How to be a hyper-inferentialist

Abstract

An “inferentialist” semantic theory for some language L aims to account for the meanings of the sentences of L solely in terms of the inferential rules governing their use. A “hyper-inferentialist” theory admits into the semantics only “narrowly inferential” rules that normatively relate sentences of L to other sentences of L. A “strong inferentialist” theory also admits into the semantics “broadly inferential” rules that normatively relate perceptual states to sentences of L or sentences of L to intentional actions. It is widely thought that only the latter of these two sorts of semantic theories is at all viable. I argue here that the opposite is so. Negatively, strong inferentialism is viciously circular: including rules into the semantic theory that relate perceptual states to sentences of the language requires us to appeal, in individuating those perceptual states, to the very meanings for which we are supposed to be inferentially accounting. Hyper-inferentialism does not face this problem because it does not appeal to any nonlinguistic states. Positively, though hyper-inferentialism is widely thought to be a theoretical non-starter, I argue here that it is a genuine theoretical possibility insofar as it essentially includes cross-perspectival inferences, inferences along the lines of the one from sentences “The ball is in front of n,” “The ball is red,” and “The lighting is good” to sentence “n sees that the ball is red.” I make the further exegetical claim that Brandom (Making it explicit, Harvard University Press, Cambridge, 1994), though unanimously taken to be a strong inferentialist, is in fact a hyper-inferentialist.

1 Introduction

An “inferentialist” semantic theory for some language L aims to account for the meanings of the sentences of L solely in terms of the inferential rules governing their use. A “hyper-inferentialist” theory admits into the semantics only “narrowly inferential” rules that normatively relate sentences of L to other sentences of L. A “strong inferentialist” theory also admits into the semantics “broadly inferential” rules that normatively relate perceptual states to sentences of L or sentences of L to intentional actions. Brandom’s (1994) semantic inferentialism is widely taken to be, according to these definitions, a strong inferentialist, rather than hyper-inferentialist theory. I argue here that this is not so. Made explicit, Brandom’s theory is a hyper-inferentialist, rather than a strong inferentialist, theory. I argue further that this is a good thing, since strong inferentialism is viciously circular: including rules into the semantic theory that relate perceptual states to sentences of the language requires us to appeal, in individuating those perceptual states, to the very meanings for which we are supposed to be inferentially accounting. Hyper-inferentialism does not face this problem because it does not appeal to any non-linguistic states. Though hyper-inferentialism is widely thought to be a theoretical non-starter, I argue here that it is a genuine theoretical possibility insofar as it essentially includes cross-perspectival inferences, inferences along the lines of the one from sentences “The ball is in front of n,” “The ball is red,” and “The lighting is good” to sentence “n sees that the ball is red.” This inclusion of cross-perspectival inferences, I argue, enables hyper-inferentialism to not only be a genuine theoretical possibility for the inferentialist, but, indeed, the only theoretical possibility.

2 Brandom’s purported “strong inferentialism”

In Making It Explicit, Brandom develops what he calls an “inferentialist” theory of meaning, a theory of meaning according to which the meaning of a sentence is understood not in terms of its representational adequacy conditions but in terms of the inferential relations that it bears to other sentences. Towards the end of Chap. 2, he distinguishes between three grades of inferentialism (1994, p. 131):

Weak Inferentialism: Inferential articulation is necessary for specifically conceptual contentfulness.

Strong Inferentialism: Broadly inferential articulation is sufficient for specifically conceptual contentfulness—that is, that there is nothing more to conceptual content than its broadly inferential articulation.

Hyper-Inferentialism: Narrowly inferential articulation is sufficient for conceptual contentfulness of all sorts.

Weak inferentialism, Brandom thinks, is a basically uncontroversial thesis that nearly everyone, with the exception of some hardcore representationalists like Fodor (1998), accepts. Given the way Brandom principally uses the term “inferentialism,” according to which inferentialism is incompatible with representationalism, “weak inferentialism” is not actually a form of inferentialism, since it is compatible with thinking that inferential and representational adequacy conditions are equally explanatorily basic or, indeed, even that representational adequacy conditions are basic and that inferential relations necessarily follow from these conditions.¹ So, the only grades of inferentialism that are aptly called “inferentialism” at all are strong inferentialism and hyper-inferentialism. According to these three definitions, the distinction between strong inferentialism and hyper-inferentialism amounts to whether the “inferences” invoked in the semantic theory are “inferences” in the broad sense of the term or “inferences” in the narrow sense of the term. Brandom then claims to be defending strong rather than hyper-inferentialism (1994, p. 132).

For the moment, I will leave aside what Brandom actually says in drawing the distinction between the broad and narrow sense of “inference,” and consider only what commentators generally take this distinction to be. Here is the standard way in which the distinction is drawn, from Wiess and Wanderer’s (2010) introduction to the definitive anthology of critical essays on Brandom’s work:

Both hyper- and strong-inferentialist agree that spelling out both inferentially sufficient conditions for, and inferentially necessary consequences of, asserting a claim, together with the propriety of an inference from one to the other, are sufficient for determining the claim’s content. They differ in how they conceive the inferential articulation, with the strong-inferentialist allowing for a more relaxed conception of the relevant notion of inferential here.

One difference concerns the possible inclusion of non-inferential circumstances and consequences as part of the claim’s inferential articulation. By way of illustration, consider the claim ‘this traffic light is red’. The appropriate circumstances of application of this claim include the visible presence of a red-coloured traffic light. This circumstance is non-inferential, in the sense that the circumstance is not itself an act of claiming. The connection between such non-inferential circumstances of application and the inferential consequences is, according to the strong-inferentialist but not the hyper-inferentialist, an inferential connection (p. 9).

According to Weiss and Wanderer, inferential relations, on the broad or “relaxed” conception, can include “inferential” relations that relate non-linguistic perceptual circumstances—for instance, a red-colored traffic light’s being visibly present to a speaker—to linguistic circumstances—for instance, that speaker’s making the claim “This traffic light is red.” On this way of distinguishing between “strong” and “hyper-” inferentialism, whereas the hyper-inferentialist includes in their semantic theory only properly inferential relations between claims, the strong inferentialist can include in their semantic theory “inferential” relations between claims and non-claims.² Almost everyone who talks about Brandom’s “inferentialism,” sympathizers and critics alike, takes it to fall on the “strong” side of this demarcation.³

A sampling of the commentaries on Brandom’s “strong inferentialism” reveals a common thread: strong inferentialism is inferentialism improperly so-called. Because there are, as an essential element of the theory, rules governing entry-moves that are not rules of inference, properly so-called, “inferentialism” or “inferential role semantics” is a somewhat misleading name for the theory. Here’s just a small sampling of this common thread. Maher (2012), who claims that the “big idea” of Brandom’s account of the content of assertions is to “expand our conception of the rational or inferential role of assertion beyond its relation to other linguistic acts,” thereby suggests that we may speak of the “rational role” of an assertion, rather than its “inferential role” (p. 29). Peregrin (2014), who tells us that, in addition to knowing how sentences “can be correctly played within the game of giving or asking for reasons in response to utterances,” speakers must also know how “they are correctly used also vis-à-vis nonlinguistic circumstances,” thus adds that, while he follows Brandom in using the name “inferentialism,” he isn’t fully satisfied with this name, since the theory essentially includes “inferences” that are “not really inferential in any straightforward sense of the word” (p. 37). Williamson (2009), who says that an inferentialist who appealed only to narrowly inferential roles “could not hope to explain how many words refer to extra-linguistic objects, or how language is used in interaction with the extra-linguistic environment” (p. 137) says that, by the inclusion of “ ‘language-entry’ rules that connect perceptual states to moves in the language game,” inferential roles are “generalized as conceptual roles” (p. 138). Kemp (2018), in giving as an example of a “language-entry rule” one’s “ ‘inferring’ (in a certain extended sense) the propriety of ‘It’s red’ from a certain perceptual situation” (p. 82), puts “inferring” in scare quotes, noting parenthetically that the term is being used “in a certain extended sense.” Making this shared sentiment explicit, Lance (1997) writes,

I think Brandom at times misrepresents his own position a bit by calling it inferentialist. ...[F]ollowing Sellars, Brandom allows for language entrance and language exit moves in his account of content and these are no less basic than are inferences proper (p. 182 n2).

We may thus use the following test for distinguishing whether a view is an instance of strong inferentialism or hyper-inferentialism: if one is a strong inferentialist, one’s position is not very well-represented by the term “inferentialism.” If one is a hyper-inferentialist, on the other hand, one’s position is well-represented by the term “inferentialism.”⁴ Now, I have picked out a few representative examples, but I could have picked out several more; nearly everyone who discusses Brandom’s view takes it to be a “strong inferentialist” rather than “hyper-inferentialist” view according to the test I have just laid out.

3 The shape of a “strong inferentialist” theory

Let me now lay out the basic shape of this “strong inferentialist” view widely attributed to Brandom. On an inferentialist picture, strong or hyper, the meaning of a declarative sentence of a given language is to be understood in terms of the rules governing its assertoric use, where particular acts of assertorically uttering it are thought of as “moves” in what Brandom calls “the game of giving and asking for reasons” (1994, p. xviii). The basic move in the game, made by assertorically uttering a declarative sentence, is the making of an assertion, or, in Brandom’s preferred terminology, the making of a claim. The meaning of an empirically significant sentence, for instance, the sentence “The ball is red,” is understood, on the strong inferentialist picture, in terms of the rules governing three basic categories of moves that can be made in a linguistic practice⁵:

• 1. language-entry moves

• 2. language-language moves

• 3. language-exit moves

Members of the middle category, language-language moves, are the simplest to understand, and are usually the go-to examples when starting to explicate strong inferentialism. For a given claim, the language-language moves are the narrowly inferential moves between this claim and the other claims. The goodness of such moves are articulated in terms of downstream and upstream inferential relations. Downstream, making the claim “The ball is red” commits one to the claim “The ball is colored,” precludes one from being entitled to the claim “The ball is green,” commits one who is also committed to claim “The cube is pink” to the claim “The ball is darker than the cube,” and so on.⁶ Upstream, making the claim “The ball is scarlet” commits one to the claim “The ball is red,” making the claim “The ball is green” precludes one from being entitled to the claim “The ball is red,” and so on. These normative relations articulate the significance of the claim “The ball is red” insofar as it is normatively related to other claims that can be made with the assertoric use of other sentences of the same language, such as “The ball is colored,” “The ball is green” and so on. It seems, however, that if this were all there was to it, then we would not account for the fact that “red” expresses an empirical concept—a concept that is essentially such that it can be non-inferentially deployed in perception. The strong inferentialist thought is that, in order to accommodate this aspect of the meaning of “red,” there must be, in addition to language-language moves, language-entry moves.

Language-entry moves connect moves in the game of giving and asking for reasons, assertions, with perceptual circumstances that are not themselves moves in the game. For instance, take a look at the following red ball:

Seeing this red ball is a perceptual circumstance such that, when you’re in this circumstance, you’re entitled to the claim “The ball is red.” The move from your being in this perceptual circumstance to your making the claim “The ball is red” is not an inference, since your being in this perceptual circumstance is not a claim. Nevertheless, according to the strong inferentialist, it is still, in an important sense, rule-governed. Specifically, it is governed by (something like) the following rule⁷:

Language-Entry Rule: If $\alpha$ is in the perceptual circumstance of seeing a red ball, then $\alpha$ is entitled to the claim “The ball is red”

Strong inferentialism permits such rules into the semantic theory. On a strong inferentialist theory, we have language-entry rules like the one above in addition to language-language rules such as the following:

Language-Language Rule: If $\alpha$ is committed and entitled to “The ball is red” and $\alpha$ is committed and entitled to “The cube is pink,” then $\alpha$ is entitled to “The ball is darker than the cube.”

There is a crucial difference between this language-language rule and the language-entry rule above it. This rule relates a player’s being committed and entitled to two claims to their being entitled to another claim. The one above it relates a player’s being in a certain perceptual circumstance to their being entitled to a claim. On strong inferentialism, this is precisely the sort of “broadly inferential” relation that we permit in our semantic theory. The thought motivating strong inferentialism is that we must permit such “broadly inferential” relations into our theory in order to explain how it is that words such as “red” are essentially such as to be used non-inferentially in perceptual responses such things as the above red ball. But there is a fundamental problem with any inferentialist theory that appeals to such rules.

4 The problem

The strong inferentialist, qua inferentialist, is committed to the claim that the content of a predicate such as “red” is to be understood in terms of the (broadly) inferential rules governing its use.⁸ We have now spelled out the strong inferentialist semantic theory in such a way that it includes the rule that if one is in the perceptual circumstance of seeing something red, then one is entitled to a claim of the form “x is red.” Such language-entry rules, are, in the words of Lance (1997), “no less basic than are [rules governing] inferences proper” in accounting for content. What, however, are these “red things” of which we speak here? They are, of course, the things that are red rather than, say, blue or yellow. But what is it for something to be red rather than blue or yellow, or rectangular for that matter? I take it that anyone who possesses the concept of being red knows the answer to this question. After all, to possess the concept of being red just is to know what it is for something to be red. I take it, however, that one can have this knowledge and not be prepared to articulate it. That is indeed the case for most speakers of English for whom this knowledge is implicit, manifested in their competence in using the word “red,” rather than explicit, articulated in a theoretical account of the concept expressed by that word. Such an account, however, is precisely what the inferentialist is committed to providing. The inferentialist project is to articulate the conceptual content of “red” in terms of the rules governing its use, for instance, in terms of the fact that making a claim of the form “x is red” commits one to “x is colored,” precludes one from being entitled to “x is green,” and so on. Once again, however, one of the rules appealed to in the strong inferentialist account as “no less basic” than these properly inferential rules is the language-entry rule that if one is in the perceptual circumstance of seeing something red, then one is entitled to a claim of the form “x is red.” So, once again, what are the “red things” of which we speak here? It seems that, if we actually try to spell out the conceptual content of “red” in accordance with the strong inferentialist account, we end up simply going in circles. The problem, of course, is that insofar as the word “red” essentially occurs in the meta-language in which we articulate the inferential rules in terms of which the content of “red” is to be understood, we are appealing to the very content for which we are supposed to be inferentially accounting. So, the reason we end up going in circles is that the account is circular!⁹

In defending the claim that this really is a problem for strong inferentialism, it is important to be clear what the ambitions of inferentialism actually are. Inferentialism aspires to be what Dummett (1993) speaks of as a “full-blooded” theory of meaning, a theory that provides an account of “the concepts expressed by the primitive terms of the language” (p. 5), terms like “red” and “ball.”¹⁰ Very few semantic theories aspire to any such account. For instance, representationalist semantic theories of the sort that are widespread in philosophy and linguistics today have no such aspiration. On a representationalist semantic theory, predicates like “red” and “ball” are assigned properties such as being red and being a ball, and, though it’s the business of the semantic theorist to make these assignments of properties to predicates, it’s not the business of the semantic theorist to specify any further what these properties actually are.¹¹ Properties like being red or being a ball are appealed to in the semantic theory as the contents of predicates like “red” and “ball,” but no of account of them is given. Rather than account for these basic contents, a representationalist semantics simply specifies how such contents compose to form complex contents. The inferentialist, on the other hand, is committed to giving an account of even the basic contents expressed by simple predicates such as “red” and “ball.” Clearly, then, insofar as the inferentialist is committed to giving an account of these contents, she is precluded from being able to appeal to these contents as primitive in her account. That, however, is precisely what the strong inferentialist does. In her account of the content of “red,” the strong inferentialist invokes as basic language-entry rules of the sort just specified, deploying the very concept for which she’s supposed to be giving an account in specifying the conditions under which it’s correct to use the expression “red.” As a result, insofar as strong inferentialism is a full-blooded theory of meaing that attempts to account for the conceptual content of expressions such as “red,” it’s circular. That’s a problem.

What are the strong inferentialist’s options in response to this problem? Insofar as she wishes to be a strong inferentialist, they are not good. The strong inferentialist must, on pain of circularity, reject one of the following two claims:

• 1. The conceptual content of the expression “red” is to be accounted for solely in terms of the rules governing its use.

• 2. The rules governing the use of the expression “red” essentially include the rule that the expression “red” is correctly applied in perceptual response to red things.

This leads to a dilemma for understanding the rules that are invoked in the “inferentialist” semantic theory. Opting for the first horn, rejecting (1), amounts to endorsing weak inferentialism. Opting for the second horn, rejecting (2), amounts to endorsing hyper-inferentialism. Let us consider each of these horns in turn.

The first horn is to reject (1), saying the rules governing the use of the expression “red” essentially include the rule that the expression “red” is correctly applied in perceptual response to red things, but the conceptual content of “red things” here is not to be accounted for solely in terms of the rules governing the use of the expression “red.” To say this is to reject strong inferentialism for “weak inferentialism,” a view which, as noted above, is not aptly called “inferentialism” at all. This is what Kremer (2010) thinks we ought to do. On Kremer’s account, understanding the conceptual content of the sentence “The ball is red” requires taking into account both the inferential dimension of its correct use—how the correct use of the sentence is connected to the correct use of other sentences such as “The ball is colored” and “The ball is green”—but also taking into account the repesentational dimension of its correct use—how the correct use of the sentence is connected to its application to particular objects in experience, such as the red ball above. The red ball above is something that can be given to us in experience, and given to us as red. This puts us in position to correctly say “The ball is red.” On this picture, no attempt is made to explain, solely in terms of the rules governing the use of “red,” what it is for something to be red. In addition to the specification of rules governing the use of “red,” we must also refer to our experience of red things, and, specifically, our experience of them as red. Kremer’s view is “weakly inferentialist,” since he maintains that recognizing the ball in experience as red is recognizing it as exemplifying a concept, one that essentially stands in inferential relations to other concepts, such as colored and green. However, these inferential relations don’t exhaust the content of the concept, on Kremer’s account. Modifying Kant’s (1998) dictum, Kremer tells us that, though representation without inference is blind, inference without representation is empty. Inferential and representational relations, according to Kremer, “are interdependent in the sense that only in concert do they give rise to cognition at all; yet they are independent in that neither can be reduced to the other” (p. 230).¹²

Now, perhaps, at the end of the day, this Kantian picture of conceptual content is the one we ought to accept. My point here is not to say that it’s wrong. My point is just that it is incompatible with inferentialism.¹³ The aspiration of inferentialism is to account for the conceptual content of “red” in terms of the rules governing its use. If one of the rules that one must appeal to in order to give this account is that “red” is correctly applied to things that one sees to be red, any such account would be viciously circular. To accept the first horn is to acknowledge this, and, in response, think that we should give up the aspiration for such an account. On this way of thinking, the proper thing to do in response to the recognition of the failure of representationalism, which aims to account for the meaning of a sentence in terms of its representational adequacy conditions and understand its inferential articulation as derivative, is not to “invert the order of explanation” and be an inferentialist, but to give up the attempt for a reductive explanation of either the representational or inferential dimension of conceptual content, in one direction or the other. Though I’ve referred to Kremer’s development of this alternative, this is essentially the position of John McDowell as well, perhaps the most outspoken critic of Brandom’s inferentialism.¹⁴ McDowell acknowledges the aim of inferentialism, as I’ve articulated above, and explicitly rejects it as having overly ambitious aspirations.¹⁵ According to McDowell (1998a), we should instead embrace a “modest” semantic theory, one that does not attempt to give an account of the concepts expressed by the primitive terms of the language. Once again, perhaps, at the end the day, this is the way to go. But to go this route, opting for horn (1) and accepting “weak inferentialism,” is to reject inferentialism.

The second horn is to reject (2), saying that the conceptual content of the expression “red” is to be accounted for solely in terms of the rules governing its use, and these rules do not include the rule that the expression “red” is correctly applied in perceptual response to red things. This, however, is precisely the sort of rule in virtue of which this view was a version of strong inferentialism rather than hyper-inferentialism. Thus, to say this is to abandon strong inferentialism for hyper-inferentialism, a view that is unanimously regarded as a theoretical non-starter. Peregrin (2014), for instance, says Brandom “rejects [hyper-inferentialism] as clearly untenable for a language containing empirical vocabulary” (p. 7). Ironically, as I’ll now show, this view that Peregrin claims Brandom “rejects as clearly untenable” is Brandom’s own.

5 Brandom’s multi-perspectival hyper-inferentialism

Let us now turn to the words that Brandom (1994) himself uses to characterize what he calls the “broad conception” of inference, in virtue of which he takes his theory to be “strong” rather than “hyper-” inferentialism:

[T]he broad conception includes the possibility of noninferential circumstances and consequences of application. In this way [...] the specifically empirical conceptual content that concepts exhibit in virtue of their connection to language entries in perception [...] are incorporated into the inferentialist picture. The use of concepts with contents of these sorts can still be understood in terms of the material inferential commitment one who uses them undertakes: the commitment to the propriety or correctness of the inference from their circumstances to their consequences of application. Conceiving such inferences broadly means conceiving them as involving those circumstances and consequences, as well as the connection between them (p. 131).

Brandom speaks here of an inference from the non-inferential circumstances of the application of the concept “red” to the consequence of application. He does not hedge or put “inference” in scarequotes as the authors discussed above do. On the strong inferentialist conception that we’ve been considering, he ought to, since the sort of “inference” he’s talking about is the move from, say, having a visibly red thing in front of one to saying “This is red,” and this is not an “inference” properly so-called. But I take it that this cannot be correct. Brandom doesn’t just say “inference” here; he says material inference, and the “move” from having a visibly red thing in front of one to saying “This is red,” while it might called an “inference” with some strain, surely can’t be called a “material inference.” That’s a technical term, and it is something that obtains between claims, or conceptual contents more generally. What then, is Brandom talking about when he is speaking of the “broad conception” of inference here? Here is a hint:

[W]hat an interpreter takes to be the circumstances under which an expression can appropriately be used in noninferential reports [...] is an important feature of the empirical content the interpreter associates with that expression [my italics] (p. 213).

Now, officially, for an interpreter take a player to be in the circumstance under which an expression can be non-inferentially used is for that interpreter to be committed to the claim that the player is in such a circumstance. I take it, then, that the “broad conception” of inference, on Brandom’s way of using the term (and no one else’s), is a conception that includes inferences from claims that say that players are in the circumstances for the non-inferential application of a concept to claims that say that they bear the consequences of applying that concept. For instance, it includes the inference from the claim that someone has a visibly red ball directly in their field of view to the claim that they are committed or entitled to the claim “The ball is red.” In the sense at issue here, this is regular old material inference, not categorically distinct from the inference from the claim that the ball is red to the claim that it is colored. It is, of course, distinct from that more standard case of a material inference—it is a material inference that involves the attribution of a normative status to another player. Still, it is an inference, properly so-called. Including such inferences in the semantic theory is compatible with hyperinferentialism, as I am using the term here.

On this reading, Brandom’s semantic theory does not appeal to rules connecting perceptual states or circumstances to moves in the language game. What the theory appeals to in order to account for the fact that some contents are essentially such as to be deployed perceptually are reliability inferences, and reliability inferences are inferences in the proper sense of the term, inferences from claims to claims. If these inferences are inferences, in the proper sense of the term, why does Brandom call them “broadly” inferential? I take it because they are inferences across scorekeeping perspectives, such that the one doing the inferring is not the one making the claim. Here is what he says on why observation reports can be counted as “broadly inferential” on his theory:

[T]he sort of authority that observation reports exhibit counts as broadly inferential because of the reliability inference it involves on the part of the attributor of such authority. Although it sounds paradoxical, for this reason the role of a sentence in noninferential reporting should also be understood as falling under the rubric “(broadly) inferential role” (pp. 188–189).

Here, it is clear that what Brandom means in saying that we can understand a non-inferential reporting use of a sentence as “(broadly) inferential” is not that it involves, on the part of the reporter, an “inference,” in some broad sense of the term, from a perceptual circumstance to its non-inferential use. Rather, Brandom means that it involves an inference, in the proper sense of the term, just not one by the reporter. Tautologically, the person who makes the non-inferential report is not doing so inferentially. Still, Brandom says, the non-inferential authority that the report has, and thus, its status as a non-inferential report, is derived inferentially. It’s not the maker of the report who makes the inference, but the attributor, who infers from the report’s being made and the reporter’s being a reliable maker of such reports that the report is authoritative. It is only in virtue of being underwritten by such inferences that the reports can be counted as having non-inferential authority. The stronger claim that Brandom makes is that all there is to a report’s having non-inferential authority is its being underwritten by these cross-perspectival inferences.

6 A hyper-inferentialist semantics

To make things more concrete, let me give a simple example of the sort of rules that I take it would belong to a semantic theory of the sort Brandom proposes.¹⁶ Suppose we’re trying to inferentially account for the meanings of set of sentences that contains, for instance, “The ball is red,” “The cube is green,” “The pyramid is scarlet,” “The octahedreon is gray,” and so on. We’ve gotten to the point in our theory where it seems that we need to consider the connection between, for instance, “The ball is red” and the circumstance in which one is able to non-inferentially deploy this sentence. There is no need to appeal to any relations between anything other than claims here. We just need to consider a wider class of claims than the ones with which we’ve concerned ourselves thus far.¹⁷

To spell this out, let X be a place holder for any of the common nouns belonging to these sentences, such as “ball,” “cube,” or “prism,” let F be a placeholder for any of the color predicates belonging to these sentences, such as “red,” “green,” or “scarlet,” and let n be a placeholder for any of the names of the speakers of the language who might use this vocabulary. Schematizing in this way, we can articulate rules such as the following:

If $\alpha$ is committed and entitled to “The X is scarlet,” then $\alpha$ is entitled to “The X is red.”

We’ll say that a player’s “scorecard” conforms to a rule of this form just in case, if it contains an attribution of the statuses in the antecedent to some player, with any actual expressions of the right types substituted for the placeholders, then it contains an attribution of the status in the consequent to that player, with the same expressions substituted for those placeholders. This sort of scorekeeping framework can be laid out completely formally, and one can officially define discursive roles as determined by scorekeeping rules of this sort, but this informal characterization will be sufficient for our purposes.¹⁸ I’ll now show how we can articulate scorekeeping rules relating nothing other than commitments and entitlements to claims that allow us to inferentially account for the fact that expressions like “red” are essentially such that they can be non-inferentially used in perceptual reports.

The first set of rules we consider are classic language-language moves, material scorekeeping principles of permissive and preclusive consequence, such as the following:

If $\alpha$ is committed and entitled to “It is day,” and “We are outside,” then $\alpha$ is (defeasibly) entitled to “The lighting is good.”

If $\alpha$ is committed to “The lighting is good,” then $\alpha$ is precluded from being entitled to “It is completely dark.”

If $\alpha$ is committed to “The X is in front of n,” then $\alpha$ is precluded from being entitled to “The X is behind n.”

And so on ...

Let us now conjunctively define a predicate “is positioned to see that” by way of the following inferential rules:

If $\alpha$ is committed to “The X is F,” $\alpha$ is committed to “The lighting is good,” and $\alpha$ is committed to “The X is in front of n,” then $\alpha$ is committed to “n is positioned to see that the X is F”

If $\alpha$ is committed to “n is positioned to see that the X is F,” then $\alpha$ is committed to “The X is F,” “The lighting is good,” and “The X is in front of n.”

Note that, given the way in which I have inferentially defined the predicate “positioned to see,” one’s being positioned to see that the ball is red does not mean that one is able to see that the ball is red. For instance, if n is completely color-blind, then n might be positioned to see that the ball is red—having the red ball in front of them in good lighting—and yet not be able to see that the ball is red because they are incapable of seeing the colors of anything. In order to actually see that the ball is red, it is not enough that one be positioned to see that the ball is red. One must also be a “capable perceiver of the colors of things.” This expression has material inferential content, as defined by rules like the following:

If $\alpha$ is committed and entitled to “n is an adult human being,” $\alpha$ is (defeasibly) entitled to “n is a capable perceiver of the colors of things”

If $\alpha$ is committed to “n is color blind,” $\alpha$ is precluded from being entitled to “n is a capable perciever of the colors of things .”

It is also, however, a reliability operator that functions in conjunction with a corresponding circumstance for response predicate, “is positioned to see that,” in enabling the inferential attribution of non-inferential entitlement, given the following rule:

RI: If $\alpha$ is committed and entitled to “n is a capable perceiver of the colors of things,” and $\alpha$ is committed and entitled to “n is positioned to see that the X is F,” then $\alpha$ is entitled to “n sees that the X is F.”

To return to our example now, and consider how it comes out on the hyperinferentialist picture just sketched, let us consider the following substitution instance of RI:

RI$^{\prime }$: (X = the ball, F = red): If $\alpha$ is committed and entitled to “n is a capable perceiver of the colors of things,” and $\alpha$ is committed and entitled to “n is positioned to see that the ball is red,” then $\alpha$ is entitled to “n sees that the ball is red”

This rule is an inferential rule, properly so-called. It is a rule of permissive consequence, relating commitment and entitlement to two claims to entitlement to a third claim. As far as the discussion here is concerned, it belongs to the same basic category of rules as the following rule, which is a paradigm of a properly inferential rule:

If $\alpha$ is committed and entitled to “The ball is red” and $\alpha$ is committed and entitled to “The cube is pink,” then $\alpha$ is entitled to “The ball is darker than the cube.”

The key difference between this rule and the rule above it is that the first rule is one that normatively relates claims involving the attribution of reliability and the attribution of normative statuses to another player. Still, both of these rules normatively relate nothing other than claims. Neither of these rules normatively relates non-linguistic circumstances to a claim. Of course, the claims that are related are about non-linguistic circumstances. But, once again, that’s true of both of these rules. The circumstance consisting in n’s being positioned to see that the ball is red is a non-linguistic circumstance, but so is the circumstance consisting in the ball’s being red. Just as having the second rule in our semantics does not require that the non-linguistic circumstance consisting in the ball’s being red figure directly into our semantic theory (in the way that such a circumstance would figure in, say, a truth-maker semantics), having the first rule in our semantics does not require that the non-linguistic circumstance consisting in n’s being positioned to see that the ball is red figure directly into our semantic theory. If the only sort of rules that figure into our semantics are rules like these, our theory is, in the sense of the term under discussion here, a form of hyper-inferentialism.

One final step is needed in order for this account to be complete. Note that the discursive significance of commitment to a claim of the form “n sees that p” must be understood in the context of the fact that seeing is a way of knowing. To see that p is to know, through visual perception, that p. So, we have the following inferential rule:

If $\alpha$ is committed to “n sees that p,” then $\alpha$ is committed to “n knows that p”

Finally, now, note Brandom’s (1994, pp. 201–204) account of what a knowledge attribution actually amounts to. To take someone to have knowledge that p, on Brandom’s account, is to take them to be committed to p, to take them to be entitled to p, and to undertake commitment to p oneself. Putting this in terms of scorekeeing rules, we have the following:

If $\alpha$ is committed to “n knows that p,” then $\alpha$ scores n as committed to p, $\alpha$ scores n as entitled to p, and $\alpha$ is committed to p.

So, by giving inferential rules through which a player can commit herself to a claim of the form “n sees that p” we have, in so doing, given rules through which a player can score another player n as entitled to p. In this way, RI inferentially underwrites the attribution of non-inferential entitlement.

Anything that was good in what we said earlier, on the strong inferentialist model, we can now translate into properly inferential terms on the hyper-inferentialist model. The content of the phrase “in the perceptual circumstance of seeing something red,” deployed in the specification of the language-entry move, can now be inferentially spelled out in terms of the above inferences. What it is to be in the perceptual circumstance of seeing something red is to be a capable perceiver of the color of things (as adult human beings who aren’t color blind generally are), to be in a position to actualize that capacity (so, looking at something that is red in good lighting), and to actually actualize it (seeing, and thereby knowing, that something is red). We can have all of this in the theory, appealing to nothing other than inferential rules, properly so-called, rules that normatively relate nothing other than claims. Though we can say everything that was good in what we said earlier on the strong inferentialist model, we do not have the same problem that we had there. Crucially, in the meta-language in which we officially articulate the semantic theory, there is no mention of red things or perceptual responses to them.¹⁹ The only mention of such things is in claims in the object language, claims whose significance is understood inferentially, in terms of their normative relations to other claims in the object language.²⁰ The key move that makes hyper-inferentialism a genuine theoretical possibility here is that the object language essentially, and not accidentally, includes vocabulary for attributing commitments and entitlements to claims to other players. The hyper-inferentialism here is thus an essentially multi-perspectival hyper-inferentialism.²¹

7 Appreciating the scope of inferentialist semantics

I have laid out, in broad outline, a hyper-inferentialist theory of meaning. In conclusion, it is worth briefly providing a diagnosis for why a hyper-inferentialist theory has seemed so implausible to commentators who’ve considered it.²² Of course, one reason is that no one has seriously tried to work it out in the detail that I have here. Perhaps once one sees an actual hyper-inferentialist semantic proposal worked out in some detail, one will no longer dismiss such theories as untenable. Though some might be swayed in this way, I suspect that many of the above quoted commentators will still look at the sort of semantics I’ve presented with serious suspicion. The general sense of suspicion, I take it, will be that on the hyper-inferentialist conception of content, we lose touch with the world; we are left, to use a widely-quoted phrase of McDowell (1994), frictionlessly “spinning in the void” (p. 11). Accordingly, to proactively respond to the sorts of criticisms this proposal is likely to get, let me conclude by diagnosing the deeper reason that commentators have dismissed hyper-inferentialism out of hand on the basis of such worries of spinning in the void: they have, I take it, systematically misunderstood the scope of inferentialist semantics. In particular, there are two important distinctions that commentators have consistently failed to properly draw: the distinction between semantics and epistemology, on the one hand, and the distinction between semantics and metasemantics, on the other. Once these two distinctions are drawn, hyper-inferentialist semantics no longer has any intuitive implausibility.

The first distinction that commentators have failed to properly draw is between the semantic theory for a language L, which articulates the conceptual contents expressed by the sentences and sub-sentential expressions of L, including those that may function to express perceptual judgments, such as the sentence “The ball is red,” and an epistemological theory pertaining to the speakers of L, which articulates how it is that a speaker comes to be entitled to make perceptual judgments that may be expressed by a certain subset of the sentences of L, such as that expressed by the sentence “The ball is red.” Even given everything we’ve said here, there is nothing stopping us from saying, in the context of our epistemological theory, that the way one comes to be perceptually entitled to the claim that the ball is red is, in the paradigm case, by seeing that the ball is red.²³ The hyper-inferentialist view proposed here as a semantic theory only commits us to the claim that, if we want an account of the conceptual content expressed, for instance, by the sentence “The ball is red” or the sentence “n sees that the ball is red,” the way we are to do this is by articulating the inferential relations that these sentences bear to other sentences of the language to which they belong. Insofar as these are sentences that can function to express perceptual entitlement, this involves prioritizing the inferential attribution of this perceptual entitlement rather than the non-inferential possession of such an entitlement. This prioritization of the perspective of the attributor in the semantic theory, however, is perfectly compatible with the prioritization of the perspective of the agent in the epistemological theory.²⁴

On the epistemological theory that is the natural complement of the semantic theory put forth here, if one is a capable perceiver of the colors of things, then one can come to be perceptually entitled to the claim that the ball is red through the act of seeing that the ball is red. For such a subject, the right way to answer the question “How do you know that the ball is red?” is to say “I see that it is.” This expresses the grounds that one has for one’s application of the concept expressed by “red” to the object picked out by “The ball,” and so this is the right way to answer a question asking for these grounds. Crucially, however, to ask for the grounds one has for one’s application of a certain concept in a particular case is distinct from asking for an account of the content of that concept in general. To say why it is that one thinks that something is red in a particular case is distinct from saying what it is to think that something is red in general. The epistemological theory that enables one to answer questions of the first sort may be distinct in form from the semantic theory that enables one to answer questions of the second sort. Of course, the two theories must be compatible, and there must be a way of articulating their connection, but they shouldn’t be conflated. The compatibility of the two theories requires that the contents of the concepts one deploys in articulating the epistemological theory be accounted for through the deployment of the semantic theory. So, for instance, insofar as the concept of a capable perceiver of the colors of things figures in the epistemological theory, we must be able to deploy the semantic theory to give an account of that concept. I have sketched here how it is that an inferentialist, properly so-called, is able to do just that.

Drawing this distinction between epistemology and semantics enables us to respond to the first way of hearing the challenge that hyper-inferentialism leaves us “spinning in the void.” In Mind and World, McDowell (1994) argues that in order for our actualizations of conceptual capacities to be rationally constrained by the world, it is insufficient for all of our actualizations of conceptual capacities to be acts of judgments. For thought to be rationally constrained by the world there must be, in addition to acts of judgment, perceptual acts—for instances, acts of seeing that such and such is the case, in which facts are made visibly manifest to subjects. It is widely thought that the hyper-inferentialist is committed to rejecting this thought, that they are committed to a kind of coherentist picture in which the only things that justify judgments are other judgments. But this is not so. It is, in fact, a crucial element of the hyper-inferentialist picture that I’ve spelled out here that one way in which a particular agent can come to be entitled to a claim with empirical content is perceptually—through a perceptual episode in which one one sees, and therein knows, that such and such is the case. It’s just that, when one wants to account for this aspect of the conceptual content of what one sees to be the case in such an episode, the way to do this is to think about the attribution of perceptual entitlement to this conceptual content, since this attribution of perceptual entitlement (unlike the perceptual entitlement itself) can be articulated inferentially. So, it is simply not the case, on a hyper-inferentialist account of content, that our acts of judgment “degenerate into moves in a self-contained game” (McDowell 1994, p. 5). Quite the contrary, the game is precisely open rather than self-contained, insofar as speakers come to be entitled to new claims—occupying new positions in the game—on the basis of seeing that things are so.²⁵

The second distinction that commentators have failed to properly draw is between the semantic theory for a language L and various aspects of (what is nowadays referred to as) the metasemantic theory for L.²⁶ Now, one must be careful wielding this distinction here, because, as Murzi and Steinberger (2017) have made clear (and as Brandom himself proposes, though not quite in these terms), inferentialism can itself be put forward as a metasemantic theory, relative to traditional representationalist semantics. For instance, one can use an inferentialist semantics to explain how it is that standard representationalist semantic contents such as sets of possible worlds are really to be understood as codifying inferential roles.²⁷ In this way, a semantic theory of one sort may serve as a kind of metasemantic theory for a semantic theory of another sort. Nevertheless, an inferentialist semantics, at least as I am understanding it here, is still a semantic theory in the sense of a theory of meanings.²⁸ To provide an inferentialist semantics for a language L is to provide a constitutive account of what the semantic contents of the expressions of L are rather than an explanatory account of why the semantic contents of the expressions of L are what they are or how they come to be what they are. In the context of an inferentialist semantics, the semantic content of an expression is understood in terms of the inferential rules governing that expression’s use, and so one task of the metasemantic theory for an inferentialist semantics will be to explain why the rules have the structure that they do. Thus, for instance, the inferentialist semantics will account for the semantics content of “red” in terms of such inferential facts as that commitment to a claim of the form “x is red” precludes one from being entitled to a claim of the form “x is green,” but explaining why it is that this fact obtains is simply not part of the task. Of course, endorsing an inferentialist semantics commits one to the claim that there is some such explanatory story to be told, but it’s not the job of the inferentialist semanticist, qua semanticist, to tell it. Now, telling the metasemantic story that explains why it is that the inferential rules are structured as they are and how it is that they come to be structured that way will, of course, involve referring to things in the world other than claims—things like red and green balls, but also such things as light waves, brain states, and so on—but that doesn’t mean that our inferentialist semantics must relate anything other than claims.

To clarify this distinction, note that it is perfectly possible to tell a metasemantic story in which the properties to which we’re actually responsive in using some vocabulary (where this responsiveness partially explains why the norms structuring the use of that vocabulary are what they are) are very different than the properties to which we take ourselves to be responsive in using that vocabulary. Indeed, I take it that, as a matter of fact, this is just what is the case with the vocabulary that has been our primary example here: color vocabulary. We take it that, when we look at a red ball and say of it that it’s red, the property that we’re responding to in saying this is the property of being red, a property that things visibly instantiate in certain lighting conditions and which is such that, if something instantiates it, it must be colored, it cannot be green (all over), and so on. Inferential semantics yields an account of this property in terms of the inferential norms governing the use of “red,” “rot,” “rojo,” or any other predicate that plays the same functional role.²⁹ I take it, however, that, as a matter of fact, the property of being red is uninstantiated.³⁰ Things in the world like raspberries and stop signs don’t actually instantiate the structure that we take them to when we ascribe to them the property of being red. Rather, there is a complex set of properties that they and we instantiate (none of which are the property of being red) that together partly explain why we have the inferential norms that we do which constitute the fact that the word “red,” as we use it, expresses the property of being red. Now, you don’t need to agree with me about the metaphysics of color to appreciate the general philosophical point here. The point is just that there can be a radical discontinuity between, on the one hand, the properties we appeal to in our metasemantic theory in order to explain the norms and, on the other hand, the properties we inferentially articulate in our semantic theory that are conferred as contents by those norms.³¹ Thus, from the perspective developed here, to think that one must refer to red things to which one stands in perceptual relations in the world in order to explain the conceptual content of “red” is to conflate two fundamentally distinct levels of explanation.

This distinction between semantics and metasemantics enables us to respond to the second way of hearing the challenge that hyper-inferentialism leaves us “spinning in the void.” On this different way of hearing the phrase, the challenge is more metaphysical than epistemological; it concerns the causal or explanatory connection (or lack thereof) between language and the extra-linguistic reality to which language-users belong. According to this challenge, the hyper-inferentialist is committed to denying that anything from the outside the practice of using language constrains the linguistic practice.³² This would, surely, be a kind of spinning in the void. But nothing about hyper-inferentialism, as a semantic theory, commits one to it. Indeed, it is perfectly compatible with hyper-inferentialism to explain the structure of the norms, mastery of which confers a grasp on a space of conceptual contents, in a way that involves appealing to things in the world instantiating the very conceptual contents on which speakers come to have a grip. I’ve just suggested that it is a mistake to try to do this in the specific case of colors that we’ve taken as our main example here. However, to switch up the example, it is plausibly part of the explanation of the fact that, in our practice, commitment to “x is ball” precludes entitlement to “x is a cube” that we’re responsive to balls in our usage of “ball,” we’re responsive to cubes in our usage of “cube,” and something’s being a ball rule’s out its being a cube.³³ So, though inferentialism entitles us to say that some properties are “mere shadows” of norms (Kraut, 2010; Sellars, 1963a; b), it doesn’t commit us to saying this about all properties. According to the inferentialist, if we want to articulate what it is that we’re saying of the Sun when we say of it that it’s a ball, the way to do this is to articulate the inferential norms governing the use of “ball.” This is the account the inferentialist provides of the property of being a ball. But nothing about this account implies that the property of being a ball is not instantiated by the Sun, and, indeed, was instantiated by the Sun long before any human beings existed.³⁴ Moreover, it’s perfectly compatible with inferentialism to tell a metasemantic story in which the objective modal relations between properties instantiated by the objects with which speakers interact in part explains the structure of the norms through which speakers grasp those very properties. Hyper-inferentialism, as an account of the contents conferred by a linguistic practice, is simply neutral with respect to questions of the relations between the contents conferred by a linguistic practice and those instantiated by extra-linguistic reality. There are, of course, important questions here, but, for the inferentialist, they should be understood as metasemantic questions, not semantic ones.

8 Conclusion

Insofar as the scope of inferentialist semantics is properly understood—that is, once we have properly drawn the distinctions between semantics, on the one hand, and epistemology and metasemantics, on the other—I see no reason for the inferentialist to rule out hyper-inferentialism as a genuine theoretical possibility. Indeed, to reiterate, given the fundamental problem with so-called “strong inferentialism” articulated above, it seems to me that hyper-inferentialism is really the only genuine candidate for an inferentialist theory of meaning. The only coherent way to be an inferentialist is to be a hyper-inferentialist. The question remains, of course, of whether one should be an inferentialist at all. For all that I’ve said in defending specifically hyper-inferentialism, I have not addressed all possible criticisms of inferentialism. The thesis that we can account for the meanings of the sentences of a language L solely in terms of the inferential rules governing their use remains a contentious one, and there are all sorts of technical and philosophical challenges that have been raised for any theory of this general sort to which I have not responded here. However, as I hope to have made clear, the inferentialist faces no particular problem accounting for the meaning of vocabulary that is essentially such as to be deployed perceptually. Nothing of this sort requires the inferentialist to break up her theory into two different kinds of “broadly inferential” rules. The only rules needed are inferential ones, properly so-called.