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Components of arithmetic theory acceptance

Colclough, Thomas M. (2024) Components of arithmetic theory acceptance. Synthese, 203. ISSN 1573-0964


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This paper ties together three threads of discussion about the following question: in accepting a system of axioms S, what else are we thereby warranted in accepting, on the basis of accepting S? First, certain foundational positions in the philosophy of mathematics are said to be epistemically stable, in that there exists a coherent rationale for accepting a corresponding system of axioms of arithmetic, which does not entail or otherwise rationally oblige the foundationalist to accept statements beyond the logical consequences of those axioms. Second, epistemic stability is said to be incompatible with the implicit commitment thesis, according to which accepting a system of axioms implicitly commits the foundationalist to accept additional statements not immediately available in that theory. Third, epistemic stability stands in tension with the idea that in accepting a system of axioms S, one thereby also accepts soundness principles for S. We offer a framework for analysis of sets of implicit commitment which reconciles epistemic stability with the latter two notions, and argue that all three ideas are in fact compatible.

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Item Type: Published Article or Volume
Colclough, Thomas M.
Keywords: Theory acceptance, Arithmetic, Implicit commitment, Epistemic stability, Semantic, Schematic
Subjects: Specific Sciences > Mathematics > Logic
Depositing User: Dr Thomas Colclough
Date Deposited: 15 Jan 2024 01:00
Last Modified: 15 Jan 2024 01:00
Item ID: 22968
Journal or Publication Title: Synthese
Official URL:
DOI or Unique Handle: 10.1007/s11229-023-04465-z
Subjects: Specific Sciences > Mathematics > Logic
Date: January 2024
Volume: 203
ISSN: 1573-0964

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