Space and Time in the Foundations of Mathematics, or Some Challenges in the Interactions with Other Sciences

Giuseppe Longo ()
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Giuseppe Longo: CNRS and Ecole Normale Supérieure, Centre Cavaillès

Chapter 93 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 2459-2486 from Springer

Abstract: Abstract 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 briefly 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 first 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 pregiven phase space of all possible dynamics.

Keywords: Concepts; Structures; Geometry; Action; Epistemology (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_116

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DOI: 10.1007/978-3-319-57072-3_116

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