1 Introduction

This text aims to defend the non-factualist interpretation of the skeptical solution against the self-refutation argument formulated by Alexander Miller. Miller argues that the non-factualist interpretation is self-refuting because it cannot reconcile the following two claims it supports: the Basic Skeptical Conclusion which states that there are no semantic facts and the rejection of the Radical Skeptical Conclusion which states that “there can be no such thing as meaning anything by any word” (Kripke, 1982, p. 68).Footnote 1 The addressed position endeavors to reconcile the above two claims by asserting that meaning ascriptions — in contrast to the descriptivist approach — possess a non-descriptive function. Nevertheless, Miller contends that this tactic fails to repel the threat of semantic nihilism, as meaning ascriptions, even if construed non-descriptively, still require certain correctness conditions to possess meaning. Furthermore, Miller notes that certain semantic facts are indispensable to determining these conditions. A supporter of the non-factualist interpretation is therefore confronted with two alternatives that contradict her own assumptions: either (1) reject the claim that there are no semantic facts or (2) accept semantic nihilism (see Miller, 2010, p. 183).

I agree with Miller that merely attributing of a non-descriptive function to meaning ascriptions is not sufficient for the non-factualist to counter the threat of semantic nihilism. Nonetheless, I outline a strategy for the non-factualist to defend her stance. My proposal posits that it is not necessary for a non-factualist to rely on semantic facts to attribute the conditions of correct use to meaning ascriptions as provided that the principle of closure of assertibility of meaning ascriptions is not in force.

The motivation for writing this defense stems from the conviction that the idea of the skeptical solution is a compelling philosophical position that has yet to be fully explored. However, it is necessary to show that there is at least one interpretation of this position that can withstand the objections raised against it. Unfortunately, Miller’s objection to the non-factualist interpretation has not received a satisfactory response from its supporters. Since the alternative factualist interpretation was also aptly criticized (see Miller, 2010, pp. 178-184), a defense of the non-factualist account seems to be indispensable to defend the skeptical solution as such.

The text proceeds as follows. Part II provides a comprehensive review of discussions on the rule-following problem and outlines two positions taken in the debate over interpreting the skeptical solution to this issue. Part III reconstructs Miller’s objection to the non-factualist interpretation of the skeptical solution. Part IV demonstrates that Miller’s argument against non-factualist interpretation is not sound, since it presupposes that the conditions of correct use of non-descriptive meaning ascriptions require appealing to some semantic fact. However, this premise assumes the closure principle of assertibility of meaning ascriptions, which is flawed within the broader context of the skeptical solution. Part V introduces the original context in which the closure principle was discussed — specifically, the problem attribution of knowledge. Part VI demonstrates that the refutation of the closure principle for the assertibility of meaning ascriptions arises directly from the skeptical solution itself. Furthermore, it shows how rejecting this principle undermines Miller’s argument against the non-factual interpretation of this solution. In Part VII, I respond to the possible objections against my defense of the non-factualist interpretation.

2 Two Interpretations of the Skeptical Solution to the Rule-Following Problem

The skeptical solution is the culmination of Saul Kripke’s proposed interpretation of Wittgenstein’s remarks on the problem of rule-following (Kripke, 1982). Kripke’s main thesis is that in response to the skeptical paradox (Wittgenstein, 1953, p. 81), Wittgenstein formulates the so-called skeptical solution (Kripke, 1982, p. 68), which accepts the skeptic’s argument that there are no semantic facts, while rejecting the skeptical conclusion that “there can be no such thing as meaning anything by any word” (see Wilson, 1998, p. 107-109). Kripke rejects this claim, as he points out that our practice of formulating meaning ascriptions does not require the kind of justification that the skeptic requires, since meaning ascriptions do not have truth conditions, but only assertibility conditions (Kripke, 1982, p. 66).

However, over time, the idea behind the skeptical solution became the subject of a separate debate between proponents of a factualist and non-factualist interpretation of the Kripkean reading of Wittgenstein’s remarks. Factualists claim that the skeptical solution consists in the rejection of classical-realist truth conditions and offers deflationary truth conditions and “minimalist” semantic facts instead (see Byrne, 1996; Davies, 1998; Kusch, 2006; Wilson, 1998). In contrast, non-factualists see the skeptical solution as a rejection of semantic facts of any kind, and as refraining from the attribution of any truth conditions, even deflationary ones, to meaning ascriptions (see Miller, 2010, p. 184).

According to the non-factualist interpretation of the skeptical solution, Kripke’s observation that there are no semantic facts leads to the conclusion that the attribution of truth conditions to meaning ascriptions results in the falsity of meaning ascriptions, and that the falsity of meaning ascriptions is equal to accepting the nihilistic claim of the skeptic that in any situation, a speaker means nothing by her words. Thus, the non-factualist argues that to avoid semantic nihilism, one needs to refrain from attributing truth-conditions of any sort (whether classical-realist or deflationary ones) to meaning ascriptions (Miller, 2010, p. 183). For this reason, she believes that the factualist interpretation, which attributes certain truth-conditions to meaning ascriptions, ultimately falls into semantic nihilism, which makes it an inadequate account of the skeptical solution (Miller, 2010, p. 179-181). Instead, she assumes that meaning ascriptions do have a non-descriptive function and, consequently, do not have any truth-conditions, because they do not express any cognitive states, like judgements or beliefs, but instead conative states, like emotions or evaluative attitudes (see Hattiangadi, 2007, p. 89; Miller, 2010, pp 183-184). Unlike beliefs or judgements, conative states do not purport to describe the way things are; hence, we do not normally take them to be the sorts of sentences that can be true or false. Thus, according to non-factualist interpretations of the skeptical solution, the role of meaning ascriptions such as “Jones means addition by ‘+’” is not to describe any facts about Jones, but to express a speaker’s agreement or disagreement with his interlocutor’s use of a given word (Šumonja, 2021, p. 1).

3 Miller’s Argument Against the Non-Factualist Interpretation of the Skeptical Solution

Initially, the skeptical solution was widely regarded as the non-factualist approach to meaning. However, from the very beginning, it was criticized by philosophers such as Wright (1984) and Boghossian (1989).Footnote 2 Nevertheless, I believe that one of the most serious objections to the discussed position was formulated by Alexander Miller (Miller, 2011, 459-461), who was previously mentioned as a proponent of the non-factualist interpretation. Miller argues that the non-factualist’s assumption, stating that meaning ascriptions lack a descriptive function, falls short in addressing the skeptical problem. This deficiency arises because the skeptical argument applies not only to sentences with a descriptive semantic function but also to those with a non-descriptive semantic function.

This objection can be illustrated as follows: Let us consider the skeptical solution to be constructed in such a way that meaning ascriptions are just a type of non-descriptive sentences, such as commands. Thus, if, at time t, I want Jones to open the window, I should say “open the window!”. Given my intention for Jones to open the window, my utterance seems to be correct. However, the skeptic may argue that my statement is incorrect, because I cannot say that it expresses my intention adequately — he suggests that “window,” based on my history of use of this term, means window up to moment t, but at the moment t and after it already means door. Thus, it seems that the attribution of a non-descriptive function to meaning ascriptions is not sufficient to refute the skeptic’s objections, because non-descriptive sentences also need the support of the fact that my utterance “open the window” expresses the command open a window, and not open a door. Accordingly, Miller suggests that the attribution of non-descriptive function to meaning ascriptions still presupposes some semantic facts that determine which non-cognitive state may be expressed by them. Therefore, Miller’s objection boils down to the claim that the skeptical problem iterates at the level of non-factualist interpretation of the skeptical solution as well; on this level, it raises the question whether the sentence Jones means addition by “+” expresses the non-cognitive state A rather than the non-cognitive state B. The non-factualist is obliged to give an answer to this question, because non-descriptive sentences require the distinction between correct and incorrect uses as much as descriptive sentences; and if no such distinction can be applied to them, then they should be seen as mere noise that is impossible to evaluate in terms of its correctness or incorrectness. However, according to Miller, the non-factualist cannot provide such an answer, because any answer would involve a certain semantic fact, and the non-factualist rejects semantic facts of any sort. Therefore, Miller’s objection against the non-factualist interpretation argues that (1) it rejects the existence of semantic facts and semantic nihilism, and that (2) the rejection of semantic facts of any sort eventually leads to semantic nihilism anyway.

Miller’s argument, illustrating the self-refuting nature of the non-factualist interpretation, can be summarized as follows:

  1. 1.

    It is not the case that words mean nothing to anyone.

  2. 2.

    There are no semantic facts.

  3. 3.

    Meaning ascriptions have a non-descriptive function.

  4. 4.

    If sentences do not have conditions for correct use, they cannot mean anything to anyone.

  5. 5.

    If sentences (both descriptive, and non-descriptive) do have conditions for correct use, then there are certain facts that determine their conditions for correct use.

  6. 6.

    Meaning ascriptions do not have conditions for correct use.

  7. 7.

    Meaning ascriptions are not meaningful.

C: It is impossible for words to mean anything to anyone.

The above argument tries to show that semantic non-factualism is inconsistent: for, on the one hand, this position rejects semantic nihilism, i.e., the claim that it is impossible for words to mean anything to anyone; on the other hand, it itself leads to this nihilism by the rejection of semantic facts of any kind.

If we want to refute the above objection, it is necessary to show that the conclusion does not follow from the premises or that one premise of the argument is wrong. It seems that the conclusion is correctly derived from the premises. Therefore, consideration must be given to whether perhaps one of the premises is wrong. It seems that premises 1–4 are sound. Premise (1) expresses the main objective of the skeptical solution, i.e., the rejection of the Radical Skeptical Conclusion. Premise (2) expresses the basic assumption of the non-factualist interpretation. Premise (3) expresses the non-factualist view of the function of meaning ascriptions. Premise (4) expresses the intuitive consequence of the absence of conditions for the correct use of sentences. Premise (5) establishes the relation between correctness conditions and semantic facts. At the same time, premises (6) and (7) seem to be valid inferences: premise (6) follows from (2) and (5), while premise (7) follows from (4) and (6). Thus, it seems that the most appropriate way to defend non-factualist interpretation is to show that premise (5), i.e., the claim that the attribution of the correctness conditions to non-descriptive sentences requires the involvement of certain semantic facts, is not sound. My objection against premise (5) is based on the claim that the attribution of certain correctness-conditions to non-descriptive sentences, such as meaning ascriptions, does not require any involvement of semantic facts if we accept that the assertibility conditions of meaning ascriptions are not governed by the closure principle.

4 Defending the Non-Factualist Interpretation of the Skeptical Solution

In the following sections, I shall try to formulate a response to Miller’s objection against non-factualist interpretation. I will demonstrate that his argument is based on a premise which presupposes something we can call “the closure principle for the assertibility of meaning ascriptions.” The principle entails that the attribution of certain correctness conditions to the meaning ascription “M” requires the fact that M expresses non-cognitive state A rather than non-cognitive state B, which is an alternative to A. I will refute this principle in four steps. In the first step, I will outline considerations on the closure principle in their original context, i.e., the problem of the attribution of knowledge. In the second step, I will demonstrate that problems concerning the closure principle affect the assertibility of meaning ascriptions as well, and that Kripke’s considerations on rule-following were to reveal this fact. In the third step, I will show that the rejection of the closure principle, as it is suggested by the skeptical solution, undermines Miller’s argument against non-factualist interpretation, as it makes meaning ascriptions assertible without the need to involve any semantic facts.

4.1 The Closure Principle and the Problem of Knowledge

The discussion about the closure principle was initiated in the field of epistemology in the context of the problem of knowledge-attribution. Here, the principle of closure states that if you know that P is true and you know that the truth of P implies the truth of Q, then you know that Q is true (Dretske, 2005, p. 27). However, Fred Dretske notes that this principle has problematic consequences, because the contraposition of this principle entails that if you know that P implies Q, but you don’t know that Q is true, then you don’t know that P is true (Dretske, 2005, p. 31). Dretske illustrates this problem in the following way: When looking at an animal in a zoo, I might think it is a zebra. Suppose that I know that if an animal is a zebra, it is not another animal, such as a cleverly painted mule meant to look like a zebra. It follows from the principle of closure that if I do not know that the animal I am looking at is not a very cleverly painted mule, then I do not know that it is a zebra (Dretske, 1970, p. 1116). Thus, given that all the evidence I have access to justifies both the claim that the animal is a zebra and the claim that it is a painted mule as well, the closure principle entails that I don’t know that the animal I am looking at is a zebra.

The rejection of the closure principle in the context of the attribution of knowledge is one of the main postulates of Dretske’s Relevant Alternatives Theory. Dretske argues against the closure principle as follows: Looking at a zebra at the zoo, I know it is a zebra. Even if I have no evidence against the thesis that the animal I am looking at is not a skillfully painted mule (since my visual experience is compatible with this possibility as well) and I know that if something is a zebra, it is not a painted mule, I can still know that the animal I am looking at is a zebra. I don’t have to rule out the fact that it is a skillfully painted mule, because, on a typical visit to the zoo, the judgment that what I am looking at is a skillfully painted mule is not a relevant alternative to the judgment that it is a zebra (Dretske, 2005, p. 33). Thus, the Relevant Alternatives Theory states that knowing that judgment J is true requires the ability to exclude not all but only relevant alternatives to J.

4.2 The Closure Principle and the Skeptical Problem

The standard debate on the idea of the skeptical solution was focused on the issue of the function of meaning ascriptions: according to non-factualists, the skeptical solution initiated a non-descriptive way of thinking about meaning ascriptions, while factualists stated that it introduced a deflationary — but still descriptive — account on this issue. Nevertheless, I argue that the importance of Kripke’s skeptical solution relies on the demonstration of how to solve the problem of the assertibility of meaning ascriptions that follows from the covert intuition that the assertibility of meaning ascriptions is governed by the closure principle.

The main idea behind Kripke’s skeptical problem is that we cannot say that Jones means addition by +, because we do not have any facts that allow us to exclude the option that he means quaddition by + (Kripke, 1982, p. 23). I believe that the intuition that grounds this claim is best explained by the closure principle for meaning ascriptions. Here, the skeptic’s problem may be reconstructed as follows: if (1) Jones means addition by + is assertible and (2) “if Jones means addition by ‘+’, then Jones does not mean quaddition by ‘+’” is assertible, then (3) “Jones does not mean quaddition by ‘+’” is assertible. And it is a contraposition of this principle which implies that when (1) if Jones means addition by +, then Jones does not mean quaddition by + is assertible, but (2) “Jones does not mean quaddition by ‘+’” is not assertible (because of the lack of proper semantic facts), then (3) Jones means addition by + is not assertible, which corresponds to the Radical Skeptical Conclusion.

4.3 The Rejection of the Closure Principle as the Core of the Skeptical Solution

I believe that the rejection of the closure principle is the main idea behind the skeptical solution that answers both the skeptical problem and Miller’s objection to the non-factualist interpretation of this solution. So how does the skeptical solution reject the closure principle? Kripke himself claims that the skeptical solution is based on the intuition that “our ordinary practice or belief is justified because – contrary appearances notwithstanding – it need not require the justification the skeptic has shown to be untenable” (Kripke, 1982, p. 66). As an answer to the skeptic’s requirement of justification, he says that “we must give up the attempt to find any fact about me in virtue of which I mean ‘plus’ rather than ‘quus’, and must then go on in a certain way” (Kripke, 1982, p. 108). I believe that these words are best explained as a rejection of the closure principle, i.e., as a claim that the assertibility of the sentence “S means addition by ‘+’” does not require the exclusion of its alternative, i.e., the sentence “S means quaddition by ‘+’.”

However, a skeptic may argue that the rejection of the closure principle is not sufficient to say that meaning ascriptions do not need any semantic facts, because rejection of the closure principle is equivalent to saying that you do not need to exclude non-relevant alternatives to assert a given meaning ascription. This way of rejecting the closure principle was adopted by Dretske’s Relevant Alternatives Theory, which states that we do not need to exclude non-relevant alternatives to attribute knowledge. Let us call this the “weak rejection of the closure principle.” On the basis of the weak rejection of the closure principle, we could argue that S means addition by + is assertible, since the skeptical alternative that S means quaddition by + is not a relevant alternative to the statement. The problem with this solution is that the skeptic can claim that her alternative is as good as the non-skeptical alternative. To recognize the skeptical alternative as a relevant alternative would force us to admit that meaning ascriptions like S means addition by + are not assertible. To counter the skeptic’s charge, then, the proponent of the non-factualist interpretation must adopt the strong rejection of the closure principle. Namely, she must recognize that not only non-relevant alternatives, but also equally good alternatives are excluded from the scope of the closure principle. It seems that this solution allows us to fend off the skeptic’s objections — when we realize that the closure principle does not apply to equally good alternatives, then any of these alternatives is assertible without the need to exclude the other ones. In other words, in a case of Jones and sentences Jones means addition by + and Jones means quaddition by +, where no meaning ascription is privileged because of compatibility of our evidence with both of them, and where both alternatives are regarded relevant, a claim that equally relevant alternatives are exempt from the closure principle does not seek to privilege one meaning ascription over the other. Instead, it states that neither needs to be privileged over the other to be assertible. Thus, the sentence S means addition by + would be assertible even if the sentence “it is not the case that S means quaddition by ‘+’” is not assertible, which is unattainable when the closure principle is in force.

4.4 The Rejection of the Closure Principle as an Answer to Miller’s Objection

I think the rejection of the closure principle not only explains the idea behind the skeptical solution, but it also allows a non-factualist to refute Miller’s objection against such a position. It follows from the genuine similarity between the skeptical problem and Miller’s objection to the non-factualist interpretation: It was precisely the impossibility to indicate the fact that Jones does not mean quaddition by + which grounds the skeptic’s claim that we cannot say that Jones means addition by +. And similarly, it was the inability to indicate the fact that a given meaning ascription expresses a non-cognitive state A rather than a non-cognitive state B which grounds Miller’s objection that the non-factualist interpretation cannot attribute any correctness conditions to meaning ascriptions. Thus, as the rejection of the closure principle makes sentences such as Jones means addition by + assertible without the need to exclude alternative sentences that explain Jones’ use of +, in the same way attributing correctness conditions to meaning ascriptions that refer to non-cognitive state A do not need to exclude alternative states that explain the use of a given meaning ascription. Consequently, a claim that S means addition by + expresses a non-cognitive function A would be assertible even if the claim that it is not the case that S means quaddition by + expresses a non-cognitive function B would not be assertible. Thus, if we abandon the requirement posed by the closure principle, then there is no reason to think that semantic facts which determine that a sentence “S” means M rather than N are necessary to make meaning ascriptions — as they are viewed by non-factualist — assertible.

5 Discussion

5.1 Closure Principle as a Solution to the Skeptical Problem

5.1.1 Closure Principle and Straight Solutions to the Rule-Following Problem

In this paper, I have demonstrated that rejecting the closure principle of assertibility of meaning ascriptions serves as an effective response to a criticism against the non-factualist interpretation of the skeptical solution. However, there is a question whether proponents of straightforward solutions to the skeptical paradox can also utilize the rejection of the closure principle in order to defend their positions. In the following section, I will explain why this particular approach is untenable within the framework of straight solutions.

I think that the incompatibility of straight solutions and the rejection of the closure principle arise from the foundational assumption inherent in straight solutions which posits that semantic facts hold a substantial or “sparse” nature. The fact that Jones means addition by + is a sparse fact implies that it is an internally consistent fact that plays a causal-explanatory role in Jones’ use of +, and that well-defined consequences can be derived from it. Therefore, an advocate of a straight solution claims that Jones uses + in such-and-such a way, because he means addition by +. And because he means addition by +, he does not use it in any other way. Thus, on the basis of straight solutions, a fact that Jones means addition by + renders the sentence Jones means addition by + true and rules out all meaning ascriptions that are incompatible with it. Since straight solutions generally uphold truth as a norm for assertibility, this implies that only one correct meaning ascription exists within a specific context.

However, rejecting the closure principle leads to the assertibility of two meaning ascriptions that at first glance appear to be inherently incompatible. This fundamentally challenges the basic premise of straight solutions, which states that there exist facts that make the statement Jones means addition by + assertible while at the same time making all meaning ascriptions incompatible with it unassertible. Furthermore, in contrast to straight solutions, on the basis of assertibility of two meaning ascriptions that appear incompatible, there is no such state of “meaning something” that privileges one meaning ascription and rules out all meaning ascriptions that are incompatible with it.

Therefore, while the basic assumption of straight solutions is that the state of meaning something — as a sparse fact — precedes and explains human action, a state of meaning something is rather deflationary; it may at best be derived from the assertibility of two incompatible meaning ascriptions, and, consequently provides no genuine justification nor explanation for an agent’s providing answers to equations involving arbitrarily large numbers. In other words, such a state would not play an important causal-explanatory role in Jones’ use of +. Therefore, the account of the state of meaning something that follows from the rejection of the closure principle of assertibility of meaning ascriptions is fundamentally at odds with the premises of straight solutions. Consequently, it is untenable to argue for the rejection of the closure principle of assertibility of meaning ascriptions within the framework of straight solutions.

5.1.2 Closure Principle and Error-Theory Interpretation of the Skeptical Solution

I believe that the method of defending a non-factualist interpretation from Miller’s critique developed in the current paper may be applied to defend other interpretations of the skeptical solution as well. In another paper, the author demonstrates how the rejection of the closure principle applies to the factualist interpretation (Wieczorkowski, 2023). Nevertheless, I believe that it may also be used to refute Miller’s argument against non-eliminativist error theory interpretation of the skeptical solution (Miller, 2015).

Miller (Miller, 2015, p. 324) notices that there are two broad sorts of error theory about a particular region of thought and talk: eliminativist error theories and non-eliminativist error theories. According to an eliminativist error theory of a region of thought and talk, all of the atomic, positive judgements that we might make within that area are false, and if we continue engaging in the practice of making such judgments, that is only because we have not yet developed a suitable hygienic replacement for the discourse concerned. According to Miller, the skeptical solution is not eliminativist in this sense: there is absolutely no suggestion in the skeptical solution that our practice of ascribing meanings will someday, in principle, be replaceable by a philosophically hygienic surrogate (Miller, 2015, p. 332). Furthermore, on the skeptical solution, our meaning-ascriptions can be fully justified despite the absence of meaning-constituting facts.

There is also another type of error theory — the non-eliminativist one — which relies on avoiding the possibility of the eventual displacement of the relevant area based on pragmatic advantages associated with the subsidiary norms. Consequently, as Miller notes, for this strategy to be applied in a given case, there has to be such a thing as complying or failing to comply with the subsidiary norm (Miller, 2015, p. 330).

However, according to Miller, the non-eliminativist error theory is completely closed off to the proponents of the skeptical solution (Miller, 2015, p. 331). Here, the subsidiary norm might be cashed out in terms of agreement with respect to inclinations on “how to go on,” and the utility of our complying with the subsidiary norm in our meaning-ascribing practice would be that we are thereby enabled to discriminate — e.g., when seeking to buy five apples — between grocers whose inclinations match ours and grocers with “bizarre” quus-like inclinations. Unfortunately, Miller notes that an error theorist about rule-following denies precisely that there are facts about norm-compliance and non-compliance. Consequently, there is no fact about whether a given course of action complies or fails to comply with a subsidiary norm, which undermines the assertibility of meaning ascriptions. In sum, non-eliminativist error theories do not provide a plausible vehicle for understanding the skeptical solution.

Nevertheless, I believe that Miller’s argument is not sound, and it can be refuted by rejecting the closure principle of assertibility of meaning ascriptions.

We may reconstruct the argument that Miller formulates against the non-eliminativist error theory interpretation as follows:

  1. 1.

    It is not the case that words mean nothing to anyone.

  2. 2.

    There are no semantic facts.

  3. 3.

    The primary function of meaning ascriptions is descriptive.

  4. 4.

    On the basis of (2) and (3), all meaning ascriptions are intrinsically false.

  5. 5.

    If meaning ascriptions are assertible even when false, then there are pragmatic subsidiary norms meaning ascriptions comply with.

  6. 6.

    By contraposition of (5), if there is no pragmatic subsidiary norms meaning ascriptions comply with, then it is not the case that meaning ascriptions are assertible even when false.

  7. 7.

    If there are pragmatic subsidiary norms meaning ascriptions comply with, then there are certain facts that determine compliance of meaning ascriptions with these norms.

  8. 8.

    By contraposition of (7), if there are no facts determining the compliance of meaning ascriptions with subsidiary norms, then there is no pragmatic subsidiary norm meaning ascriptions comply with.

  9. 9.

    If there are no semantic facts, then there are no facts determining the compliance of meaning ascriptions with subsidiary norms.

  10. 10.

    On the basis of (2) and (9), there are no facts determining the compliance of meaning ascriptions with subsidiary norms.

  11. 11.

    On the basis of (8) and (10), there is no pragmatic subsidiary norm meaning ascriptions comply with.

C: Meaning ascriptions are not assertible.

The conclusion of Miller’s argument that undermines the efficacy of subsidiary norms in rendering meaning ascriptions assertible, as derived from premises (6) and (11). Nevertheless, in order to examine the soundness of Miller’s argument, let us take a look at (8), (9), and (10). I believe that a proposition that is contained in premise (10), the antecedent of premise (8), and the consequent of premise (9) possesses some ambiguity. Namely, it does not precisely elucidate what Miller means by “complying with a subsidiary norm.” In order to resolve this ambiguity, we can turn to Immanuel Kant’s distinction between actions that conform to a rule and actions that follow a rule. According to Kant, the evaluation of an action’s conformity or nonconformity with a rule happens regardless of whether the rule was incentive to the action. In contrast, the evaluation of whether a given agent follows a rule by his action examines whether the rule is the incentive to the action.

Consequently, we can interpret the mentioned proposition in two different ways:

  1. 1.

    There is no fact that an agent S making a given meaning ascription follows a given subsidiary norm

  2. 2.

    There is no fact that a given meaning ascription made by an agent S merely conforms with a given subsidiary norm, irrespective of whether S wanted to follow this norm or not.

However, if the correct interpretation of the proposition is that there are no facts determining the compliance of meaning ascriptions with subsidiary norms is (2), then we can challenge premise (9) of Miller’s argument as unsound, given that it relies on an over-application of Kripke’s original argument, conflating skepticism about rule-following with skepticism about rule conformity. Nevertheless, it is debatable whether the absence of facts about rule-following necessarily implies a lack of facts about rule-conformity. Kripke’s original argument on rule-following does not inherently deny the possibility of determining whether an action conforms to a rule. In contrast, it raises questions about the possibility of rule-following on the basis of the observation that agent’s actions conform with two different, but in some respect incompatible, rules. Therefore, the second interpretation is less convincing. It extends Kripke’s skepticism from facts regarding rule-following to facts regarding rule conformity. Meanwhile, it seems that Kripke’s skepticism already assumes rule-conformity.

Alternatively, we can interpret the proposition that there are no facts determining the compliance of meaning ascriptions with subsidiary norms as a claim that there is no fact determining whether an agent, making a given meaning ascription, follows a specific subsidiary norm. This interpretation confirms premise (9), since the lack of semantic facts evidently implies the absence of facts about rule-following. Nevertheless, this interpretation poses a challenge to premise (8), which now should be read as a claim that if there are no facts determining whether an agent S, making a given meaning ascription, follows a given subsidiary norm, then there is no pragmatic subsidiary norm he follows. I find this claim flawed, as it presupposes the closure principle.

In turn, if we reject the closure principle of assertibility of meaning ascriptions, then the sentence “she follows such-and-such subsidiary norm” does not require any fact that the agent follows subsidiary norm A rather than norm B. Therefore, I suggest that by rejecting the closure principle, we can argue that there is no fact that an agent S, making a given meaning ascription, follows a specific subsidiary norm, all while maintaining the assertibility of a claim that S follows such-and-such subsidiary norm. Consequently, we may assert that an agent making a given meaning ascription follows a specific subsidiary norm even in the absence of facts that justify refuting alternative explanations for agent’s actions. Therefore, by rejecting the closure principle, we maintain the assertibility of meaning ascriptions despite their being genuinely false due to their descriptive function and lack of semantic facts.

5.2 Non-Factualism and the Problem of Creeping Minimalism

The presented defense of the non-factualist interpretation of the skeptical solution might encounter the objection that the proposed non-factualist stance on meaning ascriptions assumes an inflationary account of truth conditions. And if consistently applied to a deflationary truth account, it eventually leads to semantic nihilism. This objection rests on the deflationary notion that whenever I can assert that Jones means addition by +, I can also assert that Jones means addition by + is true. This maneuver is possible on the basis of the deflationary account of truth-aptness, which states that a sentence has truth conditions if it satisfies two requirements (see Boghossian, 1990):

Discipline: There must be acknowledged standards for the proper and improper use of sentences of the discourse: the discourse must be disciplined, in the sense that there must be standards in force with respect to which uses of the discourse’s sentences are judged to be appropriate or inappropriate.

Syntax: The sentences of the discourse possess the right sort of syntactic features: for example, they must be capable of conditionalisation, negation, embedding in propositional attitudes, etc. (Boghossian, 1990, p. 163).

Therefore, deflationary account on truth-aptness leads to the possibility of attributing deflationary truth-conditions to meaning ascriptions as long as they satisfy two requirements above. Nevertheless, if the non-factualist interpretation refrains from attributing any — even deflationary — truth conditions to meaning ascriptions in order to avoid semantic nihilism, then the proponent of the non-factualist interpretation is obliged to admit that meaning ascriptions fail to satisfy at least one of the aforementioned requirements. But this position is equivalent to the acceptance of semantic nihilism. Thus, the non-factualist needs to answer the following question: How to maintain semantic non-factualism and avoid semantic nihilism in the context of the deflationary account of truth-aptness?

5.2.1 The Rejection of the Deflationist Account of Truth-aptness

One approach to addressing this question arises from accepting that a deflationary account of truth-aptness is incompatible with non-factualism (Byrne, 1996, p. 341). Therefore, to uphold semantic non-factualism, one must then eschew the deflationist account of truth-aptness. A potential avenue for achieving this is by demonstrating that disciplinary and syntactic conditions alone are insufficient to attribute even deflationary truth-conditions to linguistic units like sentences. A compelling defense of this claim could emphasize that assigning a truth-condition to a sentence is permissible only if the sentence expresses a cognitive state, such as a belief, and that meaning ascriptions, properly understood, do not express such states. On this basis, a non-factualist can maintain that meaning ascriptions lack truth conditions while avoiding the criticism that her position relies on an inflationary account of truth. However, it is possible to argue that the non-factualist interpretation presupposes a genuine or inflationary perspective on cognitive states (such as belief), while a deflationary account (see Barber, 1998; Field, 2001; Schiffer, 2003) presents an equally promising position. According to the deflationary account, beliefs find grounding in belief reports, implying that every subject of belief reports can be regarded as believing tout court. Th consequently, apparently non-cognitive states, like moral evaluations, may be viewed as beliefs through reports such as “Smith believes that killing is wrong”. Accordingly, states expressed by meaning ascriptions (as they are seen by the non-factualist), may be seen as beliefs due to reports such as “Smith believes that Jones means addition by ‘+’”. However, this point of view poses a challenge to non-factualist interpretation, because it obliges the supporter of this position to accept that meaning ascriptions do have truth-conditions, at least deflationary ones. Thus, it seems that the consistency of a non-factualist interpretation depends on the possibility if rejection of the deflationist account of belief. However, determining the reliability and justification of rejecting the deflationary account of belief in favor of the non-factualist interpretation of the skeptical solution exceeds the scope of this article.Footnote 3

5.2.2 A New Bifurcation Criterion Between Factual and Non-Factual Sentences

The second, and arguably more promising, approach to defending the non-factualist interpretation relies on the claim that the existence of minimal semantic facts does not undermine the non-factualist nature of the skeptical solution. In response to a challenge stemming from a deflationary approach to truth-aptness, a non-factualist can maintain her position by stating that recognizing facts about the warranted use of expressions in our language does not imply accepting that sentences like Jones means addition by + are used to state facts (see Boyd, 2017, p. 11, Miller, 2020, pp. 13-16). This perspective is compelling because, phrased this way, the difference between the factualist and non-factualist interpretations of the skeptical solution lies not in how the skeptical solution addresses the skeptical problem, but rather in the demarcation between the factual or non-factual.

Thus, a non-factualist is confronted with the question: is there any satisfactory for bifurcating between factual and non-factual discourse that allows the envisaged interpretation of the skeptical solution to retain its non-factual character? According to the standard account distinguishing between factual and non-factual discourse, as delineated by, among others, Alfred Ayer, a sentence is factual if it is fact-stating, that is, if it expresses certain cognitive states like beliefs. Conversely, it is non-factual if it expresses certain non-cognitive states, like emotions or evaluative attitudes (Ayer, 1936, pp. 108-111). However, as Davies aptly notes, “the sceptical paradox undermines the very notion of 'fact-stating discourse' understood in the ‘Tractarian’ sense” (Davies, 1998, p. 130) — a sense that may also be ascribed to Ayer. From this standpoint, the skeptical remarks imply (1) a deflationary account of truth-aptness, thereby justifying the attribution of truth conditions (at least deflationary ones) to sentences like Jones means addition by +, (2) a minimalist conception of facts, thereby justifying that whenever we can say that a given sentence S is true, we may say that it is a fact that S. Thus, it seems that meaning ascriptions, as characterized by non-factualists, may be seen as fact-stating (at least in some minimalist sense), and, consequently, factual.

Therefore, a proponent of the non-factualist interpretation must confront the deflationary/minimalist threat to non-factualism because it appears to undermine the fundamental tenet of the non-factualist view: that there are no semantic facts of any kind. In other words, the challenge facing the non-factualist is how to preserve its non-factual character.

The most promising approach is to propose a new criterion for bifurcation between the factual and non-factual, allowing meaning ascriptions to be characterized as non-factual. As Šumonja aptly notes, the non-factualist introduces such a criterion through the concept of “explanatory direction.” According to this criterion, when discussing stones or chairs, we must think of ourselves as causally influenced by them — It is precisely this causal relationship that implies our descriptive and, consequently, factual discourse. On the other hand, when we formulate moral sentences (or meaning ascriptions, as non-factualists suggest), we talk expressively, because we are not causally influenced by any fact corresponding to these sentences. Thus, because we cannot reduce meaning ascriptions to a causal relation between facts about a speaker and his uses of language, the non-factualist is entitled to say that meaning ascriptions are not factual statements.

Another version of bifurcation through explanation was proposed by Dreier (Dreier, 2004). Dreier differentiates between expressivism and realism not on the ground of the features of ethical language and thought, but rather in terms of what features explain their content. However, a non-factualist may adopt this criterion and use it to distinguish between factual and non-factual discourses. Therefore, a non-factualist may defend her position from the threat of creeping factualism by acknowledging semantic facts and properties, as understood by the minimalist, while denying that such things are part of what explains the content of meaning ascriptions. The whole point that follows from Dreier’s account is that what matters is not the features the non-factualist thinks semantic discourse has (that is, whether there are any semantic facts), but rather which of those features explain the fact that meaning ascriptions mean what they do. Therefore, even if a non-factualist must acknowledge semantic facts due to deflationism about truth-aptness, she can deny that meaning ascriptions are to be explained in terms of these facts. On this basis, she may argue that meaning ascriptions are not factual.

Another bifurcation criterion that is also worth mentioning was formulated by Michael Williams (Williams, 2013). Williams utilizes the inferentialist framework to distinguish between expressive and descriptive discourses by examining the functional roles played by different vocabularies. However, I think that a non-factualist may also adopt this criterion and use it to distinguish between factual and non-factual sentences. According to Williams, within the inferentialist framework, certain sentences, such as those containing color terms, function as “language entry transitions,” and hence essentially involve world-word relations. Observational terms of this kind possess a specific epistemological component: any use of an observational term (e.g., “green”) is allowed when there is a thing possessing the observable quality (e.g., a green thing) (Williams, 2013, pp. 140-141). However, there exist other segments of vocabulary — moral discourse being the best example — that serve rather as language exit transitions, as justifying action, rather than merely describing world. A correct description of such expressive sentences does not take the form of “one is licensed to use the moral predicate M whenever the moral property m is present” — they do not have a simple epistemology of that sort, because they are somehow disconnected from the simple entry transactions (Williams, 2013, pp. 142-143). Thus, the non-factualist may argue that meaning ascriptions are non-factual, because, even if they have deflationary truth-conditions, their main function is to serve as language exit transitions.

6 Concluding Remarks

The considerations presented in this text address the objection formulated by Alexander Miller, who argues that the non-factualist interpretation of the skeptical solution is self-refuting. According to Miller, it is not possible to reject both semantic facts and semantic nihilism, because the rejection of semantic facts eventually leads to semantic nihilism. This is because it makes the attribution of correctness conditions to meaning ascriptions (even if taken non-descriptively) impossible. In contrast, I argue that this objection is unsound as it relies on the closure principle for meaning ascriptions. I propose that rejecting the closure principle for meaning ascriptions is not only the main idea of the skeptical solution, but also enables the non-factualist to undermine the objection formulated by Miller, as it eliminates the need for semantic facts in attributing correctness conditions to meaning ascriptions.