2026/07/01 by Julien Murzi
Psychology · Computer Science · #Child and Animal Learning Development #Logic, Reasoning, and Knowledge #Philosophy and Theoretical Science
paper · doi:10.1215/00318108-12455434
Semantic orthodoxy since Frege has it that the content of a sentence (in context) is given by its truth conditions, and that the content of a subsentential expression is given by its contribution to the truth conditions of the sentences in which it may occur. This semantic paradigm is widely adopted in contemporary philosophy of language as well as in linguistics departments. However, widespread and successful as it is, it has long been challenged on a number of grounds. Intuitionists have objected that it makes the content of mathematical sentences radically disconnected from mathematical practice. Anti-realists have charged that it delivers an unworkable, irredeemably circular account of understanding. Deflationists have accused it of relying on hopelessly obscure conceptions of truth and reference. Expressivists have lamented that it delivers a deeply flawed account of normative vocabulary. Inferentialists have attacked it on the grounds that it turns metasemantics into a mystery and that it makes semantic content unnecessarily complicated. Yet none of these critical voices has been able to offer a viable alternative semantic paradigm that can actually be used to deliver a workable semantics for fragments of natural language. As Timothy Williamson (2007: 282) famously put it, anti-realists, inferentialists, and unorthodox semanticists more generally “preferred to polish their formulations of the grand programme rather than getting down to the hard and perhaps disappointing task of trying to carry it out in practice.”In their superb book Reasoning with Attitude, Luca Incurvati and Julian Schlöder take up the challenge of providing an alternative to semantic orthodoxy head on. They set forth a novel, unorthodox semantic paradigm, inferential expressivism, as they call it, and go on to (1) show how it can be applied to key fragments of natural language—to wit, epistemic modals, moral vocabulary, attitude verbs, semantic vocabulary, conditionals, and probability talk—and (2) argue that inferential expressivism altogether avoids some of the problems that have been plaguing existing accounts, both orthodox and unorthodox, of these natural language fragments. The book is divided into ten chapters. The first two introduce, respectively, expressivism and inferentialism, and briefly discuss the main challenges they face. The third argues in favor of combining expressivism and inferentialism into inferential expressivism. The next six chapters work out in a fair amount of detail inferential expressivist accounts of the six fragments of natural language mentioned above. The tenth chapter briefly discusses areas of future work.The book is admirably written and argued. It is impossible, in such a short space, to do justice to its wealth of detailed philosophical arguments and semantic analyses. The first three chapters are largely philosophical: They provide concise and yet informative and engaging critical introductions to inferentialism and expressivism, clearly articulating the main arguments in their favor and the problems they face. Along the way, Incurvati and Schlöder also briefly introduce truth-conditional semantics as well as the now familiar distinction between semantics, postsemantics, and metasemantics, correctly observing that, whereas on the orthodox picture facts about reference and truth conditions are conceptually prior to facts about validity, on the inferentialist picture it is rather the other way round. The remaining chapters lie at the intersection between the philosophies of language and logic, logic proper, and formal semantics. Their subject matter is more technical, but the presentation is always engaging and accessible. Technical proofs are relegated to appendices.The main metasemantic principle Incurvati and Schlöder rely on when arguing in favor of their own inferential expressivist framework is what they call the Pragmatist Razor—that is, the injunction to “avoid semantic explanations that are not needed to account for the functional role of an expression or sentence” (9). For instance, if one’s account of the functional role of moral role of moral predicates—that is, of the point of having such predicates in the language—doesn’t require that those predicates have extensions, then one’s semantic account of moral predicates should not assign extensions to them. Incurvati and Schlöder’s semantic framework is thus strongly inferentialist: The meaning of an expression is not to be explained in terms of reference but is rather given by the basic rules for its correct use. More precisely, Incurvati and Schlöder’s starting point is a bilateralist account of logic (Smiley 1996; Rumfitt 2000; Warren 2020), according to which the basic rules for an expression e comprise both rules for asserting and rules for rejecting sentences in which e figures (for instance, the rules for negation include rules that allows one to move from the assertion of ¬φ to the rejection of φ, and vice versa). Incurvati and Schlöder generalize the standard bilateralist framework along two dimensions. First, they differentiate between strong, weak, and moderate forms of both assertion and rejection. Whereas the strong assertion of φ (linguistically realised by the answer ‘Yes’ to the question whether φ) can be seen as a proposal to add φ to the positive common ground (the set of sentences that are believed by the speakers in a given context), the weak assertion of φ (linguistically realised by the answer ‘Perhaps yes’ to the question whether φ) can be seen as a proposal not to add φ to the negative common ground (the set of sentences that are disbelieved by the speakers in a given context). As for moderate assertion (linguistically realised by the answer ‘Probably yes’ to the question whether φ), it is interpreted as a tentative proposal to add φ to the positive common ground. Similarly, mutatis mutandis, for strong, weak, and moderate rejection. The framework becomes a multilateralist one, in which several speech acts figure among both the premises and conclusions of basic principles. Second, Incurvati and Schlöder consider attitudes beyond those expressed by assertion and rejection, such as approval and disapproval, and take them to figure among the basic principles governing predicates such as ‘right’ and ‘wrong’.The framework is doubly expressivist: It allows the expression of attitudes toward contents to figure among the premises and conclusions of basic inference rules, and it also takes the point of the logical vocabulary to be the expression of certain basic attitudes—for instance, the point of negation is to express disbelief, the point of ‘might’ is to express one’s refraining from expressing disbelief (107), the point of ‘wrong’ is to express disapproval, and so on.The question immediately arises whether Incurvati and Schlöder’s framework faces a version of the Frege-Geach problem. According to traditional expressivism, ‘Killing is wrong’ doesn’t really have content; it simply expresses disapproval of killing. But, as Frege and Geach pointed out, embedded occurrences of expressions that are accounted for in expressivist terms cannot be plausibly taken to express attitudes—after all, the assertion of sentences such as ‘Killing isn’t wrong’ don’t express disapproval of killing. Inferential expressivists avoid the problem altogether. Sentences of the form ‘Φ-ing is wrong’, Incurvati and Schlöder argue, don’t express disapproval of Φ-ing but rather have a content that’s given by their basic inference rules (such as the principle ‘From disapproval of Φ-ing, infer that Φ-ing is wrong’ and its converse). These rules sanction the interderivability of disapproval of Φ-ing and the strong assertion of ‘Φ-ing is wrong’, but they don’t require that ‘Φ-ing is wrong’ be interpreted as a mere expression of disapproval of Φ-ing. The solution generalizes to epistemic modals, conditionals, and so on. Incurvati and Schlöder do an excellent job at suggesting that the view avoids the pitfalls of traditional expressivism while retaining its benefits (for instance, inferential expressivism accounts for the motivating character of moral judgements and avoids postulating problematic semantic values such as moral properties).The hero of the book is the basic multilateral logic BML, whose rules involve strong assertion, strong rejection, and weak rejection. Extensions of BML, which include rules for ‘wrong’, ‘might’, ‘true’, ‘probable’, and ‘if’, constitute the semantic frameworks in terms of which the inferentialist semantics for the six case studies considered in the book is given. However, BML isn’t fully classical. For reasons that we don’t have the space to review here, Incurvati and Schlöder maintain that inference rules need not preserve evidence and that their validity is to be accounted for in terms of preservation of one’s commitments (78). They then argue that meta-rules are valid only if their subproofs are evidence-preserving. As a result, the subproofs of any meta-rules are restricted so as to disallow the application of principles that don’t preserve evidence. Crucially, according to Incurvati and Schlöder, the naive rules for the truth predicate (which sanction the interderivability of any sentence and its truth predication), and semantic rules more generally, are cases in point, whence meta-rules such as classical reductio, ¬-I, →-I, and ∨-E are restricted along familiar supervaluationist lines so as to disallow the use of semantic rules within their subproofs. The output is both a diagnosis of what goes wrong in the semantic paradoxes, that they all rely on non-evidence-preserving instances of naive semantic rules, and a cure—namely, that rules that are not evidence-preserving may not be used within subproofs. This, Incurvati and Schlöder argue, suffices to block the semantic paradoxes, including the so-called revenge paradoxes (205–15).Incurvati and Schlöder’s approach to the paradoxes isn’t an essential part of their semantic framework. It is also the least convincing. For one thing, the question whether their approach is revenge-free cannot be assessed: their diagnostic machinery, which relies on notions such as evidence and evidence preservation, simply isn’t present in the object language of the theories they consider. And yet revenge paradoxes typically arise precisely when one tries to formulate in the object language a diagnosis of what goes wrong in paradoxical derivations.1 For another, their diagnosis of the paradoxes seems forced. Their main argument for thinking that semantic rules fail to preserve evidence is that instances of those rules involving definite descriptions, as in ‘It will be sunny tomorrow; therefore, what Ursula said yesterday is true’ are typically not evidence-preserving (one may have evidence that it will be sunny tomorrow while failing to know that this is what Ursula said). The problem here is that this gives us no reason for thinking that the instances of the semantic rules involved in the paradoxes, which need not involve definite descriptions, fail to preserve evidence. The problem also appears in Incurvati and Schlöder’s approach to the paradoxes of weak rejection (216–17). Incurvati and Schlöder argue that certain principles for the use of a weak rejection predicate must be restricted to sentences we understand. But they are then forced to maintain that the instances of those principles involved in a certain Liar-like paradox violate this restriction, which is tantamount to saying, implausibly, that we do not understand a Liar-like sentence that can be unproblematically formulated in the language of arithmetic with the addition of a weak rejection predicate. It should be stressed, however, that Incurvati and Schlöder’s approach to the paradoxes is but an added bonus to their overall semantic framework. The framework should be judged in the way it deals with moral terms, epistemic modals, conditionals, and other expressions. And here it certainly succeeds in setting a new standard—one that makes Williamson’s objections to critics of semantic orthodoxy, fair at the time in 2006, unfair and passé now.This research was funded in part by the Austrian Science Fund (FWF) [10.55776/COE3 and 10.55776/PAT2449425], whose support I gratefully acknowledge.