A theory of implicit commitment

Bibliographic Data

ID10813657
AuthorsMateusz Łełyk (0000-0001-5286-4511, University of Warsaw), Carlo Nicolai (0009-0003-1027-5294, King's College London, corresponding author)
Year2022
Volume200
Issue4
Publication date2022-06-30
Open AccessYes
TypeARTICLE
VenueSynthese (JOURNAL)
Journal identifiersISSN: 0039-7857 • E-ISSN: 1573-0964
PublisherSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s11229-022-03601-5
OpenAlexW4283746414
LanguageEN
Citations received5
References cited37

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 provide an axiomatization of the minimal commitments implicit in the acceptance of a mathematical theory. The theory entails that the Uniform Reflection Principle is part of one’s implicit commitments, and sheds light on why this is so. We argue that the theory has significant epistemological consequences in that it explains how justified belief in the axioms of a theory can be preserved to the corresponding reflection principle. The theory also improves on recent analyses of implicit commitment based on truth or epistemic notions

Axiom · Calculus (dental) · Epistemology · Metaphysics · Philosophy of language · Philosophy of science · Reflection (computer programming) · Reflection principle (Wiener process) · Computer Science · Epistemology, Ethics, and Metaphysics · Mathematics · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science

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