Williamson’s Argument against an Epistemological Conception of Analyticity

So, I’m about halfway through Timothy Williamson’s The Philosophy of Philosophy (POP). From what I’ve heard, POP has gotten a lot of people talking, because Williamson is largely attempting to come to the defense of traditional “armchair” philosophy. Williamson isn’t explicitly anti-X-phi (Experimental Philosophy), but he does think that armchair philosophy is still as important as ever. At the halfway point, I think I agree with his general thesis, though I disagree with some minor points, one of which is the subject of this post.

In chapter 4, Williamson argues against the idea that “failure to assent [to an analytic truth] is not merely good evidence of failure to understand; it is constitutive of such failure.” To prove his point, he wants to argue that a competent speaker of a language can reject analytic truths. He decides to use one of the simplest types of analytic case out there, “Every vixen is a vixen.” If he can show that even a competent user of the English language can reject this statement, then he will have proved his point.

There is a lot more going on in this chapter, but most of it centers around this argument. An epistemological conception of analyticity will say something along the lines of:
(ECA) “A statement (or thought) p is analytic iff anyone who truly understands p will assent to it.” Williamson considers a lot of subtle ways the defender of an epistemological conception may change it to avoid his objections, but I don’t think that’s important to my present point.

On pp85-99, Williamson discusses at length his two examples of competent speakers who reject “Every vixen is a vixen” [henceforth (V)]. The first example is Peter: Peter takes universal quantification to be existentially committing, and thus, (V) is only true if vixens actually exist. Furthermore, Peter happens to subscribe to a conspiracy theory whereby vixens, in fact, do not exist. A crazy belief, sure, but certainly it doesn’t make him linguistically incompetent. In all other respects, Peter is a competent native speaker of the English language.* Nevertheless, because Peter believes there are no vixens, he rejects (V) because he thinks it assumes that there are vixens. So (ECA) fails.

I think this first case fails, for two reasons. First, if there is a fact of the matter about the analyticity of (V), which Williamson presumes, then Peter is either wrong, and incompetently using the word “every” as a universal quantifier which is existentially committing, or right, and the vast majority of people are wrong. If there is no fact of the matter, then statements in natural language have no truth-conditions, so of course (EPA) fails, along with any other account of the truth-conditions of sentences (or statements, thoughts, etc.) of a natural language such as English.

The Peter problem is one that only arises in natural language, which ought to tip us off to the fact that it is a problem of the vagueness and ambiguity within natural language, not with (ECA) or analyticity itself. For Peter could not competently deny (V) within a logical system like basic, elementary predicate logic. The denial of (V) would result in a contradiction. Peter could construct his own system which didn’t interpret universal quantifiers in such a way, but then it would just be a different system, a different language, and incommensurate with the elementary predicate logic which Hurley and Copi made us love (or hate).

Williamson’s second example is the case of Stephen. Stephen “believes that borderline cases for vague terms constitute truth-value gaps.” (pg87) When a borderline case for a vague term comes up, Stephen recognizes it as “indeterminate,” rather than true or false. Stephen rejects (V) because there are borderline cases of vixens (Evolutionary ancestors of foxes, for example), call them x. For cases like x, “x is a vixen” is indeterminate, and therefore (V) is indeterminate. Stephen is, despite his views (which may, in fact, be accurate), a competent speaker of English. He understands (V), but does not assent to it.

The Stephen case can be answered on similar lines. Williamson takes all cases of things to be determinately vixen or not vixen—there is no middle ground. If he is right, then Stephen does not understand “Every vixen is a vixen,” because he doesn’t understand the meaning of “vixen” as being strictly determinate. Sure, Stephen may be competent in the sense of “getting by,” but if there really is a fact of the matter as to whether the statement is true or not, and Williamson is right about that fact, Stephen does not properly grasp what a “vixen” is.

On the other hand, Stephen may be right, that “vixen” is a vague term, and that there are things which are indeterminate as to whether they are vixens. If this is the case, then it is Williamson who doesn’t really grasp (V) (as well as, perhaps, most of us, because most people intuitively assent to (V)). Williamson believes there are necessary and sufficient conditions, which, though unknowable by us in totality, can pick out determinately which x’s are vixens and which not. But what are these necessary and sufficient conditions, if not part of the semantics of the word? So the dispute between someone like Stephen and Williamson is over the meaning of “vixen.” And if there is a fact of the matter, one of them is wrong, and one of them doesn’t properly understand (V).

But surely, Williamson will respond, Stephen, Peter, and I are all competent speakers of the English language. This is a sleight of hand—-by “competent,” Williamson means that they can communicate in all everyday affairs without making wildly false statements.* Well sure they can! But that doesn’t mean they infallibly grasp the meanings of words and logical operators in the language. If someone had a system to add numbers which gave outputs identical to ours except in the case of 7+5 it said 13, we wouldn’t say they understood what “+” means even though they were reliable in most circumstances (think Kripkenstein). When Williamson discusses Stephen and Peter’s competence, what he needs is semantic competence, but all he has is pragmatic, functional competence. And their semantic competence is obviously skewed, since they are giving improper truth values to basic sentences (or we are giving improper truth values to basic sentences, but the point is that someone must be right).
One final note—Williamson considers the objection that perhaps Stephen and Peter are using the words in (V) in a non-standard way, and thus are just constructing a semantics independent of standard English. His response is that “Peter and Stephen are emphatic that they intend their words to be understood as words of our common language, with their standard English senses.” (pp89) But this objection just looks to me like a straw-man. Of course Williamson’s response is accurate—Peter and Stephen think they are accurately describing standard English. But they are wrong (ex hypothesi). So much for the worse for their analyses. This isn’t an issue, because the defender of (ECA) can just say that Stephen and Peter lack semantic competence, despite the fact that they have what Williamson seems to think is important, functional competence.

*Actually, in Peter's case, this seems implausible, since Peter will not be able to assent to statements like "All unicorns have one horn."