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Another Look at Reflection

Martin Fischer

Erkenntnis 88 (2):479-509 (2021)

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Implicit commitments of instrumental acceptance: A case study.Luca Castaldo & Maciej Głowacki - forthcoming - Philosophical Quarterly.details When accepting an axiomatic theory S, we are implicitly committed to various statements that are independent of its axioms. Examples of such implicit commitments include consistency statements and reflection principles for S. While foundational acceptance has received considerable attention in this context, the study of implicit commitments triggered by weaker notions remains underdeveloped. This article extends the analysis investigating implicit commitments inherent in instrumental acceptance, comparing them with the implicit commitments involved in foundational acceptance. Concentrating on Reinhardt’s instrumentalism vis-à-vis Kripke–Feferman (...) Download Export citation Bookmark
A theory of implicit commitment.Mateusz Łełyk & Carlo Nicolai - 2022 - Synthese 200 (4):1-26.details The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still lacking. We (...) Download Export citation Bookmark 4 citations
Is the HYPE about strength warranted?Martin Fischer - 2022 - Synthese 200 (3):1-25.details In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purposes and has additional attractive properties. Download Export citation Bookmark 1 citation
In Defense of the Implicit Commitment Thesis.Ethan Brauer - 2022 - Ergo: An Open Access Journal of Philosophy 9.details The implicit commitment thesis is the claim that believing in a mathematical theory S carries an implicit commitment to further sentences not deductively entailed by the theory, such as the consistency sentence Con(S). I provide a new argument for this thesis based on the notion of mathematical certainty. I also reply to a recent argument by Walter Dean against the implicit commitment thesis, showing that my formulation of the thesis avoids the difficulties he raises. Download Export citation Bookmark
Reflecting on believability: on the epistemic approach to justifying implicit commitments.Maciej Głowacki & Mateusz Łełyk - 2024 - Philosophical Studies 181 (11):3135-3163.details By definition, the implicit commitment of a formal theory $$\textrm{Th}$$ Th consists of sentences that are independent of the axioms of $$\textrm{Th}$$ Th, but their acceptance is implicit in the acceptance of $$\textrm{Th}$$ Th. In Cieśliński (2017, 2018), the phenomenon of implicit commitments was studied from the epistemological perspective through the lenses of the formal theory of believability. The current paper provides a comprehensive proof-theoretic analysis of this approach and compares it to other main theories of implicit commitments. We argue (...) Download Export citation Bookmark

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