Suppose P and E are empirical claims and E does not entail P. Nonetheless suppose:
- I know P precisely on the grounds of E.
Here's an instance of the above (with some negations transposed). I know phlogiston theory, Q, to be false on the basis of some empirical evidence E. I surely also know that the conjunction of Q and E is false. On what grounds do I know that conjunction to be false? Surely not on the basis of E. But then what? The answer seems to be that I know it a priori, despite the conjunction being a contingent empirical claim.