In the following I argue that underlying our deductive and inductive inferential
practices are certain inferential presuppositions. In the case of induction, this is the
regularity principle while in the case of deduction, they are whatever basic rules or
axioms lie at the foundation of one’s first-order deductive system. I believe the
existence of these inferential presuppositions are indirectly indicated by Hume’s
skepticism about induction and Carroll’s paradox of deduction. I then turn to a
consideration of inference to the best explanation (IBE). I conclude that the
inferential presupposition operating behind IBE is the intelligibility principle—if
something is true there is a best explanation for it. This intelligibility principle is
one form of the Principle of Sufficient Reason (PSR). I then argue that because the
contrapositive of this principle is the presupposition underlying PSR inferences,
inferences that run from the lack of an explanation of P to P being false, that if one
is committed to endorsing IBE inferences one is logically committed to endorsing
PSR inferences. Metaphysical consequences follow.