Bangu’s random thoughts on Bertrand’s paradox

where such models are used to rule out derivations involving irrelevant factors (such as the hexed salt example) that are deemed explanatory by the deductive-nomological model. As I mentioned at the outset, my aim has not been to attack Lange’s general thesis that proofs by mathematical induction are not explanatory, but rather to undercut the argument that Lange provides for this thesis. To defend the contrary claim that certain inductive proofs are explanatory would require providing a worked-out theory of mathematical explanation, something that I have not tried to do here. What I have tried to do is to show that there are plausible ways of thinking about mathematical explanation which are in tension with key steps in Lange’s argument, and to this extent his premises are more ‘controversial’ than he admits.