A proof system that builds in the resources needed to derive a principle cannot serve as independent evidence that the principle is 'easily provable' in any epistemically meaningful sense.
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(Contrasted with purely descriptive scientific inquiry)
A normative enterprise that tells us how we ought to reason from evidence and how we ought to justify our beliefs, as distinct from merely describing how we do reason or justify beliefs
proof system(Propositional proof complexity)
A definition of the derivability symbol ⊢_P which characterizes what it means for a formula φ to be derivable from a given set of axioms and rules; equivalently, a mapping P: {0,1}* → VALID whose domain consists of all binary strings and whose range is the class of all valid formulas