The Beginnings of Formal Logic: Deduction in Aristotle's Topics Vs
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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. -
The Mechanical Problems in the Corpus of Aristotle
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications, Classics and Religious Studies Department Classics and Religious Studies July 2007 The Mechanical Problems in the Corpus of Aristotle Thomas Nelson Winter University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/classicsfacpub Part of the Classics Commons Winter, Thomas Nelson, "The Mechanical Problems in the Corpus of Aristotle" (2007). Faculty Publications, Classics and Religious Studies Department. 68. https://digitalcommons.unl.edu/classicsfacpub/68 This Article is brought to you for free and open access by the Classics and Religious Studies at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications, Classics and Religious Studies Department by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Th e Mechanical Problems in the Corpus of Aristotle Th omas N. Winter Lincoln, Nebraska • 2007 Translator’s Preface. Who Wrote the Mechanical Problems in the Aristotelian Corpus? When I was translating the Mechanical Problems, which I did from the TLG Greek text, I was still in the fundamentalist authorship mode: that it survives in the corpus of Aristotle was then for me prima facie Th is paper will: evidence that Aristotle was the author. And at many places I found in- 1) off er the plainest evidence yet that it is not Aristotle, and — 1 dications that the date of the work was apt for Aristotle. But eventually, 2) name an author. I saw a join in Vitruvius, as in the brief summary below, “Who Wrote Th at it is not Aristotle does not, so far, rest on evidence. -
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 -
The INPR Journal. Volume I, Fall 2020
Crossing: The INPR Journal. Volume I, Fall 2020. Editor in chief Emmanuel Falque Editorial coordinators William L. Connelly Domenico Cambria Editorial committee Tamsin Jones Adam Graves Martin Koci William Woody S.J. Crossing: The INPR Journal. Volume I. November 2020. 26 Rue d’Assas 75006 Paris, France. ISSN (online): 2644-9242 DOI: 10.21428/8766eb43.b95a977c Web: https://inprjournal.pubpub.org/ http://www.network-inpr.org/ Email: [email protected] Crossing : une étape fondatrice de l’INPR (English Translation on Page III) L’international Network of Philosophy of Religion (INPR) est un réseau international de jeunes philosophes et théologiens (doctorants, post-doctorants, jeunes professeurs) réunis pour travailler ensemble autour de la question de Dieu et de sa pertinence dans un monde contemporain sécularisé. Essentiellement appuyé sur la philosophie continentale, mais pas exclusivement, il s’efforce d’être au service d’un renouveau de la philosophie et de la théologie chez les jeunes générations pour aujourd’hui. Loin de rester chacune sur leur pré-carré, philosophie et théologie sont appelées aujourd’hui à se croiser et à davantage se féconder mutuellement, dans le respect de la distinction des disciplines. Et les chercheurs de différents pays, en particulier ceux qui feront la pensée de demain, doivent eux aussi mieux dialoguer, sûrs que dans la confrontation des idées se fomente le terreau d’où naissent de nouvelles pensées. Inauguré en 2015, ce réseau international compte aujourd’hui plus d’une centaine de membres personnellement engagés, de plus de dix nationalités différentes, et venus en particulier d’Europe et des États-Unis. Les membres qui constituent ce réseau ont déjà fait la preuve par plusieurs séminaires (grands colloques ou séminaires doctoraux et post-doctoraux) du bien-fondé de leur démarche commune. -
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. -
Allan Gotthelf's Teleology, First Principles, And
Reason Papers Vol. 35, no. 1 Review Essays Review Essay: Allan Gotthelf’s Teleology, First Principles, and Scientific Method in Aristotle’s Biology and James G. Lennox and Robert Bolton’s (ed.) Being, Nature, and Life in Aristotle Owen Goldin Marquette University Although readers of Reason Papers are no doubt familiar with Allan Gotthelf’s extensive efforts aimed at a more widespread appreciation of Ayn Rand’s philosophical thought, he is best known among historians of philosophy and science for his contributions to the understanding of Aristotle’s biological works, which have shed much light on Aristotle’s scientific methodology, epistemology, and metaphysics. Two new books allow us to take account of Gotthelf’s contributions to Aristotelian studies. The first is a collection of Gotthelf’s most important papers on Aristotle.1 Although the papers were written independently, there is little superfluous repetition, and taken together they constitute a comprehensive and coherent account of Aristotle’s biology and its philosophical significance. The second, which has its origin in a 2004 conference in Gotthelf’s honor, is a collection of papers on Aristotle, most of which focus on themes that Gotthelf himself has discussed.2 Some of the papers further his thought, taking it in new directions; others depart from Gotthelf in philosophically interesting ways. Gotthelf believes that one of his most important contributions to Aristotelian studies lies in his account of teleology in the biological writings. For this he gives credit to Rand (p. viii) (who personally led Gotthelf to the study of Aristotle), for she had argued that scientific explanation must identify potentials inherent in natures. -
1 Peter Mclaughlin the Question of the Authenticity of the Mechanical
Draft: occasionally updated Peter McLaughlin The Question of the Authenticity of the Mechanical Problems Sept. 30, 2013 Until the nineteenth century there was little doubt among scholars as to the authenticity of the Aristotelian Mechanical Problems. There were some doubters among the Renaissance humanists, but theirs were general doubts about the authenticity of a large class of writings, 1 not doubts based on the individual characteristics of this particular work. Some Humanists distrusted any text that hadn’t been passed by the Arabs to the Latin West in the High Middle Ages. However, by the end of the 18th century after Euler and Lagrange, the Mechanical Problems had ceased to be read as part of science and had become the object of history of science; and there the reading of the text becomes quite different from the Renaissance 2 readings. In his Histoire des mathématiques J.E. Montucla (1797) dismisses the Mechanical Problems with such epithets as “entirely false,” “completely ridiculous,” and “puerile.” William Whewell remarks in the History of the Inductive Sciences3 that “in scarcely any one instance are the answers, which Aristotle gives to his questions, of any value.” Neither of them, however, cast doubt on the authenticity of the work. Abraham Kaestner’s Geschichte der Mathematik (1796–1800) mentions doubts – but does not share them.4 Serious doubts about the authenticity of the Mechanical Problems as an individual work seem to be more a consequence of the disciplinary constitution of classical philology, particularly in nineteenth-century Germany. Some time between about 1830 and 1870, the opinion of most philologists shifted from acceptance to denial of the authenticity of the 5 Mechanical Problems. -
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. -
Posterior Analytics
POSTERIOR ANALYTICS The Posterior Analytics contains Aristotle!> epistemology and philosophy of science. His approach is broadly speaking foundational. Some of what we know can be justified by being shown to follow logically from other things that we know, but some of what we know does not need to be justified in this way. Such items of foundational knowledge are the first principles of the various sciences. In the excerpts below, Aristotle sets out the axiomatic structure of a science and presents his theory of explanation. The final chapter provides a tantalizing but obscure presentation of his ideas on the acquisition of first principles. BOOK I 1 71a All teaching and all intellectual learning result from previous cognition. This is clear if we examine all the cases; for this is how the mathematical 5 sciences and all crafts arise. This is also true of both deductive and induc tive arguments, since they both succeed in teaching because they rely on previous cognition: deductive arguments begin with premisses we are as sumed to understand, and inductive arguments prove the universal by relying on the fact that the particular is already clear. Rhetorical arguments 10 also persuade in the same way, since they rely either on examples (and hence on induction) or on argumentations (and hence on deduction). Previous cognition is needed in two ways. In some cases we must presup pose that something is! (for example, that it is true that everything is either asserted or denied truly <of a given subject». In other cases we must 15 comprehend what the thing spoken of is (for example, that a triangle signifies this); and in other cases we must do both (for example, we must both comprehend what a unit signifies and presuppose that there is such a thing). -
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). -
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.