Andrei Rodin

TL;DR: The notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this method in physics and other natural sciences as discussed by the authors. But it is difficult to apply it to the problem of topos theory and Voevodsky's axiomatization of homotopy theory.

TL;DR: In this article, a critique of l'approche habituelle de l'identite mathematique is presented, faisant un contraste avec les approches alternatives of Platon and Geach.

TL;DR: In this article, the authors check approaches to identity in mathematics by Plato, Frege, and Geach against category theory and show that they are all based on the same assumptions.

TL;DR: This paper studies the latter process in mathematics during the twentieth century and shows the role of set theory and category theory in this process and defends the following claims: (1) mathematical intuitions are subject to historical development just like mathematical concepts; (2) mathematical intuition continue to play their traditional role in today's mathematics and will plausibly do so in the foreseeable future.

TL;DR: In this article, the Indiscernibility of Identicals thesis is challenged by the notion of identical things having identical properties, which is at odds with the notion that identical things have identical properties.