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)

I present a version of Kit Fine's stratified semantics for the logic RWQ and define a natural family of related structures called RW hyperdoctrines. After proving that RWQ is sound with respect to RW hyperdoctrines, we show how to construct, for each stratified model, a hyperdoctrine that verifies precisely the same sentences. Completeness of RWQ for hyperdoctrinal semantics then follows from completeness for stratified semantics, which is proved in an appendix. By examining the base (...) category of RW hyperdoctrines, we find reason to be worried about the ontology of stratified models. (shrink)

We prove the cut-elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality.

Jc Beall has made several contributions to the theory of restricted quantification in relevant logics. This paper examines these contributions and proposes an alternative account of restricted universals. The alternative is not, however, a theory of relevant restricted universals in any real sense. It is, however, a theory of restricted universals phrased in the most plausible general quantificational theory for relevant logics—Kit Fine’s stratified semantics. The motivation both for choosing this semantic framework and for choosing the particular theory (...) of restricted quantification we use is because they are the best way of dealing with these topics from Beall’s theory-building theory picture of logic, establishing a second point of contact with Beall’s work. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular (...) the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

There are some complex experiences, such as the experiences that allow us to understand linguistic expressions and pictures respectively, which seem to be very similar. For they are stratified experiences in which, on top of grasping certain low-level properties, one also grasps some high-level semantic-like properties. Yet first of all, those similarities notwithstanding, a phenomenologically-based reflection shows that such experiences are different. For a meaning experience has a high-level fold, in which one grasps the relevant expression’s meaning, which is (...) not perceptual, but is only based on a low-level perceptual fold that merely grasps that expression in its acoustically relevant properties. While a pictorial experience, a seeing-in experience, has two folds, the configurational and the recognitional fold, in which one respectively grasps the physical basis of a picture, its vehicle, and what the picture presents, its subject, that are both perceptual, insofar as they are intimately connected. For unlike a meaning experience, in a seeing-in experience one can perceptually read off the picture’s subject from the picture’s vehicle. Moreover, this phenomenological difference is neurologically implemented. For not only the cerebral areas that respectively implement such experiences are different, at least as far as the access to those experiences’ respective high-level content is concerned. As is shown by the fact that one can selectively be impaired in the area respectively implementing the meaning vs. the seeing-in experience without losing one’s pictorial vs. semantic competence respectively. But also, unlike meaning experiences, the area implementing the seeing-in experiential folds is perceptual as a whole. For not only a picture’s subject can be accessed earlier than an expression’s meaning, but also the neural underpinnings of such folds are located in the perceptual areas of the brain. (shrink)

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories^ can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying (...) problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21]. (shrink)

Predicates like gather and ones like be numerous have both been described as ‘collective predicates,’ since they predicate something of a plurality. The two classes of predicates differ, however, with respect to plural quantifiers, which are grammatical with gather-type predicates but ungrammatical with numerous-type predicates. Here, I show that the gather/numerous opposition derives from mereological properties that are familiar from the domains of telicity and mass/count. I address problems of undergeneration and overgeneration with two technical innovations: first, I weaken the (...) property of divisibility to Champollion’s concept of stratified reference; second, I provide mechanisms to rule out accidental satisfaction of the logical property. More broadly, I place collective predication in a larger context by building empirical connections to mass/count and collectivity across semantic domains. (shrink)

As a multi-layered theory of the foundations of “‘mathematicizing’ logic”, Husserlian pure logic is stratified on three levels (sub-theoretical, theoretical, meta-theoretical), which are then themselves transversally split in two sides (apophantic and ontological). This paper investigates how symbolic knowledge works in this framework—viz. in terms of ‘How can the subjective operating with symbols be justified in the process of obtaining objective contents of knowledge?’ To do so, it innovates in showing how Husserl’s theory of semiotic intentionality provides the epistemological-transcendental (...) foundation for the syntactic-semantic correspondence of the meaning relationship that is operative at the kernel of pure logic—i.e. on the theoretical level, between systems of axioms and formal manifolds. And thereby, it bridges the gap between the two volumes of the first edition of the Logical Investigations (namely, the Prolegomena and the six Investigations). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reflections on DuchampBergson ReadymadeFederico Luisetti (bio)Translated by David Sharp[I]nside the person we must distinctly perceive, as through a glass, a set-up mechanism.—Henri Bergson, Laughter: An Essay on the Meaning of the Comic (1901)In spite of the enormous critical attention paid to Marcel Duchamp’s art and theoretical background, the dialogue with Bergsonism is mostly confined to scattered references and erudite observations.1 Paradoxically, the major obstacle to this encounter has been (...) the immense popularity of Henri Bergson’s philosophy since the initial decade of the twentieth century. Such success has come with a price, however, for the proliferation of neutralizing schematizations has progressively suffocated the specificity of his thought and subsequently impeded the understanding of his epistemological radicalism, so cherished by Duchamp and the historical avant-garde.2Consider, for example, how the specter of Bergson constantly hovers over Linda Dalrymple Henderson’s authoritative discussion of Duchamp’s scientific sources. Although Henderson recognizes the diffuse presence in Duchamp of various Bergsonian motives, because she regards Bergson as the antiscientific philosopher of the “inner self” and of “profound self-expression,”3 Bergsonian notions seem to her incompatible with the artistic revolution prompted by Duchamp. A historiographical exorcism is therefore needed in order to heal the consequences of the traumatic Bergson-Duchamp incest. Herein lies Henderson’s solution: since Duchamp rejects the aesthetic principles of the Puteaux Cubists, he also abandons Bergsonism, which represents their philosophical matrix. Thus, the Bergsonian ideas “undoubtedly” present in Duchamp’s artistic lexicon are nothing but debris accumulated in the course of his battle with the Cubist disciples of Bergson.4To counter these approaches, in the following pages I will map Duchamp’s absorption and creative distortion of Bergsonism,5 concentrating on key terms of both Bergson’s philosophy and Duchamp’s speculations on art: space, “readymade,” delay, body, virtual, circuit, machine.6 I will then discuss the theoretical implications of Duchamp’s Bergsonism and place the readymade7 within its proper context: the deconstruction of the Western metaphysics of reflection. [End Page 77]SpaceBeginning with Time and Free Will (1889), Bergson distinguishes between two types of multiplicities: on the one hand, “duration” (durée), “an internal multiplicity of succession, of fusion, of organization, of heterogeneity, of qualitative discrimination... a virtual and continuous multiplicity that cannot be reduced to numbers,” and on the other, “a multiplicity of exteriority, of simultaneity, of juxtaposition, of order, of quantitative differentiation... a numerical multiplicity, discontinuous and actual.”8 This opposition is generally understood as a clear-cut differentiation between the inner experience of time and the objective consistence of space. In Time and Free Will and Matter and Memory (1896), there are several passages that can be read accordingly, since duration is often described as a continuous, indivisible temporal experience, and space as that which “by definition, is outside us.”9Yet for Bergson space and time are mixed terms, and their internal complexity does not coincide with the semantic distinction between the two multiplicities. Deleuze has clearly formulated the central difficulty that a reductionist theory of space and time would imply, a problem of which Bergson is fully aware. Since the concept of duration has an ontological span, space must find a place within time and vice versa: “If things endure, or if there is duration in things, the question of space will need to be reassessed on new foundations. For space will no longer simply be a form of exteriority.... Space itself will need to be based in things... to have its own ‘purity’” [Deleuze, Bergsonism 49]. Hidden behind the motif of the “spatialization of time,” Bergson has devised a stratified theory of space, whose origins we can trace back to his philosophical apprenticeship [see Heidesick 29–42].Departing from Kant, Bergson introduces a boundary between the “perception of extension” and the “conception of space,” between qualitative space, which he calls “extensity” (étendue), and “abstract,” “homogeneous” space: “We must thus distinguish between the perception of extensity and the conception of space.... [S]pace is not so homogeneous for the animal as for us... determinations of space, or directions, do not assume for it a purely geometrical form” [Bergson, Time... (shrink)

Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different (...) categories, on the one hand, and the way in which the realm of Bedeutungen stratifies into logical categories, on the other hand. A proper understanding of this internality reveals how Frege's conception of the relation between language and the world is neither a form of realism nor a form of linguistic idealism. To come to understand Frege's conception of the logical categories, is to come to understand both these forms of internality by coming to understand how they hang together. (shrink)

Contemporary reflection on the concept of value oscillates between positions that advocate absolutist realism and positions that propose total relativism. The present paper aims to distance itself from these two ways of reading the topic, rejecting any monolithic conception, and proposing a stratified theory of value. Beginning with an analysis of values that differentiates them from both “goods” and “valuations,” the author outlines an understanding of value that must be investigated in its multiple, interconnected layers. The stratification starts from (...) the role of the emotional sphere and comes down to a formal and absolute conception of the concept. The goal of the paper is to outline the different levels of validity of each proposed layer, which must be recognized and differentiated, with the aim of also capturing the difficulties and ambiguities that characterize the transition from one level to another. (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)

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)

We consider arbitrary stratified languages. We study structures which satisfy the same stratified sentences and we obtain an extension of Keisler's Isomorphism Theorem to this situation. Then we consider operations which are definable by a stratified formula and modify the `type' of their argument by one; we prove that for such an operation F the sentence c = F(c) and the scheme $\varphi(c) \leftrightarrow \varphi(F(c))$ , where φ(x) varies among all the stratified formulas with no variable (...) other than x free, imply the same stratified {c}-sentences. (shrink)

Human resource management plays an important role for an organization’s sustainability endeavor. This paper attempts to provide a concise overview of the sustainability in HRM in Japanese overseas subsidiaries. The purpose of this paper is to examine two branches of business from a major Japanese multinational corporation in Hong Kong and identify the nature of sustainability in HRM in these two operations. It draws on qualitative interview data from a sample of 20 Japanese and locally hired employees and two HR (...) directors working in these two case companies with a total of 80 stories and two company interviews. A conceptual framework of sustainable HRM based on the Respect Openness Continuity model is used to examine sustainable HRM in the two Japanese subsidiaries. The results show that sustainability in HRM differs between these two case companies even though they are operated under the same Japanese headquarters. Distinctive stratified patterns of sustainability in HRM are found among the respondents in both case companies, and the nature of sustainability in HRM in these two case companies varies from each other to a large extent. The analysis of the interview data provides insight of how cultural, sectoral, and institutional factors have led to the different stratified pattern and nature of sustainability in HRM in these Japanese overseas subsidiaries. Further larger-scale research needs to be done on the case headquarters in Japan, and multinational corporations of other national origins to discover more about the patterns and nature of sustainability in HRM in a global context. (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)

It was at the turn of the the twentieth century when Francis Bradley’s metaphysics perme­ated with the spirit of German Idealism was one of the strongest trends of English aca­demic philosophy. But after the “neopositivist Brexit” launched by Russell, Moore and some other analytical thinkers it became mainly a subject for historians of idealism. An attempt is undertaken in the paper to reveal both the historical and actual significance of Bradley’s doctrine of degrees of reality along with an estimation of (...) his critics’ argu­ments and the author’s own criticisms of his “ontology of the Absolute”. Bradley’s ideal­ism is fit unto the framework of comparative ontology, in the first place by its juxtaposi­tion with mostly congenial “absolutism” of Advaita-Vedānta. The author suggests also his own version of differing and quantifying reality, in the shape of individual landscapes of reality in the context of their comparison with personal valuables. (shrink)