Friday, August 31, 2012

A puzzle

Suppose P and E are empirical claims and E does not entail P. Nonetheless suppose:

  1. I know P precisely on the grounds of E.
Surely it is possible—maybe it even follows if some appropriate closure principle holds—that I am also in a position to know the disjunction P or not E. But on what grounds am I in a position to know the disjunction? Surely not on the grounds of E, since E is if anything evidence against the conjunction (after all the negation of E would be conclusive evidence against the disjunction). So, it seems, I must know it a priori. Cf. the Explainer in Hawthorne.

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.


Brian said...

Interesting puzzle! Here's a diagnosis of what's going on. As you say, E doesn't entail P, so the conditional E-->P is not necessary. But it is, as you point out, (apparently) a priori. But what's interesting about your example isn't that it divorces apriority from necessity (Kripke's examples of the contingent a priori already did that), but that it divorces apriority from (what we might call) Cartesian certainty. Even in Kripke's examples of the contingent a priori (e.g. the case of Julius, or the case of the meter stick), we seem to be able to know the relevant propositions with complete (Cartesian) certainty, as is typical of a priori knowledge. But in your phlogiston case-- assuming your inference from E to ~Q is ampliative-- then ~(E&Q) will be "non-Cartesian" (i.e. doesn't admit of Cartesian certainty; if it did, the inference wouldn't be ampliative), despite its apparent a priori knowability. In general, it appears that: whenever we reason successfully from a known premise E to a conclusion P using ampliative methods of inference (e.g. induction, abduction)-- where successful reasoning is just knowledge-generating reasoning-- then (plausibly) the conditional E-->P will be a non-Cartesian a priori truth.

Alexander R Pruss said...

This is a case of what I think Hawthorne calls the deeply contingent a priori.

Brian Cutter said...

I haven't read the Hawthorne paper, but the characterization of these cases as "deeply contingent a priori" strikes me as slightly off the mark. In particular, it seems that the contingency of the relevant propositions is somewhat incidental, since there are relevantly similar cases involving necessary propositions. Suppose we inspect, say, 1000 samples of the watery stuff in our environment, taken from a wide range of sources, and we find that each of them is composed of H20. On the basis of the evidence E gained in the course of these inspections, we can (plausibly) come to know that water is H20. And so, we should be able to know a priori the conditional E-->(Water is H20). But, since (let’s assume) we’ve only examined a small fraction of the total quantity of water in our environment, it is consistent with E that the dominant watery stuff in our environment is not H20, and hence (plausibly) it is, in some Cartesian sense of epistemic possibility, epistemically possible that the conditional E-->(Water is H20) is false. It seems to me that this case is relevantly like the cases you’ve given, despite the fact that the relevant conditional-- E-->(water is H20)-- is not contingent. This leads me to think that the relevant difference between these cases and Kripke’s examples of the contingent a priori isn’t to be found in the relative “depth” of the contingency in the former cases, but in their status as non-Cartesian truths.