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Malament-Hogarth Machines and Tait's Axiomatic Conception of Mathematics.

In this paper I will argue that Tait's axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experien...

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Publicado en:Erkenntnis Vol. 79; no. 4; pp. 893 - 908
Autor principal: Berry, Sharon
Formato: Artículo
Publicado: Springer Nature Aug2014
Materias:
Mathematical logic
Mathematics research
Mathematical proofs
Philosophical research
Mathematical analysis
Acceso en línea:Ver este registro en EBSCOhost
Sumario:In this paper I will argue that Tait's axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.