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Ancient Logic and its Modern Interpretations

Boston: Reidel (1974)

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  1. Stoicism Bibliography.Ronald H. Epp - 1985 - Southern Journal of Philosophy 23 (S1):125-171.
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  • Aristotle's Demonstrative Logic.John Corcoran - 2009 - 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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  • The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359 - 374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...)
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  • Completion, Reduction and Analysis: Three Proof-Theoretic Processes in Aristotle’s Prior Analytics.George Boger - 1998 - 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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  • Negation and Quantification in Aristotle.Michael V. Wedin - 1990 - History and Philosophy of Logic 11 (2):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 (...)
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  • Fundacionalismo e silogística.Breno A. Zuppolini - 2014 - In Lucas Angioni (ed.), Lógica e Ciência em Aristóteles. Phi. pp. 161-202.
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  • Lewis Carroll's Visual Logic.Francine F. Abeles - 2007 - History and Philosophy of Logic 28 (1):1-17.
    John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their self-similarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...)
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  • Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic.John Corcoran - 2009 - In W. A. Carnielli (ed.), The Many Sides of Logic. College Publications. pp. 71-103.
    The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...)
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  • Aristotle's Logic at the University of Buffalo's Department of Philosophy.John Corcoran - 2009 - Ideas Y Valores 58 (140):99-117.
    We begin with an introductory overview of contributions made by more than twenty scholars associated with the Philosophy Department at the University of Buffalo during the last half-century to our understanding and evaluation of Aristotle's logic. More well-known developments are merely mentioned in..
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  • Aristotle’s Assertoric Syllogistic and Modern Relevance Logic.Philipp Julius6 Steinkrüger - 2015 - Synthese 192 (5):1413-1444.
    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 (...)
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  • Polarity and Inseparability: The Foundation of the Apodictic Portion of Aristotle's Modal Logic.Dwayne Raymond - 2010 - History and Philosophy of Logic 31 (3):193-218.
    Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results for (...)
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  • Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW]Catarina Dutilh Novaes & Edgar Andrade-Lotero - 2012 - 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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  • The Necessity in Deduction: Cartesian Inference and its Medieval Background.Calvin G. Normore - 1993 - Synthese 96 (3):437 - 454.
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  • Aristotle'S Natural Deduction Reconsidered.John M. Martin - 1997 - History and Philosophy of Logic 18 (1):1-15.
    John Corcoran?s natural deduction system for Aristotle?s syllogistic is reconsidered.Though Corcoran is no doubt right in interpreting Aristotle as viewing syllogisms as arguments and in rejecting Lukasiewicz?s treatment in terms of conditional sentences, it is argued that Corcoran is wrong in thinking that the only alternative is to construe Barbara and Celarent as deduction rules in a natural deduction system.An alternative is presented that is technically more elegant and equally compatible with the texts.The abstract role assigned by tradition and Lukasiewicz (...)
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  • An Intensional Leibniz Semantics for Aristotelian Logic.Klaus Glashoff - 2010 - Review of Symbolic Logic 3 (2):262-272.
    Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.
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  • What Is Aristotelian Ecthesis?Robin Smith - 1982 - History and Philosophy of Logic 3 (2):113-127.
    I consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue that ecthesis (...)
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  • The Existential Assumptions of Traditional Logic.Dwayne Hudson Mulder - 1996 - History and Philosophy of Logic 17 (1-2):141-154.
    There have been and continue to be disagreements about how to consider the traditional square of opposition and the traditional inferences of obversion, conversion, contraposition and inversion from the perspective of contemporary quantificational logic. Philosophers have made many different attempts to save traditional inferences that are invalid when they involve empty classes. I survey some of these attempts and argue that the only satisfactory way of saving all the traditional inferences is to make the existential assumption that both the subject (...)
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