I agree that his attitude may be hard to pin down. Keynes, however, subsequently explicitly abandoned the foundations of his Treatise argument. He rejects, however, Ramsey's attempt to elaborate the idea in terms of Charles Peirce's pragmatism.
Formal logic is concerned with nothing but the rules of consistent thought.
The application of these ideas to the logic of probability is very fruitful. Thus the calculus of probabilities belongs to formal logic. It is not getting to the bottom of the principle of induction merely to say that it is a useful mental habit. This change left much of the rest of the Treatise's treatment of probability intact. In particular, in locating the basis of degrees of belief in human rather than formal logic, Keynes retained the view that objective rational grounds were available for such beliefs.