Graduate studies at Western
|Abstract||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. This argument is hardly new. It is part of the argument in some recent papers promoting contingent a priori knowledge, such as Hawthorne (2002) and Weatherson (2005). But it is an intriguingly quick argument for a stunning philosophical conclusion, one that seems to rely on few dubious steps. I’m going to argue that it fails for a quite interesting reason. At least in natural deduction systems, some inferential rules (such as ∀-introduction) have restrictions on when they can be applied. I’m going to argue that ampliative reasoning rules cannot, in general, be applied inside the scope of suppositions, and that is why the above argument fails. I’ll argue for this conclusion by showing that a very weak ampliative rule leads, when combined with some other plausible principles, to absurd conclusions if it is applied inside the scope of suppositions. If even a weak ampliative rule cannot be used suppositionally, then it plausibly follows that no ampliative rule can be used suppositionally. The construction I’m going to use to show this is quite similar to one used by Sinan Dogramaci in his (forthcoming), though as we’ll see at the end Dogramaci and I have different views about what to take away from these arguments. Some people might think we have already seen an argument that ampliative inference rules fail in suppositional reasoning..|
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