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  1. Jason Aleksander (2004). Modern Paradoxes of Aristotle's Logic. Epoché: A Journal for the History of Philosophy 9 (1):79-99.
    This paper intends to explain key differences between Aristotle’s understanding of the relationships between nous, epistêmê, and the art of syllogistic reasoning(both analytic and dialectical) and the corresponding modern conceptions of intuition, knowledge, and reason. By uncovering paradoxa that Aristotle’s understanding of syllogistic reasoning presents in relation to modern philosophical conceptions of logic and science, I highlight problems of a shift in modern philosophy—a shift that occurs most dramatically in the seventeenth century—toward a project of construction, a pervasive desire for (...)
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  2. Edgar Jose Andrade & Edward Samuel Becerra (2008). Establishing Connections Between Aristotle's Natural Deduction and First-Order Logic. History and Philosophy of Logic 29 (4):309-325.
    This article studies the mathematical properties of two systems that model Aristotle's original syllogistic and the relationship obtaining between them. These systems are Corcoran's natural deduction syllogistic and ?ukasiewicz's axiomatization of the syllogistic. We show that by translating the former into a first-order theory, which we call T RD, we can establish a precise relationship between the two systems. We prove within the framework of first-order logic a number of logical properties about T RD that bear upon the same properties (...)
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  3. Edgar Andrade-Lotero & Catarina Dutilh Novaes (2012). Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW] Journal of Philosophical Logic 41 (2):387-418.
    We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...)
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  4. Ignacio Angelelli (1978). Analytica Priora I, $38$ and Reduplication. [REVIEW] Notre Dame Journal of Formal Logic 19 (2):295-296.
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  5. R. B. Angell (1986). Truth-Functional Conditionals and Modern Vs. Traditional Syllogistic. Mind 95 (378):210-223.
  6. E. J. Ashworth (1970). Some Notes on Syllogistic in the Sixteenth and Seventeenth Centuries. Notre Dame Journal of Formal Logic 11 (1):17-33.
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  7. Allan Bäck (1995). Aristotelian Necessities. History and Philosophy of Logic 16 (1):89-106.
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  8. Allan Bäck (1982). Syllogisms with Reduplication in Aristotle. Notre Dame Journal of Formal Logic 23 (4):453-458.
  9. John Bacon (1967). Syllogistic Without Existence. Notre Dame Journal of Formal Logic 8 (3):195-219.
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  10. A. J. Baker (1972). Syllogistic with Complex Terms. Notre Dame Journal of Formal Logic 13 (1):69-87.
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  11. A. J. Baker (1966). Non-Empty Complex Terms. Notre Dame Journal of Formal Logic 7 (1):48-56.
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  12. P. Banks (2010). O Filosofické Interpretaci Logiky Aristotelský Dialog. Studia Neoaristotelica 7 (2):197-210.
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  13. Evelyn M. Barker (1984). Unneeded Surgery on Aristotle's Prior Analytics. Notre Dame Journal of Formal Logic 25 (4):323-331.
  14. Jonathan Barnes & Susanne Bobzien (1991). Alexander of Aphrodisias' on Aristotle's Prior Analytics 1.1-7. Duckworth.
    ABSTRACT: English translation of the 2nd/3rd century Peripatetic Philosopher's Alexander of Aphrodisias commentary on Aristotle's non-modal syllogistic, i.e. on one of the most influential logical texts of all times. -/- Volume includes introduction on Alexander of Aphrodisias and the early commentators, translation with notes and comments, appendices with a new translation of Aristotle's text, a summary of Aristotle's non-modal syllogistic and textual notes.
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  15. Susanne Bobzien (2011). The Combinatorics of Stoic Conjunction. Oxford Studies in Ancient Philosophy 40 (1):157-188.
    ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...)
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  16. Susanne Bobzien (2007). Aristotle's De Interpretatione 8 is About Ambiguity. In D. Scott (ed.), Maieusis: Essays in Ancient Philosophy. Oxford University Press. 301.
    ABSTRACT: In this paper I show that, contrary to the prevalent view, in his De Interpretatione chapter 8, Aristotle is concerned with a kind of ambiguity, i.e. with homonymy; more precisely, with homonymy of linguistic expressions as it may occur in dialectical argument. The paper has two parts. In the first part, I argue that in the Sophistici Elenchi 175b39-176a5 Aristotle indubitably deals with homonymy in dialectical argument; that De Interpretatione 8 is a parallel to Sophistici Elenchi 175b39-176a5; that De (...)
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  17. Susanne Bobzien (2006). The Stoics on Fallacies of Equivocation. In D. Frede & B. Inwood (eds.), Language and Learning, Proceedings of the 9th Symposium Hellenisticum. Cambridge University Press.
    ABSTRACT: This paper discusses the Stoic treatment of fallacies that are based on lexical ambiguities. It provides a detailed analysis of the relevant passages, lays bare textual and interpretative difficulties, explores what the Stoic view on the matter implies for their theory of language, and compares their view with Aristotle’s. In the paper I aim to show that, for the Stoics, fallacies of ambiguity are complexes of propositions and sentences and thus straddle the realms of meaning (which is the domain (...)
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  18. Susanne Bobzien (2006). Ancient Logic. In Stanford Encyclopedia of Philosophy.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...)
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  19. Susanne Bobzien (2006). Logic, History Of: Ancient Logic. In Donald M. Borchert (ed.), Encyclopedia of Philosophy. Thomson Gale.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).
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  20. Susanne Bobzien (2006). Ancient Logic. Stanford Encyclopedia of Philosophy.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians.
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  21. Susanne Bobzien (2002). The Development of Modus Ponens in Antiquity: From Aristotle to the 2nd Century AD. Phronesis 47 (4):359 - 394.
    'Aristotelian logic', as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, nor did he call any arguments 'hypothetical syllogisms'. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them 'hypothetical syllogisms'; nor did (...)
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  22. Susanne Bobzien (2000). Wholly Hypothetical Syllogisms. Phronesis 45 (2):87-137.
    ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For (...)
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  23. Susanne Bobzien (1996). Logic. In Simon Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary, 3rd edition. Oxford University Press.
    ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).
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  24. Susanne Bobzien (1996). Stoic Syllogistic. Oxford Studies in Ancient Philosophy 14:133-92.
    ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which (...)
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  25. George Boger (1998). Completion, Reduction and Analysis: Three Proof-Theoretic Processes in Aristotle'sprior Analytics. History and Philosophy of Logic 19 (4):187-226.
    Three distinctly different interpretations of Aristotle?s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle?s remarkable degree of metalogical (...)
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  26. Ivan Boh (1985). Die Aristotelische Modaltheorie. Journal of the History of Philosophy 23 (2):250-253.
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  27. Eric M. Brown, Logic II: The Theory of Propositions.
    This is part two of a complete exposition of Logic, in which there is a radically new synthesis of Aristotelian-Scholastic Logic with modern Logic. Part II is the presentation of the theory of propositions. Simple, composite, atomic, compound, modal, and tensed propositions are all examined. Valid consequences and propositional logical identities are rigorously proven. Modal logic is rigorously defined and proven. This is the first work of Logic known to unite Aristotelian logic and modern logic using scholastic logic as the (...)
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  28. Hector-Neri Casta Neda (1976). Leibniz's Syllogistico-Propositional Calculus. Notre Dame Journal of Formal Logic 17 (4):481-500.
  29. Saloua Chatti & Fabien Schang (2013). The Cube, the Square and the Problem of Existential Import. History and Philosophy of Logic 34 (2):101 - 132.
    (2013). The Cube, the Square and the Problem of Existential Import. History and Philosophy of Logic: Vol. 34, No. 2, pp. 101-132. doi: 10.1080/01445340.2013.764962.
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  30. Michael Clark (1983). Review of Paul Thom, The Syllogism. [REVIEW] History and Philosophy of Logic.
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  31. John Corcoran (2009). Aristotle's Demonstrative Logic. History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
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  32. John Corcoran (2003). Aristotle's Prior Analytics and Boole's Laws of Thought. History and Philosophy of Logic. 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...)
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  33. John Corcoran (1994). The Founding of Logic. Ancient Philosophy 14 (1):9-24.
  34. Phil Corkum, Aristotle on Logical Consequence.
    Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...)
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  35. Phil Corkum (forthcoming). Is Aristotle's Syllogistic a Logic? History and Philosophy of Logic.
    Much of the last fifty years of scholarship on Aristotle’s syllogistic suggests a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning, only if it is not a theory or formal ontology, a system concerned with general features of the world. In this paper, I will argue that this a misleading interpretative framework. The syllogistic is something sui generis: by our lights, it is neither clearly a logic, nor clearly a theory, but rather exhibits certain (...)
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  36. Mauro Nasti De Vincentis (2004). From Aristotle's Syllogistic to Stoic Conditionals: Holzwege or Detectable Paths? Topoi 23 (1):113-137.
    This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle's syllogistic and the Stoic doctrine of conditionals, notably between Aristotle's metasyllogistic equimodality condition (as stated at APr. I 24, 41b27–31) and truth-conditions for third type (Chrysippean) conditionals (as they can be inferred from, say, S.E. P. II 111 and 189). In fact, as is shown in §1, Aristotle's condition amounts to introducing in his (propositional) metasyllogistic a non-truthfunctional implicational arrow '', the truth-conditions of (...)
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  37. Mustafa Dehqan (2010). Kurdish Glosses on Aristotelian Logical Texts. Philosophical Quarterly 60 (241):692-697.
    Some of the outstanding masters of Kurdish historical schools (Medresê) are usually and rightly seen as belonging to the Aristotelian tradition. In this introductory study I briefly present some manuscripts of Kurdish glosses on Aristotelian logical texts, and show that the Aristotelian logical tradition, as inherited from early Islamic philosophers, also formed an important strand in Kurdish schools. Kurdish students' peculiar approach to Aristotelian logic affected the way in which Categories, De Interpretatione and Isagoge were studied in Kurdish schools from (...)
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  38. Luc Deitz (2007). Francesco Patrizi da Cherso's Criticism of Aristotle's Logic. Vivarium 45 (1):113-124.
    Francesco Patrizi da Cherso's Discussiones peripateticae (1581) are one of the most comprehensive analyses of the whole of Aristotelian philosophy to be published before Werner Jaeger's Aristoteles. The main thrust of the argument in the Discussiones is that whatever Aristotle had said that was true was not new, and that whatever he had said that was new was not true. The article shows how Patrizi proves this with respect to the Organon, and deals with the implications for the history af (...)
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  39. Please Delete, Please Delete. This is a Duplicate.
  40. M. V. Dougherty (2004). Aristotle's Four Truth Values. British Journal for the History of Philosophy 12 (4):585-609.
  41. Jamie Dow (2010). Aristotle on the Centrality of Proof to Rhetoric. Logique Et Analyse 53 (210):101--130.
  42. Catarina Dutilh Novaes (2012). Reassessing Logical Hylomorphism and the Demarcation of Logical Constants. Synthese 185 (3):387-410.
    The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in (...)
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  43. Sten Ebbesen (1981). Commentators and Commentaries on Aristotle's Sophistici Elenchi: A Study of Post-Aristotelian Ancient and Medieval Writings on Fallacies. E.J. Brill.
    v. 1. The Greek tradition -- v. 2. Greek texts and fragments of the Latin translation of "Alexander's" commentary -- v. 3. Appendices, Danish summary, indices.
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  44. Edward M. Engelmann (2007). Aristotle's Syllogystic, Modern Deductive Logic, and Scientific Demonstration. American Catholic Philosophical Quarterly 81 (4):535-552.
    This article investigates the nature of Aristotelian syllogistics and shows that the categorical syllogism is fundamentally about showing the connection, in the premises of the syllogism, between the major and minor terms as stated in the conclusion. It discusses how this is important for the use of the syllogism in scientific demonstration. The article then examines modern deductive logic with an eye to they way in which it contrasts with Aristotelian syllogistics. It shows howmodern logic is about making necessary connections (...)
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  45. George Englebretsen (2002). Syllogistic: Old Wine in New Bottles. History and Philosophy of Logic 23 (1):31-35.
    In the late nineteenth century there were two very active lines of research in the field of formal logic. First, logicians (mostly in English-speaking countries) were engaged in formulating a generally traditional logic as an algebra, a part of mathematics; second, logicians (mostly on the continent) were busy building a non-traditional logic that could serve, not as a part of, but as the foundation of, mathematics. By the end of the First World War the former line had been pretty well (...)
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  46. George Englebretsen (1988). Preliminary Notes on a New Modal Syllogistic. Notre Dame Journal of Formal Logic 29 (3):381-395.
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  47. James Van Evra (2000). The Development of Logic as Reflected in the Fate of the Syllogism 1600–1900. History and Philosophy of Logic 21 (2):115-134.
    One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...)
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  48. Kevin Flannery (1993). Alexander of Aphrodisias and Others on a Controversial Demonstration in Aristotle's Modal Syllogistic. History and Philosophy of Logic 14 (2):201-214.
    (1993). Alexander of aphrodisias and others on a controversial demonstration in aristotle’s modal syllogistic. History and Philosophy of Logic: Vol. 14, No. 2, pp. 201-214.
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  49. S. N. Furs (1987). Computation of Aristotle's and Gergonne's Syllogisms. Studia Logica 46 (3):209 - 225.
    A connection between Aristotle's syllogistic and the calculus of relations is investigated. Aristotle's and Gergonne's syllogistics are considered as some algebraic structures. It is proved that Gergonne's syllogistic is isomorphic to closed elements algebra of a proper approximation relation algebra. This isomorphism permits to evaluate Gergonne's syllogisms and also Aristotle's syllogisms, laws of conversion and relations in the square of oppositions by means of regular computations with Boolean matrices.
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  50. Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.) (2004). Handbook of the History of Logic. Elsevier.
    Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and (...)
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