Two-dimensional (2D) semantics is a formal framework that is used to characterize the meaning of certain linguistic expressions and the entailment relations among sentences containing them. 2D semantics has also been applied to thought contents. In contrast with standard possible worlds semantics, 2D semantics assigns extensions and truth-values to expressions relative to two possible world parameters, rather than just one. So a 2D semantic framework provides finer-grained semantic values than those available within standard possible world (...) class='Hi'>semantics, while using the same basic model-theoretic resources. The 2D framework itself is just a formal tool. To develop a semantic theory for someone’s language, a proponent of 2D semantics must do three things: (i) explain what exactly the two possible world parameters represent, (ii) explain the rules for assigning 2D semantic values to a person’s words and sentences, and (iii) explain how 2D semantic values help in understanding the meanings of the person’s words and sentences. (shrink)

The theories that form the heterogeneous family of two‐dimensional or 2D semantics are rooted in the tradition of possible‐worlds semantics made popular by Saul Kripke and David Lewis. Advocates of 2D semantics agree that recognizing a dependence of truth on fact is not enough. Advocates of two‐dimensional semantics share a second trademark idea. They agree that the familiar apparatus of worlds‐cum‐intensions can be modified so as to capture both the dependencies they see. The commitments of all (...) 2D theories can basically be captured by one and the same formal framework of worlds‐cum‐intensions. David Kaplan's semantics aims to cover pure indexicals such as 'today' alongside impure indexicals such as 'you' and demonstratives such as 'this'. Kaplan starts off with two 'obvious principles': The referent of an indexical systematically depends on the respective context; and Indexicals are directly referential. (shrink)

In recent years, two-dimensional (2D) semantics has been used to develop a broadly descriptivist approach to meaning that seeks to accommodate externalists’ counterexamples to traditional descriptivism. The 2D possible worlds framework can be used to capture a speaker’s implicit dispositions to identify the reference of her words on the basis of empirical information about her actual environment. Proponents of 2D semantics argue that this aspect of linguistic understanding plays the core theoretical role of meanings: 2D semantics allows (...) us to specify a reference-fixing criterion implicit mastery of which constitutes semantic competence a particular meaning. (shrink)

The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion space in (...) terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. (shrink)

I present a case for a rapprochement between aspects of rationalism and scientific realism, by way of a general framework employing modal epistemology and elements of 2-dimensional semantics (2DS). My overall argument strategy is meta-inductive: The bulk of this paper establishes a “base case,” i.e., a concretely constructive example by which I demonstrate this linkage. The base case or constructive example acts as the exemplar for generating, in a constructively ‘bottom-up’ fashion, a more generally rigorous case for rationalism-realism qua (...) modal epistemology. The exemple I choose in D. Chalmers’ (2002) modal rationalism and R. Giere’s (1985, 1988) constructive realism. I show by way of a thorough analysis how Giere’s claims concerning modal scope are characterized as instances of Chalmers’ modal rationalism, both weak and strong. In essence, as I demonstrate via Chalmers’ notions, ceteris paribus the constructive realist ultimately opts for a comparatively wider gate, characterized by modal reasoning, to lead from the rooms of conceivability qua thought experiments and models, to the pastures of metaphysical possibility. Chalmers likewise tries to erect such a wider gate, in his general conceivability-possibility theses. Anti-realists, on the other hand, see a narrower passage and my contention herein is that they suffer from modal myopia, which hopefully the ‘corrective vision’ of Chalmers’ modal rationalism can restore. In the introduction and concluding sections I sketch out suggestions of constructing ‘inductive steps’ from my base case, to generate more extensively general claims regarding realism qua rationalism. -/- . (shrink)

Traditionally, the formulae in modal logic express properties of possible worlds. Prior introduced “egocentric” logics that capture properties of agents rather than of possible worlds. In such a setting, the article proposes the modality “know how to tell apart” and gives a complete logical system describing the interplay between this modality and the knowledge modality. An important contribution of this work is a new matrix-based technique for proving completeness theorems in an egocentric setting.

Written by an international team of leading scholars, this collection of thirteen new essays explores the implications of semantic externalism for self-knowledge and skepticism, bringing recent developments in the philosophy of mind, the philosophy of language, and epistemology to bear on the issue. Structured in three parts, the collection looks at self-knowledge, content transparency, and then meta-semantics and the nature of mental content. The chapters examine a wide range of topics in the philosophy of mind and the philosophy of (...) language, including 2D semantics, transparency views of self-knowledge, and theories of linguistic understanding, as well as epistemological debates on contextualism, contrastivism, pragmatic encroachment, anti-luminosity arguments and testimony. The scope of the volume will appeal to graduate students and researchers in epistemology, philosophy of mind, philosophy of language, cognitive science, psychology and linguistics. (shrink)

In order to block controversial predictions of 2D semantics (The Nesting Problem), Chalmers and Rabern (2014) propose adding an additional constriction called “the liveness constraint” in definitions of epistemic modals. Without this constraint, all scenario‐world pairs counterfactual to a scenario‐world pair considered as actual in a 2D matrix for a contingent a priori proposition ϕ appear problematic for 2D semantics. This is because, although it is false that ϕ in such pairs, it is a priori true that ϕ. (...) I consider two versions of 2D semantics, those with unstructured and structured intensions. I argue that the unstructured version of 2D semantics is over‐simplified and due to this, it has controversial predictions for counterfactual scenario‐world pairs – the definition of epistemic conceivability with the liveness constraint causes some contingent propositions to appear inconceivable in counterfactual scenario‐world pairs, while some other contingent propositions remain conceivable. In turn, the structured version of the 2D account of propositions has no explanation of how it is possible to possess purely qualitative knowledge without its being dependent on a particular individual or on a particular actual world. (shrink)

The paper explores the project of an ambitious modal epistemology that attempts to combine the a priori methods of Chalmers’ 2D semantics with Kripke’s modal metaphysics. I argue that such a project is not viable. The ambitious modal epistemology involves an inconsistent triad composed of (1) Modal Monism, (2) Two-Dimensionalism, and what I call (3) “Metaphysical Kripkeanism”. I present the three theses and show how only two of those can be true at a time. There is a fundamental incompatibility (...) between Chalmers’ Modal Rationalism and Kripke’s modal metaphysics. Specifically, Chalmers’ conceivability entails possibilities that a Kripkean rejects as genuinely metaphysical. However, three positive stances in modal epistemology emerge from the combinations that the triad allows. One of those offers a promising way forward for 2D modal epistemologies. But it comes with a cost, as it requires abandoning modal monism and reshaping the scope of what a priori conceivability can give us access to. (shrink)

In this paper, I mainly pursue the following two goals: on the one hand, I want to show how a central Fregean insight is tried to be captured within a two-dimensional strategy. On the other hand, I want to show that, in the light of Saul Kripke’s arguments against descriptivism, this strategy is faced with a fundamental problem. I proceed in four steps: in a first step, I bring together the passages that contain a central Fregean insight as a source (...) of inspiration for a two-dimensional reconstruction and that suggest a descriptivist reading of Frege’s view. In a second step, I shortly present Kripke’s threefold argumentation against two versions of descriptivism, which is also the basis for Kripke’s view that proper names are rigid designators. In a third step, I explain the basic idea of a Frege-inspired two-dimensional strategy which is used to reconcile theories of definite descriptions with theories of rigid designation and which is sometimes characterized as ‘neo-descriptivism’. Since the two-dimensional strategy is dependent on rigidified definite descriptions, I argue, in a fourth step, that, in the light of Kripke’s epistemological and semantic arguments, the two-dimensional strategy is problematic and untenable – though it is, nevertheless, motivated by Kripke’s modal argument. (shrink)

Spatial, physical, and semantic magnitude dimensions can influence action decisions in human cognitive processing and interact with each other. For example, in the SNARC effect, semantic numerical magnitude facilitates left-hand or right-hand responding dependent on the small or large magnitude of number symbols. SNARC-like interactions of numerical magnitudes with the radial spatial dimension (depth) were postulated from early on. Usually, the SNARC effect in any direction is investigated using fronto-parallel computer monitors for presentation of stimuli. In such 2D setups, however, (...) the metaphorical and literal interpretation of the radial depth axis with seemingly close / far stimuli or responses are not distinct. Hence, it is difficult to draw clear conclusions with respect to the contribution of different spatial mappings to the SNARC effect. In order to disentangle the different mappings in a natural way, we studied parametrical interactions between semantic numerical magnitude, horizontal directional responses, and perceptual distance by means of stereoscopic depth in an immersive virtual reality (VR). Two VR experiments show horizontal SNARC effects across all spatial displacements in traditional latency measures and kinematic response parameters. No indications of a SNARC effect along the depth axis, as it would be predicted by a direct mapping account, were observed, but the results show a non-linear relationship between horizontal SNARC slopes and physical distance. Steepest SNARC slopes were observed for digits presented close to the hands. We conclude that spatial-numerical processing is susceptible to effector-based processes but relatively resilient to task-irrelevant variations of radial-spatial magnitudes. (shrink)

In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition into acute/right/obtuse angles is extended in two steps: first zero and straight angles are added, and secondly reflex and full angles are added, in both cases extending the logical space of angles. Within the framework of logical geometry, the resulting partitions of these logical spaces yield bitstring semantics of increasing complexity. These bitstring analyses allow (...) a straightforward account of the Aristotelian relations between angular concepts. In addition, also relational concepts such as complementary and supplementary angles receive a natural bitstring analysis. (shrink)

One of the benefits of the 2D framework we looked at last week was that it explained how we could understand a sentence without knowing which proposition it expressed. And we could do this even if we give an account of understanding which is closely tied to the possible worlds semantics we use to analyse propositions. Really this can be done very easily, without appeal to any high-flying Kripkean cases. In “Analytic Metaphysics” Jackson discusses a very simple case of (...) it. I can understand an utterance of “I have a beard” without knowing which proposition it expresses. I know how the proposition is generated from context plus meaning, if X is the speaker then the sentence expresses the proposition X has a beard. And that is enough for understanding. But if I don’t know who said the sentence, so I don’t know who X is, I don’t know which proposition is expressed by that utterance. (shrink)

Sculptors, architects, and painters are three professional groups that require a comprehensive understanding of how to manipulate spatial structures. While it has been speculated that they may differ in the way they conceive of space due to the different professional demands, this has not been empirically tested. To achieve this, we asked architects, painters, sculptors, and a control group questions about spatially complex pictures. Verbalizations elicited were examined using cognitive discourse analysis. We found significant differences between each group. Only painters (...) shifted consistently between 2D and 3D concepts, architects were concerned with paths and spatial physical boundedness, and sculptors produced responses that fell between architects and painters. All three differed from controls, whose verbalizations were generally less elaborate and detailed. Thus, for the case of sculptors, architects, and painters, profession appears to relate to a different spatial conceptualization manifested through a systematically contrasting way of talking about space. (shrink)

Minimal Semantics asks what a theory of literal linguistic meaning is for - if you were to be given a working theory of meaning for a language right now, what would you be able to do with it? Emma Borg sets out to defend a formal approach to semantic theorising from a relatively new type of opponent - advocates of what she call 'dual pragmatics'. According to dual pragmatists, rich pragmatic processes play two distinct roles in linguistic comprehension: as (...) well as operating in a post-semantic capacity to determine the implicatures of an utterance, they also operate prior to the determination of truth-conditional content for a sentence. That is to say, they have an integral role to play within what is usually thought of as the semantic realm. Borg believes dual pragmatic accounts constitute the strongest contemporary challenge to standard formal approaches to semantics since they challenge the formal theorist to show not merely that there is some role for formal processes on route to determination of semantic content, but that such processes are sufficient for determining content. Minimal Semantics provides a detailed examination of this school of thought, introducing readers who are unfamiliar with the topic to key ideas like relevance theory and contextualism, and looking in detail at where these accounts diverge from the formal approach. Borg's defence of formal semantics has two main parts: first, she argues that the formal approach is most naturally compatible with an important and well-grounded psychological theory, namely the Fodorian modular picture of the mind. Then she argues that the main arguments adduced by dual pragmatists against formal semantics - concerning apparent contextual intrusions into semantic content - can in fact be countered by a formal theory. The defence holds, however, only if we are sensitive to the proper conditions of success for a semantic theory. Specifically, we should reject a range of onerous constraints on semantic theorizing (e.g., that it answer epistemic or metaphysical questions, or that it explain our communicative skills) and instead adopt a quite minimal picture of semantics. (shrink)

The ‘When Am I?’ problem, introduced by Bourne 2002, 2006, and Braddon-Mitchell 2004, creates a problem for thinking that the past is just like the present, and responses by Forrest 2004 and Forbes 2016, in which activities and processes are distinctive of the present, suggest that the past is settled. This chapter argues that the ‘When am I?’ problem arises because it takes tense metaphysically seriously but not aspect. The solution of invoking processes and activities takes aspect as seriously as (...) tense. A two-dimensional (2D) framework explains the relationship between completed processes (associated with perfective aspect) and ongoing processes (associated with progressive aspect), also explaining cases where facts about the past seem to have changed retrospectively, and cases, building on Forbes and Wildman (2022), where meanings of words have changed over time. It allows that what’s true has changed while accepting that the past is intrinsically settled. (shrink)

This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration (...) of substitution-box matrix over the enormously large problem space of 256!. Lastly, the security strength of obtained S-box is further elevated through the action of proposed algebraic group structure. The standard set of performance parameters such as nonlinearity, strict avalanche criterion, bits independent criterion, differential uniformity, and linear approximation probability is quantified to assess the security and robustness of proposed S-box. The simulation and comparison results demonstrate the effectiveness of proposed method for the construction of cryptographically sound S-boxes. (shrink)

_Insensitive Semantics_ is an overview of and contribution to the debates about how to accommodate context sensitivity within a theory of human communication, investigating the effects of context on communicative interaction and, as a corollary, what a context of utterance is and what it is to be in one. Provides detailed and wide-ranging overviews of the central positions and arguments surrounding contextualism Addresses broad and varied aspects of the distinction between the semantic and non-semantic content of language Defends a distinctive (...) and explanatorily powerful combination of semantic minimalism and speech act pluralism Confronts core problems which not only run to the heart of philosophy of language and linguistics, but which arise in epistemology, metaphysics, and moral philosophy as well. (shrink)

Lexical Semantics is about the meaning of words. Although obviously a central concern of linguistics, the semantic behaviour of words has been unduly neglected in the current literature, which has tended to emphasize sentential semantics and its relation to formal systems of logic. In this textbook D. A. Cruse establishes in a principled and disciplined way the descriptive and generalizable facts about lexical relations that any formal theory of semantics will have to encompass. Among the topics covered (...) in depth are idiomaticity, lexical ambiguity, synonymy, hierarchical relations such as hyponymy and meronymy, and various types of oppositeness. Syntagmatic relations are also treated in some detail. The discussions are richly illustrated by examples drawn almost entirely from English. Although a familiarity with traditional grammar is assumed, readers with no technical linguistic background will find the exposition always accessible. All readers with an interest in semantics will find in this original text not only essential background but a stimulating new perspective on the field. (shrink)

This practical coursebook introduces all the basics of semantics in a simple, step-by-step fashion. Each unit includes short sections of explanation with examples, followed by stimulating practice exercises to complete in the book. Feedback and comment sections follow each exercise to enable students to monitor their progress. No previous background in semantics is assumed, as students begin by discovering the value and fascination of the subject and then move through all key topics in the field, including sense and (...) reference, simple logic, word meaning and interpersonal meaning. New study guides and exercises have been added to the end of each unit to help reinforce and test learning. A completely new unit on non-literal language and metaphor, plus updates throughout the text significantly expand the scope of the original edition to bring it up-to-date with modern teaching of semantics for introductory courses in linguistics as well as intermediate students. (shrink)