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  1. The concept of given in Greek mathematics.Nathan Sidoli - 2018 - Archive for History of Exact Sciences 72 (4):353-402.
    This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced (...)
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  • Euclid’s Kinds and (Their) Attributes.Benjamin Wilck - 2020 - History of Philosophy & Logical Analysis 23 (2):362-397.
    Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at (...)
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  • Human Rationality Challenges Universal Logic.Brian R. Gaines - 2010 - Logica Universalis 4 (2):163-205.
    Tarski’s conceptual analysis of the notion of logical consequence is one of the pinnacles of the process of defining the metamathematical foundations of mathematics in the tradition of his predecessors Euclid, Frege, Russell and Hilbert, and his contemporaries Carnap, Gödel, Gentzen and Turing. However, he also notes that in defining the concept of consequence “efforts were made to adhere to the common usage of the language of every day life.” This paper addresses the issue of what relationship Tarski’s analysis, and (...)
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  • Observing logics: revisiting reason in The Brothers Karamazov.Eric Kim - forthcoming - Studies in East European Thought:1-20.
    Very often in frameworks for and presentations of The Brothers Karamazov, the modern reading public attempts to divide characters by their ability to reason. Usually Ivan is remembered for his reason, pitted against Dmitri’s passion. Adapting some terminology from mathematical logic, I propose and trace a different approach to reason in Dostoevsky’s text, to recast its canonical characters into alternative, though still fluid, categories. This exercise aims not to reinscribe or to reinterpret Dostoevsky’s novel but rather to reconsider an aspect (...)
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  • RezensionenReviews.Achim Thom, Ortrun Riha, Renate Tobies, Hubert Laitko, Wolfgang Schreier & Peter Schreiber - 2000 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 8 (1):123-127.
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  • Euclid’s book on divisions of figures: a conjecture as to its origin.David Aboav - 2008 - Archive for History of Exact Sciences 62 (6):603-612.
    It is shown how a diagram on the reverse of a Greek coin of Aegina of the fifth century b.c.e., is simply constructed with the help of Proposition 36 of Euclid’s Book on Divisions [of Figures], and it is conjectured in the absence of contemporary evidence that, since Euclid expressly designated this proposition to be the last in the book, he may have had in mind the diagram, which, some 200 years after its appearance on the coinage, may still have (...)
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  • Kaspar Schott’s “encyclopedia of all mathematical sciences”.Eberhard Knobloch - 2011 - Poiesis and Praxis 7 (4):225-247.
    In 1661, Kaspar Schott published his comprehensive textbook Cursus mathematicus in Würzburg for the first time, his Encyclopedia of all mathematical sciences. It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred authors, (...)
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