Inspired by some things Stewart Cohen and Jonathan Vogel said at the weekend’s scepticism conference, I’ve written a short note on the intersection of inductive reasoning and suppositional reasoning.
Here’s the first paragraph, which gives you a flavour of what I’m arguing against.
Here’s a fairly quick argument that there is contingent a priori knowledge. Assume there are some ampliative inference rules. Since the alternative appears to be inductive scepticism, this seems like a safe enough assumption. Such a rule will, since it is ampliative, licence some particular inference From A infer B where A does not entail B. That’s just what it is for the rule to be ampliative. Now run that rule inside suppositional reasoning. In particular, ﬁrst assume A, then via this rule infer B. Now do a step of →-introduction, inferring A → B and discharging the assumption A. Since A does not entail B, this will be contingent, and since it rests on a sound inference with no (undischarged) assumptions, it is a priori knowledge.