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Speech acts in mathematics

Synthese 198 (10):10063-10087 (2020)

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  1. A metalinguistic and computational approach to the problem of mathematical omniscience.Zeynep Soysal - 2022 - Philosophy and Phenomenological Research 106 (2):455-474.
    In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and belief on which (...)
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  • On a New Approach to Peirce’s Three-Value Propositional Logic.José Renato Salatiel - 2022 - Manuscrito 45 (4):79-106.
    In 1909, Peirce recorded in a few pages of his logic notebook some experiments with matrices for three-valued propositional logic. These notes are today recognized as one of the first attempts to create non-classical formal systems. However, besides the articles published by Turquette in the 1970s and 1980s, very little progress has been made toward a comprehensive understanding of the formal aspects of Peirce's triadic logic (as he called it). This paper aims to propose a new approach to Peirce's matrices (...)
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  • Frege: A fusion of horizontals.Francesco Bellucci, Daniele Chiffi & Luca Zanetti - 2023 - Theoria 89 (5):690-709.
    In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in (...)
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  • Analytic Philosophy in Latin America (2nd edition).Diana I. Pérez & Santiago Echeverri - 2023 - Stanford Encyclopedia of Philosophy.
    Analytic philosophy was introduced in Latin America in the mid-twentieth century. Its development has been heterogeneous in different countries of the region but has today reached a considerable degree of maturity and originality, with a strong community working within the analytic tradition in Latin America. This entry describes the historical development of analytic philosophy in Latin America and offers some examples of original contributions by Latin American analytic philosophers.
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