Ben Baker ben.baker@btinternet.com Boghossian's Implicit Definition Template Abstract: In Boghossian's 1997 paper, 'Analyticity' he presented an account of a priori knowledge of basic logical principles as available by inference from knowledge of their role in determining the meaning of the logical constants by implicit definition together with knowledge of the meanings so-determined that we possess through our privileged access to meaning. Some commentators (e.g. BonJour (1998), Glüer (2003), Jenkins (2008)) have objected that if the thesis of implicit definition on which he relies were true, knowledge of the meaning of the constants would presuppose knowledge of the very logical principles knowledge of which the account purports to explain. A consequence would seem to be that implicit definition is incompatible with privileged access. I argue that whilst it is possible for Boghossian to defend against these objections the form of argument he proposes does exhibit a subtle form of question begging such that it exhibits a transmission of warrant-failure. Key words: Knowledge of logic – Analyticity – Implicit definition – Privileged access – Warrant transmission 1. Boghossian on implicit definition and a priori justification In his paper 'Analyticity' (1997a) 1 Paul Boghossian attempted to rescue analytic accounts of the a priori from the disrepute into which they had fallen due to objections pressed by Quine and others. Central to such accounts is the claim that there is a route from implicit definition to a priori knowledge and in particular that such a route is available for the central case of basic logical knowledge. Accounts of how implicit definition could explain direct a priori knowledge seem to require that it involve the explicit stipulation of sentences that express a priori truths. 2 However, it is one lesson of Quine's 'Truth By Convention' (1936) that we cannot take the meaning of our logical constants to be fixed by the explicit stipulation 1 A shorter version had appeared as Boghossian (1996) together with a response by Gilbert Harman. 2 Harman (1996). 2 of basic logical laws, at least if this is to be a fundamental account of their meaning, for any explicit stipulation would have to presuppose logic. Boghossian's response is that one may save the idea that the meaning of the logical constants is fixed by implicit definition by saying that it is by our acceptance, in some suitably basic way, of certain inference rules, and that this may be seen as amounting to a tacit stipulation of the validity of those rules. His proposal regarding how such a semantic thesis can help in explaining basic logical knowledge is that knowledge of the meaning of the logical constants together with knowledge of how that meaning is fixed by implicit definition puts us in a position to know premises from which we may infer that the inference rules that serve to determine that meaning are valid. In more detail the account proceeds along the following lines. Boghossian characterises the thesis of implicit definition, as applied to the case of logic, as follows: Implicit Definition 3 : It is by arbitrarily stipulating that certain sentences of logic are to be true, or that certain inferences are to be valid, that we attach a meaning to the logical constants. More specifically, a particular logical constant means that logical object, if any, which makes valid a specified set of sentences and/or inferences involving it. (1997: 348) Now, call one of the specified sentences or, as I will henceforth assume, inferences for a logical constant, C, an implicit definer of C. Now suppose that we know that the above thesis is true and that M(C) is one of the implicit definers of C, as it might be one of its introduction or elimination rules. Then we know that C means what it does only if M(C) is valid. For according to Implicit Definition it is a condition of C having the meaning that it does that there is some (unique) logical object which makes its implicit definers, including M(C), valid. Thus we are in a position to knowledgeably state as a first premise: (1) If C means what it does then Μ(C) is valid. But we are generally supposed to have privileged access to the meaning of terms in our language, so given that C is a meaningful term and that one understands it, one is in a position to knowledgeably state its meaning; that is to state that 3 I give the thesis as Boghossian expresses it initial capitals here and in what follows so as to be clear it is this specific version of the thesis that is in play. 3 (2) C means what it does. But now it seems that we are in a position to infer from (1) and (2) by modus ponens that (3) Μ(C) is valid. Boghossian argues that an argument of this form can justify a thinker in believing that M(C) is valid, this justification being sufficient for knowledge. Since knowledge of these facts about the meaning of C is sufficient for knowledge of the premises of such an argument, Boghossian says that the conclusion is epistemically analytic. He argues that this can be the case without any implication that it is metaphysically analytic, true in virtue of meaning alone. Boghossian's focus in this paper is the case of logic, but a similar argument is available whatever kind of term Implicit Definition applies to. When a sentence, S(f), is an implicit definer for its ingredient term f we can run through a similar argument template: (1*) If f means what it does then S(f) is true (2*) f means what it does Therefore (3*) S(f) is true This argument however does not give us the conclusion we need. For (3) is a metalinguistic claim about the sentence S(f) whereas what needs to be explained is knowledge of the truth that sentence expresses. Accordingly when Boghossian discusses this case in his (2003b) the argument he presents is extended as follows 4 : (1#) S(f) means that p (2#) If S(f) means that p then S(f) is true (3#) S(f) is true (4#) If S(f) means that p then S(f) is true if and only if p. (5#) S(f) is true if and only if p (6#) p As can be seen the premises also differ. Boghossian claims this form is a better representation of the relevant template but that "it is not materially different" (2003b: 21, fn.3). Similarly, since C is a linguistic expression, the conclusion of the original template, that M(C) is valid, is also 4 I have added the suffix to Boghossian's numbering. 4 metalinguistic, so in this case too we need a further step, now to reach a conclusion stating the validity of a pattern of inference at the level of propositions. 5 It is an interesting question just what the required conclusion is and what might be required to reach it from Boghossian's (3) but I will not pursue it here. Following Boghossian we can call the general form of argument the Implicit Definition Template. In this paper I consider whether Boghossian is right to think that this form of argument can be a route to a priori knowledge of its conclusion. In particular I will consider the worry that since, if the thesis of Implicit Definition is correct, that C means what it does, indeed that it means anything at all, depends on there being a meaning that makes M(C), being justified in believing the minor premise of the original template – that is premise (2) – requires being justified in believing the conclusion. That this is the case is argued by BonJour (1998) and Glüer (2003). If it were then not only would the template be viciously epistemically circular but it would also seem to entail that implicit definition as Boghossian characterises it is incompatible with privileged access to meaning insofar as this is thought to be groundless. Boghossian replies to these objections in his (2003b). Whilst I don't find Boghossian's response altogether satisfactory I will argue for the compatibility of implicit definition with privileged access. However I will argue that the template exhibits a more subtle form of question begging, but one which nonetheless entails that it fails to transmit warrant from its premises to its conclusion. 2. Rule-circularity Boghossian says that A is epistemically analytic for T if "T's knowledge of the meaning of A suffices for T's justification for A" (1997: 356). Given that the template is supposed to explain how the proposition that M(C) is valid is epistemically analytic two points should be noted. First, as Boghossian acknowledges, knowledge of the premises of the template involves knowledge of meaning in a fairly broad sense (1997: 357) in which it includes knowledge of how the meaning of C is fixed. That is not 5 Ebert (2005). 5 knowledge that speakers who understand C typically possess, certainly not if its meaning is fixed by tacit stipulation. In this case it then would not be true to say that understanding the proposition that M(C) is valid is sufficient to be justified in believing it. But presumably speakers who do not know how the meaning of C is fixed have been warranted in believing that the rule is valid. To accommodate this Boghossian draws on Tyler Burge's distinction between justification in a narrow sense, in which being justified requires having reasons to which one has access, and entitlement, which is a form of warrant which does not. 6 With this distinction in place he can allow that speakers who understand it can be entitled to believe that M(C) is valid. In (1997a) the suggestion is that the facts about how meaning is determined suffice for this; in (2003b) it is the availability of the relevant instance of the template. Secondly, the justification (in the narrow sense) the template provides is inferential. 7 Thus knowledge of the meaning of the conclusion will be sufficient for justification to believe it only in the sense that it makes available such justification; to be justified in believing it one must actually draw the inference. 8 Further one must meet whatever conditions are required to acquire justification by doing so. But consider the case in which C is 'if' and M(C) is modus ponens. As noted, modus ponens is the rule of inference appealed to in the step from the premises, (1) and (2), to the conclusion, (3). Thus in the case in question the relevant instance of the schema will use the very rule which the conclusion states to be valid; it will be rule-circular as Boghossian puts it. Clearly if in order to be justified in inferences drawn by modus ponens one needed to be justified in believing that rule to be valid it would be impossible to acquire such justification by a rule-circular argument. Boghossian, however, argues that in certain cases we can be entitled to infer according to a rule, and thereby in a position to extend our knowledge when we do so, without needing antecedently to be warranted in believing it to be valid. Roughly his suggestion is that we can be entitled to infer in accordance with rules 6 Burge (1993). 7 Or so I will assume. It seems to be Boghossian's intention though it is perhaps not entirely clear in (1997a). 8 This seems to point the way to a response to Ebert's (2005) objection to the template. See Jenkins (2008). 6 which are meaning-constituting for concepts whose constitutive rules do not build in unavoidable commitments. 9 Such concepts will include our basic logical constants. On this account the facts about how meaning is fixed explain our entitlement to infer according to a basic rule. 10 So Boghossian's account takes rules of inference to be basic in determining how the meaning of the logical constants is determined and appeals to this fact in explaining how an inferential account of basic logical knowledge can avoid vicious epistemic circularity. Boghossian's meaning-based account of entitlement to rely on a rule is arguably open to a number of objections but alternative accounts of such entitlement have been proposed. 11 Here I will take it that some such account is available and that rule-circularity is compatible with the acquisition of warrant by inference. 12 3. The justification of the major premise As we have noted Boghossian's case for our knowledge of premise (1), the major premise of the modus ponens inference, is based on his thesis of Implicit Definition. This thesis combines two claims, both of which are required for the explanation of how we can know the first premise independent of knowing the conclusion to go through. The first part, which we will call Stipulation, states: It is by arbitrarily stipulating that certain sentences of logic are to be true, or that certain inferences are to be valid, that we attach a meaning to the logical constants. 9 The account is developed in Boghossian (2000), (2001), (2003a) and (2003b). The last two papers present a defence of the account in the form described in the text. 10 Entitlement to infer according to a rule should be distinguished from entitlement to believe it valid. 11 See Williamson (2003), Schechter and Enoch (2006) for criticism. The latter paper proposes an alternative account, as does Wright (2004). 12 Given that rule-circular justification is taken to be possible then it may seem to be preferable to appeal to other forms of inferential justification whose premises do not rest on controversial semantic theses (or which rest on no undischarged premises at all as in Wright (2004)). Even if alternative forms of argument are available however, the question remains whether one could acquire justification through the template. 7 As we have also noted, in the case of our basic logical constants we must understand stipulation in a somewhat broad sense so as to allow that stipulation can be tacit. The important property of stipulation for the purposes of the template is that what makes an inference rule an implicit definer of a logical constant is that it is accepted in some suitably basic way, or as we may say has a certain acceptance property. That being so we can recognize which rules are implicit definers by the fact that they have that acceptance property, hence independently of knowing that those rules are valid. If implicit definition were so understood that only rules which determine a meaning such that they are valid could be implicit definers then knowledge of the first premise would not be independent of knowledge of the conclusion. Quine and others following him have argued that it is not possible to draw a principled division between those sentences and/or rules that a defender of the analytic theory of the a priori would claim to be implicit definers for a term and other obvious principles in which that term features, so that there is no principled basis on which to say that a sentence or rule is an implicit definer. Boghossian spends a large part of (1997a) arguing that the determinacy of meaning entails that there must be such a division. I will not assess this part of his case here. Rather I will simply assume for the sake of the discussion that there is not good reason to believe that such a division cannot be drawn and the relevant acceptance property identified. 13 Even granting the possibility of some such division, there may be some question whether our knowledge of what the implicit definers of a term are would be a priori. In cases in which there is (and perhaps also if it is as if there is) explicit stipulation this might be a case of knowledge of our intentions. But what of cases in which stipulation could only be tacit? It will rather depend on what the relevant acceptance property is but perhaps we can identify the rules by some combination of introspection (what we would say about cases) and theory. Again I propose to grant that we can know what the implicit definers are a priori. The second claim is implicit in the second part of the characterisation of Implicit Definition: "a particular logical constant means that logical object, if any, which makes valid a specified set of sentences and/or inferences 13 There are also issues concerning just what acceptance of the rule involves. 8 involving it". What is implied is that if there is no such logical object then the term will lack a meaning. Let us call this claim Determination. It is this that secures the link between C meaning what it does and the validity of its implicit definers, our knowledge of which, together with our knowledge of what those implicit definers are, puts us in a position to know the first premise. It should be noted that neither Stipulation nor Determination are inevitable features of anything that might be called implicit definition. To take the Stipulation first, this posits a certain primacy of use in determining what the implicit definers of the logical constants are. But one might think of a specification of its introduction and elimination rules as a definition of a logical constant that we use, given that they do determine a meaning, but view those rules as norms of correct use, to which actual use must approximate. As regards Determination, this is a thesis Boghossian himself had come to reject in cases of tacit stipulation, and so for the basic logical constants, by the time of (2003b). He had come to be convinced by examples such as the pejorative 'Boche' as described by Dummett (1981) that the meaning of a term can be fixed by inference rules without those rules determining a semantic value. So he could no longer appeal to the template to account for our justification for believing basic inference rules such as modus ponens valid. His implicit definition-based account of entitlement to rely on the rules however does not depend on Determination, and other inferential routes to such justification may be available given that we have such entitlement. However, in the rest of this paper I will assume for the sake of the discussion that the thesis of Implicit Definition understood as Boghossian stated it in (1997a), entailing both Stipulation and Determination, holds in the cases of interest, and in particular in the case of logic, together with whatever else is required for the sort of justification for the major premise of the Template we have considered to be available. The question I will consider is whether, supposing the meaning of C to be fixed by Implicit Definition, we may assume that we do have privileged access to the meaning of C, and whether if we do the relevant instance of the template can be a route to justification of its conclusion in the way Boghossian supposes. 9 4. The justification of the minor premise Premise (2) of the template, the minor premise of the modus ponens step, is (2) C means what it does. I will assume that we are to read this as saying that C means what it in fact does, so that when C is 'if' we can read it as something like 'if' means if, where if is the concept or meaning 'if' expresses. This is something to which we would ordinarily be thought to have privileged access. But can we assume that we have such privileged access when the meaning of C is fixed by Implicit Definition? That there might be a problem emerges when we consider that there is not in general any guarantee that stipulating that certain rules are to be valid will determine a semantic value which makes those rules valid; there may be no semantic value that will do. A set of rules which we might follow can exhibit various defects that prevent their determining a meaning such that they are valid. At the extreme a pair of introduction and elimination rules may jointly engender inconsistency. If the inconsistency is not obvious it is possible that this could go unnoticed by those using the term in accordance with its meaning-constituting rules, for whom it could appear to be meaningful, to be used to make determinate claims, and so on. 14 But Determination says that C only has a meaning if the stipulated inference rules do determine a meaning. That C is an apparently meaningful term in one's language then does not guarantee that it has a meaning. It depends on certain non-trivial constraints being met. 15 This may raise a concern that knowledge of premise (2) is quite substantial and so is not something to which we can simply assume that we have privileged first-person access. But further, since according to Implicit Definition it is a condition on C meaning what it does that there is a meaning, C, which makes its implicit definers valid, that M(C) is valid 14 Consider an operator introduced as defined by rules corresponding to the left and right directions of Frege's Axiom V. Prior to the discovery that it leads to contradiction it seems that it would have been possible to use this operator at least apparently meaningfully. 15 For present purposes we need not consider how those constraints should be characterised. 10 when C means C is a condition of C meaning what it does given that it is defined in the way it is. But that M(C) is valid when C means C is in effect the required conclusion. This may raise the worry that being justified in believing (2) requires being justified in believing that condition met so that the template is viciously epistemically circular. We turn now to objections according to which this is the case. 5. BonJour on implicit definition I start by considering an objection due to Laurence BonJour against any attempt to derive a priori knowledge from implicit definition. The idea is that even if one could fix the meaning of an expression by implicit definition, knowledge that the meaning is fixed in this way would not be enough by itself to be in a position to know what that expression meant; one would have to know that the implicit definers are true in order to know that it meant. Taking his model of implicit definition from Butchvarov (1970), he claims that: offering a form of words as an "implicit definition" amounts to a stipulation that any previously unknown terms it contains are to be interpreted in such a way as to make the proposition expressed under that interpretation come out true (or perhaps, necessarily true). [...?] Thus, for example, one might stipulate that the sentence '40@8=5' is to count as a (partial) implicit definition of the symbol '@'. This, along with other stipulations of the same kind, might prove a useful way of conveying that '@' is to stand for the operation of long division (assuming that the other symbols in the sentence are already understood). But if this is the right account of implicit definition, then the justification of the proposition that 40 divided by 8 is equal to 5 (as opposed to that of the linguistic formula '40@8=5' is not a result of the implicit definition, but is rather presupposed by it: if I were not justified in advance, presumably a priori, in believing that forty divided by eight is equal to five, I would have no reason for interpreting '@' in the indicated way. (1998:50-1) This line of objection is applied to Boghossian's template by Carrie Jenkins (2008). In this case the claim would be that justification of the proposition that C means what it does presupposes justification of the 11 required conclusion so that the argument schema cannot explain that justification. Note that if this objection is correct then it would seem to entail that the meaning of C being fixed by implicit definition is incompatible with privileged access to the meaning of C. Whilst one could still be justified a priori in believing that C means what it does, assuming one could be justified a priori in believing that the logical object C means has the necessary properties to make its implicit definers valid, according to this objection this justified belief would be required as a ground for one's belief that C means that logical object, whereas groundlessness is generally held to be a mark of privileged access. At least privileged access would hold only in a qualified form. The objection as stated does not directly apply to those cases in which stipulation is tacit, such as that of the basic logical constants. In such cases there does not seem to be any question of our needing to interpret the constant. However it might perhaps be argued that something similar can be said in this case. The thought would be mere competence in using C in accordance with its meaning constituting rules is not by itself enough to be in a position to know which logical object C means. To be able to identify a logical object is the one C means I would have to know that if C is interpreted in that way its implicit definers would be valid. If that is the objection then it seems to rest on a conception of implicit definition according to which it amounts to a form of reference-fixing. On that conception even if an implicit definition does fix a meaning it does not tell us what that meaning is; one needs some independent grasp of that meaning and its properties to know that it is what C means. Though Boghossian's characterisation may invite that interpretation it is not obviously compulsory. A defender of implicit definition may say that in at least some cases an implicit definition can fully convey the meaning of the defined term 16 – in the case of a logical constant this might be its inferential role – and that one who understands the term in accordance with its implicit definition can thereby grasp that meaning. Understanding an implicitly defined term, at least sufficiently to be able knowledgeably to state its meaning, involves more than merely being disposed to use it in 16 Hale and Wright (2000). 12 accordance with the rules; it requires some appreciation of how it contributes to the content of sentences in which it occurs. But that need not require that one be able to identify an independently specifiable logical object as the meaning as this objection assumes. As far as I can see the characterisation of implicit definition on which the objection rests has not been shown to be compulsory; nor has the position of the defender of Implicit Definition been shown to be untenable. More may need to be said to give an account of how knowledge of meaning is possible given such a position but BonJour has not given us reason to think that no such account could be given. I will shortly try to sketch how such an account might go. 6. Glüer's objection Kathrin Glüer (2003) presents an objection that does not seem to rely on any tendentious conception of Implicit Definition, but simply on the dependence of meaning on the existence of a suitable semantic value that the thesis entails. Referring to the template for sentences she argues: That f means what it does depends on there in fact being something that makes S(f) true, according to premise [(2#)]. Only if there is such a fact does f have any meaning. Being justified in believing premise [(1#)] therefore, requires being justified in believing that there is something that makes S(f) true. Moreover, it requires being justified in believing that S(f). (2003: 57) What this objection does seem to assume is that since the validity of M(C) is a precondition of C meaning what it does then possessing justification for the former presupposes the possession of justification for the latter. Since the distinction between justification and entitlement is in play in Boghossian's original paper I will take it for now that justification in this passage should be understood in the narrow sense in which it requires reason for belief to which the subject has access. 17 If so then this objection too would seem to entail a denial of the compatibility of Implicit Definition 17 I will argue in effect that the objection can be sustained if it is interpreted as claiming that being justified (in the narrow sense) in believing premise (2) requires possessing justification (in the wide sense) to believe the conclusion, for I will argue that it requires being entitled to believe the conclusion. 13 with privileged access. 18 At any rate Boghossian interprets it as having that entailment. For in reply he says: most philosophers simply assume that meaning facts are first-person accessible in some privileged way, regardless of what the supervenience base for meaning facts is taken to be. For example, many philosophers believe that even if facts about meaning and concept possession were to supervene on facts that are external to the mind that that would have no tendency to undermine our privileged access to first-person facts about meaning. (2003b: 22-3) He goes on to complain that Glüer has given no special reason to believe that this assumption should be suspended when the meaning of a term is fixed by implicit definition. To be relevant to Glüer's objection the relevant externalist theses will have to include those according to which terms which fall under them may lack a meaning; such would be certain views concerning natural kind terms or an Evans-style view of Russellian proper names. Many philosophers do think that such views are perfectly compatible with privileged access. So if, as seems to be the case, Glüer is appealing a principle incompatible with that position the onus may be thought to be on her to argue for it rather than assuming it. However given that Boghossian is invoking the template to explain a priori knowledge this response does not seem altogether satisfactory. For the fact that the validity of M(C) is a precondition of C meaning what it does gives us some reason to wonder whether an account of privileged access is available which will make justification for (2) epistemically independent of the conclusion, as is required if the template is to explain how we can be justified in believing it. For one thing it is hard to see how anything to which the implicit definition theorist can legitimately appeal could explain how a speaker who understands an implicitly defined term could thereby be in a position to directly apprehend that C has that meaning. To do that it would seem to be necessary to have some sort of direct access to the meaning. To assume that one had such access would be illegitimate in the present context, for the template is supposed to explain a priori knowledge 18 Perhaps the minimal claim would be that one could not be justified in believing (2) unless one were also justified in believing that S(f). That is not obviously in conflict with privileged access. 14 without invoking an unexplained capacity for insight into necessary features of reality. But the sort of capacity for privileged access with which this assumption would credit speakers would seem to be no less mysterious, if indeed it is distinct. On the other hand the fact that C is not guaranteed to have a meaning would seem to rule out the sort of simple disquotational account of our knowledge of its meaning that might be appealed to in order explain privileged access to meaning. 19 For instances of the meaning disquotation schema 't means t' – in which t is first mentioned and then used – are not guaranteed to express truths even when t is restricted to terms which are apparently meaningfully used. Our knowledge of the minor premise thus seems to be more substantial than such an account would make it. This is so far just to say that two extreme positions do not seem to be available; but if the availability of the template is to explain how we can acquire a priori justification in the relevant cases then it seems we need some assurance that a satisfactory account can be given. If it is thought that we must suppose that we have privileged access to the meaning of our terms then it would seem that there is some onus on a theorist either to explain how a semantic thesis that is prima facie in tension can be compatible with it or to show that the semantic theory is the only tenable one. But it does not seem that Boghossian is in a position to claim the latter. Accordingly at least a sketch of an account of privileged access seems to be called for. 20 7. The compatibility of Implicit Definition with privileged access For the reasons given it seems that if we can have privileged access to the meaning of an implicitly defined term, then this must be possible even though our grounds for supposing that the term does have a meaning leave open the possibility that it is meaningless. How might that be? It would seem to require that there is, at least in favourable cases, a default presumption in favour of taking the appearance of the meaningfulness of a term at face value. Crispin Wright (2000) suggests such a position 19 Boghossian (1997: 359-60). 20 Boghossian offers an explanation for the case of logic in an Appendix to his (1997a). We will consider this explanation in section 0. 15 concerning the compatibility of privileged access with externalist theses that raise the possibility that apparently meaningful terms of certain kinds do not in fact have a meaning. On such views it is an open possibility, for all that a speaker has special first-person access to, that the relevant external conditions are not met. Nevertheless, Wright's thought is, the ordinary a priori presumption that seemingly meaningful terms in a speaker's language are meaningful could still apply. The mere possibility of perceptual illusion is not generally thought to undermine our entitlement to take perceptual appearances at face value; it is only if there is some special reason to believe it actual that the usual presumption in favour of the appearances being veridical is suspended and one might be required to justify the belief that the possibility is not actual. The suggestion in the case of meaning is that neither here is the mere possibility of what Wright calls an illusion of content sufficient to defeat the a priori presumption that an apparently meaningful term is meaningful. If there is special reason to believe the possibility actual, or perhaps reason to think that our practice is defective in some way, then the default presumption would be defeated, but otherwise it is in force and we can be justified in asserting the relevant instances of the meaning disquotation schema. Supposing that is plausible in the externalist cases, can we say something similar in cases of terms whose meaning is fixed by implicit definition? It might perhaps be suggested that we are not. In the externalist cases the possibilities in which the terms are meaningful are scenarios such as Boghossian's Dry Earth (1997b) which are similar to sceptical scenarios in perceptual cases and it may be this sort of feature that lends plausibility to Wright's view. However in a case in which we fix the meaning of a term by implicit definition we in effect presuppose that certain non-trivial constraints are satisfied and in doing so run the risk that they are not. It might seem that it is less plausible that we are entitled to a default presumption of meaningfulness in this case. Nevertheless I think that it is possible to argue that we are entitled to such a presumption in at least some cases. Again I take a suggestion from Wright, though it seems to be in the spirit of Boghossian's later views on the relation of implicit definition to entitlement. 21 The general idea is that 21 See Boghossian (2003a), (2003b). 16 we need terms governed by certain kinds of rules to engage in rational enquiry. This involves a certain unavoidable risk, but suppose that the use of a given term is necessary to our cognitive projects, that our stipulation satisfies certain general constraints intended to ensure that we do not run unnecessary risks in framing implicit definitions 22 , and that the term is apparently meaningful on the basis of that stipulation; then I think it is plausible that we could be entitled to the presumption that the term is meaningful, absent special reason to believe the definition defective. The above sort of account may draw some plausibility from the fact that ordinary speakers will not typically know what the conditions are on which the meaningfulness of the terms in question depend if the relevant semantic theses are true, and they will typically blameless in this. If that is so then in the absence of reason to doubt the term meaningful it would seem inappropriate to demand that speakers be able to produce grounds for their attributions of meaning. But what if not only is the relevant semantic thesis true but also a speaker does know that it obtains so knows that the precondition must hold if the term is to have a meaning, as would seem to be called for if the meaning is fixed by an explicit stipulation, and is certainly the case if the speaker is justified in believing (1)? Would that affect what would be required to be justified in the belief that the term was meaningful? James Pryor (2007) argues that it would in the case of the externalist theses. In his view given that one was justified in believing such a thesis one would need to produce some reason to believe that the external conditions were met if one were at the same time to be justified in believing that the term was meaningful. 23 That might be easily done given that one did stand in the necessary relations, but it would involve a qualification of privileged access. Against this it might be observed that the possibility of perceptual illusion is generally known, but that it remains the case that unless there is special reason to believe one might be suffering an illusion one need not produce reason to believe one is not in order to be justified in the perceptual beliefs one forms. 24 I am not altogether sure that 22 See Boghossian (2003a) and (2003b), and Hale and Wright (2000) for attempts to formulate such constraints. 23 He actually considers the case of thought contents but similar considerations would seem to apply to the meaning case. 24 Wright (2000). 17 this is effective in the externalist cases for in those cases speakers may be expected to have the necessary evidence and the challenge to produce it does not seem to lead to a regress. But it does seem to be relevant in the cases of implicit definition given that the above account is available. One of the motivations for an implicit definition based account is after all the thought that no relevant "evidence" is antecedently available to us. 25 If such a position is tenable then the thesis that the meaning of C is fixed by implicit definition is compatible with our having privileged access to the meaning of C; one would need no antecedent justification to believe that M(C) is valid in order to be justified in believing that C means what it does. It seems to me then that at least the sketch of an account of how implicit definition can be compatible with privileged access is available. 8. Transmission of warrant failure I have argued that assuming that the thesis of Implicit Definition is true of C we can be justified in believing both premises of the Implicit Definition Template together, and that in neither case does our justification depend on our being antecedently justified in believing the conclusion, at least if justification is understood as having reasons for belief. Does this lay to rest the worry that the argument begs the question in some way incompatible with its being a route to justified belief in its conclusion? No, because there can be more subtle ways in which an argument can beg the question in such a way that a kind of warrant for its premises fails to transmit to its conclusion. I think there is good reason to think that this is the case with the template. To take apparent meaningfulness of C at face value is in effect to presuppose that the conditions on C having a meaning are satisfied, since apparent meaningfulness does not intuitively suffice to establish that it has a meaning. As Glüer points out, according to Implicit Definition those conditions require that there is a meaning, C, which makes C's implicit definers, which include M(C), valid. Since C is the meaning C is 25 One might try to justify the claim that the implicit definers of a basic logical constant are valid by some argument. But since the argument will be rule-circular one must pragmatically presuppose that the constant is meaningful. It is thus doubtful that the argument can amount to a justification of the belief that it is. 18 determined to have they require that the "disquoted" rule corresponding to M(C) is valid. But that is just the required conclusion. So in judging that premise (2) is true we in effect presuppose that conclusion. Thus there is an epistemic dependence of that premise on the conclusion – we must be epistemically entitled to presuppose it if we are to be warranted in believing (2) – that seems to be incompatible with our warrant for the premises of the template being transmitted to the required conclusion. It seems then that a version of Glüer's claim may be sustained, if we read her as claiming that being justified in believing premise (2) requires being entitled to believe that there is something that makes M(C) valid. 26 It is also worth stressing that the objection here is not merely that our warrant for the second premise depends on our being entitled to the conclusion. It is not merely that doubt concerning the conclusion would be incompatible with being justified in believing (2) so that to be justified in believing (2) we must be entitled not to doubt the conclusion absent special reason to do so. 27 Rather it is that our first-person reasons for accepting (2) in themselves fall short of justifying it; they only do so in a context in which we are entitled to take it on trust that the necessary conditions are met, and thus that the required conclusion is true. We can thus say that premise (2) rests on the conclusion and so cannot provide support for it, at least not in the way the account requires. Against this it might perhaps be objected that it is sufficient to be entitled to discount the general possibility of meaninglessness, not anything more specific. And in an Appendix to his (1997a) Boghossian presented an account of how we can be justified in believing (2) for the special case in which C is a basic logical constant. The suggestion was that in such a case we can know premise (2) because doubt concerning the meaningfulness of such a term is self-defeating. (Some logical vocabulary is required to state the denial, so the denial states of itself that it is meaningless. This is not a contradiction but it would be pragmatically self-defeating to assert it.) He claimed that this is of more than merely pragmatic relevance. The suggestion would seem to be that one is in effect entitled to the presupposition that the preconditions of C being meaningful are satisfied and so to accept the relevant instance of the meaning disquotation schema 26 This is essentially the objection Wright (2000) makes to McKinsey-style reasoning. 27 In the terminology of Davies (2004) this would be a negative entitlement. 19 in this case. If we only need to cite this fact in explaining why we don't need to eliminate the possibility that C lacks a meaning, then perhaps it is unnecessary also to require an entitlement to believe M(C) valid if we are to be justified in believing (2). I think we can say a number of things in response. First, so far as Boghossian's argument goes the most that seems to follow is that as it happens we lack the expressive resources to entertain a doubt, which seems too parochial a fact about our concepts to explain our justification for (2). 28 Secondly, even if something stronger may be claimed, 29 it may be doubted whether the fact that doubt regarding a claim would be self-defeating is sufficient for us to be entitled to believe or trust that it is true. Perhaps if it could be claimed that it could not be doubted that our logical constants are meaningful then this could explain why we need not take the possibility of defeat seriously. Then given a default presumption in favour of meaningfulness we might have an explanation of our justification to instances of the disquotation schema, but the default presumption seems to depend on the implicit definition meeting certain conditions, which are precisely those needed to explain our entitlement to believe it successful. Finally, the fact remains that in judging that (2) is true one must presuppose that those conditions are met insofar as one's basis for that judgement does not eliminate the possibility that they are not. I would suggest that this is likely to remain true whatever particular account is given of privileged access compatible with Implicit Definition given that a defender of the template is not in a position to assume a notion of privileged access which gives us conclusive justification believing things like (2). If so then it seems that he will be forced to something like the view I have suggested or one similar enough to be open to the same sort of objection. If he thinks that an alternative account is possible he will need to provide it if he is to be in a position to claim to have explained any case of a priori knowledge. 28 See Jenkins (2008) for discussion. 29 Hale (2002) argues that for some basic logical rules we cannot doubt that they are valid. 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