat analysis as the decomposition of concepts. We can find pioneering concepts of philosophical analysis in the works of George Edward Moore and Jan Łukasiewicz, the eminent representatives of the analytic trend. While the views of the first are widely known and have been repeatedly and extensively commented on, Łukasiewicz’s conception has unfortunately not provoked many comments or studies. Therefore, in this article I would like to reconstruct Łukasiewicz’s idea of the logical analysis of concepts, point out some weaknesses, and briefly present how the semiotic take on conceptual analysis (the dominant approach in the Lvov-​ Warsaw School) was born. 2

Preliminary Remarks

In his papers and talks, Łukasiewicz clearly pursued the methodical precision in the practice of philosophy. He formulated some postulates that philosophy should be practiced in accordance with the ideal of accuracy offered by the deductive sciences. In particular, he was an ardent supporter of the use of formal methods and axiomatization in philosophy. He also advocated for the founding of a methodological institute, an institution with the objective to conduct some research in the field of methodology. We can find these tendencies in Łukasiewicz’s early work, “Analysis and Construction of the Concept of Cause” from 1906. After many years, on July 6, 1949, he wrote in his journal:

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During my stay abroad, I  prepared a dissertation on causality for the Przegląd Filozoficzny contest. I  sent the dissertation to Warsaw under the emblem “Arceo psychologiam”, which was supposed to mean “I stay away from psychology”. The dissertation got the first prize, in my opinion undeservedly. It was supposed to be an analysis and construction of the concept of cause, but at this time I understood logic too little to give a decent analysis of it. I do not recognize this dissertation today, even though Twardowski accepted it as a habilitation thesis. Łukasiewicz 2009/​2010, 359

I will return to Łukasiewicz’s opinion on his dissertation, formulated in the above passage, in the further part of my paper. From our perspective, it is important that Łukasiewicz presented an original conception of the logical analysis of concepts as a part of the preliminary remarks. These considerations “gave him a weapon and an instrument” to solve the main issue in a manner consistent with the principles of the scientific method, namely: to determine what cause is. It is worth stressing that while Łukasiewicz’s deliberations on the causal relation were the subject of several discussions and polemics, the initial methodological remarks got mostly ignored. Sometimes they were completely omitted, and attention was paid only to the fundamental issue. Although Łukasiewicz’s methodological considerations were innovatory and supposedly had an impact on the philosophical attitude of the Lvov-​Warsaw School, there was neither a historical nor a methodological discussion on it. One could even say that Łukasiewicz’s remarks seem to have fallen into oblivion, covered with a veil of silence. As I will try to show, his project was not entirely successful, but it paved the way for the dominant approach to the methods of concept clarification within the School. According to some experts, Łukasiewicz’s methodological remarks are even more valuable than the solution of the main issue. As Stanisław Kamiński noted: Solving philosophical problems is done by analyzing and constructing adequate concepts. Łukasiewicz proves this with the example of the logical analysis and the construction of the concept of cause. His very insightful and original formal remarks are probably more valuable than the substantive solution of the main issue. kamiński 1979, 284

Let us stay for a moment with Kamiński’s article. It is symptomatic that –​in the article titled “Łukasiewicz’s Concept of the Method of Philosophy” –​only two

260 Będkowski paragraphs are devoted to the method of the logical analysis of concepts: one for the summary, the other for the commentary. Here is how the attempt to present Łukasiewicz’s method looks: Firstly, we examine and define an object that falls under the concept of cause, searching for all the constitutive and consecutive properties of the object and the necessary relations between them. Then a determined concept is created at the same time, i.e. an undeniable set of properties that constitute an abstract object. In order to guarantee the adequacy of the concept with the object of investigation, it is necessary to take into account the history of the concept and to use the inductive method in the construction of this real definition. The ways of determination contained in the canons of J. S. Mill will be a valuable control procedure here. kamiński 1979, 284

Such a presentation of Łukasiewicz’s method begs a question. First of all, there are some doubts as to whether the stages distinguished by Kamiński adequately reflect Łukasiewicz’s intentions. According to the latter, the analysis of concepts is based on examining concepts themselves, not the objects that fall under the concept of cause. If there is a connection between the study of concepts and the study of objects falling under the concepts, it should be explicated. Secondly, according to Łukasiewicz, the method of logical analysis consists in searching for all the properties that make up the concept of cause. Then, among all properties, we should distinguish the constitutive and consecutive properties. The necessary relations –​which Kamiński writes about –​are precisely the relations between constitutive and consecutive properties. They do not need to be defined separately, because the relations holding between properties determine which of them are constitutive and consecutive. Thirdly, the phrase “then a determined concept is created at the same time” seems to be ambiguous or even absurd. Fourthly, Łukasiewicz mentions the stage of a concept construction, but, in contrary to Kamiński’s opinion, this is not the next stage of procedure  –​ ­following the search for properties. It either precedes it or it is identical to it instead. At least in the case of the concept of cause, the construction must precede the a­ nalysis  –​because otherwise, there is no object that could be ­analyzed. Fifthly, Kamiński’s comments on the appropriateness of a given concept are puzzling. Taking into account “the history of a concept” is not a condition formulated by Łukasiewicz.

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Łukasiewicz’s Disquisition

Let us follow Łukasiewicz’s argument. His aim is to present the definition of the logical analysis of concepts. This goal requires the definition of what is meant by “a concept” and “an analysis.” By “a concept” Łukasiewicz means “the meaning of words that do refer to concrete objects”: Every word of speech that has a meaning for itself, or every combination of words that means something but does not form a sentence, refers either to a concrete object that exists in the world around us, or to an abstract object that does not actually exist. […] It is the meaning what words or their juxtapositions refer to. By concepts I  understand the meanings of words that do not refer to concrete objects, i.e. by concepts I mean abstract objects. Łukasiewicz 1906/​1961, 9

The examples of expressions referring to real concrete objects are:  “the creator of Pan Tadeusz”, “the painting of the Holy Virgin who defends Częstochowa”, while the examples of expressions that refer to (unreal) abstract objects are: “man in general”, “geometric circle in general”. Łukasiewicz directly admits that he is not able to define what the abstract objects are, but clearly stresses that he does not treat them as mental activities or “spiritual images”. He also states that in this case he adopts the Platonic view (i.e. a certain form of conceptual realism). Łukasiewicz explicitly formulates the accusation that conceptualism is based on a logical error. In the author’s opinion, “to present something to oneself” is an ambiguous expression. In one sense it means an immanent object, in the other –​a transcendent object.2 What is surprising is the example by which Łukasiewicz illustrates what a transcendent object is. In the case of a presentation of a circle, an image (depiction, pictorial presentation) of a circle is the immanent object, while a circle in general (a ­concept of a circle) is the transcendent object. In connection with the above ontological declarations, Łukasiewicz specifies the aim of conceptual analysis: In order to give a logical analysis of the concept of cause, I will not examine what I  present myself, that is, what happens or appears in my 2 A careful reader will certainly notice that this argument was formulated by Twardowski and Höfler –​it served to reinforce the distinction between the content and the object of the presentation. Cf. (Twardowski 1894/​1977, 1–​2).

262 Będkowski consciousness when I think of a cause, or what someone else presents to him or her on this occasion –​it would be some kind of psychological analysis that does not interest me here; I will only try to define what the word “cause” means; otherwise, I will try to examine this abstract object which is the meaning of the word cause. Łukasiewicz 1906/​1961, 12

According to Łukasiewicz, the examination of an object aims to determine what properties the object has and what relations between them take place. Among the relations between the properties belonging to the object, the necessary relations, i.e. the constitutive and consecutive ones, are particularly interesting. For example, the equality of all diameters is a consecutive property of a circle, because it follows from the constitutive property of a circle which is the equal distance of all the points of the circumference from the center. In the next fragment, Łukasiewicz formulates his definition of logical ­analysis: To give a logical analysis of a concept, i.e. an abstract object, means to search for all its properties and examine the relations that occur between them, with particular emphasis on the necessary relations, i.e. with the marking of constitutive and consecutive features.3 Łukasiewicz 1906/​1961, 12

The author reserves the right to have doubts as to whether such a task can be solved at all. He points out two main difficulties. First of all, in the case of any object it is not possible to calculate all its properties. The so-​called relative properties of the object (i.e., in fact, relations in which the object remains with other objects) are especially problemat­ic. There are an infinite number of such properties (relations). Secondly, the analysis requires that the object of analysis exists, e.g. a chemist analyzes a sample of a substance. However, abstract objects do not exist in the real sense, i.e. not like concrete objects, but they are only created by the human mind. This gives rise to a doubt: what do we actually analyze when we analyze the concept of cause? Łukasiewicz presents two possibilities: we analyze the concrete objects, which colloquial, everyday speech calls causes (as the meaning of the word “cause” from the general language), or the abstract objects created

3 It seems that Łukasiewicz adopts Twardowski’s definition of analysis here. Cf. (Twardowski 1901, 63).

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by scientists (i.e. the meaning of the expression “cause (in general)” belonging to the chosen scientific language). None of these possibilities seems right to Łukasiewicz. The first one because analyzing what is called ”causes” in colloquial speech would not be a task for a philosopher, but perhaps for a lexicographer. An abstract object is the object of philosophical analysis is an abstract object –​the meaning of the word “cause in general,” which is “only an empty sound” in everyday speech (Łukasiewicz 1906/​1961, 13). The word “cause” in colloquial language refers to objects, but in Łukasiewicz’s opinion we do not know why (due to what properties). The second possibility is rejected by the author, because scientists create various –​ mutually incoherent –​concepts of cause. Therefore, Łukasiewicz states: I think there is only one way to avoid these difficulties. One has to come to accept the idea that there is no ready-​made abstract object called a cause, the analysis of which could be carried out, and such an object has yet to be created. Łukasiewicz 1906/​1961, 13

In order to create an abstract object that is the concept of cause, or cause in general, it is necessary to select in an appropriate and methodical way the properties that this object will consist of4. This act is a construction of the concept and will eventually make it possible to carry out an analysis, i.e. to indicate all the properties that make up the concept. In the next part, Łukasiewicz introduces an interesting distinction between the ideal abstract objects and the real abstract objects. The former in reality “do not correspond to anything”, and the author’s examples include the number e, four-​dimensional solid figures, the logical concepts of reason and consequence, and contradictory objects. The real abstract objects “include” real concrete objects; in other words: some concrete objects “fall under” these general objects –​ their examples are: neuron in general, strike in general, acceleration in general. As it turns out, Łukasiewicz is interested in the concept of cause understood as a real abstract object, i.e. as an abstract object under which certain concrete objects fall. Therefore, the next steps of the analysis should be carried out with the use of inductive and deductive methods (the deductive method is sufficient to create ideal concepts, ensuring that the selected properties are 4 Łukasiewicz does not impose any limitations on the source of these properties (however, if the constructed notion is to be empirically adequate, the properties should be associated with the objects falling under a given notion).

264 Będkowski not contradictory). The inductive method is designed to examine the objects which are called “causes” in science or in everyday life. In order to determine their characteristics, the method of agreement and the method of difference (the so-​called Mill’s canons) should be used. They will allow us to determine the properties shared by all causes and the characteristics that distinguish causes from other objects. The deductive method, on the other hand, is to be used to “determine the exact meaning [!]‌of found properties, to examine their consecutive properties, to indicate the relations between them, and to determine whether any contrary or contradictory properties have crept into the content of the concept [!]” (Łukasiewicz 1906/​1961, 16). To create a scientific, i.e. noncontradictory, unambiguous and consistent with reality, concept of cause is the ultimate aim of the analysis and the construction of the concept of cause. Łukasiewicz describes the result of the analysis as follows: Perhaps even it [the constructed concept  –​M.  B.] will not always be ­consistent with what colloquial speech calls a cause in a more or less unstable and inaccurate way. If there is such a discrepancy, I will not be able to prevent it. You will simply have to renounce the name of the cause of something that does not fall under the concept of cause, just as you have to renounce the name of carbonic acid to the chemical compound marked as CO2, which is not an acid but an anhydride of acid. Łukasiewicz 1906/​1961, 13

As we can see, Łukasiewicz puts emphasis on the fact that the constructed concept meets certain requirements set by the standards of the scientific method. Obtaining such a result may come at a cost –​e.g., inconsistency of the concept with the common concepts –​however, this does not need to be regretted. Let us recapitulate the points of Łukasiewicz’s argument: 1. Concepts are the meanings of words that do not refer to concrete objects, in other words: concepts are abstract objects. 2. Abstract objects are not mental activities or spiritual images given in internal experience. Concepts are Platonic entities (although, they are constructed by the human mind). 3. Each object has properties; they are connected by different relations, among which there are necessary relations. 4. To give an analysis of an object is to list all its properties. 5. A definition of conceptual analysis: To give a logical analysis of a concept, i.e. an abstract object, means to search for all its properties and examine the relations that hold between them, with particular emphasis on the

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necessary relations, i.e. with the marking of the constitutive and consecutive properties. 6. Abstract objects do not exist in the real sense; they are created only by the human mind –​in particular, you cannot have them in front of you as an object of analysis. 7. Concrete objects called “causes” in everyday speech (by given name) are not the objects of analysis. 8. Abstract objects constructed by scientists are not the objects of analysis. 9. The concept of cause (meaning of the name “cause in general”) has to be constructed. 10. There is a distinction between the abstract objects of real meaning (i.e. real abstract objects or real concepts) and the abstract objects of ideal meaning (i.e. ideal abstract objects or ideal concepts). 11. The method of induction and deduction should be used in the construction of real concepts. In the construction of ideal concepts –​the deductive method is sufficient (it guarantees that there is no contradiction between the properties). 12. The constructed concept should be noncontradictory, unambiguous and consistent with reality –​therefore, scientific. 4

Several Aporias

I think it is clear that Łukasiewicz has a few difficulties in his attempts to formulate his method. From today’s perspective, the following could be regarded as minor deficiencies: he inconsistently introduces quotation marks indicating metalinguistic uses, he does not respect the difference between a concept and its content, he does not explicate the relation between a concept (as an abstract object) and the objects that fall under it (belong to its scope). Of course, these defects can be explained by the state of the development of semiotic apparatuses at that time but without a doubt they remain the flaws of Łukasiewicz’s theory. What is more, he failed to avoid more serious errors which are connected with inconsistent or incomplete presentation of the following issues: 1. Łukasiewicz argues that he shares the Platonic view on the nature of concepts. However, he further argues that they are constructed by the mind. Is it possible to defend such a position? 2. Łukasiewicz refrains from analyzing specific objects called “causes” but stresses the importance of the inductive research aimed at determining the properties of objects. Is not the inductive determination of the

266 Będkowski properties of causes just an analysis of the concrete objects commonly referred to as “causes?” And further on: will the instability of colloquial speech not affect the result of construction? 3. It is not certain how Łukasiewicz understands the relations between referring to, naming and indicating objects that he introduces. The author refers to these relations using the following terms:  “what a given word indicates” and “the meaning of a given word”. It seems that Łukasiewicz identifies these relations. 4. The distinction between the names indicating concrete objects and the names not indicating concrete objects raises doubts, especially the identification of the latter with the names indicating abstract objects. This distinction is not exhaustive because empty names are also the names that do not indicate concrete objects. 5. Similar doubts apply to the category of abstract objects –​does it also cover mathematical objects in addition to concepts? Here, I am not up to the task of giving these problems the attention they undoubtedly deserve. I will confine myself to demonstrating the continuity of Łukasiewicz’s thoughts with the approaches later adopted in the lws. Arguably, we are able to easily solve a few of the aforementioned problems, e.g. to correct the formulations given in the paper using some modern, more developed conceptual frameworks (while remaining close to Łukasiewicz’s intentions). He seems to use the terms “what a given word indicates” and “the meaning of a given word” interchangeably. It can therefore be pointed out that: the meaning1 of name “X” = the designatum of name “X”. At least for those cases where “X” is a concrete name. Łukasiewicz defines concepts as the designata of names that are not concrete (i.e. which do not refer to specific objects) and which he identifies with abstract names. Łukasiewicz is not consistent in the way he introduces abstract names, e.g. one can have doubts whether the name “cause” or only “cause in general” is abstract –​and whether or not the first name can (in a given context) function as an abbreviated substitute for the second. The first set of examples given by the author illustrating this distinction uses only the second schema of constructing abstract names. Moreover, it is worth noting that in addition to concepts, Łukasiewicz recognizes the existence of other abstract objects, e.g. the concept of a number e = number e in general but it is something different than the number e itself (Łukasiewicz does not say anything about its status –​ nor about the status of numbers in general). We can therefore propose the following convention:  the designatum of name “X in general” = the concept of X. That is to say, concepts are the designata of the names built  –​from the perspective of natural language  –​in a

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non-​standard way. One may even assume that the words built according to this scheme do not belong to the general language (Łukasiewicz 1906/​1961, 13). Then, we can propose that the concept of X = the meaning2 of name “X”. That is, the meaning2 of the word “horse” is the concept of a horse, i.e. the designatum of the name “horse in general”. Objects falling under the concept, or embraced by it, would therefore belong to the scope determined by the meaning2 of the name. If we look at the function of concepts, their ontological status and the procedure of analysis, which consists in indicating their properties as abstract objects, it seems quite natural that on the basis of Łukasiewicz’s comments it is possible to identify meaning2 with connotation. “Connotation” –​defined as a characteristic set of properties –​seems to be a suitable candidate for a substitute for “concept.” Of course, the properties that make up a connotation belong to a set of connoted properties, but one cannot say that the connotation has these properties (in the literal sense). Bearing these reservations in mind, we can say that: the concept of X = the meaning2 of name “X” = the connotation of name “X.” To sum up, the following interpretation seems quite natural and consistent with Łukasiewicz’s intentions and is tidying his argument: (a) the meaning1 of name “X” = the designatum of name “X”; (b) the designatum of name “X in general” = the concept of X = the meaning2 of name “X”; (c) the concept of X  =  the meaning2 of name “X”  =  the connotation of name “X”. 5

Further Evolution of Conceptual Analysis in the lws

As we read in the introduction, Łukasiewicz stated that although Twardowski accepted “Analysis and Construction of the Concept of Cause” as a habilitation dissertation, he himself “stopped recognizing it” after years. The opinion of the Competition Committee is intriguing: The work is characterized by independence, clarity and methodicalness. Maybe the definition of causal relationship given by the author could have been achieved with a smaller effort of analytical process; in terms of content, it is impossible to agree with the author’s arguments regarding the temporal relation between cause and effect; there is also no proof of the reality of the concept of the cause constructed by the author. Undoubtedly, the work testifies to an energetic consideration of the very

268 Będkowski problem of causality, independent of any formulas and authorities, and to a highly developed sense of scientific rigor. N. N. 1906, iii

The assumption that the definition of causal relationship could have been formulated with a smaller effort of analytical process indicates –​in my opinion –​ that the Committee might have reservations about the value of the analytical part (its novelty or internal consistency): that in fact, apart from the discussion of psychologism, it does not contribute too much to the issue, and substantive considerations could have been made without this initial part. What is also interesting is the justification of the verdict, which seems to sound respectful but still distanced: Of the four works to be published, the work with the emblem “Arceo psychologiam” is the best. This work treats its subject from the well-​established author’s position in the most versatile and the most comprehensive manner, and at the same time, in the most systematic and ­methodical way. Because the prize –​as it follows from the very essence of the competition –​is to be awarded not to the work absolutely good, but the best from the submitted, it is necessary to award this work. N. N. 1906, iv

The relationships indicated above may at times seem trivial to the people familiar with the contemporary logical apparatuses, in particular:  semiotic (even in textbook versions). It is worth emphasizing, however, that in the Lvov-​ Warsaw School, the relations between the indicated concepts were the subject of lively discussions. The members of the School postulated various conventions and presented these relations in different ways, and the matter seems to be open even today. I would like to underline two things at this point. First of all, it is assumed that it was under the influence of Łukasiewicz’s views that Twardowski changed his psychological attitude and moved to the side of moderate antipsychologism. This change was reflected in, among other things, his famous treatise on actions and products (Twardowski 1911/​1965; cf. Brandl 1998). At the stage of preparing his competition paper, Łukasiewicz had already been influenced by Husserl’s views, and in his subsequent works he gave his convictions more and more profound and better form (Łukasiewicz 1907/​1961; cf. Rojszczak 1998; Betti 2006). Secondly, it was Mill’s theory of connotation that after several years established itself as the dominant –​especially in logic textbooks –​the approach to

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concepts. Although Mill’s treatise had already been quoted by Twardowski in his habilitation and by Łukasiewicz in the article under discussion, Leśniewski was actually the first and the main spokesman for the theory of Mill in the School. In my opinion, due to the fact that Mill’s theory of connotation is a good substitute for Łukasiewicz’s concept and Leśniewski’s authority, Mill’s conception met –​despite its unquestionable deficiencies! (Ajdukiewicz 1934a) –​with acceptance. It is worth recalling Łukasiewicz’s recollections of the circumstances of his first meeting with Leśniewski: It has turned out that Leśniewski is going to print an article in thePrzegląd Filozoficzny [Philosophical Review] containing criticism of some of my views expressed in my book Principle of Contradiction in Aristotle. This criticism was written with such a scientific accuracy that it was impossible to find any mistake. I remember that when Leśniewski said goodbye to me after an hour’s discussion and I went to the Scottish Café as usual, I  declared to my waiting colleagues that I  was going to close my logical business. A company was established which competition I will not be able to withstand. Łukasiewicz 2009/​2010, 315

Łukasiewicz emphasized Leśniewski’s ability to think precisely. He admired Twardowski’s skills and merits, but he also stated: However, I  did not learn the precision of thinking from Twardowski. What it means to think well, I learned only in Warsaw from Leśniewski. Łukasiewicz 2009/​2010, 361

“Próba dowodu ontologicznej zasady sprzeczności” [An Attempt at a Proof of the Ontological Principle of Contradiction] is, of course, the article Łukasiewicz mentions above. The importance of this article lies in the fact that Leśniewski, contrary to Łukasiewicz’s beliefs, provides a proof of the principle of contradiction but it also contains other polemical remarks, e.g. against Łukasiewicz’s conviction according to which no negative judgment is synonymous with an affirmative one. Leśniewski uses the categories of designating and connoting which serve him in, among other things, defining the equivalence of sentences and criticizing Łukasiewicz’s approach to empty and contradictory names. Interestingly, Leśniewski himself is not a faithful exponent of the Mill’s theory. He rejects the equivalence of the sentences “Aristotle was the creator of logic” and “Stagyrite was the creator of logic” because he believes that the

270 Będkowski names “Aristotle” and “Stagyrite” connote nonequivalent properties. In particular, “Aristotle” connotes the attribute of having the name “Aristotle”, while “Stagyrite” does not. Whereas according to Mill, proper names are not connotative names at all (Mill 1843/​1974, 33). 6

Some Divergences

As Kazimierz Ajdukiewicz noted in 1937: Twardowski became the founder of his own philosophical school (the so-​c alled Lvov School), which, stressing the need for clear thinking, turned its main efforts towards conceptual analysis. Of Twardowski’s numerous students […] the most faithful followers of the program of concept clarification are T. Kotarbiński and T. Czeżowski. ajdukiewicz 1937/​2006, 252

This program of concept clarification started, of course, with Twardowski. According to him, the analysis of concepts is connected with the analysis of their content, aimed at determining what properties make up the content of the concept. In Twardowski’s opinion, the content of the concept constitutes the meaning of the name. In his anti-​psychological approach, Łukasiewicz first of all rejected the distinction between the concept and the content of the concept. According to Twardowski and Höfler, it is properties that build the content of the concept but Łukasiewicz thought that properties make up the concept itself, i.e. an abstract object which is the “meaning” of an abstract name (although instead of “meaning,” one should rather talk about “designatum”). Over time, the program of concept clarification was developed primarily in the field of semiotics. This is due to the postulated parallelism between epistemology (psychology) and semiotics adopted by the School, and specifically to the postulated analogy between the contents of concepts and the meanings of names. Undoubtedly, it is worth emphasizing that in the Lvov-​Warsaw School, the decompositional conception of analysis has always been connected to the analysis of concepts understood as the meanings of certain linguistic expressions. Notably, Józef Maria Bocheński saw that as an essential feature of the whole of analytic philosophy (cf. Bocheński 1985/​1993)! Since the members of the School addressed the issue of concept clarification in close connection with the theory of definitions, they preferred in particular to consider the different types of definitions (e.g. considering their structure or intention) and the criteria for their correctness. The alleged

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parallelism between epistemology and semiotics naturally raises a number of questions, e.g. how the concept of connotation has been assimilated –​especially in the works of “the most faithful followers of the program of concept clarification.” Leśniewski’s early works are based on Mill’s ideas. Even thoughLeśniewski was critical of his own works from the so-​called philosophical-​grammatical period, they still had a great impact on other members of the Lvov-​Warsaw School. Kotarbiński was particularly susceptible to Leśniewski’s authority and he borrowed from Leśniewski Mill’s theory of connotation as a theory of concepts and meaning. In Kotarbiński’s Elementy [Elements], the content of concept is equated with the meaning of name, i.e. its content: “The content of concept M is the meaning of name »M«” (Kotarbiński 1929/​1990, 98). Moreover, as the author notes, “speculation on concepts develops almost exclusively in the context of the analysis of the use of names, especially general names. This allows for the use of semantic terminology in a lecture of relevant views” (Kotarbiński 1929/​ 1990, 98). In Elements (1929/​1990) he speaks of the content of name, which is characterized according to Mill’s definition of connotation. Kotarbiński refers to Mill’s original treatise (1843/​1974) but also to the Polish summary by Adolf Dygasiński from 1879 (Kotarbiński 1929/​1990, 15). A few years earlier, i.e. in 1921, the Polish translation of Jevons’ Logic by Czesław Znamierowski was published (Jevons’ earlier translated textbooks did not present the concept of connotation), which undoubtedly meant that in the 1920s the notion of connotation had already been settled in the Polish literature on the subject. In his “Uwagi o znaczeniu wyrazów” [Notes on the Meaning of Words] –​from the 1960s –​ Kotarbiński discusses the meaning of name as connotation and gives a purely reistic view of this approach (of course, he already shows some concern in Elements but there he focuses on “sets” as demanding a reistic paraphrase, not on “properties” (Kotarbiński 1962). Let us take a look at the different approaches to the relations between the concepts of concept, content, meaning and connotation. Ajdukiewicz in “O znaczeniu wyrażeń” [On the Meaning of Expressions] (1931) criticizes the theory of connotation as meaning and does not accept the identification of connotation with meaning. In Logiczne podstawy nauczania [Logical Foundations of Teaching] (1934b), he made a distinction between the full, characteristic, pleonastic, constitutive and linguistic content. The linguistic content of a name is identified with its connotation and it is determined by meaning. As Ajdukiewicz notes: “Some people equate the meaning of a name with its connotation. However, this is wrong. Each name has a meaning [linguistic, being a

272 Będkowski type of psychological meaning, i.e. the thought associated with an expression –​ M. B.], while not every name […] has a connotation” (Ajdukiewicz 1934b, 21). However, in Zarys logiki [The Outline of Logic] (1953) he already identifies the concept (not the content of concept!) with the meaning of name, and in Logika pragmatyczna [Pragmatic Logic] (1965) he states, regarding the correspondence between the content of concepts and the content of names: “The content of a concept is identical to the content of a name, of which the concept is a meaning” (Ajdukiewicz 1965, 50). Czeżowski writes in a relatively late article “Konotacja i denotacja” [Connotation and Denotation] (dated 1958–​1963): Thus, having distinguished one of the different ways of understanding of the term “meaning” we should take a distinct name for it. For this purpose, I propose the term “connotation” which, although understood in various ways, can be easily adapted to our needs as an artificial one, not burdened with the associations of everyday language. Thus, we will talk about the meaning of term as its connotation, and the relation between the meaning of term and the term itself will be called the relation of ­connotation czeżowski 1963/​1971, 105

As we can see, the concept of connotation as an explication of the concept of meaning was initially treated by Ajdukiewicz with some reservations. However, apart from these doubts, it was soon approved as an equivalent of the concept or its content (especially but not only in textbooks). It can be seen that in the 1960s the concept of connotation was already well established: Kotarbiński defended its consistency with reism, while for Czeżowski it was a natural substitute for the concept of meaning. In the tradition of the Lvov-​Warsaw School two opposing tendencies can be observed in respect to the aforementioned concepts. If we take into account the following pairs of concepts: meaning –​connotation, content –​meaning, concept –​content of a concept, we will notice that one of the tendencies is to identify them, while the other is to differentiate them. The former is represented by Łukasiewicz. The latter is represented, among others, by Kotarbiński and Ajdukiewicz. In Elements Kotarbiński clearly distinguishes concept, the content of concept and the object of concept. Ajdukiewicz, on the other hand, in one of his later works, “Proposition as the Connotation of a Sentence” (1967a), states that sense determines connotation and connotation determines denotation; in his “Intensional Expressions” (1967b), on the other hand, he distinguishes between propositions and contents (simple and full).

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Twardowski himself meant by “a concept”, a non-​pictorial presentation (as opposed to images) which is the meaning of a name corresponding to this presentation. On the other hand, by “the content of a concept” he meant the whole of properties that the object falling under the given concept has (Twardowski 1901, 60, 64). Twardowski gives some examples: the content of the concept of God consists of all the characteristics of God: spirituality, eternity, omnipotence, omniscience, etc., the content of the concept of a square: two-​ dimensionality, quadrilateralism, rectangularity, equilateralism. He emphasizes that the ­content of a concept is always one and the same, but there may be different concepts of the same object –​due to what properties concerning the object someone is aware of at a given moment (Twardowski 1901, 60). With the passage of time and under the influence of Łukasiewicz’s criticism, Twardowski modifies his views. Later, in “O czynnościach i wytworach”[On Actions and Products] by the meaning of name “N” Twardowski means the whole consisting of the shared properties of psychophysical products which we reach through abstraction. He explicitly refers to Husserl and his “ideal of Bedeutung.” Dąmbska defines Twardowski’s idea of meaning in terms of sets of properties –​i.e. in fact, as a connotation (Twardowski 1911/​1965, 236, cf. Brykczyński 2005, 57). In the article “Analysis of »analysis«” Anna Brożek and Jacek Jadacki also identify concepts with connotations (Brożek and Jadacki 2006, 95). Therefore, they define the decompostional type of analysis as diffractional analysis, the aim of which is to indicate the properties that belong to the connotation of a term corresponding to a given expression (Brożek and Jadacki 2006, 97)5. 7

Conclusions

Probably some will treat the discrepancies described above as a terminological curiosity, behind which there is no interesting problem. I  believe otherwise. I think that these discrepancies are fundamental, above all, regarding two issues: firstly, the ontology of language and the mind and secondly, the development of the logical culture. The issues of the relation between meaning and content, psychological and linguistic meaning, the function of expressions, the bearers of truth and the levels of description of linguistic expressions (expressions-​types, expressions-​tokens) seems to be crucial for understanding how language really works. In turn, the definition of language directly affects

5 A reader interested in the modern applications of Łukasiewicz’s method of analysis may read (Jadacki 2008).

274 Będkowski the concept of practical logic and the formation of logical knowledge, skills and rational attitudes among people. Both of these issues were the key interests of the members of the Lvov-​Warsaw School. Nowadays, it is not any different. As I wrote in the beginning, both Łukasiewicz and Moore can be regarded as the pioneers of the 20th century philosophical analysis. A comparison of their approaches would be very interesting and fruitful. It is a task at least for a separate paper but I would like to mention some of the possible issues which deserve to be undertaken. First, in my opinion both conceptions of analysis are rooted in the theoretical frameworks developed in 19th century, especially in the ideas developed in Brentano’s circle (cf. van der Schaar 2013), presented among others in logic textbooks (e.g. Höfler’s). Second, both philosophers rejected psychologism and were dealing with some serious aporias concerning the object, the aim and the procedure of analysis. One of the most confusing aspects of Moore’s conception is his claim that the object of analysis is a property being the meaning of a given word –​not the expression itself nor its sense (cf. Soames 2003, 37). As I was trying to show, Łukasiewicz conceptions is dealing with similar difficulties. However, contrary to Moore, Łukasiewicz treated an analysis as tightly connected with its linguistic form, what Bocheński was treating mistakenly as an essential feature of every form of analysis developed in analytic philosophy (cf. Bocheński 1993). Third, in my opinion, the most significant difference between the aforementioned approaches lies in fact that Moore was searching for analytic (reportive) definitions (Daly 2010, 45–​50) and Łukasiewicz –​for the synthetic (stipulative) ones. Moore tried to emphasize the fact that an analysis is concerned with providing ‘real definitions’, not the ‘verbal ones’. Regrettably, the relation between this two kinds of definitions as well as the distinction between meaning and connoted property were described somewhat obscurely. Łukasiewicz did care for the adequacy of definitions but was inclined to think that the natural language expressions are vague in their nature and that the analysis of a given concept should be preceded by its construction.

References

Ajdukiewicz, K. 1931. O znaczeniu wyrażeń [On the Meaning of Expressions]. In: Księga Pamiątkowa Polskiego Towarzystwa Filozoficznego we Lwowie, 31–​76. English translation as Ajdukiewicz 1978a. Ajdukiewicz, K. 1934a. Sprache und Sinn. Erkenntnis 4: 100–​138. English translation as Ajdukiewicz 1978b.

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Ajdukiewicz, K. 1934b. Logiczne podstawy nauczania [Logical Foundations of Teaching]. Warszawa: Nasza Księgarnia. Ajdukiewicz, K. 1937/​2006. Kierunki i prądy filozofii współczesnej [Directions and Tendencies in Contemporary Philosophy]. In:  K. Ajdukiewicz. 2006. Język i poznanie [Language and Knowledge]. Vol. 1. Warszawa: Wydawnictwo Naukowe pwn. Ajdukiewicz, K. 1953. Zarys logiki [The Outline of Logic]. Warszawa:  Państwowe Zakłady Wydawnictw Szkolnych. Ajdukiewicz, K. 1965. Logika pragmatyczna [Pragmatic Logic]. Warszawa: Wydawnictwo Naukowe pwn. English translation: Ajdukiewicz 1974. Ajdukiewicz, K. 1967a. Intensional Expressions. Studia Logica xx: 63–​86. Ajdukiewicz, K. 1967b. Proposition as the Connotation of a Sentence. Studia Logica xx: 87–​98. Ajdukiewicz, K. 1974. Pragmatic Logic. Dordrecht, Boston, Warszawa: D. Reidel Publishing Company, pwn –​Polish Scientific Publishers. Ajdukiewicz, K. 1978a. On the Meaning of Expressions. In: Ajdukiewicz 1978c, 1–​34. Ajdukiewicz, K. 1978b. Language and Meaning. In: Ajdukiewicz 1978c, 35–​66. Ajdukiewicz, K. 1978c. The Scientific World-​Perspective and Other Essays. 1931–​1963. Edited and with an introduction by J. Giedymin. Dordrecht, Boston: D. Reidel Publishing Company. Beaney, M. 2014. Analysis. In: The Stanford Encyclopedia of Philosophy (Summer 2018 Edition). Edited by E.N. Zalta. Betti, A. 2006. The Strange Case of Savonarola and the Painted Fish –​On the Bolzanization of Polish Thought. In: Actions, Products, and Things: Brentano and Polish Philosophy. Edited by A. Chrudzimski and D. Łukasiewicz. Philosophy & Mind, Vol. 8. Frankfurt: Ontos Verlag. Bocheński, J.M. 1985/​1993. O filozofii analitycznej [On Analytic Philosophy]. In:  Bocheński 1993, 35–​49. Bocheński, J.M. 1993. Logika i filozofia. Wybór pism [Logic and Philosophy: Selected Papers]. Edited by J. Parys. Warszawa: Wydawnictwo Naukowe pwn. Brandl, J. L. 1998. Twardowski’s Distinction between Actions and Products. In:  The Lvov-​Warsaw School… 1998, 23–​34. Brożek A. and J. Jadacki. 2006. Analiza “analizy” [Analysis of “Analysis”]. Studia Philosophiae Christianae 42 (1): 37–​54. Brykczyński, P. 2005. Kazimierza Twardowskiego koncepcja wytworów czynności [Kazimierz Twardowski’s Conception of the Products of Actions]. Filozofia Nauki 13 (2): 27–​68. Czeżowski, T. 1963/​1971. Konotacja i denotacja [Connotation and Denotation]. In: Semiotyka polska… 1971, 104–​111. English translation as: Czeżowski 1979. Czeżowski, T. 1979. Connotation and Denotation. In:  Semiotics in Poland 1894–​1969. 1979, 73–​80.

276 Będkowski Daly, C. 2010. An Introduction to Philosophical Methods. Peterborough: Broadview Press. Höfler, A. 1927. Logika propedeutyczna dla szkół średnich [Propedeutic Logic for High Schools]. Translated by Z. Zawirski. Lwów Księgarnia Naukowa. Höfler, A. and A. Meinong. 1890. Logik. Philosophische Propädeutik. Th. 1. Prague, Wien, Leipzig. https://​plato. stanford. edu/​archives/​sum2018/​entries/​analysis. Jadacki, J.J. 2008. Categories. In: Logic, Methodology and Philosophy of Sciences at Warsaw University. Vol. 4. Edited by J. Odrowąż-​Sypniewska. Warszawa: Wydawnictwo Naukowe Semper, 84–​90. Kamiński, S. 1979. Łukasiewicza koncepcja metody filozofii [Łuksiewicz’s Conception of Philosophical Method]. Roczniki Filozoficzne 27 (1): 283–​289. Kotarbiński, T. 1929/​1990. Elementy teorii poznania, logiki formalnej i metodologii nauk [Elements of the Theory of Knowledge, Formal Logic and Methodology of Sciences]. Dzieła wszystkie. Vol. 1. Edited by W. Gasparski et al. Wrocław, Warszawa, Kraków, Gdańsk, Łódź: Zakład Narodowy im. Ossolińskch, Wydawnictwo pan. English translation as: Kotarbiński 1966. Kotarbiński, T. 1962. Uwagi o znaczeniu wyrażeń [On the Meaning of Expressions]. In: Semiotyka polska … 1971, 83–​89. English translation as Kotarbiński 1979. Kotarbiński, T. 1966. Gnosiology: The Scientific Approach to the Theory of Knowledge. Oxford, New York: Pergamon Press. Kotarbiński, T. 1979. Comments on the Meaning of Words. In:  Semiotics in Poland… 1979, 52–​58. Łukasiewicz, J. 1906/​1961. Analiza i konstrukcja pojęcia przyczyny [Analysis and Construction of the Concept of Cause]. In: Łukasiewicz 1961, 9–​65. Łukasiewicz, J. 1907/​1961. Logika a psychologia [Logic and Psychology]. In: Łukasiewicz 1961, 63–​65. Łukasiewicz, J. 1961. Z zagadnień logiki i filozofii [Selected Issues of Logic and Philosophy]. Edited by J. Słupecki. Warszawa: Państwowe Wydawnictwo Naukowe. Łukasiewicz, J. 2009/​2010. Pamiętnik (fragmenty) [Diary  –​fragments]. Edited by P. Surma. Rocznik Historii Filozofii Polskiej 23: 313–​380. Mill, J.S. 1843/​1974. A System of Logic Ratiocinative and Inductive Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation. Edited by J. M. Robson. Toronto, London: University of Toronto Press, Routledge and Kegan Paul. N.N., 1906. Umotywowanie wyroku sądu konkursowego [Justification of the Opinion of the Competition Committee]. Przegląd Filozoficzny 9(2): I–​VII. Rojszczak, A. 1998. Truth-​Bearers from Twardowski to Tarski. In:  The Lvov-​Warsaw School… 1998, 73–​84. Schaar van der, M. 2013. G.F. Stout and the Psychological Origins of Analytic Philosophy. Basingstoke: Palgrave Macmillian. Semiotics in Poland 1894–​1969. 1979. Edited by J. Pelc. Dordrecht, Boston: D. Reidel Publishing Company, Warsaw: pwn–​Polish Scientific Publishers.

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Semiotyka polska 1894–​1969 [Polish Semiotics 1894–​1969]. 1971. Edited by J. Pelc. Warszawa: Państwowe Wydawnictwo Naukowe. Soames, S. 2003. Philosophical Analysis in the Twentieth Century, Vol. 1:  The Dawn of Analysis. Princeton: Princeton University Press. The Lvov-​Warsaw School and Contemporary Philosophy. Edited by K. Kijania-​Placek and J. Woleński. Dordrecht, Boston, London: Kluwer Academic Publishers. Twardowski, K. 1894/​1977. On the Content and Object of Presentations. Translated by R. Grossmann. The Hague: Martinus Nijhoff. Twardowski, K. 1901. Zasadnicze pojęcia dydaktyki i logiki do użytku w seminariach nauczycielskich i w nauce prywatnej [Main Concepts of Didactics and Logic for Pedagogical Schools and Private Teaching]. Lwów: ptp. Twardowski, K. 1911/​1965. O czynnościach i wytworach. Kilka uwag z pogranicza psychologii, gramatyki i logiki [On Actions and Products. Some Remarks in the Limit of Psychology, Grammar and Logic]. In: K. Twardowski. Wybrane pisma filozoficzne [Selected Philosophical Papers]. Warszawa:  Państwowe Wydawnictwo Naukowe, 217–​240. English translation as: Twardowski 1911/​1999. Twardowski, K. 1911/​1999. Actions and Products: Some Remarks on the Borderline of Psychology, Grammar, and Logic. In: Twardowski 1999, 103–​132. Twardowski, K. 1924. O istocie pojęć [On the Essence of Concepts]. Lwów: Polskie Towarzystwo Filozoficzne. English translation as: Twardowski 1924/​1999. Twardowski, K. 1924/​1999. On the Essence of Concepts. In: Twardowski 1999, 73–​98. Twardowski, K. 1999. On Actions, Product and Other Topics in Philosophy. Edited by J. Brandl and J. Woleński, Amsterdam, Atlanta: Rodopi.

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Kotarbiński’s Methodological Reism: Framework and Inspirations Alicja Chybińska Abstract Tadeusz Kotarbiński (1886–​1981) was a Polish philosopher, a member of the Lvov-​ Warsaw School and a direct student of Kazimierz Twardowski’s (a founder of the lws). He contributed to ontology, semantics, ethics (including praxeology), and methodology. Kotarbiński is famous for reism, i.e., a doctrine according to which only concrete things (bodies) exist. There are two widely accepted aspects of reism: ontological and semantic. The aim of this paper is to reconstruct the third aspect of Kotarbiński’s conception: methodological reism. Moreover, Kotarbiński’s reism is discussed in a wider context (its sources and inspirations are presented).

Keywords concrete thing –​Tadeusz Kotarbiński –​Lvov-​Warsaw School –​methodological reism –​ ontological reism –​semantic reism

Tadeusz Kotarbiński, a Polish philosopher, a member of the Lvov-​Warsaw School, and a direct student of Kazimierz Twardowski (a founder of the Lvov-​ Warsaw School), was the creator of the thought-​provoking conception of reism. The great resonance of Kotarbiński’s idea is proved by the number of papers concerning reism. Firstly, reism was juxtaposed with a similar conception of Franz Brentano’s (see, e.g., Chrudzimski and Smith 2004 and Kotarbiński 1967); some commenters tracked the roots of reism and found connections with Stanisław Leśniewski’s ontology (see, e.g., Woleński 1987). Secondly, reism was widely discussed as it concerns specific issues (see, e.g., Woleński 1990, Sinisi 1990, Kotarbińska 1967/​1990). The point is that there are two commonly discussed aspects of this conception: ontological and semantic. The aim of this paper is to reconstruct the methodological aspects of reism: its framework of inspirations.

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Methodological Reism –​a Framework1

It is widely assumed that reism, a philosophical conception introduced by Tadeusz Kotarbiński, had two aspects: the ontological and the semantic.2 Sometimes it is also claimed that reism ultimately became a kind of methodological program. The methodological aspect of reism (shortly: a methodological reism) was not explicitly elaborated on or even formulated by Kotarbiński. Thus, it needs to be reconstructed. I have proposed such a reconstruction elsewhere (Chybińska 2018) and in this paper I shall recapitulate my main theses already elaborated upon. Reism was discussed by Kotarbiński in many places (see References) and various aspects of reism changed over time.3 Traditionally, it has been claimed that there are two reistic theses or aspects –​the ontological (about the world) and the semantic (about language). They may be couched in the following way: R1. Ontological thesis: For every object O: if O exists, then O is a concrete object (a thing or a body).4 R2. Semantical thesis: For every sentence S: if S is meaningful, then either there are no abstract names in S or S may be paraphrased so that there would be no abstract names in S.5 1 The text was created as a part of the project „Philosophy from the Methodological Point of View” (2015/18/E/HS1/00487), financed by the National Science Center (Poland). 2 See, e.g., “It is commonplace by now that there are two theories of reism: the semantic and the material theory” (Hiż 1990, 47). 3 “But [reism] has also evolved in one more respect: at first it was claimed that any declarative sentence which cannot be freed from abstract terms is a nonsense; now it is less radical; it does not challenge those who think otherwise, but merely suggests a program. It persuades one to try to do without names that are not names of things when one describes reality, and to always leave in such a description: some name(s) of things” (Kotarbiński 1968/​1968, 458). 4 According to Kotarbiński, people are counted as concrete objects. “Since every object is a thing or a person, and »entity« and »individual« are extensional equivalents of »object,« then to put it briefly, nothing else exists but things and persons  –​of course, if the word »exists« is understood in its fundamental sense. In that fundamental sense: A exists, is the same as: a certain object is A, which is equivalent to the formulations: some entity is A, some (at least one) individuals are A, etc. Each of these formulations can either be shortened into: something is A, or expanded pedantically: for some x, x is A. Now the reist deems that only things and persons exist, since it is true only of things and persons that certain objects are things or persons” (Kotarbiński 1949/​1979, 45). 5 “What is the requirement formulated by that doctrine? This only –​that all ultimate formulations, and hence, also all ultimate explanations of words, should include no nouns and adjectives other than concrete nouns and concrete adjectives. The point is not, of course, that such ultimate explanations should consist of concrete nouns and/​or concrete adjectives

280 Chybińska It has been noted that the theses of reism may not be analyzed with clarity in reistically sense-​ful language (shortly: in reistic language). That is why I will comment on them in language with more ontological commitments. Suppose the universe of objects is divided into concrete ones (things, bodies) and abstract ones; abstract objects are the ones which are not things or bodies, that is, features, relations, states of affairs, events, processes, and so on. Kotarbiński claimed that abstract objects are not genuine objects and he called them “hypostases” (apparent objects). Suppose the universe of names is divided into concrete ones and abstract ones. Let us assume that a name is concrete when it refers only to concrete objects (like “elephant,” “red,” “doctor”) and a name is abstract when it refers only to abstract objects (like “happiness,” “redness,” “love,” “accident”). Kotarbiński stated that abstract names are not genuine names and he called them “onomatoids” (or “apparent names”). Theses R1 and R2 are logically independent: one may accept one of them and, at the same time, reject the second one. In other words, an ontological reist does not have to deem every sentence which contains abstract names or which cannot be paraphrased so that it would not contain abstract names meaningless. And a semantical reist does not have to accept that only concrete objects exist. However, both Kotarbiński and his commenters tried to use R1 to justify R2 and the other way round.6 Kotarbiński did not confine himself to formulating theses about the world and language: he also associated the presence of apparent names with defectiveness (“defects in thinking”). The best method of eradicating such defects in thinking, which originate from wrong suggestions of language, would be to avoid all such stigmatized words. kotarbiński 1949/​1979, 41

alone, to the exclusion of connectives, negation particles, copulas, etc. The essential point is that these ultimate explanations should include no nouns and adjectives other than concrete ones. Instead of »noun or adjective« let us say briefly »term.« The principle of reism can then be formulated as follows: let us see to it that we know how to reduce every statement to a form which contains no other terms than concrete ones” (Kotarbiński 1949/​1979, 42–​43). 6 See “Thus reism, from an ontological doctrine with a semantic spicing, has evolved into a semantic doctrine with an ontological spicing” (Kotarbiński 1968/​1968, 458); “[Kotarbiński] wanted to renounce dealing with traditional ontological or epistemological problems and confine himself to preparing the linguistic tools appropriate to philosophy” (Grzegorczyk 1990, 39). Compare also (Przełęcki 1990).

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Among the aforementioned “defects in thinking” are the unclarity of thinking and the “stigmatized words,” which are apparent names. Sentences with apparent names, which cannot be paraphrased so that there would not be abstract names in them, are nonsensical. On the one hand, Kotarbiński identifies sentences which actually contain abstract names with sentences which can be reistically paraphrased, and calls both of them “nonsensical.” On the other hand, he conditionally accepts sentences with apparent names for their pragmatic merits: The concretist has nothing against metaphorical formulations, against using words in their secondary senses. Without sentences with nouns and adjectives other than the names of things and persons we could not communicate briefly and quickly. In lectures, let us not renounce the apparent names of properties, relations, events, etc. The point is only that we should know in each case how to eliminate any such apparent term, for only then shall we interpret correctly reality, which consists exclusively of things and persons. kotarbiński 1949/​1979, 46

Kotarbiński admits that “presence [of apparent names] may often reduce the length of the statement” (Kotarbiński 1990a, 5). One may use apparent names in “probationary” versions of statements provided that one is able to eliminate them in “ultimate” versions of statements (see section 3); in this account, only sentences which do not have reistic paraphrases are nonsensical, but sentences which can be paraphrased are not. Yet Kotarbiński would perhaps admit that “probationary sentences” are somehow defective and “worse” than sentences which contain only concrete names.7 I will not discuss all the methodological difficulties of reism in this paper (some observations are made in section 3). What should be emphasized is the fact that the concept of clarity, and unclarity respectively, are methodological ones. Clarity does not concern the structure of the world (objects are not clear or unclear) or the reference of language; it is a value of theses,

7 Compare also: “The point is, however, to eliminate names other than the names of objects. Let me hasten with an example of a reistic interpretation of sentences. »Prudence inheres in wisdom« simply means: »Every man who is wise is prudent.« »Bonds of brotherhood related Orestes to Electra« simply means: »Orestes was Electra’s brother.« A reist by no means demands that the use of sentences with abstract expressions like the names of qualities or relations be completely abandoned” (Kotarbiński 1990a, 4).

282 Chybińska utterances, texts or papers. Therefore clarity is a methodological concept characteristic of normative methodology; and for Kotarbiński, who associated the presence of apparent names with the unclarity of utterances, the methodological aspect of reism (or the reistic methodological thesis) may and should be distinguished. As has been already stated, Kotarbiński did not explicitly formulate a methodological thesis of reism. There are several suggestions how it could be reconstructed. I shall begin with presenting some version of the relation between the lack of apparent names and clarity. (i) For every sentence S: S is clear iff S does not contain apparent names. According to (i), the lack of apparent names in a sentence is both a sufficient and necessary condition of the clarity of a sentence. In consequence, (i) states that the class of a clear sentence is equal to the class of sentences containing only concrete names. (ii) For every sentence S: if S does not contain abstract names, S is clear. According to (ii), lack of apparent names is sufficient but not necessary condition of clarity. Thus (ii) allows that some clear sentence may contain apparent names (which would not be consistent with Kotarbiński’s standpoint). Another version assumes that lack of apparent names is a necessary condition of clarity: (iii) For every sentence S: if S is clear, S does not contain abstract names. Finally, one may formulate the relation in a weaker way and assume that the lack of apparent names just favors clarity or that there is concomitance between clarity and the lack of apparent names. (iv) For many sentences S: S does not contain abstract names and S is clear. Let us now consider which of the theses (i)-​(iv) were accepted by Kotarbiński. He would rather refuse (i)  and (ii):  he avowed that there were unclear sentences which contain only concrete names. He would also reject (iv) as well for he believed in stronger relations between the presence of apparent names and unclarity. Therefore he would probably choose the version (iii). However, I believe that what one may find in Kotarbiński’s papers supports (iv): Kotarbiński just provided us with examples of sentences which become clearer after removing ­apparent names. Statements (iii) and (iv) stipulate some relations between the clarity of a sentence and the lack/​presence of abstract names. Meanwhile, methodological reism was thought to be a set of normative postulates expressed as practical directives. Let us observe how statements about relations may be reformulated so that they would be directives. Let us firstly paraphrase (iii) so that it could concern some action: (iii’) If O speaks clearly, then O does not use apparent names.

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Assuming (iii) we may formulate a first version of the postulate of methodological reism (PMR1): PMR1: If O wants to speak clearly, O should not use apparent names. PMR1 can and should be weakened since Kotarbiński conditionally accepted the presence of apparent names. PMR2: If O wants to speak clearly, O should not use apparent names apart from shortened or substitute expressions. Assuming (iv) we may formulate the following postulate: PMR3: If O wants to speak clearly, O should avoid apparent names. PMR1 is the strongest and PMR3 is the weakest version of the postulate of methodological reism. 2

Methodological Reism –​Inspirations

Even though methodological reism generates numerous difficulties, it is still a thought-​provoking conception. In order to better grasp the main idea standing behind methodological reism, it is worth considering the context of its emergence. And the context dates back to the philosophical standpoint of Twardowski, Kotarbiński’s teacher. 2.1 Twardowski’s Influence on His Students Undoubtedly Twardowski broadly influenced his students. This is commonly accepted in the literature: The influence of Kasimir Twardowski on modern Polish philosophy is all-​ pervasive. smith 1989, 313

Twardowski’s scientific attitudes towards metaphysics, semantics and philosophy in general, and his fascination with the absoluteness of truth has had a decisive influence on his students. schaar 2015, 162

Twardowski was a talented teacher […] and he exerted, through his teaching, a powerful influence on generations of young Polish philosophers, such as Jan Łukasiewicz, Kazimierz Ajdukiewicz, Stanisław Leśniewski (who, in turn, taught Alfred Tarski), and Tadeusz Kotarbiński. This influence regarded first of all, matters of method: Twardowski laid emphasis on «small philosophy», namely on the detailed, systematic analysis of

284 Chybińska specific problems –​including problems from the history of philosophy –​ characterized by rigor and clarity, rather than on the edification of whole philosophical systems and comprehensive world-​views. betti 2016

It is especially in relation to the early stages [of the development of reism] that Twardowski’s influence is most strongly felt. smith 1990, 138

Even Kotarbiński agreed with that: The Lvov School is composed of Twardowski and his progeny; The Warsaw School is a triumvirate: Łukasiewicz, Leśniewski, Tarski and their satellites: Łukasiewicz –​a long time direct student of Twardowski; Leśniewski –​also Twardowski’s student; Tarski –​a student of both Łukasiewicz and Leśniewski, so certainly Twardowski’s philosophical grandson. kotarbiński 1952, 180

Kotarbiński was Twardowski’s student: he took part in Twardowski’s lectures while studying in the Lvov University and he also wrote his Ph.D. thesis under Twardowski’s supervision (his dissertation was titled Utylitaryzm w etyce Milla i Spencera [Utilitarianism in Mill’s and Spencer’s Ethics] and it was defended in Lvov in 1912). Therefore, there is no doubt that Kotarbiński was also influenced by Twardowski. The question is how one may characterize this influence. Did Twardowski influence Kotarbiński in a positive or negative way? In the next section I will reconstruct the concept of influence and then try to present the relations between Twardowski’s and Kotarbiński’s conceptions. 2.2 The Concept of Influence The concept of influence is manifold and careful analysis of that concept has been carried out by Anna Brożek (2019). In this section I will refer to the essential claims of her paper. Substantive influence of one person on another is called by Anna Brożek (2019) “resonance.” Resonance may be displayed in two spheres: (a) teaching and (b) views (standpoints). According to Brożek, “in the sphere of the teaching of philosopher A, one may distinguish: –​ »the spirit« of A’s teaching; –​ A’s didactic methods; –​ the contents of A’s teaching” (Brożek 2019).

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In so far as it concerns the sphere of views, it includes: –​ “the conceptual scheme and terminology which A uses; –​ the questions that A poses –​namely A’s problems; –​ the ways how A answers these questions (and justifies them) –​namely A’s methods; –​ the answers given by A –​namely A’s theses and systems of theses”. In short: “A’s influence on other philosophers may concern at least terminology, problems, methods or theses”. Resonance may take place “in three kinds of attitude to influencing spheres: the approval, non-​approval or even disapproval of elements of somebody’s thought. Approval takes place when B accepts A’s concepts/​terminology, problems, methods or theses. Non-​approval occurs when B modifies A’s concepts/​terminology, problems, methods or theses. Finally, disapproval occurs when B rejects A’s concepts/​terminology, problems, methods or theses. If B’s reception of A’s philosophy is favorable, then we say that B is an adherent, follower or epigone of A. If B’s reception of A’s philosophy is not favorable (and consists in modification or disapproval), then B is called »a critic« of A” (Brożek 2019). Clearly, A may be B’s follower in one area and, at the same time, B’s critic in a different one. In the next section I consider which kind of resonance may be detected between Twardowski and Kotarbiński. 2.3 Twardowski’s Influence on Kotarbiński Kazimierz Ajdukiewicz counted Kotarbiński among “the most faithful followers of the program of explaining concepts” formulated by Twardowski (Ajdukiewicz 1937, 252–​253). On the one hand, Kotarbiński admitted that he owed much to his teacher, especially as it concerned methodological matters. In the “Introduction” to his Elementy teorii poznania, logiki formalnej i metodologii nauk [officially ­translated as Gnosiology. The Scientific Approach to the Theory of Knowledge (Kotarbiński 1966)] he wrote: My heartfelt thanks are due to all those who have spared me friendly assistance and those of whose work I have availed myself directly or indirectly. In the first place I wish to name Professor Kazimierz Twardowski, my principal teacher in my university studies. I  should be glad to win his approval for the opinion, expressed in the present book, concerning the scope of the epistemological knowledge required for further teachers. I should also be glad to come close to the model of simplicity, clarity and assimilability of exposition, which I was provided by all his works.

286 Chybińska I should also be glad to contribute to popularizing his didactic, and not only didactic, principle, which recommends that we should be very particular about the meanings of the words we use, and thus avoid vagueness in thought and speech. kotarbiński 1966, xii

On the other hand, Kotarbiński rejected some of Twardowski’s views (in one place, this strong statement can be read: “I did not accept most of Twardowski’s philosophy” [Nie przejąłem na ogół filozofii Twardowskiego] (Kotarbiński 1960)). Kotarbiński was not keen on understanding philosophy as a conglomerate of various disciplines: I missed the vision of philosophy as a firm set of problems (not to mention the solutions of these problems). As a consequence, when I realized that this set is unsound and mosaic I began developing the project to eliminate the term “philosophy” (as long as it reasserts an unsound conglomerate). kotarbiński 1970, 28–​29

Nevertheless, in a subsequent part of the passage quoted above Kotarbiński admits: By and large, it is a matter of terms or classifying [a technical one]; nevertheless thanks to analyzing this technical problem one may come to a positive conclusion: it is worth realizing that the term “philosophy” has many meanings and distinguish three meanings of the term. kotarbiński 1970, 28–​29

This is an illustrative example of the constructive dimension of unfavorable resonance. The starting point is negative: A rejects some of B’s thesis (Kotarbiński rejects Twardowski’s understanding of philosophy). Yet, on the basis of such a critique of B’s views –​and thanks to that critique –​A coins his own meaning of the term, or creates a new concept. It is questionable whether he would come to such a conclusion without the negative starting point. Actually, the most important difference between Twardowski and Kotarbiński lay in their ontological commitments; while Twardowski’s ontology was rich and included such objects as abstract or even universal objects8, Kotarbiński was an ontological monist (reist) and deemed only material things to 8 This is a certain simplification but I have no space to discuss it here in detail.

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exist. Ontological commitments may influence one’s viewpoint in fields other than ontology, e.g., in ethics (an ethicist who claims that values are objective has to accept that such objects as values exist). And as we have already observed, ontological commitments strongly influenced Kotarbiński semantical and methodological views. In the next section I will try to demonstrate that Twardowski indeed contributed to the rise of Kotarbiński’s reism, both in a positive and negative way. This resulted from the fact that, as I am strongly convinced, Twardowski and Kotarbiński shared some methodological principles but differed in other areas. Moreover, it is Twardowski’s influence that justifies the need to distinguish the methodological aspect of reism. 2.4 Twardowski’s Influence on the Rise of Reism 2.4.1 Positive Influence (a) Language as a Tool of Thinking and a Source of Faulty Thinking There are some theses on the background of reism that were common to Twardowski and Kotarbiński. Both of them agreed that language is a tool of thinking and that language shapes or influence one’s thinking. Twardowski noted a direct connection between thinking and speaking: Not only does human speech influence our thinking indirectly, i.e., as a tool thanks to which we become familiar with somebody else’s thoughts. It is the precise form, or structure, of the language which shapes our thinking. Thus our thinking depends on speech. twardowski 1906/​2015

Kotarbiński seemed to follow Twardowski in claiming that quality of speaking is closely connected with quality of thinking: he blamed language for misguiding one’s thinking. As we have seen above, Kotarbiński (1949/​1979) discussed “defects in thinking” which result from “wrong suggestions of language” and the use of apparent names. The best method of eradicating such defects in thinking, which originate from wrong suggestions of language, would be to avoid all such stigmatized words. kotarbiński 1949/​1979, 41

Kotarbiński thought that language may be deceptive:  when one uses some words, he begins to think that the objects, which the words refer to, do exist.

288 Chybińska The category of apparent names is vast: it includes not only the names of abstract objects, but also the names of states of affairs. Once the existence of the alleged objects of such names is admitted, once we agree to the existence of such qualities or relations, human thought is made to wade through a mire of apparent ontological problems. They in turn impose aliteral interpretation of the expressions like “a quality inheres” in an object in the same way as a nail is embedded in a wall: whereas, in point of fact, their meaning is only metaphorical. kotarbiński 1990a, 4

The problem of the deceptive role of language may be illustrated by the following example. If one comments about something by saying “Good riddance to bad rubbish” and expects that in the world there is such an object like a riddance, one is deceived; the source of deception is language. Competent users of language are not likely to be misled: they know that there are idiomatic expressions in language and the words appearing in such expressions are usually not used in their typical meaning. According to Kotarbiński, a similar deception takes place in the case of sentences in which abstract names appear. If one says “All values are objective” and he expects that in the world there is such an object as a value, he is also deceived. Interestingly, Twardowski made a similar observation. Perhaps this was a direct inspiration for Kotarbiński. Twardowski believed that when one utters some word, e.g., a noun, he “[has] in mind something that exists” (Twardowski 1906/​2015). This works properly when words refer to existing objects, like “table,” “bush” or “human being.” The problem may arise when one, adjusted to associating words with the objects, extrapolates this pattern to all the words he uses. [T]‌he majority of nouns in our speech refer to existing people or things: “table,” “bush,” “human being,” “fly,” etc. Not surprisingly, when we use a noun, we have in mind something that exists. By analogy, we do the same when we claim that some event happened “by accident” or that someone “was born with a silver spoon in their mouth” or, in contrary, that they experienced “a chapter of accidents.” We assume then that an “accident,” a “spoon,” a “chapter” in this context also refer to real, existing objects. The influence of the speech on our thinking suggests that there is something more behind it, namely the mental organization of a human being. twardowski 1906/​2015

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Twardowski just observed this tendency and claimed that neither “chance” nor “happiness” refer to existing objects. Yet, he did not formulate any postulates of eliminating such words; he only advises one to be cautious with them. (b) The Principle of Clarity in Scientific Activity and Teaching Secondly, both Twardowski and Kotarbiński accepted the postulate of clarity (of philosophical texts or any utterances). Twardowski explicitly presented his viewpoint in a concise paper “On Clear and Obscure Styles of Philosophical Writing” (Twardowski 1919/​1979). His main thesis was that every philosophical problem may be, and should be, displayed in a clear (understandable9) way. The question then arises […]of whether the style of philosophical writing and/​or speaking must in certain cases be obscure. […] Many people think […] that sometimes even a clear-​thinking philosopher who wishes to express his thoughts as clearly as possible is unable to do so because of the intricacy of the matters and issues he is discussing. twardowski 1919/​1979, 1

[W]‌e may quietly assume that an author who does not know how to express his thoughts clearly does not know how to think clearly either. twardowski 1919/​1979, 2

Kotarbiński followed his teacher in this attitude. As Barry Smith puts it, “it is Twardowski who is more than anyone else responsible for the rigorous thinking and simplicity of expression that is so characteristic of Kotarbiński’s work” (Smith 1990, 137). Kotarbiński reviled the unclarity of utterances and opted for “clearness, distinctness and definiteness in understanding expressions;” moreover, he sought for tools which would help to remove the vices of thinking and speaking. [T]‌he concept of an unclear, indistinct and vague understanding may also be applied to other expressions –​namely those which are not terms. All these shortcomings may be collected under the name of blurred meaning; let us contrast them to clearness, distinctness and definiteness 9 Twardowski did not differentiate between “clear” and “understandable” style.

290 Chybińska in understanding expressions, let us realize that these shortcomings often account for verbal controversies, and finally let us search out some methods of eliminating the shortcomings. Kotarbiński 1966, 25

What is similar in Twardowski’s and Kotarbiński’s attitudes is the “educational aspect”. They both paid attention to teaching their students how to make their ideas as clear as possible. Kotarbiński put it in the following way: [Twardowski] was convinced that someone who thinks in a clear way is able to express his ideas in a simple and clear way. He demanded the realization of this principle from his students, and from himself above all. Strivinging for clarity of thinking and speaking, he employed a method of summarizing. He assumed that in order to summarize someone else’s thought we have to paraphrase it, or put it in our own words; and this cannot be done unless we have a comprehensive understanding of that thought. Yet in order to have a comprehensive understanding of ­someone else’s thought, we have often to clarify it, analyze and paraphrase. kotarbiński 1960, 15

Kotarbiński tried to embody these principles in his own teaching: The responsibilities of the secondary school teacher undoubtedly include the striving to make the pupils understand meanings of words as clearly and as distinctly as possible. This task acquires particular importance in the teaching of those disciplines which in library catalogues are called philosophical. This is so because the principal shortcomings of those disciplines, which also account for protracted controversies –​for example, in epistemology, ontology, general theory of value, etc. –​do not consist in defective observation or experimentation, or in using the wrong forms of inference, but are mainly reducible to the habit of thinking, and correspondingly speaking, vaguely. kotarbiński 1949/​1979, 40

Shortly speaking, the positive influence of Twardowski on Kotarbiński’s reism may be summarized as: (a) perceiving language as a tool of thinking; (b) observing the connection between the vices of speaking and the vices of thinking; (c) respecting the principle of clarity and embodying it both in teaching and in scientific work.

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2.4.2 Negative Influence (a) Different Ontological Commitments As it has been stated before, Kotarbiński disagreed with Twardowski as it concerns ontological commitments. Kotarbiński’s ontology was monistic and simple: he accepted only the existence of things. Other objects, e.g., events, processes, states of affairs, features or mental images, were rejected and called “hypostases.” In contrast, Twardowski’s ontology was rich: he did not reject the existence of abstract or universal entities. Moreover, Twardowski’s other conceptions, like the conception of actions and products, were founded on these commitments. Kotarbiński put it in a simple way: “the reists will find it more difficult to reach an agreement with those ontologists who accuse them of an excessive simplification of reality” (Kotarbiński 1949/​1979, 47). However, I shall immediately note that this was not the case with Twardowski; Kotarbiński praised him for his tolerance and open-​minded approach. (b) Accepting Abstract Entities Twardowski elaborated on mental phenomena or immanent objects; therefore he deemed abstract objects to exist. It is one of the best known positions of psychology […] that every mental phenomenon intends an immanent object. The existence of such a relation is a characteristic feature of mental phenomena which are, by means of it, distinguished from physical phenomena. twardowski 1977, 1

Such a standpoint could not be accepted by Kotarbiński: From the standpoint of reistic somatism, efforts are being made to interpret basic psychological statements as statements about persons (the latter being, of course, identical with certain physical objects). There would be, for instance, such statements as: “X experiences as follows: A is B.” As applied to a given case this would yield: “John sees so: this is black.” kotarbiński 1949/​1979, 49–​50

Kotarbiński also refused the way in which Twardowski understood the concept of concept. His view on the concept of concept (of one’s having a concept) was formulated in the following way: “John has a concept of crime” means “John understands a word »crime« or a synonymous one.” One understands a word if and only if one realizes

292 Chybińska what the word means; therefore one understands a name if and only if one realizes the set of features ascribed to the object to which the name refers. kotarbiński 1974, 39

Kotarbiński claimed explicitly that his stance in this matter differed from the one accepted in Twardowski’s school: My understanding of the concept of concept differs from the approach taken in Twardowski’s school. Twardowski distinguished two ways of presenting an object: direct [naoczne] and indirect [nienaoczne]. I present to myself an object in a direct way when I see something (or remember that I saw it or imagine that I am seeing it). Directly presenting an object results in creating an image [wyobrażenie] of the object […]. According to Twardowski, one may create an image of an object by means of seeing, hearing or touching it, and such a terminological convention differs from a typical one. […] In this case, “one has a concept of some objects” means that one presents to himself this object in an indirect way. kotarbiński 1974, 39–​40

(c) Accepting Abstract Names Twardowski agreed that abstract objects exist; he also accepted abstract names in language. There is a plethora of striking examples in his papers; let us look at one passage: Some objects of knowledge are given to us, more or less directly, by inner and outer experience. These include, above all, the majority of relations, like equality and variety, similarity and opposition, compatibility […], quantitative relations, relations of coexistence and consequence. There are also concepts created on the basis of data provided by both types of experience: the concept of change, substance […] or cause. twardowski 1965

Relations, events, concepts of change or substance and so on were rejected by Kotarbiński and blamed for “logical evil:” Hypostases, equivocation, chaotic utterances, unclear words –​they are expressions of logical evil which semantics contends with. And I distinguish two main sources of hypostases: the presence of so-​called apparent names and the Platonist interpretation of general names. kotarbiński 1974, 16

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They are such words as “smoothness,” “relationship,” “tune,” “shift,” and, generally, what are called names of properties, relations, contents, events, etc. All these nouns and adjectives which have the appearances of concrete terms but are not concrete terms, we take the liberty of calling apparent names or onomatoids. Hence the world of terms is divided into concrete terms (or genuine terms) and apparent terms (or onomatoids), and the principle of reism requires elimination fromall ultimate formulations of all onomatoids, so that only concrete terms –​singular, general and empty –​are left. kotarbiński 1949/​1979, 44

Kotarbiński stated firmly that Twardowski’s dissertation “On Actions and Products” was “a presentation of classical semantics based on hypostases” (Kotarbiński 1952, 181). The aforementioned quotation is important in one more aspect. Kotarbiński admitted that having faced Twardowski’s standpoint on such semantics, he “put much effort into accomplishing the task of discarding deceptive apparent names from one’s worldview” (Kotarbiński 1952, 181). This shows that Kotarbiński’s reism was not only based on rejecting abstract objects and abstract names. It seems that it, at least partially, emerged from Twardowski’s standpoint and his rich ontological commitments or assumptions. 3

Conclusions

Identyfying the kind of influence may be difficult. Apart from the problems discussed in (Brożek 2019), uncovering the real motivations standing behind one’s viewpoint is often loaded with the risk of overinterpretation. Authors rarely declare whom they have been influenced byand tracking influence or an idea’s heritage usually boils down to interpretation and identifying alleged influence. Things go even better when it comes to negative influence. Would A figure out his conception if it was not for B’s work criticized by A? Fortunately, this is not the case with Twardowski and Kotarbiński. Kotarbiński confirmed in many places that he owes much to his teacher and, as I have tried to show, it concerns his reism as well. Let me add that such a way of reism’s emergence was perhaps possible thanks to Twardowski’s pedagogical approach. As Kotarbiński (1993) himself admitted, Twardowski was open and tolerant; he neither promoted his ideas over others’ nor forced his own philosophical solutions on his students. In such an atmosphere Kotarbiński’s reism had a chance to emerge.

294 Chybińska The context of reism, including its sources or inspirations, is worthy of investigations and further considerations. Despite some drawbacks, reism was an original Polish conception; what should be pointed out is its wide scope: it aimed at solving vital questions in the domain of ontology, semantics and methodology. Did it succeed? Let readers judge. Nevertheless, Kotarbiński’s methodological contribution is remarkable. Bogusław Wolniewicz called Kotarbiński “the Reist himself, that grand seigneur of Polish philosophy” and appreciated that “while [Kotarbiński] was there, he gave a warrant by his own person that nothing really bad may happen to that philosophy; the standards will be kept up” (Wolniewicz 1990, 204). Marian Przełęcki expressed his greatest admiration for Kotarbiński’s methodological input in the following words: [Reism is a tool] of explicating complicated conceptions and it demolishes the barricades of verbal disputes. I regret that the content of Elementy [Elements], the exposition of a reistic school of thinking, is nowadays not included as a part of the curriculum of teaching philosophy. Everyone who passed the school of Elementy was marked forever. Members of the “reistic brotherhood” all over the world are recognizable thanks to their common Elementy-​like language and the rules of responsible thinking, speaking and disputing which they all share. przełęcki 2005, 110



Acknowledgements

I would like to express my sincere gratitude to Professor Anna Brożek for her valuable comments and suggestions which helped me to improve this paper.

References

Ajdukiewicz, K. 1937. Kierunki i prądy filozofii współczesnej [Trends and Currents of the Contemporary Philosophy]. In: K. Ajdukiewicz. 1960. Język i poznanie [Language and Cognition]. Vol. I. Warsaw: pwn, 249–​263. Betti, A. 2016. Kazimierz Twardowski. In: Stanford Encyclopedia of Philosophy. Edited by E. N. Zalta, https://​plato.stanford.edu. Brożek, A. 2019. Interpersonal and Intertextual Relations in the Lvov-​Warsaw School. In: Interdisciplinary Investigations into the Lvov-​Warsaw School. Edited by A. Drabarek, M. Radzki and J. Woleński. Palgrave [forthcoming].

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Chrudzimski, A. and B. Smith. 2004. Brentano’s Ontology:  From Conceptualism to Reism. In:  The Cambridge Companion to Brentano. Edited by D. Jacquette. Cambridge: Cambridge University Press, 197–​219. Chybińska, A. 2018. Metodologiczny postulat reizmu. Zarys analizy [Postulate of Methodological Reism. Outline of Analysis]. Filozofia Nauki 26(4): 89–​110. Grzegorczyk, A. 1990. Consistent Reism. In: Kotarbiński … 1990, 39–​45. Hiż, H. 1990. A Note about Reism. In: Kotarbiński … 1990, 47–​52. Kotarbińska, J. 1967/​1990. Puzzles of Existence. In: Kotarbiński … 1990, 53–67. Original­ ly as: Kłopoty z istnieniem. In: Kotarbińska 1990, 332–​350. Kotarbińska, J. 1990. Z zagadnień teorii nauki i teo­rii języka [Some Problems of the Theory of Science and the Theory of Language]. Warszawa: PWN. Kotarbiński: Logic. Semantics and Ontology. 1990. Edited by J. Woleński. Dordrecht: Kluwer Academic Publishers. Kotarbiński T. 1949/​1979. The Reistic or Concretistic Approach. In:  Semiotics in Poland… 1979, 40–​51. Originally as:  O postawie reistycznej, czyli konkretystycznej. Myśl Współczesna 10 (41): 3–​11. Kotarbiński, T. 1952. Odpowiedź [na tekst Bronisława Baczki o poglądach społeczno-​ politycznych Kotarbińskiego”] [Answer [to Bronisław Baczko’s Text on Kotarbiński’s Socio-​Political Views]]. In: Kotarbiński 1993, 170–​182. Kotarbiński, T. 1960. Nauczyciele sztuki nauczania [Teachers of the Art of Teaching]. In T. Kotarbiński. Sprawność i błąd [Efficiency and Error]. Warszawa:  Państwowe Zakłady Wydawnictw Szkolnych, 10–​18. Kotarbiński, T. 1966. Gnosiology. The Scientific Approach to the Theory of Knowledge. Oxford, Wrocław: Pergamon Press, Ossolineum. Kotarbiński, T. 1967. Franciszek Brentano jako reista [Brentano as a Reist]. Studia Filozoficzne 2: 31–​43. Kotarbiński, T. 1968/​1968. Reism: Issues and Prospects. Logique et Analyse xi (44): 441–​ 458. Originally as:  Reizm:  problemy i perspektywy rozwoju. In:  Kotarbiński 1993, 218–​232. Kotarbiński, T. 1970. Jak zacząłem filozofować, jak filozofuję i jak innym radzę to czynić [How I Began Doing Philosophy, How I Do It and How I Suggest Doing It]. In: T. Kotarbiński. Studia z zakresu filozofii, etyki i nauk społecznych [Studies on Philosophy, Ethics and the Social Sciences]. Wrocław: Ossolineum, 25–​33. Kotarbiński, T. 1974. Kurs logiki dla prawników [Course of Logic for Lawyers]. Warsaw: pwn. Kotarbiński, T. 1990a. Philosophical Self-​Portrait. In: Kotarbiński … 1990, 1–​6. Kotarbiński, T. 1993. Dzieła wszystkie. Ontologia, teoria poznania i metodologia nauk [Ouevre. Ontology, Theory of Knowledge, Methodology of Sciences]. Wrocław: Ossolineum.

296 Chybińska Przełęcki M. 1990. Semantic Reasons for Ontological Statements: the Argumentation of a Reist. In: Kotarbiński … 1990, 85–​96. Przełęcki, M. 2005. W dziewięćdziesięcioletnia rocznicę urodzin Tadeusza Kotarbińskiego [On Tadeusz Kotarbiński’s 90th Anniversary]. In: M. Przełęcki, Horyzonty metafizyki [The Horizons of Metaphysics]. Warsaw: Wydawnictwo Naukowe Semper, 110–​112. Schaar, M. van der. 2015. Kazimierz Twardowski: A Grammar for Philosophy. Leiden: Brill. Semiotics in Poland 1894–​1969. 1979. Edited by J. Pelc. Dordrecht, Warszawa: Reidel, pwn Polish Scientific Publishers. Sinisi, V. F. 1990. Kotarbinski’s Theory of Pseudo-​Names. In: Kotarbiński… 1990, 119–​135. Smith, B. 1989. Kasimir Twardowski: an Essay on the Borderlines of Ontology, Psychology and Logic. In: The Vienna Circle and the Lvov-​Warsaw School. Edited by K. Szaniawski. Dordrecht: Kluwer, 313–​373. Smith, B. 1990. On the Phases of Reism. In: Kotarbiński … 1990, 137–​183. Twardowski, K. 1906/​2015. Independence of Thinking. In: K. Twardowski. On Prejudices, Judgments and Other Topics in Philosophy. Edited by A. Brożek and J. Jadacki. Amsterdam: Brill, Rodopi, 81–​90. Twardowski, K. 1919/​1979. On Clear and Obscure Styles of Philosophical Writing. In: Semiotics in Poland… 1979, 1–​2. Originally as: O jasnym i niejasnym stylu filozoficznym (1919). In: Twardowski 1965, 346–​348. Twardowski, K. 1965. Wybrane pisma filozoficzne [Selected Philosophical Papers]. Warszawz: pwn. Twardowski, K. 1977. On the Content and Object of Presentations. A Psychological Investigation. The Hague: Martinus Nijhoff 1977. Woleński, J. 1987. Reism and Leśniewski’s Ontology. History and Philosophy of Logic 7: 167–​176. Woleński, J. 1990. Kotarbiński, Many-​Valued Logic, and Truth. In: Kotarbiński… 1990, 191–​197. Wolniewicz B. 1990. Concerning Reism. In: Kotarbiński… 1990, 199–​204.

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Interdisciplinarity: Analysis of the Concept and Some Examplifications in the Lvov-​Warsaw School Anna Brożek Abstract Recently the term “interdisciplinary” is becoming more and more popular. Despite this, there is no satisfactory definition of “interdisciplinary studies.” That is why both scholars and grant-​funding institutions have no good criteria for distinguishing essential usages of this term from inessential ones. The first part of this paper aims to provide an approximate analysis of the concept of interdisciplinarity, that is a definition indicating some essential examples of interdisciplinarity and listing some exemplifications of research which are not interdisciplinary in any essential sense of the word. Some problems of interdisciplinary research, including the assumed division and hierarchy of sciences as well as the need for a specific language of interdisciplinary research is discussed. In the second part of the paper, Kazimierz Twardowski’s research is discussed as an example of interdisciplinarity in one of the essential senses of the word. His investigations are contrasted with the investigations of those of his students, namely Jan Łukasiewicz and Władysław Witwicki, who became “intradisciplinary” ­researchers.

Keywords Analysis  –​hierarchy of sciences  –​interdisciplinarity  –​intradisciplinarity  –​Jan ­Łukasiewicz –​ Kazimierz Twardowski

1 Introduction1 The first part of my paper concerns the concept of interdisciplinary research. In the second part, I try to show in which sense the research in the Lvov-​Warsaw School falls under the concepts of interdisciplinarity proposed in the first part. 1 The text was created as part of the project „Philosophy from the Methodological Point of View” (2015/18/E/HS1/00487), financed by the National Science Center (Poland).

298 Brożek The term “interdisciplinarity” has been exceptionally fashionable in recent years and, therefore, is often overused. It occurs in various contexts and with various shades of meaning. The fashion for interdisciplinarity manifests itself in the fact that interdisciplinary projects are highly rated by “grant-​providing” institutions. It sometimes happens that it is a sine qua non condition imposed in competitions for research projects. Therefore, the researchers are willing to declare the interdisciplinary nature of their projects having, many a time, no idea in which sense they are using the term and whether or not it relates, in its essential sense, to their enterprises. The problem is that both the researchers and reviewers of research projects do not have any conceptual tools which would serve to distinguish projects or research which are interdisciplinary in the essential sense of this term from the projects or research that are only apparently interdisciplinary (or are interdisciplinary in one of the inessential senses of the word). The question of the distinction between substantial and apparent interdisciplinarity is independent from the question of whether interdisciplinary research is in fact more valuable than monodisciplinary research. I will come back to this problem later. The aims of the paper are constructive. That is why I am not going to present any more or less systematic review of concepts connected to the term “interdisciplinary research”. Let me only note that the frequency of the use of this term is accompanied by great conceptual chaos. Any overview of usages of this term would have to be partial and incomplete and, moreover, it could not lead to formulation of any valuable definition which would be adequate with respect to all occurrences of the word. Instead of such a survey, I propose to order the problem of interdisciplinarity from the point of view of the possible methodological relations between scientific disciplines. From this perspective, I will present some essential examples of interdisciplinarity and some inessential uses of the term. The term “interdisciplinary” is used with respect to the objects of various ontic category (concepts, methods, conferences and even… disciplines). In my opinion, in the most essential sense of the term, it refers to scientific research and its results, namely to theses and sets of theses (i.e., theories). 2

The Aspects of Scientific Disciplines

Relations between scientific disciplines are multilayered and complex. From a methodological point of view, disciplines may be different with respect to: (a) their domain;

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(b) the language in which they refer to domain (a)  (i.e., the conceptual scheme); (c) the problems which concern objects from domain (a) (i.e., the questions which are posed in these disciplines); (d) the knowledge about domain (a) (i.e., the set of accepted theses); (e) the methods of achieving knowledge (d) and the methods of justifying it. It is convenient to call (a)-​(e) “aspects of a given discipline.” For simplicity, I  will interpret these aspects as (respectively) sets of:  objects, expressions, questions, theses and methods. Comparing two disciplines therefore requires determining what relations take place between their aspects. The basic relations between sets are the relations of: (i) identity (X is identical to Y), (ii) inclusion (X is included in Y), (iii) intersection (X intersects with Y), and (iv) exclusion (X is excluded from Y). Any relations (i)–​(iv) may hold between the aspects of any pair of disciplines. For instance, the set of objects of discipline A may be identical to the set of objects of discipline B; it may happen that one of these sets is included in another, that the sets intersect, or that they are excluded. It is similar with other aspects. This gives many possible relations between two disciplines. One may, for instance, imagine disciplines A and B such that: the domain of A is identical to the domain of B, the set of problems of A is included in the set of problems of B, the language of A is included in the language of B; the sets of methods of A and B intersect but the set of their theses are excluded. In what follows, two kinds of relations are especially important: relations between domains and relations between methods. Obviously, to some degree, the dependency between two disciplines in one aspect influence the dependency between them in another aspect. One has to add that the very distinction between scientific disciplines is to some degree problematic. The fact that such-​and-​such research belongs to such-​and-​such discipline is often only conventional and is justified sometimes only institutionally, e.g., by the fact that such-​and-​such research is made in such-​and-​such university department. It is also a fact that usually there are many various sets of theses about the same object. It happens that these theses are mutually excluded, namely they cannot be together true. They are distinguished by talking about different theories. In fact –​every theory may be considered as a separate discipline. The fact that a given set of theories is distinguished as a separate discipline is usually again caused institutionally or genetically (the followers of these theories work in the same faculty or these theories have, metaphorically speaking, some methodologically common antecessor).

300 Brożek 3

The Domain of Scientific Disciplines

Various objects (and objects of various ontological statuses) may be included to the domain of a given scientific discipline. Firstly, objects may be considered to be individuals or sets (or species). For instance, in biology the description of individuals belonging to a given species is a point of departure of the description of a species itself. In history and art theory, one concentrates, first of all, on individuals but the genetic factor is present in the conceptual scheme used in the description. Secondly, the individuals may be more or less complex. An atom, a cancer cell, and a piece of rock are all individuals, as are such complex entities like some ecosystem, some system of law, the culture of a given country… Thirdly, a given scientific research project may be determined, on the one hand, by its material object, i.e., by the set of certain individuals taken in their entirety, and, on the other hand, by its formal object, i.e., by the particular properties or set of properties of the material object of this research. A man as an individual or man as a species is the material object of many disciplines which approach it from different perspectives, that is they have different formal objects. The last difference requires some comment. There is a difference between the individual in a given aspect and the individual together with properties which represent this aspect (for instance, the difference between examining some countries with respect to their legal systems and these countries together with the legal systems which are in force there). This question is of great importance as we will see later. Let us assume that the relation between the domains of two disciplines is the relation of inclusion. We sometimes say that one discipline is a particularization of another; for instance the mechanics of liquids is a particularization of the mechanics of bodies. It seems that the distinction of particularized disciplines is useful only if there is an aspect which may be applied to the particularizing discipline but may not be applied to the particularized one. In order words, the formal object of particularization is richer than the formal object of superior discipline. 4

Relations between the Domains

Having in mind the distinction between the material object of a given discipline and its formal object (the set of aspects with respect to which the material objects are examined), we can say that the following relations between the domains of disciplines A and B are possible (in the diagram: Am –​the material

301

Interdisciplinarity table 16.1 Dependencies between material and formal objects of scientific disciplines

Relations between formal objects of theories A and B Af = Bf Am = Bm Relations between the Am ≠ Bm Am ⊂ Bm material objects Am × Bm of theories A Am ⊃⊂ Bm and B

Af ≠ Bf Af ⊂ Bf

Af × Bf

Af ⊃⊂ Bf

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

object of theory A, Bm –​the material object of theory B, Af –​the formal object of theory A, Bf –​the formal object of theory B):2 Having these things distinguished, we may move to present some essential concepts of interdisciplinarity. (The cells important for our consideration above are bold and placed on a slate background.) 5

Material Interdisciplinarity

The first of these essential concepts is the concept of material interdisciplinary research. A necessary condition of such research is a situation in which the formal domains of two disciplines are excluded, and their material domains are identical or intersect; this situation corresponds to cells (4) or (12) of our diagram. Informally speaking, this occurs in situations when two (or more) disciplines examine –​at least partially –​the same material object but in different aspects. Examples of cell (4): a given country is examined with respect to geography, climate, sociology, ethnology etc; some lake is examined with respect to its geological genesis, its flora and fauna, its ecosystem; the human mind is examined with respect to the physiological processes, its psychical counterparts, its logical representation, etc. Example of cell (12): human beings are subsets of 2 For the sake of simplicity, I’m omitting the situation in which the inclusion takes place in the opposite direction.

302 Brożek the domains of informatics and anatomy –​but these disciplines are interested in different aspects of human beings (their anatomical structure or their communicational activity respectively). Let us now say clearly and firmly: the identity of material object together with the diversity of formal objects is only a necessary but definitely not a sufficient condition of the interdisciplinarity of a certain research. The fact that one or more researchers practicing different disciplines describe their material object in their own respects does not make the “sum” of the results of their research interdisciplinary. It is only the point of departure. In order to make the research interdisciplinary sensu stricto, the results of this research have to be somehow integrated by the scientists practicing it, namely they (or some external researchers) must consciously combine these results with the aid of some logical connections. Usually this consists in explaining a thesis formulated in one discipline by theses formulated in another second discipline or in justifying facts stated in one discipline with facts stated in another. Let us look at some examples taken from the empirical sciences. In the analyzed case, the fact stated in one discipline is explained by the fact stated in the other (usually because it may not be explained inside the first one): The biological fact that there are such-​and-​such plants around the lake Wigry in Poland is explained by the geographical fact that there is such and such climate and geological foundation in this lake. The linguistic fact that there are so many names of snow in Eskimo languages is explained by the climatic conditions of the lives of the users of these languages and the various importance of various kinds of snow for them. The cultural fact of the existence of law which regulates human behavior is explained by the fact that some biological adaptive behaviors exist (cf. Brożek 2015). 6

The Language of Interdisciplinary Research

The concept of interdisciplinarity may be applied only if at the point of departure, there are two separate disciplines using two separate languages. If the interdisciplinary thesis is to explain or justify the facts stated in the first discipline by theses of the other discipline, the interdisciplinary theory has to contain the elements of both initial disciplines. It is clear that interdisciplinary research requires a suitable integrating language: a language that contains parts of languages entering into interdisciplinary relations. Creating an interdisciplinary language has to be distinguished from conceptually reducing one language to another, which consists in reducing the concepts of one discipline to the concepts of another discipline. In the case

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of interdisciplinary language, the initial languages remain separate; the new language only introduces some new predicates referring to relations between the terms of two different disciplines. 7

Formal Interdisciplinarity

The second essential concept of interdisciplinarity is the concept of research in which the material domains of disciplines are excluded and the formal domains are identical or at least intersect; this situation corresponds to cells (13) or (15) of table 16.1. Practically, such research occurs when some aspect of research which is fruitfully applied in one discipline is “moved” (“carried”) to another discipline in which it originally did not occur –​with the intention that it may be equally fruitful there. Such research may be called “formal interdisciplinarity” (in the literature, the term “transdisciplinarity” is also applied in this case). Historical examples of such research are, for instance, the use of the theory of systems originally being fruitfully applied in biology and then being carried to cybernetics, engineering, sociology etc. Another example is game theory –​invented in the context of gambling and then successfully used in economics, sociology, computer science, biology and ethics. Finally –​the conceptual scheme of the theory of evolution, first used in biology, has been transferred to many other disciplines and is sometimes even considered the theory of “everything.” 8

The Language of Formally Interdisciplinary Theories

Let us note that the formal object of a given discipline is connected, even more than the material domain, with other aspects, first of all with conceptual schemes and with the methods used by this discipline. The aspects of research are expressed in a given conceptual scheme and indicate such and such methodological procedures. For instance, if one examines human behavior as a game, one would see “strategies,” “payments” etc. in any behavior. In this perspective, one may see nothing more in the examined domain than is indicated in a given conceptual scheme. The following danger is connected with such a transfer of concepts. If the concepts are to be transferred from one domain to another, they have to be poorer and more general with respect to the initial concepts. In order to transform concepts from the initial domain to another, they have to be devoid of some elements of connotation (they become more general).

304 Brożek 9

The Status of Formal Disciplines

The object of formal disciplines is understood variously and these understandings may be placed between two extremes. On the one hand, they may be interpreted as objectless, “pure” disciplines (at least, as devoid of material object). On the other hand, they are sometimes understood as having a rich object. In what follows, I take the second interpretation as the point of departure. Note the necessary condition for some research to deserve the name “interdisciplinary” (in the strict sense of the word): formal and material objects of one of the “integrated” disciplines should either be identical, crossing, or excluded with the objects of the other –​wherein the objects of at least one pair are not identical. Figuratively speaking, they should be equiponderant in some way: there cannot be a relation of inclusion between them (the appropriate cells are marked on table 16.1 with a light gray background). Given that, what is the status of formal disciplines –​for example mathematics and logic? Let us take an element of the formal object of mathematics –​e.g., the relation/​operation of adding. All beings that are countable or have measurable properties enter into this relation; all these entities belong to the material object of mathematics. NB. If every real being were countable or had measurable properties, then the material object of mathematics would be identified with the entire (real) world. Let us now take an element of the formal object of logic –​for example, the relation of consequence. This relation connects, on the one hand, certain mental entities, scil., beliefs, and on the other hand, some linguistic entities, scil., sentences (expressing beliefs). Thus, part of the material object of logic would be a set of beliefs and sentences. Now let us assume that the material object of physics includes measurable entities, and the material subject of psychology includes, i.a., convictions. The material object of mathematics would then be a superset in relation to the material object of physics (because it cannot be ruled out that at least some mental entities are measurable, and thus belong to the material object of mathematics). These disciplines, however, have different (in particular, mutually exclusive) formal subjects. Therefore, possible interdisciplinary studies linking physics and mathematics would have to be aimed at formulating statements about the relation between these formal objects (e.g., between weight and number –​or between physical interaction and arithmetical addition). On the ground of the made assumptions, the material object of logic would intersect with the material object of psychology (because the latter includes

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beliefs, but not only them). Here, too, possible interdisciplinary research –​psychological and logical  –​would have to be aimed at formulating statements about overlapping relations between, for example, mental associations between beliefs and the logical relation of consequences between them (or between sentences expressing them). If I am not mistaken –​neither interdisciplinary (understood in such –​ the essential  –​way), physico-​logical research, nor so (essentially) understood interdisciplinary psychologico-​logical research has been carried out so far. Let us add that metalogical studies as such are not interdisciplinary: they concern many disciplines (scientifically respected) of science, but the latter are simply material objects of these studies. 10

The Need for Interdisciplinarity

When is interdisciplinary research really needed? Firstly, it happens when the problem formulated in a given discipline may not be solved from the perspective accepted (so far) in this discipline and by the use of methods accepted in it (that is, some questions occur which cannot be exhaustively answered within the existing form of this discipline). Secondly, it may happen that we look for explanations of primitive sentences (or assumptions) which are accepted in a given discipline without justification. Thirdly, interdisciplinary research is needed when we notice the inadequacy of our theory and we see the need to generalize it. 11

Interdisciplinary Research versus Division of Science

As I  have mentioned in the introduction to this paper, existing divisions of science as a whole into particular disciplines are conventional and sometimes controversial. Let us assume, however, counterfactually, that a certain division has been carried out according to a uniform principle and is logically correct (complete and disjoint). It seems that interdisciplinary research in the first sense (that is, material interdisciplinarity) is a form of research at the intersection of adjacent disciplines, and interdisciplinary research in the second sense (that is, formal interdisciplinarity) is a study combining distant disciplines.

306 Brożek It is sometimes said that interdisciplinary research is desired in order to break rigid divisions of disciplines. Interdisciplinary research understood as borderline research may lead to the emergence of a new discipline (this is the case of, for example, cultural studies or cognitive science). In turn, trans-​ domain research may lead to unification. Generally speaking, interdisciplinary research is a somehow transitory stage in the development of science as a whole. Let us put here the question of how interdisciplinary research is related to reduction and naturalization procedures. Interdisciplinary research should be distinguished from research that aims at reducing one discipline to another. In reducing, one states that every thesis of the first discipline is synonymous with a certain thesis of the second discipline, is equivalent to it or at least draws a certain thesis of the second theory. As part of the reduction, one of the disciplines, figuratively speaking, dissolves into the other. However, interdisciplinary studies may but do not have to be the starting point of such a reduction. 12

Traps of Interdisciplinarity

The majority of the traps of interdisciplinary research are connected with the language in which the results of such research is expressed. The necessary features of this language were listed in § 6. Let us repeat once again that domain interdisciplinarity requires the creation of a special language in which interdisciplinary theses may be expressed. In practice, such languages are usually not constructed precisely enough. It happens that the same term is used in different senses in different disciplines. Moreover, many terms used in various disciplines of science also have some meanings in ordinary, loose language. For that reason, one often has the impression that interdisciplinary researchers slip on the surface of many languages, from one sense to another and, as a consequence, the theses formulated by them are also imprecise. The traps of trans-​domain research are equally serious. As I have already said, by moving aspects of one domain to another, the conceptual scheme which serves to examine this aspect has to be appropriately prepared, free from initial associations. In practice, one often forgets about it, particularly in popular presentation of a certain problem. The terms used initially in discipline A are later used in discipline B with the same meaning shade as was used in the original discipline A.

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Using Kazimierz Twardowski’s expression, one may say that, unfortunately, the style of interdisciplinary research is simply obscure. 13

Overuses of the Term “Interdisciplinary”

After presenting two essential concepts (or kinds) of interdisciplinarity, let me move on to some inessential concepts of it. The first overuse of the term “interdisciplinary” was already mentioned (cf. § 5)  but it is worth repeating. Let me stress once again that the research in which no interdisciplinary theses are formulated (or, weaker: if one even does not aim to formulate such theses) is not interdisciplinary sensu stricto. Speaking loosely, in the present specializations two researchers may speak on the materially same subject and not even understanding each other. Secondly, there is no interdisciplilarity (in any essential sense of the word) in research in which one discipline serves as an ancillary discipline to the other (example: history makes use of paleography; paleography somehow “does not exist” without history), or when one discipline is the logical basis of the other (example: the function of formal logic in formalized disciplines; cf. § 9). Thirdly (cf. § 9), the application of a certain formal (logical or mathematical) tool to a certain field does not deserve the name of “interdisciplinary ­research” either. Fourthly, another uninteresting use of the term “interdisciplinary” occurs when an “interdisciplinary conference” or “interdisciplinary grant” or “interdisciplinary project” is understood as a conference or grant/​project in which representatives of different disciplines simply participate, however, without entering into any substantive theoretical relations. Fifthly, there is no need to refer to interdisciplinary research where the initial question can be satisfactorily answered within suitable individual ­disciplines. Sixthly, there is no (in any case –​no longer) interdisciplinarity where one discipline is reduced to another. 14

The Approximate Character of the Analysis of Interdisciplinarity

The characteristics of interdisciplinarity presented here are only approximative: they take into account the undoubted designates of this term and the undeniable non-​designates of the term, but leave a certain degree of blur. There

308 Brożek may be some other concepts of interdisciplinarity that deserve attention. However, I do not have space to discuss them here. From what has been said, the following conclusion may be drawn. It is important for interdisciplinary researchers to indicate precisely what is claimed in interdisciplinary theses (and also in some cases, what is not claimed in them). The point is that interdisciplinary research should actually push science forward rather than becoming a modernized form of dilettantism. 15

Twardowski’s Interdisciplinary Research

And now  –​I  shall make the announced move to the examples within the Lvov-​Warsaw School. Among the historians of philosophy there is a belief that Twardowski’s students were not linked by any specific philosophical ideas and especially not by worldviews. There are few explanations of this fact. One of them was the theoretical program realized by Twardowski. What Twardowski did, falls under the contemporary category of interdisciplinarity. Here are some justifications of this claim. Twardowski’s famous work “On Actions and Products” had a subtitle: “Remarks from the Borderline of Psychology, Grammar and Logic” (Twardowski 1912). Maria van der Schaar comments on this fact in such a way: Twardowski’s philosophical method may be characterized as involving all three disciplines. Logical analysis has to combine psychological analysis with grammatical distinctions. schaar 2015, 24

Others of Twardowski’s works were entitled:  “Psychology vs. Physiology and Philosophy” (Twardowski 1897) and “On the Method of Psychology. An Introduction to the Comparative Methodology of Scientific Research” (Twardowski 1910). In fact, Twardowski examined problems situated on the borders between physiology, psychology, grammar, logic, and philosophy not only in the texts cited above, but in many of his own studies as well as during his university classes. Jan Łukasiewicz described in 1949 Twardowski’s seminar as follows: All the time one talked about whether conviction is a psychical phenomenon of a specific kind or if it is a complex of ideas; all the time one spoke about images, presentations, concepts, their content and object and one

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never knew whether these analyses belonged to psychology, to logic or to grammar. łukasiewicz 2013, 65

Łukasiewicz speaks ironically here and this is because from his perspective, the research provided by Twardowski lacked methodological transparency. However, this description is very well suited to what nowadays is done in cognitive studies and other paradigmatic interdisciplinary research. Only the scope of disciplines and tools is presently different than in Twardowski’s times. Was Twardowski’s research interdisciplinary in the essential sense of the word? If yes, then there should be some interdisciplinary theses formulated and explored by him, theses which join the concepts of different disciplines. In my opinion, the following theses may be considered exemplary interdisciplinary theses which were discussed in Twardowski’s milieu: Man thinks (always or almost always) in words. Judgements are expressed in sentences. One sentence may express many judgements. One judgement may be expressed by many sentences. Presentations are expressed in names. All kinds of actual reasoning are mental operations performed on sentences taking into account the logical (syntactic as well as semantic) relation between these sentences. 16

The Situation of Philosophy in Twardowski’s Time

At the turn of the 19th and 20th century, two trends coexisted with each other within the sciences, philosophy included. The first tendency was of a disintegrative character. From individual disciplines of science  –​with philosophy at the forefront –​gradually more specialized or, as it could be said, more mono-​disciplinary sciences were distinguished. The second tendency was  –​ inversely –​of an integrative character. Philosophy as a whole –​or individual philosophical disciplines or even individual problem groups within these disciplines –​became part of broader interdisciplinary research (in our essential sense). This was a Twardowskian tendency. It should be emphasized that in joining this second tendency, Twardowski was a loyal pupil of Franz Brentano. Only thanks to the atmosphere of specific interdisciplinarity among Brentano’s students –​just as among representatives of Twardowski’s school –​could scholars be found of such diverse theoretical interests and such diverse ways of realizing these interests as: Anton Marty, a philosopher of language; Carl Stumf, an experimental psychologist; Alexius

310 Brożek Meinong, a metaphysician; Sigmund Freud, a psychoanalyst; Edmund Husserl, a phenomenologist; Christian von Ehrenfels, a Gestalt-​psychologist, Rudolf Steiner, a mystic –​and, of course, Twardowski himself. 17

Twardowski’s “Intradisciplinary” Students

Some of Twardowski’ students, just like Brentano’s students, became, let us say, intradisciplinary thinkers: they specialized themselves only in well-​defined directions. The intensive development of these disciplines was a favorable condition of these specializations. The most significant example is the opposition between the two earliest students of Twardowski:  Władysław Witwicki and Łukasiewicz. Witwicki received a Ph.D. in 1901 based on the dissertation A Psychological Analysis of Ambition (Witwicki 1900). Later, as the creator of the conception of cratism, he received a chair of psychology in the University of Warsaw. His psychological analyses of religious beliefs and one of the earliest Polish textbook for psychology are famous examples of his intradisciplinary research.3 Łukasiewicz received a philosophical degree one year later, in 1902, based on the dissertation “On Induction as the Inversion of Deduction” (Łukasiewicz 1903). In the following years, he gradually turned into a mathematical logician and withdrew with his early interests almost completely. He is famous for his three valued logic, inquiries into sentential calculus, and metalogic. He also became a professor in Warsaw but he had the chair of mathematical logic at the Faculty of Mathematics. The differences between Witwicki and Łukasiewicz became so deep that there were few contact points between these representatives of different orientations of Twardowski’s school. The inner tension and animosities which happed in the Lvov-​Warsaw School are presented by Witwicki in his letter to Twardowski dated January 11, 1920. Here, Witwicki answers Twardowski’s letter in which the latter encouraged the former to prepare an article about the weaknesses of Warsaw logicians. Constantly [I hear about] expressions and expressions; and the “word »bibi«”; and if b, then if a, then b; and the principle of reduction and 3 The fact that certain scientists’ research is intradisciplinary should not be confused with the fact that they practice more than one discipline separately. Witwicki did not practice interdisciplinary studies (in the essential sense); however, he practiced, besides philosophy and psychology, for example, the history of art.

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logic without the principle of reduction; and with the theory of types or without the theory of types; products and logical sums; trivalent logics with truth and without the truth; and any group of axioms in which truth is tortured along with common sense. If at least a man would become smarter because of all that, if only scientists could make any use of that. On the other hand, Łukasiewicz’s diagnosis of the situation was the following: Witwicki was my competitor in Twardowski’s seminar. Twardowski tried to treat us equally. It was not easy because we worked in different fields and in different directions. Witwicki has no talent or passion for creative, scientific work. He wrote a psychology textbook, published popular works in philosophy and history of art and he translated Plato. łukasiewicz 2013, 63

This is how Witwicki and Łukasiewicz each saw it from their personal perspectives. However, were they in fact so far from each other? Probably not as far as other psychologists and mathematical logicians could be. The common elements in their thoughts were “interdisciplinary” stamps inherited from Twardowski. By Witwicki, these stamps manifested in striving for conceptual precision and clarity and providing a clear distinction for psychological investigations. One may easily note this by comparing Witwicki’s psychology textbook with contemporary ones: despite Witwicki’s texts not being perfectly clear, they are much clearer than recent ones. Of course, psychology as a discipline has changed a lot since the times of Witiwcki. But the fast development of the domain was not accompanied by equally fast and deep reflection over the language of the discipline. By Łukasiewicz, Twardowski’s interdisciplinary stamps may be easily seen in his concern about providing interpretations for his formal systems. This was also the philosophical genesis of his thought, and even his disappointment of what was done in Twardowski’s seminar; this seminar alone inspired Łukasiewicz to propose the program of axiomatization of philosophy. 18

Conclusions

Let us recapitulate the content of this paper. Firstly, I  have proposed here the approximative characteristics of interdisciplinary research. These characteristics indicate some essential examples of

312 Brożek interdisciplinarity and some counterexamples of research which is sometimes called “interdisciplinary” but does not fall under this concept in any important sense. Secondly, two essential concepts of interdisciplinarity are: the concept of material interdisciplinarity (when the material domains of two disciplines are identical or intersect but formal domains are excluded) and formal interdisciplinarity (when material domains are excluded but formal are the same). Thirdly, a necessary condition of material interdisciplinarity is that there are some theses which connect concepts of the initial disciplines. Fourthly, interdisciplinary research requires special languages in order to avoid conceptual misunderstandings. Fifthly, interdisciplinary research assumes that there are some borders between disciplines and that there is a certain rigid division of sciences. Interdisciplinary research may lead to some changes in this division. In particular, it may be a transitory stage in the process of the emergence of a new discipline or, to the contrary, in the process of unification. Finally, I have tried to show that Twardowski’s philosophical investigations fall under the concept of material interdisciplinary research. This is one of the reasons that Twardowski inspired so many different thinkers and that his students went in so different theoretical directions. In fact, many of them became monodisciplinary researchers. Witwicki and Łukasiewicz serve as good ­examples.4 In the end, let us come back to the question of whether interdisciplinary studies are to be better, more valuable that intradisciplinary ones. I  see no reason for such a claim. As I have tried to show, interdisciplinary research is something transitory in the development of science as a whole. Of course, sometimes we need such transitions. But what we need constantly is intradisciplinary research and narrow, specialized disciplines.

References

Brożek, B. 2015. O naturalizacji prawa [On Naturalization of Law]. In: J. Stelmach et al. (eds.). 2015. Naturalizm prawniczy. Interpretacje [Legal Naturalism. Interpretations]. Kraków: Wolters Kluwer, 24–47.

4 Let me add applications of the theory of actions-​products to many disciplines and Ajdukiewicz’s analysis of transcendental idealism.

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Łukasiewicz, J. 1903. O indukcji jako inwersji dedukcji [On Induction as the Inversion of Deduction]. In: J. Łukasiewicz. 1998. Logika i metafizyka [Logic and Metaphysics]. Miscellanea. Warszawa: Wydział Filozofii i Socjologii UW, 203–​227. Łukasiewicz, J. 2013. Pamiętnik [Memorials]. Warszawa:  Wydawnictwo Naukowe ­Semper. Schaar, M.  van der. 2015. Kazimierz Twardowski:  a Grammar for Philosophy. Amsterdam: Rodopi. Twardowski, K. 1897. Psychology vs. Physiology and Philosophy. In:  Twardowski 1999, 41–​64. Twardowski, K. 1910. On the Method of Psychology. An Introduction to the Comparative Methodology of Scientific Research. In: K. Twardowski. 2014. On Prejudices, Judgments and Other Topics in Philosophy. Amsterdam: Rodopi, 61–72. Twardowski, K. 1912. Actions and Products. Remarks from the Borderline of Psychology, Grammar and Logic. In: Twardowski 1999, 103–​132. Twardowski, K. 1999. On Actions, Products and Other Topics in Philosophy. Amsterdam: Rodopi. Witwicki, W. 1900. Analiza psychologiczna ambicji [Psychological Analysis of Ambition]. Przegląd Filozoficzny iii (4): 26–​49. Witwicki, W. 1920. Letter to Kazimierz Twardowski, dated January 11. [Unpublished.].

Index of Names Adler, Friedrich 80 Adorno, Theodor Wissengrund 81, 98 Ajdukiewicz, Kazimierz 45, 47, 49–​51, 53, 54, 56, 65, 67, 68, 73, 246, 254, 255, 269–​272, 274, 274, 283, 285, 294 Ajdukiewicz, Maria 255 Albert, Hans 81, 98 Andersen, Hanne 184, 194 Angelelli, Ignacio 226 Anscombe, Gertrude Elizabeth Margaret 179 Aristotle (Stagirite) 95, 128, 129–​131, 134, 145, 147, 148, 165–​170, 177, 179, 196, 208, 219, 233, 234, 237, 248, 269, 270 Armstrong, David 26 Artemov, Sergei 175, 178 Audi, Robert 146 Augustin, Saint 221 Avenarius, Richard 80 Azzouni, Jody 189, 192 Backhaus, Jürgen 83, 98 Baczko, Bronisław 295 Baker, Alan 184–​186, 192 Barnes, Jonathan 177 Barnett, Dene Ira 227 Baron, Simon 185, 192 Bartoszek, Adam 115, 122 Barwise, Jon 189, 190 Bassler, O. Bradley 189, 192 Baudrillard, Jean 82 Bealer, George 17, 24, 27, 38 Beaney, Michael 258, 275 Będkowski, Marcin 1–​6, 56–​74, 257–​277 Beets, François 227 Bekker, Ernst Immanuel 79 Below, Georg von 78, 79, 85 Berger, Stefan 124 Berkeley, George 90 Betti, Arianna 233, 237, 268, 275, 284, 294 Béziau, Jean-​Yves 165, 178 Bidwell, George 159 Blair, John Anthony 41, 42, 54 Blaustein, Leopold 242, 244, 245, 255 Bloch, Marc 84

Bocheński, Józef M. 47, 49, 54, 137, 178, 196, 204, 226, 235, 270, 274, 275 Böckler, Georg Andreas 171 Bogalska-​Czajkowska, Ewa 115, 122 Bolzano, Bernard 275 Bondyra, Krzysztof 122 Boole, George 200 Booth, Robert 39 Borkowski, Ludwik 179, 238 Boršić, Luca 179 Borsuk, Karol 185, 186 Brandl, Johannes L. 255, 268, 275, 277 Brentano, Franz 14, 18, 25, 38, 64, 138, 208, 230, 274, 278, 295, 309, 310 Bricmont, Jena 82, 95, 100 Bridgmann, Percy Williams 90, 96 Broad, Charlie Dunbar 152, 153 Brouwer, Luitzen Egbertus Jan 210 Brown, Sable 158 Brożek, Anna 1–​6, 14, 38, 55, 56–​74, 257, 273, 275, 284, 285, 293, 294, 296–​313 Brykczyński, Piotr 273, 275 Brzechczyn, Krzysztof 3, 6, 101–​125 Brzeziński, Jerzy 123 Buchowski, Michał 123 Buczkowski, Piotr 109, 111, 112, 114, 115, 117, 122, 123 Bühler, Karl 246, 255 Burbelka, Jolanta 106–​109, 123 Burge, Tyler 31 Burke, Peter 98 Burwood, Stephen 127, 147 Butler, Jimmy 30 Cappelen, Herman 10, 12, 20, 21, 26, 31, 35, 36, 38 Carey, Susan 19, 38 Carnap, Rudolf 81, 95, 97, 98, 153, 158, 159, 195, 197, 198, 204, 205, 210, 226 Carretero, Mario 124 Carrier, Martin 93, 100 Cave, Peter 157 Chalmers, David 31 Chickering, Roger 85, 98 Childers, Timothy 237

316  Chrudzimski, Arkadiusz 275, 278, 295 Chrysippus 233 Church, Alonso 226 Chwistek, Leon 155, 218 Chybińska, Alicja 1–​6, 56–​74, 257, 278–​296 Clark, Eve Vivienne 19, 38 Cohen, Herman 128, 129 Cohen, Robert S. 98 Colyvan, Mark 185, 186, 192 Cometti, Jean-​Pierre 228 Comte, August 143, 144 Copeland, Brian Jack 230, 235, 237 Corcoran, John 228 Costa, Newton da 203 Crocco, Gabriella 168, 178 Curry, Haskell Brooks 168 Czajkowski, Wojciech 115, 122, 123 Czermak, Johannes 204 Czeżowski, Tadeusz 13, 14, 20, 38, 51, 56, 62–​65, 73, 146, 151, 155, 158, 159, 256, 270, 272, 275 Dahms, Hans-​Joachim 98 Dahrendorf, Ralf 98 Daly, Chris 186, 193, 274, 276 Dąmbska, Izydora 127, 146, 148 Darwin, Charles 85 Davidson, Donald 94 Davis, Martin 179 Dawson, John W. Jr. 189, 193 Dedekind, Richard 212 Deleuze, Gilles 82 De Morgan, Augustus 48 DePaul, Michael Raymond 15, 38, 39 Descartes, René 32, 96, 134, 137 Detlefsen, Michael 209, 226 Deutsch, Max 11, 12, 14, 15, 25, 28, 30, 31, 38 Devitt, Michael 31, 38 Dewey, John 92, 95, 96, 98 Dilthey, Wilhelm 78, 88 Diodoros 236, 238 Donnellan, Keith 25 Drabarek, Anna 294 Droysen, Gustav 78 Duhem, Pierre 90, 95, 96 Dummett, Michael 135 Dunbar, Robin Ian MacDonald 21, 38 Duns Scotus 203 Dyck, Maarten van 100

Index of Names Dygasiński, Adolf 271 Dziemidok, Bohdan 127, 146 Ehrenfels, Christian von 310 Einstein, Albert 88, 90, 96 Engels, Friedrich 106 Euclid 169 Evans, Gareth 26, 31, 38 Fallis, Don 189, 193 Fayerabend, Paul 81, 87, 89, 95, 96, 98 Feigl, Herbert 87, 95 Feferman, Solomon 178 Fellner, Günter 86, 96, 98 Field, Hartry 182, 193 Fields, John Charles 188 Findlay, John 230 Fisette, Denis 38 Fitting, Melvin 178 Foley, Richard 28, 38 Font, Joseph Maria 237 Frank, Philipp 80, 90, 91, 96–​98 Frankfurt, Harry 82, 98 Frege, Gottlob 13, 135, 166–​168, 178, 195, 196, 198, 204, 205, 208, 216, 220, 225, 226 Fréchette, Guillaume 38 Freud, Sigmund 310 Fumerton, Richard 16, 21, 22, 38 Gabbay, Dov 205 Galileo, Galilei 64 Garrido, Ángel 238 Gasparski, Wojciech 276 Geach, Peter Thomas 157, 159, 238 Genzen, Gerhard 209 Gerhardt, Ute 78, 93, 98 Gettier, Edmund 11, 24–​26, 38 Ghiselin, Michael T. 123 Giedymin, Jerzy 275 Gilbert, Paul 127, 147 Gillet, Eric 227 Głąbik, Czesław 147 Gochet, Paul 227 Gödel, Kurt 31, 167, 168, 173, 177–​179 Goldman, Alvin 24, 39 Goodman, Nelson 225, 226 Gopnik, Alison 10, 12, 22, 24, 39 Greenberger, Daniel 99 Grever, Maria 124

317

Index of Names Griesemer, James Richard 102, 121, 123 Grimshaw, Mike 235, 237 Groarke, Louis 50, 53, 54 Grzegorczyk, Andrzej 226, 280, 295 Guyer, Paul 205 Habermas, Jürgen 81, 98 Hacking, Ian 151, 151, 159 Hájek, Petr 237 Hales, Thomas Callister 185, 193 Hamami, Yacin 189, 193 Hanna, Robert 195, 196, 205 Hansen, Reginald 83, 98 Harley, David 179 Hartmann, Ludo Moritz 78, 85, 86, 98 Hasle, Per F.V. 235, 237 Haussmann, Thomas 95 Hayek, Friedrich August von 82, 83, 96 Hegel, Georg Wilhelm Friedrich 196 Heijenoort, Jean van 178 Helling, Ingeborg 92, 98 Hempel, Carl Gustav 79, 86, 95, 98 Hermes, Hans 205 Hilbert, David 166, 178, 189, 190, 193, 210 Hintikka, Jaakko 169, 178 Hiż, Henryk 279, 295 Hobsbawm, Eric 84, 98 Höfler, Alois 261, 270, 274, 276 Horkheimer, Max 80 Horecka, Aleksandra 5, 6, 241–​256 Hume, David 90, 95 Husserl, Edmund 14, 18, 25, 39, 208, 268, 273, 310 Iggers, Georg 84, 99 Ivanyk, Stepan 1–​6, 56–​74, 257 Jacquette, Dale 295 Jadacki, Jacek Juliusz 2, 41–​55, 57, 73, 127, 134, 138, 139, 146, 147, 179, 273, 275, 276, 296 Jadczak, Ryszard 132, 147 Jäger, Friedrich 99 Jaeger, Werner 177 Jan Kazimierz 246, 255 Jaśkowski, Stanisław 203, 209 Jaworska, Krystyna 147 Jenkins, Carrie S. Ichikawa 12, 30, 35, 36, 39 Jenkinson, A.J. 177 Jevons, William Stanley 271

Johnson, Raph Henry 41, 42, 54 Jordan, Zbigniew Antoni 153, 159, 210, 227 Jung, Gertraud 99 Kahle, Reinhard 189, 190, 193 Kambartel, Friedrich 205 Kamiński, Stanisław 259, 260, 276 Kant, Immanuel 88, 90, 91, 93, 95, 128, 129, 134, 137, 166, 168, 178, 195, 196, 198, 204, 205 Kaplan, David 26 Kaufmann, Felix 79, 92, 94, 98 Kaulbach, Friedrich 205 Kauppinen, Antti 10, 39 Kautski, Karl 106, 123 Kazakov, Yevgeny 178 Kearns, John T. 206, 210, 211, 218, 222, 226 Kelsen, Hans 79, 92 Kennedy, Juliette 168, 179 Kenny, Antony J.P. 238 Kieseppä, Illkka 99 Kijania-​Placek, Katarzyna 277 Kim, Jaegwon 22, 39 Kisielewski, Stefan 130, 132, 134, 147 Kitcher, Philipp 87, 97, 99, 100 Klawiter, Andrzej 113–​115, 117, 123, 124 Kleszcz, Ryszard 3, 6, 126–​149 Knobe, Joshua 30 Kocka, Jürgen 84 Koertge, Noretta 96, 97, 99 Komorowska-​Mach, Joanna 11, 39 Kornblith, Hilary 13, 21, 29, 39 Kostić, Daniel 184, 193 Kotarbińska, Janina 6, 278, 281, 295 Kotarbiński, Tadeusz 4–​6, 43, 50, 54, 56, 67–​69, 73, 150–​152, 156, 159, 210, 219, 226, 233, 270–​272, 276, 278–​296 Kovač, Srećko 4, 165–​179, 196, 204, 205 Kraft, Victor 94 Kripke, Saul Aaron 25, 31 Křiž, Anronin 237 Krzywicki, Ludwik 106, 124 Kuhn, Thomas 81, 95, 96 Kuipers, Theo A.F. 123 Künne, Wolfgang 152, 159 Kusch, Martin 97 Lacan, Jacques 82 Lachmanowa, Irena 158, 159

318  Lakatos, Imre 81, 189 Lamprecht, Karl 78, 79, 84, 85, 94, 98 Lange, Marc 184, 185, 193 Langford, Simon 186 Łastowski, Krzysztof 104, 109, 110, 123, 124 Latour, Bruno 82 Leibniz, Gottfried Wilhelm 134, 169 Lenin –​ cf. Vladimir Ilyich Ulyanov  Leonardo da Vinci 171 Lepenies, Wolf 81, 99 Leśniewski, Stanisław 5, 6, 71, 155, 206–​228, 233, 269, 271, 278, 283, 284 Lewis, David Kellogg 20, 39 Lewy, Casimir (Kazimierz) 3, 4, 6, 150–​160 Liebig, Justus 89 Liggins, David 186, 193 Linsbichler, Alexander 83, 99 Lorenz, Chris 102, 103, 124 Lu-​Adler, Huaping 195, 196, 205 Ludwig, Kirk 10, 16, 23, 34, 36, 39 Łukasiewicz, Jan Leopold 4–​6, 15, 39, 46, 47, 51, 54, 56, 57, 62–​65, 69–​73, 137, 138, 147, 165, 167–​169, 171, 172, 177, 179, 200, 201, 208, 218, 220, 227, 229–​238, 257–​270, 272–​276, 283, 284, 297, 308–​313 Łukomska, Agata 257 Luschei, Eugene C. 211, 227 Macdonald, Margaret 159 MacFarlane, John 195–​197, 204, 205 Mach, Ernst 80, 86–​91, 95, 96, 98–​100 Machery, Edouard 11, 39 MacIntyre, Alasdair 94 Mahrburg, Adam 128, 131 Majer, Ondrej 237 Małkiewicz, Andrzej 115, 122 Mallon, Ron 39 Mancosu, Paolo 186, 188, 193 Mannheim, Karl 80 Marty, Anton 208, 309 Marx, Karl 80–​82, 84, 86, 101, 103, 106, 118, 121–​125 Massonius, Marian 134 McCall, Storrs 179, 227 McFalls, Laurence H. 99 Meinecke, Friedrich 78, 85 Meinong, Alexius 230, 238, 276, 309/​310 Menger, Carl 77, 78, 82 Mervis, Carolyn B. 35

Index of Names Messner, Johannes 79, 100 Michalski, Konstanty 128 Miéville, Denis 219, 227 Mill, John Stuart 95, 144, 208, 285, 264, 268–​271, 276, 284 Minari, Pierluigi 172, 175, 176, 179 Minio-​Paluello, Lorenzo 177 Mises, Richard von 79, 82, 91, 92, 94, 100 Mises, Ludwig von 83, 92, 100 Moore, George Edward 72, 133, 135, 150, 152, 158, 159, 257, 258, 274 Mordell, Louis 188, 193 Morgan, Lewis 106 Mukařowsky, Jan 242 Mulligan, Kevin 228 Müller, Johannes 89 Murawski, Roman 235, 238 Natorp, Paul 128, 129 Neurath, Otto 80, 83, 94, 96, 97 Newman, John Henry 152 Newton, Isaac 44, 45, 54 Nichols, Shaun 39 Nietzsche, Friedrich 90 Nowaczyk, Adam 72, 73 Nowak, Leszek 3, 6, 101, 103, 106, 114, 115, 117–​125 Nowakowa, Izabela 106, 125 Nowicki, Andrzej 133, 147 Occam, William 89 Odrowąż-​Sypniewska, Joanna 276 O’Neil, M.P. 227 Oppenheim, Paul 79, 86 Ossowski, Stanisław 5, 241, 255, 256 Overgaard, Søren 127, 147 Pacuła, Stanisław 127 Panasiuk, Ryszard 125 Panza, Marco 189, 193 Paprzycka, Katarzyna 30, 39, 123 Paprzycki, Marcin 123 Parsons, Talcott 93 Pascal, Blaise 132–​134, 148 Paśniczek, Jacek 6 Patterson, Douglas 209, 227 Peeters, Marc 210, 227 Pelc, Jerzy 135, 136, 147, 242, 242, 248, 255, 276, 277, 296

Index of Names Piaget, Jean 143, 147 Piecha, Thomas 193 Pilot, Harald 98 Pincock, Christopher 184, 193 Pinder, Chris 159 Pinna, Giovanni 123 Plato 11, 36, 129, 134, 229, 235, 236, 261, 264, 265 Plourde, Jimmy 228 Poincaré, Henri 90, 91, 96 Popper, Karl Raimund 79, 81, 83, 90, 92, 94–​98 Prior, Arthur Norman 5, 229–​231, 233–​238 Przełęcki, Marian 280, 294, 296 Przybysz, Piotr 123, 125 Pust, Joel 24, 38 Putnam, Hilary 11 Quine, Willard van Orman 16, 95, 96, 156, 180–​183, 193, 216, 234 Radzki, Mateusz 294 Ramsey, William 28, 39 Rav, Yehuda 189, 190, 193, 194 Räz, Tim 185, 194 Recanati, François 26, 31, 39 Reichenbach, Hans 81, 91, 95, 99 Reisch, George 96, 99 Reiter, Wolfgang 99 Rej, Mikołaj 151 Resnik, Michael David 182, 194 Reutlinger, Alexander 184, 194 Rey, Abel 90 Richard, Sébastien 5, 6, 206–​228 Rickert, Heinrich 78, 93 Rickey, V. Frederick 228 Ringer, Fritz 78, 93, 94, 99 Riška, Augustín 232, 238 Rojszczak, Artur 276 Rosch, Eleanor 35 Ross, David 177 Rota, Gian-​Carlo 188, 194 Routley-​Sylvan, Richard 66, 73 Rowbottom, Darrell Patrick 39 Rubens, Robert 100 Rüsen, Jörn 84, 99 Russell, Bertrand 25, 90, 155, 179, 206, 212–​218, 220, 221, 225, 227 Rybařiková, Zuzana 5, 6, 229–​238

319 Salamucha, Jan 169, 179 Salmon, Wesley 79, 87, 94, 99, 100 Sarton, George 100 Sato, Masayuki 102, 125 Savonarola 275 Schaar, Maria van 274, 276, 283, 296, 308, 313 Scheler, Max 80 Schlick, Moritz 79, 88, 90, 91, 99 Schlipp, Paul Arthur 204 Schmitt, Carl 79 Schmoller, Gustav 77–​79, 82, 83 Schroeder, Ernest 223, 226 Schroeder-​Heister, Peter 193 Schurz, Gerhard 93, 100 Schütz, Alfred 93 Schwitzgebel, Eric 10, 12, 22, 24, 39 Searle, John Rogers 15, 18, 19, 26, 39, 40 Selberg, Atle 188 Sellars, Wilfrid 204 Shafir, Eldar 28, 40 Shapiro, D. 178 Shapiro, Stewart 194, 226 Simmel, Georg 93 Simons, Peter 225, 228, 230, 234, 238 Simpson, Stephen 190, 194 Sinisi, Vito S. 278, 296 Śliwa, Paweł 122 Słupecki, Jerzy 220, 228, 237, 276 Smeaton, Amethe 226 Smith, Barry 278, 284, 289, 295 296 Śniadecki, Jan 131 Snow, Charles Percy 80/​81, 100 Soames, Scott 274, 277 Sobociński, Bolesław 218, 219, 222, 223, 226, 228 Socrates 1, 10, 12, 203, 216, 217, 222 Sokal, Alan 82, 95, 100 Sorensen, Roy 23, 27, 40 Sosa, Ernest 24, 29, 35, 40 Spadoni, Carl 171, 179 Spencer, Herbert 144, 285 Spinoza, Baruch 134, 137 Srzednicki, Jan T. 228 Stadler, Friedrich 3, 38, 55, 77–​100 Stagirite –​ cf. Aristotle  Stammler, Rudolf 79 Stanosz, Barbara 72, 73 Stegmüller, Wolfgang 95 Steinberger, Florian 195, 197, 205 Steiner, Rudolf 310

320  Stelmach, Jerzy 312 Stich, Stephen 39 Strawson, Peter Frederick 25, 28, 29, 37, 40, 157, 160 Striker, Gisela 178 Stumf, Carl 309 Sukale, Michael 100 Surma, Piotr 238, 276 Surma, Stanisław J. 227, 232 Świętorzecka, Kordula 4, 177, 179, 195–​205 Szabó Gendler, Tamar 34, 40 Szaniawski, Klemens 238, 296 Szczepański, Marek Stanisław 122 Szubka, Tadeusz 3, 6, 150–​160 Tałasiewicz, Mieszko 2, 9–​40 Tarski, Alfred 153–​156, 158, 159, 165, 168, 178, 206–​208, 227, 276, 283 Tatarkiewicz, Władysław 3, 6, 126, 127, 128, 130–​148, 248, 255, 256 Thomas, Ivo 178, 204 Thomas, Saint 134 Thomson, Judith Jarvis 33, 40 Tiles, Mary 196, 205 Tolley, Clinton 195, 196, 205 Topitsch, Ernst 79, 100 Topolski, Jerzy 102, 125 Traczykowski, Dominik 1–​6, 56–​74, 257 Transwell, F. 189, 194 Turing, Alan 4, 165, 168–​171, 177, 179 Twardowski, Kazimierz 5, 6, 14, 18, 25, 40, 41, 51, 55–​57, 64–​66, 74, 128, 129–​132, 137, 138, 230, 241, 243, 255, 261, 262, 267–​270, 273, 275–​277, 278, 283–​293, 296, 297, 306–​313 Ulam, Stanisław 185, 186 Ulyanov, Vladimir Ilyich (Lenin) 80, 91 Urquhart, Alasdair 157, 160 Verantius, Faustus –​cf. Faust Vrančić  Vernant, Denis 209, 216, 228 Virilio, Paul 82 Vrančić, Faust (Faustus Verantius) 171 Wallis, Mieczysław 5, 6, 241, 242, 244–​249, 256 Weber, Max 78, 79, 84, 86, 88, 92–​94, 99, 100

Index of Names Wehler, Ulrich 84 Weryho, Władysław 131 Weyl, Hermann 97 Whitehead, Alfred North 212–​217, 227 Williamson, Timothy 12, 16, 17, 19, 20, 23, 26, 32, 35, 37, 40 Windelband, Wilhelm 87, 152 Wisniewski, Edward Joseph 12, 28, 40 Wisdom, John 150 Wiśniewski, Ryszard 127, 133, 138, 147, 148 Wittgenstein, Ludwig 152, 165, 170, 171, 179 Wittkau, Annette 83, 100 Witwicki, Władysław 5, 241, 242, 244, 247, 297, 310–​313 Wójcicki, Ryszard 199, 200, 203, 205 Wojtasiewicz, Olgierd 159, 227 Wójtowicz, Krzysztof 4, 180–​194 Woleński, Jan 55, 66, 74, 127, 138, 148, 149, 208, 210, 228, 231, 238, 256, 277, 278, 294, 296 Wolniewicz, Bogusław 294, 296 Wolff, Christian 196 Wood, Allen 205 Woods, John 205 Woodger, Joseph Henry 178, 228 Woźniczka, Maciej 147 Wright, Georg Henrik von 95, 100 Wright, James D. 125 Wybraniec-​Skardowska, Urszula 238 Yablo, Stepen 186, 194 Young, J. Michael 205 Zalta, Edward N. 178, 193, 237, 238, 275, 295 Zamoyski, A 147 Żarnecka-​Biały, Ewa 169, 179 Zawiła-​Niedźwiecki, Janusz 34, 40 Zawirski, Zygmunt 276 Zegzuła-​Nowak, Joanna 138, 149 Zeilinger, Anton 99 Zermelo, Ernst 221 Ziegenfuss, Werner 99 Ziemacki, Józef Kazimierz 132 Zilsel, Edgar 80 Ziółkowski, Andrzej 11, 34, 40 Znamierowski, Czesław 271