Therefore, the claim that primitive recursion over a computable base provides 'no a priori assurance' of computability conflates formal proof within a model with the broader epistemological warrant supplied by Church's Thesis.
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A logical argument written in strict, symbolic form that follows explicit rules, showing that something must be true.
a priori(Frege treats 'analytic' as entailing 'a priori' for arithmetic.)
Knowable independently of empirical experience; here treated as a consequence of analyticity.
computability(computer science and philosophy of mathematics)
The study of what problems can or cannot be solved by following a step-by-step procedure (algorithm) on a computer.
model(Possible worlds interpretation of S5 adapted for modal nonmonotonic logic)
A pair <I, S> where I is a set of literals (a state description / possible world) and S is a set of complete, consistent sets of literals (interpretations) with I ∈ S
primitive recursion(computability theory / recursive function theory)
A restricted kind of recursion in which a function h with first argument n+1 is defined in terms of h with first argument n, with all other arguments unchanged.