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Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs
Studia Humana, 2020 The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics.
Krajewski Stanisław
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Analyzing and Critic of Ibn Sina’s Explanation on Triple Division of Theoretical Wisdom [PDF]
Journal of Philosophical Investigations, 2021 Ibn Sina, as a Muslim Philosopher, has given a famous triple division of knowledge and wisdom that is relying on Aristotelian philosophical tradition. Ibn Sina tries to rationalize his triple division of knowledge and wisdom based on many properties of ...
Qodrotallah Qorbani +2 more
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Wronski's Foundations of Mathematics [PDF]
Science in Context, 2016 ArgumentThis paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators.
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Mathematical foundations of moral preferences [PDF]
Journal of The Royal Society Interface, 2021 One-shot anonymous unselfishness in economic games is commonly explained by social preferences, which assume that people care about the monetary payoffs of others. However, during the last ten years, research has shown that different types of unselfish behaviour, including cooperation, altruism, truth-telling, altruistic punishment, and trustworthiness
Valerio Capraro, Matjaž Perc
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Univalent Foundations and the UniMath Library [PDF]
, 2018 We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the ...
A Borel +13 more
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Mathematical Foundations of Supersymmetry [PDF]
, 2011 In our exposition of mathematical SUSY, we use the language of T-points to build supermanifolds up from their foundations in graded linear algebra (superalgebra). Though our treatment is similar to the many pioneering works in supergeometry, however we prove some deeper results related to the Frobenius theorem as well as give a full treatment of ...
Carmeli C., Caston L., FIORESI, RITA
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, 2018 Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations.
Marquis, Jean-Pierre
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Mathematical foundations of consciousness
Journal of Applied Logic, 2009 We employ the Zermelo-Fraenkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo-Fraenkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied
Miranker, Willard L. +1 more
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mizar-items: Exploring fine-grained dependencies in the Mizar Mathematical Library [PDF]
, 2011 The Mizar Mathematical Library (MML) is a rich database of formalized mathematical proofs (see http://mizar.org). Owing to its large size (it contains more than 1100 "articles" summing to nearly 2.5 million lines of text, expressing more than 50000 ...
A. Grabowski, I. Lakatos, S.G. Simpson
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Des fondements vers l’avant. Sur la rationalité des mathématiques et des sciences formalisées
Philosophia Scientiæ, 2005 Forward foundations. On the rationality of mathematics and of formalized sciences. — The failure of logicism for the question of foundations of mathematics invites us to consider this question under an epistemological point of view, in terms of ...
Michel Paty
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