The University of Chicago Aristotle on the Necessity
Total Page:16
File Type:pdf, Size:1020Kb
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. -
UNDERSTANDING MATHEMATICS to UNDERSTAND PLATO -THEAETEUS (147D-148B Salomon Ofman
UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO -THEAETEUS (147d-148b Salomon Ofman To cite this version: Salomon Ofman. UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO -THEAETEUS (147d-148b. Lato Sensu, revue de la Société de philosophie des sciences, Société de philosophie des sciences, 2014, 1 (1). hal-01305361 HAL Id: hal-01305361 https://hal.archives-ouvertes.fr/hal-01305361 Submitted on 20 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNDERSTANDING MATHEMATICS TO UNDERSTAND PLATO - THEAETEUS (147d-148b) COMPRENDRE LES MATHÉMATIQUES POUR COMPRENDRE PLATON - THÉÉTÈTE (147d-148b) Salomon OFMAN Institut mathématique de Jussieu-PRG Histoire des Sciences mathématiques 4 Place Jussieu 75005 Paris [email protected] Abstract. This paper is an updated translation of an article published in French in the Journal Lato Sensu (I, 2014, p. 70-80). We study here the so- called ‘Mathematical part’ of Plato’s Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. -
Mapping the Meaning of Knowledge in Design Research Kristina Niedderer University of Hertfordshire
V.2:2 April 2007 www.designresearchsociety.org Design Research Society ISSN 1752-8445 Mapping the Meaning of Knowledge in Design Research Kristina Niedderer University of Hertfordshire Knowledge plays a vital role in our life This question has arisen for design in Table of Contents: in that it reflects how we understand the UK, as well as more generally for the world around us and thus deter- creative and practice-led disciplines Articles: 1 Mapping the Meaning of Knowledge mines how we act upon it. In this sense, (CPDs), because research regulations in Design Research knowledge is of particular importance and requirements in the UK remain Kristina Niedderer for designers because they act to shape silent about what knowledge and our world. Conventionally, knowledge understanding mean in the context of 3 Call for Papers: Design Research creation has been assumed by (design) their specifications while implicitly pri- Quarterly research. However developments of oritising propositional knowledge over Case Studies in Research: Knowledge using practice within research have knowledge that cannot be expressed in and Inquiry pointed to knowledge creation within that form (Niedderer 2007). and through practice. This has raised This has led to a number of prob- Listings: the question of the meaning, role and lems concerning the role and format 14 Current Research in Design: format of knowledge in both research of knowledge in research and practice ToCs from Leading Design Journals and practice, and about the compatibil- in the UK. For example, because of the ity between knowledge of research and language-based mode of proposition- 21 Upcoming Events Worldwide practice. -
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 -
Phenomenal Concepts and the Problem of Acquaintance
Paul Livingston Phenomenal Concepts and the Problem of Acquaintance Abstract: Some contemporary discussion about the explanation of consciousness substantially recapitulates a decisive debate about ref- erence, knowledge, and justification from an earlier stage of the ana- lytic tradition. In particular, I argue that proponents of a recently popular strategy for accounting for an explanatory gap between phys- ical and phenomenal facts — the so-called ‘phenomenal concept strategy’ — face a problem that was originally fiercely debated by Schlick, Carnap, and Neurath. The question that is common to both the older and the contemporary discussion is that of how the presence or presentation of phenomenal experiences can play a role in justify- ing beliefs or judgments about them. This problem is, moreover, the same as what was classically discussed as the problem of acquain- tance. Interestingly, both physicalist and non-physicalist proponents of the phenomenal concept strategy today face this problem. I con- sider briefly some recent attempts to solve it and conclude that, although it is prima facie very plausible that acquaintance exists, we have, as yet, no good account of it. My aim in this paper is to demonstrate that proponents of a recently popular physicalist strategy for explaining consciousness — what has been called the phenomenal concept strategy — share with certain anti-physicalist phenomenal realists a common problem, which was also a problem for Schlick, Carnap, and Neurath in the days of the Vienna Circle. Though it has implications for ontology and metaphys- ics, this problem is essentially one about justification: how can judg- ments, claims, or beliefs about phenomenal experience be justified, at Correspondence: Email: [email protected] Journal of Consciousness Studies, 20, No. -
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. -
Logic, Argumentation & Reasoning
Logic, Argumentation & Reasoning Interdisciplinary Perspectives from the Humanities and Social Sciences Volume 24 General Editor Shahid Rahman (Lille, UMR 8163) Managing Editor Juan Redmond (Universidad de Valparaiso, Chile) Area Editors Argumentation and Pragmatics Frans H. van Eemeren (Amsterdam) Zoe McConaughey (Lille, UMR 8163) Tony Street (Faculty of Divinity, Cambridge) John Woods (British Columbia/King’s College) Argumentation and Rhetoric Gabriel Galvez-Behar (Lille, UMR 8529) Leone Gazziero (Lille) André Laks, (Princeton/Panamericana) Ruth Webb (Lille, UMR 8163) Decision Theory, Mathematics, Economy Jacques Dubucs (IHPST-Paris 1) Karine Chemla (CNRS, SPHERE UMR7219, Université de Paris) Sven Ove Hansson (Stockholm) Cognitives Sciences. Computer Sciences Yann Coello (Lille) Eric Gregoire (CRIL-Lens) Henry Prakken (Utrecht) François Recanati (ENS, Paris) Epistemology and Philosophy of Science Gerhard Heinzmann (Nancy) Sonja Smets (ILLC, Amsterdam) Göran Sundholm (Leiden) Logic Michel Crubellier (Lille, UMR 8163) Dov Gabbay (King’s College) Tero Tulenheimo (Lille, UMR 8163) Political Science and Sociology Jean-Gabriel Contamin (Lille) Franck Fischer (Rutgers) Josh Ober (Stanford) Marc Pichard (Lille, MESHS-Nord Pas de Calais) Logic, Argumentation & Reasoning (LAR) explores links between the Humanities and Social Sciences, with theories (including decision and action theory) drawn from the cognitive sciences, economics, sociology, law, logic, and the philosophy of science. Its main ambitions are to develop a theoretical framework -
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. -
THE CONDEMNATION of 1277 the First Known Case of Academic
CHAPTER TWO THE CONDEMNATION OF 1277 Th e fi rst known case of academic condemnation at Oxford occurred in 1277. On March 18th of that year Robert Kilwardby, Archbishop of Canterbury, condemned as erroneous a series of propositions that were being upheld in the arts faculty involving grammar, logic, and natural philosophy.1 Th is event and its sequels, the Condemnation of 1284 and the Condemnation of Richard Knapwell, form the most examined ele- ment in the history of academic condemnation at Oxford, with the possible exception of the events around the condemnation of John Wyclif and the Oxford Lollards in 1381–82. Th ere is a large body of literature on this topic, and various aspects of it have been hotly debated over the past century.2 1 Th e condemnation, including the propositions, can be found in Chartularium Universitatis Parisiensis, ed. H. Denifl e and E. Chatelain, (Paris, 1889–97), 1:558–60. It also exists (with minor variations in the wording of the propositions) in the Collectio errorum in Anglia et Parisius condemnatorum; see Henryk Anzulewicz, “Eine weitere Überlieferung der Collectio errorum in Anglia et Parisius condemnatorum im Ms. Lat. Fol. 456 der Staatsbibliothek Preussicher Kulturbesitz zu Berlin,” in Franziskanische Studien 74 (1992), pp. 375–99, at pp. 380–81. Th ere also exists a letter from Kilwardby to Peter of Confl ans in which he defends his action; Franz Ehrle, “Ein Schreiben des Erzbishofs von Canterbury Robert Kilwardby zur Rechtfertigung seiner Lehrverurtheilung vom 18. Marz 1277,” in Archiv für Literatur- und Kirchengeschichte des Mittelalters, ed. H. -
Kilwardby, Robert 00
K 16/5/05 4:13 pm Page 33 KILWARDBY, ROBERT 00 appearing in Muslim Spain within his lifetime. Here, his Arab Civilization: Challenges and Response. Edited by original tables were studied by *Maslama of Madrid and G.N. Atiyeh and I.M. Oweiss. 98–111. Albany: SUNY his pupils whose adaptation, more accurate than the Press, 1988. original, adjusted the tables to make them useful to Van Dalen, Benno. “Al-Khwarismi’s Astronomical Tables astronomers in the West. This version was then translated Revisited.” In Samso and Casulleras, I: 195–252. MICHAEL C. WEBER by *Adelard of Bath and *Pedro Alfonso, and it is only this Latin version that survives complete whereas in Arabic only selections from the original survive. Al-Khwarizmi’s two other surviving works are the Geography and the Extraction of the Jewish Calendar. It KILWARDBY, ROBERT appears that the Geography represents an important Robert Kilwardby died at the papal court in Viterbo, advance over *Ptolemy’s work of the same name. It has Italy, on September 11, 1279. Although aspects of his been speculated that al-Khwarizmi’s work was based on career as an intellectual and churchman are known, noth- a world map constructed by a collection of scholars for ing is really known about his early life except that he al-Ma’mun; the Geography represents superior knowl- studied at Paris. It would be nice to know if he studied edge of the Islamic lands and the areas visited by Muslim with the natural philosopher Richard Fishacre at Oxford traders and merchants. The work on the Jewish calendar in the early 1240s, for instance: it is possible and some of is curious. -
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.