The aim of this paper is to generalize a pair of concepts that are widely used in the history of science, in art history and in historical linguistics – the concept of internal and external history – and to replace the often very vague talk of ‘historical narratives’ with this conceptual framework of internal versus external history. I argue that this way of framing the problem allows us to see the possible alternatives more clearly – as a limited number of (...) possible relations between internal and external history. Finally, I argue that while external history is metaphysically prior to internal history, when it comes to historical explanations, we need both. (shrink)

Lakatos's Proofs and Refutations is usually understood as an attempt to apply Popper's methodology of science to mathematics. This view has been challenged because despite appearances the methodology expounded in it deviates considerably from what would have been a straightforward application of Popperian maxims. I take a closer look at the Popperian roots of Lakatos's philosophy of mathematics, considered not as an application but as an extension of Popper's critical programme, and focus especially on the core ideas of this programme (...) as they appeared where Popper specifically addressed philosophical problems concerning mathematics. (shrink)