Hybrid languages are expansions of propositional modal languages which can refer to worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work has focussed on a more constrained system called $\mathscr{H}$. We show in detail that $\mathscr{H}$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations and a syntactic characterization. The key result to emerge is that $\mathscr{H}$ corresponds to the fragment of first-order logic which is invariant for generated (...) submodels. We then show that $\mathscr{H}$ enjoys interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage $\mathscr{H}$. Finally, we provide complexity results for $\mathscr{H}$ and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}$. (shrink)

The theory of collective agency and intentionality is a flourishing field of research, and our understanding of these phenomena has arguably increased greatly in recent years. Extant theories, however, are still ill-equipped to explain certain aspects of collective intentionality. In this article we draw attention to two such underappreciated aspects: the failure of the intentional states of collectives to supervene on the intentional states of their members, and the role of non-human factors in collective agency and intentionality. We propose a (...) theory of collective intentionality which builds on the ‘interpretationist’ tradition in metasemantics and the philosophy of mind as initiated by David Lewis and recently developed further by Robbie Williams. The collective-level analogue of interpretationism turns out to look different in some ways from the individual-level theory, but is well-suited to accommodating phenomena such as hybrid collective intentionality. Complemented with Kit Fine’s theory of variable embodiment, such a theory also provides a diachronic account of intentional collectives. (shrink)

Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of infinite models and have undecidable satisfiability (...) problems. (shrink)

Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with additional inference (...) rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of constructive hybrid logics. This shows that constructive hybrid logics are a viable enterprise and opens up the way for future applications. (shrink)

This chapter surveys hybrid theories of well-being. It also discusses some criticisms, and suggests some new directions that philosophical discussion of hybrid theories might take.

In this paper, the authors present a presuppositional account for a class of evaluative terms that encode both a descriptive and an evaluative component: slurs and thick terms. The authors discuss several issues related to the hybrid nature of these terms, such as their projective behavior, the ways in which one may reject their evaluative content, and the ways in which evaluative content is entailed or implicated (as the case may be) by the use of such terms.

The recent resurgence of extreme-right movements and the nationalist turn of many governments across the world have reignited the relevance of discussions within educational philosophy about the teaching of national identity in schools. However, the conceptualisation of national identity in previous iterations of these debates have been largely Western and Eurocentric, making the past theoretical literature about these questions less relevant for post-colonial settings. In this paper, I imagine a new approach for teaching national identity in post- colonial contexts, founded (...) on postcolonial conceptions of identity and in particular, the concept of hybridity. I first develop a postcolonial account of national identity by drawing on Homi Bhabha’s thinking about cultural identity, drawing on his concepts of liminality, splitting, and ambivalence. Then, building on Bhabha’s notion of hybridity, I propose a distinction between national identity portrayals as either fixed or malleable. Finally, I demonstrate the implications of such a conceptual distinction on the way that national identity is taught in post-colonial schools; by way of an example, I envision a concrete approach to teaching national identity that views national identity as malleable rather than fixed, set in a hypothetical postcolonial school in the Philippines. By beginning from postcolonial assumptions about national identity, I hope to indicate new directions that the debates about the teaching of national identity in schools might proceed. (shrink)

ABSTRACT When does a state of affairs constitute a harm to someone? Comparative accounts say that being worse off constitutes harm. The temporal version of the comparative account is seldom taken seriously, due to apparently fatal counterexamples. I defend the temporal version against these counterexamples, and show that it is in fact more plausible than the prominent counterfactual version of the account. Non-comparative accounts say that being badly off constitutes harm. However, neither the temporal comparative account nor the non-comparative account (...) can correctly classify all harms. I argue that we should combine them into a hybrid account of harm. The hybrid account is extensionally adequate and presents a unified view on the nature of harm. (shrink)

This paper is a survey of recent ‘hybrid’ approaches to metaethics, according to which moral sentences, in some sense or other, express both beliefs and desires. I try to show what kinds of theoretical issues come up at the different choice points we encounter in developing such a view, to raise some problems and explain where they come from, and to begin to get a sense for what the payoff of such views can be, and what they will need to (...) do in order to earn that payoff. (shrink)

The transgressive ontological character of hybrids—entities crossing the ontological binarism of naturalness and artificiality, e.g., biomimetic projects—calls for pondering the question of their ethical status, since metaphysical and moral ideas are often inextricably linked. The example of it is the concept of “moral considerability” and related to it the idea of “intrinsic value” understood as a non-instrumentality of a being. Such an approach excludes hybrids from moral considerations due to their instrumental character. In the paper, we revisit the boundaries of (...) moral considerability by reexamining the legitimacy of identifying intrinsic value with a non-instrumental one. We offer the concept of “functional value,” which we define as a simultaneous contribution to the common good of the ecosystem and the possibility to disclose the full variety of aspects of a being’s identity. We argue that such a value of hybrids allows us to include them into the scope of moral considerability. (shrink)

The recent resurgence of extreme-right movements and the nationalist turn of many governments across the world have reignited the relevance of discussions within educational philosophy about the teaching of national identity in schools. However, the conceptualisation of national identity in previous iterations of these debates have been largely Western and Eurocentric, making the past theoretical literature about these questions less relevant for post-colonial settings. In this paper, I imagine a new approach for teaching national identity in post-colonial contexts, founded on (...) postcolonial conceptions of identity and in particular, the concept of hybridity. I first develop a postcolonial account of national identity by drawing on Homi Bhabha’s thinking about cultural identity, drawing on his concepts of liminality, splitting, and ambivalence. Then, building on Bhabha's notion of hybridity, I propose a distinction between national identity portrayals as either fixed or malleable. Finally, I demonstrate the implications of such a conceptual distinction on the way that national identity is taught in post-colonial schools; by way of an example, I envision a concrete approach to teaching national identity that views national identity as malleable rather than fixed, set in a hypothetical postcolonial school in the Philippines. By beginning from postcolonial assumptions about national identity, I hope to indicate new directions that the debates about the teaching of national identity in schools might proceed. (shrink)

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model. This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems (...) for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems for a spectrum of different hybrid logics. (shrink)

The transgressive ontological character of hybrids—entities crossing the ontological binarism of naturalness and artificiality, e.g., biomimetic projects—calls for pondering the question of their ethical status, since metaphysical and moral ideas are often inextricably linked. The example of it is the concept of “moral considerability” and related to it the idea of “intrinsic value” understood as a non-instrumentality of a being. Such an approach excludes hybrids from moral considerations due to their instrumental character. In the paper, we revisit the boundaries of (...) moral considerability by reexamining the legitimacy of identifying intrinsic value with a non-instrumental one. We offer the concept of “functional value,” which we define as a simultaneous contribution to the common good of the ecosystem and the possibility to disclose the full variety of aspects of a being’s identity. We argue that such a value of hybrids allows us to include them into the scope of moral considerability. (shrink)

This is a draft of a chapter for the Routledge Handbook of Metaethics, edited by David Plunkett and Tristram McPherson. I offer an overview of hybrid views in metaethics, with main focus on hybrid cognitivist views such as those defended by Daniel Boisvert and David Copp, and on hybrid expressivist views such as those defended by Michael Ridge and myself.

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school , the method remains little known. In our view this has deprived temporal logic of a valuable tool.The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives (...) rise to well-behaved logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full first-order expressive strength, is demonstrated for a weaker local language capable of defining the Until operator; we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths. (shrink)

The main aim of the present paper is to use a proof system for hybrid modal logic to formalize what are called false-belief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief. We consider two different versions of the Smarties task, involving respectively a shift of perspective to another person and to another time. Our formalizations disclose that despite this difference, the two versions of the Smarties task have exactly the same underlying logical structure. (...) We also consider the Sally-Anne task, having a more complicated logical structure, presupposing a “principle of inertia” saying that a belief is preserved over time, unless there is belief to the contrary. (shrink)

This paper proposes a novel account of the contents of memory. By drawing on insights from the philosophy of perception, I propose a hybrid account of the contents of memory designed to preserve important aspects of representationalist and relationalist views. The hybrid view I propose also contributes to two ongoing debates in philosophy of memory. First, I argue that, in opposition to eternalist views, the hybrid view offers a less metaphysically-charged solution to the co-temporality problem. Second, I show how the (...) hybrid view conceives of the relationship between episodic memory and other forms of episodic thinking. I conclude by considering some disanalogies between perception and memory and by replying to objections. I argue that, despite there being important differences between memory and perception, those differences do not harm my project. (shrink)

In virtue of what is something a reason for action? That is, what makes a consideration a reason to act? This is a metaphysical or meta-normative question about the grounding of reasons for action. The answer to the grounding question has been traditionally given in ‘pure’, univocal terms. This paper argues that there is good reason to understand the ground of practical normativity as a hybrid of traditional ‘pure’ views. The paper 1) surveys the three leading ‘pure’ answers to the (...) question of a normative ground, 2) examines one or two of the most difficult problems for each, proposing along the way a new objection to one, and 3) argues that a particular hybrid view about normative grounds –‘hybrid voluntarism’ – avoids each of the main problems faced by the three leading ‘pure’ views. (shrink)

Structural problems are examined with pairing two chambers, one selected by election and the other by sortition, into a traditional bicameral system. It is argued that an all-purpose legislative chamber modeled on existing elected chambers is a mismatch for sortition and that purported benefits of maintaining partisan elections alongside sortition are illusory. Alleged benefits of a hybrid bicameral system are shown to be outweighed by a variety of harmful effects. Furthermore, even if those harms are not substantiated, the continued existence (...) of an elected chamber will likely result in the delimitation of the sortition chamber. Combining many different sorts of minipublics with different characteristics and functions is preferable, and a possible multibody sortition legislative system is presented. Finally, an alternative way forward for sortition is proposed by peeling away individual topic areas from elected bodies and transferring them to sortition bodies. (shrink)

In this paper, I have two primary goals. First, I show that the causal-based story approach in A hybrid formal theory of arguments, stories and criminal evidence is ill suited to negative causation. In the literature, the causal-based approach requires that hypothetical stories be causally linked to the explanandum. Many take these links to denote physical or psychological causation, or temporal precedence. However, understanding causality in those terms, as I will show, cannot capture cases of negative causation, which are of (...) interest to the Law. In keeping with this, I also discuss some of the difficulties Hybrid Theory invites by remaining silent on the nature of the causal links. In my second aim, I sketch a way for Hybrid Theory to overcome this problem. By replacing the original, underlying causal structure with contrastive causation in the law, Hybrid Theory can represent reasoning in which the evidence that is appealed to is causally linked via negative causation to the explananda. (shrink)

Until now, the mass spread of fake news and its negative consequences have implied mainly textual content towards a loss of citizens' trust in institutions. Recently, a new type of machine learning framework has arisen, Generative Adversarial Networks (GANs) – a class of deep neural network models capable of creating multimedia content (photos, videos, audio) that simulate accurate content with extreme precision. While there are several areas of worthwhile application of GANs – e.g., in the field of audio-visual production, human-computer (...) interactions, satire, and artistic creativity – their deceptive uses, at least as currently foreseeable, are just as numerous and worrying. The main concern is linked to the so-called “deepfakes”, fake images or videos that simulate real events with extreme precision. When trained on a human face, GANs can make the face assume hyper-realistic movements, expressions and (verbal and non-verbal) communication abilities. This technology poses an urgent threat to the governance of democratic processes concerning the production of public opinions and political discourses, with significant potential for reality-altering and disinformation. After a short introduction of their current technical state-of-the-art, in this paper we want to enquire the GANs` socio-technical system alongside different and intertwined philosophical accounts. Firstly, we will argue about the conditions that make perceived a GANs-generated content as trustworthy, arguing also about the general effects GANs might have on the perceived trustworthiness of individuals. Thereafter, we will discuss about the inadequacy to approach GANs only as perception-altering technology. Against this backdrop, we will propose a theoretical turn that considers the human-machine relationships of trustworthiness as elements of a broader hybrid socio-technical systems. This turn come up with political repercussions that we will discuss in the last part of the paper. (shrink)

Bex analyzes the case with an informal version of his hybrid theory, which combines scenario construction and argumentation. Arguments based on evidence can be used to reason about alternative scenarios. Bex claims that his hybrid theory provides the best of both worlds by combining cognitively feasible story‐based reasoning with more detailed rational argumentation. However, like the argument‐based approach, the hybrid theory does not provide a systematic account of uncertainty.

: In recent literature supporting a hybrid view between metaethical cognitivism and noncognitivist expressivism, much has been made of an analogy between moral terms and pejoratives. The analogy is based on the plausible idea that pejorative slurs are used to express both a descriptive belief and a negative attitude. The analogy looks promising insofar as it encourages the kinds of features we should want from a hybrid expressivist view for moral language. But the analogy between moral terms and pejorative slurs (...) is also problematic. In this paper, I argue for two main ways in which we should distinguish between two different types of pejorative terms: slurs, on the one hand, and what I call general pejorative terms, on the other. I examine the problems with the analogy between slurs and moral terms and conclude that general pejorative terms like ‘jerk’ are a better candidate on which to model the potential dual-use behavior of moral terms. So if hybrid theorists are looking for a dual-use model for moral language, they should be careful to base their analogies on general pejoratives, rather than slurs. (shrink)

Hybrid theories are metaethical theories concerning the content of sentences about moral value. These theories claim that sentences with ethical content express two kinds of mental state. One state is an affect‐like state. The other is a belief‐like state. The expressed affect‐like state will involve a moral attitude of some kind, such as approval, but it is not part of the truth‐conditions of the sentence. We can divide hybridists into two kinds.

Sentences containing predicates of personal taste (for example, ‘tasty’, ‘funny’) and aesthetic predicates (for example, ‘beautiful’) give rise to an acquaintance inference: They convey the information that speakers have first-hand experience with the object of predication and they can only be uttered appropriately if that is the case. This is surprisingly hard to explain. I will concentrate on aesthetic predicates, and firstly criticize previous attempts to explain the acquaintance phenomena. Second, I will suggest an explanation that rests on a speech (...) act theoretical version of hybrid expressivism, according to which, in uttering ‘X is beautiful’ speakers perform two illocutionary acts simultaneously: an expressive and an assertive one. I will spell out this suggestion in detail and defend it against objections. Considering puzzles related to the acquaintance inference will lead to a new argument for a promising version of hybrid expressivism in meta-aesthetics. (shrink)

Hybrid identities are sentences in a special second order language with identity. The model classes of sets of hybrid identities are called hybrid solid varieties. We give a Birkhoff-type-characterization of hybrid solid varieties and develop a hybrid equational logic.

This essay characterizes the perception of the visual hybrid as nonconceptual, introducing the terminology of nonconceptual content theory to aesthetics. The visual hybrid possesses a radical but nonetheless exemplary aesthetic composition and is well established in culture, art, and even design. The essay supplies a philosophical analysis of the results of cross-cultural experiments, showing that while categorization or conceptual hierarchization kicks in when the visual hybrids are juxtaposed with linguistic descriptions, no conceptual scheme takes effect when participants are presented with (...) mere visual hybrids. In isolation, the hybrids do not lend themselves to classification. I draw four conclusions from these experimental outcomes: 1. The perception of visual hybrids follows the structure of a nonconceptual mental content, because the original categories or concepts of the hybrids’ components are not combined into one, and their properties are not applied to one another, therefore none of the components reconstructs the other such that it is introduced to a new category. 2. Language freezes the hybridity of the visual hybrid into conceptuality. 3. Given that language has a freezing effect in the case of an extreme visual phenomenon such as the hybrid, it is all the more restraining in moderate artistic compositions, such as visual metaphors, in which properties of one component (the source) are applied to the other (the target). In those, nonconceptuality emerges from relatively organized compositions, forms, and relations, and from the dependence of objects and their properties on perceptual context. 4. Thus, the nonconceptualist terminology is suitable for the analysis of aesthetic perception in general and aesthetic perception’s relation to language. Keywords aesthetics, perception, nonconceptual content, hybrids, visual metaphors. (shrink)

ABSTRACT In 1929 and 1934–1935, the physical anthropologist Harry L. Shapiro voyaged in the South Seas on the Mahina-I-Te-Pua and the Zaca, measuring mixed-race islanders, including the descendants of the Bounty mutineers on Pitcairn Island. His research in Polynesian hybridity reflects the growing cultural and scientific investment of the United States in the Pacific during this period. Shapiro's oceanic adventures and intimate encounters prompted him to discount typological speculation and emphasize instead the liberal Boasian program in physical anthropology, giving him (...) the confidence to refigure his evaluations of racial difference. The seaborne investigatory enterprise came to influence U.S. racial thought, adding impetus to the condemnation of racism in science. On his return from the South Seas, Shapiro tried to get his fellow physical anthropologists to issue a manifesto opposing the harnessing of their science to racial discrimination and prejudice. (shrink)

We show that every extension of the basic hybrid logic with modal Sahlqvist axioms is complete. As a corollary of our approach, we also obtain the Beth property for a large class of hybrid logics. Finally, we show that the new completeness result cannot be combined with the existing general completeness result for pure axioms.

Hybrid organisations combine different elements from the for-profit and non-profit domains, and they usually operate in a resource-scarce environment. For these reasons, they continuously face various resources constraints, yet their hybrid nature could be translated into an opportunity. The purpose of our study was to investigate how a hybrid organisation can overcome resource constraints in developing countries by exploiting their own hybrid nature. In the unique research setting offered by Kenyan social enterprises, we identified five creative approaches implemented by social (...) enterprises. Finally, we present a grounded model that clearly explains which hybrid harvesting strategies can be implemented to overcome resource constraints, exploiting their hybrid potential. Our work contributes to knowledge about resource constraints in the social entrepreneurship literature and extends social bricolage theory. Limitations and future research approaches are also presented. (shrink)

As of Volume 9 (1994/95) John Benjamins Publishing Company is the official publisher of the Belgian Journal of Linguistics, the annual publication of the Linguistic Society of Belgium. Each volume is topical and includes selected papers from the international meetings organised by the LSB.

Sometimes logical support for a conclusion is provided exclusively by premises which are independently relevant to that conclusion. At other times, support is provided exclusively by independently irrelevant premises. On still other occasions, relevant and irrelevant premises may collectively offer a distinctive pattern of support. This paper provides a rigorous account of some of these differences in terms of a tripartite classification of convergent, linked and hybrid arguments. These various arguments are defined, diagrammed, and some of their logical properties are (...) explored. (shrink)

ABSTRACT In 1929 and 1934–1935, the physical anthropologist Harry L. Shapiro voyaged in the South Seas on the Mahina-I-Te-Pua and the Zaca, measuring mixed-race islanders, including the descendants of the Bounty mutineers on Pitcairn Island. His research in Polynesian hybridity reflects the growing cultural and scientific investment of the United States in the Pacific during this period. Shapiro's oceanic adventures and intimate encounters prompted him to discount typological speculation and emphasize instead the liberal Boasian program in physical anthropology, giving him (...) the confidence to refigure his evaluations of racial difference. The seaborne investigatory enterprise came to influence U.S. racial thought, adding impetus to the condemnation of racism in science. On his return from the South Seas, Shapiro tried to get his fellow physical anthropologists to issue a manifesto opposing the harnessing of their science to racial discrimination and prejudice. (shrink)

Prompted by recent recognitions of the omnipresence of horizontal gene transfer among microbial species and the associated emphasis on exchange, rather than isolation, as the driving force of evolution, this essay will reflect on hybridization as one of the central concerns of nineteenth-century biology. I will argue that an emphasis on horizontal exchange was already endorsed by ‘biology’ when it came into being around 1800 and was brought to full fruition with the emergence of genetics in 1900. The true (...) revolution in nineteenth-century life sciences, I maintain, consisted in a fundamental shift in ontology, which eroded the boundaries between individual and species, and allowed biologists to move up and down the scale of organic complexity. Life became a property extending both ‘downwards’, to the parts that organisms were composed of, as well as ‘upwards’, to the collective entities constituted by the relations of exchange and interaction that organisms engage in to reproduce. This mode of thinking was crystallized by Gregor Mendel and consolidated in the late nineteenth-century conjunction of biochemistry, microbiology and breeding in agro-industrial settings. This conjunction and its implications are especially exemplified by Wilhelm Johannsen’s and Martinus Beijerinck’s work on pure lines and cultures. An understanding of the subsequent constraints imposed by the evolutionary synthesis of the twentieth century on models of genetic systems may require us to rethink the history of biology and displace Darwin’s theory of natural selection from that history’s centre. (shrink)

This paper presents a theory of reasoning with evidence in order to determine the facts in a criminal case. The focus is on the process of proof, in which the facts of the case are determined, rather than on related legal issues, such as the admissibility of evidence. In the literature, two approaches to reasoning with evidence can be distinguished, one argument-based and one story-based. In an argument-based approach to reasoning with evidence, the reasons for and against the occurrence of (...) an event, e.g., based on witness testimony, are central. In a story-based approach, evidence is evaluated and interpreted from the perspective of the factual stories as they may have occurred in a case, e.g., as they are defended by the prosecution. In this paper, we argue that both arguments and narratives are relevant and useful in the reasoning with and interpretation of evidence. Therefore, a hybrid approach is proposed and formally developed, doing justice to both the argument-based and the narrative-based perspective. By the formalization of the theory and the associated graphical representations, our proposal is the basis for the design of software developed as a tool to make sense of the evidence in complex cases. (shrink)

In this paper we discuss two hybrid languages, ℒ and ℒ, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using A and ↓ to bind special state variables.This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the modal idea (...) of canonical models with the classical idea of witnessed maximal consistent sets. The languages ℒ and ℒ provide us with two extreme examples of the issues involved. In the case of ℒ, we can combine these ideas relatively straightforwardly with the aid of analogs of the Barcan axioms coupled with a modal theory of labeling. In the case of ℒ, on the other hand, although we can still formulate a theory of labeling, the Barcan analogs are not valid. We show how to overcome this difficulty by using COV*, an infinite collection of additional rules of proof which has been used in a number of investigations of extended modal logic. (shrink)

Psychologists of concepts’ traditional assumption that there are many properties common to all concepts has been subject to devastating critiques in psychology and in the philosophy of psychology. However, it is currently unclear what approach to concepts is best suited to replace this traditional assumption. In this article, we compare two competing approaches, the Heterogeneity Hypothesis and the hybrid theories of concepts, and we present an empirical argument that tentatively supports the former over the latter.

‘Hybrid’ theories of personal good, defended by e.g. Parfit, Wolf, and Kagan, equate it, not with a subjective state such as pleasure on its own, nor with an objective state such as knowledge on its own, but with a whole that supposedly combines the two. These theories apply Moore's principle of organic unities, which says the value of a whole needn't equal the sum of the values its parts would have by themselves. This allows them, defenders say, to combine the (...) attractions of purely subjective and purely objective views. This common understanding of the theories is, however, mistaken. At the most fundamental level they don't combine a subjective and an objective element but two objective ones. Once this is understood, their attraction as hybrid theories diminishes: the value in their wholes may be just the sum of the values in their parts. (shrink)

Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I (...) show soundness and completeness for both deductions and refutations. (shrink)

A provoking new approach to how we understand metaphors thoroughly comparing and contrasting the claims made by relevance theorists and cognitive linguists. The resulting hybrid theory shows the complementarity of many positions as well as the need and possibility of achieving a broader and more realistic theory of our understanding.

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, (...) numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas. (shrink)

In this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of modal logic in which it is possible to name worlds and evaluate expressions with respect to particular worlds. We motivate this combination of (...) ideas in the introduction, and devote the rest of the article to defining, axiomatising, and proving a completeness result for $\mathcal {HPTT}$. (shrink)

This study addresses the problem of Arrovian preference aggregation. Social rationality plays a crucial role in the standard Arrovian framework. However, no assumptions on social rationality are imposed here. Social preferences are allowed to be any binary relation (possibly incomplete and intransitive). We introduce the axiom of hybrid invariance, which requires that if social preferences under two preference profiles make the same judgment, then a social preference under a “hybrid” of the two profiles must extend the original judgment in a (...) certain way. Then, we characterize the structure of decisive coalitions under hybrid invariance. (shrink)

This is an extended version of the lectures given during the 12-thConference on Applications of Logic in Philosophy and in the Foundationsof Mathematics in Szklarska Poręba. It contains a surveyof modal hybrid logic, one of the branches of contemporary modal logic. Inthe first part a variety of hybrid languages and logics is presented with adiscussion of expressivity matters. The second part is devoted to thoroughexposition of proof methods for hybrid logics. The main point is to showthat application of hybrid logics (...) may remarkably improve the situation inmodal proof theory. (shrink)