Close Range

Williamson on Intuitions

I’ve been reading Williamson’s new book (which is awesome!), and I just got to chapter 7, where he’s wondering what “intuitions” are supposed to be. He mentions Bealer’s suggestion that they’re intellectual seemings, and here’s what he says about Bealer’s favorite example, Naive Comprehension (i.e., that every predicate has a set as its extension):

“For myself, I am aware of no intellectual seeming beyond my conscious inclination to believe Naive Comprehension, which I resist because I know better.” (p.217)

I found this very strange. Yes, Naive Comprehension seems true to me, even though I know full well that it’s inconsistent -- just as the Muller-Lyer arrows seem to be different lengths, even though I know full well that they aren’t. But I have no inclination whatsoever to believe Naive Comprehension, conscious or otherwise. I mean, I used to sometimes feel inclined to believe it, even after I learned about Russell’s paradox, because (for instance) I wouldn’t recognize it right away as the axiom that generates Russell's paradox. But now I’m always able to recognize it right away, and I have no inclination to believe it.

Likewise when I’m looking at the Muller-Lyer arrows. I’m not at all inclined to believe that they’re the same length. I know the trick. Or consider my friend Enrico, who has the zombie intuition, but said that I should stab him if he ever gives up materialism (true story, he made me promise). I think it’s safe to assume that he has no inclination whatsoever to believe that zombies are possible, even when it seems to him that they are possible.

And anyway, this is a very strange thing for Williamson of all people to say. As those of you who’ve read chapter 4 know, his all-purpose counterexample to epistemic characterizations of analyticity is the stubborn philosopher with funny views about logic who has no disposition whatsoever (even a little! even subconsciously!) to assent to the sentence 'every vixen is a vixen'. Surely if this guy’s stubborn enough to have no disposition to assent to 'every vixen is a vixen', I’m stubborn enough to have no inclination to believe Naive Comprehension!

Soames on the Contingent A Priori

Saul Kripke famously argued that some propositions are both contingent and knowable a priori. For instance, one who introduces the term ‘one meter’ as a rigid designator for the length of a certain stick s at time t is meant to be in a position to know a priori that if s exists at t then the length of s at t is one meter. Call this the meter proposition. Scott Soames (2003) says that neither the meter proposition nor any of Kripke’s other examples are genuine examples of a priori contingencies. Soames observes that the baptizer’s knowledge of the meter proposition would have to be based partly on the knowledge that the term ‘one meter’ refers in his language to the length of an object iff the length of that object is one meter. Call this further proposition the R-proposition. The question of whether the meter proposition is known a priori therefore turns on the question of whether the R-proposition is known a priori. Soames offers the following reason for denying that the R-proposition and related propositions can be known a priori: “If they could be so known, then non-English speakers should be able to know them simply by reflecting on and reasoning about them—which of course they cannot.” (2003,408-9)

Soames does, however, admit that there are genuine a priori contingencies, for instance, that if actually Princeton has a philosophy department then Princeton has a philosophy department. Call this the Princeton proposition. The argument for the contingency of the Princeton proposition is straightforward: Its antecedent will be true at all worlds—since it is true at all worlds that in our world Princeton has a philosophy department—including those worlds in which Princeton has no philosophy department. At such worlds, the conditional as a whole is false; hence, the Princeton proposition is contingent. The argument for its a priority is equally straightforward, for one can know a priori, of any proposition that one entertains, that it is true iff true in one’s own world.

I’m going to argue that Soames’s stated reason for denying that the R-proposition can be known a priori should be rejected on the grounds that it’s equally a reason for denying that the Princeton proposition can be known a priori. So Soames’s argument against the a priority of the meter proposition fails. And this isn’t merely an ad hominem attack, for it is widely assumed that such propositions as the R-proposition cannot be known a priori, yet it is difficult to find (or imagine) any reason for assuming this other than the one Soames supplies. So unless there is some flaw in the reasoning behind the a priority of the Princeton proposition (and there isn’t), we are left with no satisfactory reason for supposing these semantic facts to be knowable only a posteriori.

Soames seems to have in mind something like the following argument in the passage quoted above (I’ve added some charitable bells and whistles):

(P1) A proposition p can be known a priori only if, necessarily, if p is true then anyone who understands p and is suitably intelligent can come to know p simply by reflecting on and reasoning about it.   
(P2) The R-proposition is true and some suitably intelligent individuals understand it but cannot know it simply by reflecting on and reasoning about it.
(C) So the R-proposition cannot be known a priori.

The reasoning behind P2 is straightforward: just as non-French speakers can understand the proposition that the term ‘un pouce’ refers in French to the length of an object iff the length of that object is one meter without being in any position to know whether it is true or false, non-English speakers can understand the R-proposition perfectly well without being in any position to know whether it is true or false.

But P1, together with the following premise P2*, entails that the Princeton proposition cannot be known a priori:

(P2*) Possibly, the Princeton proposition is true and some individuals understand it and are suitably intelligent but cannot know it simply by reflecting on and reasoning about it.

The possible individuals in question will be inhabitants of a world other than our own in which Princeton has a philosophy department. In order for them to understand the Princeton proposition—which is, at least in part, a proposition about our world—they have to be able to think about our world. Singling out a specific nonactual world in thought is no small feat, but we may suppose that their mental capacities far exceed our own and that they are able to get our world uniquely in mind by imagining it in full detail. They nevertheless will not be in a position to know the Princeton proposition simply by reflecting on and reasoning about it. For although they can know that its antecedent (which is true in their world iff Princeton has a philosophy department in our world) is true simply by reflecting on and reasoning about it, they cannot know that its consequent (which is true in their world iff Princeton has a philosophy department in their world) is true simply by reflecting on and reasoning about it. Consequently, they cannot know whether the conditional itself is true simply by reflecting on and reasoning about it.

So P2* is true. So either P1 is true, in which case it follows that the Princeton proposition cannot be known a priori, or P1 is false. The Princeton proposition can be known a priori. So P1 is false, Soames’s argument that the meter proposition cannot be known a priori fails, and we lose the standard (and perhaps only) reason for taking R-propositions to be knowable only a posteriori.