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Greek mathematics and Greek logic

In John Corcoran (ed.), Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 35--70 (1974)

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  1. Aristotle’s Assertoric Syllogistic and Modern Relevance Logic.Philipp 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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  • The Beginnings of Formal Logic: Deduction in Aristotle’s Topics Vs. Prior Analytics.Marko Malink - 2015 - Phronesis 60 (3):267-309.
  • Traditional Logic, Modern Logic and Natural Language.Wilfrid Hodges - 2009 - Journal of Philosophical Logic 38 (6):589-606.
    In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately (...)
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  • La formazione del metodo aristotelico della dimostrazione.Piero Tarantino - 2011 - Humanitas 63:157-173.
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  • Reductio Ad Absurdum From a Dialogical Perspective.Catarina Dutilh Novaes - 2016 - Philosophical Studies 173 (10):2605-2628.
    It is well known that reductio ad absurdum arguments raise a number of interesting philosophical questions. What does it mean to assert something with the precise goal of then showing it to be false, i.e. because it leads to absurd conclusions? What kind of absurdity do we obtain? Moreover, in the mathematics education literature number of studies have shown that students find it difficult to truly comprehend the idea of reductio proofs, which indicates the cognitive complexity of these constructions. In (...)
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  • El Programa de Análisis Aristotélico.Michel Crubellier - 2017 - Revista de Humanidades de Valparaíso 10:29.
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  • Atoms, Complexes, and Demonstration: Posterior Analytics 96b15-25.Owen Goldin - 2004 - Studies in History and Philosophy of Science Part A 35 (4):707-727.
    There is agreement neither concerning the point that is being made in Posterior analytics 96b15–25 nor the issue Aristotle intends to address. There are two major lines of interpretation of this passage. According to one, sketched by Themistius and developed by Philoponus and Eustratius, Aristotle is primarily concerned with determining the definitions of the infimae species that fall under a certain genus. They understand Aristotle as arguing that this requires collating definitional predictions, seeing which are common to which species. Pacius, (...)
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  • Logic and Aesthetics in Epistemology.Mildred Rose Payne - 1990 - Dissertation, University of Hawai'i
    The purpose of this dissertation is to present historical evidence in favor of the thesis that many forms of dichotomy appearing in the history of epistemology are related to the duality represented by the mathematical concepts of continuity and discreteness. Parts 1 and 2 give a descriptive and historical account of epistemological dichotomies appearing during the development of mathematics and logic. In part 3, the implications of these dichotomies for general philosophy are explored by means of a collage of analytic, (...)
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  • Renewing Foundations -.Andrei Rodin - unknown
    This is the first part of a work in progress, which contains Introduction, explaining the whole project, and a chapter on Euclid's "Elements". The idea of the book is to describe foundations in mathematics in their history from Euclid until today (making a reasonable choice of material) and then provide a project of future foundations of mathematics. Further historical parts of the book will contain chapters on "New Elements of Geometry" by Arnauld (first published in 1667), Hilbert's "Grundlagen der Geometrie" (...)
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  • Logical Constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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