On Forms of Justification in Set Theory

Australasian Journal of Logic 17 (4):158-200 (2020)
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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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Author Profiles

Giorgio Venturi
University of Campinas
Claudio Ternullo
Universitat de Barcelona
Neil Barton
University of Oslo

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