Theoretical analysis motivates uniform reflection principles in axiomatic arithmetic via constructive omega-rules, highlighting their foundational epistemic warrant.
Reflection principles are of central interest in the development of axiomatic theories. Whereas they are independent statements they appear to have a specific epistemological status. Our trust in those principles is as warranted as our trust in the axioms of the system itself. This paper is an attempt in clarifying this special epistemic status. We provide a motivation for the adoption of uniform reflection principles by their analogy to a form of the constructive ω ω -rule. Additionally, we analyse the role of informal arithmetic and the conception of natural numbers as an inductive structure, also with regard to extra conceptual resources such as a primitive truth predicate.
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Martin H. Fischer (2021) studied this question.
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