DOCSLIB.ORG

225 Aristotle on the Transcendentals MICHAEL J. LOUX N This Paper, I

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
225 Aristotle on the Transcendentals MICHAEL J. LOUX N This Paper, I Aristotle on the Transcendentals MICHAEL J. LOUX n this paper, I want to examine two claims found in Aristotle's Metaphysics : (A) the claim that notions like being and unity do not constitute genera and (B) the claim that such notions are not univocally predicable of all things. I want, in particular, to consider the view (expressed by Porphyry, William of Ockham, and J. L. Ackrill) that (A) entails (B). I shall argue that the alleged entailment cannot hold since while (A) is true, (B) is false. I The claim that neither being nor unity can function generically is discussed in a number of places. The most detailed discussion of the thesis is found in Metabhysics B 3, 998 b 22-27, where Aristotle says :1 But it is not possible that either being (Tb 6v) or unity (ib guv)should be a single genus of things, for the differentiae of any genus must each of them have being and be one (xai elvoctxat clvai) but it is not possible for the genus taken apart from its species (any more than for the species of the genus) to be predicated of the differentiae, so that if unity or being is a genus, no differentia will either have being or be one (ours 8v Aristotle is fairly explicit about the leading premise of this argument. The premise is (1) Genera are not predicable of their differentiae. For Aristotle, a genus is a kind or sort whose members belong to a variety of less general kinds or species. (1) Tells us that a genus is not predicable of the characteristics by which its species are distinguished. Provisionally, we can take Aristotle to be referring to true predication in (1), to be saying that propositions of the form 'D is a G' (where 'G' and 'D' range over genera and their differentiae, respectively) are never true. Aristotle's use of (1) to derive (A) is straightforward. He asks us to assume that being and unity are genera. Qua genera, they must have 225 differentiae; and, by (1), they cannot be predicable of these differen- tiae. Aristotle claims, however, that being and unity are predicable of every notion that could serve to differentiate them into species. Thus, we have a contradiction, and the assumption falls. But why is it that being and unity are predicable of all possible candidates as differentiae? Aristotle's response, I take it, is that being and unity are universally predicable notions. For Aristotle, 'being' and 'one' are terms that hold true of every item in every category; they are what the Medievals called transcendental terms and what I shall call T-Words. Once we expose this point, it becomes clear that the argument in Metaphysics B 3 extends beyond being and unity. Aristotle deals with these notions because, in his account, they are the most important (or only) transcendentals; nevertheless, it is best to construe the pas- sage as incorporating, if only implicitly, a general argument against all transcendental genera. Viewed in this way, the argument focuses on the claim (2) Some transcendental (Call it 'T' ) is a genus. Structurally, the attack on (2) takes the form of a reductio. Thus, from (1) and (2), we can derive (3) T is not predicable of its differentiae; but since, by (2), T is a transcendental, it follows that (4) T is predicable of its differentiae, so that (5) (2) is false, or, more perspicuously, no transcendental is a genus. This argument hinges on (1) ; and when we confront it with examples, (1) seems true. Thus, 'Rationality is an animal' and 'Being three sided is a figure', are, in accordance with (1), both false. But while these examples confirm (1), they do not provide the sort of insight we are likely to demand. For a more detailed defense of (1), we must turn to Topics VI 6, 144 a 32-b 1, where Aristotle says : Again, see if the genus be predicated of the differentiae; for the general view is that the genus is predicated, not of the differentia, but of the objects of which the differentia is predicated. Animal (e.g.) is predicated of man or ox or other walking animals, not of the actual differentia itself which we predicate of the species For if animal is to be predicated of each of its differentiae, then animal would be predicated of the species several times over; for the differentiae are predicates of the species. The claim here is that if we assume the negation of (1), an undesirable 226 .
Load more

Recommended publications
  • Existence As a Real Property
    Francesco Berto Existence as a Real Property The Ontology of Meinongianism For Graham Priest, Long-distance teacher Prologue: Much Ado About Nothing Some philosophers think that something’s having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself. I really don’t know, in a way, what more conclusive evidence one can have about anything, ultimately speaking. –Saul Kripke, Naming and Necessity 1 In an episode of The Today Show of some years ago, Gene Shalit – NBC’s film and book critic, famous for his wits – reviews several books sharing the feature of bearing entertaining titles. The highpoint of the monologue comes with Nonexistent Objects, by the UCLA philosopher Terence Parsons. Shalit wonders how one could write a whole book on things that do not exist!1 This whole book, too, is about things that do not exist. But if one stops to think, one may find that, in a sense, there is nothing special about this. There are, in fact, thousands of books speaking about unreal things. You have probably read quite a few of them: Sir Arthur Conan Doyle’s stories portrait the adventures of the detective Sherlock Holmes; The Lord of the Rings speaks at length of Gandalf the wizard. Doyle represents Sherlock Holmes as a detective living in London, Baker Street (precisely, at number 221b), describes his remarkable observational and deductive abilities, makes of him the arch-enemy of the criminal mastermind Moriarty. J.R.R. Tolkien characterizes Gandalf as a wizard with a pointy hat and a grey robe (a white one, from a certain point of the story onwards), a heavy pipe-herb 1 The anecdote is reported by Roy Sorensen [2003], p.
    [Show full text]
  • Logic and Ontology
    Logic and Ontology Nino B. Cocchiarella Abstract A brief review of the historical relation between logic and ontology and of the opposition between the views of logic as language and logic as calculus is given. We argue that predication is more fundamental than membership and that di¤erent theories of predication are based on di¤erent theories of universals, the three most important being nominalism, conceptualism, and realism. These theories can be formulated as formal ontologies, each with its own logic, and compared with one another in terms of their respective explanatory powers. After a brief survey of such a comparison, we argue that an extended form of conceptual realism provides the most coherent formal ontology and, as such, can be used to defend the view of logic as language. Logic, as Father Bochenski observed, developed originally out of dialectics, rules for discussion and reasoning, and in particular rules for how to argue suc- cessfully.1 Aristotle, one of the founders of logic in western philosophy, described such rules in his Topics, where logic is presented in this way. Indeed, the idea of logic as the art of arguing was the primary view of this subject in ancient philos- ophy. It was defended in particular by the Stoics, who developed a formal logic of propositions, but conceived of it only as a set of rules for arguing.2 Aristotle was the founder not only of logic in western philosophy, but of ontol- ogy as well, which he described in his Metaphysics and the Categories as a study of the common properties of all entities, and of the categorial aspects into which they can be analyzed.
    [Show full text]
  • Extension and Comprehension in Logic: an Essay in Doctrine
    Document generated on 09/24/2021 9:48 p.m. Laval théologique et philosophique Extension and Comprehension in Logic An Essay In Doctrine Joseph C. Frisch Volume 24, Number 2, 1968 URI: https://id.erudit.org/iderudit/1020127ar DOI: https://doi.org/10.7202/1020127ar See table of contents Publisher(s) Laval théologique et philosophique, Université Laval ISSN 0023-9054 (print) 1703-8804 (digital) Explore this journal Cite this article Frisch, J. C. (1968). Extension and Comprehension in Logic: An Essay In Doctrine. Laval théologique et philosophique, 24(2), 215–257. https://doi.org/10.7202/1020127ar Tous droits réservés © Laval théologique et philosophique, Université Laval, This document is protected by copyright law. Use of the services of Érudit 1968 (including reproduction) is subject to its terms and conditions, which can be viewed online. https://apropos.erudit.org/en/users/policy-on-use/ This article is disseminated and preserved by Érudit. Érudit is a non-profit inter-university consortium of the Université de Montréal, Université Laval, and the Université du Québec à Montréal. Its mission is to promote and disseminate research. https://www.erudit.org/en/ Extension and Comprehension in Logic An Essay In Doctrine Although the words ‘extension’ and ‘comprehension’ have been used in logical textbooks for more than three hundred years without anyone offering a serious appraisal of their validity, the question arises whether this sort of vocabulary is well-grounded, and whether logicians can defend their position concerning this manner of speaking. Let us examine whether the words ‘extension’ and ‘comprehension’ may be employed legitimately within the domain of logic, or whether these two words convey adequately the meaning intended by logicians.
    [Show full text]
  • The Problem of the Transcendentals
    The Problem of the Transcendentals Ligerz, March , Philipp Blum Being is not a genus Suppose Being were a genus and substances one of its species, substantial being the specific difference. substantial alsois, soitisitselfamongtheexemplarsofthegenus. Doesitbelongtothespeciesofsubstances or not? If it does, then it is a substance and is substantial. But then it is separated and the same in kind as its exemplars, and shares with them itself – a third man problem if there ever was one. If it does not belong to itself, on the other hand, then it is not a substance and not separated – but how can it then be, and be the specific difference of a species? If animal were predicable of rational, taken apart from rational animal, then rational would be an animal, but then rational would be animal, i.e. all animals would be rational and rational would not mark out a species among the genus, but be the same as animal. How being can be unified even if it is not a genus is one of the problems set for the Metaphysics to solve. The question is involved already in the th aporia of Met. Beta: πρὸς δὲ τούτοις εἰ καὶ ὅτι μάλιστα ἀρχαὶ τὰ γένη εἰσί, πότερον For if the universal is always more of a principle, evidently the δεῖ νομίζειν τὰ πρῶτα τῶν γενῶν ἀρχὰς ἢ τὰ (15) ἔσχατα κατη- uppermost of the genera are the principles; for these are pred- γορούμενα ἐπὶ τῶν ἀτόμων; καὶ γὰρ τοῦτο ἔχει ἀμφισβήτησιν. εἰ icated of all things. There will, then, be as many principles of μὲν γὰρ ἀεὶ τὰ καθόλου μᾶλλον ἀρχαί, φανερὸν ὅτι τὰ ἀνωτάτω things as there are primary genera, so that both being and unity τῶν γενῶν· ταῦτα γὰρ λέγεται κατὰ πάντων.
    [Show full text]
  • Jean Buridan's Theory of Individuation
    c Peter King, in Individuation and Scholasticism (SUNY 1994), 397–430 BURIDAN’S THEORY OF INDIVIDUATION* 1. Introduction URIDAN holds that no principle or cause accounts for the individuality of the individual, or at least no principle or B cause other than the very individual itself, and thus there is no ‘metaphysical’ problem of individuation at all—individuality, unlike gen- erality, is primitive and needs no explanation. He supports this view in two ways. First, he argues that there are no nonindividual entities, whether existing in their own right or as metaphysical constituents either of things or in things, and hence that no real principle or cause of individuality (other than the individual itself) is required. Second, he offers a ‘semantic’ inter- pretation of what appear to be metaphysical difficulties about individuality by recasting the issues in the formal mode, as issues within semantics, such as how a referring expression can pick out a single individual. Yet although there is no ‘metaphysical’ problem of individuation, Buridan discusses two associated problems at some length: the identity of individuals over time and the discernibility of individuals. The discussion will proceed as follows. In §2, Buridan’s semantic frame- work, the idiom in which he couches his philosophical analyses, will be * References to Buridan are taken from a variety of his works (with abbreviations listed): Questions on Aristotle’s “Categories” (QC); Questions on Aristotle’s “Physics” (QSP); Questions on Aristotle’s “De caelo et mundo” (QCM); Questions on Aristotle’s “De anima” (QA); Questions on Aristotle’s “Metaphysics” (QM); Treatise on Supposi- tion (TS); Sophismata; Treatise on Consequences (TC).
    [Show full text]
  • Aristotelian Predicables, Universality and Realism the Logic of Comparison in Topics As Denying the View That Aristotle Was a Realist*
    ARISTOTELIAN PREDICABLES, UNIVERSALITY AND REALISM THE LOGIC OF COMPARISON IN TOPICS AS DENYING THE VIEW THAT ARISTOTLE WAS A REALIST* Giampaolo Abbate (Centro de Filosofia da Universidade de Lisboa) 1. The question The paradigmatic passage on how Aristotle introduces the dispute about universals is undoubtedly the seventh aporia of the third book of Metaphysics:1 Besides this, even if the genera are in the highest degree principles, should one regard the first of the genera as principles, or those which are predicated directly of the individuals? This also admits of dispute. For if the universal is always more of a principle, evidently the uppermost of the genera are the principles; for these are predicated of all things. There will, then, be as many principles of things as there are primary genera, so that both being and unity will be principles and substances; for these are most of all predicated of all things. But it is not possible that either unity or being should be a genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus to be predicated of the differentiae taken apart from the species (any more than for the species of the genus to be predicated of the proper differentiae of the genus); so that if unity or being is a genus, no differentia will either be one or have being. But if unity and being are not genera, neither will they be principles, if the genera are the principles. Again, the intermediate classes, whose concepts include the differentiae, will on 1 III, 3, 998b 14 – 999a 23.
    [Show full text]
  • JS Mill and Aristotle
    Document generated on 10/01/2021 12:29 p.m. Laval théologique et philosophique Essential Predication and the Syllogism : J.S. Mill and Aristotle James Donaldson Volume 31, Number 2, 1975 URI: https://id.erudit.org/iderudit/1020480ar DOI: https://doi.org/10.7202/1020480ar See table of contents Publisher(s) Laval théologique et philosophique, Université Laval ISSN 0023-9054 (print) 1703-8804 (digital) Explore this journal Cite this article Donaldson, J. (1975). Essential Predication and the Syllogism : J.S. Mill and Aristotle. Laval théologique et philosophique, 31(2), 193–205. https://doi.org/10.7202/1020480ar Tous droits réservés © Laval théologique et philosophique, Université Laval, This document is protected by copyright law. Use of the services of Érudit 1975 (including reproduction) is subject to its terms and conditions, which can be viewed online. https://apropos.erudit.org/en/users/policy-on-use/ This article is disseminated and preserved by Érudit. Érudit is a non-profit inter-university consortium of the Université de Montréal, Université Laval, and the Université du Québec à Montréal. Its mission is to promote and disseminate research. https://www.erudit.org/en/ ESSENTIAL PREDICATION AND THE SYLLOGISM : J. S. MILL AND ARISTOTLE James D o n a l d s o n I N his System of Logic J. S. Mill goes to some pains to point out thatdiet the de omni vel nullo, known as the principle of the syllogism, rests on or is valid only in the case of essential predication.' How Mill is right in this assertion and how he is wrong in his next assertion is the subject of this paper.
    [Show full text]
  • Philosophical Perspectives on the Humanities 1 from Porphyry's
    Humanities 116: Philosophical Perspectives on the Humanities 1 From Porphyry’s Isagoge, on the five predicables Porphyry’s Isagoge, as you can see from the first sentence, is meant as an introduction to the Categories. In it he discusses five important words that Aristotle uses constantly, but never defines in a clear and organized way. (The closest Aristotle comes is in Topics 1.4–5, which I used to assign for this course. But I find that it isn’t very understandable.) The five words (traditionally called “the five predicable”) are: “genus,” “species,” “differentia,” “proprium,” and “accident.” They describe five ways in which, according to Aristotle, one predicate (property, characteristic) can apply to many things. Below are brief excerpts from Porphyry’s already brief discussion. Most of what he says here is taken more or less directly from Aristotle, just reorganized. (Porphyry also had his own more original ideas; we’ll see some of them next time.) To put the whole thing even more briefly: you can define a species (for example, hu- man) by giving its genus (animal, apparently, or maybe mortal animal) and its differentia (rational). (So the definition would be: “a human is a rational animal,” or: “a human is a rational mortal animal.”1) The differentia belongs to all the members of the species and only to them. (For example: all humans are rational, and, at least among mortal animals, only humans are rational.) But a differentia isn’t just any characteristic like that. For example: among mortal animals, all humans and only humans are “risible” (able to laugh).
    [Show full text]
  • OBJ (Application/Pdf)
    OIT TIIE AXIOM 01* ABSTRACTIOK Ain) RUS3ELL»S PARADOX V A THESIS SUBMITTED TO THE EACUDTY OE ATLAHTA UITIVERSITY IN PARTIAL PUIPILLMENT OP THE REQUIRMENTS POR THE DEGREE OP TIASTER OP SCIENCE BY RALPH SHIRLEY HAYNES DEPARTMENT OP LM.THEMATICS ATLANTA, GEORGIA AUGUST I960 Ip^ LcC \ SjO' 2^^ ACKIIOWLEDGEI-IEITTS The writer expresses sincere appreciation to hr. Lonnie Cross for suggesting this problem and for his helpful suggestions and counsel during its development. ii TABLE OP C0LTEET3 Page ACKIIOV/LEDGLIEIITS ii Chapter I. IETPlODUCTIOIT 1 II. JIATHEI.IATICAL LOC-IC AED ITOTATIOE 5 Sets and Subsets 5 Propositions and Basic Operations .... 6 Quantifiers 9 Bound and Free Yariables 10 III. TtlE AXIOM AEL TEE PARADOX 12 Axioms in Cantor^^s Set Theory 12 The Russell Paradox . »15 Symbolic Representation of the Axiom and the Paradox 15 lY. ON THE EOE-EXISTEECE OP THE PARADOXES IE TI-IE THEORY OP SETS OR LOGIC 16 Lemma and Corollary 17 Application of Lemma to Russell^s Paradox 18 Applicability of the Lemma to Other Paradoxes 19 BIBLIOGRAPHY iii CHAPTER I INTRODUCTIOH Mathematics is one of the most interesting and challeng¬ ing subjects known to mankind. This is due primarily to the fact that it involves logic, logic as a science was developed by Aristotle (384-322 B. C.) and the scholastic philosophers of the Mddle Ages. Aristotle was considered more as a logician than a mathematician because of his gneat interest in logic and his attempt to systematize classical logic. Probably because of the development of logic by philosophers, many leading colleges and universities have traditionally taught it in the philosophy department of the school.
    [Show full text]
  • Gödel's Basic Logic Course at Notre Dame
    Logic Lectures G¨odel’s Basic Logic Course at Notre Dame Edited by Miloˇs Adˇzic´ and Kosta Doˇsen Faculty of Philosophy, University of Belgrade Cikaˇ Ljubina 18-20, 11000 Belgrade, Serbia, and Mathematical Institute, Serbian Academy of Sciences and Arts Knez Mihailova 36, p.f. 367, 11001 Belgrade, Serbia email: [email protected], [email protected] April 2017 arXiv:1705.02601v3 [math.HO] 16 Jun 2017 LOGIC LECTURES iii Abstract. An edited version is given of the text of G¨odel’s unpublished manuscript of the notes for a course in basic logic he delivered at the University of Notre Dame in 1939. G¨odel’s notes deal with what is today considered as important logical problems par excellence, completeness, decidability, independence of axioms, and with natural deduction too, which was all still a novelty at the time the course was delivered. Full of regards towards beginners, the notes are not excessively formalistic. G¨odel presumably intended them just for himself, and they are full of abbreviations. This together with some other matters (like two versions of the same topic, and guessing the right order of the pages) required additional effort to obtain a readable edited version. Because of the quality of the material provided by G¨odel, including also important philosophical points, this effort should however be worthwhile. The edited version of the text is accompanied by another version, called the source version, which is quite close to G¨odel’s manuscript. It is meant to be a record of the editorial interventions involved in producing the edited version (in particular, how the abbreviations were disabridged), and a justification of that later version.
    [Show full text]
  • Chapter 1: Critical Analysis of Logical Theories †1
    Volume 2: Elements of Logic. Book 1: General and Historical Survey of Logic Chapter 1: Critical Analysis of Logical Theories †1 §1. Logic's PromisesP 1. Begin, if you will, by calling logic the theory of the conditions which determine reasonings to be secure. A conception at once more exact and more extended may be looked for in the sequel. †2 Meantime, this description will serve for our preparatory studies of the yet unvisited country into which we propose to push our explorations. Logic, then, is a theory. The end of any theory is to furnish a rational account of its object. A theory directly aims at nothing but knowing. Maybe, if it be sound, it is likely, some day, to prove useful. Still, fairness forbids our making utility the criterion of the excellence of the theory. One must acknowledge that such a way of thinking would not abase logic, as it does the generality of the sciences. To judge of logic by its applications would only be to judge of it by how far it does, or does not, in a certain manner, help us to understand things. Clearly, it is the proper aim of any theory to do that. Looking at the matter on the other side, this very consideration tends to show that the touchstone of utility is superfluous and impertinent for logic. Suppose the science supports the test; what then? That would merely show that it aids the understanding. Grant that it is a sound theory, and it must have been prepared to do that, application or no application.
    [Show full text]
  • QUESTIONS on PORPHYRY's ISAGOGE, QQ. 1-3 DUNS SCOTUS Translated by Jacob Archambault [QUESTION 1: WHETHER LOGIC IS a SCIENCE] 1
    QUESTIONS ON PORPHYRY'S ISAGOGE, QQ. 1-3 DUNS SCOTUS Translated by Jacob Archambault [QUESTION 1: WHETHER LOGIC IS A SCIENCE] 1. We ask whether logic is a science. It seems not: For a manner of knowing (modus sciendi) is not itself a science (scientia); logic is a manner of knowing. Therefore, etc. The major is evident by analogy: the manner of seeing is not sight. The proof of the minor is from Aristotle's Metaphysics II1 “It is absurd to seek at once both the knowledge and the manner of knowing it.” And this is explained [thus]: 'manner of knowing', i.e. 'logic2'. 2. Again, in Metaphysics VI3 Aristotle divides the sciences into the mathematical, natural, and divine or metaphysical, and logic is contained under none of these. 3. Again, a science is from what is proper to it, just as a demonstration is according to Aristotle in Posterior Analytics I4; logic is from what is common5; therefore, etc. 4. For the opposite: Knowledge (scientia) is the effect of a demonstration; But in logic, many things are shown by demonstration; therefore, etc. 5. Again, the following is per se: 'the logician is knowing' (logicus est sciens), therefore, logic is a science; for when the predication is per se, what holds for the particular also holds in the abstract. 6. We must say that logic is a science, for the things taught in it are concluded by demonstration just as in other sciences; therefore they are known (sciuntur), since “a demonstration is a syllogism effecting knowledge 6 ”. There are likewise in logic all the things required for demonstration: that is, a subject, [and] a datum (passio) demonstrable from that subject through a medium – that is, a definition.
    [Show full text]