This paper discusses a number of methodological issues with mainstream formal semantics and then investigates whetherWittgenstein’s later work provides an alternative approach that is able to avoid these issues.

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 a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call (...) constructing formal semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis , is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken to (...) be that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

Abstract The purpose of this paper is twofold: (i) we will argue that formal semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts, namely ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of, and relations between, objects of various ontological types; and (ii) we show that accounting for these differences amounts to a new formal semantics; one (...) that integrates lexical and compositional semantics in one coherent framework and one where formal semantics is embedded with a strongly typed ontology; an ontology that reflects our commonsense knowledge of the world and the way we talk about it in ordinary language. We will show how in such a framework a number of challenges in the semantics of natural language are adequately and systematically treated. (shrink)

With a few notable exceptions formal semantics, as it originated from the seminal work of Richard Montague, Donald Davidson, Max Cresswell, David Lewis and others, in the late sixties and early seventies of the previous century, does not consider Wittgenstein as one of its ancestors. That honour is bestowed on Frege, Tarski, Carnap. And so it has been in later developments. Most introductions to the subject will refer to Frege and Tarski (Carnap less frequently) —in addition to the (...) pioneers just mentioned, of course— , and discuss the main elements of their work that helped shape formal semantics in some detail. But Wittgenstein is conspicuously absent whenever the history of the subject is mentioned (usually briefly, if at all). (shrink)

When in 1980, on the Third Amsterdam Colloquium, Johan van Benthem read a paper with the title ‘Why is Semantics What?’ (cf. [1]), I was puzzled: Wasn’t it obvious what semantics is? Why did our concept of it stand in need of justification? Later, much later, I came to appreciate what Van Benthem was doing in this paper (and in some others). Questioning the ‘standard model’, the assumptions on which the working semanticists silently agree, Van Benthem opened up (...) a space of issues to be discussed, questions to be asked, routes to be explored, that had been hidden from view by the unreflective endorsement of just one possible, albeit fruitful way of doing semantics. History, by the way, has proven him right on many points: the monolithic approach that dominated formal semantics of natural language in the seventies, and which relied heavily on Montague’s seminal papers, has given way to a multitude of different ways of tackling semantic issues, using different formal techniques. Some limitations, in particular the almost exclusive focus on sentences as the primary units of analysis, have been overcome. In another respect, however, I feel that the message of Van Benthem’s paper has not caught on sufficiently. He urges semanticists to take more interest in the properties of their tools, arguing that such questions are important if we are to come to a real, deep understanding of what semantics is. Such ‘meta-level’ considerations, although certainly less scarce than they used to be, are still not an everyday concern of the working semanticist. (shrink)

In this paper I will be concerned with the question of the extent to which semantics can be thought of as a purely formal exercise, which we can engage in in a way that is neutral with respect to how our formal system is to be interpreted. I will be arguing, to the contrary, that the features of the formal systems which we use to do semantics are closely linked, in several different ways, to the (...) interpretation that we give to those formal systems. The occasion for this question, and the main example that I will use to illustrate my answer to it, is the close relationship between the formal systems employed in recent statements of apparently competing accounts of epistemic modals with the dynamic, expressivist, and relativist theoretical paradigms. The structure of the paper will be straightforward. In part 1, I will briefly introduce four theories of epistemic modals – one dynamic theory, two expressivist theories, and one relativist theory. Then in part 2 I’ll show that one expressivist theory is formally equivalent to the dynamic theory, that the other is formally equivalent to the relativist theory, and that the two expressivist theories are themselves essentially notational variants. I’ll use these facts to pose our central question: if these theories have so much formally in common, then doesn’t that suggest that we can separate the task of constructing a formal semantics from the task of deciding between competing interpretations of it? Finally, in part 3 I’ll answer that question in the negative. There are at least three reasons why formal semantics cannot be separated from questions of interpretation that are illustrated by the theories I introduce in part 1. (shrink)

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few (...) statements about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no longer (...) play a distinctive role. This account employs a new notion of semantic. (shrink)

Formal thought disorder (FTD) is a clinical mental condition that is typically diagnosable by the speech productions of patients. However, this has been a vexing condition for the clinical community, as it is not at all easy to determine what “formal” means in the plethora of symptoms exhibited. We present a logic-based model for the syntax–semantics interface in semantic networking that can not only explain, but also diagnose, FTD. Our model is based on description logic (DL), which (...) is well known for its adequacy to model terminological knowledge. More specifically, we show how faulty logical form as defined in DL-based Conception Language (CL) impacts the semantic content of linguistic productions that are characteristic of FTD. We accordingly call this the dyssyntax model. (shrink)

An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...) which can be used to generate terms instantiating types from this selected set when applied to terms designating certain other Semantic Types, including almost all the terms specifying clinical tasks. Usage of such operators thus provides a useful and economical way of specifying clinical tasks. The operators allow us to define a mapping between those types within the UMLS which do not represent clinical tasks and those which do. This mapping then provides a basis for an ontology of clinical tasks that can be used in the formulation of computer-interpretable clinical guideline models. (shrink)

Truthmaker semantics is a recent development in formal and philosophical semantics, with similar motivation and scope to possible worlds semantics. The technical background is rather different, however, and results in a more fine-grained hyperintensional notion of content, allowing us to distinguish between classically equivalent propositions. After briefly introducing the main ideas, this entry will describe the technical apparatus of state spaces and the central notions of content and partial content. It will then outline applications of truthmaker (...) semantics in language, logic, and other areas of philosophy. (shrink)

As formal theoretical linguistic methodology has matured, recent years have seen the advent of applying it to objects of study that transcend language, e.g., to the syntax and semantics of music (Lerdahl & Jackendoff 1983, Schlenker 2017a; see also Rebuschat et al. 2011). One of the aims of such extensions is to shed new light on how meaning is construed in a range of communicative systems. In this paper, we approach this goal by looking at narrative dance in (...) the form of Bharatanatyam. We argue that a semantic approach to dance can be modeled closely after the formal semantics of visual narrative proposed by Abusch (2013, 2014, 2021). A central conclusion is that dance not only shares properties of other fundamentally human means of expression, such as visual narrative and music, but that it also exhibits similarities to sign languages and the gestures of non-signers (see, e.g., Schlenker 2020) in that it uses space to track individuals in a narrative and performatively portray the actions of those individuals. From the perspective of general human cognition, these conclusions corroborate the idea that linguistic investigations beyond language (see Patel-Grosz et al. forthcoming) can yield insights into the very nature of the human mind and of the communicative devices that it avails. (shrink)

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of (...) QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

This paper compares several models of formalization. It articulates criteria of correct formalization and identifies their problems. All of the discussed criteria are so called “semantic” criteria, which refer to the interpretation of logical formulas. However, as will be shown, different versions of an implicitly applied or explicitly stated criterion of correctness depend on different understandings of “interpretation” in this context.

This essay develops a structurally minimal account of semantics and consciousness grounded in the concept of pre-reflective self-relation. It begins by distinguishing information from communication, thereby separating formal signal processing—paradigmatically articulated in the work of Claude Shannon—from questions of meaning and experience. Self-relation is then introduced not as a mental act, but as an ontological phase relation between actuality and possibility, formally expressed as a ↔ ia. On this basis, the essay reconstructs a dynamic sequence from rotation and (...) iteration to fields and attractors, yielding a notion of rudimentary semantics as a non-neutral ordering of differences. Semantics is thus shown to be structurally operative prior to life and consciousness. A precise tipping condition is identified in which biological systems bind such differences to their own persistence, giving rise to orientation. Consciousness does not constitute an additional ontological layer, but a phenomenal localization of this already structured semantics. The central conclusion is that self-relation implies no universal consciousness, but an ontologically necessary capacity for consciousness—universal as structure, local as appearance. (shrink)

The redundancy theory says that truth predicates make no descriptive contribution to sentences that contain them. The theory has a strong initial plausibility, and it—or its close relatives—has been defended by the likes of Frege, Ramsey, Ayer, and Strawson. Despite this illustrious history, the redundancy theory is often cited today for its problems. Most notably, the theory allegedly cannot account for the full range of constructions involving truth predicates. These charges are used to motivate purportedly more sophisticated accounts of truth (...) that are compatible with contemporary approaches to semantics. This paper positively develops the redundancy theory as the view that truth predicates are ‘semantically vacuous’, as the expression is used in formal semantics. It is then shown that this semantic vacuity theory of truth can overcome the standard objections while retaining the core insights of the original. (shrink)

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant (...) implication. I then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)

This essay develops a formal model of semantic dynamics inspired by Ferdinand de Saussure's distinction between signifier and signified. Each semantic point is represented as a fourfold structure {p, ip, -p, -ip}; operators O act on these structures as mixtures of identity, rotation, and antonymic transitions. The model introduces the notion of a semantic attractor, which does not operate on words directly but on the operators themselves, gradually reweighting their coefficients. Over repeated iterations, this teleological influence suppresses antonymic detours (...) and amplifies the path from signifier to signified. -/- Taking \emph{Value} as a universal attractor, the essay shows how the process converges toward fixed forms: a stable operator O* and a stable sentence vector M*. These fixed points are the semantic analogue of attractors in chaos theory, revealing how meaning can stabilize in a field otherwise prone to drift and dispersion. -/- In this perspective, \emph{Value} is not simply a lexical entry or contested doctrine, but a formative principle---a gravitational center within the semantic field that bends discourse toward coherence. The essay thereby connects semiotic theory, dynamical systems, and the philosophical question of value as a universal orientation. (shrink)

Semantics is what gives meaning to a logical language. Introductory books in formal logic almost invariably employ Tarskian semantics, a truth semantics that defines an interpretation as a variable assignment over a non-empty domain of discourse together with a signature interpretation. The problem with this semantics is that it generally dictates the undecidability of classical first-order logic due to an infinity of infinite models. In computational logic, decidability is a synonym for computability, and hence Tarskian (...) semantics is not appropriate. In contrast, Herbrand semantics, also a truth semantics, provides us with finite, propositional-logic style, interpretations that guarantee decidability—even if at the price of fixed interpretations for first-order formulae or theories. (shrink)

Formalization of the semantics of generics has been considered extremely challenging for their inherent vagueness and context-dependence that hinder a single fixed truth condition. The present study suggests a way to formalize the semantics of generics by constructing flexible acceptance conditions with comparative probabilities. Findings from our in-depth psycholinguistic experiment show that two comparative probabilities—cue validity and prevalence—indeed construct the flexible acceptance conditions for generics in a systematic manner that can be applied to a diverse types of generics: (...) Acceptability of IS_A relational generics is mostly determined by prevalence without interaction with cue validity; feature-describing generics are endorsed acceptable with high cue validity, albeit mediated by prevalence; and acceptability of feature-describing generics with low cue validity is mostly determined by prevalence irrespective of cue validity. Such systematic patterns indicate a great potential for the formalization of the semantics of generics. (shrink)

This paper defends the view that common nouns have a dual semantic structure that includes extension-determining and non-extension-determining components. I argue that the non-extension-determining components are part of linguistic meaning because they play a key compositional role in certain constructions, especially in privative noun phrases such as "fake gun" and "counterfeit document". Furthermore, I show that if we modify the compositional interpretation rules in certain simple ways, this dual content account of noun phrase modification can be implemented in a type-driven (...) formal semantic framework. In addition, I also argue against traditional accounts of privative noun phrases which can be paired with the assumption that nouns do not have a dual semantic structure. At the most general level, this paper presents a proposal for how we can begin to integrate a psychologically realistic account of lexical semantics with a linguistically plausible compositional semantic framework. (shrink)

This paper provides a new framework for formalizing conditional obligations in natural language: it pairs a unary deontic operator with trivalent semantics for the indicative conditional and Kratzer's assumption that the antecedents of conditionals restrict the scope of modals in the consequent. Combining these three ideas, we obtain a fully compositional theory of "if" and "ought'" that validates plausible principles for deontic reasoning. Moreover, it resolves classical challenges such as the "if A then ought A" problem, the paradox of (...) the miners and the modeling of contrary-to-duty obligations (e.g., Chisholm's quartet). All in all, our proposal is attractive from a logical point of view and squares well with general theories of natural language reasoning. (shrink)

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers (...) faces a number of problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (shrink)

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. (shrink)

This article extends our earlier work From Rotations to Spirals: A Matrix Model of Sentence-Level Semantic Dynamics by introducing the teleological component that had previously been left aside. In the quaternionic extension of the sentence matrix formalism, semantic states are described by a real dimension of actualization and three orthogonal imaginary axes. The axes i and j account for possibilities and goal-orientations, while the real component reflects their stabilization in discourse. Teleological attractors are represented as imaginary targets whose influence is (...) strongest in the distance and vanishes at the point of realization. The resulting dynamics differ fundamentally from gravitational laws: rather than a monotone pull towards what already exists, teleology organizes through the absence of what is not yet realized. Formally, the model is expressed as a drift induced by the gradient of a teleological potential, with feedback on the real component and underdamped oscillations around the attractor. Beyond individual goals, the third imaginary axis k is introduced as the dimension of collective values and norms. These higher-order attractors shape the entire semantic landscape and stabilize discourse over extended timescales. Their detailed mathematical treatment will be developed, however, in a subsequent article. (shrink)

This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material inferences. Extant versions, however, include only propositional logic. This paper extends the framework so as to recover classical first-order logic. The goal is to formulate a theory in which consequence relations can be nonmonotonic and supraclassical, while obeying the deduction-detachment theorem and disjunction simplification, while also including conjunctions that behave (...) multiplicatively as premises and counterexamples to the usual quantifier rules. The paper explains these constraints and shows how they can be met jointly. The result is a first-order version of implication-space semantics that has all the virtues for which inferentialists and inferential expressivists praise propositional implication-space semantics. (shrink)

One of the hottest philosophical debates in recent years concerns the nature of the semantics/pragmatics divide. Some writers have expressed the reserve that this might be merely terminological, but in my view it ultimately concerns a substantive issue with empirical implications: the scope and limits of a serious scientific undertaking, formal semantics. In this critical note I discuss two arguments by Recanati: his main methodological argument —viz. that the contents posited by what he calls ‘literalists’ (which are, (...) on my own view, the very same ones that theoreticians in the formal semantics tradition seek to characterize) play no relevant role in communication—, and some phenomenological considerations regarding the “Availability Principle” that he appeals to in order to buttress that main argument. (shrink)

In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given (...) this enrichment, we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine’s proposed solution to Frege’s puzzle. We argue that Fine has mis-diagnosed his own solution–his attempted solution does not deny compositionality. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle. (shrink)

In “Is semantics possible?” Putnam connected two themes: the very possibility of semantics (as opposed to formal model theory) for natural languages and the proper semantic treatment of common nouns. Putnam observed that abstract semantic accounts are modeled on formal languages model theory: the substantial contribution is rules for logical connectives (given outside the models), whereas the lexicon (individual constants and predicates) is treated merely schematically by the models. This schematic treatment may be all that is (...) needed for an account of validity in a formal setting, but it does not help to understand how proper and common nouns function in reality (not in models). Putnam then initiated the empirical study of such nouns to indicate, (i), that the popular Frege-Carnap account of them as (“disguised” compound) predicates is empirically incorrect, and, (ii), that they offer a new paradigm for a naturalistic semantics of natural languages. We take Putnam’s program a couple of steps further. First, we investigate the semantics of common nouns and argue that they refer (to kinds), rather than apply by satisfaction/truth to a designation/denotation. Second, we point to general results about semantics as a theory whose fulcrum is the reference relation rather than satisfaction in models and validity across them. (shrink)

This paper develops Semantic Cluster Theory, arguing that abstract concepts—such as love, justice, freedom, or trust—are not fixed semantic units but networked structures defined by their surrounding vocabulary (“semantic clusters”). A concept’s meaning arises from: -/- the configuration of its peripheral lexical nodes, -/- the directional vector connecting these nodes, and -/- the strength of their internal edges. -/- Because multiple clusters may coexist within an individual mind, Selective Normalization emerges: people adopt one cluster as the “true meaning” while reclassifying (...) alternative clusters under different labels. This framework explains why misunderstanding, value conflict, and conceptual divergence occur even when speakers use the same word. -/- The paper formalizes cluster-based meaning, analyzes vector alignment as the basis of interpersonal understanding, and introduces the phenomenon of expansion events, in which a concept’s network grows when new lexical nodes are integrated without contradiction. Part I establishes the theoretical foundation for Parts II and III, which address specialized concepts and AI–human cognitive compatibility. (shrink)

There is a prevalent notion among cognitive scientists and philosophers of mind that computers are merely formal symbol manipulators, performing the actions they do solely on the basis of the syntactic properties of the symbols they manipulate. This view of computers has allowed some philosophers to divorce semantics from computational explanations. Semantic content, then, becomes something one adds to computational explanations to get psychological explanations. Other philosophers, such as Stephen Stich, have taken a stronger view, advocating doing away (...) with semantics entirely. This paper argues that a correct account of computation requires us to attribute content to computational processes in order to explain which functions are being computed. This entails that computational psychology must countenance mental representations. Since anti-semantic positions are incompatible with computational psychology thus construed, they ought to be rejected. Lastly, I argue that in an important sense, computers are not formal symbol manipulators. (shrink)

This book investigates context-sensitivity in natural language by examining the meaning and use of a target class of theoretically recalcitrant expressions. These expressions – including epistemic vocabulary, normative and evaluative vocabulary, and vague language – exhibit systematic differences from paradigm context-sensitive expressions in their discourse dynamics and embedding properties. Many researchers have responded by rethinking the nature of linguistic meaning and communication. Drawing on general insights about the role of context in interpretation and collaborative action, I develop an improved contextualist (...) theory of CR-expressions within the classical truth-conditional paradigm: Discourse Contextualism. The aim of Discourse Contextualism is to derive the distinctive linguistic behavior of a CR-expression from a particular contextualist interpretation of an independently motivated formal semantics, along with general principles of interpretation and conversation. It is shown how in using CR-expressions, speakers can exploit their mutual grammatical and world knowledge, and general pragmatic reasoning skills, to coordinate their attitudes and negotiate about how the context should evolve. The book focuses primarily on developing a Discourse Contextualist semantics and pragmatics for epistemic modals. The framework is also applied to other categories of epistemic vocabulary, normative and evaluative vocabulary, and vague adjectives. Similarities/differences among these expressions, and among context-sensitive expressions more generally, have been underexplored. Accounts are developed of (e.g.) the role of presupposition in collaborative action and discourse; the interpretation of context-sensitive expressions in embedded contexts; interactions among logic, semantics, pragmatics, metasemantics, and substantive normative issues; the role of truth and truth-value intuitions in semantic theorizing; allegedly "subjective" attitude verbs such as 'find'; and vagueness ("Vagueness as Contextual Indecision"), which may be of broader interest. The development of Discourse Contextualism in this book sheds light on general features of meaning and communication, and the diverse ways context affects and is affected by uses of language. (shrink)

Much ado – and increased complexity – is generally the case when it comes to checking formally the (intended) meaning of programs, as formal semantics for programs are typically extrinsic to both them and the formal grammars that generate the programming languages in which they are written. The van Wijngaarden grammars, on the contrary, have an intrinsic semantics in the sense that their rules contain or express the (intended) meaning of the terminal strings generated by them. (...) This intrinsicness allows for preservation of meaning both in syntactic change and context-sensitive conditions. In order better to show the intrinsicness of the semantics of the van Wijngaarden grammars I contrast them with the attribute grammars, a frequent choice when the semantic analysis of programming languages is called for (e.g., in compilation). (shrink)

Can an artefactual system preserve the operative semantics of a person without claiming to be that person? This paper presents an audit protocol for semantic footprints: domain-bounded, intervention-grounded traces of stable sign–object–interpretant commitments in an artefactual system. The protocol operationalises semantic surrogacy as a falsifiable competence claim, rather than a metaphysical identity thesis, and provides a discipline for avoiding common partition artefacts (context leakage, cue-based overfitting, and stylometric ‘ghost’ persistence). Building on a companion framework that defines a Semiotic Adequacy (...) Test (SAT) for minimal agency in bio–artefactual continuity, we treat SAT’s criteria C1–C4 as inherited infrastructure and contribute four audit-facing components: (i) a formal negative criterion (Π*) for non-generating partitions, (ii) an admissibility firewall for estimators of semiotic density ρ and context plasticity κ, (iii) a minimal intervention suite do(I) suitable for replication, and (iv) a catalogue of failure modes with diagnostics suitable for pre-registration and third‑party review. The result is a practical, intervention-auditable methodology for evaluating semantic surrogacy claims in artefactual systems without collapsing them into avatars/proxies, stylometry, or human-likeness scores. (shrink)

Semantic analysis in early analytic philosophy belongs to a long tradition of adopting geometrical methodologies to the solution of philosophical problems. In particular, it adapts Descartes’ development of formalization as a mechanism of analytic representation, for its application in natural language semantics. This article aims to trace the mathematical roots of Frege, Russel and Carnap’s analytic method. Special attention is paid to the formal character of modern analysis introduced by Descartes. The goal is to identify the particular conception (...) of “form” developed by the analytic tradition, from Descartes to early analytic philosophy, and to determine its relation to similar notions, like ‘function’ and ‘syntax’. Finally, I focus on how Frege, Russell and Carnap’s methods of semantic analysis fit the general characterization of formal analysis previously developed. (shrink)

The distinction between the semantic content of a sentence or utterance and its use is widely employed in formal semantics. Semantic minimalism in particular understands this distinction as a sharp dichotomy. I argue that if we accept such a dichotomy, there would be no reason to posit the existence of semantic contents at all. I examine and reject several arguments raised in the literature that might provide a rationale for assuming semantic contents, in this sense, exist, and conclude (...) that Ockham’s razor should be applied to these postulated entities. Since the notion of “semantic content” doubles both as what a semantic theory is a priori supposed to account for and as the product of that same theory, it is methodologically unsound to appeal to this notion to fend off criticisms of and counterexamples to semantic theories. (shrink)

This paper proposes a reversal of the standard strategy for dealing with semantic paradox. Rather than beginning with paradoxical sentences and diagnosing what has gone wrong, it starts from a general account of linguistic pathology and asks which sentences instantiate it. I argue that interpretability is a necessary condition of communication, and that certain forms of semantic disorders—most notably permanent ambiguity and self-denial—constitute genuine pathologies of language. Central to study is a distinction between two roles played by truth: one that (...) secures the link between language and world, and another that operates affirmatively within language itself. I argue that self-reference, often treated as a source of paradox, is better understood as a structural enabling condition, while the pathological effects arise from a specific internal use of truth. On this basis, I outline a principled strategy for containing semantic pathology and indicate how it can be formally implemented without sacrificing legitimate expressive resources. (shrink)

This paper provides a general introduction to Semantic Cluster Theory, a framework that explains abstract concepts—such as love, ethics, freedom, or selfhood—not as fixed meanings but as networks of surrounding lexical nodes (“semantic clusters”). It outlines three key structures shared across human cognition: -/- Conceptual Network Formation — abstract terms gain meaning through surrounding vocabulary and its directional organization. -/- Selective Normalization — individuals adopt one cluster as the “true meaning” while relegating other possible clusters to secondary labels. -/- Cluster (...) Divergence — misunderstanding, value conflict, and disciplinary discontinuities arise from differences in cluster structure rather than differences in opinion. -/- This Part 0 serves as the structural groundwork for the following three papers (Parts I–III), which develop: -/- Part I: formal theory of semantic clusters, -/- Part II: cluster discontinuity in specialized concepts (ethics, philosophy, social terms), -/- Part III: cognitive compatibility between AI and humans through network-based modeling. -/- Together, the series proposes a unified approach to meaning, cognition, and conceptual divergence across human and artificial minds. (shrink)

A precise formulation of the structure of modern evolutionary theory has proved elusive. In this paper, I introduce and develop a formal approach to the structure of population genetics, evolutionary theory's most developed sub-theory. Under the semantic approach, used as a framework in this paper, presenting a theory consists in presenting a related family of models. I offer general guidelines and examples for the classification of population genetics models; the defining features of the models are taken to be their (...) state spaces, parameters, and laws. The suggestions regarding the various aspects of the characterization of population genetics models provide an outline for further detailed research. (shrink)

Fictional names pose a difficult puzzle for semantics. We can truthfully maintain that Frodo is a hobbit, while at the same time admitting that Frodo does not exist. To reconcile this paradox I propose a way to formalize the interpretation of fiction as ‘prescriptions to imagine’ (Walton 1990) within an asymmetric semantic framework in the style of Kamp (1990). In my proposal, fictional statements are analyzed as dynamic updates on an imagination component of the interpreter’s mental state, while plain (...) assertions are updates on a belief component. Proper names – regular, empty, or fictional – are uniformly analyzed as presupposition triggers. The possibility of different attitude components referentially depending on each other is what ultimately allows us to account for the central paradox mentioned above. (shrink)

It is common practice in formal semantics to assume that the context specifies an assignment of values to variables and that the same variables that receive contextually salient values when they occur free may also be bound by quantifiers and λs. These assumptions are at work to provide a unified account of free and bound uses of third person pronouns, namely one by which the same lexical item is involved in both uses. One way to pursue this account (...) is to treat quantifiers and λs as monsters in Kaplan’s sense. We argue that this move should be avoided and explore an alternative route based on the idea that there is a variable assignment coordinate in the context and a variable assignment coordinate in the circumstance of evaluation, with the definition of truth in context identifying them. One fundamental challenge that arises in pursuing a unified account is to explain the difference in the way the gender presuppositions of bound and free pronouns project. The proposal that emerges from the attempt to meet this challenge is a non-indexical account of free third person pronouns and a new conception of the role and structure of assignment functions. (shrink)

This paper develops an update semantics for weak necessity modals like ‘ought’ and ‘should’. I start with the basic approach to the weak/strong necessity modal distinction developed in Silk 2018: Strong necessity modals are given their familiar semantics of necessity, predicating the necessity of the prejacent of the actual world (evaluation world). The apparent “weakness” of weak necessity modals derives from their bracketing the assumption that the relevant worlds in which the prejacent is necessary (deontically, epistemically, etc.) need (...) be candidates for actuality. ‘Should φ’ can be accepted without needing to settle that the relevant considerations (norms, preferences, expectations, etc.) that actually apply, given the facts, verify the necessity of φ. I formalize these ideas within an Update with Centering framework. The meaning of ‘Should φ’ is explained, fundamentally, in terms of how its use updates attention toward possibilities in which φ is necessary. The semantics is also extended to deontic conditionals. The proposed analyses capture various contrasting logical properties and discourse properties of ‘should’ and ‘must’ — e.g., in sensitivities to standing contextual assumptions, entailingness, and force — and provide an improved treatment of largely neglected data concerning information-sensitivity. (shrink)

Our manuscript addresses the foundational question of cognitive science: how do we know? Specifically, examination of the mathematics of acquiring mathematical knowledge revealed that knowing-within-mathematics is reflective of knowing-in-general. Based on the correspondence between ordinary cognition (involving physical stimuli, neural sensations, mental concepts, and conscious percepts) and mathematical knowing (involving objective particulars, measured properties, abstract theories, and concrete models), we put forward the functorial semantics of mathematical knowing as a formalization of cognition. Our investigation of the similarity between mathematics (...) and cognition led us to argue against the compartmentalization of scientific knowledge and ordinary cognition, and make a case for the understanding of the basic science of knowing in terms of functorial semantics. Recognizing functorial semantics as an elementary form of cognition can help advance cognitive science the way calculus helped in the advancement of physics. (shrink)

This paper analyzes why specialized academic concepts—such as ethics, subject, freedom, or normativity—systematically diverge from their everyday counterparts. I argue that these terms do not refer to unified meanings but to high-density conceptual clusters formed through strong, stable semantic edges within expert communities. In contrast, everyday language retains low-density, weakly structured clusters, producing inevitable meaning gaps. -/- Using the framework of Selective Normalization, I show how individuals adopt one conceptual cluster as the “proper” meaning while denormalizing all others as different (...) notions (“mere morality”, “social rules”, “philosophical jargon”). This structural asymmetry explains why public discourse, ethical debates, and academic communication routinely fail. -/- The paper introduces depth-based cluster analysis, where conceptual depth is measured by a term’s derivational reach—how many coherent conceptual branches emerge once a core node is activated. This clarifies why specialists appear to “jump too fast”: their high-density clusters generate many justified derivations, while non-experts lack the necessary edges. -/- Finally, the paper formalizes depth fraud, the use of deep vocabulary without the underlying network, resulting in incoherence and interpretive failure. The framework provides a unified account of conceptual misunderstanding across ethics, philosophy, education, and public communication. (shrink)

The linguistic turn provided philosophers with a range of reasons for engaging in careful investigation into the nature and structure of language. However, the linguistic turn is dead. The arguments for it have been abandoned. This raises the question: why should philosophers take an interest in the minutiae of natural language semantics? I’ll argue that there isn’t much of a reason - philosophy of language has lost its way. Then I provide a suggestion for how it can find its (...) way again. (shrink)

Since 1976 Hilary Putnam has on many occasions proposed an argument, founded on some model-theoretic results, to the effect that any philosophical programme whose purpose is to naturalize semantics would fail to account for an important feature of every natural language, the determinacy of reference. Here, after having presented the argument, I will suggest that it does not work, because it simply assumes what it should prove, that is that we cannot extend the metatheory: Putnam appears to think that (...) all we may determinately say about the relations between words and entities in the world is what the model theory tells us, but he has never offered justifications for that. At the end of the article, I will discuss the apparently reliable intuition that seems to me to be at the root of the argument, that is that, given a formal theory, there is an infinite number of ways of connecting it to, or of projecting it onto, the world. I will suggest that we should resist this intuition, because it rests on a very doubtful notion of world, which assumes that for any class of objects there is a corresponding property. (shrink)