In Defense of Semantic Holism

- In Defense of Semantic Holism -
 Brandom vs. Fodor/Lepore

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Introduction
    In this paper I propose to assess Jerry Fodor's and Ernest Lepore's (Fodor 2000; Fodor and Lepore 2005) arguments against conceptual role semantics (henceforth CRS). In the first section I present their main contention against those forms of CRS which hold that the internal role of a symbol(s) determines its content or meaning (henceforth CCRS). Their core argument is designed to establish the implausibility of all versions of CCRS, by showing how the latter is forced into an irresolvable dilemma concerning precisely to what the extent conceptual role determines conceptual content.  I follow Greenberg and Harman (2005) in arguing that their argument fails to establish that such implausibility obtains, showing that the dilemma that CCRS is allegedly forced into is a false one, and proceed to qualify some of their contentions.

           In the second section, I focus on Fodor and Lepore's (2005) arguments against a particular brand of CCRS in the inferential role semantics (henceforth IRS) advanced by Robert Brandom (1995, 2005). First, I take issue with Fodor and Lepore's claim that IRS is incapable to give a behavioral account of concept use, being forced to a quandary concerning underdetermination which renders the functional account of conceptual specification in terms of rule following  explanatorily vacuous. I then dispute their claims for semantic atomism and compositionality, waged against IRS and the latter's commitment to semantic holism. I refute the claim that IRS is incapable of explaining how concept acquisition is possible, on pains of circularity, and that as a result it sets insuperable obstacles for a theory of learning. My contention, following Brandom (2005), is that IRS can provide an account for those processes required for learning without  advocating compositionality. In other words, within the framework of IRS, all the standard features associated with learning obtain while endorsing a semantic holistic account, thus showing that semantic atomism is not the only plausible candidate for theorizing learning.

I - Semantic Black Boxes?

     One may characterize CRS as a thesis about semantics, or one about the philosophy of mind. In the former sense, the meaning of a linguistic expression is nothing but the systematic relations it bears to other expressions in the language. In the latter sense, the content of a mental state is nothing but the systematic relations it bears to other mental states. In both cases, these relations may be broadly understood to be informational, causal, inferential, or otherwise. This is important to note, since Fedor and Lepore reserve the name CRS for those theories which deliberately conflate the two levels of explanation, and so for them crucially information-theories are not a species of CSR, but actually in conflict with it. For them, it is the confusion between the mental and the semantic that is a "bad idea" wholesale, since it results in a view of conceptual content delivered entirely to an internalized symbolic economy, which results in creating spurious epistemic impasses for any theory of communication. Since information-theories do not depend on anything like a pragmatics of language delivered to an internalized system of inferences or rules, they don't have to run the epistemological gauntlet Fodor and Lepore deem fatal for CSR, in creating an insurmountable gulf for communication. It is the construal of this epistemic gulf, allegedly besieging CSR, that shall occupy me for the rest of this section.

       In both its semantic and mental aspects, CRS has it that the role that a symbol plays is to be understood in holistic terms, or what we might call a 'top bottom' approach: rather than construing content from the 'bottom up' taking it to be derived out of semantic primitives from which complex expressions are composed, CRS denies that content is intrinsic to any symbol or state prior to its use within a symbolic economy. In this regard, CSR is the likely position to hold for anyone who, following Quine or Sellars, adopts deflationary standards for representation, truth, or reference. More precisely, rather than construing representations as higher-order abstractions which derive their content or meaning from foundational semantic primitives, conceptual representations are to be construed as rules for relating symbols to other symbols[1].

         In this regard, notwithstanding Fodor and Lepore's reluctance to conflate issues of semantics with those of epistemology or psychology, it is instructive to note that CRS originates as a way to rework the problematic of representation in an epistemological context. Both Quine and Sellars are reacting to peculiar iterations of foundationalism, and they take the latter to be their primary targets. For the former, the main interlocutors were those in favor of the rationalist position according to which representational content was negotiated through the distinction between analytic and synthetic truths, as well as dubiously inflated conceptions of meaning, synonymy and reference[2]. For the latter, the main interlocutors were those empiricist forms of foundationalism that began by distinguishing that which was immediately given to the mind, from that which was added by the mind[3]. Although in its full scope, CRS needn't be aligned to the strong behaviorist bent of its forefathers, it should be stressed that the articulation between the semantic and mental aspects of CRS hinges precisely on whether epistemology ought to be thought about in continuity with such deflationary standards. Such an alternative has it that any theory of knowledge will not concerned with concept possession, but rather with a functional account of concept use or role. As Brandom puts it elegantly: "I accept what I take to have been a lesson Kant taught: to think of concepts as rules or norms we bind ourselves by... For us (post-) Kantians, the principal question does not concern our grip on concepts (e.g. are they clear and distinct?), but their grip on us." (Brandom, 2005, Pg. 334). And again, despite the pragmatic bent that Brandom's inferentialist program gives to what is a variegated assortment of positions under the label 'CSR', the core idea that remains in every case is that understanding representations in terms of conceptual role in the philosophy of mind is just the obverse of taking the semantic content of a symbol or expression to be defined by the role it plays to other symbols. In any case, in what follows I continue Greenberg and Harman's (2005) liberal use of the term CRS to understand "any theory that holds that the content of mental states or symbols is determined by any part of their role or use in thought." As indicated above, this needn't be constrained to inferential role, although it is the latter that will ultimately be my focus. Fortunately, nothing in my argument will depend on this difference in terminology, although I hope to have indicated why the discrepancy is philosophically grounded, and not just a stylistic divergence.

    That being said, Fodor and Lepore's main line of attack against CRS attempts to target those variants of CSR for which conceptual role constitutively involves something like the internal usage of terms, i.e. where having a concept would imply having internalized the systems of rules, inferences or implications tethered to such a concept. Such an economy would entail that the meaning of a symbol is holistically articulated, insofar as its content derives from the relations it bears to the other symbols in the theory. It is in this sense in which CSR stands for a semantic holism. The argument they offer is relatively straightforward: how is it possible for two people to ever share a concept, and so how is it possible that communication could ever take place, if it is thoroughly implausible that one's internalized system of inferences and implications, associated with a given word/symbol, is shared in its totality? Since the notion of a shared language becomes immensely problematic, so does communication as an intersubjective capacity. The argument is thus one which is simultaneously about communication and one about psychology; it is formulated in the following passage: "How can we use the form of words “It’s raining” to communicate to you our belief that it’s raining unless the word “raining” means the same to all of us? And, how can it mean the same to all of us if, on the one hand, its meaning is determined by its inferential role and, on the other hand, no two people could conceivably agree on all the inferences in which “raining” occurs (to say nothing of all the “correct inferences” in which it occurs)?" (Fedor and Lepore, 2005, pp 186). As interpreted by Greenberg and Harman, the genera gist of the argument that Fodor and Lepore provide can be synthesized as follows, qualifying their reconstruction for clarity (Greenberg and Harman, 2005, pp 28):

    The Argument for Epistemic/Semantic Opacity

  1) Empirical Prediction - For any pair of concept-mongers, S and S', the set of inferences/implications that they internally associate with a symbol x in a given language L are (likely) to be dissimilar.

With this in mind, CRS may pursue one of two possibilities. Either:

2)  For any given pair of symbols a and b in a given language L, a has the same conceptual content than b if and only if there is no internalized relation of inference/implication from/to a to/from another symbol (or set of symbols) c that is not an internalized relation of inference/implication from/to b to/from another symbol (or set of symbols) c.

Or

3) For any given pair of symbols a and b in a given language L, a has the same conceptual content than b if and only if there is a subset d of specifiable internal relations of inference/implication from/to a to/from another symbol (or set of symbols) c that is coextensive with a subset e of specifiable internalized relations inference/implication from/to b to/from another symbol (or set of symbols) c.

 If (2) obtains, Fodor and Lepore argue that:

(4a) It is likely that for any two concept-mongers S and S' whose concepts are articulated in the terms of a language L, no symbol x of L has the same conceptual role for S than it does for S'.

(5a) As a result, no two people ever mean the same thing or convey the same conceptual role, given that their thoughts/expressions lack the same content.

(6a) No people deploy the same intentional laws, and so CSR fails as a theory of communication, i.e. no two people ever share or understand another person's concepts.

   Although Fodor and Lepore take (5) and (6) to be thoroughly implausible, it must be said that they offer no independent argument for it. For a proponent of CRS could consistently maintain that we may be able to clarify exhaustively the conceptual role of a given symbol within our linguistic economy, however difficultly, through progressive interlocution (for example, perhaps through what Brandom calls 'deontic scorekeeping'). It seems possible two people might come to agree with respect to their use for a subset of symbols that they share the exact same role, however minimal such a subset might be (perhaps some primitive forms of mathematical concepts might be of this 'clear and distinct sort?).  This might be true, even if we ought to accept that for the most part we do not really 'agree' with each other on the basis of sharing the same concepts or not, and even if we might naively believe that we do.

           Indeed, nothing in the abovementioned argument indicates what it is precisely about epistemic opacity that renders agreement impossible; it simply entails that, strictly speaking, it is overwhelmingly possible concept-sharing is not a reasonable standard to base our theories of communication. Yet, the CRS-defender would insist, this has no bearing on our capacity to agree with others or not; Fodor and Lepore confuse agreement which is a matter of assent, with knowledge. Let us pause in this issue for a moment.

     The tacit premise at work here seems to be that agreement presupposes knowledge, i.e. one cannot agree to x if one does not know what x is. And since, if (1) obtains, such knowledge would be so remotely accessible, it would follow CRS delivers us into an epistemological black box for intersubjective conceptual knowledge, as a result of its semantic commitments. But, again, this needn't be the case. For one might insist that all agreement requires is that some suitably restricted set of shared commitments about the inferential role that a symbol bears be sufficient to mobilize agreement or disagreement, without for this reason, accepting that only such a subset is relevant for the meaning of the concept in question, i.e. assuming that premise (3) fails. Thus, one might claim, all that agreement/disagreement requires is that one might be capable of suitably isolating those inferences/implications that might be relevant for the concept determination that the users of the symbol may in a given context.

         Greenberg and Harman stress this point in consideration of color concepts; there it is clear that concept boundaries might be dissimilar between two subjects, and this doesn't preclude them from agreement "... the boundaries between what counts for them as red  or orange are slightly different and the boundaries between what counts for them as green and blue are slightly different. Still, they disagree about a color when John calls it red and Mary calls it green." (Greenberg and Harman, 2005, pp. 19)

           In any case, nothing in Fodor and Lepore's argument seems to give reasons for why such opacity in the sense defined would be so remotely inconceivable, or lead to such calamitous epistemic consequences, or such dire constraints for communicational practice. Greenberg and Harman present another related defense for CRS,  by distinguishing an unstated assumption that motivates their case. The assumption in question is the following one:

(1a) If all aspects of internal use are relevant to meaning and the aspects of one person's internal use are not exactly the same as those of another person's, then the two people do not mean the same thing by their terms.

         The that point Greenberg and Harman wish to stress by pointing this assumption out is that it is consistent to hold that although all aspects of internal use are relevant to determining conceptual meaning/content, the question of which aspect(s) bears on the meaning of a term can be taken to be a contingent matter relative to contextual conditions or utterance/use. This means that, for any given specifiable implicational/inferential relation that a symbol holds to another,  saying that such a relation is relevant to its meaning is not to say that in every case a variation in those relations will result in a change of meaning. By the same token, just because any modification in such relation might not result in a change of meaning in a given case, it does not mean that in every case such a variation will not result in a change of meaning, i.e. that the relation is irrelevant to the internalized conceptual content. The examples proposed by Greenberg and Harman are excellent: "To say that a given aspect of internal use is relevant to meaning is to say that there is a possible case in which a difference in that aspect makes for a difference in meaning, not to say that a difference in that aspect always makes for a difference in meaning. (Similarly, whether the number of students in a class is odd or even depends on the number of students in the class, but that does not imply that two classes with different numbers of students cannot both have an even number of students)" (Ibid, pp. 19). And of course, such a revision is completely compatible with the idea that certain uses might be relevant to the meaning of the concept in every case, i.e. it is true for every case that the concept odd cannot be taken to be applied to the same situation as the concept even, or decimal (understood in their standard definitional roles). This means that (2) above ought to be revised to read the following:

2')  For any given pair of symbols a and b in a given language L, and in a given dialogic circumstance p, a has the same conceptual content than b if and only if for p there is no contextually relevant internalized relation of inference/implication from/to a to/from another symbol (or set of symbols) c that is not a contextually relevant internalized relation of inference/implication from/to b to/from another symbol (or set of symbols) c.

  Once this is pointed out, it turns out that contextually irrelevant relations of inference/implication may be altered without thereby changing the concept's meaning. This is obviously not analogous to (3), since the irrelevance of a set of given relations for a concept is merely contextually defined. The question here becomes how to understand 'relevance' in Greenberg and Harman's sense more precisely. The following is a proposal for (Relevance):

(Relevance): For every inferential/implicational relation R from/to a given symbol a to/from another symbol (or set of symbols) c, there is a circumstance p, such that a change in R entails a change in the internalized conceptual content associated with a, such that if the relevant relation R is altered, one wouldn't count as using that concept.

        The requirement for (Relevance) allows one to stipulate about the role that seemingly contingent relations bear for CCRS. Interestingly, this issue seems proximally to be part of what motivates Fodor and Lepore's (2005) questions to IRS. They ask:

        "We’re also not clear what Brandom thinks about the status of utterly contingent inferences like “If it’s a plant in my backyard and it’s taller than 6 feet, then it’s a tree”. he does apparently endorse the idea that “[the concept-constitutive inferences] must include … those that are materially [sic] correct” (MIE, p. 657). But what he gives as examples are two he borrows from Sellars: “A is to the East of B” --> “B is to the West of A” and “Lightning is seen” --> “Thunder will be heard soon”. We find this puzzling since the first of these strikes us as arguably conceptually necessary (whatever that means) and the second strikes as arguably nomologically necessary (whatever that means). So even if we granted that both are concept-constitutive, we would still want to know whether clear cases of purely contingent hypotheticals are too; and, if they aren’t, how Brandom proposes to do without an analytic/synthetic distinction." (Fedor and Lepore, 2005, pp. 183)

     This is of course the core of the dilemma for CCRS for the choice between (2) and (3). Greenberg and Harman's suggestion is that we can accept both that every inferential relation is concept constitutive, that is to say relevant, while accepting that contingent inferences obtain in the sense in that such relevance is capable of altering conceptual constitution within specific context of use. Or put the point somewhat differently: even if we accept conceptual role determines meaning, this needn't entail that meaning is identical to conceptual role.  To return to our earlier example: that the concept even numbered classroom members may be correlated at a given time and context with a cardinal extensional determinant (say, two) as what specifies its conceptual content, such a determinant could change without necessarily altering the integrity of the concept, e.g. say two more class members arrive late.   With this in mind, Fodor and Lepore might nevertheless insist that in order to isolate those inferential relations that are context sensitive requires something from CCRS which no proponent of the theory has been prepared to satisfactorily give. Namely, they would require, as they do for IRS, an explanation of why and how are the relevant contextual circumstances which determine conceptual content in the use of a symbol defined. In other words, on which basis ought we determine that it is still a concept that we are using and not another? How do we know which inferential relations support which conceptual content at a given time and in a given circumstance, without defining something like analytic and synthetic properties?

  Translational accounts of meaning, for example, define that the meaning of an expression a in a language L is determined by the capacity to find a paraphrase/translation for the term in another language L', nothing is said about which relations come to bear in which circumstances. Thus, is if a plays a functionally equivalent conceptual role to an expression b in a language L', such that they may be translated one into the other, it will not follow that every difference will result in a difference in translation. This leaves the problem of how to construe the role of contingent inferences/implications/relations unanswered, even if as Greenberg and Harman claim, the strategy of the argument is merely meant to indicate that Fedor and Lepore would need quite a bit more to discount the breadth of positions associated with CCRS than their argument provides.

    That being said, the second horn of the dilemma, that is opting for premise (3), fares no better in Fedor and Lepore's eyes, for reasons we can surmise from what we've said above. Their main claim is that if (3) obtains, then the CCRS is forced to accept that:

 (4b) For every symbol a in a language L, its conceptual constitution is merely a subset of the inferential relations that it holds to other symbols in the language (or other languages); such that those relations that do not form a part of this subset can be said to be contingent as opposed to necessary.

(5b) Therefore, for every concept, we can distinguish between the set of semantically constitutive relations which are context-independent (analytic), and those which are context-determined but by the same token not semantically constitutive (synthetic). Both sets together make up the whole of conceptual role associated with any given symbol.

(6b) Therefore, CCRS is committed to the synthetic/analytic distinction.

      We have already seen how Greenberg and Harman reject this assumption in their rejection of premise (3). Namely, by disambiguating conceptual role from meaning, they leave it open that the relevance that any given inferential relation may have to concept constitute won't entail that such a claim is analytic, i.e. context-independent for concept alteration. Additionally, they point out that although traditional accounts of analycity, as castigated by Quine and others, have it that analytic relations/truths are a priori, while it clearly doesn't follow for CCRS that knowledge of the conceptual role for a given symbol is also a priori, even if its semantically constitutive. I won't belabor these points, since they have been dealt with elsewhere. In the next section I propose to examine a second roster of arguments offered by Fodor and Lepore, geared this time towards a specific variant of CCRS, namely Robert Brandom's inferentialist program.

II - In Defense of Semantic Holism

    We have already seen how Fodor and Lepore question CCRS as a plausible candidate for a theory of communication on the basis of what they take to be excessive demands for conceptual constitution, resulting in cases of epistemic opacity that vitiate their plausibility. In what follows, I focus on their arguments to extend this line of attack against a specific version of CCRS, namely inferential role semantics, which are designed to show the implausibility of the "top-bottom" approach favored by semantic holism. By the same token, I seek to indicate, following Brandom (2005), that their arguments in favor of semantic atomism fail, i.e. why their presumed defense of a "bottom-up" approach depends on an unpersuasive case against the semantic holist of an inferentialist bent. With regards to semantic atomism, Fodor and Lepore claim that:

        "Qua “bottom-up” theorists, we think something like this: for non-idiomatic expressions in productive languages, the meaning of a sentence is ontologically dependent on the meaning of its subsentential constituents. This is to say, at the very least, that in such languages the sentences have the contents that they do because their constituent expressions have the contents they do, and not vice versa. In fact, we hold this principle in a very strong form; on the one hand, the meaning of a sentence S in a language L must be computable by algorithm from the meanings of its constituents on pain of L being unproductive or S being idiomatic. On the other hand, we know of no reason why it should be possible (algorithmically or otherwise) to recover the mmeanings of the constituents of S from the meaning of S." (Fodor and Lepore, 2005, pp. 182)
  

       By parity of reasoning, in epistemic terms, it will follow that just the content of words is prior to the content of sentences, the content of mental states is prior to judgment, and therefore to the capacity to engage in explicit inferences of the sort IRS thinks constitutes the basis for semantic holism. Put differently, this can be expressed by saying that it is possible to have knowledge-of prior to having knowledge-that, where we should understand that the latter in fact depends or supervenes on the former, both nomologically or ontologically (Ibid).  And although Fodor and Lepore think that sentential knowing-that may plausibly be stipulated to enjoy such priority for cases of radical interpretation or translation. In fact, they go even as much to suggest that even language-learning might also exhibit such a priority.

         This might seem intuitively at odds with their championing of semantic atomism, but it needn't be so. For it is coherent to claim that there is a basic class of semantic constituents which form the epistemic bedrock of the language learner, and that these constituents are nevertheless sentientially constituted. All that the theory requires is that the subject be capable of deriving the content of derived complex expressions by projection from semantic primitives, as well as analysis of simple constituents, e.g. that learning word-content requires the capacity to have acquired the relevant sentence-contents. This would hold while insisting that the epistemic dependence of word-content on sentence-content does not entail the ontological/nomological-dependence of the latter on the former. Semantic holism, in their view, requires both claims; while semantic atomism is potentially open to the former, and necessarily closed to the latter. As it turns out, their argument will run on the grounds that projectibility and so learning actually seems impossible from a semantic holistic perspective. So they claim, Brandom fails to meet the difficult requirement they set for holism: "Brandom has to show that (and how) word meanings might be ontologically dependent on sentence meanings (rather than vice versa) in a language that’s productive and systematic." (Ibid).        

       Their first (peripheral) claim is to dispute the plausibility that any Gentzen-based semantic account for logical terms could serve as a model for lexical or conceptual analysis. Recall that such a framework begins by specifying general operational parameters for logical constants in terms of introduction and elimination rules, in order to then generalize these to circumstance and consequences of application for a given expression in a language (Brandom, 1995, pp 653). Just to use the simplest examples: the introduction rule for the logical-constant for conjunction "&" is "P, Q --> P&Q". Similarly the elimination rule for the same would be "P&Q --> P, Q", etc (Ibid).

       From the start, Fodor and Lepore protest that it is thoroughly unclear how to deal with the meaning of non-logical terms within such a framework, i.e. singular terms such as "tree" or "red", that are not logical constants. That is, they find it utterly perplexing that one should expect to define introduction or elimination rules for these terms in natural languages, and fear that any such attempt might relapse into question-begging forms of verificationism or surreptitious identification procedures, e.g. "x is a tree iff it is a tree", etc (Fodor and Lepore, 1995, pp 183).

             Although this criticism is largely tangential to their main line of attack, we should preemptively notice that it actually misses the point of IRS, which requires that there is no content for a logical constant or singular term that is not definable in terms of its logical conditions for implication and consequence within a language. Therefore, the definition of logical constants is nothing but the grounds on which any such term might acquire any meaning whatsoever, by entering within the inferential economy. Thus, the 'top-bottom' approach advocated by IRS is crucially not concerned with the formal semantics of specified terms within an already given language, but rather with giving a philosophical semantics where the task is to define generally how specifiable items must function in order to be counted as semantically contentful for any language user. The former concerns questions of composition/decomposition and association for the computation of semantic value on the background of an accepted notion of semantic content, while the latter concerns the procedural or pragmatic consideration of how semantic values are correlated with semantic interpretants at large, and not just a specified subset. The latter concerns the articulation between questions of meaning and understanding that, following Dummett, IRS deems essential; Fodor and Lepore elide the distinction.  Brandom's own disambiguation of this distinction is highly illuminating: "I am recommending a “top-down” order of semantic explanation, which talks first about what sentences express, and only later about the contribution that the presence of individual words makes to what sentences containing them express. The context is the project I have been calling “philosophical” semantics, by contrast to “formal” semantics. The former concerns how expressions have to be used, or how items must function, in order properly to be thought of as semantically contentful. The latter concerns how, once semantic interpretants of some sort have been associated with some expressions or other items, they can be understood as determining what semantic interpretants are associated with others." (Brandom, 2005, pp 332)

         In short, Brandom insists that while formal semantics can obviate the philosophical-semantic issue about how to coordinate questions of meaning with questions of understanding, and thus the question of how this can be obviated by the formal semantics since it rests on pre-established notion of semantic content. Here the inferentialist focus on the pragmatics or use conditions which are proper to the investigation of philosophical semantics belie the worries that Fodor and Lepore think must apply when defining possession conditions; to 'have' a concept is nothing but to be able to use it and the task for the philosopher then becomes to specify what it means to use the concept correctly in terms of the user's doxastic commitments, e.g. "... to define the inferential role of an expression "&"... one thereby specifies that anyone who is committed to P and committed to Q, is thereby to count also as committed as to P&Q, and that anyone who is committed to P&Q is thereby committed to both P and to Q" (Brandom 2000, pp 62)  In this regard, the threat of having to run a specter-invoking slew of verificationist standards come to bear by running a Gentzen-style semantics is moot: the deflationary strategy pursued by IRS renders these terms explanatorily irrelevant, and explains content-preserving use in terms of inference rather than reference, or truth, and so irrespective or any stipulated verification procedures. And although terms such as 'true' or 'reference' might come to bear within the scope of a well-defined formal semantics, as we suggested above,  Brandom insists in that they play no part in a philosophical semantics of the sort he is proposing for his IRS. In response to Dummett, he claims: "Formal semantics must be done in an expressively powerful meta-language, and in that context it can be all right to appeal to the expressive capacities of terms such as ‘true’ and ‘refers’. Doing so only becomes a problem when one seeks to appeal to them at the outset of one’s explanatory enterprise in philosophical semantics...My explanatory deflation of ‘true’ and ‘refers’, based on an anaphoric account of their expressive roles, disqualifies them from playing a certain kind of explanatory role in philosophical semantics." (Brandom, 2005, pp. 343)

     Incidentally, the issue concerning the split between possession and use conditions maps back onto issues concerning the status of contingent inference within CCRS, within the inferentialist program. In continuity with their earlier attack, Fodor and Lepore argue that the status of contingent sentences remains opaque in Brandom's account at a loss for a analytic/synthetic distinction. I believe Brandom could respond to these worries much like Greenberg and Harman do, as we surmised above, by simply disambiguating between meaning and inferential role; so that contingent sentences may be said to express the subset of those relevant relations/conditions which are context-sensitive, i.e. which although relevant, as all inferences are, to concept constitution, do not for this reason alter the meaning of the concept in every context of use. Of course, the strict inferentialist couldn't accept of contingent inferences if by these we mean that in every such context an alteration of such relation would not result in meaning change for the concept at hand. But this does not require reactivating the synthetic/analytic distinction, since contingent inferences would be simply be defined in terms of their role within context-sensitive contexts, without compromising their relevance for concept constitution. Since there is no difference between conceptual necessity and nomological/ontological necessity for Brandom, the argument we pointed out above deployed as a general strategy for CCSR fails even in its qualified form against IRS. This being said, it goes without saying that to stipulate that purely contingent sentences within an inferentialist account would be trivially true, since IRS systematically excludes any content that would be considered stricto sensu irrelevant for conceptual constitution. As Brandom himself puts it: "Making It Explicit is clear about not treating any inferences essentially involving an expression as in principle semantically irrelevant, in the sense of having no bearing on what one is saying by using that expression. This is a radical policy, which requires giving up many things we have become accustomed to say about conceptual content. Indeed, in a certain sense it involves in the end giving up the idea of conceptual content – since the essential contrast between inferences that articulate the contents expressed by the use of locutions and those that do not goes missing." (Ibid. pp 333)

       As it turns out, the distinction between the two kinds of semantic explanation comes to bear more definitively at a later stage of the debate, as we shall see. Before we go on to assess this, however, we should briefly diffuse one further argument that Fodor and Lepore make against Brandom's pragmatic account of conceptual competence, as opposed to accounts to conceptual use. They argue that any such account that privileges 'know-how' in describing one's conceptual abilities one is lead to a serious underdetermination problem with respect to which rules a specific occasion of overt behavior corresponds too. This objection should be taken to be tacitly supporting the claim against the plausibility of conflating the epistemology of translation and the psychology of leaning with semantics.  The argument may be reconstructed for clarity as follows (Fodor and Lepore, 1995. pp 185):

The Argument Against Behavioral Explanations of Intentional States

1) For any given overtly observable interpretable behavior where it might be said "S acts in accordance with rule R1" it follows that such behavior also is in accordance to any rule R2 that is equivalent to R1, i.e. to any rule that shares the same inferential content.

2) It is possible for any behavior-displaying agent to act in accordance to a rule without being thereby consciously aware of which rule they are acting in accordance to.

3) Inferential-role semantics has it that for any case where one observes that "S acts in accordance to R1", then irrespective of how many different rules may be said to be equivalent to R1, it is certain that their behavior  accords with R1 and not some stipulated equivalent rule R2, i.e. the underdetermination problem fails.

C1) Therefore, IRS proponents argue inconsistently since they claim that the specific rules which define concept use are simultaneously underdetermined by overt intentional behavior, and that such behavior only accords to some (arbitrary) rules.

C2) Therefore, IRS fails to account for the intentional content of mental states and concept use in terms in terms of overt behavior.

   The argument above conflates three crucial distinctions that Brandom disentangles in his account, namely: the capacity to accord to rules, the capacity to grasp rules, and the capacity to follow rules (Brandom, 1995, Chapter 1). The former is resolutely a case a non-intentional behavior which corresponds to what Sellars would have called sentience, but which also applies to non-organic capacity to register a semantic stimulus. The second and third terms pertain to beings who are already within the space of reasons and so qualify as sapient. Full-blown sapient creatures follow rules insofar as they undertake specific doxastic commitments, and can be challenged to justify and revise their beliefs by engaging in the game of 'giving and asking for reasons'. Machines, on the other hand, merely accord to rules, since they possess no intentional states, at least in principle. Once this is pointed out, it is easy to see why the argument offered by Fodor and Lepore falls apart without much trouble. Premise (3) can be rejected right off the bat; accordance admits un underdetermination of conceptual content, while grasping or following does not.  Non-sapient creatures, at a loss for intentionality, might be said to accord to norms, and perhaps an indefinite number of them, i.e. the underdetermination problem obtain, but none the worse for it. Accordance is transparent to the substitution of equivalents. On the other hand, sapient, intentionality-endowed creatures can be said to grasp or follow rules if and only they can be challenged to give reasons and justify their commitments, and in this territory equivalence substitution becomes (progressively) opaque. Thus while grasping an implicit norm (say, by infants) merely requires the capacity to evaluate and correct the functional dispositions one and others exhibit, following an explicit rule requires that such a capacity be extended to the point where it becomes possible to formulate what one is acting in accordance to. This entails competence in deploying conditional vocabulary, among other things.

           Observers might progressively learn, keeping track of their deontic scorekeeping, narrow down potential candidates until the intentional agent becomes capable of expressing his/her implicit following of norms in the form of an explicit rule. That being said, contrary to what Fodor and Lepore stipulate, although it is correct to say that salient behavior may accord to a variety of rule-candidates (both in intentional and non-intentional agents), social dialogic procedures for cross-examination allow one to specify and disambiguate which rules the agent is following, if they so happen to achieve this capacity. But this is a distinctively rational capacity proper to those subjects fully imbedded in the logical space of reasons, while mere accordance is weaker, exhibited by non-sentient beings as well as sentient and sapient beings, all in the same functional level of explanation. And although we certainly must model functional accordance in the same intentional terms that we in which we frame our normative vocabulary this is not to confuse the two levels by endowing it with an ontological status, i.e. it does not mean that we must attribute mental states intentional status to merely accordance-exhibiting behavior[4].  

     The final point I wish to stress in as brief a manner as possible concerns Fodor and Lepore's central attack against semantic holism in favor of semantic atomism. The core of the issue, they argue, is that semantic holism cannot explain how learning takes place, since by default it is not committed to semantic compositionality, i.e. in rejecting the latter is becomes impossible to account both for the projectibility and the systematicity of language, these being necessary features for any semantic theory that purports to explain how indefinitely many new compounds with determinate semantic values may be composed from semantic primitives. In other words, Fodor and Lepore contend that compositionality is necessary to account for how syntactic combinations with fixed semantics values can generate complex expressions which are also semantically determinate by being systematically related to those initial combinations. But the real stumbling block for IRS that results from this is in their estimation finally one about epistemic productivity. Compositionality is meant to explain how subjects can understand and compose indefinitely new expressions in a given language, by attaining mastery of the modes of formation and rules proper to the simple expressions in the language (what may perhaps be called 'lexical primitives'). Therefore, if such productivity cannot be accounted for, then it will not be clear how it is that subjects are ever in a position not just to learn new expressions in the language, but how they can learn at all. Since ""knowing-how" doesn't compose", the inferentialist owes us an account of how we can even begin to acquire and use new concepts if not on the basis of fundamental lexical primitives that ground the subject's capacity to respond to whatever circumstances might he/she happen to find themselves in. Fodor and Lepore argue that since IRS can't account for compositionality in using epistemological criteria to determine conceptual mastery, they will fail to explain the productivity required for learning:  "You can know how to recognize good examples of pets (in favorable circumstances) and how to recognize good examples of fish (in favorable circumstances) without having a clue how to recognize good examples of pet fish in any circumstances (for example, because the conditions that are favorable for recognizing fish may screen the conditions that are favorable for recognizing pets; or vice versa). We think, and we have said loudly, frequently, but to little avail, that this line of argument generalizes to the conclusion that there can be no epistemic conditions on concept possession. If that’s right, the question how an Inferentialist can account for compositionality is seen to be the crux that he must resolve." (Fodor and Lepore, 2005, pp 189).

    The argument above suggests the following reasoning:

      The Argument for Compositionality

1) IRS construes conceptual mastery in terms of capacity to reliably respond in the appropriate circumstances (circumstances where we are 'warranted' to respond in such a determinate  way).

2) A given subject S can be reliable in responding to two different circumstances p and q, without for this reason being capable of reliably responding to a compound situation p and q.

C1) Therefore, it is possible for a subject S to have the concept x that corresponds to p, and concept y that corresponds to q, without for this reason having the concept z that corresponds to p and q, i.e. the semantic value of "x and y" is not computable from the semantic values of the constituent concept x and that of the constituent concept y.

C2) Therefore,  reliable responsive dispositions are not compositionally generalizable.

5) Any semantic account suited to give a theory of learning requires that one be able to explain how a subject S may come to acquire/learn composite concepts on the basis of simpler ones, i.e. it will need to explain the projectibility and systematicity of language.

6) The capacity to explain projectibility and systematicity requires that we explain concept acquisition/learning compositionally.

C3) Thus, any account that construes conceptual-possession in epistemic terms, and in particular restricting the latter to the capacity to issue reliable differential dispositions, will necessarily fail to give a theory of learning.

C4) Therefore, IRS will not be able to account as a theory for concept learning.

         Notice that the argument above does not say anything about holism; it is left open that a behavioral account of concept possession as concept use might fail even if endorsing semantic atomism. The argument is thus to be supplemented by the claim, suggested strongly by (C2), that productivity demands compositionality, and the latter the priority of subsentential semantics to sentential semantics, i.e. it will require endorsing a 'bottom-up' approach to formal semantics. And although, as we saw above, Fodor and Lepore reserve judgment about whether semantic atomism obtains or not, they insist that either atomism or at least some qualified 'molecularism', as Dummett calls it, would help meet the demands of compositionality not met by an inferentialist account. Namely, they argue that "...if molecularism is true, then the content of a concept would not be sensitive to all the inferences it’s involved in, (or even to all the “correct” inferences it’s involved in) but only to the ones that belong to the same “molecule” that the concept does." (Ibid: pp. 190) Yet because they think that even molecularism requires a distinction between analytic/synthetic expressions, strict semantic holism won't do. This is clear if we keep in mind that the molecularist alternative would cash the compositionality requirement in terms of how 'molecular', rather than atomic primitives, determine the semantic values of complex expressions in the language. As a result, Fodor and Lepore seem to suggest that either IRS runs with something like the molecularist/atomist alternative, but thereby reactivate the analytic-synthetic distinction, or else they remain tethered to strict holism in which case they become incapable of accounting for compositionality, and thus fail to account for learning.

     As it turns out, Brandom's (2005) response to Fodor and Lepore allows us to see where precisely the argument for compositionality goes wrong. In his more recent work on formal semantics, Brandom shows how one can account for systematicity and projectibility, and so for productivity, without semantic atomism/molecularism of the sort that Fodor and Lepore deem inescapable. In order to do so, he accounts for logical, modal, and non-logical expressions in terms of incompatibility semantics: for set of sentences s that content of s is the set r of all sentences that are materially incompatible with s (Brandom, 2005, pp 335-336). A given sentence p entails q if and only if the set of those sentences that are incompatible with q are incompatible with p. The negation of p is the set of sentences s that follow from the set r of all sentences incompatible with p. As a result, that which is incompatible with not-p can change, while the semantic value of p remains fixed. As Brandom accordingly develops: "One consequence is that one can alter the semantic interpretant of not-p (what is incompatible with it), while holding fixed the semantic interpretant of p (what is incompatible with it), by altering what is incompatible with something, r, that is incompatible with p. So the semantics does not have the semantic sub-formula property; one cannot compute the semantic value of a compound expression such as not-p as a function of the semantic value of its component, p. In this specific sense, it is a holistic semantics." (Ibid, pp. 336)

     Yet the semantic value of logically compound sentences are derived from the semantic values of less complex sentences, and in this sense it constitutes a form of 'molecularism'. However, it is the value of many (and in the limit case all) of the simpler sentences in order to compute this, and not just those which are subformulae of the compound sentence the semantic value of which is in the process of being computed. Brandom's retort in this regard is definitive and necessary to disassociate learning from compositionality, and deserves to be quoted in full here:

 "The semantics is projectible and systematic, in that semantic values are determined for all syntactically admissible compounds, of arbitrary degrees of complexity. It is learnable - at least in principle, putting issues of contingent psychology aside, in the ideal sense we have been working with. For the capacity to distinguish the incompatibility sets of primitive propositions is, in the context of the semantic definitions of the connectives in terms of incompatibilities I have offered, sufficient by algorithmic elaboration for the capacity to distinguish the incompatibilities of all their logical (including modal-logical) compounds - and hence for the practical capacity to distinguish what is a consequence of what.

          What semantic projectibility, systematicity and leanability-in-principle require then, is not semantic atomism and compositionality, but semantic recursiveness with respect to complexity. That is entirely compatible with the semantics being holistic, in the sense of lacking the semantic sub-formula property, which is the hallmark of atomism and compositionality. " (Ibid: pp 336-337)

 This allows us to see precisely what is wrong in Fodor and Lepore's argument; namely premise (6) as tacitly supported in the jump from (C1) to (C2), i.e. the claim that if the semantic sub-formula property fails, and hence if compositionality fails, then projectibility and systematicity must also fail as well. What Brandom allows us to see is that one can agree in that the semantic value of complexes is determined from simpler constituents, without for this reason having the semantic value of such complex expressions be computable from its corresponding primitives, i.e. it explains projectibility and systematicity without the semantic sub-formula property. That a semantics modeled on incompatibility relations may explain productivity without compositionality entails that the requirement that learning require compositionality, and by extension semantic atomism, is a false one. Recursivity is weaker than compositionality, but none the worse for it, all it requires is the abandonment of an artificially constrictive property. At this juncture, one might wonder if there's any good reason to reserve the name compositionality for only those semantic models that strictly obey the semantic sub-formula property, although the stakes of the debate become mostly terminological at this juncture. For it is clear that while Fodor and Lepore's examples show that compositionality, in their terms, might in fact fail to obtain in certain cases, it certainly does not show that it cannot obtain in others. For it could be that a given concept behaves compositionally, without for this reason suggesting that one's semantics cash all concept-mastery out in terms of compositionality as a necessary condition. 

     On any account, what this entails is that while IRS has it that inferential role exhausts conceptual content, mastering inferential role requires more than the mere capacity to reliably respond to the relevant stimuli in cases of perceptual recognition. For while it is perfectly true to say that one might cannot compute the value of "p and q" from the semantic values of p and q, if even if one knows in which circumstances to respond to situations where p and q are warranted use by recognition, it doesn't follow that if one were to know the inferential role of p and q one wouldn't know the inferential role of p and q. As we have seen, inferential role, construed around an incompatibility semantics, requires that one be able to determine recursiveness "between levels", i.e. one needs to look at many or all of the lesser complex sentences inferentially related to a given sentence, and not just those in the sub-formulae of the compound (Ibid; pp. 336). Inferential competence exceeds strict compositionality requirements, while manages to meet productivity requirements Thus, the claim that because reliable responsive dispositions don't compose when recognizing ideal exemplars for concepts does not entail anything of importance. And with this in mind, one might insist that if one were to master the inferential role of p and q one would have thereby necessarily mastered the role for 'p and q' without for this reason endorsing the semantic sub-formula property, or letting go off semantic holism.

         Finally, although inferential competence must be construed as a kind of differential disposition in any case, what the post-Sellarsian CRS enjoins us to do is precisely to articulate a multi-leveled semantics capable of distinguishing between different kinds of dispositional transitions. Brandom follows Sellars (1954) in distinguishing between: a) perceptual/recognition (from non-sentential to sentential; language-entry transitions), b) intra-sentential (sentence input to sentence output), and c) action-producing (sentential inputs to non-sentential outputs; language-exit transitions). Inferential role comprises the articulation between all three levels while Fodor and Lepore's argument shows only that compositionality fails on occasion at the first level[5]. Once these three levels are in place, IRS is capable of  laying a multifaceted account of the possible kinds of inferential connection between sentences: 1) commitment-preserving inferences that generalize deductive inferences to material occasions; 2) entitlement-preserving inferences that generalize inductive inferences to material occasions; and 3) incompatibility entailments that are modally robust (Ibid, pp. 354). This is not the place to attempt to unpack the fine-grained details of such a semantic account or its feasibility, but it goes without saying that Fodor and Lepore's construal of the relevant reliable responsive dispositions in terms of recognition, and so restricting itself to the first level of perceptual reliability, for their claims about compositionality. I hope to have showed to some extent that these claims fall short of their pretentions, and so that the case against IRS and semantic holism fails as well.

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[1] Brandom, Robert, Making it Explicit, Harvard University Press, 1998.

[2] Quine, W.V, Word and Object, MIT Press, 1964.

[3] These constitute, albeit not exclusively, iterations of what Sellars calls 'The Myth of the Given'.

[4] As Peter Wolfendale has put it elegantly, in the order of evolution we progress from accordance, to grasping, to following. In the order of explanation we go from following, to grasping, to accordance.

[5] This multi-layered account is crucial for the development of monotonic and non-monotonic inferences.