Is 'p is a priori' itself a priori?

My most recent posts have been far too long by blogging standards, so I am determined here to be brief. Most philosophers (though not all, e.g., anyone who holds the Quine-Putnam indispensibility thesis) believe the following sentences are true:
(1) "'2+3=5' is true a priori"
(2) "'The earth is round' is true a posteriori"
The question is: are (1) and (2) true a priori or a posteriori? Put metaphorically, does experience teach us that logical theorems are known independently of experience? I am not sure there are any non-question-begging arguments to be given one way or the other; if there is one, I would love to hear it.

That's all I wanted to say. If you are curious about what motivated me to think about this question, keep reading. There are two motivating sources:
First, my dissertation, which deals with the academic year Carnap, Tarski, and Quine spent together at Harvard in 1940-41. In a private conversation Carnap had with Quine, one way they formulate the difference between themselves is as follows.
Carnap: 'p is analytic in language L' is itself an analytic statement.
Quine: 'p is analytic in L' is a synthetic statement, to be settled by a behavioristic investigation into the linguistic habits of L-speakers.
Granted, 'analytic' is not identical to 'a priori' -- but for Carnap, they were extensionally equivalent, and the question above is very close to this issue.
Second, for the last 10 years, van Fraassen has been suggesting that we think of empiricism not as a theory or assertion but as a stance. (See "Against Naturalized Epistemology" (1995) in On Quine and 2002's The Empirical Stance.) The primary argument he offers is that empiricism, if conceived as an assertion, is self-defeating: "All knowledge about the world is a posteriori" (or any other slogan intended to capture the empiricist's thesis) will be difficult to construe as having experience as its source. And, van Fraassen says, if the empiricist thesis cannot be justified on the basis of experience alone, then it fails to live up to its own standards, and is therefore self-defeating. But van Fraassen is assuming that "such-and-such is a posteriori" must itself be an a posteriori claim. And that is taking for granted an answer to my question above.


Anonymous said...

Well, to give an even briefer response, I guess I lean toward a somewhat conventionalist view of the a priori. Something is a priori if we've decided to treat it as such. This doesn't automatically settle the question, I suppose, but I think that if we're unsure as to whether we've decided to treat something as a priori, we haven't quite made the decision, so I suspect that whether a claim is a priori should end up itself being automatically a priori on my view. As you say, that seems to have been Carnap's view, and I think I'm pretty close to him on issues involving the a priori.

Of course, if it's a priori that something is a priori, that suggests it should also be a priori that something isn't, though for some reason I feel less confident about that latter claim.

Kenny said...

About a year or two ago, I had a roommate who was a cognitive scientist taking his first philosophy class, and he had to write about whether or not there were some a priori truths, and he decided to take just this tack, suggesting that the answer to this question should be a priori.

I like this notion of a "stance" that you've mentioned a few times. Is there some place this is introduced and discussed so I can read more about it? Because it really seems that something like empiricism isn't a proposition that is itself capable of being true or false, but rather a stance that can be useful or not.

Anyway, addressing the basic concern of the post, it seems that a prior means something like "knowable through pure reasoning". If we accept a computational model of reasoning, then the halting problem will show that any statement that can be known to be true a priori, can also be known to be a priori in an a priori way. However, there will be no a priori means of deciding that something is not a priori, so "p is a posteriori" may well not be a priori in many cases, even though "p is a priori" always is on this model. (That is, when each of these statements is true.)

Greg Frost-Arnold said...

Protagoras- Thanks for stopping by; I read Neurath's Boat regularly. I think many people (well, many philosophers) share that last intuition of yours, viz. "'p is a priori' is a priori" is intuitively more appealing/ acceptable etc. than "'p is a posteriori' is a posteriori." And perhaps Kenny's point about the Entscheidungproblem can be used to underwrite that intuition.

1. The most extended discussion of the notion of a stance that I know of is in chapter 2 (I think) of van Fraassen's Empirical Stance (2002). It's highly readable.

2. I don't know much about the computational model of reasoning, but do its propoents say that (e.g) the Godel sentence -- or the undecidable sentences of first-order logic -- are a posteriori? That doesn't sound right to me; maybe I've misunderstood your post. But my guess is that something similar to your idea is (at least part of) why Carnap takes the position he does: after Godel shows how to formalize '...is provable,' Carnap generalizes from provability's aprioricity to analyticity's aprioricity.

Anonymous said...

On a more or less traditional view of the a priori such as that of Bealer or Bonjour, a subject understands a proposition, reflects on it and then undergoes and act of "rational insight" or "intuition". So to determine whether my belief that p is a priori or empirical I would need to undergo some sort of higher order reflection and determine what went on in my mind when I came to believe that p. So the question of whether "p is a priori" is a priori, boils down to a question of whether first-person judgments about one's own mental states are a priori. Some use the term a priori in a way that includes things like introspection but (more or less) traditional rationalists like BonJour disagree. I agree with Protagoras that how we carve up these things is largely a pragmatic concern but, on the other hand, if we count "I have a headache" as a priori its pretty clear that we aren't approaching the same philosophical problem that Kant or even the logical empiricists were. So if judments about one's own mental states are not a priori and the Bealer/Bonjour account of the a priori is correct then "P is a priori" is not a priori. this is not to say that it is a matter of ordinary sensory experience but rather something like introspection.

CosmicParoxysms said...

Mike, I was just thinking along your lines when I read your comment and thought, "there we go, someone who finally thinks like me."

However, one brief question though: true a priori judgments can be made, theoretically, by any rational agent. In this respect, they have objectivity.

On the other hand, a posteriori judgments depend on the external world - if I understand the whole distinction correctly. Therefore, a rational agent - no matter how hard she tries - may not be able to reach all a posteriori statements.

So theoretically, even though I think that "p is a priori" is not a priori, it doesn't seem like a posteriori either - since it doesn't depend on the external world and can be reached objectively.

My two cents...

Anonymous said...

It seems to me (I would provide references if doing this slightly more seriously) that there is often a conflation between several notions when the a priori is discussed. One is whether what the statement is about concerns non-empirical matters. The other is whether it is capable of being known "independently" of experience. The "independently" is in quotation marks because it hides a bunch of different possibilities. Does it mean "having never had an experience"? Does it mean "never having had an experience that somehow speaks to the issue in question"? And so on. All of these affect your answer to any question of the a priori.

Of course, there are the further complications that a priori seems to involve certainty, which is then further conflated with unrevisability in many cases.

Keith Douglas