FOM: Decidable axioms sets and algorithms in proofs

[Neil Tennant]

Torkel,
perhaps it's the intuitionist in me saying that if I know the set of axioms
to be recursive, then I do indeed have an algorithm to decide whether or not
a formula is an axiom. 
Can you make plausible any (necessarily classical0 predicament in which one
knows the set of axioms to be recursive, but one does *not* have such an
algorithm?
(Sorry, that zero should have been a right parenthesis.)

Neil Tennant