Programação
Abstract
The received philosophical view is that while science is based on observation or experiment, mathematics is based on axioms, definitions and deductive proofs. This talk aims to draw on the experimental nature of mathematics. In particular, it aims to demonstrate that dealing with impossibilities in mathematics, such as in proofs by contradiction (PbCs) can be better appreciated from the perspective of mathematical thought experiments (MTEs), rather than from the perspective of deductive proofs.
The talk will also stress the importance of thought experiments as one of the advantageous mathematical methods. Traditionally either they are claimed to be impossible because mathematics is considered to be a priori; or they are regarded very broadly, i.e. that any mathematical reasoning is a thought experiment. This talk will determine the genuine MTEs.
Recommended reading
Irina Starikova “Thought experiments in mathematics: from fiction to facts” in Sriraman Bharath (ed.) Handbook of the History and Philosophy of Mathematical Practice. Springer, 2023.
Irina Starikova and Jean Paul Van Bendegem “Revisiting the Mutilated Chessboard or the Many Roles of a Picture” Logique et Analyse, 255, 2021, pp. 289-312
Irina Starikova and with Marcus Giaquinto “Thought Experiment in Mathematics” in The Routledge Companion to Thought Experiments by James Robert Brown (ed.) 2018, pp. 257-78
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