DOCSLIB.ORG

The Metaphysics of the Syllogism 31

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Metaphysics of the Syllogism 31 The Metaphysics Of The Syllogism 31 COLLOQUIUM 2 The Metaphysics of the Syllogism Edward C. Halper University of Georgia Abstract This paper addresses a central metaphysical issue that has not been recognized: what kind of entity is a syllogism? I argue that the syllogism cannot be merely a mental entity. Some counterpart must exist in nature. A careful examination of the Posterior Analytics’s distinction between the syllogism of the fact and the syllogism of the reasoned fact shows that we must set aside contemporary logic to appreciate Aristotle’s logic, enables us to understand the validity of the scientific syllogism through its content rather than its form, and explains the priority of the scientific syllogism over other valid syllogisms. The opening chapters of Posterior Analytics II help us to distinguish the entities that scientific syllogism must include as its terms; namely, a genus, an essential nature, and essential attributes of the genus. Often, the attributes are found in closely linked sequences. By exploring why there are such sequences and how they are linked, the paper argues that sequences of genus, nature, and sequential attributes are the basis in nature for the process of reasoning that we call the syllogism: we come to grasp the syl- logism over time but the sequences to which it refers exist together in things. So under- stood, the syllogism, like knowledge of forms and truths, exists in us and in the world. Keywords syllogism – logic – validity – scientific syllogism – essential nature – essential attributes I Ancient philosophy has been so intensely studied for so long that it seems un- likely that any major issue remains unexplored. It will, therefore, come as something of a surprise to realize that the issue I will discuss here is not just unexplored by contemporary scholars but wholly unrecognized, even in pass- ing. The issue can be stated simply: What is an Aristotelian syllogism? Of © Koninklijke Brill NV, Leiden, 2018 | doi 10.1163/22134417-00331P05Downloaded from Brill.com09/25/2021 03:26:46PM via free access 32 Halper course, there has been a great deal of discussion of the syllogistic forms and especially of how to represent them in a formal deductive system. My question is ontological: what sort of entity is the syllogism? Aristotle defines the syllogism as “a discourse (logos) in which certain things being stated, something other than what is stated follows of necessity, from their being so” (Prior Analytics I 1, 24b18–20, Jenkinson translation). Aristotle goes on to explain that what is “stated” are two premises that contain three terms and that what “follows of necessity” is a conclusion that contains two of these terms. (Although he uses “syllogism” to signify only valid syllogisms, the Prior Analytics considers all possible syllogistic forms in order to determine which are valid. Hence, it is more convenient to use “syllogism” to refer to the form, regardless of its validity.) The Greek word that is here rendered “discourse,” logos, could as well be understood as “process of reasoning.” In any case, Aristotle’s definition is nota- bly opaque on what the syllogism is, on why a conclusion would follow from what is posited, and on why the inference would be necessary. Contrast Aristotle’s definition of a (valid) syllogism with his account of true propositions: An affirmation is a positive assertion of something about something, a denial a negative assertion. It is possible to assert of what holds that it does not hold and of what does not hold that it does, as well as to assert of what holds that it does hold and of what does not hold that it does not. (De Interpretatione 6, 17a25-29, my translation) Propositions are true when they express what holds in the world. A valid syl- logism, that is, a “perfect syllogism” needs “nothing other than what has been stated to make plain what necessarily follows” (APr. 24b22–25, Jenkinson translation). Whereas something in the world makes a proposition true, a syl- logism is recognized as valid from itself, independently of anything in the world. Nonetheless, the syllogism is used to draw inferences about the world. Why does a valid syllogism whose premises are true yield a conclusion that is also true? Inasmuch as the syllogism is a tool for deriving or, at least, affirming some truths about the world on the basis of others, the assertions that constitute a sound syllogism must be linked together somehow not only in our minds, but also in the world. What is it in the world that allows a syllogism whose prem- ises are true to yield a true conclusion? Again, a syllogism that was merely valid might, conceivably, lack a connection with the world, but it is impossible to suppose that a sound syllogism would not have something in the world that would somehow correspond to it. This something must be more than whatever Downloaded from Brill.com09/25/2021 03:26:46PM via free access The Metaphysics Of The Syllogism 33 it is that corresponds to the sound syllogism’s three propositions, for their very connection in the syllogism signifies something about the world: three true sentences need not be a syllogism. My concern here is what this could be. Thus, to ask “what is a syllogism?” in the way I am proposing here, is to ask, “what is it in the world that corresponds with and, thereby, legitimates a sound Aristotelian syllogism?” Why can we assume that a logos that we can recognize to be valid only from what it states also applies to the world? Inasmuch as the Posterior Anyalytics aims to show how to use the syllogism to arrive at scien- tific knowledge of the world, my question is crucial for understanding this work. Again, a logos is either a series of sentences or a process of reasoning. Maybe it would not be too surprising if there were some pattern in the sentences or in the reasoning to which our human intellect must somehow give its assent. The primary rule of inference in contemporary logic, modus ponens, may be just such a pattern. What is difficult to understand is why such a pattern, process of reasoning, or discourse—or whatever else it might be—must also hold of the world. Why can reasoning about the world be a way to discover what is true of the world? Someone might think this question could be answered by identifying “truth- makers” in the world that make each premise of a valid syllogism true and then by showing that they imply a third truthmaker that makes the conclusion true. The issue is what sort of thing in the world this implication would be. Since merely being true does not suffice for three sentences to constitute a syllogism, there must be something in the world besides the three truthmakers that somehow makes them into a syllogism. What could this be? To coin a term, what is the “soundness maker”? This is the question I am posing here. In short, to ask, “what is a syllogism?” in the way I am proposing here is to ask, “what is it in the world that constitutes the peculiar process of inference that is an Aristotelian syllogism?” Can processes of inference exist in the world or is there, rather, something else in the world that allows there to be sound mental inference? So understood, the question is about the relation of logic to the world. This was once a central question for philosophers. In the Tractatus Wittgenstein understands the structure of logic as the structure of the world as well as the structure of language; in his later work, logic comes to be a collec- tion of grammatical features of our language, features we often find useful— though not always, as Graham Priest likes to remind us.1 Even if we had no other reason to raise the question, it would be interesting to inquire into how Aristotle understands his logic to relate to the world. 1 In multiple books and articles. See, for example, Priest 2006. Downloaded from Brill.com09/25/2021 03:26:46PM via free access 34 Halper II In fact, though, we have good reasons from Aristotle’s philosophy to raise this question. In the De Anima Aristotle maintains that the form that is a thing’s essential nature exists both in the thing and in the mind, albeit in the former with matter and in the latter without (III 4, 429a13–18). In this respect, the in- telligible form parallels the sensible form that exists in an object and in the pertinent sense organ of the sensing animal. In other words, the essential na- ture that we know also exists, albeit with matter, in the thing known. The exis- tence of this nature in our minds is necessary if we are to know the object, Aristotle maintains. Were our minds to have an image or representation of the object, we would not have knowledge; nor would we have real knowledge if we grasped the object by somehow sending out a beam of light or something else, as bats grasp the world, and as Plato seems to think we sense (Timaeus 45c). The paradigmatic essential natures that we know are the essential natures of substances. But there is no reason to suppose that only substances have es- sential natures: Aristotle speaks of knowledge of: mathematical entities (quan- tities) (Metaphysics K 3, 1061a28–b3), colors (Metaph. I 7, 1057a18–b34; De Sensu 3), and grammar (Categories 1a29–b3). Indeed, in the Metaphysics he claims that substances have essences most properly, but that instances of other cate- gories have essences as well, albeit derivatively (Z 4, 1030a38–32).
Load more

Recommended publications
  • Aristotle's Assertoric Syllogistic and Modern Relevance Logic*
    Aristotle’s assertoric syllogistic and modern relevance logic* Abstract: This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic. Keywords: Aristotle, Syllogism, Relevance Logic, History of Logic, Logic, Relevance 1.
    [Show full text]
  • 7.1 Rules of Implication I
    Natural Deduction is a method for deriving the conclusion of valid arguments expressed in the symbolism of propositional logic. The method consists of using sets of Rules of Inference (valid argument forms) to derive either a conclusion or a series of intermediate conclusions that link the premises of an argument with the stated conclusion. The First Four Rules of Inference: ◦ Modus Ponens (MP): p q p q ◦ Modus Tollens (MT): p q ~q ~p ◦ Pure Hypothetical Syllogism (HS): p q q r p r ◦ Disjunctive Syllogism (DS): p v q ~p q Common strategies for constructing a proof involving the first four rules: ◦ Always begin by attempting to find the conclusion in the premises. If the conclusion is not present in its entirely in the premises, look at the main operator of the conclusion. This will provide a clue as to how the conclusion should be derived. ◦ If the conclusion contains a letter that appears in the consequent of a conditional statement in the premises, consider obtaining that letter via modus ponens. ◦ If the conclusion contains a negated letter and that letter appears in the antecedent of a conditional statement in the premises, consider obtaining the negated letter via modus tollens. ◦ If the conclusion is a conditional statement, consider obtaining it via pure hypothetical syllogism. ◦ If the conclusion contains a letter that appears in a disjunctive statement in the premises, consider obtaining that letter via disjunctive syllogism. Four Additional Rules of Inference: ◦ Constructive Dilemma (CD): (p q) • (r s) p v r q v s ◦ Simplification (Simp): p • q p ◦ Conjunction (Conj): p q p • q ◦ Addition (Add): p p v q Common Misapplications Common strategies involving the additional rules of inference: ◦ If the conclusion contains a letter that appears in a conjunctive statement in the premises, consider obtaining that letter via simplification.
    [Show full text]
  • Finding an Interpretation Under Which Axiom 2 of Aristotelian Syllogistic Is
    Finding an interpretation under which Axiom 2 of Aristotelian syllogistic is False and the other axioms True (ignoring Axiom 3, which is derivable from the other axioms). This will require a domain of at least two objects. In the domain {0,1} there are four ordered pairs: <0,0>, <0,1>, <1,0>, and <1,1>. Note first that Axiom 6 demands that any member of the domain not in the set assigned to E must be in the set assigned to I. Thus if the set {<0,0>} is assigned to E, then the set {<0,1>, <1,0>, <1,1>} must be assigned to I. Similarly for Axiom 7. Note secondly that Axiom 3 demands that <m,n> be a member of the set assigned to E if <n,m> is. Thus if <1,0> is a member of the set assigned to E, than <0,1> must also be a member. Similarly Axiom 5 demands that <m,n> be a member of the set assigned to I if <n,m> is a member of the set assigned to A (but not conversely). Thus if <1,0> is a member of the set assigned to A, than <0,1> must be a member of the set assigned to I. The problem now is to make Axiom 2 False without falsifying Axiom 1 as well. The solution requires some experimentation. Here is one interpretation (call it I) under which all the Axioms except Axiom 2 are True: Domain: {0,1} A: {<1,0>} E: {<0,0>, <1,1>} I: {<0,1>, <1,0>} O: {<0,0>, <0,1>, <1,1>} It’s easy to see that Axioms 4 through 7 are True under I.
    [Show full text]
  • Marko Malink (NYU)
    Demonstration by reductio ad impossibile in Posterior Analytics 1.26 Marko Malink (New York University) Contents 1. Aristotle’s thesis in Posterior Analytics 1. 26 ................................................................................. 1 2. Direct negative demonstration vs. demonstration by reductio ................................................. 14 3. Aristotle’s argument from priority in nature .............................................................................. 25 4. Priority in nature for a-propositions ............................................................................................ 38 5. Priority in nature for e-, i-, and o-propositions .......................................................................... 55 6. Accounting for Aristotle’s thesis in Posterior Analytics 1. 26 ................................................... 65 7. Parts and wholes ............................................................................................................................. 77 References ............................................................................................................................................ 89 1. Aristotle’s thesis in Posterior Analytics 1. 26 At the beginning of the Analytics, Aristotle states that the subject of the treatise is demonstration (ἀπόδειξις). A demonstration, for Aristotle, is a kind of deductive argument. It is a deduction through which, when we possess it, we have scientific knowledge (ἐπιστήμη). While the Prior Analytics deals with deduction in
    [Show full text]
  • C.S. Peirce's Abduction from the Prior Analytics
    Providence College DigitalCommons@Providence Community Scholar Publications Providence College Community Scholars 7-1996 C.S. Peirce's Abduction from the Prior Analytics William Paul Haas Follow this and additional works at: https://digitalcommons.providence.edu/comm_scholar_pubs Haas, William Paul, "C.S. Peirce's Abduction from the Prior Analytics" (1996). Community Scholar Publications. 2. https://digitalcommons.providence.edu/comm_scholar_pubs/2 This Article is brought to you for free and open access by the Providence College Community Scholars at DigitalCommons@Providence. It has been accepted for inclusion in Community Scholar Publications by an authorized administrator of DigitalCommons@Providence. For more information, please contact [email protected]. WILLIAM PAUL HAAS July 1996 C.S. PEIRCE'S ABDUCTION FROM THE PRIOR ANALYTICS In his Ancient Formal Logic. Professor Joseph Bochenski finds Aristotle's description of syllogisms based upon hypotheses to be "difficult to understand." Noting that we do not have the treatise which Aristotle promised to write, Bochenski laments the fact that the Prior Analytics, where it is treated most explicitly, "is either corrupted or (which is more probable) was hastily written and contains logical errors." (1) Charles Sanders Peirce wrestled with the same difficult text when he attempted to establish the Aristotelian roots of his theory of abductive or hypothetical reasoning. However, Peirce opted for the explanation that the fault was with the corrupted text, not with Aristotle's exposition. Peirce interpreted the text of Book II, Chapter 25 thus: Accordingly, when he opens the next chapter with the word ' Ajray (¿y-q a word evidently chosen to form a pendant to 'Errctyuyrj, we feel sure that this is what he is coming to.
    [Show full text]
  • The Axiom of Choice and Its Implications
    THE AXIOM OF CHOICE AND ITS IMPLICATIONS KEVIN BARNUM Abstract. In this paper we will look at the Axiom of Choice and some of the various implications it has. These implications include a number of equivalent statements, and also some less accepted ideas. The proofs discussed will give us an idea of why the Axiom of Choice is so powerful, but also so controversial. Contents 1. Introduction 1 2. The Axiom of Choice and Its Equivalents 1 2.1. The Axiom of Choice and its Well-known Equivalents 1 2.2. Some Other Less Well-known Equivalents of the Axiom of Choice 3 3. Applications of the Axiom of Choice 5 3.1. Equivalence Between The Axiom of Choice and the Claim that Every Vector Space has a Basis 5 3.2. Some More Applications of the Axiom of Choice 6 4. Controversial Results 10 Acknowledgments 11 References 11 1. Introduction The Axiom of Choice states that for any family of nonempty disjoint sets, there exists a set that consists of exactly one element from each element of the family. It seems strange at first that such an innocuous sounding idea can be so powerful and controversial, but it certainly is both. To understand why, we will start by looking at some statements that are equivalent to the axiom of choice. Many of these equivalences are very useful, and we devote much time to one, namely, that every vector space has a basis. We go on from there to see a few more applications of the Axiom of Choice and its equivalents, and finish by looking at some of the reasons why the Axiom of Choice is so controversial.
    [Show full text]
  • Catalogue of Titles of Works Attributed to Aristotle
    Catalogue of Titles of works attributed by Aristotle 1 To enhance readability of the translations and usability of the catalogues, I have inserted the following bold headings into the lists. These have no authority in any manuscript, but are based on a theory about the composition of the lists described in chapter 3. The text and numbering follows that of O. Gigon, Librorum deperditorum fragmenta. PART ONE: Titles in Diogenes Laertius (D) I. Universal works (ta kathalou) A. The treatises (ta syntagmatika) 1. The dialogues or exoterica (ta dialogika ex terika) 2. The works in propria persona or lectures (ta autopros pa akroamatika) a. Instrumental works (ta organika) b. Practical works (ta praktika) c. Productive Works (ta poi tika) d. Theoretical works (ta the r tika) . Natural philosophy (ta physiologia) . Mathematics (ta math matika) B. Notebooks (ta hypomn matika) II. Intermediate works (ta metaxu) III. Particular works (ta merika) PART TWO: Titles in the Vita Hesychii (H) This list is organized in the same way as D, with two exceptions. First, IA2c “productive works” has dropped out. Second, there is an appendix, organized as follows: IV. Appendix A. Intermediate or Particular works B. Treatises C. Notebooks D. Falsely ascribed works PART THREE: Titles in Ptolemy al-Garib (A) This list is organized in the same way as D, except it contains none of the Intermediate or Particular works. It was written in Arabic, and later translated into Latin, and then reconstructed into Greek, which I here translate. PART FOUR: Titles in the order of Bekker (B) The modern edition contains works only in IA2 (“the works in propria persona”), and replaces the theoretical works before the practical and productive, as follows.
    [Show full text]
  • Saving the Square of Opposition∗
    HISTORY AND PHILOSOPHY OF LOGIC, 2021 https://doi.org/10.1080/01445340.2020.1865782 Saving the Square of Opposition∗ PIETER A. M. SEUREN Max Planck Institute for Psycholinguistics, Nijmegen, the Netherlands Received 19 April 2020 Accepted 15 December 2020 Contrary to received opinion, the Aristotelian Square of Opposition (square) is logically sound, differing from standard modern predicate logic (SMPL) only in that it restricts the universe U of cognitively constructible situations by banning null predicates, making it less unnatural than SMPL. U-restriction strengthens the logic without making it unsound. It also invites a cognitive approach to logic. Humans are endowed with a cogni- tive predicate logic (CPL), which checks the process of cognitive modelling (world construal) for consistency. The square is considered a first approximation to CPL, with a cognitive set-theoretic semantics. Not being cognitively real, the null set Ø is eliminated from the semantics of CPL. Still rudimentary in Aristotle’s On Interpretation (Int), the square was implicitly completed in his Prior Analytics (PrAn), thereby introducing U-restriction. Abelard’s reconstruction of the logic of Int is logically and historically correct; the loca (Leak- ing O-Corner Analysis) interpretation of the square, defended by some modern logicians, is logically faulty and historically untenable. Generally, U-restriction, not redefining the universal quantifier, as in Abelard and loca, is the correct path to a reconstruction of CPL. Valuation Space modelling is used to compute
    [Show full text]
  • Traditional Logic II Text (2Nd Ed
    Table of Contents A Note to the Teacher ............................................................................................... v Further Study of Simple Syllogisms Chapter 1: Figure in Syllogisms ............................................................................................... 1 Chapter 2: Mood in Syllogisms ................................................................................................. 5 Chapter 3: Reducing Syllogisms to the First Figure ............................................................... 11 Chapter 4: Indirect Reduction of Syllogisms .......................................................................... 19 Arguments in Ordinary Language Chapter 5: Translating Ordinary Sentences into Logical Statements ..................................... 25 Chapter 6: Enthymemes ......................................................................................................... 33 Hypothetical Syllogisms Chapter 7: Conditional Syllogisms ......................................................................................... 39 Chapter 8: Disjunctive Syllogisms ......................................................................................... 49 Chapter 9: Conjunctive Syllogisms ......................................................................................... 57 Complex Syllogisms Chapter 10: Polysyllogisms & Aristotelian Sorites .................................................................. 63 Chapter 11: Goclenian & Conditional Sorites ........................................................................
    [Show full text]
  • Equivalents to the Axiom of Choice and Their Uses A
    EQUIVALENTS TO THE AXIOM OF CHOICE AND THEIR USES A Thesis Presented to The Faculty of the Department of Mathematics California State University, Los Angeles In Partial Fulfillment of the Requirements for the Degree Master of Science in Mathematics By James Szufu Yang c 2015 James Szufu Yang ALL RIGHTS RESERVED ii The thesis of James Szufu Yang is approved. Mike Krebs, Ph.D. Kristin Webster, Ph.D. Michael Hoffman, Ph.D., Committee Chair Grant Fraser, Ph.D., Department Chair California State University, Los Angeles June 2015 iii ABSTRACT Equivalents to the Axiom of Choice and Their Uses By James Szufu Yang In set theory, the Axiom of Choice (AC) was formulated in 1904 by Ernst Zermelo. It is an addition to the older Zermelo-Fraenkel (ZF) set theory. We call it Zermelo-Fraenkel set theory with the Axiom of Choice and abbreviate it as ZFC. This paper starts with an introduction to the foundations of ZFC set the- ory, which includes the Zermelo-Fraenkel axioms, partially ordered sets (posets), the Cartesian product, the Axiom of Choice, and their related proofs. It then intro- duces several equivalent forms of the Axiom of Choice and proves that they are all equivalent. In the end, equivalents to the Axiom of Choice are used to prove a few fundamental theorems in set theory, linear analysis, and abstract algebra. This paper is concluded by a brief review of the work in it, followed by a few points of interest for further study in mathematics and/or set theory. iv ACKNOWLEDGMENTS Between the two department requirements to complete a master's degree in mathematics − the comprehensive exams and a thesis, I really wanted to experience doing a research and writing a serious academic paper.
    [Show full text]
  • The Beginnings of Formal Logic: Deduction in Aristotle's Topics Vs
    Phronesis 60 (�0�5) �67-309 brill.com/phro The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics Marko Malink Department of Philosophy, New York University, 5 Washington Place, New York, NY 10003. USA [email protected] Abstract It is widely agreed that Aristotle’s Prior Analytics, but not the Topics, marks the begin- ning of formal logic. There is less agreement as to why this is so. What are the distinctive features in virtue of which Aristotle’s discussion of deductions (syllogismoi) qualifies as formal logic in the one treatise but not in the other? To answer this question, I argue that in the Prior Analytics—unlike in the Topics—Aristotle is concerned to make fully explicit all the premisses that are necessary to derive the conclusion in a given deduction. Keywords formal logic – deduction – syllogismos – premiss – Prior Analytics – Topics 1 Introduction It is widely agreed that Aristotle’s Prior Analytics marks the beginning of formal logic.1 Aristotle’s main concern in this treatise is with deductions (syllogismoi). Deductions also play an important role in the Topics, which was written before the Prior Analytics.2 The two treatises start from the same definition of what 1 See e.g. Cornford 1935, 264; Russell 1946, 219; Ross 1949, 29; Bocheński 1956, 74; Allen 2001, 13; Ebert and Nortmann 2007, 106-7; Striker 2009, p. xi. 2 While the chronological order of Aristotle’s works cannot be determined with any certainty, scholars agree that the Topics was written before the Prior Analytics; see Brandis 1835, 252-9; Ross 1939, 251-2; Bocheński 1956, 49-51; Kneale and Kneale 1962, 23-4; Brunschwig 1967, © koninklijke brill nv, leiden, ���5 | doi �0.��63/�5685�84-��34��86 268 Malink a deduction is (stated in the first chapter of each).
    [Show full text]
  • Aristotle on Principles As Elements
    Aristotle on Principles as Elements Marko Malink, New York University Draft, September 2016 Abstract: In his discussion of the four causes, Aristotle claims that ‘the hypotheses are material causes of the conclusion’ ( Physics 2.3, Metaphysics Δ 2). This claim has puzzled commentators since antiquity. It is usually taken to mean that the premises of any deduction are material causes of the conclusion. By contrast, I argue that the claim does not apply to deductions in general but only to scientific demonstrations. In Aristotle’s view, the theorems of a given science are composites composed of the indemonstrable premises from which they are demonstrated. Accordingly, these premises are elements, and hence material causes, of the theorems. Given this, Aristotle’s claim can be shown to be well-motivated and illuminating. 1. Hypotheses are material causes of the conclusion In Physics 2.3 and its doublet in Metaphysics Δ 2, Aristotle distinguishes the so-called four causes. The first of them is characterized as ‘that from which as a constituent something comes to be’. 1 Since antiquity, this type of cause is known as the ‘material cause’. 2 Aristotle illustrates it by a series of examples as follows: 1 τὸ ἐξ οὗ γίγνεταί τι ἐνυπάρχοντος, Phys. 2.3 194b24 (= Metaph. Δ 2 1013a24–5). 2 The ancient commentators refer to it as ὑλικὸν αἴτιον (Alex. Aphr. in Metaph. 349.2, 351.5, 353.20, Philop. in Phys. 243.21, 243.30, 246.25–247.11, 249.6, Simpl. in Phys. 314.27, 319.20, 320.13, Asclep. in Metaph. 305.22–4, 306.9–14).
    [Show full text]