One of the earliest discussions of the so-called 'bad company' objection to Neo-Fregeanism, I show that the consistency of an arbitrary second-order 'contextual definition' (nowadays known as an 'abstraction principle' is recursively undecidable. I go on to suggest that an acceptable such principle should satisfy a condition nowadays known as 'stablity'.

[Michael Potter] If arithmetic is not analytic in Kant's sense, what is its subject matter? Answers to this question can be classified into four sorts according as they posit logic, experience, thought or the world as the source, but in each case we need to appeal to some further process if we are to generate a structure rich enough to represent arithmetic as standardly practised. I speculate that this further process is our reflection on the subject matter already obtained. This (...) suggestion seems problematic, however, since it seems to rest on a confusion between the empirical and the metaphysical self. /// [Bob Hale] Michael Potter considers several versions of the view that the truths of arithmetic are analytic and finds difficulties with all of them. There is, I think, no gainsaying his claim that arithmetic cannot be analytic in Kant's sense. However, his pessimistic assessment of the view that what is now widely called Hume's principle can serve as an analytic foundation for arithmetic seems to me unjustified. I consider and offer some answers to the objections he brings against it. (shrink)

This influential 1888 publication explained the real numbers, and their construction and properties, from first principles.