Williamson on the A Priori and the Analytic more

Forthcoming in a Symposium on TPoP in PPR. Williamson on the A Priori and the Analytic NYU In The Philosophy of Philosophy, Timothy Williamson provides us with a provocative, insightful and richly argued account of philosophical inquiry. According to the picture he lays out, philosophy is often interested in claims about the metaphysically necessary and the metaphysically contingent. But such claims should not be understood as being about meanings or concepts; nor should our knowledge of them be explained exclusively in terms of our grasp of their ingredient meanings or concepts. Rather, our knowledge of metaphysical modalities derives from our general competence with assessing counterfactuals; and that competence is not usefully described as being either a priori or a posteriori. Hence, that venerable distinction should be demoted from its central place in the theory of knowledge and replaced by a distinction between armchair knowledge and non-armchair knowledge. Since, as Williamson conceives it, the natural sciences are also capable of armchair knowledge, the upshot is a Quinean blurring of the distinction between philosophy and mathematics, on the one hand, and the more empirical disciplines on the other. There is an enormous amount that it would have been good to discuss: even those who end up disagreeing with Williamson on many of his central claims will have reason to admire his illuminating discussions of a host of fundamental topics. Owing to limitations of space, I will concentrate on those bits that most closely intersect with my own work – Williamson’s discussions of the a priori and the analytic. Williamson’s view of the a priori is subtle. His is not the crude view that nothing is a priori knowable, that all knowledge is a posteriori. It is not even the more refined view that the distinction is somehow ill defined. Rather, his view is that the distinction between the a priori and the a posteriori, while definable clearly enough, and while applying clearly enough in a wide range of cases, ultimately doesn’t cut the epistemic facts at the joints. It obscures the epistemic patterns that matter most. The point is not that we cannot draw a line somewhere with traditional paradigms of the a priori on one side and traditional paradigms of the a posteriori on the other. Surely we can; the point is that doing so yields little insight. The distinction is handy enough for a rough initial description of epistemic phenomena; it is out of place in a deeper theoretical analysis, because it obscures more significant epistemic patterns. We may acknowledge an extensive category of armchair knowledge, in the sense of knowledge in which experience plays no strictly evidential role, while remembering that such knowledge may not fit the stereotype of the a priori, because the contribution of experience was far more than enabling. For example, it should be no surprise if we turn out to have armchair knowledge of truths about the external environment. (169) 1 Williamson’s argument for this begins with the observation that distinction between the a priori and the a posteriori depends on the distinction between sense experience’s playing an evidential role in justifying a belief and its playing a merely enabling role. Sense experience plays an evidential role in my knowledge that this shirt is green, but only an enabling role in my knowledge that all green things are colored: it was required only so that I may grasp the concepts green and colored. However, Williamson claims, in a large number of central cases, sense experience is doing something in between these two things: while not playing a strictly evidential role, it is doing much more than merely enabling the thinker to have the relevant belief. We need to decide, therefore, whether to identify a priori knowledge with knowledge in which sense experience is playing a merely enabling role, or whether to identify it with knowledge in which sense experience is not playing a strictly evidential role, even if that role exceeds a merely enabling one. Unfortunately, no matter how we decide this question, we will get results that are intuitively incorrect: cases that intuitively belong together will be grouped separately and vice versa. Hence, the distinction between the a priori and the a posteriori should be discarded (and replaced by the distinction between armchair and non-armchair knowledge). If we ask how we know that in a large class of central cases sense experience’s contribution is neither strictly evidential nor merely enabling, the answer depends on two further big claims of Williamson’s book: first, that knowledge of modal claims is knowledge of counterfactual conditionals; and, second, that the role played by sense experience in our knowledge of counterfactual conditionals is often neither strictly evidential nor merely enabling. In defending the latter claim, Williamson appeals to the imagination-based account of knowledge of counterfactuals that he had outlined earlier in the book (chapter 5, sec 3).1 Roughly speaking, that account involves the idea that, in evaluating a counterfactual like (6) If the bush had not been there, the rock would have ended up in the lake (asserted in a certain context about a given rock, bush and lake), “one supposes the antecedent and develops the supposition, adding further judgments within the supposition by reasoning, offline predictive mechanisms and other offline judgments….To a first approximation, one asserts the counterfactual if and only if the development leads one to add the consequent.” (1523) Even if we were to accept Williamson’s description of our actual procedures for evaluating counterfactuals as correct, we would still be owed an explanation of why those evaluations count as knowledge. Williamson is not explicit about this. His only remarks on this score seem to suggest that it is the safety of our imagination-based procedures – their reliability in actual and 1 I am very doubtful that knowledge of modal claims can be reduced to knowledge of counterfactuals. It seems to me that, on any plausible account, knowledge of logical, mathematical and constitutive truths will be presupposed in accounting for our knowledge of counterfactuals. But limitations of space prevent me from discussing this point. 2 relevantly similar circumstances – that qualifies them to be sources of knowledge. As Williamson himself remarks, his account is the “merest sketch” (155) of an epistemology for counterfactuals. It’s a very interesting sketch, but one that leaves many fundamental questions unanswered, including Goodman’s famous problem of cotenability: in imagining the antecedent to be true, which bits of our background knowledge are we allowed to retain and which bits do we need to discard? Furthermore, it relies on several only dimly understood notions, such as that of the “offline” application of a cognitive faculty. It is steeped in psychological speculation (“the default for the imagination may be to proceed as “realistically” as it can, subject to whatever deviations the thinker imposes by brute force” and “an attractive suggestion is that some kind of simulation is involved”). And it seems to depend on a controversial (and to me, implausible) reliabilist criterion for knowledge. If we grant Williamson his epistemology for counterfactuals, then his claim that, in our knowledge of counterfactuals, sense experience may play neither a strictly evidential role nor one that is merely enabling is plausible. For it is plausible that, on that account, even when sense experience does not survive as part of our total evidence, “it can mold our habits of imagination and judgment in ways that go far beyond a purely enabling role.” (165) The insight that Williamson is giving voice to here is that if we think of the reliability of our cognitive mechanisms as epistemically relevant, then we will have to think that sense experience may play a more than enabling role in explaining a given judgment, a role that will be epistemically relevant (since it influences reliability) without being strictly evidential. My own view, though, is that the proffered epistemology for counterfactuals is too speculative and controversial to support anything very consequential. However, let’s concede Williamson’s account for the purposes of argument along with its attendant claim about the possible role of sense experience in our knowledge of counterfactuals. I would have thought that the natural solution to the challenge that that concession poses for the theory of the a priori is to say that knowledge is a priori provided that the role of sense experience in generating it was purely enabling, a posteriori otherwise. Williamson thinks that can’t be right because he thinks that it would lead one to classify as knowable only a posteriori many philosophically significant modal judgments that most philosophers would regard as paradigms of a priori knowledge. For he thinks that there is no question but that sense experience plays a more than enabling role in the following item of knowledge: (27) It is necessary that whoever knows something believes it. How does Williamson know that sense experience has to be playing a more than enabling role in our knowledge of (27)? He offers two considerations, one tied to this particular example and one more general. The example-specific consideration is that 3 Many philosophers, native speakers of English, have denied (27)…They are not usually or plausibly accused of failing to understand the words “know” or “believe.” (168) Williamson’s thought seems to be that it is only if assent to (27) is necessary for possession of the ingredient concepts, that we could say that whatever experience was required for assent to (27) was merely enabling. But assent to (27) is not necessary for possession of the ingredient concepts, as is shown by the number of competent philosophers who deny it. Hence, we can’t say that the experience that was required for assent to (27) was merely enabling. One problem with this argument is that it ignores the possibility that the difference between those who grasp (27) and assent to it and those who grasp (27) and don’t assent to it is not sense experience per se but rather the exercise of a faculty of a priori insight. This idea may be fraught with difficulty, but it cannot just be ignored. A second problem is that we are already aware, from reflection on the paradox of analysis, that analytic truths do not have to be transparent. If correct analyses can sometimes be informative, that must be because they don’t always seem correct. So we can’t conclude from the fact that a person competent with word w denies S(w) that S(w) is not analytic for that person. Finally, showing that (27) would not come out a priori on the proposed definition doesn’t show that there are lots of other similarly problematic cases. It is at this point that Williamson can (and does – see p. 166) appeal to his general discussion of epistemological conceptions of analyticity and its attendant denial that there are any constitutive understanding-assent links: no particular sentence (or inference) need by assented to (or performed) by a thinker as a condition of that thinker’s understanding a given word. We need to turn, then, to look at Williamson’s case for that general claim. The idea that there are such links has, of course, traditionally exerted considerable influence within philosophy. Even Quine, who may be thought to be its most implacable enemy, came around to saying that the deviant logician merely changes the subject (see Quine 1970, p81). So Williamson’s claim that there are no such links, three prima facie plausible examples of which are given below, is very interesting and very radical. (A) Necessarily, whoever understands the sentence “Every vixen is a female fox” assents to it. (B) Necessarily, whoever understands the sentence “All squares have four sides” assents to it. (C) Necessarily, whoever understands “and” is prepared to infer from any sentence of the form “A and B” to “A.” 2 2 Commitment to such links need involve no commitment to a use-dispositional analysis of meaning. 4 Why have philosophers been so tempted by such understanding assent links?3 There are two main arguments, one from below and one from above. The argument from below stems from intuitions about meaning ascriptions: under sufficiently ideal conditions, no one who understands “square,” for example, could deny that squares are four-sided. In the case of the logical constants, there is a further argument, one from above: it’s hard to see what else could constitute meaning conjunction by ‘and’ except being prepared to use it according to some rules and not others (most plausibly, the standard introduction and elimination rules for ‘and’). Accounts that might be thought to have a chance of success with other words -information-theoretic accounts, for example, or explicit definitions, or teleological accounts -don’t seem to have any purchase in the case of the logical constants. Now, Williamson thinks that there are no understanding-assent links -- none. Why is he so confident that all such links fail? He can’t have thought of each and every one of them and come up with a counterexample to each. The answer is that he thinks he’s got a general recipe for generating a counterexample to any putative link that might be proposed. Take any word w and any meaning M. Suppose it is maintained that T’s assenting to the sentence S(w) is required for T to mean M by w. Then we can always describe a case of an expert on M who becomes convinced, however incorrectly, by a complex theoretical argument, that S is false and so refuses to assent to it but who, by any ordinary standards, still fully understands w. So there can be no S such that assenting to it is necessary for T to mean M by w. Ditto for any inference rule I(w), inference in accordance with which is said to be necessary for T to mean M by w. In a previous exchange, I had suggested to Williamson that conjunction-elimination seemed as safe an example of a meaning-constituting rule as one could wish for and so that it would be an especially good test of the general effectiveness of his recipe.4 In Chapter 4, Williamson aims to provide a counterexample to the analyticity of conjunction-elimination. He describes the case of Simon, an expert on the philosophy of language who has views on vagueness. Simon holds that borderline cases constitute truth-value gaps. He generalizes classical two-valued semantics by treating the gap as a third value and by conforming his practice to Kleene’s weak three–valued tables. According to these tables, a conjunction is indefinite (neither true nor false) if at least one conjunct is, irrespective of the value of the other conjunct. Furthermore, Simon regards truth and indefiniteness as designated (acceptable) semantic values for an assertion: what matters to him is to avoid falsity. So he accepts sentences that are either true or indefinite. It is easy to see that someone with Simon’s semantic commitments would have reason to reject conjunction elimination as a rule of inference, for there could be cases where “A” is simply false 3 For convenience, I lump the case of inference under the “understanding/assent” label. I also won’t be fussy about the distinction between meanings and concepts since it won’t matter for anything that follows. 4 At the Joint Session of the Mind Association and the Aristotelian Society held in Belfast in the summer of 2003. 5 while “B” is indefinite. In such cases “A and B” would be indefinite, but “A” false. Thus, the corresponding instance of conjunction elimination would have a designated premise and an undesignated conclusion, and so Simon would reject it. This, then, is the basis for Williamson’s confidence that not even something as seemingly safe as conjunction elimination is required for meaning and by ‘and.’ I am not persuaded. I don’t believe that Simon presents us with an intelligible counterexample to the analyticity of conjunction elimination; and I don’t believe that Williamson has provided us with a general recipe for dispatching any understanding-assent link that might be proposed. To see why, imagine that Simon has come to the view that someone other than John Wilkes Booth shot Lincoln. According to him, Booth had a co-conspirator, Schmidt, who was actually responsible for pulling the trigger. Both men were there, in Lincoln’s box at Ford’s theater, but it was Schmidt that shot Lincoln, not Booth. So Simon asserts “Schmidt, not Booth, shot Lincoln.” However, Simon is very willing to assent to the sentence “Booth saw the balding Lincoln and shot him,” since he takes Booth to have been there and seen Lincoln, and, since he regards the first conjunct as indefinite, he regards the whole sentence as indefinite and so acceptable. So, he is willing to assert “Booth saw the balding Lincoln and shot him” but not to assert “Booth shot Lincoln.” In fact he rejects “Booth shot Lincoln.” It’s not clear to me that we understand what it is that we are saying about Simon, for two reasons. First, it’s not clear that we understand the notion of assent or belief that is being invoked. It is certainly not clear that it is the same notion of assent (or belief) that is implicated in the understanding-assent links thesis, which is clearly the notion of assenting to something as (or believing it to be) true. This notion we understand well enough. But what is it to assent to something as indefinite or believe it indefinite? (This is not the question: What is it to believe that something is indefinite? That could be glossed as the question: What is it to believe true that something is indefinite.) The problem is especially severe in Simon’s case because he is said to classify any sentence as indefinite if it is borderline; and there are so many such sentences. Thus, he would be willing to assent to “Lincoln was bald” but also to “Lincoln was not bald” and even to “Lincoln was both bald and not bald.” He would exhibit a similar pattern for any other borderline sentence. This stretches my grip on the notion of assent (or belief) to the breaking point. Second, Williamson’s assurances notwithstanding, I am not persuaded that Simon really does mean what we do by ‘and’ since he denies that it follows from “Booth saw the balding Lincoln and shot him” that Booth shot Lincoln. Williamson is adamant that a refusal to see Simon as meaning the same as us would be misguided and unwarranted. After all, Simon insists that he is using the same meaning as we are, that we are simply mistaken to think that conjunction elimination is constitutive of our shared meaning, and so on and so forth. 6 But such insistence is not sufficient to make it true. What matters is that, when we look at the example as described, we should find it intuitive that Simon means the same as we do by ‘and’ rather than some other, perhaps closely related, meaning. But, as I have just been saying, I don’t find that intuitive. So I’m not persuaded that we have been given a general recipe with which to dispatch any understanding-assent link that might be proposed. 5 This brings us to the argument from above for the existence of understanding-assent links. I am most tempted by this argument in the case of the logical constants, although the case of theoretical terms in science is compelling as well. In both of those cases, it is tempting to think, faute de mieux, that understanding the meaning of a word involves grasping its constitutive conceptual/inferential role. It goes without saying that there are many outstanding problems for such an account of meaning; but that could of course be said about any account of meaning. Williamson is well aware that inferentialism will continue to look plausible for a certain range of words unless some alternative account is given of the difference between understanding and not understanding words in that range. In a section of his Chapter 4 he attempts to sketch such an alternative. But what he is able to give, on such a complex matter, in the course of eight pages, raises more questions than it answers. His picture claims that our meanings are determined socially. A solitary individual is capable of meaning – Williamson rejects those readings of Wittgenstein’s private language argument that contend otherwise. But “when an individual does use a shared language, as such, individual meaning is parasitic on social meaning.” (125) How do societies determine these social meanings? The answer is that “a complex web of interactions and dependences can hold a linguistic or conceptual practice together even in the absence of a common creed that all participants at all times are required to endorse.” (125) This repeats the rejection of inferentialism but without providing a substantive alternative. Williamson rightly worries about how, on this picture, we might make sense of the synonymy of two expressions belonging to two distinct social languages. His answer is that two expressions are synonymous when they have exactly the same semantic properties; and that truth-conditional semantics provides us with a rich enough store of such properties: extension, intension, intensional isomorphism, character, conventional implicature. It is possible for two words belonging to two different social languages to have the same truth conditional properties. However, as Williamson is quick to recognize, we can easily think of pairs of expressions that are intuitively not synonymous but that share all their semantic properties as so identified. 5 Even if Williamson were right that there are no atomic understanding-assent links of the form -necessarily, one understands w only if one accepts S(w) – that wouldn’t show that there aren’t clusters of such links of the form: necessarily, anyone who understands w accepts S(w) or S’(w) ….or S*(w). A friend of epistemological analyticities might well be satisfied with the existence of such clusters. Unfortunately, I can’t pursue this thought here either. 7 Consider “phlogiston” (an example discussed by Williamson himself (129)). This term is semantically atomic, has no conventional implicatures, fails to refer with respect to any circumstance of evaluation (since it designates rigidly, if at all) and fails to refer in any context of utterance (since it is non-indexical). Still, it is clearly not synonymous with “aether,” even though it shares all of its semantic properties as so identified. By contrast, the inferentialist would be able to provide a good explanation of why “aether” is not synonymous with “phlogiston.” Furthermore, someone need not count as understanding “phlogiston” just by knowing its semantic properties as so identified. Once again, the inferentialist would have a good explanation for this: since such a person need not have grasped the expression’s constitutive inferential role, he need not count as understanding it. Williamson tries to argue that this consideration does nothing to support an inferentialist account of understanding on the grounds that knowing the meaning of a term never qualifies one, all by itself, for “full participation” in the practice of using that term (129). He gives the examples of “gob” and “mouth” which, he says, mean the same, but are not appropriately used in all the same contexts. Someone may know that “gob” means “mouth” and yet not be fully competent to use it, by failing to grasp its slang coloring. It seems to me, though, that a huge gulf separates the “gob” and “phlogiston” examples. Someone may be missing some subtle aspect of the tone of “gob” if all he knows is that it means mouth; and so may not count as fully understanding it. But someone who knows about “phlogiston” only that it’s a non-referring theoretical term counts as not understanding it at all. Williamson says: Although no particular piece of knowledge is necessary for participation, such abject ignorance is not sufficient. We should resist the temptation to build all qualifications for participation in the practice of using a term into its meaning, on pain of turning semantic theory into a ragbag of miscellaneous considerations…(129) Well, if we don’t want to use “understanding w” to mark the contrast between being competent to use w and not being competent to use w, then let’s use some other expression to do so – for example, the expression “competent to use w.” We will then need to decide what it takes for someone to be competent to use w and the most plausible answer is that a person would have to know some of the sentences or inferences in which w is correctly used. Of course, not any old correct sentences or inferences, but rather those that really are constitutive of competence. And now we are back at the same spot we thought we had abandoned – trying to figure out which bits of a word’s role are constitutive of “competence” with it and which aren’t. In conclusion, I am not persuaded that there are no assent conditions on understanding or meaning, and so not convinced that sense experience is guaranteed to play a more than enabling role in our knowledge of (27) and similar modal judgments. As a result, I am not yet convinced that we need to demote the distinction between the a priori and the a posteriori from its central place in the theory of knowledge.6 6 For helpful comments I am grateful to Sinan Dogramaci, Anna-Sara Malmgren, Christopher 8 Peacocke, Stephen Schiffer, Declan Smithies and Crispin Wright. 9