Polynomial-time reducibility as a canonical equivalence relation depends on the Church-Turing thesis applied to feasibility, which Wilfried Sieg and others treat as a substantive empirical assumption.

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Church-Turing thesis(Presented as a thesis about the upper bound of computational power, not a proven fact.): The thesis that no computational system stronger than the class of Turing machines exists.
Equivalence relation(One of the three conditions in the inconsistent triad): A relation that is reflexive, symmetric, and transitive; identity relations are standardly taken to be equivalence relations.
Feasibility(as used in logic and computation): Whether something is actually possible to do in practice, considering real-world limitations like time and resources—not just theoretically possible.
Polynomial-time reducibility(as used in computer science and computational theory): A way of transforming one difficult problem into another difficult problem such that if you can solve the second one quickly, you can solve the first one quickly too.

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