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An Arithmetization of Logical Oppositions

In Jean-Yves Béziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Basel, Switzerland: Birkhäuser. pp. 215-237 (2016)

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  1. Is Classical Mathematics Appropriate for Theory of Computation?Farzad Didehvar - manuscript
    Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...)
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  • End of the square?Fabien Schang - 2018 - South American Journal of Logic 4 (2):485-505.
    It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern of (...)
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  • Making Sense of History? Thinking about International Relations.Fabien Schang - 2014 - In Leonid Grinin, Ilya V. Ilyin & Andrey V. Korotayev (eds.), Globalistics and Globalization Studies. Aspects & Dimensions of Global Views. Volgograd, Oblast de Volgograd, Russie: pp. 50-60.
    Can international relations (IR) be a distinctive discipline? In the present paper I argue that such a discipline would be a social science that could be formulated within the perspective of comparative paradigms. The objections to scientific methods are thus overcome by the logic of international oppositions, in other words a model takes several paradigms into account and considers three kinds of foreign relation (enemy, friend, and rival) in the light of three main questions: what is IR about (ontology); what (...)
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