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Consider someone who has somehow come to adopt the unreflective practice of inferring according to Prior’s introduction and elimination rules for the ‘tonk’ connective: 1. (I) A/A tonk B; (E) A tonk B/ B. If we suppose that we are allowed to use inferences in accord with these rules in mounting a justification for them, then it would seem that we could justify them as follows:15 1. ‘P tonk Q’ is true iff ‘P’ is true tonk ‘Q’ is true 2. P 3. ‘P’ is true 4. ‘P’ is true tonk ‘Q’ is true 5. ‘P tonk Q’ is true 6. P tonk Q 7. If P, then P tonk Q Meaning Postulate Assumption 2, T‐scheme 2, tonk‐introduction 4, 1, biconditional‐elimination 5, T‐scheme 6, logic Here line 7 expresses a canonical statement of tonk‐introduction dependent just on the meaning postulate in line 1. So this template is available to explain how someone for whom inference in accordance with tonk introduction was already part of their unreflective practice could arrive at an explicit justification for it. (p.248) And an exactly corresponding example could be constructed to yielda ‘justification’ for the principle of tonk elimination. Or consider the following example (due to Marcus Guaquinto). Let R be the rule that, for any P, P, therefore All snow is white. Now, we seem to be in a position to mount a justification for it along the following lines. Pick any proposition P: 1. P 2. All snow is white 3. If P, then All snow is white Assumption 1, R Conditional Weakening Therefore, the inference from P to all snow is white is truth‐preserving. Since this is independent of the particular proposition P that is chosen, then, for any proposition P, the inference from P to ‘All snow is white’ is truthpreserving. Clearly, we cannot simply assert that rule‐circular justifications are acceptable and leave it at that. The question is whether there is some intuitively plausible constraint that they should be made to satisfy that will repel the bad company they would otherwise keep while leaving in place the justificatory arguments that interest us. I will begin by discussing the second half of the problem about begging the question. Begging the Question: Reasonable Employment of a Rule Could we be entitled to use a rule of inference without first being justified in the corresponding general claim that that rule is valid? It seems to me that we can if a plausible—perhaps even inescapable—account of what determines the meanings of our logical constraints is true. Let me explain. By virtue of what does ‘and’ mean conjunction and refer to a certain truth function, and ‘if, then’ mean conditional and refer to a distinct truth function? That these expressions mean what they do cannot be a primitive fact about them; there must be facts by virtue of which these semantic facts obtain. As I see it, the most plausible—perhaps the only plausible—account has it that our constants mean what they do by virtue of their conceptual role: ‘if, then’ means what it does by virtue of participating in some inferences and not in others. How, exactly, is this to be understood? The thought is that there is a particular set of inferences involving ‘if, then’ that are meaningconstituting for a thinker: of all the inferences that ‘if, then’ can and does participate in, a specific subset is responsible for fixing its meaning. Given (p.249) that subset, ‘if, then’ means that unique logical concept, if any, whose semantic value makes the inferences in that subset truth‐preserving. The qualification is necessary because for all that a conceptual role theory can guarantee, a specified conceptual role may fail to determine a unique, or indeed, any meaning for the constant in question.16 Any such approach to the meanings of the constants faces, it must be conceded, a formidable number of obstacles. First, there is the impression, much encouraged by Carnap and the middle Wittgenstein, that doctrines of implicit definition lead inexorably to irrealist conclusions, that to view a fundamental logical principle as an implicit definer is to subscribe to some sort of conventionalism or nonfactualism about its truth. Second, there is the charge, levelled by Quine, that an implicit definition view of logic leads to a vicious regress, because the very logical vocabulary allegedly being defined has to be used to formulate the stipulations. Third, there is the difficulty, also urged by Quine, of saying which of the many sentences a thinker may be disposed to assert serve as implicit definers of its ingredient terms. Fourth, there is the problem, most often discussed in connection with Arthur Priori’s ‘tonk’ example, of saying what conditions a set of implicit definers must meet if it is to define a genuinely meaningful term. Finally, there is the difficulty of showing how any such account would succeed in determining a unique logical concept. Some of these questions have satisfactory answers.17 Others await one. It is hard to believe, however, that they do not all have satisfactory answers because it is very hard to see what other type of theory could explain the meanings of our logical constants. In any event, the present essay should be seen as issuing a large IOU on the outstanding problems for a conceptual‐role semantics. I am interested in what we should say about the epistemology of logic, if, as seems likely, a conceptual‐role semantics provides the correct account of the meaning of the logical constants. With that in mind, I want to propose the following principle: (L) If M is a genuinely meaning‐constituting rule for S, then S is entitled to infer according to M, independently of having supplied an explicit justification for M. Notice that (L) does not require that S know that M is meaning‐constituting for S (p.250) if S to be entitled to infer according to M but only that M be meaning‐constituting for S. Is there anything that speaks in favour of (L) independently of the fact that it helps with the problem about rule‐circularity? It seems to me that there is, that (L) is intuitively plausible. If it is true that certain of our inferential dispositions fix what we mean by our logical words (in the language of thought), then it is very plausible that we should be entitled to act on those inferential dispositions prior to, and independently of, having supplied an explicit justification for the general claim that they are truth‐preserving, for without those dispositions there is nothing about whose justification we can intelligibly raise a question about: without those dispositions we could not even have the general belief whose justification is supposed to be in question. The only items that are candidates for being justified are either contentful items or certain kinds of transition between contentful items (inferences). But if it is true that there could be no contentful items unless certain dispositions are already in place, there cannot be a serious question whether those dispositions are ones to which we are entitled.18 Our difficulty was to find a source for our entitlement to rely on a given rule of inference, independently of having supplied a justification for the general claim that that rule is truth‐preserving, so that we are able to use that reliance to supply that justification. What I am urging is that that entitlement is precisely what flows naturally from a conceptual‐role account of the meanings of our logical words. This proposal does, of course, bring to the fore the question: what makes a rule meaning‐constituting? This is one of the questions that still awaits a definitive answer. My present concern, however, is just to emphasize that our problem about our entitlement to employ a rule of inference reduces to that problem, a problem that any conceptual‐role semantics faces. Dealing With Bad Company With (L) in place, we are now poised to resolve the problem of bad company. For (L) suggests the following restriction on rule‐circular justifications: (RC) S’s rule‐circular argument for a rule of inference M will confer warrant on S’s belief that M istruth‐preserving, provided that M is a genuinely meaning‐constituting rule for S. (p.251) Two questions arise. First, does (RC) yield the right results as far as rule‐circular justifications are concerned? Does it exclude the justification of unwanted rules? Second, can anything of an intuitive nature be said to support it? If we apply to (RC) to our problematic examples above, it is easy to see that they are immediately ruled out. R is not meaning‐constituting: it is obviously not part of the meaning of ‘all’ that ‘All snow is white’ can be inferred from any proposition. Indeed, it is because we have an independent purchase on what ‘All snow is white’ means that we know that R is not truth‐preserving and, hence, that it would be embarrassing to endorse a theory that said otherwise. Similarly in the case of ‘tonk.’ It is readily shown, by attempting to construct a truth‐table for ‘tonk’, that its introduction and elimination rules do not determine a meaning for it’; there is no proposition expressed by sentences of the form ‘A tonk B.’ In fact, it should be clear that (L) will not allow any invalid rules to be circularly justified. For if M is genuinely meaning‐constituting, as (L) insists it has to be, then it has a semantic value that makes M truth‐preserving. As far as the question of the intuitive support for (RC) is concerned, that question recapitulates the case for (L). If (L) is correct, then the source of our entitlement to the use of a rule of inference is distinct from our entitlement to the corresponding belief that it is valid if the rule is meaning‐constituting. Thus, it may be used to confer warrant on its conclusion. Begging the Sceptic’s Question It is time now to turn to the final problem I outlined for a rule‐circular justification, its capacity to move the appropriate sceptic. The point at issue is prefigured in Dummett’s discussion when he says that rulecircularity will be damaging only to a justificatory argument that is addressed to someone who genuinely doubts whether the law is valid, and is intended to persuade him that it is. . . . If, on the other hand, it is intended to satisfy the philosopher’s perplexity about our entitlement to reason in accordance with such a law, it may well do so. The philosopher does not seriously doubt the validity of the law and is therefore prepared to accept an argument in accordance with it. He does not seek to be persuaded of the conclusion; what he is seeking is an explanation of its being true.19 Before inquiring into the significance of this, let us make sure that we do not underestimate all that a rule‐circular justification is capable of accomplishing. First, it is not at all similar to a grossly circular argument in that it is not trivially guaranteed to succeed. For one thing, the relevant premises from which, by a (p.252) single application of the rule the desired conclusion is to follow, may not be available. For another, not all rules are self‐supporting. Second, the rule‐circular argument for MPP asks in effect that it be granted that one application of MPP and from that it promises to deliver the conclusion that MPP is necessarily truth‐preserving, truth‐preserving in any possible application. Finally, this one application will itself be one to which we are entitled if, as seems plausible, MPP is meaning‐constituting. For all that, it is nevertheless true that if we were confronted by a sceptic who doubted the validity of MPP in any of its applications, we could not use this argument to rationally persuade him. Doubting the rule, he would rightly reject this particular argument in its favour. Since, by assumption, we have no other sort of argument to offer him, it seems that we are powerless to persuade him of the rightness of our position. The question is: what is the epistemic significance of this fact?But could not we say to him: ‘Look, MPP is meaning‐constituting. If you reject it, then you simply mean something different by “if, then” and therefore there is no real disagreement after all.’ But if our sceptic were playing his cards right, he would deny that MPP is meaning‐constituting. To persuade him otherwise we would have to offer him an argument and that argument would in turn have to use MPP. And then we would be right back where we started, faced with the question: what is the epistemological significance of the fact that we are unable to persuade the sceptic about MPP? In the passage cited above, Dummett seems to think that its significance lies in the way in which it highlights a distinction between two distinct projects: quelling the sceptic’s doubts versus explaining to a non‐sceptic why MPP is valid. But I do not really understand what it would be to explain why a given logical law is true. What could it mean except something along the lines of a conventionalism about logical truth, an account which really does aspire to explain where logical truth comes from? As we have seen, however, there are decisive objections to conventionalism, objections that probably generalize to any explanatory project of that form. The question that we need to be asking, I think, is rather this: Can we say that something is a real warrant for believing that p if it cannot be used to answer a sceptic about p? Is it criterial for my having a genuine warrant for believing that p that I be able to use it to persuade someone who doubts whether p? Well, in fact, we are very drawn to the idea that if I am genuinely justified in believing that p, then, in principle, I ought to be able to bring you round as well—or, at the very least, I ought to be able to take you some distance towards rational belief in p. Of course, you may not understand the warrant that I have; or, being more cautious than I, you may not assign it the same weight that I do. But, prescinding from these and similar considerations, how could I be genuinely justified in believing something and yet be totally unable to have any sway with you? As Thomas Nagel puts it in his recent book The Last Word: ‘To reason is to think (p.253) systematically in ways that anyone looking over my shoulder ought to be able to recognize as correct. It is this generality that relativists and subjectivists deny.’20 Notice how naturally it comes to Nagel to equate the claim that there are objectively valid reasons, reasons that would apply to anyone anywhere, with the epistemic claim that anyone exposed to them ought to be able to recognize them as reasons. There is a principle behind this thought, one that we may call the ‘principle of the universal accessibility of reasons’. If something is a genuine reason for believing that p, then, subject to the provisos just made, its rationalizing force ought to be accessible from any epistemic standpoint. I think that this principle has played a very large role in our thinking about justification. It is what explains, it seems to me, why the theory of knowledge is so often centred on a refutation of scepticism. We take it to be criterial of our having a genuine warrant for a given proposition that we be in a position to refute a sceptic about p. If my discussion of logic has been on the right track, however, then one of its main lessons is that this principle is false. For consider: we cannot accept the claim that we have no warrant whatsoever for the core logical principles. We cannot conceive what such a warrant could consist in (whether this be a priori or a posteriori) if not in some sort of inference using those very core logical principles. So, there must be genuine warrants that will not carry any sway with a sceptic. Answering the sceptic about modus ponens cannot be criterial for whether we are warranted in believing modus ponens. To put this point another way: we must recognize a distinction between two different sorts of reason— suasive and non‐suasive reasons. And we have to reconcile ourselves to the fact that in certain areas of knowledge, logic featuring prominently among them, our warrant can be at most non‐suasive, powerless to quell sceptical doubts. It seems to me that this is a conclusion that we have reason to accept entirely independently of our present concern with knowledge of logic, that there are many other compartments of knowledge in which our warrant can be at most non‐suasive. One such area concerns our knowledge of the existence of other minds; another concerns our knowledge of the external world. I think that in both of these areas it is very unlikely that we will be able to provide warrants for our belief that would be usable against a determined and level‐headed sceptic. Conlusion It is not open to us to regard our fundamental logical beliefs as unjustifiable. And yet it is hard to see how they might be justified without the benefit of deductive (p.254) reasoning. What sort of case have we been able to make for the claim that rule‐circular arguments can provide genuine justifications for their conclusions? It seems to me that the case is substantial. First, a rule‐circular argument, unlike a grossly circular one, is not trivially guaranteed to succeed. Second, by relying on a small number of applications of a particular rule, a successful rule‐circular argument delivers the conclusion that that rule is necessarily truth‐preserving, truth‐preserving in any possible application.21 Finally, these applications of the rule will be applications to which the thinker is entitled, provided that the rule in question is meaning‐constituting. This case is constructed on the basis of several independently plausible elements. First, that the meanings of the logical constants are determined by their conceptual roles, and that not every conceptual role determines a possible meaning. Second, that if an inferential disposition is meaningconstituting, then it is a fortiori reasonable, justifiably used without supporting argument. Third, that something can be a warrant for something even if it is powerless to bring about a determined sceptic. Putting these elements together allows us to say that we are justified in our fundamental logical beliefs in spite of the fact that we can produce only rule‐circular arguments for them. The price is that we have to admit that we cannot use this form of justification to silence sceptical doubts. It is arguable, however, that, with respect to something as basic as logic, that was never in prospect anyway.