Titlebook: Axiomatic Method and Category Theory; Andrei Rodin Book 2014 Springer International Publishing Switzerland 2014 Categorical logic.David Hi

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Harnessing Hospitality for Human Flourishing the current mathematical practice (“applications”). It is opposed in this sense to the “Bolzano-Frege-Peano-Russell tradition” (making part of today’s Analytic philosophy), which attempts to provide Formal Axiomatic Method with a philosophical underpinning disregarding its problematic status in the

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Omowumi Ogunyemi,Andrew Onwudinjotes the apple when green, and B when it is red then . = . (it is the same thing) but the properties of . and . are different: they have a different color. This is at odds with the Indiscernibility of Identicals thesis according to which identical things have identical properties.

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Nathaniel C. Lupton,Michael Pirsonon and concentration” (Lawvere 2003, p. 213) and generalize upon some examples of axiomatic thinking due to Lawvere and Voevodsky. I begin with the unification, then turn to the concentration and, finally, discuss the place and the special character of logic in the New Axiomatic Method.

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Oludolapo Afolami,Ruqayyah BaderinwaIn the standard textbooks Hilbert’s philosophy of mathematics is commonly labelled . and under this title distinguished from Brouwer’s ., on the one hand, and Russell’s ., on the other hand. However, as Hintikka (1997a) rightly remarks, this popular name is very misleading.

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Moyinoluwa Okunloye,Amaka OkpallaThe replacement of the equivalence . by the identity . = . discussed by Frege (Sect. .) allows for an interpretation, which differs from Frege’s. Namely, equivalence . can be understood as an invertible . (rather than relation), which turns . into . and vice versa; then the identity = becomes the identity . this transformation.

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Hilbert: Making It FormalIn the standard textbooks Hilbert’s philosophy of mathematics is commonly labelled . and under this title distinguished from Brouwer’s ., on the one hand, and Russell’s ., on the other hand. However, as Hintikka (1997a) rightly remarks, this popular name is very misleading.

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Identity Through Change, Category Theory and Homotopy TheoryThe replacement of the equivalence . by the identity . = . discussed by Frege (Sect. .) allows for an interpretation, which differs from Frege’s. Namely, equivalence . can be understood as an invertible . (rather than relation), which turns . into . and vice versa; then the identity = becomes the identity . this transformation.