Aristotle on Principles As Elements
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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. -
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. -
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. -
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). -
Philosophy 302: Plato and Aristotle Course Description This Course
Philosophy 302: Plato and Aristotle Course Description This course surveys the essential content of the philosophies of Plato and Aristotle and considers more briefly some of the earlier thinkers whose ideas form the immediate context for their works. We will begin with dialogues in which Plato's is thought to give a reasonable accurate depiction of his mentor Socrates, and will focus on the ethical theses defended in these works and on the standards for knowledge presupposed by them. We will then observe how these theses and standards, in combination with certain ideas and problems from pre-Socratic thought, lead Plato to develop the first philosophical system: an integrated set of ideas about the fundamental nature of reality, man, knowledge, and value. We will then turn to Aristotle’s formulation of the principles of logic and the structure of science. Finally, we will study Aristotle's own philosophical system, with a focus on the ways in which it is similar to and different from Plato's. Instructor and Course Information Instructor: Gregory Salmieri ([email protected], 412-576-2990) Meetings: Friday 11:30am – 2:30pm, Murray Hall 115 Required Books Reeve (tr.), Plato: Republic, Hackett (ISBN-10: 0872207366, ISBN-13: 978-0872207363). [Amazon] [Barnes and Noble] Irwin and Fine (tr.), Aristotle: Selections (ISBN-10: 0915145677, ISBN-13: 978-0915145676). [Amazon] [Barnes and Noble] Adamson, Classical Philosophy, Oxford University Press (ISBN-10: 0199674531, ISBN-13: 978- 0199674534). [Amazon] [Barnes and Noble] Additional readings available online. Grading There will be ten quizzes over the course of the semester, administered through Sakai, which will be collectively worth 20% of the grade, two papers each worth 30% of the grade, and a final exam worth 20%. -
The University of Chicago Aristotle on the Necessity
THE UNIVERSITY OF CHICAGO ARISTOTLE ON THE NECESSITY OF WHAT WE KNOW A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE HUMANITIES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHILOSOPHY BY JOSHUA MENDELSOHN CHICAGO, ILLINOIS JUNE 2019 TABLE OF CONTENTS ACKNOWLEDGMENTS . iv ABSTRACT . v 1 INTRODUCTION . 1 1.1 Aristotle on what we know ........................... 1 1.2 Previous approaches ............................... 7 1.3 Some first steps toward an answer ....................... 25 1.4 Chapter breakdown ................................ 34 2 ARISTOTLE’S DURABILITY ARGUMENTS . 36 2.1 Knowledge in the Categories ........................... 36 2.1.1 Knowledge as a relative: Categories 7 . 36 2.1.2 Knowledge as a state: Categories 8 ................... 51 2.1.3 The tension between the two principles . 59 2.2 When what is changeable goes out of view: Nicomachean Ethics VI.3 . 66 2.2.1 The sense of “necessity” ......................... 74 2.2.2 A Platonic precursor: Theaetetus 163c–164b . 75 2.3 Durability and demonstration: Posterior Analytics I.6 . 79 2.4 Knowledge of sensible particulars: Metaphysics Ζ.15 . 86 2.5 Taking stock ................................... 88 3 THE OBJECT OF KNOWLEDGE . 90 3.1 The introduction of the Forms ......................... 93 3.2 The irrelevance of the Forms .......................... 96 3.3 Essentiality and necessity: Posterior Analytics I.4 . 102 3.3.1 “Of all” and “per se” . 103 3.3.2 Per se predications and necessity . 108 3.3.3 “Universal” ................................112 3.3.4 Demonstrative necessities concerning individuals . 115 3.4 Per se necessity in natural science . 120 3.4.1 Per se necessity in biology: Parts of Animals II.3 . -
Al-Farabi's Short Commentary on Aristotle's Prior Analytics
Al-Farabi’s Short Commentary on Aristotle’s Prior Analytics Translated, with an Introduction and Notes, by Nicholas Rescher University of Pittsburgh Press AL-FARABI’S SHORT COMMENTARY ON ARISTOTLE’S PRIOR ANALYTICS AL-FARABI’S SHORT COMMENTARY ON ARISTOTLE’S PRIOR ANALYTICS Translated from the Original Arabic with Introduction and Notes BY NICHOLAS RESCHER Professor of Philosophy in the University of Pittsburgh UNIVERSITY OF PITTSBURGH PRESS 1963 Library of Congress Catalog Card Number 63-10581 Printed in Great Britain by Butler & ‘Tanner Ltd, Frome and London This book is dedicated, with gratitude and with love, to my mother and to the memory of my father. PREFACE This English version of al-Farabi’s “Short Commentary on Prior Analytics”, made from Mlle Mubahat Tirker’s recent edition of the Arabic text (Revue de la Faculté des Langues, d Histoire, et de Géographie de? Université d Ankara, vol. 16 [1958]), is the first appearanceof this treatise in a European language. It is hoped that this addition to the dozen or so Arabic logical texts now accessible to the non- Orientalist will contribute to a wider appreciation of the great mass of work constituting the Arabic contribution to logic, which remains so largely terra incognita. I wish to thank Mrs. Shukrieh Kassis and especially Mr. Seostoris Khalil for help with the translation. I am in- debted to Mr. Storrs McCall, Dr. J. Ackrill, and particu- larly to Professor D. M. Dunlop for reading my typescript and suggesting needed improvements. Although some strengths of this work owetheir existence to others, all of its weaknesses and errors must be laid at my own door. -
The Conceptions of Self-Evidence in the Finnis Reconstruction of Natural Law
St. Mary's Law Journal Volume 51 Number 2 Article 4 4-2020 The Conceptions of Self-Evidence in the Finnis Reconstruction of Natural Law Kevin P. Lee Campbell University School of Law Follow this and additional works at: https://commons.stmarytx.edu/thestmaryslawjournal Part of the Catholic Studies Commons, Jurisprudence Commons, Law and Philosophy Commons, Legal History Commons, Logic and Foundations of Mathematics Commons, Natural Law Commons, Other Philosophy Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Recommended Citation Kevin P. Lee, The Conceptions of Self-Evidence in the Finnis Reconstruction of Natural Law, 51 ST. MARY'S L.J. 413 (2020). Available at: https://commons.stmarytx.edu/thestmaryslawjournal/vol51/iss2/4 This Article is brought to you for free and open access by the St. Mary's Law Journals at Digital Commons at St. Mary's University. It has been accepted for inclusion in St. Mary's Law Journal by an authorized editor of Digital Commons at St. Mary's University. For more information, please contact [email protected]. Lee: Self-Evidence in the Finnis Reconstruction of Natural Law ESSAY THE CONCEPTIONS OF SELF-EVIDENCE IN THE FINNIS RECONSTRUCTION OF NATURAL LAW KEVIN P. LEE* I. Introduction ........................................................................................... 414 A. Locating Finnis’ Claim to Self-Evidence .................................... 416 1. The Separation of Fact and Value ........................................ 416 2. The First Principles of Practical Reason ............................. 419 a. Basic Goods are the First Principles of Practical Reason ................................................................................ 421 b. Basic Goods are Dispositions ........................................ 421 c. Basic Goods are Apodictic ............................................. 422 II. Two Conceptions of Self-Evidence ................................................... 426 A. Finnis and Leonine Thomism ..................................................... -
Essence and Necessity, and the Aristotelian Modal Syllogistic: a Historical and Analytical Study Daniel James Vecchio Marquette University
Marquette University e-Publications@Marquette Dissertations (2009 -) Dissertations, Theses, and Professional Projects Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study Daniel James Vecchio Marquette University Recommended Citation Vecchio, Daniel James, "Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study" (2016). Dissertations (2009 -). 686. http://epublications.marquette.edu/dissertations_mu/686 ESSENCE AND NECESSITY, AND THE ARISTOTELIAN MODAL SYLLOGISTIC: A HISTORICAL AND ANALYTICAL STUDY by Daniel James Vecchio, B.A., M.A. A Dissertation submitted to the Faculty of the Graduate School, Marquette University, in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Milwaukee, Wisconsin December 2016 ABSTRACT ESSENCE AND NECESSITY, AND THE ARISTOTELIAN MODAL SYLLOGISTIC: A HISTORICAL AND ANALYTICAL STUDY Daniel James Vecchio, B.A., M.A. Marquette University, 2016 The following is a critical and historical account of Aristotelian Essentialism informed by recent work on Aristotle’s modal syllogistic. The semantics of the modal syllogistic are interpreted in a way that is motivated by Aristotle, and also make his validity claims in the Prior Analytics consistent to a higher degree than previously developed interpretative models. In Chapter One, ancient and contemporary objections to the Aristotelian modal syllogistic are discussed. A resolution to apparent inconsistencies in Aristotle’s modal syllogistic is proposed and developed out of recent work by Patterson, Rini, and Malink. In particular, I argue that the semantics of negation is distinct in modal context from those of assertoric negative claims. Given my interpretive model of Aristotle’s semantics, in Chapter Two, I provide proofs for each of the mixed apodictic syllogisms, and propose a method of using Venn Diagrams to visualize the validity claims Aristotle makes in the Prior Analytics. -
Aristotle on Sign-Inference and Related Forms Ofargument
12 Introduction degree oflogical sophistication about what is required for one thing to follow from another had been achieved. The authorities whose views are reported by Philodemus wrote to answer the charges of certain unnamed opponents, usually and probably rightly supposed to be Stoics. These opponents draw· on the resources of a logical STUDY I theory, as we can see from the prominent part that is played in their arguments by an appeal to the conditional (auvTJp.p.EvOV). Similarity cannot, they maintain, supply the basis of true conditionals of the Aristotle on Sign-inference and kind required for the Epicureans' inferences to the rion-evident. But instead of dismissing this challenge, as Epicurus' notoriously Related Forms ofArgument contemptuous attitude towards logic might have led us to expect, the Epicureans accept it and attempt· to show that similarity can THOUGH Aristotle was the first to make sign-inference the object give rise to true conditionals of the required strictness. What is oftheoretical reflection, what he left us is less a theory proper than a more, they treat inference by analogy as one of two species of argu sketch of one. Its fullest statement is found in Prior Analytics 2. 27, ment embraced by the method ofsimilarity they defend. The other the last in a sequence offive chapters whose aim is to establish that: is made up of what we should call inductive arguments or, if we .' not only are dialectical and demonstrative syllogisms [auAAoyw,uol] effected construe induction more broadly, an especially prominent special by means of the figures [of the categorical syllogism] but also rhetorical case of inductive argument, viz. -
Colloquium 7 What Use Is Aristotle's Organon? Robin Smith
Colloquium 7 What Use Is Aristotle's Organon? Robin Smith My title is ambiguous. I might be construed as asking what use we, today, as philosophers, can make of the collection of treatises which has been known since the time of the Aristotelian commentators as the "organon." These treatises are, in the main, a collection of works on logic and closely related subjects, including fallacious arguments and demonstrative sci- ence. Tradition regarded them as giving Aristotle's account of scientific philosophical method: the "instrument" necessary for the attainment of knowledge. It was as such that Francis Bacon rejected Aristotle's Organon and offered his own as its replace- ment. Scientific method, he thought, should be a way to attain new knowledge; but he saw in the Aristotelian procedures he had learned at school nothing but rules for argumentation and deduction, which could never lead to the enlargement of what one already knew. For the purposes he took to be important, then, he found the Aristotelian instrument useless. More recent philosophical interpretation of Aristotle has been perhaps more sympathetic to its philosophical superstructure. If we regard the picture of demonstrative science of the Posterior Analytics as an account of scientific explanation rather than an account of scien- tific discovery, its plausibility is much greater. However, the logical theories on which Aristotle relies, especially its theory of inference, are now more or less universally recognized to be inadequate to any formalization even of the sciences Aristotle himself knew: Greek mathematical demonstrations steadfastly resist any translation into categorical syllogisms. Even the use of modern formal methods to interpret Aristotle's works seems at best to permit us to congratulate him for having come close, in his awkward way, to something we have a much better grasp of now.