Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


2012 | 3 | 1 | 83-114

Article title

ΑΝΑΛΥΣΙΣ ΠΕΡΙ ΤΑ ΣΧΗΜΑΤΑ Restoring Aristotle’s Lost Diagrams of the Syllogistic Figures

Authors

Content

Title variants

Languages of publication

EN

Abstracts

EN
The article examines the relevance of Aristotle’s analysis that concerns the syllogistic figures. On the assumption that Aristotle’s analytics was inspired by the method of geometric analysis, we show how Aristotle used the three terms (letters), when he formulated the three syllogistic figures. So far it has not been appropriately recognized that the three terms - the major, the middle and the minor one - were viewed by Aristotle syntactically and predicatively in the form of diagrams. Many scholars have misunderstood Aristotle in that in the second and third figure the middle term is outside and that in the second figure the major term is next to the middle one, whereas in the third figure it is further from it. By means of diagrams, we have elucidated how this perfectly accords with Aristotle's planar and graphic arrangement. In the light of these diagrams, one can appropriately capture the definition of syllogism as a predicative set of terms. Irrespective of the tricky question concerning the abbreviations that Aristotle himself used with reference to these types of predication, the reconstructed figures allow us better to comprehend the reductions of syllogism to the first figure. We assume that the figures of syllogism are analogous to the figures of categorical predication, i.e., they are specific syntactic and semantic models. Aristotle demanded certain logical and methodological competence within analytics, which reflects his great commitment and contribution to the field.

Year

Volume

3

Issue

1

Pages

83-114

Physical description

Dates

published
2012-02-11

Contributors

References

  • Ackrill, J.L. (ed.), 1987, A New Aristotle Reader, Oxford.
  • Apostle, H.G., 1981, Aristotle’s Posterior Analytics. Translated with Commentaries and Glossary. Grinnel, Iowa.
  • Barnes J., 1994, Aristotle’s Posterior Analytics. Translated with Notes. Oxford.
  • Barnes, J., Bobzien S., Flannery, K., Ierodiakonou, K., 1991, Alexander of Aphrodisias, On Aristotle Prior Analytics, I.1‑7, London.
  • Bekker, I., 1831, Aristotelis Opera, I‑III, Berlin.
  • Bonitz, H., 1870, Index Aristotelicus, Berlin.
  • Brunschwig, J., 1967, Aristote, Topiques I‑IV, Paris
  • Detel, W., 1993, Aristoteles: Analytica Posteriora, Übersetzt und erläutert, Berlin.
  • Ebert, Th., Nortmann, U., 2007, Aristoteles: Analytica Priora, Buch I, Übersetzt und erläutert, Berlin.
  • Фохт, Б. А., 1998, Аристотель, Аналитики, пер. с греч., Минск.
  • Leśniak, K., 1973, Arystoteles, Analityki pierwsze i wtóre, przełożył, wstępem i komentarzem opatrzył, Warszawa.
  • Mignucci, M., 1969, Aristotele: Gli Analitici Primi, Traduzione, introduzione e commento. Napoli.
  • Mignucci, M., 1975, L’argomentazione dimostrativa in Aristotele. Commento agli Analitici Secondi I. Padova.
  • Mignucci, M., 2007, Aristotele: Gli Analitici secondi. Testo greco di fronte, Roma.
  • Παπανδρέου, A., 1995, Αριστοτέλους το Όργανον Αναλυτικά πρότερα. Μετά σχολίων. Αθήνα.
  • Παπανδρέου, A., 1999, Αριστοτέλους το Όργανον Αναλυτικά ύστερα Α. Μετά σχολίων. Αθήνα.
  • Pellegrin, P., 2005, Aristote, Seconds Analytique, Prèsentation and traduction, Paris.
  • Ross, W.D., 1949. Aristotle’s Prior and Posterior Analytics: A Revised Text with Introduction and Commentary, Oxford.
  • Smith, R., 1989. Aristotle: Prior Analytics, Indianapolis - Cambridge.
  • Smith, R., 1997, Aristotle’s Topics. Books I and VIII, Oxford.
  • Striker, G., 2009, Aristotle: Prior Analytics, Book I, Translated with an Introduction and Commentary, Oxford.
  • Tredennick, H., 1938, Aristotle: Prior Analytics, Cambridge, Mass.
  • Tredennick, H., 1960, Aristotle: Posterior Analytics, Cambridge, Mass.
  • Zanatta, M., 1996, Organon di Aristotele, Vol. I‑II. Torino.
  • Zekl, G. H., 1998, Aristoteles, Erste Analytik. Zweite Analytik, Hamburg.
  • Anton, P., 1975, “Some Observations on Aristotle’ Theory of Categories”, Diotima 3, pp. 67‑81.
  • Bäck, A.T., 2005, Aristotle’s Theory of Predication, Leiden–Boston–Köln.
  • Berti, E., (ed.), 1981. Aristotle on Science: The Posterior Analytics, Padova
  • Berti, E., 1984, “L’analisi geometrica della tradizione euclidea e l’analitica di Aristotele”, in: G. Giannantoni, M. Vegetti (cur.), La scienza ellenistica, Napoli, pp. 95‑127.
  • Berti, E., 1993, “Aristotele e l’analisi matematica greca”, in: A. Repola Boatto (cur.), Filosofia logica matematica dal periodo classico al nostro secolo, Ancona, pp. 41‑53.
  • Bocheński, I.M., 1951, Ancient Formal Logic, Amsterdam.
  • Bolton, R., Smith, R. (ed.), 1994, Logic, Dialectic, and Science in Aristotle, Pittsburgh.
  • Bobzien, S., 1996, “Stoic Syllogistic”, OSAPh 14, pp. 133‑192.
  • Бочаров, В.А., 1984, Аристотель и традиционная логика: анализ силлогистических теорий, Москва.
  • Buddensiek, F., 1994. Die Modallogik des Aristoteles in den Analytica Priora A, Hildesheim.
  • Byrne, P.H., 1997, Analysis and Science in Aristotle, New York.
  • Cacouros, M., 1996, « Un manuel de logique organisé par Jean Chortasménos et destiné à l’enseignement (catalogage du manuscrit) », REByz 54, pp. 67‑106.
  • Corcoran, J. (ed.), 1974, Ancient Logic and Its Modern Interpretations, Dordrecht - Holland.
  • Cosenza, P., 1972, Tecniche di transformazione nella sillogistica di Aristotele, Napoli.
  • Crivelli, P., 2012, “Aristotle’s logic”, in: C. Schields (ed.), The Oxford Handbook of Aristotle, Oxford, pp. 113‑149.
  • Dorion, L.‑A., 2002, « Aristote et l’invention de la dialectique », in: M. Canto‑Sperber, P. Pellegrin (eds.), Le style de la pensée. Recueil de textes en hommage à Jacques Brunschwig, Paris, pp. 182‑220.
  • Drechsler, M., 2005, Interpretationen der Beweismethoden in der Syllogistik des Aristoteles, Frankfurt am Main.
  • Ebbinghaus, K., 1964, Ein formales Modell der Syllogistik des Aristoteles, Göttingen.
  • Eide, T., 1995, “Aristotelian ‘Topos’ and the Greek Geometry”, SO 70, pp. 5‑21.
  • Einarson, B., 1936, “On Certain Mathematical Terms in Aristotle’s Logic”, AJPh 57, pp. 33‑54; 151‑72.
  • Englebretsen, G., 1981, Three logicians. Aristotle, Leibniz, and Sommers and the syllogistic, Assen.
  • Englebretsen, G., 1992, “Linear Diagrams for Syllogism (with Relationals)”, Notre Dame Journal of Formal Logic 33, pp. 37‑69.
  • Englebretsen, G., 1998, Line diagrams for logic: drawing conclusions, Lewiston, N.Y.
  • Frede M., 1974, „Stoic vs. Aristotelian Syllogistic“, AGPh 56, pp. 1‑32.
  • Gabbay, D. M., Woods, J., 2004, Handbook of the History of Logic, vol. I, Amsterdam.
  • Geach, P.T., 1972, Logic matters, Berkeley.
  • Gili, L., 2010, La Sillogistica di Aristotele. La riduzione di tutte le deduzioni valide al sillogismo, Lampi di Stampa 2010.
  • Gili, L., 2011, La sillogistica di Alessandro di Afrodisia. Sillogistica categorica e sillogistica modale nel commento agli Analitici Primi di Aristotele. Hildesheim.
  • Graham, D.W., 1987, Aristotle’s Two Systems, Oxford.
  • Hintikka, J., Remes, U., 1974, The method of Analysis, Dordrecht–Holland.
  • Ierodiakonou, K., 2002, “Aristotle‘s Use of Examples in the Prior Analytics”, Phronesis 47 , pp. 127‑152.
  • Johnson, F., 1989. “Models for modal syllogisms”, Notre Dame Journal of Formal Logic 30, pp. 271–284.
  • Kahn, Ch. H., 1978, “Questions and Categories: Aristotle’s doctrine of categories in the light of modern research”, in: H. Hiż (ed.), Questions, Dordrecht–Holland, pp. 227‑ 277.
  • Keyt, D., 2009, “Deductive Logic”, in: G. Anagnostopoulos, A Companion to Aristotle, Malden–Oxford–Chichester, pp. 31‑50.
  • Kneale, W. & M., 1962, The Development of Logic, Oxford.
  • Knorr, W. R., 1986, The Ancient Tradition of Geometrical Problems. Boston–Basel–Stuttgart.
  • Κουσούλης, Σ., 2001, Η Αριστοτέλεια συλλογιστική, Αθήνα.
  • Lear, J., 1980, Aristotle and Logical Theory, Cambridge.
  • Lear, J., 1988, Aristotle: the desire to understand, Cambridge.
  • Lee, T.S., 1984, Die griechische Tradition der aristotelischen Syllogistik, Göttingen.
  • Луканин, Р. К., 1984, «Органон» Аристотеля, Москва.
  • Lucchetta, G. A., 2008, Un problematico impiego di diagrammi matematici e di modelli analogici in Aristotele. De memoria et reminiscentia 2, 452b7‑23, in: Migliori, M., Fermani, A. (eds.), Platone e Aristotele: Dialettica e logica, Brescia, pp. 171‑ 185
  • Łukasiewicz, J., 1957, Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Oxford (Polish translation: Warszawa 1988).
  • Malink, M., 2006, “A reconstruction of Aristotle’s modal syllogistic”, History and Philosophy of Logic 27, pp. 95–141.
  • Malink, M., 2008, “Τῷ vs. Τῶν in Prior Analytics 1.1–22”, CQ 58, pp. 519‑536.
  • McKirahan, R. D., 1992, Principles and Proofs. Aristotle’s Theory of Demonstrative Science, Princeton.
  • Mendell, H., 1998, “Making sense of Aristotelian Demonstration”, OSAPh 16, pp. 160‑225.
  • Menn, S., 2002, “Plato and the Method of Analysis”, Phronesis 47, pp. 193–223.
  • Mignucci, M., 2002, «Syllogism and Deduction in Aristotle’s Logic», in: M. Canto‑Sperber, P. Pellegrin (eds.), Le style de la pensée. Recueil de textes en hommage à Jacques Brunschwig, Paris, pp. 244‑266.
  • Negro, C., 1967, La sillogistica di Aristotele, Bologna.
  • Netz, R., 1999, The Shaping of Deduction in Greek Mathematics. A Study in Cognitive History, Cambridge.
  • Nortmann, U., 1996. Modale Syllogismen, mögliche Welten, Essentialismus: eine Analyse der aristotelischen Modallogik, Berlin - New York.
  • Patzig, G., 1959, Die aristotelische Syllogistik. Logisch‑philologische Untersuchung bei das Buch A der ‘Ersten Analytiken’ Göttingen (English translation: Dordrecht 1968).
  • Patterson, R., 1995, Aristotle’s Modal Logic: Essence and Entailment in the Organon, Cambridge.
  • Raphael, S., 1974, “Rhetoric, Dialectic and Syllogistic: Argument Aristotle’s Position in Rhetoric I‑II”, Phronesis 19, pp. 153‑167.
  • Rijen, J. van, 1988, Aspects of Aristotle’s Logic of Modalities, Dordrecht.
  • Rijk, L.M. de, 2002, Aristotle - Semantic and Ontology, Vol. 1: General Introduction. The Works on Logic; Vol. II: The Metaphysics. Semantics in Aristotle’s Strategy of Argument, Leiden.
  • Rini, A., 2011, Aristotle’s Modal Proofs: Prior Analytics A 8 ‑22 in Predicate Logic, Springer
  • Rose, L.E., 1968, Aristotle’s Syllogistic, Springfield–Illinois.
  • Schmidt, K.J., 2000. Die modale Syllogistik des Aristoteles: Eine modal‑prädikatenlogische Interpretation, Paderborn.
  • Schramm, M., 1962, Die Bedeutung der Bewegungslehre des Aristoteles für seine beiden Lösungen der zenonischen Paradoxie, Frankfurt/M.
  • Slomkowski, P., 1997, Aristotle’s Topics. Leiden.
  • Striker, G., 1996, “Perfection and Reduction in Aristotle’s Prior Analytics”, in: M. Frede, G. Striker (eds.), Rationality in Greek Thought, Oxford, pp. 203‑219.
  • Striker, G., 1998, Aristotle and the Uses of Logic, in: J. Gentzler, Method in Ancient Philosophy, Oxford, pp. 209‑226.
  • Suchoń, W., 1996, Sylogistyka. Interpretacja zakresowa, Kraków.
  • Suchoń, W., Wesoły, M., Żarnecka‑Biały E., 2003, Three Studies in Aristotelian Semantics, Kraków.
  • Thom, P., 1981, The Syllogism, München.
  • Thom, P., 1996. The Logic of Essentialism: An Interpretation of Aristotle’s Modal Syllogistic, Dordrecht, Boston.
  • Thomason, S. K., 1993, “Semantic analysis of the modal syllogistic”, Journal of Philosophical Logic 22, pp. 111–128.
  • Weidemann, H., 2004, “Aristotle on the Reducibility of all Valid Syllogistic Moods to the Two Universal Moods of the First Figure (APr A 7, 29b1‑25)”, History and Philosophy of Logic 25, pp.73‑78.
  • Wesoły, M., 1984, “Verso un’ interpretazione semantica delle categorie di Aristotele”, Elenchos 5, pp. 103‑140.
  • Wesoły, M., 1990, ‘Lira dalle undici corde’: per l’interpretazione del fr. 5 G.‑ P. di Ione di Chio, AION 12, pp. 89‑98.
  • Wesoły, M., 1992, “Towards the Analytic Interpretation of Aristotle’s Syllogistic” (in Polish), SPhP 9, pp. 21‑45.
  • Wesoły, M., 1996, “Aristotle’s Lost Diagrams of Analytical Figures”, Eos 74, pp. 53‑64.
  • Wesoły, M., 1999, „Analiza w greckiej geometrii i analityka Arystotelesa”, in: E. Piotrowska, D. Sobczyńska (red.), Między matematyką a przyrodoznawstwem, Poznań, pp. 19‑40.
  • Wesoły, M., 2003, “An Analytic Insight into Aristotle’s Logic”, in: Suchoń, W., Wesoły, M., Żarnecka‑Biały, E., pp. 9‑63; 191‑199.
  • Wesoły, M., 2012, „Plato’s analytic System in Aristotle’s critical account“, in: Platons Hermeneutik und Prinzipiendenken im Licht der Dialoge und der antiken Tradition, Festschrift für Thomas Alexander Szlezák zum 70. Geburtstag, Hildesheim, pp. 247‑275.
  • Wesoły, M., 2013, « Il faut examiner ces points e les définir mieux »: à propos d’une indication d’Aristote dans les Premiers Analytiques (I 37), (in preparation).
  • Żarnecka‑Biały, E., 1995, Noises in the history of logic, Kraków.
  • Żarnecka‑Biały, E., 1995, Historia logiki dawniejszej, Kraków.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.ojs-doi-10_14746_pea_2012_1_4
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.