Brian Rabern

This paper examines Venn diagrams as a case study in visual representation. Venn diagrams have a clear formal structure and well-defined correctness conditions. The central question is whether they possess a recursive syntax and corresponding compositional semantics analogous to those developed for formal and natural languages. Existing research notably fails to provide a compositional semantics for Venn diagrams. This may suggest a fundamental divide between linguistic and visual representation, or instead a case of representation that resists compositional analysis. The paper presents two approaches to the syntax of Venn diagrams—a region-first approach and a cell-first approach—and develops a compositional semantics for each. In doing so, it clarifies the similarities and differences between linguistic representation and diagrammatic representation, and it suggests new avenues for interpreting other forms of visual representation.

Large language models have demonstrated notable performance across various logical reasoning benchmarks. However, it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a unified benchmark designed to isolate three fundamental skills in formal reasoning: (i) formal symbolization—translating premises into first-order logic; (ii) countermodel construction—formulating a finite structure in which all premises are true while the conclusion is false; and (iii) validity assessment—deciding whether a conclusion follows from a given set of premises. Items are drawn from the two-variable fragment of first-order logic (without identity) and are presented in both natural English and a Carroll-style language with nonce words. All examples are verified for correctness and non-triviality using the SMT solver Z3. Across leading models, performance is high on validity but substantially lower on symbolization and countermodel construction, suggesting reliance on surface-level patterns rather than genuine symbolic or rule-based reasoning.

Semantics is the systematic study of linguistic meaning. The past fifty years have seen an explosion of research into the semantics of natural languages. There are now sophisticated theories of phenomena that were not even known to exist mere decades ago. Much of the early work in natural language semantics was accompanied by extensive reflection on the aims of semantic theory, and the form a theory must take to meet those aims. But this meta-theoretical reflection has not kept pace with recent theoretical innovations. The aim of this volume is to re-address these questions concerning the foundations of natural language semantics in light of the current state-of-the-art in semantic theorizing. The volume addresses a range of foundational questions about formal semantics: what is the best methodology for semantic theorizing, and should experimental techniques play a crucial role? How should we understand the use of formal tools such as model theory, and are there better formal alternatives? How should we think about compositionality? What does semantic theory tell us about the language faculty or linguistic competence? What are the advantages of dynamic semantics? How do formal semantic theories relate to philosophical notions of context, content, interpretation, and propositions?

We assess the compatibility of Variabilism -- the view that bare singular uses of proper names are best modeled as individual variables -- with the arguments and insights of Kripke's _Naming and Necessity_. After clarifying the view and tracing its historical development, we present a presuppositional variant that treats names as assignment-dependent variables constrained by naming presuppositions, akin to pronouns. We argue that this account accommodates Kripke's three central arguments against Descriptivism (semantic, epistemic, and modal), as well as his circularity constraint. We then show how this view naturally integrates with Kripke's causal-historical metasemantics and captures the anaphoric behavior of names in discourse -- participating in co-indexing relations, appearing in binding configurations, and co-varying with quantifiers. These phenomena are hard to explain on a strict Millian view but follow naturally from a variabilist semantics.

The principle of Conditional Excluded Middle has been a matter of longstanding controversy in both semantics and metaphysics. The principle suggests (among other things) that for any coin that isn't flipped, there is a fact of the matter about how it would have landed if it had been flipped: either it would have landed heads, or it would have landed tails. This view has gained support from linguistic evidence indicating that ‘would’ commutes with negation (e.g., ‘not: if A, would C’ is equivalent to ‘if A, would not C’). There is, however, a long list of operators that similarly appear to commute with negation, even though the corresponding excluded middle principles are indefensible. We suggest that the data supporting Conditional Excluded Middle is best explained as a pragmatic effect.

At the turn of the century, electronic mail emerged as a core mode of communication, fundamentally transforming the way individuals and organizations interact. In this digital age, one ubiquitous representational device is the email address. Given the importance of email addresses in our lives, it is natural to ask: what do email addresses represent? And how do they represent it? Given that email addresses have a semantic interpretation, and that they have a formal syntax, it is reasonable to assume that they have a compositional semantics. Do they? If so, what is it?

Wittgenstein's builder language is commonly taken to motivate a skepticism about systematic semantic theorizing. This paper argues that such skepticism goes too far. I show that the example admits a simple compositional analysis that accommodates demonstratives, gestures, and directive utterances without undermining the emphasis on use that motivates it. The analysis does not compete with Wittgenstein’s philosophical aims, but helps to clarify the scope and limits of the lessons his example supports.

In this paper, we clarify, unpack, and ultimately resist what is perhaps the most prominent argument for the compatibility of free will and determinism: the epistemic argument for compatibilism. We focus on one such argument as articulated by David Lewis: (i) we know we are free, (ii) for all we know everything is predetermined, (iii) if we know we are free but for all we know everything is predetermined, then for all we know we are free but everything is predetermined, (iv) if for all we know we are free but predetermined, then it is really possible that we are, so (v) compatibilism. We uncover how the crucial epistemic modality underlying (iv) must be understood, and contend that, understood this way, the libertarian can resist (iv). Importantly, however, resisting the argument does commit the libertarian to what has been called “flip-flopping”—but we argue that this is perfectly coherent. We conclude by articulating two crucially ways the libertarian can resist the argument, by saying that we can know that determinism is false "from the armchair".

Deontic necessity modals (e.g. 'have to', 'ought to', 'must', 'need to', 'should', etc.) seem to vary in how they interact with negation. According to some accounts, what forces modals like 'ought' and 'should' to outscope negation is their polarity sensitivity -- modals that scope over negation do so because they are positive polarity items. But there is a conflict between this account and a widely assumed theory of if-clauses, namely the restrictor analysis. In particular, the conflict arises for constructions containing a bound pronoun in the if-clause. This note spells out the core conflict.

There is an important analogy between languages and games. Just as a scoresheet records features of the evolution of a game to determine the effect of a move in that game, a conversational score records features of the evolution of a conversation to determine the effect of the linguistic moves that speakers make. Chess is particularly interesting for the study of conversational dynamics because it has language-like notations, and so serves as a simplified study in how the effect of an assertion depends on, as well as evolves, the scoreboard. In this paper, we offer a compositional semantics for chess notation and a simple formal picture for determining the full information conveyed by an entry. We will also discuss an alternative model resembling accounts of centered assertion.

A common framing has it that any adequate treatment of quotation has to abandon one of the following three principles: (i) The quoted expression is a syntactic constituent of the quote phrase; (ii) If two expressions are derived by applying the same syntactic rule to a sequence of synonymous expressions, then they are synonymous; (iii) The language contains synonymous but distinct expressions. In the following, a formal syntax and semantics will be provided for a quotational language which adheres to all three principles. The point here is not merely to provide a “possibility proof”, but to reveal the hard constraints on the theory of quotation, and to highlight certain assumptions at the syntax/semantics/post-semantics interfaces.

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference.

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to get a purely mathematical problem.

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for a wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt.

The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims about synonymy and substitution while respecting the compositionality principle. Thus, Salmon (Philos Rev 115(4):415, 2006) and Glanzberg and King (Philosophers’ Imprint 20(2):1–29, 2020) offer occurrence-based accounts of variable binding, and Pagin and Westerståhl (Linguist Philos 33(5):381–415, 2010c) argue that an occurrence-based semantics delivers a compositional account of quotation. Our thesis is this: the occurrence-based strategies resolve the apparent failures of substitutivity in the same general way as the standard expression-based semantics do. So it is a myth that a Frege-inspired occurrence-based semantics affords a genuine alternative strategy.

This chapter provides a general overview of the issues surrounding so-called semantic monsters. In section 1, I outline the basics of Kaplan’s framework and spell out how and why the topic of “monsters” arises within that framework. In Section 2, I distinguish four notions of a monster that are discussed in the literature, and show why, although they can pull apart in different frameworks or with different assumptions, they all coincide within Kaplan’s framework. In Section 3, I discuss one notion that has spun off into the linguistics literature, namely “indexical shift”. In Section 4, I emphasize the connection between monsters and the compositionality of asserted content in Kaplan’s original discussion. Section 5 discusses monsters and the more general idea of re-interpretation or meaning-shift. Section 6 closes with a brief survey of where monsters may dwell, and pointers to avenues for future research.

ABSTRACT Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's ‘objectual’ interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields the undesirable result that any attempt to ‘quantify in’ to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality.

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of 'will' both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form 'will(φ)'.

Montague and Kaplan began a revolution in semantics, which promised to explain how a univocal expression could make distinct truth-conditional contributions in its various occurrences. The idea was to treat context as a parameter at which a sentence is semantically evaluated. But the revolution has stalled. One salient problem comes from recurring demonstratives: "He is tall and he is not tall". For the sentence to be true at a context, each occurrence of the demonstrative must make a different truth-conditional contribution. But this difference cannot be accounted for by standard parameter sensitivity. Semanticists, consoled by the thought that this ambiguity would ultimately be needed anyhow to explain anaphora, have been too content to posit massive ambiguities in demonstrative pronouns. This article aims to revived the parameter revolution by showing how to treat demonstrative pronouns as univocal while providing an account of anaphora that doesn't end up re-introducing the ambiguity.

Almost entirely ignored in the linguistic theorising on names and descriptions is a hybrid form of expression which, like definite descriptions, begin with 'the' but which, like proper names, are capitalised and seem to lack descriptive content. These are expressions such as the following, 'the Holy Roman Empire', 'the Mississippi River', or 'the Space Needle'. Such capitalised descriptions are ubiquitous in natural language, but to which linguistic categories do they belong? Are they simply proper names? Or are they definite descriptions with unique orthography? Or are they something else entirely? This paper assesses two obvious assimilation strategies: (i) assimilation to proper names and (ii) assimilation to definite descriptions. It is argued that both of these strategies face major difficulties. The primary goal is to lay the groundwork for a linguistic analysis of capitalised descriptions. Yet, the hope is that clearing the ground on capitalised descriptions may reveal useful insights for the on-going research into the semantics and syntax of their lower-case or 'the'-less relatives.

In contemporary natural languages semantics one will often see the use of special brackets to enclose a linguistic expression, e.g. ⟦carrot⟧. These brackets---so-called denotation brackets or semantic evaluation brackets---stand for a function that maps a linguistic expression to its "denotation" or semantic value (perhaps relative to a model or other parameters). Even though this notation has been used in one form or another since the early development of natural language semantics in the 1960s and 1970s, Montague himself didn't make use of this notation in his series of groundbreaking papers on semantics. That raises the question: When was the ⟦.⟧-notation introduced to semantics? This note answers that question.

Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the two-dimensional semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators.

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics.