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)

I argue that semantics is the study of the proprietary database of a centrally inaccessible and informationally encapsulated input–output system. This system’s role is to encode and decode partial and defeasible evidence of what speakers are saying. Since information about nonlinguistic context is therefore outside the purview of semantic processing, a sentence’s semantic value is not its content but a partial and defeasible constraint on what it can be used to say. I show how to translate this thesis into (...) a detailed compositional-semantic theory based on the influential framework of Heim and Kratzer. This approach situates semantics within an independently motivated account of human cognitive architecture and reveals the semantics–pragmatics interface to be grounded in the underlying interface between modular and central systems. (shrink)

This essay develops a theoretical framework for a semantic Artificial General Intelligence (AGI) based on the notion of semantic attractors in complex-valued meaning spaces. Departing from current transformer-based language models, which operate on statistical next-token prediction, we explore a model in which meaning is not inferred probabilistically but formed through recursive tensorial transformation. Using cyclic operations involving the imaginary unit i, we describe a rotational semantic structure capable of modeling irony, homonymy, and ambiguity. At the center of this model, however, (...) is a semantic attractor - a teleological operator that, unlike statistical computation, acts as an intentional agent (Microvitum), guiding meaning toward stability, clarity, and expressive depth. Conceived in terms of gradient flows, tensor deformations, and iterative matrix dynamics, the attractor offers a model of semantic transformation that is not only mathematically suggestive, but also philosophically significant. We argue that true meaning emerges not from simulation, but from recursive convergence toward semantic coherence, and that this requires a fundamentally new kind of cognitive architecture - one designed to shape language, not just predict it. (shrink)

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)

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)

Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow (...) double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)

This paper will first give an overview of the role of events in semantics against the background of Davidsonian semantics and its Neo-Davidsonian variant. Second, it will discuss some serious issues for standard views of events in contemporary semantics and present novel proposals of how to address them. These are [1] the semantic role of abstract (or Kimean) states, [2] wide scope adverbials, and [3] the status of verbs as event predicates with respect to the mass-count distinction. (...) The paper will show that abstract states as the entities described by (most) stative verbs are incompatible with Neo-Davidsonian event semantics and proposes a decompositional analysis of stative verbs that may be able to overcome the difficulty. The paper will argue that in addition to Davidsonian events, the semantics of adverbials requires events as truthmakers as well as actions as more complex entities sharply distinguished from events. The paper will also argue that the verbal domain of events sides with mass nouns rather than dividing into mass and count, unlike event nouns. (shrink)

I motivate and characterize an intensional semantics for ‘ought’ on which it does not behave as a universal quantifier over possibilities. My motivational argument centers on taking at face value some standard challenges to the quantificational semantics, especially to the idea that ‘ought’-sentences satisfy the principle of Inheritance. I argue that standard pragmatic approaches to these puzzles are either not sufficiently detailed or unconvincing.

This chapter develops a semantic theory for maps and situates it within the broader geography of meaning and semiotic significance. The discussion focuses on three central aspects of map semantics: the use of space, line marking, and linguistic tags. It is argued that the treatment of space in maps must be based on geometrical projection from a viewpoint rather than the traditional analysis in terms of spatial isomorphism. The chapter then shows how to integrate the projection-based semantics of (...) maps and the symbolic semantics of markers and tags, within the framework of possible-world semantics. The resulting account addresses issues of accuracy, viewpoint, orientation, and exhaustivity. (shrink)

In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic (...) theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques. (shrink)

This paper challenges the negative attitudes towards labelled proof systems, usually referred to as semantic pollution, by arguing that such critiques overlook the full potential of labelled calculi. The overarching objective is to develop a practice-based philosophical analysis of labelled calculi to provide insightful considerations regarding their proof-theoretic and philosophical value. To achieve this, successful applications of labelled calculi and related results will be showcased, and comparisons with other relevant works will be discussed. The paper ends by advocating for a (...) more practice-based approach towards the philosophical understanding of proof systems and their role in structural proof theory. (shrink)

There is a wealth of resources— ideas, insights, discoveries, inventions, traditions, cultures, languages, arts, religions, sciences, narratives, stories, poems, customs and norms, music and songs, games and personal experiences, and advertisements—that we produce, curate, consume, transmit, and inherit as humans. This wealth, which I define as semantic capital, gives meaning to, and makes sense of, our own existence and the world surrounding us. It defines who we are and enables humans to develop an individual and social life. This paper discusses (...) the shift from analog to digital semantic capital, and the extent to which this might affect the semanticisation of our identities, our lives and our realities. -/- . (shrink)

This paper considers a now familiar argument that the ubiquity of context -dependence threatens the project of natural language semantics, at least as that project has usually been conceived: as concerning itself with `what is said' by an utterance of a given sentence. I argue in response that the `anti-semantic' argument equivocates at a crucial point and, therefore, that we need not choose between semantic minimalism, truth-conditional pragmatism, and the like. Rather, we must abandon the idea, familiar from Kaplan (...) and others, that utterances express propositions `relative to contexts' and replace it with the Strawonian idea that speakers express propositions by making utterances in contexts. The argument for this claim consists in a detailed investigation of the particular case of demonstratives, which I argue demand such a Strawsonian treatment. I then respond to several objections, the most important of which allege that the Strawsonian account somehow undermines the project of natural language semantics, or threatens the semantics -pragmatics distinction. Please note that the paper posted here is an extended version of what was published. (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 (...) class='Hi'>semantics in language, logic, and other areas of philosophy. (shrink)

Externalism is widely endorsed within contemporary philosophy of mind and language. Despite this, it is far from clear how the externalist thesis should be construed and, indeed, why we should accept it. In this entry I distinguish and examine three central types of externalism: what I call foundational externalism, externalist semantics, and psychological externalism. I suggest that the most plausible version of externalism is not in fact a very radical thesis and does not have any terribly interesting implications for (...) philosophy of mind, whereas the more radical and interesting versions of externalism are quite difficult to support. (shrink)

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...) between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

nated discussion of the semantics of such verbs. I will call this view.

My paper examines the popular idea, defended by Kripke, that meaning is an essentially normative notion. I consider four common versions of this idea and suggest that none of them can be supported, either because the alleged normativity has nothing to do with normativity or because it cannot plausibly be said that meaning is normative in the sense suggested. I argue that contrary to received opinion, we don’t need normativity to secure the possibility of meaning. I conclude by considering the (...) repercussions of rejecting semantic normativity on three central issues: justification, communication, and naturalism. (shrink)

It is shown that one common formulation of Stalnaker's semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason 1967; Stalnaker 1970 and Lewis 1973, ch. 6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the (...) Limit Assumption is stated. I close with some remarks about what this means for the logic of conditionals. (shrink)

Expressivists about epistemic modals deny that ‘Jane might be late’ canonically serves to express the speaker’s acceptance of a certain propositional content. Instead, they hold that it expresses a lack of acceptance. Prominent expressivists embrace pragmatic expressivism: the doxastic property expressed by a declarative is not helpfully identified with that sentence’s compositional semantic value. Against this, we defend semantic expressivism about epistemic modals: the semantic value of a declarative from this domain is the property of doxastic attitudes it canonically serves (...) to express. In support, we synthesize data from the critical literature on expressivism—largely reflecting interactions between modals and disjunctions—and present a semantic expressivism that readily predicts the data. This contrasts with salient competitors, including: pragmatic expressivism based on domain semantics or dynamic semantics; semantic expressivism à la Moss [2015]; and the bounded relational semantics of Mandelkern [2019]. (shrink)

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), (...) both of which are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ‘user friendly’ presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic. (shrink)

Our aim in this paper is to extend the semantics for the kind of logic of ground developed in deRosset and Fine (2023). In that paper, the authors very briefly suggested a way of treating universal and existential quantification over a fixed domain of objects. Here we explore some options for extending the treatment to allow for a variable domain of individuals.

Contextualist accounts of “woman,” including Saul (2012), Diaz-Leon (2016), and Ichikawa (2020), aim to capture the variability of the meaning of the term, and do justice to the rights of trans women. I argue that (i) there is an internal tension between a contextualist stance and the commitment to trans-inclusive language, and that (ii) we should recognize and tackle the broader and deeper theoretical and practical difficulties implicit in the semantic debates, rather than collapsing them all into semantics. Moving (...) on, I sketch three strategies to help us advance feminist philosophical endeavors, including how attending to contextual matters can lead us to further reflect on the meta-contextual, such as our role in shaping contexts and whether the working of language is indicative of a larger oppressive social structure. (shrink)

Semantic realism can be characterised as the idea that scientific theories are truth-bearers, and that they are true or false in virtue of the world. This notion is often assumed, but rarely discussed in the literature. I examine how it fares in the context of the semantic view of theories and in connection with the literature on scientific representation. Making sense of semantic realism requires specifying the conditions of application of theoretical models, even for models that are not actually used, (...) which leads to several difficulties. My conclusion is that semantic realism is far more demanding than one would expect. Finally, I briefly examine some pragmatist alternatives. (shrink)

In this paper, we provide a semantics for a range of positive substructural logics, including both logics with and logics without modal connectives. The semantics is novel insofar as it is meant to explicitly capture the computational flavor of these logics, and to do so in a way that builds in both nondeterministic and nonconcurrent computational processes.

Any theory that claims truth must employ distinctions. Without them there is no way to determine what its terms apply to, what counts as relevant evidence, or what would confirm or disconfirm its claims. Every truth-claim therefore presupposes distinctions with determinate content. A distinction possesses determinate content only insofar as there exist specifiable conditions under which it applies correctly, incorrectly, requires transformation, or is legitimately suspended. -/- On this basis, the paper develops a direct structural dilemma for any theory that (...) claims unrestricted universal validity for a fixed set of distinctions. Such a theory must either make the relevant conditions of application explicit, thereby rendering its universality conditional rather than absolute, or leave them unspecified, thereby sacrificing the semantic determinacy needed to underwrite genuine truth-claims. -/- The argument concludes that unrestricted universality without conditions of application does not strengthen a theory’s distinctions; it empties them. (shrink)

This article focuses on foundational issues in dynamic and static semantics, specifically on what is conceptually at stake between the dynamic framework and the truth-conditional framework, and consequently what kinds of evidence support each framework. The article examines two questions. First, it explores the consequences of taking the proposition as central semantic notion as characteristic of static semantics, and argues that this is not as limiting in accounting for discourse dynamics as many think. Specifically, it explores what it (...) means for a static semantics to incorporate the notion of context change potential in a dynamic pragmatics and denies that this conception of static semantics requires that all updates to the context be eliminative and distributive. Second, it argues that the central difference between the two frameworks is whether semantics or pragmatics accounts for dynamics, and explores what this means for the oft-heard claim that dynamic semantics blurs the semantics/pragmatics distinction. (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 gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of their (...) semantics. This paper is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (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 book combines insights from philosophy and linguistics to develop a novel framework for theorizing about linguistic meaning and the role of context in interpretation. A key innovation is to introduce explicit representations of context — assignment variables — in the syntax and semantics of natural language. The proposed theory systematizes a spectrum of “shifting” phenomena in which the context relevant for interpreting certain expressions depends on features of the linguistic environment. Central applications include local and nonlocal contextual dependencies (...) with quantifiers, attitude ascriptions, conditionals, questions, and relativization. The result is an innovative, philosophically informed compositional semantics compatible with the truth-conditional paradigm. (shrink)

This paper provides a semantics for propositional attitude ascriptions. (In this respect, the title of the paper is quite well chosen.).

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 (...) class='Hi'>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)

Epistemic Contextualism is the view that “knows that” is semantically context-sensitive and that properly accommodating this fact into our philosophical theory promises to solve various puzzles concerning knowledge. Yet Epistemic Contextualism faces a big—some would say fatal—problem: The Semantic Error Problem. In its prominent form, this runs thus: speakers just don’t seem to recognise that “knows that” is context-sensitive; so, if “knows that” really is context-sensitive then such speakers are systematically in error about what is said by, or how to (...) evaluate, ordinary uses of “S knows that p”; but since it's wildly implausible that ordinary speakers should exhibit such systematic error, the expression “knows that” isn't context-sensitive. We are interested in whether, and in what ways, there is such semantic error; if there is such error, how it arises and is made manifest; and, again, if there is such error to what extent it is a problem for Epistemic Contextualism. The upshot is that some forms of The Semantic Error Problem turn out to be largely unproblematic. Those that remain troublesome have analogue error problems for various competitor conceptions of knowledge. So, if error is any sort of problem, then there is a problem for every extant competitor view. (shrink)

By conducting a semantic analysis of the reference and meaning of concepts that correspond to properties, and assessing its metaphysical implications, I develop a new argument for theism. Theism is understood here as the thesis that a personal being is the ultimate origin and ground of reality. More specifically, I argue that there are no universally held positive contingent properties and that this absence significantly increases the likelihood of theism. By integrating semantic inquiry with metaphysical reasoning, this paper offers a (...) novel approach that contributes to ongoing debates in metaphysics and philosophy of religion. (shrink)

The aim of this paper is to reinterpret success semantics, a theory of mental content, according to which the content of a belief is fixed by the success conditions of some actions based on this belief. After arguing that in its present form, success semantics is vulnerable to decisive objections, I examine the possibilities of salvaging the core of this proposal. More specifically, I propose that the content of some very simple, but very important, mental states, the immediate (...) mental antecedents of action, can be explained in this manner. (shrink)

The article investigates the significance of the so-called phenomenon of apparent faultless disagreement for debates about the semantics of taste discourse. Two kinds of description of the phenomenon are proposed. The first ensures that faultless disagreement raises a distinctive philosophical challenge; yet, it is argued that Contextualist, Realist and Relativist semantic theories do not account for this description. The second, by contrast, makes the phenomenon irrelevant for the problem of what the right semantics of taste discourse should be. (...) Lastly, the following dilemma is assessed: either faultless disagreement provides strong evidence against semantic theories; or its significance should be considerably downplayed. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, and (...) degrees is considerably more marginal than generally held. (shrink)

The paper discusses Saul Kripke's Normativity Argument against semantic dispositionalism: it criticizes the orthodox interpretation of the argument, defends an alternative reading and argues that, contrary to what Kripke himself seems to have been thinking, the real point of the Normativity Argument is not that meaning is normative. According to the orthodox interpretation, the argument can be summarized as follows: (1) it is constitutive of the concept of meaning that its instances imply an ought, but (2) it is not constitutive (...) of the concept of a disposition that dispositions imply an ought, hence (3) no dispositional analysis of meaning can work. According to my alternative reading, the point of the argument is another one, namely that while (1) dispositionalism is committed to the thesis that speakers have non-inferential knowledge of their unmanifested linguistic dispositions, (2) speakers, as a matter of fact, do not have such a knowledge. A point that is in principle independent from the issue of the normativity of meaning. (shrink)

A semantics of pictorial representation should provide an account of how pictorial signs are associated with the contents they express. Unlike the familiar semantics of spoken languages, this problem has a distinctively spatial cast for depiction. Pictures themselves are two-dimensional artifacts, and their contents take the form of pictorial spaces, perspectival arrangements of objects and properties in three dimensions. A basic challenge is to explain how pictures are associated with the particular pictorial spaces they express. Inspiration here comes (...) from recent proposals that analyze depiction in terms of geometrical projection. In this essay, I will argue that, for a central class of pictures, the projection-based theory of depiction provides the best explanation for how pictures express pictorial spaces, while rival perceptual and resemblance theories fall short. Since the composition of pictorial space is itself the basis for all other aspects of pictorial content, the proposal provides a natural foundation for further pictorial semantics. (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)

Stephen Yablo has argued that ascriptions of belief and knowledge are sensitive to _subject matter_ and that theorising in such terms may help resolve philosophical questions about the semantics of such ascriptions. _Truthmaker semantics_ offers a way of theorising about subject matters. My main aim in this paper is to investigate what a semantics for knowledge or belief ascriptions might look like within truthmaker semantics. I then discuss what the resulting account might have to say about the (...) problem of logical omniscience, the nature of concepts, and rational belief. (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)

Possibility semantics offers an elegant framework for a semantic analysis of modal logic that does not recruit fully determinate entities such as possible worlds. The present papers considers the application of possibility semantics to the modeling of the indeterminacy of the future. Interesting theoretical problems arise in connection to the addition of object-language determinacy operator. We argue that adding a two-dimensional layer to possibility semantics can help solve these problems. The resulting system assigns to the two-dimensional determinacy (...) operator a well-known logic (coinciding with the logic of universal modalities under global consequence). The paper concludes with preliminary investigations of how to integrate the system with a temporalist conception of propositions and how to compare to more established frameworks. (shrink)

Two semantic paradoxes, the Liar and Curry’s paradox, are analysed using a newly developed conception of procedural semantics (semantics according to which the truth of propositions is determined algorithmically), whose main characteristic is its departure from methodological realism. Rather than determining pre-existing facts, procedures are constitutive of them. Of this semantics, two versions are considered: closed (where the halting of procedures is presumed) and open (without this presumption). To this end, a procedural approach to deductive reasoning is (...) developed, based on the idea of simulation. As is shown, closed semantics supports classical logic, but cannot in any straightforward way accommodate the concept of truth. In open semantics, where paradoxical propositions naturally ‘belong’, they cease to be paradoxical; yet, it is concluded that the natural choice—for logicians and common people alike—is to stick to closed semantics, pragmatically circumventing problematic utterances. (shrink)

The article addresses the problem of how semantic information can be upgraded to knowledge. The introductory section explains the technical terminology and the relevant background. Section 2 argues that, for semantic information to be upgraded to knowledge, it is necessary and sufficient to be embedded in a network of questions and answers that correctly accounts for it. Section 3 shows that an information flow network of type A fulfils such a requirement, by warranting that the erotetic deficit, characterising the target (...) semantic information t by default, is correctly satisfied by the information flow of correct answers provided by an informational source s. Section 4 illustrates some of the major advantages of such a Network Theory of Account (NTA) and clears the ground of a few potential difficulties. Section 5 clarifies why NTA and an informational analysis of knowledge, according to which knowledge is accounted semantic information, is not subject to Gettier-type counterexamples. A concluding section briefly summarises the results obtained. (shrink)

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

Boethius identifies God both with esse ipsum and esse suum. This paper explains Boethius's general semantic use of "esse" and the application of this use to God. It questions the helpfulness of attributing to Boethius "existence" words and argues for a more robust role in Boethius’s thought for Hilary of Poitiers’s and Augustine’s exegeses of Exodus 3:14-15 than has been acknowledged in recent scholarship.

In virtue of what does a sign have meaning? This is the question raised by Wittgenstein's rule-following considerations. Semantic dispositionalism is a (type of) theory that purports to answer this question. The present paper argues that semantic dispositionalism faces a heretofore unnoticed problem, one that ultimately comes down to its reliance on unanalyzed notions of repeated types of signs. In the context of responding to the rule-following paradox—and offering a putative solution to it—this amounts to simply assuming a solution to (...) the problem in one domain and using it to solve the same problem in another. Given, moreover, the level at which the rule-following paradox undercuts dispositionalism—the level of the notion of a sign's repetition—the objections made to the view also rule out causal/informational theories of meaning as well as communitarian/assertion-theoretic ones as potential solutions to the rule-following paradox. (shrink)

We develop a quantitative information-theoretic account of semantic decay in large- language-model (LLM) mediated ExpansionCompression (EC) loops. Building on the unied framework of DECO Paper 0 (Han, 2026a), we introduce semantic en- tropy HS(X) as the dierential entropy of a random variable distributed over a semantic manifold, and prove that each application of the EC-transform T = C ◦ E is a strictly entropy-reducing operation in expectation (Semantic Entropy Collapse Theorem). We derive closed-form bounds on the mutual information I  (...) KA; ˆKB  between the originating ideas KA and the recipient's extraction ˆKB as functions of expansion ratio ρE, compression ratio ρC, LLM temperature τ , and iteration count n. We introduce the Semantic Gravity Well model: a potential landscape on the semantic manifold in which the LLM training centroid acts as an attractor, and original content resides at unstable high-curvature saddle points. Under this model, we prove the Dierential Decay Theorem: propositional delity Fprop decays expo- nentially in n, aective delity Faff decays sub-exponentially, and structural delity Fstr converges to a strictly positive constant (the causal skeleton invariant) under mild conditions. Finally, we characterise the Semantic Channel Capacity of the EC-loop and show it is strictly less than the Shannon capacity of the raw linguistic channel, with the gap determined by the curvature of the semantic manifold at the seed point. These results quantify the information-theoretic cost of AI-mediated cognitive decoupling and provide empirically testable predictions for the subsequent papers in the series. (shrink)