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On Forms of Justification in Set Theory

Barton, Neil and Ternullo, Claudio and Venturi, Giorgio (2019) On Forms of Justification in Set Theory. [Preprint]

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Abstract

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barton, Neilbartonna@gmail.com0000-0002-3637-1730
Ternullo, Claudio
Venturi, Giorgio
Keywords: justification; set theory; continuum hypothesis
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics
Depositing User: Dr. Neil Barton
Date Deposited: 13 Jul 2020 14:50
Last Modified: 13 Jul 2020 14:50
Item ID: 17461
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics
Date: 2019
URI: https://philsci-archive.pitt.edu/id/eprint/17461

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