Selections from Prior Analytics
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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. -
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. -
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 -
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. -
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. -
Syllabus for B.H.M.S. (Degree) Course
SYLLABUS FOR B.H.M.S. (DEGREE) COURSE As per the Homoeopathy (DEGREE Course) BHMS regulation, 1983, (as amended up to 2019) ANATOMY Instructions: I. (a) Instructions in anatomy should be so planed as to present a general working knowledge of the structure of the human body; (b) The amount of detail which a student is required to memorise should be reduced to the minimum; (c) Major emphasis should be laid on functional anatomy of the living subject rather than on the static structures of the cadaver, and on general anatomical positions and broad relations of the viscera, muscles, blood-vessels, nerves and lymphatics and study of the cadaver is the only means to achieve this; (d) Students should not be burdened with minutes anatomical details which have no clinical significance. II. Though dissection of the entire body is essential for the preparation of the student of his clinical studies, the burden of dissection can be reduced and much saving of time can be effected, if considerable reduction of the amount of topographical details is made and the following points are kept in view:- (1) Only such details as have professional or general educational value for the medical students. (2) The purpose of dissection is to give the student an understanding of the body in relation to its function, and the dissection should be designed to achieve this goal. (3) Normal radiological anatomy may also form part of practical or clinical training and the structure of the body should be presented linking functional aspects. (4) Dissection should be preceded by a course of lectures on the general structure of the organ or the system under discussion and then its function. -
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. -
Reviving Material Theories of Induction John P. Mccaskey 1
Reviving Material Theories of Induction John P. McCaskey 1. Reviving material theories of induction John D. Norton says that philosophers have been led astray for thousands of years by their attempt to treat induction formally (Norton, 2003, 2005, 2010, 2014, 2019). He is correct that such an attempt has caused no end of trouble, but he is wrong about the history. There is a rich tradition of non-formal induction in the writings of, among others, Aristotle, Cicero, John Buridan, Lorenzo Valla, Rudolph Agricola, Peter Ramus, Francis Bacon, and William Whewell. In fact, material theories of induction prevailed all through antiquity and from the Renaissance to the mid-1800s. Recovering these past systems would not only fill lacunae in Norton’s own theory but would highlight areas where Norton has not freed himself from the straightjacket of formal induction as much as he might think. The effort might also help us build a new theory of induction on the ground Norton has cleared for us. This essay begins that recovery and invites that rebuilding.1 2. Formal vs. Material theories of induction The distinction between formal and material theories of induction was first drawn, at least under those names, in the 1840s. The inductive system of Francis Bacon had prevailed for two hundred years, and some philosophers were starting to complain about that, most influentially a professor at Oxford University named Richard Whately.2 Bacon’s induction was an extension of Renaissance classification logic (“topics-logic”). It was orderly and methodical, but it was not 1 The essay will not defend particular formal systems against Norton’s attacks. -
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). -
1 the Aristotelian Method and Aristotelian
1 The Aristotelian Method and Aristotelian Metaphysics TUOMAS E. TAHKO (www.ttahko.net) Published in Patricia Hanna (Ed.), An Anthology of Philosophical Studies (Athens: ATINER), pp. 53-63, 2008. ABSTRACT In this paper I examine what exactly is ‘Aristotelian metaphysics’. My inquiry into Aristotelian metaphysics should not be understood to be so much con- cerned with the details of Aristotle's metaphysics. I am are rather concerned with his methodology of metaphysics, although a lot of the details of his meta- physics survive in contemporary discussion as well. This warrants an investigation into the methodological aspects of Aristotle's metaphysics. The key works that we will be looking at are his Physics, Meta- physics, Categories and De Interpretatione. Perhaps the most crucial features of the Aristotelian method of philosophising are the relationship between sci- ence and metaphysics, and his defence of the principle of non-contradiction (PNC). For Aristotle, natural science is the second philosophy, but this is so only because there is something more fundamental in the world, something that natural science – a science of movement – cannot study. Furthermore, Aristotle demonstrates that metaphysics enters the picture at a fundamental level, as he argues that PNC is a metaphysical rather than a logical principle. The upshot of all this is that the Aristotelian method and his metaphysics are not threatened by modern science, quite the opposite. Moreover, we have in our hands a methodology which is very rigorous indeed and worthwhile for any metaphysician to have a closer look at. 2 My conception of metaphysics is what could be called ‘Aristotelian’, as op- posed to Kantian. -
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. -
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.