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Normativity in logic. (English) Zbl 1314.03051
Dybjer, Peter (ed.) et al., Epistemology versus ontology. Essays on the philosophy and foundations of mathematics in honour of Per Martin-Löf. Based on the conference, “Philosophy and foundations of mathematics: Epistemological and ontological aspects”, Uppsala, Sweden, May 5–8, 2009. Dordrecht: Springer (ISBN 978-94-007-4434-9/hbk; 978-94-007-4435-6/ebook). Logic, Epistemology, and the Unity of Science 27, 243-263 (2012).
Summary: Incompleteness – the absence of alternative natural numbers – can be ascribed to a ready-made normativity, inducing a rigid departure syntax/semantics. Geometry of Interaction, set in the non-commutative universe of von Neumann algebras, makes normative assumptions explicit, thus rending possible their internalisation, a possible way out from the semantic aporia. As an illustration, we define an alternative “model”: logspace integers.
For the entire collection see [Zbl 1254.03006].

MSC:
03F50 Metamathematics of constructive systems
03B40 Combinatory logic and lambda calculus
03D15 Complexity of computation (including implicit computational complexity)
03F52 Proof-theoretic aspects of linear logic and other substructural logics
03H15 Nonstandard models of arithmetic
46L10 General theory of von Neumann algebras
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