Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders’s proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind’s Habilitationsrede, to which Manders’s account is compared. I (...) conclude with an examination of three possible stances towards extensions via ideal elements. (shrink)

It is often possible to know what a speaker intends to communicate without knowing what they intend to say. In such cases, speakers need not intend to say anything at all. Stanley and Szabó's influential survey of possible analysis of quantifier domain restriction is, therefore, incomplete and the arguments made by Clapp and Buchanan against Truth Conditional Compositionality and propositional speaker-meaning are flawed. Two theories should not always be viewed as incompatible when they associate the same utterance with different propositions, (...) as there may be many ways to interpret speakers that are compatible with their intentions. (shrink)

Domain constraint, the requirement that analogues be selected from "the same category," inheres in the popular saying "you can't compare apples and oranges" and the textbook principle "the greater the number of shared properties, the stronger the argument from analogy." I identify roles of domains in biological, linguistic, and legal analogy, supporting the account of law with a computer word search of judicial decisions. I argue that the category treatments within these disciplines cannot be exported to general informal logic, (...) where the relevance of properties, not their number, must be the logically prior criterion for evaluating analogical arguments. (shrink)

In this paper, I discuss two concerns for pluralist truth theories: a concern about a key detail of these theories and a concern about their viability. The detail-related concern is that pluralists have relied heavily upon the notion of a domain, but it is not transparent what they take domains to be. Since the notion of a domain has been present in philosophy for some time, it is important for many theorists, not only truth pluralists, to be clear on (...) what domains are and what work they can do. The viability-related concern is that it’s not clear how a pluralist truth theory could explain the truth-conditions of mixed atomic propositions. To address this concern, truth pluralists should recognize something to which they have not been sufficiently attentive: that some atomic propositions belong to more than one domain. But, recognizing this requires rethinking the relationships between the nature of propositions, their membership in domains, and their truth. I address these issues and propose an understanding of them that is preferable to the best existing account of them, that offered by Michael Lynch. (shrink)

Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the underlying (...) logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e., properties which can be determined to hold of a process on the basis of a finite amount of information about its execution.These ideas lead to the following programme. A metalanguage is introduced, comprising• types = universes of discourse for various computational situations;• terms = PROGRAMS = syntactic intensions for models or points. A standard denotational interpretation of the metalanguage is given, assigning domains to types and domain elements to terms. The metalanguage is also given a logical interpretation, in which types are interpreted as propositional theories and terms are interpreted via a program logic, which axiomatises the properties they satisfy. The two interpretations are related by showing that they are Stone duals of each other. Hence, semantics and logic are guaranteed to be in harmony with each other, and in fact each determines the other up to isomorphism. This opens the way to a whole range of applications. Given a denotational description of a computational situation in our metalanguage, we can turn the handle to obtain a logic for that situation. (shrink)

Source domain verification has not received as much attention as criteria for metaphor identification in the study of conceptual metaphor. In this paper, we provide a replicable approach to source...

This paper develops co-ordinated multiple-domain supervenience relations to model determination and dependence relations between complex entities and their constituents by appealing to R-related pairs and by making use of associated isomorphisms. Supervenience relations are devised for order-sensitive and repetition-sensitive mereologies, for mereological systems that make room for many-many composition relations, as well as for hierarchical mereologies that incorporate compositional and hylomorphic structure. Finally, mappings are provided for theories that consider wholes to be prior to their parts.

Cross-domain descriptions are descriptions of features pertaining to one domain in terms of vocabulary primarily associated with another domain. Notably, we routinely describe psychological features in terms of the sensory domain and vice versa. Sorrow is said to be ‘bitter’ and fear ‘cold’. Music can be described as ‘happy’, ‘sad’, ‘mournful’, and so on. Such descriptions are rife in both everyday discourse and literary writings. What is it about psychological features that invites descriptions in sensory terms and what is it (...) about the sensory that invites descriptions in terms of the psychological? Drawing on the literature on polysemy, this paper sheds light on cross-domain descriptions pertaining to the sensory and the psychological domains. (shrink)

Abstract:Diagnostic classification systems in psychiatry have continued to rely on clinical phenomenology, despite limitations inherent in that approach. In view of these limitations and recent progress in neuroscience, the National Institute of Mental Health (NIMH) has initiated the Research Domain Criteria (RDoC) project to develop a more neuroscientifically based system of characterizing and classifying psychiatric disorders. The RDoC initiative aims to transform psychiatry into an integrative science of psychopathology in which mental illnesses will be defined as involving putative dysfunctions in (...) neural nodes and networks. However, conceptual, methodological, neuroethical, and social issues inherent in and/or derived from the use of RDoC need to be addressed before any attempt is made to implement their use in clinical psychiatry. This article describes current progress in RDoC; defines key technical, neuroethical, and social issues generated by RDoC adoption and use; and posits key questions that must be addressed and resolved if RDoC are to be employed for psychiatric diagnoses and therapeutics. Specifically, we posit that objectivization of complex mental phenomena may raise ethical questions about autonomy, the value of subjective experience, what constitutes normality, what constitutes a disorder, and what represents a treatment, enablement, and/or enhancement. Ethical issues may also arise from the (mis)use of biomarkers and phenotypes in predicting and treating mental disorders, and what such definitions, predictions, and interventions portend for concepts and views of sickness, criminality, professional competency, and social functioning. Given these issues, we offer that a preparatory neuroethical framework is required to define and guide the ways in which RDoC-oriented research can—and arguably should—be utilized in clinical psychiatry, and perhaps more broadly, in the social sphere. (shrink)

This book is about normativity and reasons.

Broad‐complex, Tramtrack, and Bric‐à‐brac/poxvirus and zinc finger (BTB/POZ) is a conserved domain found in many eukaryotic proteins with diverse cellular functions. Recent studies revealed its importance in multiple developmental processes as well as in the onset and progression of oncological diseases. Most BTB domains can form multimers and selectively interact with non‐BTB proteins. Structural studies of BTB domains delineated the presence of different interfaces involved in various interactions mediated by BTBs and provided a basis for the specific inhibition (...) of distinct protein‐interaction interfaces. BTB domains originated early in eukaryotic evolution and progressively adapted their structural elements to perform distinct functions. In this review, we summarize and discuss the structural principles of protein‐protein interactions mediated by BTB domains based on the recently published structural data and advances in protein modeling. We propose an update to the structure‐based classification of BTB domain families and discuss their evolutionary interconnections. (shrink)

We show that metric spaces and continuous functions between them are domain representable using the category of Scott-Ershov domains. A notion of effectivity for metric spaces is thereby inherited from effective domain theory. It is shown that a separable metric space with an effective metric can be represented by an effective domain. For a class of spaces, including the Euclidean spaces, the usual notions of effectivity are obtained. The Banach fixed point theorem is a consequence of the least fixed (...) point theorem for domains. A notion of semieffective domains is introduced and used to give a new proof of Ceitin's theorem. (shrink)

In this paper, I will defend a new compositional semantics for single-domain free logic. This semantics makes use of a distinction between the semantic value of a singular term and its semantic referent. The semantic value of a singular term is conceived of as a set that either contains the semantic referent or no element at all. The semantic referent is the object that the term designates. Before I will introduce this new semantics for single-domain predicate and an S5-type modal (...) logic in detail, I will present five related problems of compositionality of the standard semantics for these logical systems. After that I will show in detail how my new proposed alternative semantics can be used to solve nearly all of the outlined five problems. (shrink)

This book describes the mathematical aspects of the semantics of programming languages. The main goals are to provide formal tools to assess the meaning of programming constructs in both a language-independent and a machine-independent way, and to prove properties about programs, such as whether they terminate, or whether their result is a solution of the problem they are supposed to solve. In order to achieve this the authors first present, in an elementary and unified way, the theory of certain topological (...) spaces that have proved of use in the modelling of various families of typed lambda calculi considered as core programming languages and as meta-languages for denotational semantics. This theory is now known as Domain Theory, and was founded as a subject by Scott and Plotkin. One of the main concerns is to establish links between mathematical structures and more syntactic approaches to semantics, often referred to as operational semantics, which is also described. This dual approach has the double advantage of motivating computer scientists to do some mathematics and of interesting mathematicians in unfamiliar application areas from computer science. (shrink)

The proposition expressed by an utterance of a quantified sentence depends on a domain of discourse somehow determined by the context. How does the context of utterance determine the content of the domain of discourse? Many philosophers would approach this question from the point of view of an expressive theory of linguistic communication, according to which the primary function of language is to enable speakers to convey the propositional contents of their thoughts to hearers. This paper argues that from this (...) point of view there is no persuasive treatment of the determinants of the domain of discourse. The argument focuses on an abnormal case in which the domain the speaker has in mind is not evident to the hearer. In this way the question concerning the determinants of the domain of discourse is used to challenge the expressive theory of communication. (shrink)

The purpose of this paper is to provide a simple yet comprehensive organizing scheme for the responsible conduct of research (RCR). The heuristic offered here should prove helpful in research ethics education, where the many and heterogeneous elements of RCR can be bewildering, as well as research into research integrity and efforts to form RCR policy and regulations. The six domains are scientific integrity, collegiality, protection of human subjects, animal welfare, institutional integrity, and social responsibility.

My topic in this paper is social understanding. By this I mean the cognitive skills underlying social behaviour and social coordination. Normal, encultured, non-autistic and non-brain-damaged human beings are capable of an impressive degree of social coordination. We navigate the social world with a level of skill and dexterity fully comparable to that which we manifest in navigating the physical world. In neither sphere, one might think, would it be a trivial matter to identify the various competences which underly this (...) impressive level of performance. Nonetheless, at least as far as interpersonal interactions are concerned, philosophers show a rare degree of unanimity. What grounds our success in these interactions is supposed to be our common mastery of folk psychology. (shrink)

Metacognition is the capacity to evaluate the success of one's own cognitive processes in various domains; for example, memory and perception. It remains controversial whether metacognition relies on a domain-general resource that is applied to different tasks or if self-evaluative processes are domain specific. Here, we investigated this issue directly by examining the neural substrates engaged when metacognitive judgments were made by human participants of both sexes during perceptual and memory tasks matched for stimulus and performance characteristics. By comparing (...) patterns of fMRI activity while subjects evaluated their performance, we revealed both domain-specific and domain-general metacognitive representations. Multivoxel activity patterns in anterior prefrontal cortex predicted levels of confidence in a domain-specific fashion, whereas domain-general signals predicting confidence and accuracy were found in a widespread network in the frontal and posterior midline. The demonstration of domain-specific metacognitive representations suggests the presence of a content-rich mechanism available to introspection and cognitive control. (shrink)

My topic in this paper is social understanding. By this I mean the cognitive skills underlying social behaviour and social coordination. Normal, encultured, non-autistic and non-brain-damaged human beings are capable of an impressive degree of social coordination. We navigate the social world with a level of skill and dexterity fully comparable to that which we manifest in navigating the physical world. In neither sphere, one might think, would it be a trivial matter to identify the various competences which underly this (...) impressive level of performance. Nonetheless, at least as far as interpersonal interactions are concerned, philosophers show a rare degree of unanimity. What grounds our success in these interactions is supposed to be our common mastery of folk psychology. (shrink)

Drawing on the work–family enrichment theory, the present study investigates the cross-domain effects of ethical leadership on employees’ family and life satisfaction. Moreover, it focuses on the mediating role of work–family enrichment and the moderated mediation process of family-supportive supervisor behaviors underlying the relationship between ethical leadership and employees’ family and life satisfaction. Using a sample of 371 employees and their immediate supervisors in China, we found that WFE mediated the relationship between ethical leadership and employee-rated and supervisor-rated family and (...) life satisfaction. Moreover, FSSB positively moderated the relationship between ethical leadership and WFE, such that the relationship was strengthened when FSSB were higher. Furthermore, the mediations of WFE between ethical leadership and employee-rated and supervisor-rated family and life satisfaction were also positively moderated by FSSB, such that the indirect effects were stronger when FSSB were higher. The theoretical and managerial implications of our findings are further discussed. (shrink)

What counts as human rationality: reasoning processes that embody content-independent formal theories, such as propositional logic, or reasoning processes that are well designed for solving important adaptive problems? Most theories of human reasoning have been based on content-independent formal rationality, whereas adaptive reasoning, ecological or evolutionary, has been little explored. We elaborate and test an evolutionary approach, Cosmides' social contract theory, using the Wason selection task. In the first part, we disentangle the theoretical concept of a “social contract” from that (...) of a “cheater-detection algorithm”. We demonstrate that the fact that a rule is perceived as a social contract — or a conditional permission or obligation, as Cheng and Holyoak proposed — is not sufficient to elicit Cosmides' striking results, which we replicated. The crucial issue is not semantic, but pragmatic: whether a person is cued into the perspective of a party who can be cheated. In the second part, we distinguish between social contracts with bilateral and unilateral cheating options. Perspective change in contracts with bilateral cheating options turns P & not-Q responses into not-P & Q responses. The results strongly support social contract theory, contradict availability theory, and cannot be accounted for by pragmatic reasoning schema theory, which lacks the pragmatic concepts of perspectives and cheating detection. (shrink)

In the first part of this paper I present a defence of the Austinian semantic approach to incomplete quantifiers and similar phenomena (section 2-4). It is part of my defence of Austinian semantics that it incorporates a cognitive dimension (section 4). This cognitive dimension makes it possible to connect Austinian semantics to various cognitive theories of discourse interpretation. In the second part of the paper (sections 5-7), I establish connections between Austinian semantics and four particular theories: • the theory of (...) reference and modes of presentation in terms of information files (see e.g. Perry 1993), • the theory of discourse interpretation as involving a process of context selection (see Sperber and Wilson 1986), • the theory of informational structure (for a survey, see Lambrecht 1994), • the theory of mental spaces (Fauconnier 1985). (shrink)

Wulf Gaertner provides a comprehensive account of an important and complex issue within social choice theory: how to establish a social welfare function while restricting the spectrum of individual preferences in a sensible way. Gaertner's starting point is K. J. Arrow's famous 'Impossibility Theorem', which showed that no welfare function could exist if an unrestricted domain of preferences is to be satisfied together with some other appealing conditions. A number of leading economists have tried to provide avenues out of this (...) 'impossibility' by restricting the variety of preferences: here, Gaertner provides a clear and detailed account, using standardized mathematical notation, of well over forty theorems associated with domain conditions. Domain Conditions in Social Choice Theory will be an essential addition to the library of social choice theory for scholars and their advanced graduate students. (shrink)

The archetypal Rumely domain is the ring \widetildeZ of algebraic integers. Its constructible Boolean algebra is atomless. We study here the opposite situation: Rumely domains whose constructible Boolean algebra is atomic. Recursive models (which are rings of algebraic numbers) are proposed; effective model-completeness and decidability of the corresponding theory are proved.

Suppose there is a domain of discourse of English, then everything of which any predicate is true is a member of that domain. If English has a domain of discourse, then, since ‘is a domain of discourse of English’ is itself a predicate of English and true of that domain, that domain is a member of itself. But nothing is a member of itself. Thus English has no domain of discourse. We defend this argument and go on to argue to (...) the same conclusion without relying on the supposition that English is a language which contains the predicate ‘is a domain of discourse of English’. (shrink)

This article offers a unified theory of the licensing of Negative and Positive Polarity Items, focusing on the acceptability conditions of PPIs of the some-type, and NPIs of the any-type. It argues that licensing has both a syntactic and a semantic component. On the syntactic side, the acceptability of PIs is checked in constituents; in fact, for any given PI, only some constituents, referred to as `domains', are eligible for the evaluation of that PI. The semantic dimension of licensing (...) consists in the sensitivity of PIs to the monotonicity properties of the syntactic environments they find themselves in. Two pieces of evidence support the semantic dimension of what I call the ‘environment-based’ approach defended here: PIs are subject to flip-flop and certain inferences affect their acceptability by modifying the monotonicity of their environment. A third property, called ‘entanglement’ and so far unnoticed, is described: the acceptability of PIs depends on the acceptability of other PIs in the same syntactic environment. The latter property is exploited to determine what semantic property some is sensitive to: it turns out that, contrary to the consensus among researchers, some is acceptable in the complement of the set of environments in which any is acceptable, and vice versa. (shrink)

When trust is broken, how should we determine who is at fault? Previous discus- sions of broken trust typically attribute the fault to trusters who place trust foolishly or trustees who act in an untrustworthy manner. These discussions take for granted the ability of the truster and trustee to communicate and understand the boundaries of what is being entrusted, that is, the domain of trust. However, the boundaries of entrusted domains are not always clear to either party which can (...) result in broken trust despite the best efforts of both truster and trustee. In this paper, I argue that deter- mining who to blame when trust is broken is a messy affair in which disagreements over fault regularly arise. I introduce three features of trust domains that take center stage in negotiations regarding who is at fault when trust is broken: scope, rigidity and ordering. (shrink)

The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is. Although this has led previous researchers to argue for domain-specific constraints that are tied to different kinds/domains, an exciting possibility is that kinds/domains themselves (...) can be learned. General cognitive constraints, when combined with rich inputs, can establish domains, rather than these domains necessarily preexisting prior to learning. Knowledge is structured and richly differentiated, but its “skeleton” must not always be preestablished. Instead, the skeleton may be adapted to fit patterns of co-occurrence, task requirements, and goals. Finally, we argue that for models of development to demonstrate genuine cognitive novelty, it will be helpful for them to move beyond highly preprocessed and symbolic encodings that limit flexibility. We consider two physical models that learn to make tone discriminations. They are mechanistic models that preserve rich spatial, perceptual, dynamic, and concrete information, allowing them to form surprising new classes of hypotheses and encodings. (shrink)

A novel problem or task may seem difficult at first, but with enough practice, it can become easy and routine. Practice and the process of learning is often accompanied by some mild cognitive uneas...

(Open Access.) Quantifiers frequently figure in works of fiction. But occurrences of quantificational expressions within fictions seem no more inevitably to be associated with real domains than uses of names within fictions seem inevitably to be associated with existing referents. The paper outlines some philosophical puzzles resulting from this apparent lack of associated domains, puzzles that are broadly analogous to more familiar ones raised by the apparently nonreferential nature of many fictional names. The paper argues, in the light (...) of an important disanalogy between quantifiers and names, that the quantificational puzzles are substantive, in that they cannot be resolved merely by appealing to the possibility of empty domains. It then argues that, despite the cited parallels between occurrences of quantifiers and names within fictions, promising treatments of fictional names do not always straightforwardly generalise to provide accounts of the quantificational phenomena: the quantificational puzzles are therefore not only substantive but also distinctive. The paper provides further testament to the depth and interest of the problems involving content that are generated by fiction, by identifying a very wide range of previously neglected cases, while also helping to situate within a broader context the notoriously hard philosophical challenges posed by fictional names. (shrink)

We argue that a comprehensive theory of reciprocals must rely on a general taxonomy of restrictions on the interpretation of relational expressions. Developing such a taxonomy, we propose a new principle for interpreting reciprocals that relies on the interpretation of the relation in their scope. This principle, the Maximal Interpretation Hypothesis (MIH), analyzes reciprocals as partial polyadic quantifiers. According to the MIH, the partial quantifier denoted by a reciprocal requires the relational expression REL in its scope to denote a maximal (...) relation in REL’s interpretation domain. In this way the MIH avoids a priori assumptions on the available readings of reciprocal expressions, which are necessary in previous accounts. Relying extensively on the work of Dalrymple et al. (Ling Philos 21:159–210, 1998), we show that the MIH also exhibits some observational improvements over Dalrymple et al.’s Strongest Meaning Hypothesis (SMH). In addition to deriving some attested reciprocal interpretations that are not expected by the SMH, the MIH offers a more restrictive account of the way context affects the interpretation of reciprocals through its influence on relational domains. Further, the MIH generates a reciprocal interpretation at the predicate level, which is argued to be advantageous to Dalrymple et al.’s propositional selection of reciprocal meanings. More generally, we argue that by focusing on restrictions on relational domains, the MIH opens the way for a more systematic study of the ways in which lexical meaning, world knowledge and contextual information interact with the interpretation of quantificational expressions. (shrink)