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Chapitre D'ouvrage Année : 2020

Space and Time in the Foundations of Mathematics, or some challenges in the interactions with other sciences

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Résumé

Our relation to phenomenal space has been largely disregarded, and with good motivations, in the prevailing foundational analysis of Mathematics. The collapse of Euclidean certitudes, more than a century ago, excluded ‘’geometric judgments’’ from certainty and contributed, by this, to isolate the foundation of Mathematics from other disciplines. After the success of the logical approach, it is time to broaden our foundational tools and reconstruct, also in that respect, the interactions with other sciences. The way space (and time) organize knowledge is a cross-disciplinary issue that will be briefy examined in Mathematical Physics, Computer Science and Biology. This programmatic paper focuses on an epistemological approach to foundations, at the core of which is the analysis of the ‘’knowledge process’’, as a constitutive path from cognitive experiences to mathematical concepts and structures. When frst presented, in 2001, it opened to way to the idea that phylogenetic trajectories, in biology, co-construct the space of possibilities, in contrast to physical theories which assume a pre-given phase space of all possible dynamics.
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hal-03318941 , version 1 (11-08-2021)

Licence

Paternité - CC BY 4.0

Identifiants

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Giuseppe Longo. Space and Time in the Foundations of Mathematics, or some challenges in the interactions with other sciences. Bharath Sriraman. Handbook of the Mathematics of the Arts and Sciences, Springer, 2020, 3319570730, 978-3319570730. ⟨10.1007/978-3-319-70658-0_116-1⟩. ⟨hal-03318941⟩
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