Avicenna's Theory of Science: Logic, Metaphysics, Epistemology

Avicenna’s Theory of Science

The publisher and the University of California Press Foundation gratefully acknowledge the generous support of the Joan Palevsky Imprint in Classical Literature

THE BERKELEY SERIES IN POSTCLASSICAL ISLAMIC SCHOLARSHIP

Series Editors

Asad Q. Ahmed, University of California, Berkeley

Margaret Larkin, University of California, Berkeley

1. The Light of the World: Astronomy in al-Andalus, by Joseph Ibn Naḥmias and edited, translated, and with a commentary by Robert G. Morrison

2. Language between God and the Poets: Maʿnā in the Eleventh Century, by Alexander Key

3. Reason and Revelation in Byzantine Antioch: The Christian Translation Program of Abdallah ibn-al-Faḍl, by Alexandre M. Roberts

4. Avicenna’s Theory of Science: Logic, Metaphysics, Epistemology, by Riccardo Strobino

Avicenna’s Theory of Science

Logic, Metaphysics, Epistemology

Riccardo Strobino

UNIVERSITY OF CALIFORNIA PRESS

University of California Press

Oakland, California

© 2021 by Riccardo Strobino

Cataloging-in-Publication Data is on file at the Library of Congress.

ISBN 978-0-520-29747-0 (cloth : alk. paper)

ISBN 978-0-520-96981-0 (ebook)

Manufactured in the United States of America

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To Tony Street

μέγα βιβλίον μέγα κακόν

—CALLIMACHUS, FR. 465 PFEIFFER

Contents

List of Illustrations

Acknowledgments

Note on Citation, Transliteration, and Translation

Introduction

PART I. SCIENTIFIC KNOWLEDGE AND SCIENTIFIC INQUIRY

1. Conception and Assertion

2. Scientific and Nonscientific Assertions

3. The Types and Order of Scientific Inquiry

PART II. THE ORGANIZATION OF SCIENTIFIC KNOWLEDGE

4. The Internal Structure of a Science

5. Division and Hierarchy of the Sciences

PART III. MODALITY

6. Necessity and Scientific Reasoning

7. Scientific Attributes

8. The Logic of Essence

PART IV. CAUSALITY AND EXPLANATION

9. Causal and Noncausal Demonstration

10. Explanation across Sciences, Subordination, and the Transfer of Demonstration

11. The Four Causes in Demonstration and Definition

PART V. DEFINITION

12. Definition and Description: Structure and Types

13. The Epistemology of Essence

Conclusion

Appendix A. Conditions of Certainty

Appendix B. The Logic of Scientific Reasoning

Appendix C. A Map of Kitāb al-Burhān (Book of Demonstration)

Appendix D. English-Arabic Glossary

Notes

References

Index of Subjects

Index of Lemmata

Index of Avicenna’s Works with Passages Cited

Index of Aristotle’s Works with Passages Cited

Index of Other Authors’ Works with Passages Cited

Illustrations

FIGURE

1. Generality and explanation with multiple chains of middle terms

TABLES

1. Types of scientific knowledge

2. Prior and better known

3. Assertion, belief, and deduction

4. Principles of scientific and nonscientific deductions in Burhān I, 4

5. Why-questions

6. Types and order of inquiry

7. Subjects and attributes of the sciences (selection)

8. First classification of the sciences (by subject)

9. Second classification of the sciences (by principles, questions, and subjects)

10. Analysis of subject and attribute of a scientific proposition in Ṭūsī’s commentary on Išārāt I, 15

11. Per se 2 attributes of numbers and extended magnitudes in Ilāhiyyāt III

12. Inseparability, constituents, and implicates

13. Types of demonstration in Burhān I, 7

14. Types of demonstration in Burhān III, 3

15. Why-demonstration and that-demonstration of one question and of two questions, in one science and in two sciences

16. Conception, differentiating expression, definition, and description

17. Types of definition

18. Notions defined in Avicenna’s Kitāb al-Ḥudūd

Acknowledgments

Precisely listing all tributaries of a long river. This was the image that first came to mind when I set out to write these heartfelt acknowledgments. But it soon became clear that mentioning each individual who has contributed, directly or indirectly, to the making of this book would be a doomed enterprise. I wish to thank, first, those who supported me when this project was just an idea and in its early stages. When I was still a doctoral student at Scuola Normale Superiore, longer ago than I care to remember, Amos Bertolacci taught me Arabic and introduced me to Avicenna; he is therefore the one I consider, quite literally, my own First Teacher (which also gives me a Gutas Number 2, much to my delight). Without the understanding and encouragement of Massimo Mugnai, who was then my supervisor on a dissertation concerned with fourteenth-century Latin logic, and the (strenuous) insistence of the late Francesco Del Punta, I never would have taken up and seriously pursued Arabic while working at the same time on an altogether different topic. But it was ultimately not until I was offered a generous postdoctoral position in Bochum and Cambridge by Cornelia Schöck and Tony Street that I had the opportunity to focus on what was to become in the subsequent years the theme of a complex dance. Tony Street in particular opened the gate of verification for me in the field of Arabic logic, in a process of dialogue on Avicenna and the post-Avicennan tradition that continues to this day. My debt to him would be impossible to assess, and my gratitude to acknowledge in full. This book is dedicated to him.

An endless list of friends and colleagues helped clarify my thoughts on general and specific issues, in several cases saving me from factual, interpretive, or stylistic errors. Here is a tentative, and certainly incomplete, list of those who have contributed in various ways, with their time, energy, and ideas: Paul Thom, Khaled El-Rouayheb, Calvin Normore, David Bronstein, Marko Malink, Dag Hasse, Charles Burnett, Jon McGinnis, Asad Ahmed, Ahmed Alwishah, Mohammad Esmaeili, Wilfrid Hodges, Stephen Read, Silvia Di Vincenzo, Tommaso Alpina, Sten Ebbesen, Alexander Kalbarczyk, Nora Kalbarczyk, Adam Crager, Anne Mahoney, Robert Morison, John Marenbon, Joep Lameer, Stephen Menn, Jacob Rosen, and Chris Martin. I also wish to thank the copy editor of this project, Sharon Langworthy, for her Olympian effort on the manuscript, and the Center for Middle Eastern Studies at the University of California Berkeley, which generously supported production at a critical stage. The ultimate responsibility for any remaining error rests—it goes without saying—solely on my shoulders.

Finally, I am grateful in ways that I cannot properly express to my extraordinary wife Chiara for always being a force of nature, for her unfailing support over the years, and for bearing with me especially in the past few months, as I was incessantly working on the final version of the manuscript only shortly after our son Leone had just come into this world and started blessing our lives with his smiles.

Medford, 12 January 2021

Note on Citation, Transliteration, and Translation

Avicenna’s works are cited by title, book, chapter, page, and line numbers from the Cairo edition of the Kitāb aš-Šifāʾ (Book of the Cure), Forget’s edition of al-Išārāt wa-t-tanbīhāt (Pointers and Reminders) (supplemented by Dunyā’s edition for Ṭūsī’s commentary) and Dānešpažūh’s edition of the Kitāb an-Nağāt (Book of Salvation).¹ References to the logic of the Nağāt are based on the sequence of chapters printed in Dānešpažūh’s edition and correspond to the chapter numbers of Ahmed’s English translation. References to the Išārāt, unless otherwise noted, are always to the logic. Hence, instead of writing I, 1, 6 for part I, path 1, chapter 6, I write I, 6 (path one, chapter six). Alfarabi’s Kitāb al-Burhān is always quoted without abbreviation to avoid confusion with Avicenna’s Burhān.

In all cases, line numbers are counted starting from the first printed line of text on any given page (excluding book and chapter titles), regardless of what numbers appear in the margins.

I use traditional Latin abbreviations for the titles of Plato’s and Aristotle’s works and the corresponding page and line numbers from the editions of Stephanus and Bekker. Book numbers of Aristotle’s works are indicated by a Greek capital letter (for example, An. Post. A7, Top. E4, Met. Δ30). The Greek commentators Alexander of Aphrodisias, Themistius, Philoponus, and pseudo-Philponus are cited according to their standard editions from the Commentaria in Aristotelem Graeca.

I have adopted the transliteration guidelines established in 1935 by the German Oriental Society (Deutsche Morgenländische Gesellschaft) with the following exception: -aw and -ay for the diphthongs instead of -au and -ai.

In translated texts, I have used the following signs:

(. . .)  to indicate a parenthetical remark by the author of the passage

[. . .]  to indicate my own explanatory additions or comments to the English translation, including numbers or letters

Introduction

Most of those who pretend to be philosophers learn logic but do not use it, resorting ultimately to natural inclination, galloping about it like one who lets the reins fall slack and does not pull on the bit.

—AVICENNA, ILĀHIYYĀT I, 8

Avicenna (ca. 970–1037) is the most influential philosopher in the Arabic-Islamic tradition. His thought is profoundly shaped by the ideal of science and scientific knowledge, and a full appreciation of this fact presupposes an adequate understanding of his views concerning the nature of scientific knowledge and the requirements that a discipline must meet in order to qualify as a science.

At the heart of Avicenna’s essentialist epistemology are two central problems. The first is the identification of (i) the conditions under which an assertion may be characterized as certain and therefore be taken to express a scientific truth. The second is the identification of (ii) the conditions under which a complex term may be characterized as an adequate conceptual representation of the essence of an object and therefore be taken to express a real definition. These two sets of conditions determine in turn the nature of the principles assumed in each science for the derivation of its own theorems, the way in which boundaries between sciences are drawn, and more generally, the hierarchical order and arrangement of scientific knowledge in its various domains. At the same time, Avicenna is concerned with central aspects of the logic of scientific reasoning, including the logical form of scientific statements, the structure of demonstrative proofs and the types of admissible argument forms, the conditions for reasoning from an impossibility, the relation between demonstration and definition, and the order of inquiry.

Avicenna’s conception of science and scientific knowledge, which lies at the intersection of logic, metaphysics, and epistemology, has never been the object of a systematic study, despite its centrality for his philosophical and scientific work. This is a lamentable gap not just in Avicenna scholarship but also for the history of philosophy as a whole. The primary purpose of this book is to fill this gap by offering the first comprehensive account of Avicenna’s theory of science, focusing in particular on his interpretation of the model introduced by Aristotle in the Posterior Analytics. The most elaborate version of this interpretation is developed by Avicenna in his Kitāb al-Burhān (Book of Demonstration), though related texts make important contributions too.

The main thesis of this book may be reduced to two interconnected contentions. The first contention is that Avicenna understands and develops his theory of science as a genuine—if undeniably ambitious—theoretical framework for actual scientific reasoning and for regimenting every suitable domain of scientific inquiry into a properly structured Aristotelian science. This is especially true if we think of an Aristotelian science in its final and canonical form, which ideally reflects the complete set of relations holding between the subject of a science and its attributes. It is possible, and perhaps even plausible, to think that Aristotle himself saw his own theory of science as aiming to accomplish an analogous task. But the Posterior Analytics (in fact the two Analytics as a whole) can hardly be taken to present a logic of scientific reasoning that is both adequate and ready to use, primarily because of the limited expressive power of the underlying logical system, which focuses on categorical propositions and syllogistic deductions. Moreover, even if we set aside the obscurities and interpretive problems raised by individual passages of the Posterior Analytics—a rather difficult work not only for neophytes but also for specialists—many aspects of Aristotle’s model are frequently discussed in it only in an embryonic form (a notable case in point is his theory of scientific attributes, as we shall see in chapter 7). Avicenna’s Burhān can therefore be seen, first and foremost, as an attempt to bring some central aspects of Aristotle’s theory of science from potency to act.

The second contention is that, in pursuit of this general strategy, Avicenna develops an extensive battery of conceptual tools and introduces a series of novel ideas in the context of Aristotelian epistemology. While both kinds of innovations are often locally motivated by specific technical needs, they almost invariably presuppose a theoretical framework of much broader significance, which is worthy of being investigated in its own right for its philosophical content.

To put the necessity of this study in perspective, an additional consideration is in order. Avicenna’s commitment to the view that philosophical method as well as individual scientific disciplines should somehow conform to the standards set out by Aristotle in the Posterior Analytics is a well-established tenet in modern scholarship.¹ And Avicenna’s attempt to cast his own metaphysics, of all disciplines, in a mold inspired by the principles of Aristotelian epistemology has been illustrated successfully in recent years (whether the attempt itself is successful is a separate—and largely irrelevant—issue, at least for our present purposes).² This leaves little room for doubt about Avicenna’s commitment to the idea that the path charted by the Posterior Analytics must always be taken seriously, in metaphysics as well as in every other science (at least relative to the degree of exactness allowed by its subject). But the question of how Avicenna’s commitment shapes and affects his reception of Aristotle’s theory of science, prompting a sustained effort to turn that theory into a genuine logic of scientific reasoning, has been all but neglected. In other words, the question of the applicability of an Aristotelian scientific method to individual sciences has typically been approached from within the sciences themselves, that is to say, by asking whether (or to what extent) the structure and conceptual vocabulary of a given science conforms to certain logical and epistemological standards. What this book aims to show, by contrast, is that, and how, this ideal of applicability influences Avicenna’s theory of science itself, driving an elaborate effort of recalibration of the Aristotelian logic of scientific reasoning.

THE ELEMENTS OF AVICENNA’S THEORY OF SCIENCE

The Arabic term ʿilm, just as its Greek and Latin counterparts epistēmē and scientia, means both (i) scientific knowledge and (ii) science.³

Scientific knowledge, according to Avicenna, may be either conceptual or propositional. The first kind is encapsulated by the notion of conception (taṣawwur) and is typically associated with definition (ḥadd) or description (rasm); the second kind is encapsulated by the notion of assertion (taṣdīq) and is typically associated with propositions (qaḍāyā), especially the premises and conclusions of deductions (qiyāsāt).

Scientific knowledge by assertion is connected to the idea of certainty (yaqīn), which is the distinctive mark of demonstration (burhān). Certainty is in turn an epistemic state characteristically defined in terms of modally firm beliefs (iʿtiqād) involving various kinds of necessity (ḍarūra). Certain assertions are either self-warranting and self-evident (bayyin bi-nafsihī), as in the case of immediate principles (mabādiʾ), or else inferentially and causally justified, as in the case of questions (masāʾil), that is to say, the theorems of a science.

Scientific knowledge by conception, by contrast, is connected to the idea of an adequate conceptual representation of the essence of an object. An adequate conceptual representation is expressed by a peculiar kind of differentiating or explanatory expression (qawl mufaṣṣil), that is to say, by a real definition that captures the complete ordered sequence of essential attributes of the object.

Modality and explanation are therefore critical aspects of Avicenna’s conception of scientific knowledge and play an essential role in his characterization of its nature, both with regard to assertion and demonstration and with regard to conception and definition.

A science is identified by three elements: its subject (mawḍūʿ), principles (mabādiʾ), and questions (masāʾil). Every science is a structured domain of interconnected and (ideally) certain truths, expressed by scientific assertions that may have various logical forms (categorical and hypothetical, conditional or disjunctive). Some scientific assertions are immediate (the principles of a science), while others are non-immediate (the questions of a science). Non-immediate assertions are proved either by categorical or by hypothetical deductions.

Scientific questions reflect a variety of types and stages of scientific inquiry (maṭālib) concerning, in particular, whether (hal) something exists or has a certain attribute, why (limā) it exists or has a certain attribute, and what (mā) subjects (mawḍūʿāt) and attributes (ʿawāriḍ or aʿrāḍ) are. Scientific explanations account for the relation between causes (ʿilal, asbāb) and effects (maʿlūlāt) and ultimately rest on the essences (ḥaqāʾiq or ḏawāt), natures (ṭabīʿāt), or quiddities (māhiyyāt) of the subjects and attributes of a science, which are captured by definitions.

AVICENNA’S KITĀB AL-BURHĀN

While the present study is not a commentary, Avicenna’s Burhān lies at its heart. For a better understanding of the organization of the former, it is therefore worth taking a preliminary look at the structure of the latter. The Burhān is the fifth section (fann) of the logic (manṭiq) of the Kitāb aš-Šifāʾ (Book of the Cure), that is to say, of Avicenna’s most comprehensive philosophical and scientific summa. The text is roughly three times the length of the Posterior Analytics and is divided into four treatises. Methodologically, the Burhān is not a running commentary but it still follows quite closely the order and arrangement of its source, in conformity with the style of commentary per modum expositionis typical of the Šifāʾ.⁴ If we take the Posterior Analytics as its baseline, Avicenna’s Burhān looks like a sequence of oscillatory movements that deviate more or less significantly from that baseline depending on the difficulty of a locus and the problem under discussion. The amplitude of such oscillations may vary quite dramatically. At the opposite ends of the spectrum are two complementary tendencies. In some cases, Avicenna relies on Aristotle’s text merely as the starting point of an independent discussion, frequently introducing new conceptual vocabulary or subtle distinctions. In other cases, he works much more closely on the text and presents an interpretation of problems that directly emerge from it. In between lies a vast array of attitudes and approaches varying from chapter to chapter, which may result in abbreviations, omissions, reformulations, transpositions, or rearrangements of the material. Sometimes multiple chapters in Aristotle are condensed into a single chapter in Avicenna, while at other times a single chapter in Aristotle is split into multiple chapters in Avicenna. For a detailed synopsis of the content of individual treatises and chapters, the reader is encouraged to consult appendix C ("A Map of Kitāb al-Burhān") at the end of the book.

The first of the aforementioned tendencies is most evidently exemplified by the first treatise and by part of the second treatise. The first treatise, which consists of twelve chapters, looks like an extensive gloss on Posterior Analytics (An. Post.) A1 (on the idea of preexistent knowledge) and A2 (on the definition of scientific and demonstrative knowledge, the conditions on scientific premises, and the taxonomy of scientific principles). The treatise opens with two preliminary chapters (Burhān I, 1 and I, 2) on the goal, benefit, and rank of the book, in the tradition of Alexandrian kephalaia, introducing the vocabulary of conception and assertion, the notions of definition and deduction, and the idea that the theory of scientific demonstration and definition represents the culmination of logic. In the first treatise, Avicenna appears to exploit particularly significant junctures, problems, and examples in An. Post. A1 and A2 almost as pretexts to introduce the full range of theoretically relevant themes that will be later explored, in the subsequent treatises of the book, in closer connection with Aristotle’s text. To give a brief illustration of Avicenna’s methodology, here are a few examples, which are discussed more extensively in the following chapters. The opening line of the Posterior Analytics (all teaching and all learning involving reason come from preexistent knowledge; An. Post. A1, 71a1–2) becomes a natural starting point, in Burhān I, 3, for an elaborate exegetical effort to recast the language of preexistent knowledge in terms of the vocabulary of conception and assertion. In a similar vein, in Burhān I, 6, Avicenna turns the problem of the possibility of inquiry, raised by Aristotle’s reference to Meno’s paradox in An. Post. A1, into a discussion of his own foundationalist framework. The classification of the types and order of scientific inquiry, which in the Posterior Analytics only appears at the beginning of book B, is presented by Avicenna already in the first treatise (Burhān I, 5) as one of the central themes of the work, before being discussed again, in Burhān IV, 1, in closer connection with An. Post. B1 and B2. Finally, Avicenna examines in detail two critical properties of scientific principles (explanatoriness and priority) in Burhān I, 7–10 and I, 11, respectively, before concluding the analysis of the first treatise, in Burhān I, 12, with a detailed survey of the types of principles listed by Aristotle in An. Post. A2 (axioms, definitions, postulates, hypotheses). Burhān I, 7–10 is an especially significant cluster of chapters that collectively represent a fascinating microcosm of insights into Avicenna’s understanding of scientific reasoning. The discussion ranges from the definition of demonstration (a deduction consisting of premises that are certain) and its classification into types associated with different kinds of explanation, to the distinction between causal and noncausal certainty and the analysis of induction and experience. In this case, too, the early and more systematic treatment of an especially significant theme, namely the distinction between demonstration of the fact and demonstration of the reason why in Burhān I, 7, foreshadows the more textually oriented presentation of a subsequent chapter (Burhān III, 3) in tandem with An. Post. A13.

The other notable example of the first tendency is a cluster of four chapters in the second treatise (Burhān II, 6–9) dealing with two key issues that are loosely inspired by An. Post. A7. The first issue concerns the distinctive elements that characterize the internal structure of a science (Burhān II, 6). The second issue concerns the resulting constraints on the interrelations among different sciences, which determine a comprehensive, hierarchical picture of the organization of scientific knowledge as a whole. In this picture, an especially prominent role is assigned to metaphysics, which is supposed to provide the ultimate justification of the non-evident principles of the other sciences (Burhān II, 7). In the same context, Avicenna also offers an elaborate account of the conditions under which kind crossing and the transfer of a demonstration from one science to another are possible (Burhān II, 8–9). Without being any less rich in innovations, philosophical sophistication, and digressions, the remaining parts of the Burhān, namely the first part of the second treatise, the third treatise, and the fourth treatise, proceed almost always in lockstep with the argument and text of the Posterior Analytics: in particular, the first part of the second treatise corresponds to An. Post. A3–11, the third treatise to An. Post. A12–34, and the fourth treatise to An. Post. B.

STRUCTURE OF THE BOOK

This is not an easy book to read. Its theme is difficult and its structure complex. Methodologically, it engages simultaneously in philosophical analysis and textual interpretation. Discussions are often technical and presuppose knowledge of Aristotle’s Posterior Analytics, combined at times with an arguably unhealthy interest in its finer points. Little to nothing has been written on the subject before, especially in comparison to the flourishing industry of modern scholarship on the Posterior Analytics. Furthermore, many of the problems and questions addressed in this study have an ambivalent nature. While most are ultimately rooted, one way or another, in Aristotle’s text (though more or less recognizably so, depending on the occasion), in Avicenna they take on, more often than not, a fully independent life. This requires a constant balancing act between two impulses, namely the temptation to engage with Avicenna’s interpretation of Aristotle’s text in the form of a supercommentary on the Posterior Analytics and the urge to extract the main philosophical points from Avicenna’s analysis in order to identify his contributions as an original theorist.

I have strived to overcome these obstacles in two ways. First, since Avicenna’s Burhān has never been translated into a Western language (with the exception of a chapter in the twelfth century in Latin, and other excerpts in modern studies), my analysis is frequently accompanied by translations, as I hope to enable a reader with no Arabic to anchor—and verify—my interpretive claims against the evidence on which they are based. Second, I have tried as much as possible to give a clear structure and division to the argument, especially when it does not follow the order and arrangement of Avicenna’s text.

The book is divided into five parts, each of which corresponds to a thematic cluster. Four appendices complement the main text: (i) a summary of the conditions of certainty (appendix A), (ii) a brief excursus on the logic of scientific reasoning (appendix B), (iii) a detailed synopsis of the contents of the Burhān (appendix C), and (iv) an English-Arabic glossary of technical terms (appendix D). The structure of the book primarily reflects the need to document in detail the original contributions of Avicenna’s theory of science, the extent and nature of his innovations, and their broader philosophical significance. It therefore focuses selectively on the parts of the Burhān (or related texts) in which those contributions most evidently come to the surface. The order and arrangement of topics depends on their relevance for an adequate reconstruction of Avicenna’s theory of science. This is inevitably the product of frequent interpretive choices, rather than being a reflection of the order in which they appear in Avicenna’s text.

Part I (Scientific Knowledge and Scientific Inquiry) identifies, in three chapters, the building blocks of Avicenna’s theory of science (conception and assertion), a set of basic types of scientific and non-scientific assertions, and the taxonomy and order of scientific inquiry. The content of part I selectively tracks some of the main themes of Burhān I.

Part II (The Organization of Scientific Knowledge) focuses, in two chapters, on the innovative framework developed by Avicenna in Burhān II, 6–7 to account for the way in which scientific knowledge coalesces into different individual domains of interconnected truths (the internal structure of a science, with its principles, subject, and questions) and for the way in which those domains are mutually related (the division and hierarchy of the sciences).

The clusters of themes explored in parts III, IV, and V concern the two key requirements of scientific knowledge (necessity and explanatoriness) and the type of scientific principle that paradigmatically encapsulates them both, that is to say, definition.

Part III (Modality), in its three chapters, resumes the thread of the discussion from Burhān II, 2–5 as well as drawing on relevant material from two other areas of Avicenna’s logic: the theory of the predicables introduced in his Madḫal and a fragment of the formal logic developed in his Qiyās. The general goal is to illustrate in detail the modal component in the definition of scientific knowledge by looking at how it is deployed in the context of scientific reasoning. The main themes here are the notion of necessity associated with demonstration, the theory of scientific attributes, and various aspects of Avicenna’s logic of essence, including the distinction between different kinds of inseparability and his account of reductio proofs in the sciences.

Part IV (Causality and Explanation) explores the other component associated with the definition of scientific knowledge. Its three chapters, which are textually based on Burhān I, 7–10, II, 9, III, 3–5, and IV, 5, 8–9, deal in turn with the distinction between causal demonstration (burhān limā) and noncausal demonstration (burhān anna), subordination and explanation across different sciences, and Avicenna’s interpretation of the four causes, including his understanding of the manners in which the latter are absorbed into the logical structure of demonstrations and definitions.

Part V (Definition) is devoted to the focal principle toward which both the modal and the explanatory dimensions of scientific knowledge ideally converge. The last two chapters of the book, broadly based on Burhān I and especially Burhān IV, illustrate in detail the internal structure of definitions, their components, their types and functions, and various heuristic methods for their discovery.

Since this is already a ponderous book, in an attempt to minimize redundancies I have decided to keep the introduction short. The reader should be able to form a sufficiently comprehensive view of its contents and main narrative by reading in sequence the short introductions to the five parts, followed by the conclusion. My hope is that, after taking the shorter route, starting all over again from the beginning and reading the book in its entirety will not appear to be just a futile, Sisyphean task.

PART I

Scientific Knowledge and Scientific Inquiry

Avicenna’s theory of science is concerned with two kinds of scientific knowledge, conceptions and assertions, and with a number of fundamental questions that articulate the basic types and the order of scientific inquiry. Each stage in the process of inquiry corresponds to a particular kind of question. What is the meaning of a term? What is the essence of an object? Does a certain subject exist? Does a subject have a certain attribute? Why does a subject have a certain attribute? Answers to such questions come systematically in the form of distinctive types of conceptions or assertions.

Ideas and problems from Aristotle’s theory of science are translated by Avicenna into the language of conception and assertion in a dynamic process of transformation of the doctrine of the Posterior Analytics. If all teaching and all learning involving reason presuppose some form of preexistent knowledge, conception and assertion are the characteristic elements into which such knowledge may be analyzed. The scientific knowledge of a conclusion acquired by demonstration is equivalent to its justified assertion. And the assertion of a conclusion requires the prior conception and assertion of its premises as well as the prior conception of the conclusion itself.¹ Classical problems of Aristotelian epistemology are also investigated by Avicenna through the lens of conception and assertion. Objections against the possibility of inquiry (Meno’s paradox) and against the possibility of scientific knowledge (skeptical arguments pointing to the inevitability of infinite regress or circular reasoning) are formulated—and solved—in a language whose constitutive elements are conceptions and assertions. At the same time, new problems arise as a result of Avicenna’s interventions on the Aristotelian framework. How does the distinction between potential and actual knowledge play into his broader set of admissible logical forms? Again, if the process of search for principles must inevitably come to a stop, what do primary and immediate conceptions and assertions look like? And how do we come to know them? Conceptions and assertions are the provenance and destination of scientific reasoning. In a science both the starting points and the things that are sought fall in one category or the other. Complex conceptions are acquired by definition and description, starting from simpler, immediate conceptions that are ultimately acquired by abstraction from the domain of perception, while derivative assertions are acquired by demonstration from various kinds of immediate assertions (chapter 1).

The identification of the epistemic character of the basic kinds of immediate assertion is a central component of Avicenna’s theory of science. The distinction between certain and non-certain assertions isolates the domain of scientific discourse from other domains of nonscientific or prescientific discourse. Certainty is the distinctive mark of scientific assertions—immediate and non-immediate alike—and a constitutive element in the definition of demonstration (a deduction consisting of premises that are certain and entailing a conclusion that is also certain). Avicenna’s account of certainty is in turn dependent on the notion of belief and requires a combination of truth and necessity. And the certainty of immediate assertions that serve as principles of scientific deductions is associated with different kinds of necessity and with different sources. Such necessity may be epistemic or ontological, and its sources may be either internal, as in the case of primary propositions like the law of the excluded middle, or external, as in the case of evident propositions based on perception or experience. A classification of deductive principles based on their epistemic status and the corresponding division of arguments based on the epistemic status of their premises and conclusions allows Avicenna to cast a wide net over different forms of reasoning encountered in the process of scientific inquiry as well as in the rejection of competing theories. In this connection, the classification of nonscientific statements (assertions that may mistakenly be held to be true—or even necessary—just because they are widely accepted) or pseudo-scientific statements (assertions based on estimations that are false but may nonetheless appear compelling) is an integral part of Avicenna’s epistemological project (chapter 2).

Scientific inquiry involves three main groups of questions. The first group of questions is concerned with whether something exists or whether a subject has a certain attribute. Do physical qualities exist? Do circles exist? Are humans capable of laughter? Are triangles such that the sum of their internal angles is equal to two right angles? The first two examples fall in the category of what Avicenna calls simple if-questions (hal basīṭ), while the last two examples fall in the category of what he calls compound if-questions (hal murakkab). The first group is therefore associated with two basic kinds of assertions: existential and predicative. The second group of questions is concerned with what a term means or what constitutes the essence of an object. What is the meaning of even times even? What is the meaning of void? What is an eclipse? What is a triangle? The first two examples fall in the category of what-questions relative to the meaning of a name (mā bi-ḥasab al-ism), while the last two examples fall in the category of what-questions relative to the essence of an object or event. The second group is therefore associated with two different kinds of conceptions: nominal definitions (or descriptions) and real definitions. The third group of questions is concerned with why something exists or why a certain attribute belongs to a subject. Why do circles exist? Why do the four elements exist? Why are broad-leaved plants deciduous? Why does the moon undergo eclipses? The first two examples fall in the category of why-questions relative to the existence of a subject, while the last two examples fall in the category of why-questions relative to whether a subject has a certain attribute. The third group is associated with the same kinds of assertions as the first group (existential and predicative), which in this case answer a why-question rather than just an if-question. The taxonomy of scientific inquiry and its types of questions (if-questions, what-questions, why-questions) is accompanied by a rigorous account of their relative order, ranging from the simple identification of the meanings of terms in a science to the establishment of the existence of subjects, the investigation of the essences of subjects and attributes, the investigation of the necessary attributes of subjects, and the identification of the causes in virtue of which those necessary attributes belong to their subjects (chapter 3).

1

Conception and Assertion

THE TWO PATHS OF SCIENTIFIC KNOWLEDGE

The distinction between conception (taṣawwur) and assertion (taṣdīq) is a characteristic feature of Arabic logic. Conception is primarily concerned with the sort of knowledge involved in concept formation and in the analysis of concepts, terms, definitions, and descriptions. Assertion is concerned with the sort of knowledge involved in the ascription of truth to propositions and in the analysis of deduction and demonstration.¹

Avicenna is neither the first nor the last in this tradition to use conception and assertion as building blocks of logic and, more specifically, as basic elements of a logic of scientific reasoning. Alfarabi before him employs the two notions extensively in his own account of demonstration and definition and understands the internal organization of material logic in Aristotle (the five sections of the Arabic Organon coming after the Prior Analytics) to depend on an underlying classification of different types of assertions.² In Avicenna, however, the use of the distinction becomes pervasive and its significance systematic, so much so that in post-Avicennan logic conception and assertion coalesce into a central theme of discussion and, starting in the thirteenth century, are regularly listed among the candidates for the proper subject matter of logic itself.³

The distinction between conception and assertion plays a foundational role in Avicenna’s theory of science and marks the boundary between two distinct but intimately connected modes of scientific knowledge (ʿilm).⁴ At the beginning of the section on demonstration in the Nağāt, he writes:

Text 1.1: Nağāt I, 102 (i)–(ii), pp. 112.5–113.1 (Ahmed 2011, p. 87, transl. modified; cf. also Gutas 2012, p. 395)

All scientific knowledge is either [(a)] the conception of some notion or [(b)] assertion. Conception may exist without assertion, for example when one has a conception of the statement that void exists without asserting it, or when one has a conception of the notion of human, in which case (as with any simple [notion]) there is no assertion or denial.

Every assertion and every conception are either [(bb)–(ab)] acquired through investigation or [(ba)–(aa)] exist at the beginning. Assertions are acquired [(bba)] through deduction and [(bbb)] through things we have mentioned that resemble it. Conceptions are acquired [(aba)] through definitions and [(abb)] through other things that we will mention.

In Text 1.1, conceptions and assertions are identified as the two fundamental types of scientific knowledge. Each of them is further divided into two classes: conceptions and assertions that are acquired through investigation (yuktasabu bi-baḥṯ), as opposed to conceptions and assertions that exist in some primary way at the beginning of the process of inquiry (wāqiʿ ibtidāʾan). Investigation is a technical term in Avicenna’s logical vocabulary alluding to the articulation of a discursive line of reasoning (naẓar is often used in a similar sense). In this passage, it means two distinct things. In the case of assertions, acquisition through investigation means acquisition through deduction (direct or indirect) and other argument forms such as induction, example, or enthymeme discussed in the treatment of formal logic. In the case of conceptions, acquisition through investigation means acquisition through definition or description, whose rigorous theoretical treatment is the prerogative of the theory of science (as opposed to dialectic). It is important to note that the distinction between what is acquired through investigation and what is not acquired through investigation in Text 1.1 is not a distinction between acquired and innate (Avicenna vigorously rejects innatism) but rather one between different kinds of objects and modes of acquisition. According to this preliminary characterization, illustrated in table 1, scientific knowledge turns out to be one of four things: (aa) a primary conception, (ab) an acquired conception, (ba) a primary assertion, or (bb) an acquired assertion.⁵

The distinction between acquired and non-acquired conceptions and assertions is critical for the formulation of Avicenna’s own version of epistemological foundationalism, namely the doctrine that scientific knowledge ultimately presupposes indemonstrable first principles on which everything else depends. In other words, in order for scientific knowledge to be possible, there must be (i) immediate assertions that are not grounded in other assertions and (ii) immediate conceptions that are not in turn dependent on other conceptions. In the continuation of Text 1.1, Avicenna evokes the fatal threat of an infinite regress to argue that the process of acquisition of conceptions and assertions must come to a stop at immediate items of each kind:

Text 1.2: Nağāt I, 102 (iii), p. 113.2–6 (Ahmed 2011, pp. 87–88, transl. modified; cf. also Gutas 2012, p. 395)

Deductions have parts that are asserted and others that are conceptualized, while definitions have parts that are conceptualized. This does not result in an infinite regress, in such a way that knowledge of these parts becomes available only through the acquisition of other parts whose characteristic is this, namely to go on infinitely. Rather, [the process] comes to a stop at things that are objects of assertion and objects of conception immediately (bi-lā wāsiṭa).

The two sources of acquired assertions and conceptions are deductions and definitions. Deductions and definitions may both be analyzed into parts. The parts of a deduction are its premises and conclusion, which may in turn be analyzed into terms. Premises and conclusions are objects of assertion, while terms are objects of conception. The parts of a definition are the terms of which it consists, each of which is an object of conception. Both scientific knowledge that is acquired through deduction and scientific knowledge that is acquired through definition must ultimately rest on a (finite) number of immediate assertions and conceptions. The same is true a fortiori of demonstration, which is a particular type of deduction, involving premises and conclusions that are certain.

RANKS OF CONCEPTION AND ASSERTION

In Burhān I, 1, Avicenna develops a more precise taxonomy of conception and assertion and discusses in greater detail their relation to definition and deduction. I look more closely at the texts on which the taxonomy is based in chapter 2 for Avicenna’s analysis of assertion and deduction and in chapter 12 for his treatment of conception and definition. For the moment, I just wish to give a preliminary characterization of how conception and assertion concretely serve as the main building blocks of Avicenna’s theory of science. The taxonomy of Burhān I, 1 deals with the two types of acquired scientific knowledge, which may be obtained either by means of thought (al-ʿilm al-muktasab bi-l-fikra) or in a manner that does not involve thought (al-ḥāṣil bi-ġayr iktisāb fikrī).⁶ Thought (fikra) is a technical term that designates a faculty of the soul whose peculiar activity is to aid the intellect (ʿaql) in combining or separating concepts in propositional compounds that are amenable to truth and falsehood. Scientific knowledge acquired by means of thought is associated by Avicenna with the domain of assertion, and in this capacity, thought indirectly provides the basis of deductive reasoning. Scientific knowledge that is not acquired through thought, by contrast, is associated with the domain of conception. Both domains are arranged in ranks (marātib). In the case of assertion, ranks are determined by an underlying series of beliefs (iʿtiqād) of decreasing epistemic strength, ranging from certainty (yaqīn) to mere supposition (ẓann).⁷ In the case of conception, ranks are associated with various aggregates of notions or attributes, which may be essential or accidental and jointly proper to something or common to it and other things. In this framework, assertion stands to deduction as conception stands to definition and description. Consequently, the hierarchical arrangement of the different types of assertions and conceptions induces a parallel hierarchical arrangement of deductive arguments and of definitions and descriptions. In particular, Avicenna identifies three ranks of assertion:

(aa) certain (yaqīn);

(ab) resembling certain (šabīh bi-l-yaqīn); and

(ac) persuasive, based on supposition or opinion (iqnāʿī ẓannī).

Each of them is associated, as we shall see in chapter 2, with various types of belief and characterizes the premises and conclusions of a particular kind of deductive argument, that is to say,

(aa) demonstrative (burhānī),

(ab) dialectical (ğadalī) or fallacious (muġāliṭī), and

(ac) rhetorical (ḫiṭābī).

The ranks of conception, by contrast, are four. They are determined by four basic ways of collecting the attributes of an object. These may involve

(ba) an aggregate of essential notions (maʿānin ḏātiyya) proper to the object,

(bb) an aggregate of essential notions common to the object and something else,

(bc) an aggregate of accidental notions (maʿānin ʿaraḍiyya) proper to the object, or

(bd) an aggregate of accidental notions common to the object and something else.⁸

Each of these four corresponds, as we shall see in chapter 12, to a distinctive kind of differentiating expression (qawl mufaṣṣil). A differentiating expression is a complex term involving different ordered sets of essential or accidental attributes, by means of which something is made known (taʿrīf) and distinguished (tamyīz) from all other things or from some other things only. The four kinds of differentiating expression are:⁹

(ba) complete definition (ḥadd tāmm),

(bb) incomplete definition (ḥadd nāqiṣ),

(bc) complete description (rasm tāmm), and

(bd) incomplete description (rasm nāqiṣ).¹⁰

Conception and assertion are not only the basic ingredients of Avicenna’s definition of scientific knowledge, of his account of demonstration and definition, and of his characterization of certainty and other forms of nonscientific assertions. They are also essential elements in his account of the goal (ġaraḍ) and utility (manfaʿa) of the theory of science, which represents the culmination of logic. The goal of the logic of scientific reasoning is to investigate (i) the conditions under which deductive arguments bring about conclusions that are certain, consisting of epistemically and modally stable beliefs; and (ii) the conditions under which complex linguistic expressions qualify as real definitions that articulate adequately the conception of essences. This requires, in Avicenna’s language, the identification of adequate demonstrative and definitional matters (mawādd), that is to say, suitable assertions or premises, capable of bringing about certainty through demonstration, and suitable conceptions or terms, capable of bringing about the complete conceptualization of an object of inquiry through its definition.¹¹ The utility of the theory of science lies in the identification of methods or paths (ṭuruq) for the attainment of certain assertions and real conceptions and in the specification of the criteria of adequacy of both.¹²

TEACHING AND LEARNING INVOLVING REASON

The first actual application of the distinction between conception and assertion in Avicenna’s interpretation of the Posterior Analytics is linked with the dramatic incipit of Aristotle’s work, namely the contention that all teaching and all learning involving reason come from preexistent knowledge (An. Post. A1, 71a1–2). As noted in the introduction, the first two chapters of the Burhān deal with classical problems of Alexandrian exegetical methodology (the goal and rank of the book), and it is only in Burhān I, 3 that Avicenna starts to engage directly with Aristotle’s text. The chapter is an elaborate gloss on the notion of preexistent knowledge and deals with various questions raised by the latter: (i) what preexistent knowledge consists of, (ii) how preexistent knowledge is compatible with ignorance of what is sought, and more generally (iii) how what is known and what is not (yet) known are related.

A list of alternative modes of teaching and learning isolates a preliminary set of notions against which the sort of teaching and learning Avicenna is interested in for the purposes of scientific discourse must be contrasted:¹³

Text 1.3: Burhān I, 3, p. 57.1–9

[(i)] One kind of teaching and learning involves craftsmanship (ṣināʿī), like learning carpentry and the art of dyeing, and it is through assiduous practice of the activities [proper to] those arts that it comes about. [(ii)] Another kind involves dictation (talqīnī), like the dictation of a certain poem or of [the sounds and utterances of] a certain language, and it is through the assiduous articulation of those sounds and utterances resulting in a habit that it comes about. [(iii)] Another kind involves discipline (taʾdībī), and it is through the instruction [imparted by the teacher] to his learner that it comes about. [(iv)] Another kind involves the unquestioning adoption of a tradition (taqlīdī), which consists in the fact that someone gets used to believing in a certain view, and it is with respect to the trust placed in the teacher that it comes about for him. [(v)] Another kind involves being reminded (tanbīhī), as in the case of one who knows that lodestones attract iron but is neglectful of this fact at the right time and does not understand it, when he perceives a lodestone attracting iron; and so he is puzzled by it. But if one says to him: This is the lodestone whose condition you are familiar with, then at that moment he is reminded of it and ceases to be puzzled.¹⁴ Or as in the case of one who discusses by means of first principles (awāʾil) without understanding them because of some imperfection in the expression or in his reason, and so one strives to establish them for him. [(vi)] There are other kinds but none of them involves reason or thought.

The significance of Text 1.3 is both exegetical and systematic. On the one hand, it illustrates Avicenna’s flexibility in incorporating elements alien to the Greek commentary tradition of the Posterior Analytics and peculiar to the Arabic-Islamic tradition (for instance, the notion of taqlīd). But on the other hand, it also introduces the notion of reminding or being reminded (tanbīh) as a separate mode of knowledge directly associated with first principles. Interestingly, Avicenna seems to take the notion of tanbīh as a type of teaching and learning falling outside the scope of discursive reason (which coincides with the domain of acquired conceptions and assertions). Since elsewhere this mode is frequently associated with induction (istiqrāʾ) and the grasp of first principles, which cannot be acquired through more primitive conceptions or assertions, it is tempting to read this remark as part of Avicenna’s general understanding of immediate conceptions and assertions as the kind of preexistent knowledge that all knowledge involving reason (in the technical sense of I, 3) is said to presuppose.¹⁵

More important for our purposes, however, is Avicenna’s use of the philosophical vocabulary of conception and assertion in the analysis of the notion of preexistent knowledge itself. In addressing the question of what it means for teaching and learning to involve reason (ḏihnī), Avicenna (i) concretely spells out the Aristotelian notion of preexistent knowledge in terms of conception and assertion and (ii) articulates their mutual relations.¹⁶ He writes:

Text 1.4: Burhān I, 3, p. 57.9–15

[Teaching and learning] involving reason and thought are the ones that are obtained by means of an audible or intelligible discourse whose characteristic it is [(a)] to bring about a belief (iʿtiqād) or a view (raʾy) that did not exist, or [(b)] to bring about a conception that did not exist.¹⁷ Such teaching and learning involving reason obtain sometimes between two men and sometimes between a man and himself in two respects. For example, one is a teacher with respect to having the intuition of the middle term in the deduction and a learner with respect to acquiring the conclusion from the deduction. The teaching and learning are one in essence but two according to the point of view. For one and the same thing, namely being driven to the acquisition of what is unknown by means of what is known (iktisāb al-mağhūl bi-l-maʿlūm), is called learning with regard to the one in whom it comes about and teaching with regard to the one from whom it comes about, that is to say the efficient cause, like moving and being moved.

In Text 1.4, Avicenna translates the notion of preexistent knowledge from the opening line of the Posterior Analytics into his own language of conception and belief, where belief is in turn the notion in terms of which assertion is typically characterized. In the same passage, Avicenna also incidentally hints at his own definition of logic, which he understands to be a canonical instrument by means of which reason moves from what is known to what is unknown. Teaching and learning involving reason are therefore an expression of what logic itself encapsulates in a more abstract form: a process of cognitive transfer from what is known to what is unknown.¹⁸

PREEXISTENT CONCEPTIONS AND ASSERTIONS

Teaching and learning involving reason presuppose some form of preexistent knowledge. But what does preexistent knowledge look like? For Avicenna the notion applies to conceptual and to propositional knowledge alike, and its source may be either internal or external. Preexistent knowledge of what is sought must be distinct from the knowledge acquired through teaching and learning but at the same time relevant to it. It must be, in other words, potential knowledge of what is sought without being actual knowledge of it.

In his analysis of preexistent knowledge in An. Post. A1, Aristotle illustrates his general contention with a reference to various types of inferential procedures (deduction, induction, example, enthymeme). These inferential procedures are analyzed by Avicenna in terms of relations among assertions. If an assertion is non-immediate, then it must derive from preexistent knowledge, and such preexistent knowledge may be characterized precisely in Avicenna’s conceptual vocabulary. His analysis involves three components: (i) the conception of the conclusion, (ii) the conception of the premises, and (iii) the assertion of the premises. He writes:

Text 1.5: Burhān I, 3, p. 58.1–6

Prior to assertion is knowledge of three things. The first is [(i)] the conception of what is sought (maṭlūb), even if it is not yet asserted.¹⁹ The second is [(ii)] the conception of the statement (qawl) that precedes [what is sought] in rank. The third is [(iii)] the assertion of the statement that precedes [what is sought] in rank. From knowledge of these three things there follows [(iv)] the assertion of what is sought. Regardless of whether the preceding statement represents a deduction (qiyās), an induction (istiqrāʾ), an example (tamṯīl), an enthymeme (ḍamīr), or something else, one or more premises are necessary in order for an assertion that did not exist to be acquired; and knowledge of them comes about in two ways, first with respect to conception and then with respect to assertion.

Prior to conception is the conception of the parts of a definition or a description, and nothing else.

Any argument form, whether it be inductive or deductive (demonstrative, dialectical, or rhetorical) that aims to produce an assertion requires three kinds of preexistent knowledge, all of which are relevant to what the argument seeks to establish, that is to say, its conclusion. The first requirement is that the conclusion must be an object of conception. The second requirement is that the premises of the argument must be objects of conception. Avicenna refers to them collectively as the statement that precedes what is sought, which must refer both to the individual premises (the first two occurrences of qawl in Text 1.5) and to their arrangement into an argument (the third occurrence of qawl in Text 1.5). The third requirement is that the premises of the argument must be objects of assertion. These are necessary and sufficient conditions for the assertion of the conclusion.

A non-immediate conception, by contrast, presupposes only the conception of the parts of its definition or description. In the last sentence of Text 1.5, Avicenna states the necessary conditions of conception only with regard to the nonpropositional case, even though it is plausible to assume that the kind of conception discussed in (i) and (ii) presupposes in turn the conception of the terms occurring in the premises. The first case illustrates the kinds of preexistent knowledge presupposed when what is sought is an assertion, which involves propositional knowledge. The second case illustrates the kinds of preexistent knowledge presupposed when what is sought is the conception of a complex term. In the former case, an assertion presupposes both the prior conception of the nexuses expressed by premises and conclusion (where the conclusion is the assertion itself) and the prior assertion of the nexuses expressed by the premises. In the second case, the conception of a complex term such as a definition or a description only presupposes the prior conception of its parts, that is to say, of certain simpler terms, without any prior assertion (and, obviously, without any prior conception of a predicative nexus, given that in principle no such nexus exists in the case of terms).

POSSIBILITY OF INQUIRY AND POSSIBILITY OF SCIENTIFIC KNOWLEDGE

Two problems arise in connection with the view that all teaching and learning involving reason come from preexistent knowledge. First, in what sense is preexistent knowledge not the same as knowledge of what is sought? How do they differ? For example, how is knowledge of the premises of an argument not identical with knowledge of its conclusion? And, if we can only either fully possess knowledge of what is sought or be altogether ignorant of it, how is inquiry possible in the first place? Second, if all preexistent knowledge presupposed by teaching and learning involving reason can only in turn be acquired through teaching and learning involving reason, then the process seems inevitably bound to result either in an infinite regress or in a vicious circle.

The first problem is a version of Meno’s paradox and concerns the possibility of inquiry. The second problem consists of two skeptical objections against the possibility of scientific knowledge. Avicenna addresses the first problem and a variant of the first objection from the second problem (the argument from infinite regress) in Burhān I, 6. He then deals with another variant of the second problem (including both the argument from infinite regress and the argument from circularity) in Burhān II, 1, which is concerned with the analysis of An. Post. A3 and where Avicenna specifically substitutes the notions of teaching and learning involving reason with that of demonstrative scientific knowledge.

Meno’s Paradox: Knowledge in Potency and Knowledge in Act

Avicenna’s solution to the first problem rests on a distinction between potential and actual knowledge, while his solution to the second problem is an expression of his commitment to a foundationalist epistemology. What is especially interesting for our purposes is that in both cases the two problems are framed and solved using the distinction between conception and assertion.

Avicenna’s formulation of Meno’s paradox may be reconstructed as follows:²⁰

(i) For any x, either one knows x in every respect or one is ignorant of x in every respect;

(ii) If one knows x in