History of Logic from Aristotle to Gödel

by Raul Corazzon | e-mail: rc@ontology.co

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Selected Bibliography on the Logic of Aristotle: General and Introductory Readings

INTRODUCTORY READINGS ON ARISTOTLE'S LOGIC

  1. "Logic, Dialectic and Science in Aristotle." 1994. Ancient Philosophy no. 14.

    Special issue edited by Robert Bolton and Robin Smith.

    Contents: Introduction by the Editors 1; John Corcoran: The founding of logic 9; Timothy Smiley: Aristotle's completeness proof 25; Gisela Striker: Modal vs. assertoric syllogistic 39; James G. Lennox: Aristotelian problems 53; Michael Ferejohn: The immediate premises of Aristotelian demostration 79; Robert Bolton: The problem of dialectical reasoning in Aristotle 99; Robin Smith: Dialectic and the syllogism 133-151.

  2. Allen, James. 1995. "The Development of Aristotle's Logic: Part of an Account in Outline." Boston Area Colloquium in Ancient Philosophy no. 11:177-205.

  3. Barnes, Jonathan. 1959. "Aristotle's Theory of Demonstration." Phronesis no. 14:123-152.

    Reprinted in: J. Barnes, M. Schofield, R. Sorabji (eds.) - Articles on Aristotle Vol 1 - London, Duckworth, 1975, pp. 65-87

  4. ———. 1996. "Grammar on Aristotle's Terms." In Rationality in Greek Thought, edited by Frede, Michael and Striker, Gisela, 175-202. New York: Oxford University Press.

    "However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself block the path to polyadicity. The later Peripatetics were conservative creatures and they lacked logical imagination. Moreover, Aristotle himself had assured them that his syllogistic was adequate for all serious scientific needs. As for Aristotle, his service to logic is nonpareil, and it would be grotesque to chide him for lack of inventiveness. It is true that, in logical grammar, he did not climb above the level which he attained in the de Interpretatione. But the Analytics does not represent a fatal, or even a new, grammatical excursion. And the story of Aristotle's fall, like the story of the fall of Adam, is a myth." pp. 201-202

  5. Bastit, Michel, and Follon, Jacques, eds. 2001. Logique Et Métaphysique Dans L'organon D'Aristote. Louvain: Peeters.

    Actes du colloque de Dijon

  6. Berg, Jan. 1983. "Aristotle's Theory of Definition." In Atti Del Convegno Internazionale Di Storia Della Logica, edited by Michele, Abrusci, Casari, Ettore and Mugnai, Massimo, 19-30. Bologna: CLUEB.

  7. Bochenski, Joseph. 1951. "Non-Analytical Laws and Rules in Aristotle." Methodos no. 3:77-79.

  8. Bolton, Robert. 1990. "The Epistemological Basis of Aristotelian Dialectic." In Biologie, Logique Et Métaphysique Chez Aristote, edited by Devereux, Daniel and Pellegrin, Pierre, 185-236. Paris: Éditions du CNRS.

  9. ———. 1994. "The Problem of Dialectical Reasoning in Aristotle." Ancient Philosophy no. 14:99-132.

  10. Brunschwig, Jacques. 1990. "Rémarques Sur La Communication De Robert Bolton." In Biologie, Logique Et Métaphysique Chez Aristote, edited by Devereux, Daniel and Pellegrin, Pierre, 237-262. Paris: Éditions du CNRS.

  11. ———. 1991. "Sur Quelques Malentendus Concernant La Logique D'Aristote." In Penser Avec Aristote, edited by Sinaceur, Mohammed Allal, 423-428. Paris: Éditions érès.

  12. Calogero, Guido. 1927. I Fondamenti Della Logica Aristotelica. Firenze: Le Monnier.

    Second edition with appendixes by Gabriele Giannantoni and Giovanna Sillitti - Firenze, La Nuova Italia, 1968.

  13. Charles, David. 2000. Aristotle on Meaning and Essence. New York: Oxford University Press.

  14. Dancy, Russell M. 1975. Sense and Contradiction: A Study on Aristotle. Dordrecht: Reidel.

  15. Deslauriers, Marguerite. 2007. Aristotle on Definition. Leiden: Brill.

  16. Detel, Wolfgang. 2006. "Aristotle's Logic and Theory of Science." In A Companion to Ancient Philosophy, edited by Gill, Mary Louise and Pellegrin, Pierre, 245-269. Malden: Blackwell.

  17. Devereux, Daniel. 1990. "Comments on Robert Bolton's the Epistemological Basis of Aristotelian Dialectic." In Biologie, Logique Et Métaphysique Chez Aristote, edited by Devereux, Daniel and Pellegrin, Pierre, 263-286. Paris: Éditions du CNRS.

  18. Ebert, Theodor. 1977. "Zur Formulierung Prädikativer Aussagen in Den Logischen Schriften Des Aristoteles." Phronesis no. 22:123-145.

  19. Gohlke, Paul. 1936. Die Entstehung Der Aristotelischen Logik. Berlin: Junker und Dünnhaupt.

    "In this monograph Dr. Wilke attempts to distinguish within the text of the Organon the different strata which mark the stages of development in Aristotle's logic. This development, he believes, is essentially the history of Aristotle's discovery of the quantity of judgments and the ever increasing role of the particular proposition, which means the gradual emancipation of logic from its metaphysical (i. e. Platonic) background. In the development of the doctrine of modality Dr. Gohlke finds a second means of distinguishing different chronological strata and a third in the changing theory of method, particularly in the supposed alteration of Aristotle's attitude toward the object of demonstration."

    From: Harold Cherniss - Review in The American Journal of Philology, 1938, 59, pp. 120-122

  20. Gourinat, Jean-Baptiste. 2001. "Principe De Contradiction, Principe Du Tiers-Exclu Et Principe De Bivalence: Philosophie Première Ou Organon?" In Logique Et Métaphysique Dans L'organon D'Aristote, edited by Bastit, Michel and Follon, Jacques, 63-91. Louvain: Peeters.

  21. Hintikka, Jaakko. 1993. "Commentary on Smith." Proceedings of the Boston Area Colloquium in Ancient Philosophy no. 9.

    Commentary on: R. Smith - What use is Aristotle's Organon? (1999)

    Reprinted in: Lloyd P. Gerson (ed.) - Aristotle. Critical assessments - Vol. I: Logic and metaphysics - New York, Routldge, 1999, pp. 20-27

  22. ———. 1995. "Commentary on James Allen the Development of Aristotle's Logic: Part of an Account in Outline." Boston Area Colloquium in Ancient Philosophy no. 11:206-215.

  23. Lear, Jonathan. 1980. Aristotle and Logical Theory. Cambridge: Cambridge University Press.

  24. Leszl, Walter. 1970. Logic and Metaphysics in Aristotle. Aristotle's Treatment of Types of Equivocity and Its Relevance to His Metaphysical Theories. Padova: Antenore.

  25. ———. 2004. "Aristotle's Logical Works and His Conception of Logic." Topoi.An Internationale Review of Philosophy no. 23:71-100.

    "I provide a survey of the contents of the works belonging to Aristotle's Organon in order to define their nature, in the light of his declared intentions and of other indications (mainly internal ones) about his purposes. No unifying conception of logic can be found in them, such as the traditional one, suggested by the very title Organon, of logic as a methodology of demonstration. Logic for him can also be formal logic (represented in the main by the De Interpretatione), axiomatized syllogistic (represented in the main by the Prior Analytics) and a methodology of dialectical and rhetorical discussion. The consequent lack of unity presented by those works does not exclude that both the set of works called Analytics and the set of works concerning dialectic (Topics and Sophistici Elenchi) form a unity, and that a certain priority is attributed to the analytics with respect to dialectic."

  26. Lukasiewicz, Jan. 1929. Elements of Mathematical Logic. Warsaw: Warsaw University.

    English translation by Olgierd Wojtasiewicz edited with footnotes by Jerzy Slupecki, New York, Macmillan, 1963.

  27. ———. 1979. "Aristotle on the Law of Contradiction." In Articles on Aristotle. Vol. 3: Metaphysics, edited by Barnes, Jonathan, Schofield, Malcolm and Sorabji, Richard, 50-62. London: Duckworth.

    Translated by Jonathan Barnes.

    Originally published as Über den Satz des Widespruchs bei Aristoteles - in: Bulletin International de l'Académie des Sciences de Cracovie, Cl. d'histoire et de philosophie, 1910. Already ranslated into English by V. Wedin as On the principle of contradiction in Aristotle in The Review of Metaphysics 24, 1970/71 pp. 485-509.

  28. ———. 1993. Über Den Satz Des Widerspruchs Bei Aristoteles. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 5).

    Translated from the Polish O zasadzie sprzecznosci u Arystotelesa (1910) by Jacek Barski; with a preface by Joseph Bochenski-

    Translated in Italian as: Del principio di contraddizione in Aristotele - A cura di Gabriele Franci e Claudio Antonio Testi; presentazione di Maurizio Matteuzzi - Macerata, Quodlibet, 2003.

    Translated in French as: Du principe de contradiction chez Aristote - Paris, Édition Éclat, 2000

  29. Mariani, Mauro. 2000. "Numerical Identity and Accidental Predication in Aristotle." Topoi.An Internationale Review of Philosophy no. 19:99-110.

  30. Menne, Albert, ed. 1962. Logico-Philosophical Studies. Dordrecht: Reidel.

  31. Menne, Albert, and Öffenberger, Niels, eds. 1982. Über Den Folgerungsbegriff in Der Aristotelischen Logik. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 1)

  32. ———, eds. 1985. Formale Und Nicht-Formale Logik Bei Aristoteles. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 2)

  33. ———, eds. 1988. Modallogik Und Mehrwertigkeit. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 3)

  34. Mignucci, Mario. 1985. "Puzzles About Identity. Aristotle and His Greek Commentators." In Aristoteles. Werk Und Wirkung: Paul Moraux Gewidmet. Erster Band: Aristoteles Und Seine Schule, edited by Wiesner, Jürgen, 57-97. Berlin: de Gruyter.

    "Aristotle's conception of identity is too large a subject to be analyzed in a single article. I will try to discuss here just one of the many problems raised by his views on sameness. It is not, perhaps, the most stimulating question one could wish to see treated, but it is a question about logic, where I feel a little more at ease than among the complicated and obscure riddles of metaphysics. My subject will be Aristotle's references to what is nowadays called 'Leibniz' Law'(LL):if two objects x and y are the same, they both share all the same properties.

    (...)

    First, I will consider Aristotle's statements about (LL) and the analyses he gives of some supposed counterexamples to this principle. Secondly, the interpretations of his view among his Greek commentators will be taken into account and their distance from the position of the master evaluated. As Professor Moraux has taught us, the study of the Aristotelian tradition often gives us the opportunity of understanding Aristotle's own meaning better." pp. 57-58

  35. ———. 1996. "Aristotle's Theory of Predication." In Studies on the History of Logic. Proceedings of the Third Symposium on the History of Logic, edited by Ignacio, Angelelli and Cerezo, Maria, 1-20. Berlin, New York: de Gruyter.

  36. Öffenberger, Niels, and G., Vigo Alejandro. 1997. Südamerikanische Beiträge Zur Modernen Deutung Der Aristotelischen Logik. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 7)

  37. Öffenberger, Niels, and Skarica, Mirko, eds. 2000. Beiträge Zum Satz Vom Widerspruch Und Zur Aristotelischen Prädikationstheorie. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 8)

  38. Öffenberger, Niels, and Surdu, Alexandru, eds. 2004. Rumänische Beiträge Zur Modernen Deutung Der Aristotelischen Logik. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 9)

    "In keeping with the fundamental aims of the series Zur modernen Deutung der Aristotelischen Logik -- i.e. to make available articles otherwise difficult to trace -- the editors of this IXth volume present essays from Romania, together with a brief overview of the history of logic in Romania. Although the essays were published in two major international languages -- mainly in French, with some in German -- they appeared in Romanian journals which have a limited circulation in the West. Studies have been selected for their focus on major areas of Aristotelian logic: the theory of categories, syllogistics, logical principles and the theory of knowledge; an additional theme is the historical significance of Theophil Corydaleu's work. All these combine to give a comprehensive view of contemporary Aristotle scholarship in Romania."

  39. Parry, William, and Hacker, Edward. 1991. Aristotelian Logic. New York: State University of New York Press.

  40. Pasquale, Gianluigi. 2006. Aristotle and the Principle of Non-Contradiction. Sankt Augustin: Academia Verlag.

    Traduzione italiana: Il principio di non-contraddizione in Aristotele - Torino, Bollati-Boringhieri, 2008.

    Index: Introduction 9; I. The PNC as a law of reality and thought 17; II. The PNC as indemonstrable principle 69; Conclusion 111; Bibliography 119; Index of names 127-128.

    "The aim of this study is to discuss the formulation of the principle of non-contradiction (PNC) based on the text of Aristotle. It does not deal with the whole Aristotle's Metaphysics. We take certain passages selectively from chapter 3 and chapter 4 of the Metaphysics, with a view to interpreting the PNC as a law of being.

    Our discussion focuses mainly on how Aristotle regards the PNC as a law of reality and a law of thought. Then we shall see the possibility of knowing the PNC by way of intuitive understanding. This leads us to affirm that the PNC is a supreme principle that we cannot demonstrate. The only way Aristotle thinks it possible to speak about the principle in question is by way of confutation, using a dialectical argument: in order to proceed with the confutational proof, the opponent must say something which is meaningful for himself and for others. Aristotle distinguishes proper demonstration from a dialectical argument. We shall also try to specify the dialectical method that Aristotle uses to prove the PNC.

    This study has two chapters. The first chapter deals with the PNC as a law of reality and thought. This has two parts: the first part deals with Metaph. IV, 3, 1005b 19-20; IV, 3, 1005b 26-27; IV, 6, 1011b 15-20 and the secand part analyses Metaph. IV, 3, 1005b 24-26; IV, 3, 1005b 28-31. These passages treat the PNC as a law of reality and thought respectively.

    We shall interpret the PNC as a law of being from two points of view: first, based on the different types of opposition that Aristotle explains in the Categories, we shall see the meaning of «contradiction» that Aristotle understands in the formulation of PNC. Our conclusion will be that the greatest opposition that Aristotle has conceived in his whole work is the contradiction between being and non-being. The other oppositions such as contraries, privation and relatives, are oppositions that do not produce contradiction. As we shall see, the opposition between the relatives father and son, between privations vision and blindness, and between the contraries white and black, could not be predicated at the same time of the same subject in the same respect. But they are different from the sense of contradiction that Aristotle conceived in the formulation of the PNC -- because they do not distinguish absolutely the two extreme existences being and non-being." pp. 9-10

  41. Perreiah, Alan R. 1993. "Aristotle's Axiomatic Science: Peripatetic Notation or Pedagogical Plan?" History and Philosophy of Logic no. 14:87-99.

    "To meet a dilemma between the axiomatic theory of demonstrative science in "Posterior analytics" and the non-axiomatic practice of demonstrative science in the physical treatises, Jonathan Barnes has proposed that the theory of demonstration was not meant to guide scientific research but rather scientific pedagogy. The present paper argues that far from contributing directly to oral instruction, the axiomatic account of demonstrative science is a model for the written expression of science. The paper shows how this interpretation accords with related theories in the "Organon", including the theories of dialectic in "Topics" and of deduction in "Prior analytics"."

  42. Rijk, Lambertud Marie de. 2002. Aristotle: Semantics and Ontology. Volume I: General Introduction. The Works on Logic. Leiden: Brill.

    From the Preface: "In this book I intend to show that the ascription of many shortcomings or obscurities to Aristotle resulted from persistent misinterpretation of key notions in his work. The idea underlying this study is that commentators have wrongfully attributed anachronistic perceptions of `predication', and statement-making in general to Aristotle. In Volume I, what I consider to be the genuine semantics underlying Aristotle's expositions of his philosophy are culled from the Organon. Determining what the basic components of Aristotle's semantics are is extremely important for our understanding of his view of the task of logic -- his strategy of argument in particular.

    In chapter 1, after some preliminary considerations I argue that when analyzed at deep structure level, Aristotelian statement-making does not allow for the dyadic 'S is P' formula. An examination of the basic function of `be' and its cognates in Aristotle's philosophical investigations shows that in his analysis statement-making is copula-less. Following traditional linguistics I take the `existential' or hyparctic use of `be' to be the central one in Greek (pace Kahn), on the understanding that in Aristotle hyparxis is found not only in the stronger form of `actual occurrence' but also in a weaker form of what I term `connotative (or intensional) be' (1.3-1.6). Since Aristotle's `semantic behaviour', in spite of his skilful manipulation of the diverse semantic levels of expressions, is in fact not explicitly organized in a well-thought-out system of formal semantics, I have, in order to fill this void, formulated some semantic rules of thumb (1.7).

    In chapter 2 I provide ample evidence for my exegesis of Aristotle's statement-making, in which the opposition between `assertible' and `assertion' is predominant and in which `is' functions as an assertoric operator rather than as a copula (2.1-2.2). Next, I demonstrate that Aristotle's doctrine of the categories fits in well with his view of copula-less statement-making, arguing that the ten categories are `appellations' ('nominations') rather than sentence predicates featuring in an `S is P' formation (2.3-2.4). Finally, categorization is assessed in the wider context of Aristotle's general strategy of argument (2.5-2.7).

    In the remaining chapters of the first volume (3-6) I present more evidence for my previous findings concerning Aristotle's `semantic behaviour' by enquiring into the role of his semantic views as we find them in the several tracts of the Organon, in particular the Categories De interpretatione and Posterior Analytics. These tracts are dealt with in extenso, in order to avoid the temptation to quote selectively to suit my purposes."

  43. ———. 2002. Aristotle: Semantics and Ontology. Volume Ii: The Metaphysics, Semantics in Aristotle's Strategy of Argument. Leiden: Brill.

    From the Preface to the first volume: "The lion's part of volume two (chapters 7-11) is taken up by a discussion of the introductory books of the Metaphysics (A-E) and a thorough analysis of its central books (Z-H-O). I emphasize the significance of Aristotle's semantic views for his metaphysical investigations, particularly for his search for the true ousia. By focusing on Aristotle's semantic strategy I hope to offer a clearer and more coherent view of his philosophical position, in particular in those passages which are often deemed obscure or downright ambiguous.

    In chapter 12 1 show that a keen awareness of Aristotle's semantic modus operandi is not merely useful for the interpretation of his metaphysics, but is equally helpful in gaining a clearer insight into many other areas of the Stagirite's sublunar ontology (such as his teaching about Time and Prime matter in Physics).

    In the Epilogue (chapter 13), the balance is drawn up. The unity of Aristotelian thought is argued for and the basic semantic tools of localization and categorization are pinpointed as the backbone of Aristotle's strategy of philosophic argument.

    My working method is to expound Aristotle's semantic views by presenting a running commentary on the main lines found in the Organon with the aid of quotation and paraphrase. My findings are first tested (mainly in Volume II) by looking at the way these views are applied in Aristotle's presentation of his ontology of the sublunar world as set out in the Metaphysics, particularly in the central books (ZHO). As for the remaining works, I have dealt with them in a rather selective manner, only to illustrate that they display a similar way of philosophizing and a similar strategy of argument. In the second volume, too, the exposition is in the form of quotation and paraphrase modelled of Aristotle's own comprehensive manner of treating doctrinally related subjects: he seldom discussed isolated problems in the way modern philosophers in their academic papers, like to deal with special issues tailored to their own contemporary philosophic interest."

  44. Sainati, Vittorio. 1968. Storia Dell' "Organon" Aristotelico. I: Dai "Topici" Al "De Interpretatione". Firenze: Le Monnier.

  45. ———. 1973. Storia Dell' "Organon" Aristotelico. Ii: L'analitica. Parte Prima. La Crisi Epistemologica Della Topica. Firenze: Le Monnier.

    Ristampato con il titolo: Dalla Topica all'Analitica in Teoria, 2, 1993 pp. 1-117

  46. ———. 1993. "Aristotele. Dalla Topica All'analitica." Teoria.Rivista di Filosofia no. 2:1-117.

    Scritto nel 1973.

  47. Sisson, Edward. 1939. "The Copula in Aristotle and Afterwards." Philosophical Review no. 48:57-64.

  48. Smith, Robin. 1993. "What Use Is Aristotle's Organon?" Proceedings of the Boston Area Colloquium in Ancient Philosophy no. 9:261-285.

    Reprinted in: Lloyd P. Gerson (ed.) - Aristotle. Critical assessments - Vol. I: Logic and metaphysics - New York, Routldge, 1999, pp. 1-19

  49. Solmsen, Friedrich. 1929. Die Entwicklung Der Aristotelischen Logik Und Rhetorik. Berlin: Weidmannsche Buchhandlung.

    Reprinted Hildesheim, Georg Olms, 2001

  50. Sorbi, Luca. 1999. Aristotele: La Logica Comparativa. Firenze: Olschki.

    Due volumi: I (1999); II (2002).

  51. Striker, Gisela. 1998. "Aristotle and the Uses of Logic." In Method in Ancient Philosophy, edited by Genttzler, Jyl, 209-226. New York: Oxford University Press.

    "Aristotle, as we all know, invented formal logic. Over the last fifty years or so, scholars have learned to recognize that what he presented in the first few chapters of the Prior Analytics (An. pr.) is the real thing -- a system of formal logic, whether or not the inspiration for the discovery of the syllogism had anything to do with Platonic division. We no longer hear about the magical force of the middle term or the alleged demonstrative power of first figure syllogisms as opposed to, say, the superficial subtleties of Stoic logic. Although Aristotle's syllogistic covers only a small part of' the field of modern mathematical logic, what he offered contained all the elements of a formal deductive system. He introduces the system of syllogistic moods by defining its technical terms, stating and justifying the primitive rules, and then providing formally correct proofs of the derivative rules. In other words, he developed a complete system of natural deduction, limited indeed by the assumption that all propositions must be simple subject-predicate sentences, but otherwise flawless. (1)

    (...)

    Aristotle was interested both in logic as a theory and in its more humdrum uses in philosophical, or indeed everyday, argument, and more than half of the text of the Prior Analytics is concerned with the uses of logic in argument, rather than with either the exposition of a formal system or what we would calf logical theory. This is what one should expect, since Aristotle invented formal logic for the purposes of his general theory of argument, not just as a formal theory of deductive proof or an 'underlying logic' for demonstrative science. (5) In order to show how the perspective of a general theory of argument differs from that of logical theory, I will argue that although syllogistic can be shown to be complete in the modern logician's sense, it was not considered by its author to be complete in the sense relevant to his project. A deduction system is complete in the modern sense if it allows one to deduce all (and only) the valid formulae.

    What Aristotle has in mind when he set out to show that 'every deductive argument (sullogismos) is one of the (syllogistic) figures' (A23 40b20-22) was the claim that every valid deductive argument can be formulated as one or more syllogisms in the narrow sense. This, as Aristotle recognized, is not the case (A 44. 50b2-3). However, I will also argue that he thought syllogistic captured at least a necessary component of every valid deductive argument, and perhaps that it was indeed sufficient as an account of the logical form of scientific demonstration. Finally, I will illustrate the role of formal syllogistic in the theory of argument by a few examples from the second half of book A and from book B." pp. 210-211

    (1) This summarizes the conclusion of J. Corcoran, 'Aristotle's Natural Deduction System', in idem (ed.), Ancient Logic and its Modern Interpretations (Dordrecht: Reidel. 1974), 122-3.

    (5) Corcoran 'Aristotle's Natural Deduction System'. 98.

  52. Surdu, Alexandru. 2006. Aristotelian Theory of Prejudicative Forms. Hildesheim: Georg Olms.

    Zur Modernen Deutung der aristotelischen Logik (Band 10).

    "Alexandru Surdu is an outstanding representative of the Romanian school of Aristotle research. The special characteristic of this school is that its members have not based their research solely on the An. pr. and the De int. but have also paid particular attention to the Categories. This volume contains a thorough modern interpretation of the Categories in which the author takes into account commentators in the Greek, Latin and modern traditions, for example Adolf Trendelenburg.

    The symbolic-logical-mathematical presentation of the first chapter of the Categories with reference to the difference between the predicative types 'dicitur de' and 'inesse', especially in the case of the ante-predicative 'universal accidence' allows the author to elaborate the 'prejudicative forms' which carry no values of truth and do not come into being through assent or denial. Using an original interpretation of these 'prejudicative forms' the author is able to reveal forms and modes similar to those of syllogistics which have hitherto been unknown to either traditional or symbolic logic."

  53. Theron, Stephen. 2002. "The Interdependence of Semantics, Logic, and Metaphysics as Exemplified in the Aristotelian Tradition." International Philosophical Quarterly no. 42:63-91.

    "We need to recognize, or to remember, the priority of being to truth and not to conflate them. We need to explicate the origin of thinking (abstraction) as at one remove from immediate sense-experience.

    Syllogistic logic then emerges as a true causal account of reasoning in general; it is not some primitive attempt to outline a formal logical system. An account of suppositio as controlling the analogous uses of our finite store of words in reference to an infinite reality itself shaped by crisscross patterns of likenesses, governs the general picture supplied here."

  54. Thompson, Manley. 1953. "On Aristotle' Square of Opposition." Philosophical Review no. 62:251-265.

  55. Viano, Carlo Augusto. 1955. La Logica Di Aristotele. Torino: Taylor.

  56. ———. 1983. "La Proposizione in Aristotele." In Atti Del Convegno Internazionale Di Storia Della Logica, edited by Michele, Abrusci, Casari, Ettore and Mugnai, Massimo, 3-18. Bologna: CLUEB.

  57. Vuillemin, Jules. 1967. De La Logique À La Théologie. Cinq Études Sur Aristote. Paris: Flammarion.

    Nouvelle version remaniée et augmentée par l'auteur editée et prefacée par Thomas Benatouil - Louvain-La-Neuve, Peeters, 2008.

  58. Wedin, Michael. 1978. "Aristotle on the Existential Import of Singular Sentences." Phronesis no. 23:179-196.

  59. ———. 1990. "Negation and Quantification in Aristotle." History and Philosophy of Logic no. 19:131-150.

    "Two main claims are defended. The first is that negative categorical statements are not to be accorded existential import insofar as they figure in the square of opposition. Against Kneale and others, it is argued that Aristotle formulates his O statements, for example, precisely to avoid existential commitment. This frees Aristotle's square from a recent charge of inconsistency. The second claim is that the logic proper provides much thinner evidence than has been supposed for what appears to be the received view, that is, for the view that insofar as they occur in syllogistic negative categoricals have existential import. At most there is a single piece of evidence in favor of the view -- a special case of echthesis or the setting out of a case in proof."

  60. Weidemann, Hermann. 1980. "In Defence of Aristotle's Theory of Predication." Phronesis.A Journal for Ancient Philosophy no. 25:76-87.

  61. ———. 1989. "Aristotle on Inferences from Signs (Rhetoric I 2, 1357 B 1-25)." Phronesis no. 34:343-351.

  62. Wieland, Wolfgang. 1967. "Zur Deutung Der Aristotelischen Logik." Philosophische Rundschau no. 14:1-27.

  63. Williams, C.J.F. 1985. "Aristotle's Theory of Descriptions." Philosophical Review no. 94:63-80.

RELATED PAGES

Index of the Section: History of Logic from Aristotle to Gödel

The Logical Works of Aristotle:

Aristotle's Logic: General Survey and Introductory Readings

Aristotle's Earlier Dialectic: the Topics and Sophistical Refutations(in preaparation)

Aristotle's De Interpretatione: Semantics and Philosophy of Language

Aristotle's Prior Analytics: the Theory of Categorical Syllogism

Aristotle's Prior Analytics: the Theory of Modal Syllogism (in preaparation)

Aristotle's Posterior Analytics: The Theory of Demonstration (in preaparation)

On the website "Theory and History of Ontology" (www.ontology.co)

Bibliography on Aristotle's Categories:

Semantics and Ontological Analysis in Aristotle's Categories

Categories A - J

Categories K - Z