I sometimes get asked why I take a priori reasoning seriously; after all empiricists should eschew such talk! Real empiricists do not engage the rationalist on their own turf…in true Type-Q style I should deny that there is an a priori/a posteriori or an analytic/synthetic distinction and deny as well that talk of possible worlds is meaningful. But I don’t.
Let us define A Priori knowledge as follows
APK=def justified necessarily true belief
Let us define A Priori justification as follows
APJ=def justification that is not based on experience (i.e. not based on sensing, perception, memory or introspection)
A Priori justification usually takes the form of a ‘rational seeming’ which phenomenologically is a kind of ‘seeing’ that something could or couldn’t be the case. One has an immediate intuition that the proposition couldn’t possibly be true (or false). So, for example, when I consider simple propositions like that A=A, ((P–>Q) & P) –>Q, and (P v ~P) <–> ~(P & ~P) I find it unimaginable that they could be false. It is this phenomenology which leads people to argue along the lines of ++
++ APJ –> APK
Since it seems to one unimaginable that P is false (or true) one concludes that it must be true (i.e. that it is necessarily true). It is also taken to be the case that the history of philosophy has demonstrated that experience cannot teach that something is necessary and so APJ is the only route to APK.
Now as an empiricist I want to deny that we have a priori knowledge but I want to allow there to be a priori justification. In other words I want to allow that rational seemings can provide justification even though they don’t provide (necessary) knowledge this is because rational seemings are, according to me, ultimately themselves dependent on how the world turns out. Suppose for the sake of argument that the above simple propositions are not in fact necessarily true. Suppose that they are just extremely well confirmed empirical generalizations. That is, suppose that the regularities of our Humean world regularly, and up until now reliably, provide us the kinds of experiences that justify instances of these propositions. Suppose further that you have organisms evolving in this environment. These organisms will likely develop systems that encapsulate these propositions. To these organisms these propositions will seem to be unimaginably false (or true) but they are not necessary truths (ex hypothesi) and they are ultimately justified by the organism’s ancestor’s experiences. But these propositions are true; it’s just that they aren’t necessarily true. So one can have knowledge that has a priori justification but that is not a priori knowledge. Now I am not here trying to give an argument for this view. I only mean to be pointing out that this is perfectly compatible with the empiricist view and so if one is careful one can be an empiricist and still think that we can have knowledge on the basis of a priori reasoning.
So far I have been only talking about knowledge of how the world actually is. Nothing has been said about the way it could be. reasoning about modality seems to me to be fundamentally rooted in our ability to imagine or conceive of various situations. Conceivability has traditionally thought to be a guide to what is possible and to be bounded only by what is contradictory. That this be true is certainly conceivable (just as is the empiricist version above). We may not know that it is true but it does seem like a possibility. So, for instance, it is almost impossible to see what it could even mean to say that (A=A) is false…I mean that would have to mean that there was some thing picked out by ‘A’ which was identical to itself in some conceivable situations but was not identical to itself in other conceivable situations. That just intuitively seems contradictory! But, wait, we can have rational seemings in the absence of necessary truth. So, famously, when some people offered “proofs” of the parallel postulate they were accepted as correct until some mistake in the proof was discovered. If so, then there was a time when people could have a priori justification for something which turns out to be demonstrably false. So perhaps our intuition that justifies our belief in (A=A) and the like are also suspect. As a counter example David Rosenthal talks about identity statements like (A=A) beg the question by assuming the notion of rigid designation. If one doesn’t assume that it is of course not necessary. But it seems to me that the 2-D response has legs here: we can have both. Intuitions about rigidity are explained by the secondary intension and the corresponding kinds of possibility. Intuitions about the non-necessity of identities are explained by the primary intension and the corresponding kind of possibility. In short then as long as we see rational intuition as defeasible justification (defeasible in particular by experience) then we can accept the a priori justification of (A=A) in the absence of defeaters which we have yet to find anyway
To sum up then; I think I can know that for any A, A=A a priori but not that (A=A) yet even so I think that I have good justification for believing (A=A) and ~(P & ~P) and so we have good justification of modal talk.