Why Is Proof the Only Way to Acquire Mathematical Knowledge?

This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition's truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowle...

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Detalles Bibliográficos
Publicado en:Australasian Journal of Philosophy Vol. 102; no. 2; pp. 333 - 354
Autor principal: Lange, Marc
Formato: Artículo
Publicado: Taylor & Francis Ltd Jun2024
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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        au: Lange, Marc
        affil: The University of North Carolina at Chapel Hill
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        Mathematics
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        Proposition (Logic)
        Induction (Logic)
        Evidence
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          Mathematics
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          Induction (Logic)
          Evidence
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        proof
      ab: This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition's truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation.
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    language: English
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