Year: 2021
Type: article
Abstract: This volume aims to explore philosophical issues related to intensionality in mathematics, and critically examine how concerns about intensionality have driven much recent work in both philosophy and mathematics, particularly in formal philosophy and mathematical logic.Intensional issues, in mathematics and elsewhere, are often most easily characterised in contrast to extensional ones.Consider the case of algorithms: two algorithms may have quite different descriptions, and indeed quite different characteristics-one may run in linear time, while the other has merely polynomial running time-and yet compute the same outputs.According to a purely extensional standard they would thus be considered identical, since they compute the same function, but intensionally they are distinct.Set theory, on the other hand, is often considered a paradigmatic case of an extensional discipline: the fact that two sets have the same members is sufficient for them to be identical, regardless of how those sets are described, and indeed this principle is codified in axiomatic set theories such as ZFC by the axiom of extensionality.These examples indicate how intensional approaches to mathematics can usefully be characterised in terms of their treatment of the notion of identity.If the identity of two items (terms, sentences, functions, proofs, etc.) can be established by examining the objects that fall under their extensions, then the approach in question is an extensional one.On the other hand, if establishing identity requires considering additional aspects that are connected to the way in which such items are defined or presented, then the approach is intensional.(Consider for example the question of whether two algorithms which compute the same function can be considered to be the same algorithm) In other words, we can say (in a somewhat circular manner) that if an approach does not distinguish between two different presentations of the same object or concept, B
Source: Synthese
Authors: Marianna Antonutti Marfori, Paula Quinon
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,780
Funder: Agence Nationale de la Recherche
OpenAlex ID: W3134095740