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Article Dans Une Revue Philosophia Mathematica Année : 2011

Reflections on Concrete Incompleteness

Résumé

How do we prove true, but unprovable propositions? Gödel produced a statement whose undecidability derives from its "ad hoc" construction. Concrete or mathematical incompleteness results, instead, are interesting unprovable statements of Formal Arithmetic. We point out where exactly lays the unprovability along the ordinary mathematical proofs of two (very) interesting formally unprovable propositions, Kruskal-Friedman theorem on trees and Girard's Normalization Theorem in Type Theory. Their validity is based on robust cognitive performances, which ground mathematics on our relation to space and time, such as symmetries and order, or on the generality of Herbrands notion of prototype proof.
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hal-03319505 , version 1 (12-08-2021)

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  • HAL Id : hal-03319505 , version 1

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Giuseppe Longo. Reflections on Concrete Incompleteness. Philosophia Mathematica, 2011, 19 (3), pp.255-280. ⟨hal-03319505⟩
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