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The intensionality of the predicate '_ is recursive'

G. Lee Bowie's "An Argument Against Church's Thesis" provides an opportunity to clarify some points about our concepts of recursive and computable. In [1], G. Lee Bowie argued that there is a noncomputable recursive function and that there are computable functions which are very likely nonrecursive. Against his first claim, I shall argue, primarily, that Bowie has instead exposed the intensional character of the predicate ' is recursive.' Against his second claim, I shall argue that he has used an eccentric sense of 'computable/