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Tim’s recipe for generating a counterexample to understanding-assent links is interestingly different from Paolo’s. Paolo’s example turns on a disability. Tim goes in the other direction. His counterexamples consist of experts on logic and language who have allowed their linguistic behavior to be influenced by the somewhat kooky theories of logic and language that they have developed as adults. In some ways, this can seem a more promising strategy. It can seem easier to make it plausible that someone has retained a concept C by making him an expert on C than by giving him a disability with respect to C.Here is how the recipe is supposed to work. Take any constant C and any rule R. Suppose it is maintained that T’s inferring according to the rule R is required for T to have C. Then we can always describe a case of an expert on C who becomes convinced, however incorrectly, by a complex theoretical argument, that R is invalid and so refuses to infer according to it but who, by any ordinary standards, still fully understands C. So there can be no R such that inferring according to it is necessary for T to have C. Tim, too, uses his recipe to generate a putative counterexample to 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 threevalued 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 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 Tim’s confidence that not even something as seemingly safe as conjunction elimination is required for meaning and by ‘and’. Now, I find Tim’s examples as hard to understand as Paolo’s, although they raise different issues. I do not believe that Simon presents us with an intelligible counterexample to the analyticity of conjunction elimination; and I do not believe that Tim has provided us with a general recipe for dispatching any understanding–assent link that might be proposed. To get a sense of how puzzling Tim’s Simon would be, 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 assents to: (0) Schmidt, not Booth, shot Lincoln. However, Simon is very willing to assent to the sentence (1) 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. He is not willing to assent to: (2) Booth shot Lincoln. In fact he rejects (2). If we continue to spin the case out, we would have to say that Simon is also willing to assent to: (3) Booth didn’t see the balding Lincoln and shot him. He would also assent to: (4) Booth saw the balding Lincoln and didn’t shoot him.Also to: (5) Booth didn’t see the balding Lincoln and didn’t shoot him. As well as to: (6) Lincoln is both bald and not bald. When I look at the description of this case, I find myself with no clear intuitions about what Simon is saying or thinking. I certainly do not think: “Oh, he clearly means conjunction by ‘and’ ”. Tim has replied to this by saying: Obviously, if we have just met Simon, and know nothing about his background beliefs, we are likely to find his combined reactions to (1) and (2) utterly bewildering. We may reasonably wonder whether he knows what the word ‘and’ means. In practice, independently of his reaction to (1), since it is so well known that Booth shot Lincoln we may also find Simon’s rejection of (2) initially puzzling, and wonder whether he is using the name ‘Booth’ to refer to the man we mean. Once we become aware of Simon’s conspiracy theory of the assassination, we realize that there was no linguistic misunderstanding over (2); we simply disagree with him about the historical facts. Similarly, once we become aware of Simon’s deviant theory of logic, an explanation of his unwillingness to deduce (2) from (1) in terms of linguistic incompetence looks much less attractive. On theoretical grounds, Simon holds that borderline cases for vague terms induce truth-value gaps, and that such gaps should be treated by Kleene’s weak three-valued tables, which coincide with the classical two-valued tables when all the constituent sub-sentences are true or false but make the complex sentence gappy when at least one sub-sentence is gappy. Simon also thinks that it is legitimate to assent to gappy sentences as well as to true ones; what matters is to avoid falsity. Since he thinks that Booth saw Lincoln and regards Lincoln as a borderline case for the vague term ‘bald’, he thinks that ‘Booth saw the balding Lincoln’ is gappy, and that (1) inherits its gappiness. He concludes that it is legitimate to assent to (1). The gappiness does not infect (2). Simon rejects (2) as straightforwardly false. Of course, Simon would be quick to point out that in conversational terms it would be highly misleading to assert (1) on grounds of its gappiness when one’s audience had no reason to suspect that one was doing so. In the absence of special background assumptions, asserting ‘A(P)’ leaves it open whether ‘A(P)’ is true or gappy, on Simon’s view. If one knows that ‘A(P)’ is gappy because it has the gappy constituent ‘P’, one can therefore make a simpler and more informative assertion by simply asserting that ‘P’ is gappy, omitting the other material in ‘A(P)’ as irrelevant. On Simon’s view, one can gain the effect of asserting that ‘P’ is gappy without going meta-linguistic by asserting ‘P and not P’. Thus if Simon asserts (1), his audience is entitled for Gricean reasons to assume that he is not doing so merely on the grounds that ‘Lincoln was bald’ is gappy, since otherwise he is being conversationally uncooperative and should have said something like ‘Was Lincoln bald? Well, he was and he wasn’t’ instead. The default conversational assumption is that one is not dealing with borderline cases; under that assumption one can defeasibly move from ‘P and Q’ to ‘P’ and to ‘Q’. Nevertheless, according to Simon, the move is not deductively valid, and the case of (1) and (2) is a counterexample. Once Simon has explained his view, it is much less plausible that his unwillingness to infer (2) from (1) manifests linguistic incompetence. It looks much more like a case of theoretical disagreement. (Williamson 2011 , 502) Tim raises many interesting points and there is a huge amount to be said in reply. Here I have space only to make a start. First, a small terminological point. To call someone who is as sophisticated about logic and language as Simon is, “linguistically incompetent”, would be obviously misleading, just as it would be to so label Vann McGee for doubting Modus Ponens. All that the inferential role theorist is committed to saying is that, if Simon succeeds in altering his behavior with ‘and’ and flouts a meaning-constituting rule for ordinary conjunction, then he necessarily means something different by ‘and’ than ordinary conjunction. It is better to call this “meaning change” rather than incompetence. Second, it might not be such a big meaning change (assuming we know how to measure such things). The new concept might play many of the same roles we associate with ordinary conjunction. It just would not be ordinary conjunction. (Can we always rely on there being a sharp fact of the matter whether there has or there has not been meaning change? It would be surprising if meaning facts were more determinate than facts in other domains, so a certain amount of indeterminacy about meaning change would have to be allowed for as well.) Third, Tim says that once we know about Simon’s deviant theory of logic, the explanation in terms of change of meaning “looks much less attractive”. I disagree with this assessment. There are two large reasons. First, in deciding whether Simon is best described as expressing one meaning versus another by ‘and’, we cannot rely on the fact that he has arrived at his inferential role for ‘and’ on the basis of theorizing. Second, I believe that explanations in terms of meaning change, rather than theory change, can sometimes be the most attractive. I will develop each point in turn. When you look at formulations of inferential role semantics, you find that theorists want to identify the concept-constituting inferences with those that are “primitively compelling” (Peacocke) or that incorporate “underived conceptual roles” (Schiffer). The inferences that are said to be conceptconstituting for a thinker are those that the thinker finds compelling, is willing to engage in, without the benefit of any prior theory. As Peacocke puts it in connection with possession of the concept of conjunction: “On any theory, this possession-condition will entail that thinkers must find the transition from A and B to A compelling, and must do so without relying on any background information” (Peacocke 2004 , 172; quoted in Williamson 2007 , 125). This is obviously a very important feature of inferential role theories. It would make no sense to identify a meaning-constituting inferential rule for a constant with a derived rule for that constant, arrived at on the basis of rationally optional theorizing involving inferences with that very constant. Such a procedure can lead you to all sorts of mistaken views about what the meaning-constituting inferences for that constant are. Simon’s deviant inferences, however, are obviously highly derived. He does not find them primitively compelling, but compelling only on the basis of lots of (bad) theorizing. No inferential role theorist would look to those derived inferences to say what concept Simon expresses by ‘and’. They would look, rather, to the rules that Simon found primitively compelling, before engaging in all of that bad theorizing. By assumption, those rules are just the standard ones. So far, then, we have not yet got a counterexample to the necessity of conjunction elimination for possession of conjunction. To get one, we would have to argue that even a non-theoretically minded analogue of Simon’s, who did not have fancy views about vagueness and gappiness, but who exhibited the same pattern of behavior with ‘and’ as has been stipulated for Simon, would clearly be credited with possession of ordinary conjunction. I do not believe that many would be sympathetic to such a verdict.2 7. Does not the mere fact that it is possible for Simon to intelligibly question whether conjunction elimination is valid, however, show that conjunction elimination is not meaning-constituting? This brings me to the second large point I signaled above. I believe that the inferential role theorist can explain what Simon is up to in a way that is consistent with the theorist’s commitments. Consider a different case. I think it is very plausible that our pre-Einsteinian ancestors worked with a notion of simultaneity of which it was analytic that it denoted a 2-place relation. They would not have understood how simultaneity – or time order more generally – could be relative to an observer’s frame of reference, and so a 3-place relation. Einstein, however, came along and claimed just that. Here we can mimic something that Tim might want to say: Surely, Einstein was not just committing some linguistic mistake. Surely, once we know about his Special Theory of Relativity, an explanation of his unwillingness to deduce “x stands in a 2place relation to y” from “x is simultaneous with y” in terms of a change in the meaning of ‘simultaneous’ becomes much less attractive. I do not agree that an explanation that invokes a change of meaning is far less attractive. At any rate, I think that there is a perfectly good story in terms of change of meaning that can preserve many of the features of the case that seem worth preserving. (Grice and Strawson made this point some time ago.) On the story I have in mind, Einstein is proposing that we get a better theory of motion if we work with 3-place simultaneity relations rather than with 2-place ones – that is, if the explanatory role for which we need a notion of simultaneity is filled by a particular kind of 3-place relation, rather than the classical 2-place one. This accommodates the Einsteinian achievement without having to deny that 2placedness was constitutive of the classical notion. Similarly, we do not have to deny that the Parallels Postulate is constitutive of Euclidean space just because we recognize that the best theory of physical space may involve spaces that are non-Euclidean. Hence, I do not think it is true that once we become aware of someone’s substantive reasons for preferring one theory of ‘X’ over another, that we can no longer think of the disagreement as involving a change in the meaning of ‘X’. It might be thought that in helping ourselves to the notion of meaning change, as opposed to mere change in belief, we are begging the question against Quine. Two points: first, the Quinean claim that there are no determinate facts about meaning change has yet to be earned; second, Paolo and Tim do not express the same general skepticism about determinate meaning facts as Quine does. Tim, in particular, is quite clear that he believes that there are determinate facts about meaning. It is just that he does not think they are constituted by facts about inference rules. At this point, we come face to face with another question: perhaps we do not have to think that there has been no change in meaning. How do we know whether there has been one? How do we know which inference rule is, and which inference rule is not, constitutive of someone’s having concept C? 8. Paolo presses this question, too Should we say that the acceptance of a logical rule is part of the possession condition for some logical constant if we find its instances easy and natural, if we apply it as a matter of course and irreflectively, and if we expect that anybody else would do the same? Unfortunately, a criterion of this kind is unlikely to work. What inferences different people find easy and natural varies greatly. Presumably, what was easy and natural for Gödel in the early thirties was not what is easy and natural for me now. One might try to overcome this problem by saying that the logical rules to be taken into account are the rules that are found easy and natural by everybody, or almost everybody. But this too would give rise to obvious difficulties. First: being easy and natural is a matter of degree. How easy and how natural should a rule be to be taken into account? At least at first sight, there is no principled way to draw the line. For example: for most people, Modus Tollens is slightly less easy and less natural than Modus Ponens. But only slightly. Does this slight difference matter? Is acceptance of Modus Tollens necessary to have the concepts of conditional and negation? Second: not only do different people find different inferences easy and natural, but the same person may apply a certain rule with great ease when she is reasoning on a certain topic (holidays, for example) and have a lot of trouble with it when she is reasoning on some other topic (abstract algebra, say). Being easy and natural are topic-dependent. What topics are to be regarded as relevant? Again, no principled answer seems possible. Third: let us imagine we have settled in some way the previous two problems. We might discover that the inferences which we have decided to count as easy and natural for everybody do not suffice to determine uniquely the denotation of logical constants. For example, they might be insufficient to establish whether “or” stands for inclusive or exclusive disjunction, or which truth-value should be assigned to “Every P is Q” when there are no P. For Peacocke and Boghossian this would be a problem for the reason explained at the outset. (408) Paolo insists that the question here is not epistemic. Note that the problem is not that of actually deciding whether this or that specific rule is or is not constitutive of some logical concept. The problem with the syllogism in Barbara and Modus Ponens is not that we do not have all the data required to establish whether they are or are not constitutive of the logical concepts they involve. The problem is that we have not been told what sort of data would be relevant to establish this. Notice also that the problem is not one of vagueness. The case of Modus Tollens is not like the case of a man who is neither clearly bald nor clearly not bald. To establish whether a man is bald or not, I know that I must apply a certain criterion: then it may happen that, in a particular case, the criterion does not give a clear verdict and I remain uncertain. In the case of Modus Tollens, I have simply no idea of what the relevant criterion might be like. (409) What I want to say in reply is that, in an important sense, the only legitimate residual question in this vicinity is epistemic. We have already been told what we are looking for. We are looking for those conditions that are necessary for having concept C. If we are working within an inferential framework, we are asking which inference rules are necessary for possessing concept C. Paolo says: “we have not been told what sort of data would be relevant to establish this”. We have “no idea what the relevant criterion might be like”. Why, in addition to being told that we are looking to find out which inference rules are necessary for possession of C, must there be criteria by which this matter is to be decided? It is, indeed, very common in discussions of this topic, to think that there have to be behavioral markersby which concept-constituting inferences are to be recognized. I think it is a mistake to look for such markers. The idea that there have to be such behavioral markers is encouraged by reflection on the case where a word is introduced via explicit stipulation. Suppose I introduce the word “flurg” as follows: (7) By “flurg” I shall mean: “Any murder committed on a Tuesday”. If I am rational, then, as a mere result of this stipulation, I will exhibit a certain kind of assent behavior. For example, I will assent to (8) A flurg always occurs on a Tuesday. and I will do so without the benefit of any empirical evidence. I will not regard any empirical evidence as bearing upon its acceptability in any direct way, and so forth. Such assent behavior can be regarded as ‘criterial’ for (7)’s having a meaning-constituting status for me. Now, of course, in the case of the basic logical constants, there is no question of having introduced them via explicit stipulation (one would need some constants in order to make any stipulations). When we think of an inference rule as having concept-constituting status for a particular constant, there is a natural tendency to think of it as a sort of tacit analogue of an explicit stipulation. Then it becomes natural to ask how to identify the tacit analogues of the assent behavior that’s criterial in the explicit case. There is a mistake here. The reason that we may expect my characteristic assent behavior in the explicit case depends on the fact that, in such a case, I know my definition and know that it has definitional status for me. In the explicit case, all such facts are open to view. However, matters are different in the tacit case. A rule R can be concept-constituting for C in S’s idiolect without S knowing that it is. As a result, S can come rationally to question R on the sorts of highly theoretical grounds that Tim describes. Such questioning by S need not mean that R is not concept-constituting for S’s having C, but it does mean that ordinary speakers, who are not trained to think about such matters, can change their concepts without knowing that they have. How can we tell whether that has happened? In the usual way, clearly being used both by Paolo and Tim – via intuitive judgments about possible cases.*