Normativity of meaning: An inferentialist argument

This paper presents a new argument to defend the normativity of meaning, specifically the thesis that there are no meanings without norms. The argument starts from the observation inferentialists have emphasized that incompatibility relations between sentences are a necessary part of meaning as it is understood. We motivate this approach by showing that the standard normativist strategy in the literature, which is developed in terms of veridical reference that may swing free from the speaker’s understanding, violates the ought-implies-can principle, but ours does not. In addition, our approach is superior because, unlike the dominant approach, it can be extended from declarative sentences to non-representational uses of language. In this paper, however, we only formulate the argument for the base case that involves incompatibility relations between declarative sentences. The goal is not to derive norms from something that is not normative, but to explicate the distinctive type of normativity that is built into meaning as it is understood by language-users. The explication proceeds in two steps. (1) For any sentence s a speaker understands, there is another sentence s’ that is (and is understood by the speaker as) incompatible with s. (2) In virtue of understanding this incompatibility of meanings, she ought not to be committed to both s and s’. This prohibition is not derived from instrumental practical reason, nor is it based on representational correctness, but its source is the incompatibility of meanings.


Introduction
The claim that linguistic meaning and/or mental content is normative has been widely discussed, but the topic remains controversial. 1 The debate is bifurcated depending on whether one focuses on linguistic meaning or mental content.In this paper, we concentrate on linguistic meaning. 2 Our goal is to defend semantic normativism by means of a new argumentative strategy that shifts the focus away from veridical reference to incompatibility relations between sentences.Normativism about meaning has two variants: meaning engendered normativism (ME) and meaning determining normativism (MD).In this paper, we are only concerned to defend ME.Our thesis is that there cannot be meanings without norms.Therefore, our thesis does not constitute an explanation of meaning.The goal of this paper is not to derive ME from facts that are not normative, but to explicate the normativity that is built into facts about meaning.At present, we see this relative modesty of ME as an advantage over MD, which, in contrast, commits one to an explanation of meaning in terms of norms. 3onsequently, however, it might seem misleading that we characterize our argument for ME normativism as "an inferentialist argument".After all, the distinction between inferentialism and representationalism is typically used to contrast two competing explanatory strategies in a theory of meaning. 4It therefore bears emphasizing that our argument takes no stance in that debate.But there is a different sense in which our argument is grounded in inferential relations, as we will explain below, in Sect. 4.
Arguments for ME have been inspired by the insight that linguistic expressions have conditions for correct/incorrect use.In such arguments, following Kripke (1982), to whom this insight is often attributed, authors usually concentrate on declarative sentences.In response, however, anti-normativists have argued that the representational correctness of a given declarative sentence itself does not entail any deontic or evaluative consequence on how to use it. 5We agree, but we resist the anti-normativist conclusion by drawing a different lesson from this shortcoming.The lesson is to shift the focus of attention from representational relations to inferential relations, which 1 Proponents of normativism include Kripke (1982), Boghossian (1989, 2005), Brandom (1994), Whitting  (2007, 2009, 2010), Ginsborg (2011), Peregrin (2012), Gibbard (2013), Hlobil (2015), and Stovall (2020), whereas opponents include Bilgrami (1993), Glüer (1999), Wikforss (2001), Hattiangadi (2006, 2007,  2009), Bykvist and Hattiangadi (2007), and Glüer & Wikforss (2009, 2015). 2 We do not presuppose any particular commitments regarding the relationship between linguistic meaning and mental content.However, those who maintain that content is (inter-)dependent on meaning might extrapolate from our argument about the normativity of meaning to the normativity of content. 3We follow the exposition by Glüer & Wikforss (2009/2018, p. 3) and distinguish the two variants of normativism by using the terms 'engendered' and 'determining'.To prevent confusion, however, there are two points to note.First, the terminology of 'meaning engendered normativism' may misleadingly invoke an idea of a causal relation, and thus a temporal ordering, but the only relation our thesis involves is the entailment from meaning to norms.Second, as Glüer & Wikforss (2009/2018, p. 80, footnote 3) explicitly caution, they sometimes use the terms 'engendered' and 'determining' quite differently, when they argue against normativism.In particular, Glüer & Wikforss (2009) take the distinction to imply two orders of metaphysical determinationthat are opposite and thus mutually exclusive (Glüer & Wikforss  2009, p. 33).Our defense of ME remains neutral with respect to the topic of metaphysical determination. 4 For a defense of inferentialism, see especially Sellars (1953), Dummett (1975), Brandom (1994). 5See, e.g., Glüer (1999), Wikforss (2001), Hattiangadi (2006, 2007, 2009) , Boghossian, (2005), Glüer &  Wikforss (2009, 2009/2018).constitute another aspect of meaning, and to argue for ME on the basis of the latter. 6s we will show, this shift in approach is fundamentally motivated by the need to focus on meaning as it is understood by language-users.In this regard, the inferentialist approach provides a promising starting point.When one comes to understand the meaning of a given sentence and thereby how to use it, one understands various inferential relations involving the sentence. 7Moreover, there is another motivation for adopting the inferentialist approach.We believe that only it has resources to extend an argument for ME from declarative sentences to linguistic expressions in general, crucially, including those that have no representational content.This is so because our focus on inferential relations between declarative sentences is an instance of the generally pragmatist approach to study meaning in terms of use-conditions.Meaning is essential to everything we can do with words, not exclusively to assertion.Accordingly, the scope of ME should not be limited to truth-apt discourse.We therefore recognize as a criterion of adequacy for an argument for the normativity of meaning that it can be extended to all kinds of language use. 8In conclusion, after formulating the argument for ME with a narrow focus on declarative sentences, we will lay out a blueprint for such an extension.While its detailed implementation has to be postponed for another occasion, this prospect constitutes an important reason, in its own right, for shifting the focus from representational relations to inferential relations in the debate on the normativity of meaning.
Whileanti-normativists, too, acknowledge that speakers face obligations, permissions, and prohibitions concerning language use, they typically seek to explain these normative constraints in terms of instrumental practical reason. 9Therefore, the normativist needs to demonstrate specifically that there are norms that govern language use, whose source is distinctively semantic.We respond to this challenge by arguing that correctness/incorrectness conditions based on inferential relations, in fact, do entail deontic consequences.The argument will be built upon the observation that meaning essentially involves incompatibility relations between sentences.10Notice that the incompatibility need not be a matter of contradiction, p and not-p.A contradiction only constitutes formal incompatibility.Because the other type is constituted by incompatible contents, it may be called material incompatibility (see, e.g., Sellars,  1953 and Brandom, 1994).For instance, consider the incompatibility between sentences 'The first apple I ate today was green (all over)' and 'The first apple I ate today was red (all over)'.Specifically, we will argue that every declarative sentence s is incompatible with some other declarative sentence s'; and due to this incompatibility relation between the two sentences one ought not to be committed to both s and s' at the same time.Importantly, the prohibition is not grounded in truth.For, even if both s and s' are false, the prohibition only forbids the speaker to be committed to both at the same time.Instead, the prohibition depends on the respective meanings of s and s' which are incompatible.In conclusion, we will briefly indicate in terms of use-conditions how this core idea of incompatibility relations that are normatively significant can be extended to discourse that is not truth-apt.
The paper is structured as follows.In Sect.2, we briefly review the debate on ME normativism and formulate the central issue in terms of what we call 'the Argument Schema'.In Sect.3, we first examine several arguments for ME normativism in the literature that focus on representational correctness and then identify their common source of failure.In Sect.4, we present our alternative argument that instead construes correctness/incorrectness conditions in terms of inferential relations.In Sect.5, we reply to several anticipated objections from anti-normativists.Finally, in Sect.6, we lay out a blueprint for an extension of our argument beyond declarative sentences.

From Kripke's observation to the Argument Schema
One of the contemporary roots of ME normativism is traced back to Kripke's wellknown discussion on Wittgenstein's rule following considerations.Therefore, it is helpful to present the prima facie plausibility of ME normativism by reviewing how Kripke's discussion has been interpreted by normativists.To be clear, however, our argument for ME normativism is independent of the exegesis of Kripke's text.Thus, also those who deny that Kripke defends ME normativism (e.g., Guardo, 2014) can nevertheless accept our argument.In setting up his skeptical challenge about meaning, Kripke writes, 'So it ought to be agreed that if I meant plus, then unless I wish to change my usage, I am justified in answering (indeed compelled to answer) '125', not '5" (Kripke, 1982, p. 11; added italics).According to Kripke, the semantic fact that I mean plus by 'plus' entails normative facts about how I may or may not use the word -for instance, I may (or even ought to) answer '125' to the question 'What is 57 plus 68?', whereas I may not answer '5'.As is well known, this assumption plays a crucial role in the skeptical challenge Kripke formulates with respect to meaning.
We believe that Kripke's observation on the normativity of meaning is ultimately right.It is not entirely clear, however, how Kripke justifies it.Based on Kripke's discussion, Paul Boghossian famously reconstructed one possible justification.Boghossian writes: 'The normativity of meaning turns out to be, in other words, simply a new name for the familiar fact that, regardless of whether one thinks of meaning in truththeoretic or assertion-theoretic terms, meaningful expressions possess conditions of correct use' (Boghossian, 1989, p. 513).Let us summarize his point as the following thesis.
For any subject S, for any expression e: (1) If S means something by e,11 there is a correctness/incorrectness condition C for the use of e.
Boghossian suggests this as an unshakable platitude about meaningfulness. 12lthough there are also other arguments for ME normativism discussed in the literature, the Kripke-Boghossian approach is taken most seriously by critics.These anti-normativists agree with Boghossian about the platitudinal status of (1), that is, they admit that there is a certain type of correctness that is essential to meaningfulness. 13They insist, however, that the existence of correctness conditions does not entail normativity in the sense that is at issue in the original discussion of rule-following 14 We can always talk about correctness when there is a standard with which things accord or not.However, it is not clear-or so anti-normativists insist-that such a standard must be accompanied by a normative force to the effect that one ought to, may, or may not do such and such.Therefore, to defend ME, one needs to show that correctness/incorrectness conditions indeed entail deontic statuses in the case of meaning.Specifically, we need to establish a thesis of the following form that connects semantic correctness to normativity.For any subject S, for any expression e: (1) If S means something by e, there is a condition C of correct/incorrect use of e.
(2) If there is a condition of correct/incorrect use of e, there is a normative constraint N on S's use of e.
Let us call this the Argument Schema for ME normativism.We call it a schema because it has several choice points to be filled, such as how to define the correctness/incorrectness condition of use, how to define the normative constraint, and whether e should be a sentence or some subsentential expression.Among these, however, the first choice point is crucial, because the other choices depend on it.Most authors, including both proponents and critics of ME normativism, prefer to define the correctness/incorrectness condition in terms of truth or some related representational notions. 15This line of thought leads to what is sometimes called the 'Simple Argument' for ME normativism.In the literature on the normativity of meaning the Simple Argument functions as the standard template for attempts to defend ME normativism.Therefore, in the next section, we will examine several criticisms of this argument and its variants in order to identify a decisive difficulty in the representationalist line of elaborating the Argument Schema.This failure, then, will motivate our subsequent inferentialist strategy to exploit the same schema.

Criticisms of the Simple Argument and its variants
There are three lessons we will draw in this section from criticisms of the Simple Argument in the literature.They concern (1) the defeasibility of semantic norms, (2) their modal force, and, most importantly, (3) the role of understanding, in contrast to reference, as the source of normative constraint.
Given the primary role of truth or some related representational relation in various well-known theories of meaning, it is natural for many philosophers to spell out the notion of semantic correctness in the first step of the Argument Schema in representational terms.Indeed, this approach yields a highly plausible reading of the first step.According to this reading, the correct use is the veridical use, that is, the use that yields true descriptions.Following this approach, one fills out (1), as follows: (1r) If S means M by e, S veridically applies e to x iff x is M.
We call this (1r) because it interprets the correctness at issue in terms of a referential or representational relation between linguistic expressions and objects in the world.
The next question is exactly what type of normative constraint does (1r) entail.As we will point out below, there are several options available here.However, given the apparently intuitive idea that truth is what we ought to aim at when we describe things, many authors find it natural to spell out the normative constraint as an obligation to veridical use of language.This leads to the following elaboration of the second step of the Argument Schema: (2r) If S veridically applies e to x iff x is M, S ought to apply e to x iff x is M.
The combination of (1r) and ( 2r) is sometimes called the Simple Argument (see e.g., Glüer & Wikforss 2009/2018, p. 12).This argument is often regarded as what Boghossian's elaboration of Kripke's argument for ME normativism amounts to, and therefore it has been the main target of the critics of ME normativism.
As already mentioned in Sect.2, the critics of the Simple Argument mostly focus on its second step.Therefore, the three lessons we will draw are also based on criticisms of the second step in the argument.To begin with, there seems to be a counterexample to (2r), assuming that it is not always the case that we ought to tell the truth, regardless of circumstances.Suppose, for example, that Gertrude, being pursued by someone who tries to murder her, is hiding in my house.Even though 'is in my house' is veridically applied to Gertrude in this situation, if asked by the prospective murderer, I would not be obliged to say 'Gertrude is in my house', given that this would bring about a morally impermissible result of her being murdered.After all, it seems that we are sometimes allowed to lie if that is required by a more important norm (e.g., 'One ought to do what is morally right!').There is a quick reply to this challenge, however.The alleged counterexample does not necessarily show that the semantic obligation at issue does not exist; it shows at most that if there is such an obligation, it is defeasible.Indeed, most norms are defeasible.And we need not assume that the semantic norm, whatever it may be, is exceptional in this regard.Thus, the first challenge poses no substantial threat to (2r).Rather, it yields our lesson (1): if there is a semantic norm, it will be defeasible. 16he second criticism of (2r) is more serious and, in our view, indicates a fundamental difficulty with the Simple Argument.As correctly pointed out by Hattiangadi (2006,  pp.226-227; 2007, p. 180), the obligation stated in (2r) -S ought to apply e to x iff x is M -is too demanding.No speaker can apply, say, the word 'green' to all the objects that are green in the universe.There are two independent reasons for this.For one thing, there are simply too many green objects.For another, even if S had an infinitely long time, S would still be unable to apply 'green' to many green things about which there is no evidence available to S (e.g., a buried emerald on Mars).It is widely accepted, however, that one ought to do something only if one can do it.(2r) violates this widely accepted principle about obligation.Because the ought-implies-can principle should be respected, we find (2r), as it stands, unacceptable.
However, it may still appear that proponents of the Simple Argument can dodge this criticism from impossibility by elaborating alternative versions of the argument, in particular by weakening (2r).There appear to be at least two possible ways to do so.First, one might simply abandon the direction of the obligation that is too demanding, while retaining the other direction, thus: (2r ←) If S veridically applies e to x iff x is M, S ought to apply e to x only if x is M.
Upon closer look, however, this formulation turns out to be too weak.(2r ←) does not entail any obligation of true applications.Indeed, (2r ←) is even consistent with a permission to apply 'green' to an object that is not green, because its contrapositive only denies the obligation to apply 'green' to non-green objects (Bykvist & Hattiangadi,  2007, p. 280).However, there is a more promising version of the weakening strategy, in which the normative instruction is not an obligation but a permission (Whiting,  2009, p. 544, 2010, p. 216; Peregrin, 2012, p. 88).
(2r') If S veridically applies e to x iff x is M, S may apply e to x iff x is M.
We believe that the dismissive attitude towards this option, for instance in the overview of normativism by Glüer & Wikforss (2009, 2009/2018), reflects a prescriptivist misconception that ME normativism must be based on a positive obligation.As already mentioned, we agree with the critics that ME normativists should bear the burden of demonstrating that semantic correctness entails normative constraint.However, the normative constraint need not be a positive obligation.It may be a permission or a prohibition instead, although one might legitimately wonder how a mere permission could normatively constrain our use of language.In contrast to (2r ←), however, (2r') does entail a normative constraint.This is seen by taking the contraposition of the consequent of (2r'): If S veridically applies e to x iff x is M, S may not apply e to x iff x is not M. Thus, (2r') entails a negative obligation, or prohibition, on the use of e. Furthermore, in contrast to (2r), (2r') cannot be simply criticized on the basis that there are too many M things in the universe.After all, (2r') only obliges S not to apply e.This normative constraint can be followed however many M things there are in the universe, and however limited the available evidence about M things might be.From this discussion we draw lesson (2): an argument for ME normativism is more likely to succeed if it focuses on a normative constraint that is weaker than a positive obligation.
There may be room for proponents of the Simple Argument to accommodate the above lessons concerning the defeasibility and modal force of semantic norms, but our third lesson reveals a problem that is fatal to the general approach the Simple Argument embodies.That approach seeks to define correctness/incorrectness conditions objectively, namely in terms of reference and truth.Instead, we contend, as our lesson (3), that normativists should take as the starting point meaning as it is understood. 17he crucial problem is that the standard normativist strategy to define correctness in terms of veridical reference violates the ought-implies-can principle.As already noted, it is uncontroversial that people must be able, in principle, to follow the norms they are subjected to.Therefore, there are no unknowable norms.However, if correctness/incorrectness conditions are defined in terms of veridical reference, then a speaker could be subjected to semantic norms that are unknowable, not only to the speaker but even to her linguistic community.Let us illustrate this problematic consequence by means of a Twin Earth scenario. 18alt, who lived in England in the 1700s, has just been unknowingly adopted and transferred to Twin Earth, which is the exact duplicate of the Earth except for one difference.On Twin Earth the transparent liquid falling from clouds, flowing in rivers, and running from the tap does not consist of H 2 O but of a chemical substance with a different microstructure, XYZ. 19Besides the difference in microstructure, the two liquids are indistinguishable.Now, imagine that Walt -who is on Twin Earth but believes to be on the Earth -pours the apparently familiar transparent liquid from the tap into his glass.If he is asked, 'What is it?,'he will surely answer, 'This is water'.In doing so, however, Walt violates (2r').According to Putnam's semantic analysis of natural kind terms, 'water' only refers to the substance that has the same microstructure as what Walt and other speakers in his linguistic community on Earth have been calling 'water', which is H 2 O, not XYZ (Putnam, 1975, pp.224-225).Yet, in this situation, how can Walt possibly obey (2r'), namely, in this instance, the prohibition not to apply 'water' to something that is not water?After all, Walt doesn't know, and cannot know, that the liquid consists of a different chemical substance from the one he has been calling 'water'.In fact, in Walt's historical context in the 1700s, no one is in a position to know that water is H 2 O. Thus, (2r') entails a norm that is impossible to follow, which is a violation of the ought-implies-can principle.
Crucially, the problem cannot be solved by revising (2r').If the conditions for correctness/incorrectness are objective, and thus independent of meaning as it is understood, the normativist needs to accept, implausibly, that speakers are bound by semantic norms that are unknowable to them.Thus, the thought experiment reveals a fundamental reason why the representational approach to elaborate the Argument Schema-i.e., the Simple Argument and its variants-falls prey to the criticism from impossibility.Truth and falsity, in terms of which the correctness condition was defined, are objective, specifically something that holds independently of our understanding.An application of a word is either veridical or not, whether or not we can tell which status it has.As much as it is humanly impossible to make sure that we apply the word to every object in its extension, it is also impossible to completely eliminate its non-veridical applications.At best, we can make sure that we always apply the word veridically according to our understanding of its meaning (cf.Glüer, 1999, Sect.8).Specifically, this means that ME cannot be based on truth as a norm.For, as we just saw, even if we understand the meaning of 'water', we still might not fully know its extension and therefore might apply the word to wrong objects without understanding that this is what we do.That is why normativists should turn away from veridical reference and instead focus on meaning as it is understood.
The key question, then, is how to characterize meaning as it is understood. 20In general, patterns of language-use reveal how speakers understand the meanings of the expressions they use.Language-use involves reference and predication, but also other elements one might focus on in order to come to grips with meaning as it is understood, for instance, patterns of inference.It is typically a good inference to move from 'Streets are wet' to 'It is raining'.Here the goodness of the inference depends on the meanings of the two sentences involved.The patterns of inference I enact between the two sentences reveal, in part, my understanding of their meanings.In this connection, we can introduce the inferentialist idea that underlies the argument we will next formulate for ME normativism.As already indicated, we are not trying to explain meaning, so the commitment in question does not concern explanatory priority assigned to inference over representation.Instead, the argument will adopt and explicate the following idea: the understanding of meaning essentially involves an understanding of incompatibility relations between, at least, two sentences.As we will explain in the next section, this idea is a particular instance of what Robert Brandom calls linguistic rationalism.

An inferentialist argument
As already noted, the argument we formulate in this section will focus specifically on inferential relations between declarative sentences, though its strategy can be extended to use-conditions in general.To begin with, let us rehearse the Argument Schema, within which we will elaborate our alternative argument for ME normativism.
For any subject S, for any expression e: (1) If S means something by e, there is a correctness/incorrectness condition C for the use of e.
(2) If there is a condition of correctness/incorrectness for the use of e, there is a normative constraint N for S's use of e.
Whereas the Simple Argument focuses on a correctness condition and interprets it as a truth-condition, we propose to focus on an incorrectness condition and interpret it in terms of the inferential relation of incompatibility.This shift is motivated by the fundamental lesson that normativists should redefine the correctness/incorrectness condition such that it is essentially understood by language-users.Incompatibility is a plausible candidate because it seems clear that no speaker can competently use a sentence without understanding some relations of incompatibility between it and others sentences. 20One may wonder what exactly we mean by 'understanding'.There are different accounts of this notion.The intellectualists explain understanding in terms of beliefs -in the case of inferential relations, in terms of beliefs about rules of inferences (e.g., Carnap 1952).The pragmatists, in turn, argue that understanding cannot be explained without a reference to something other than belief, in particular to skills that are exercised in practice -in the case of inferential relations, to an ability to enact norms of an inferential practice without representing them (e.g.Wittgenstein 1953/2001, Sellars 1954, Searle 1983, Brandom 1994,  Devitt 2006, Greenberg and Harman 2006).For the purpose of our argument, however, the debate between pragmatist and intellectualist accounts of understanding can be put to the side.
Once we use the relation of incompatibility between sentences to define an incorrectness condition C, it is natural to focus on prohibition, or negative obligation (i.e., ought-not-to-do) to articulate the corresponding normative constraint N. Thus, we are led to the following elaboration of the Argument Schema.
For any subject S, any declarative sentence s: (1i) If S means something by s, there is some sentence s' that is (and S understands as) incompatible with s. (2i) If s' is (and S understands it as) incompatible with s, S ought not to commit herself to both s and s'.
By focusing on the deontic modality of prohibition instead of positive obligation, this modified argument is able to evade the charge that was fatal to the Simple Argument-i.e., the charge that the relevant norm is impossible to follow.To be sure, one might sometimes carelessly incur incompatible commitments, but that is by no means inevitable.Thus, the ought-implies-can principle is respected, as our second lesson from Sect. 3 requires.Also note that we are not claiming that the prohibition to avoid incompatible commitments is indefeasible.Adopting the first lesson above, we remain open to admit that the prohibition might be defeated by some other norms that are more important, either due to their different character or due to specific circumstances.Importantly, notice that the incompatibility requirement (1i) expresses is neutral with respect to competing explanations of incompatibility-and of meaning, in general.This is important because it makes (1i) prima facie acceptable regardless of specific commitments in a theory of meaning or in the philosophy of logic.In particular, inferentialists can endorse an explanation of incompatibility as a primitive inferential relation, while representationalists may seek to explain incompatibility in terms of truth-conditions.Moreover, formalists may insist on a reduction of incompatibility to a contradiction, while logical expressivists may deny that and still accept (1i).Given this theoretical neutrality of the incompatibility requirement, however, it might appear odd that we nevertheless characterize our argument as "an inferentialist argument".In short, we do this because (1i) refers to incompatibility as an inferential relation between sentences.After explaining this in Sect.4.1.,we will argue in Sect.4.2.for the crucial step, namely (2i), by explicating the normative significance of incompatibility.

The incompatibility requirement
In this section, we establish the first step of our inferentialist argument: (1i) If S means something by s, there is some sentence s' that is (and S understands as) incompatible with s. 21Our defense of (1i) is a version of the idea 'All determination is negation.' 22A sentence can have a determinate content only by virtue of excluding, that is, by being incompatible with, the content of at least one other sentence.Thus, the notion of incompatibility we rely on is a semantic relation between assertable contents, paradigmatically expressed by declarative sentences. 23If s were compatible with any s´, then s could be asserted come what may.This would mean that s has no determinate meaning at all.For instance, if the sentence 'The ball is red' was compatible with any sentence, including any sentence about the same ball, e.g.'The ball is blue', it would tell us nothing.This shows that standing in an incompatibility relation with at least one other sentence is required for a sentence to mean anything at all.Based on this observation, we claim that if a subject means something by a given sentence, there must be at least one other sentence that is incompatible with that sentence.This incompatibility requirement is what (1i) expresses.Thus, our defense of (1i) is based on the observation that some incompatibility relations between sentences are a necessary part of the meaning of any sentence and that, therefore, a speaker can competently use a sentence only if she understands some such incompatibilities.This is a characteristically inferentialist observation because the understood incompatibilities are inferential relations between assertable contents, paradigmatically expressed by declarative sentences, although it can be generalized in terms of use-conditions to discourse that is not truth-apt.
However, it is crucial not to confuse incompatibility as an inferential relation with inferentialism as a specific explanatory strategy in the theory of meaning.While our argument presupposes the former, it is independent of the latter.To clarify how these two ideas are related, it is helpful to contextualize (1i) against the background of 'linguistic rationalism,' which Brandom characterizes as an inferentialist idea that underlies, but does not entail, inferentialism as an explanatory project.Brandom writes: 'Propositional contents are essentially what can serve as both premises and conclusions of inferences.This inferentialist idea might be called "linguistic rationalism".Linguistic rationalism is not a standard part of the armamentarium of semantic assertibilism, but I think it is what is required to make that explanatory strategy work.' (Brandom, 2000, p, 189; emphasis added).Thus, according to linguistic rationalism, which Brandom here distinguishes from the explanation of meaning, it is necessary that 22 Melamed (2012) provides an illuminating discussion of different interpretations of this principle in modern philosophy downstream from Spinoza.Notice that here 'negation' should be understood as incompatibility in general, not as logical negation strictly speaking, because (1i-b) holds also for a language without a negation operator.Also note that even if all conceptually determinate content is contrastive with something, we are not suggesting that any content is contrastive with everything else.Most differences we can apprehend do not make a semantic difference.For instance, the difference between predicates 'red' and 'triangle' is semantically redundant, because these predicates determine two distinct determinables, color and shape, respectively.Understanding that an object is not-red makes no difference to understanding that it is triangular, just like understanding that an object is not-square makes no difference to understanding that it is blue.Thus, color and shape are two independent determinables, each nesting a cluster of contrastively inter-defined conceptual determinants.For the role of incompatibility in the determination of conceptual content, see Brandom's discussion of the metadistinction between two kinds of difference -mere difference and incompatibility -in his interpretation of Hegel's account of determinate negation (Brandom 2019,  pp.133-168). 23In addition, incompatibility is also a metaphysical relation between some properties.The relationship between metaphysical incompatibility and semantic incompatibility, however, is a topic in its own right, and our argument is independent of any particular view in this regard.
there are inferential relations between meaningful sentences.Notice that this necessity claim says nothing, as such, about the constitution of meaning.Brandom's point is that those who seek to explain meaning in terms of assertibility conditions must presuppose the necessity claim because the assertibility conditions are constituted by inferential relations.Crucially, however, the necessity claim does not entail this or any other explanatory strategy in the theory of meaning.
Our incompatibility requirement (1i), then, is a particular instance of the necessity claim of linguistic rationalism since our claim only concerns the inferential relation of incompatibility between sentences.Now it can be seen how our argument can be 'inferentialist' in a relevant sense without incurring a commitment to inferentialism as a position in the theory of meaning.Semantic inferentialism and representationalism are two competing strategies to give a philosophical account of meaning.As such, the primary concern of inferentialism is to establish that inferential relations between sentences are explanatorily prior to, or at least as primitive as, reference and truth.24However, our observation above says nothing about the explanatory primacy between inference and representation-and this should be so, since, after all, our purpose in this paper is to defend ME normativism, not MD.Nonetheless, we acknowledge that the incompatibility requirement is an essential part of semantic inferentialism because the incompatibility requirement is a particular instance of linguistic rationalism.
It is worth emphasizing that since our argument invokes inferential relations only to interpret the incompatibility requirement, the argument can be accepted by theorists of many persuasions.In particular, it is an advantage that the commitment to linguistic rationalism allows us to remain neutral about the potentially controversial question of how to explain our key notion of incompatibility.On the one hand, some thoroughgoing inferentialists such as Sellars and Brandom claim that meaning-constitutive inferential relations, such as the incompatibility between 'The ball is blue' and 'The ball is red', should be conceived as semantically primitive. 25they are called material inferential relations.But there are others who oppose the idea of material inference, for instance, by claiming that the goodness of any such inference should be ultimately explained in terms of logically valid inference.According to this formalist view, our incompatibility requirement should be explained by appealing to the logical contradiction among a set of three sentences, for example, (1) 'This ball is blue,' (2) 'If this ball is blue, then it is not red', and (3) 'This ball is red'.The bridging conditional (2) stays implicit in the original statement of material incompatibility, but making it explicit enables an explanation of the incompatibility solely on the basis of contradiction.On the other hand, representationalists oppose the very idea that some inferential relations, whether material or formal, are semantically primitive.They insist that such inferential relations should be explained in terms of representational notions such as reference and truth instead.Thus, representationalists would explain the material incompatibility between the two sentences above (or the logical contradiction among the three) in terms of the impossibility of the sentences to be true at the same time.Importantly, our argument does not depend on any commitment with respect to these controversial points concerning explanatory primacy.To repeat, our argument only requires that some incompatibility relations are essential to meaning as it is understood, however the incompatibility might be philosophically theorized.Therefore, as far as (1i) is concerned, both formalists and representationalists can accept our argument.26

Prohibition against incompatible commitments
Now, let us justify the remaining step of our argument: (2i) If s' is (and S understands it as) incompatible with s, S ought not to commit herself to both s and s'.We will do it in two steps.First, we argue that (2i-a) if s' is incompatible with s, and S understands this, then S has a reason to avoid committing herself to both s' and s.Then, we argue that (2i-b) if S has a reason to avoid committing herself both s and s', S ought not to do so.
Intuitively, (2i-a) seems plausible as it stands and in no need of further support.But this is the crucial step in our argument for ME normativism , so we want to be as careful as we can.Therefore, let us suppose an anti-normativist who insists, as follows: incompatibility is just incompatibility; it need not be understood as something that gives me a reason to avoid it.To persuade such an opponent, let us appeal to a thought experiment by Huw Price, which reveals, we want to show, an essential connection between incompatibility and its reason-giving character.Suppose that two persons (You and Me) are discussing where Fred is now: Me: 'Fred is in the kitchen.' (Sets off for kitchen.)You: 'Wait!Fred is in the garden.'Me: 'I see.But he is in the kitchen, so I'll go there.' (Sets off.)You: 'You lack understanding.The kitchen is Fred-free.'Me: 'Is it really?But Fred's in it, and that's the important thing.'(Leaves for kitchen.)(Price, 1990, p. 224; added italics).
Notice that in this dialogue I do not understand my claim that Fred is in the kitchen as a reason to deny your claim that he is in the garden -or your claim as a reason to retract my claim.For if I did, I would deny your claim or retract mine.Nothing prevents me from doing so.Nonetheless, I endorse both claims.In this situation, it is unavoidable to conclude, as Price's interlocutor correctly does, that I do not understand these claims as being incompatible. 27Now, what implication does this conclusion from Prices's thought experiment have for our argument?It shows that anyone who understands what incompatibility is, by the same token, also understands that if two claims are incompatible with each other, there is a reason to avoid committing oneself to both of them at the same time.In other words, anyone who denies this reasongiving nature of incompatibility does not understand the notion of incompatibility our argument employs.
As to (2i-b), we cannot do anything more substantial than point out that it is an instance of an intuitively plausible principle connecting normativity and reason: If there is a reason to do A, then one ought to do A, whereas if there is a reason not to do A, then one ought not to do A. This principle, combined with its converse, is proposed by Foot (1972, p. 309) and more recently advocated, among others, by Scanlon (1998), Raz (1999), and Parfit (2011, pp.267-269).However, we do not need the converse-direction of the bi-conditional. 28Instead, we take the plausibility of the relevant direction of the principle at face value and consider that the burden of proof is on those who want to deny it.It is also worth reminding that the prohibition we derive here is defeasible.Therefore, it is not sufficient for rejecting (2i-b) to simply indicate a case in which a subject understands the incompatibility of some sentences but nonetheless is allowed to assert both for the sake of some more important cause. 29inally, it is worth emphasizing that our normative thesis (2i)-if two sentences are incompatible and the subject understands this, then she ought not to herself-is immune to the most crucial problem facing the Simple Argument and its variants, namely the criticism from impossibility.As we have shown, the ought-implies-can principle is violated, if one seeks to ground ME in veridical reference.In the case of our normative thesis, however, ignorance of some specific truth poses no problem because we derive the norm of prohibition from an aspect of meaning any speaker necessarily understands, namely from an incompatibility relation between a sentence she is using and another sentence she understands to be incompatible with it .Therefore, there is no basis for the worry that a speaker might not be in a position to obey the prohibition due to her ignorance of it.

Possible objections
We expect three main objections to the argument for ME normativism we have presented above.First, anti-normativists may insist that since the alleged prohibition against incompatible commitments normatively constrains the speech acts of asserting, the norm in question is pragmatic rather than semantic (cf., Glüer & Wikforss,  2009, 2009/2018, pp.37-38).We acknowledge that the prohibition restricts how one ought to speak and in that sense it is a pragmatic norm.Our crucial point remains, however, that it is also, and fundamentally, a semantic norm because its source is incompatibility between meanings.We argued, in (2i), that the prohibition necessarily follows from the requirement that a given declarative sentence be incompatible with another one -i.e., it follows independently of any contingent practical aim the speaker happens to pursue.Then, in (1i), relying on linguistic rationalism, we argued that this incompatibility requirement, in turn, follows from the semantic fact that a given sentence has a meaning, understood by a speaker.The meaning of the sentence consists, at least partly, of incompatibility relations with other sentences.Thus, the prohibition necessarily follows from the semantic fact that sentences s and s' have incompatible meanings.In other words, a speaker cannot mean anything by a sentence if she is not prohibited from combining it with some other sentence.
The above reply also shows why anti-normativists are wrong, if they claim that the semantic norm we have identified is based on practical reason and therefore contingent on the ends one happens to pursue.What is not contingent, as we have shown, is the contrastive structure of meaning.It is both required to confer determinate content to sentences and sufficient to generate a prohibition against making incompatible commitments.Notice that the pattern of this reply applies to varieties of the same criticism.For example, one might object that the prohibition against incompatibility is epistemic since it regulates how the subject should form and update her beliefs.Furthemore, one might argue that it is a norm of rationality because a subject who violates it would be accused of being irrational.Again, we are happy to accept any of these possible categorizations of the norm at issue.Our crucial claim remains, however, that it is nonetheless an essentially semantic norm in the sense explicated above.After all, there is no reason to think that categorizations of norms as illustrated above must be mutually exclusive or disjoint, while, of course, they do not completely overlap with each other.The prohibition against incompatibility might be pragmatic, epistemic, and rational, but it is also semantic.
This reply to the anti-normativist challenge clarifies an important structural feature of our argument: the incompatibility requirement, which follows from meaning, according to linguistic rationalism, plays the pivotal role in connecting meaning and normativity.However, this observation might encourage anti-normativists to raise a new challenge.They might claim that the argument begs the question, since the normativity we need to establish is built into the incompatibility requirement which we simply assume without an argument.Thus, they might continue, we smuggle in the crucial element of normativity at the very outset of our argument.We admit that we certainly do not aim to pull the trick of deriving normativity from something that is not normative.Rather, we seek to explicate the normativity that is built into meaning.As to the accusation of question-begging, however, what we assume is, in fact, undeniable to anyone who accepts linguistic rationalism, that is, to everyone except semantic atomists.Here is what we assume: if a competent speaker asserts s, then there is another sentence s' that is (and she understands as) incompatible with s.When Getrude competently asserts 'This ball is blue', there is another sentence, say, 'This ball is red' which is (and she understands to be) incompatible with the first.We cannot see how anyone who is not a semantic atomist could deny this claim, which is a concrete instance of the incompatibility requirement we assume as the first premise of the argument. 30ndeed, the third objection we anticipate accepts the incompatibility requirement and the inferentialist idea we use to motivate it in Sect.4.1, but uses the latter to deny our normative conclusion.To recall, according to linguistic rationalism, incompatibility relations between sentences are a part of the meanings of the sentences, as they are understood.This is an example of what Glüer and Wikforss call an 'internal' relation.The objection, then, is that relations cannot be both internal and normative.Glüer & Wikforss (2009, 2009/2018, pp.45-52) make this objection when they argue against the normativity of mental content, but it could be applied to our argument as well.Glüer and Wikforss offer several arguments for this critical contention against CE normativism.Most of them cannot be transformed into arguments against ME normativism, but there is one that may seem to threaten ME (cf., ibid., pp.47-49): (i) we cannot meaningfully use a sentence in a way that violates the inferential relations internal to the meaning of that sentence; however, (ii) a normative constraint must be violatable; therefore, the inferential relations internal to the meaning cannot normatively constrain the use of that sentence.Now, as it stands, this argument fails.While (ii) is plausible (what point would there be for a normative constraint if one could never violate it), (i) seems very implausible.After all, we can meaningfully use a sentence in a way that violates an incompatibility relation internal to its meaning (e.g., we can assert 'This ball is blue all over, and it is red all over').What is internal to the meaning of that sentence is that this is incompatible and therefore ought to be avoided, not that what ought to be avoided is actually always avoided.Thus, (i) seems to rest on an illicit identification of an internal relation with our performances in accordance with that relation.In fact, Glüer  and Wikforss (ibid., 49) admit that (i) is oversimplified and too strong. 31Taking into account our occasional irrationality, they concede, it is more realistic to adopt a weaker version: (i') we violate an internal relation only if we are under a mitigating condition (e.g., we are not fully awake, cognitively overloaded, and so on).According to them, however, such exceptional violatability under mitigating conditions is not yet enough 30 It might be pointed out that here we assume that the language at issue is rich enough to contain either the negation or contrastive predicates so that a pair of necessarily incompatible sentences can always be constructed.We believe that it is not unfair to anti-normativists to assume this modest condition, since they usually make their case by focusing on English or other natural languages that obviously satisfy it.At this stage, however, anti-normativists might dig their heels in and object that there can be a language that does not satisfy even this weak condition.For example, they might continue, there can be a language consisting of only one sentence, X, which means, say, that it is raining now (e.g., X is true if and only if it is raining at the time when X is uttered).Now, we admit that for some representational theorists of meaning such a language would be conceptually possible.It is beyond the scope of this paper to argue against this apparent possibility.Yet even if such an extremely poor language were possible, it is questionable to what extent it would undermine our argument.After all, if X ever means anything, it is always possible to come up with some sentence, Y, that means something incompatible with it (e.g., the rain has stopped).Now, according to our argument, it follows that if the poor language consisting of X is extended with Y, one ought not to commit oneself to both X and Y.That is, one is still prohibited, on the condition specified above, from undertaking incompatible commitments.Anti-normativists might resist this response by denying the extendability of the poor language, but that would make its status as a genuine language even more questionable. 31They make the admission with respect to the CE version of the principle, but it plausibly applies also to a discussion of ME.
It is highly questionable, however, whether this modification makes their critical argument more plausible than its original version, especially when it comes to ME.First, the weakened (i') still seems clearly implausible in the case of ME,32 since a speaker can easily assert, 'This ball is blue all over, and it is red all over', even outside of any mitigating conditions, for instance, in order to deceive someone into believing that she doesn't understand color concepts.Moreover, the strengthened (ii') no longer seems as plausible as its original version.After all, there seems to be a point for a normative constraint even if it can be violated only under a mitigating condition-it gives us a reason for trying to avoid being under a mitigating condition on a relevant occasion (e.g., you should try not to be drunk, when you make a presentation at a conference). 33Overall, it seems that the suggested modification of the argument is not only helpless in saving its questionable first premise but even positively harmful by making the second premise less plausible than it originally was.

Conclusion
The goal of this paper was not to derive ME from facts that are not normative, but to explicate the normativity that is built into facts about meaning.To that end, we have argued that since every sentence s is incompatible with some other sentence s', these incompatibility relations between sentences constitute prohibitions against making incompatible commitments.My understanding of the incompatibility between two sentences gives me a reason not to use the sentences in ways that would result in incompatible commitments.Paradigmatically, this means that I ought not to assert both s and s', although there are also indirect ways to incur incompatible commitments.Not every sentence is amenable to assertion, however.At the outset, we emphasized that an important reason in favor of adopting our approach is the prospect it opens up for extending ME normativism from declarative sentences to uses of language that are not truth-apt.A detailed articulation of that extension must be postponed until another occasion, but we want to conclude by laying out a blueprint for this line of future work.
It is not difficult to appreciate that there are incompatibility relations also between sentences that are not truth-apt.For instance, when it is permissible to say 'Hello!' it is not permissible to say 'Goodbye!,' and vice versa.Indeed, it is part of understanding the meanings of 'Hello!' and 'Goodbye!' to understand this incompatibility -and, consequently, to understand that one ought not to make both speech acts in the same circumstances.While here, too, incompatibility is the feature that generates normativity, it clearly cannot be construed in terms of incompatible commitments.By saying 'Hello!' or 'Goodbye!' one does not commit oneself to anything.Therefore, the normativist needs to move to a higher level of generality and specify how incompatibility relations between sentences can be characterized in terms of use-conditions.
The incompatibility requirement we have identified constitutes use-conditions only for declarative sentences. 34But one might try to extend the same idea to other kinds of sentences, as follows.Every sentence, in virtue of its meaning, carries a prohibition against a combination with some other sentence.We have shown that in the case of declarative sentences this prohibition arises from the meanings of a pair of sentences which, if asserted, would saddle the speaker with commitments that are incompatible because they cannot be jointly true.But greetings and expressives, for instance, cannot be true or false, so what is the source of the incompatibility between 'Hello!' and Goodbye!' or 'Wow! and 'Meh'?We believe that here, too, the source is meaning, even though the speaker cannot understand it without understanding the relevant illocutionary force.It is a task for another occasion to explain how the incompatibility requirement is built into use-conditions across different kinds of sentences.In light of these examples and the brief outline, however, the prospect for extending our approach beyond declarative sentences seems promising.