José Antonio Pérez-Escobar: Structural analogies in mathematics and the disagreement between Turing and Wittgenstein

Tuesday November 5 2024 @11:30 (CEST)
Sala B, Edificio de Humanidades, UNED & online

Abstract
The foundational crisis in mathematics of the 19th century led to a renewal of the analogies used to describe mathematics. In particular, structural analogies became popular (e.g., Hilbert’s building analogy) and contributed to the shaping of particular images of mathematics and regulating mathematical practice. This is a backdrop that heavily influenced Turing’s and the later Wittgenstein’s opposite views of mathematics, the former endorsing it, and the latter very originally departing from it.
Turing and Wittgenstein’s disagreements during Wittgenstein’s lectures in Cambridge have been previously discussed to understand their conflicting views. I will argue that their views can be further understood by analyzing the structural (dis)analogies they employ, in turn defending both Turing and Wittgenstein of some of their most famous criticisms.

Bio
José Antonio Pérez-Escobar is assistant professor in the Department of Logic, History, and Philosophy of Science at UNED. He holds a PhD in neuroscience from the University of Heidelberg and another in philosophy of science from ETH Zurich. He currently focuses on the philosophy of mathematics and general philosophy of science.