이 논문은 화이트헤드의 수학적 배경을 통해 인식론의 전개 과정을 살펴보는 것이다. 그의 철학을 유기체 철학 혹은 과정철학이라고 부를 때, 그것은 근대의 헤겔 철학을 연상시키는 경우가 종종 있다. 그러나 화이트헤드의 유기체 철학은 비계량 기하학에 해당하는 사영 기하학 및 위상학을 통해 자신의 인식론을 전개하고 있다. 이와는 달리 데카르트와 뉴턴을 통해 인식론을 전개한 흄의 인식론은 계량 기하학을 초석으로 삼은 점과 대조를 이룬다. 근대 과학의 추상성은 일상과 과학을 분리하는 방향으로 나갔음을 흄의 인식론은 통해 명확히 밝혀진다. 흄의 인식론적 회의는 계량 기하학의 한계를 보여준다. 그 대안으로 (...) 우리는 화이헤드의 인식론을 제시하였다. 화이트헤드는 자신의 인식론의 전제가 되는 사영 기하학과 위상학을 통해 일상 경험과 과학을 화해시키려는 노력을 전개하였다. 화이트헤드는 자신의 감각 경험을 보여주는 의미관련이론과 시공간이론을 제시하는 연장적 결합을 통해 일상과 과학에 대한 이분법적 구도를 극복하고 인과성의 정당성을 확보한다. 이 글에서는 그런 매개적 지점을 찾는데 초점을 두었음을 밝힌다. (shrink)

We analyze model-theoretic connected components in extensions of a given group by abelian groups which are defined by means of 2-cocycles with finite image. We characterize, in terms of these 2-cocycles, when the smallest type-definable subgroup of the corresponding extension differs from the smallest invariant subgroup. In some situations, we also describe the quotient of these two connected components. Using our general results about extensions of groups together with Matsumoto–Moore theory or various quasi-characters considered in bounded cohomology, we obtain new (...) classes of examples of groups whose smallest type-definable subgroup of bounded index differs from the smallest invariant subgroup of bounded index. This includes the first known example of a group with this property found by Conversano and Pillay, namely the universal cover of [Formula: see text], as well as various examples of different nature, e.g. some central extensions of free groups or of fundamental groups of closed orientable surfaces. As a corollary, we get that both non-abelian free groups and fundamental groups of closed orientable surfaces of genus [Formula: see text], expanded by predicates for all subsets, have this property, too. We also obtain a variant of the example of Conversano and Pillay for [Formula: see text] instead of [Formula: see text], which was not accessible by the previously known methods. (shrink)

If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would still (...) expect it to follow that a sum of connected self-connected individuals is self-connected too. In this paper, we present some surprising countermodels which show that this conjecture is incorrect. (shrink)

In this chapter I provide an elementary exposition of the development of Whitehead's view of objectivity and his theory of extension, with particular focus on explaining how macroscopic objects of ordinary perception and the whole structure of space-time arise out of the units of his ontology, namely, the actual occasions. I also review the scholarship on Whitehead's view of extension and discuss the major problems that arise in connection with the theory in his magnum opus, Process and Reality.

To explore the motivations underpinning corporate social responsibility (CSR) decisions in China, a country characterized by extensive government intervention, this paper investigates whether building a good relationship with the government is a political incentive that is driving firms to conduct CSR by examining the effects of political connections on the latter. Our results indicate that politically connected firms exhibit better CSR. However, the effect is considerably more significant for firms with existing political relationships. Additionally, findings show that the effect (...) is more prominent in firms for which political connections are more valuable, namely, non‐state‐owned enterprises, small firms, and firms operating in less market‐oriented cities, indicating that CSR can serve as a differentiation strategy to compete against other bidders. Dividing CSR activities into economic, environmental and social aspects, we find that the social‐based activities are more likely to be driven by political motivations. By categorizing CSR and political connections, this paper not only expands the scope of political CSR and renders the generated results that have been mixed together more distinguishable, but also provides a more precise understanding of the fundamental drivers of CSR in China from the perspective of resource exchange. (shrink)

Let S be a set, P the class of all subsets of S and F the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P into a fuzzy closure operator J* defined in F. This enables us to give the notion of canonical extension of a deduction system and to (...) give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. (shrink)

This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation (...) or weak pseudocomplementation. These classes are shown to be canonical and dual relational structures are given in a generalized Kripke-style. The fact that the negation is dually self-adjoint plays an important role here, as it implies that it sends arbitrary joins to meets and that will allow us to define the dual structures in a uniform way. (shrink)

The proofs of some results of abstract algebraic logic, in particular of the transfer principle of Czelakowski, assume the existence of so-called natural extensions of a logic by a set of new variables. Various constructions of natural extensions, claimed to be equivalent, may be found in the literature. In particular, these include a syntactic construction due to Shoesmith and Smiley and a related construction due to Łoś and Suszko. However, it was recently observed by Cintula and Noguera that both of (...) these constructions fail in the sense that they do not necessarily yield a logic. Here we show that whenever the Łoś–Suszko construction yields a logic, so does the Shoesmith–Smiley construction, but not vice versa. We also describe the smallest and the largest conservative extension of a logic by a set of new variables and show that contrary to some previous claims in the literature, a logic of cardinality \ may have more than one conservative extension of cardinality \ by a set of new variables. In this connection we then correct a mistake in the formulation of a theorem of Dellunde and Jansana. (shrink)

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

In this paper we extend Wittgenstein’s notion of family resemblance to translation, interpretation, and comparison across traditions. There is no need for universals. This holds for everyday concepts such as green and qing 青, philosophical concepts such as emotion and qing 情, as well as philosophical categories such as form of life and dao 道. These notions as well as all other concepts from whatever tradition are family resemblance concepts. We introduce the notion of quasi-universal, which connects family resemblance concepts (...) from a limited number of traditions. The possibility and necessity of extending family resemblance concepts across traditions dissolves the false antinomy of universalism versus relativism. (shrink)

This article introduces and motivates the notion of a “properly extensive” quantity by means of a puzzle about the reliability of certain canonical length measurements. An account of these measurements’ success, I argue, requires a modally robust connection between quantitative structure and mereology that is not mediated by the dynamics and is stronger than the constraints imposed by “mere additivity.” I outline what it means to say that length is not just extensive but properly so and then (...) briefly sketch an application of proper extensiveness to the project of providing a reductive ground for metric quantitative structure. (shrink)

Accounts of causal explanation are standard in philosophy of science. Less common are accounts of experimentation to investigate causal relations: detailed discussions of the specific kinds of experiments scientists design and run. Silva, Landreth, and Bickle’s account of “connection experiments” derives directly from landmark experiments in “molecular and cellular cognition.” We start with its key components, and then using a detailed case study from recent social neuroscience we emphasize and extend three features of SLB’s account: a division of distinct (...) types of connection experiments, each providing a different type of evidence for a hypothesized causal relationship; the typically downward-looking nature of the experimental search for mediating causes in mainstream neurobiology; and most importantly, the centrality of multiple-experiment research programs, with each experiment designed such that if successful its results can be integrated with the others, toward the goal of confirming multiple-phenomena causal pathways. Our extension of SLB’s account complements existing philosophical work on experimentation in neurobiology. (shrink)

This paper investigates a limitation of the model of belief and knowledge prevailing in mainstream economics, namely the state-space model. Because of its set-theoretic nature, this model has difficulties in capturing the difference between expressions that designate the same object but have different meanings, i.e., expressions with the same extension but different intensions. This limitation generates puzzling results concerning what individuals believe or know about the world as well as what individuals believe or know about what other individuals believe or (...) know about the world. The paper connects these puzzling results to two issues that are relevant for economic theory beyond the state-space model, namely, framing effects and the distinction between the model-maker and agents that appear in the model. Finally, the paper discusses three possible solutions to the limitations of the state-space model, and concludes that the two alternatives that appear practicable also have significant drawbacks. (shrink)

The present paper studies two approaches to the expressiveness of propositional modal logics based on first-degree entailment logic, FDE. We first consider the basic FDE-based modal logic BK and certain systems in its vicinity, and then turn to some FDE-based modal logics in a richer vocabulary, including modal bilattice logic, MBL. On the one hand, model-theoretic proofs of the definability of connectives along the lines of [McCullough, “Logical connectives for intuitionistic propositional logic”, Journal of Symbolic Logic 36, 1 (1971): 15–20. (...) DOI: 10.2307/2271511] and [[17] Wansing, “Logical connectives for constructive modal logic”, Synthese 150, 3 (2006): 459–482. DOI: 10.1007/s11229-005-5518-5] are given for various FDE-based modal logics. On the other hand, building on [Odintsov and Wansing, “Disentangling FDE-based paraconsistent modal logics, Studia Logica 105, 6 (2017): 1221–1254. DOI: 10.1007/s11225-017-9753-9], expressibility is considered in terms of mutual faithful embeddability of one logic into another logic. A distinction is drawn between definitional equivalence, which is defined with respect to a pair of structural translations between two languages, and weak definitional equivalence, which is defined with respect to a weaker notion of translations. Moreover, the definitional equivalence of some FDE-based modal logics is proven, especially the definitional equivalence of MBL and a conservative extension of the logic BK□×BK□, which underlines the central role played by BK among FDE-based modal logics. (shrink)

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that (...) extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice. (shrink)

In the following pages I examine Schopenhauer’s contribution to the debate about the extension of the moral community, concretely, to the basis principles of the animal ethics. In the first section, I describe the role of the compassion in the ethics, as propounds Schopenhauer. In the second, I focuse on the correlation ‘suffering - intellectual capacity’ as criterion to feel compassion, and I emphazise the limits of the empathy in Schopenhauer’s philosophy too. In the third section, I examine the value (...) of the compasión in connection with the denial of the will and with the pessimistic point of wiew. Finally, I stress the aspects that I consider the most important oder debatable of Schopenhauer’s position. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better (...) understanding of what are the common properties of any two constructors, say disjunction and conjunction. (shrink)

The results established in this paper are in connection with the Relative Internal Set Theory (R.I.S.T.). The main result is the general principle of choice: Let α be a level and let Φ(x, y) be anαexternalαbounded formula of the language of R.I.S.T.. Suppose that to each elementx, dominated by α, corresponds an elementy x such that Φ(x, y x ) holds, then there exists a function of choice ψ such that, which is a very general principle of choice, for (...) everyx dominated by α, Φ(x, ψ(x)) holds. More than that, we establish that if all the elementsy x are uniformly dominated by a level β then we can prescribe that the function of choice is also dominated by β. (shrink)

In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations (...) of the logic and propose a comparison with certain other modal systems. In particular, we prove that $\textbf{m}\textbf{D}_{\textbf{2}}$ is neither normal nor regular. On the basis of the axiomatization of $\textbf{D}_{\textbf{2}}$, we give an axiomatization of $\textbf{m}\textbf{D}_{\textbf{2}}$. We also give another axiomatization which is not based on the axiomatization of $\textbf{D}_{\textbf{2}}$. Furthermore, we give a natural Kripke-style semantics for $\textbf{m}\textbf{D}_{\textbf{2}}$ and prove the respective adequacy theorems. (shrink)

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...) it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

This volume contains papers presented at the second international workshop on extensions of logic programming, which was held at the Swedish Institute of Computer Science, Stockhom, January 27-29, 1991. The 12 papers describe and discuss several approaches to extensions of logic programming languages such as PROLOG, as well as connections between logic programming and functional programming, theoretical foundations of extensions, applications, and programming methodologies. The first workshop in this series was held in T}bingen in 1989 and its proceedings areavailable as (...) LNCS 475. The third workshop will be held in Bologna in 1992. (shrink)

We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B V, thenA×B is a homomorphic image of some well-connected algebra ofV.We prove:• each varietyV of Nelson algebras with PQWC lies in the fibre –1(W) for some varietyW of Heyting algebras having PQWC, • for any varietyW of Heyting algebras with PQWC the least and the (...) greatest varieties in –1(W) have PQWC, • there exist varietiesW of Heyting algebras having PQWC such that –1(W) contains infinitely many varieties (of Nelson algebras) with PQWC. (shrink)

Originating from work in operations research the cutting plane refutation systemCP is an extension of resolution, where unsatisfiable propositional logic formulas in conjunctive normal form are recognized by showing the non-existence of boolean solutions to associated families of linear inequalities. Polynomial sizeCP proofs are given for the undirecteds-t connectivity principle. The subsystemsCP q ofCP, forq≥2, are shown to be polynomially equivalent toCP, thus answering problem 19 from the list of open problems of [8]. We present a normal form theorem forCP (...) 2-proofs and thereby for arbitraryCP-proofs. As a corollary, we show that the coefficients and constant terms in arbitrary cutting plane proofs may be exponentially bounded by the number of steps in the proof, at the cost of an at most polynomial increase in the number of steps in the proof. The extensionCPLE +, introduced in [9] and there shown top-simulate Frege systems, is proved to be polynomially equivalent to Frege systems. Lastly, since linear inequalities are related to threshold gates, we introduce a new threshold logic and prove a completeness theorem. (shrink)

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental recognition (...) of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

Engineering programs in the United States have been experimenting with diverse pedagogical approaches to educate future professional engineers. However, a crucial dimension of ethics education that focuses on the values, personal commitments, and meaning of engineers has been missing in many of these pedagogical approaches. We argue that a value-based approach to professional ethics education is critically needed in engineering education, because such an approach is indispensable for cultivating self-reflective and socially engaged engineers. This paper starts by briefly comparing two (...) prevalent approaches to ethics education in science and engineering: professional and philosophical. While we acknowledge that both approaches help meet certain ethics education objectives, we also argue that neither of these is sufficient to personally engage students in authentic moral learning. We make the case that it is important to connect ethics education to the heart, which is extensively driven by values, and present a value-based approach to professional ethics education. We provide some classroom practices that cultivate a safe, diverse, and engaging learning environment. Finally, we discuss the implications of a value-based approach to professional ethics education for curriculum design and pedagogical practice, including opportunities and challenges for engineering faculty eager to incorporate value-based inquiry into their classrooms. (shrink)

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalisation of the theory of canonical extension to the setting of first order logic. We define a notion of canonical extension for coherent categories. These are the categorical analogues of distributive lattices and they provide categorical semantics for coherent logic, the fragment of first order logic in the connectives ∧, ∨, 0, 1 and ∃. We describe a universal property (...) of our construction and show that it generalises the existing notion of canonical extension for distributive lattices. Our new construction for coherent categories has led us to an alternative description of the topos of types, introduced by Makkai in [22]. This allows us to give new and transparent proofs of some properties of the action of the topos of types construction on morphisms. Furthermore, we prove a new result relating, for a coherent category C, its topos of types to its category of models. (shrink)

The language of standard propositional modal logic has one operator (? or ?), that can be thought of as being determined by the quantifiers ? or ?, respectively: for example, a formula of the form ?F is true at a point s just in case all the immediate successors of s verify F.This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and (...) generalized quantifiers: the combined generalized quantifier conditions of conservativity and extension correspond to the modal condition of invariance under generated submodels, and the modal condition of invariance under bisimulations corresponds to the generalized quantifier being a Boolean combination of ? and ? (shrink)

Transfer RNAs (tRNAs) represent the most abundant class of RNA molecules in the cell and are key players during protein synthesis and cellular homeostasis. Aberrations in the extensive tRNA biogenesis pathways lead to severe neurological disorders in humans. Mutations in the tRNA splicing endonuclease (TSEN) and its associated RNA kinase cleavage factor polyribonucleotide kinase subunit 1 (CLP1) cause pontocerebellar hypoplasia (PCH), a heterogeneous group of neurodegenerative disorders, that manifest as underdevelopment of specific brain regions typically accompanied by microcephaly, profound (...) motor impairments, and child mortality. Recently, we demonstrated that mutations leading to specific PCH subtypes destabilize TSEN in vitro and cause imbalances of immature to mature tRNA ratios in patient‐derived cells. However, how tRNA processing defects translate to disease on a systems level has not been understood. Recent findings suggested that other cellular processes may be affected by mutations in TSEN/CLP1 and obscure the molecular mechanisms of PCH emergence. Here, we review PCH disease models linked to the TSEN/CLP1 machinery and discuss future directions to study neuropathogenesis. (shrink)

The main motivation of this paper is the study of first-order model theoretic properties of structures having their roots in modal logic. We will focus on the connections between ultrafilter extensions and ultrapowers. We show that certain structures (called bounded graphs) are elementary substructures of their ultrafilter extensions, moreover their modal logics coincide.

Of all the cases made against classical logic, Michael Dummett's is the most deeply considered. Issuing from a systematic and original conception of the discipline, it constitutes one of the most distinctive achievements of twentieth century British philosophy. Although Dummett builds on the work of Brouwer and Heyting, he provides the case against classical logic with a new, explicit and general foundation in the philosophy of language. Dummett's central arguments, widely celebrated if not widely endorsed, concern the implications of the (...) relation between meaning and use for both the inference rules that govern logical connectives and the relation between truth and its recognition. It is less often noted that Dummett has a further argument against classical logic, one based on the semantic and set-theoretic paradoxes. That is the topic of this paper. (shrink)

We prove an Omitting Types Theorem for certain algebraizable extensions of first order logic without equality studied in [SAI 00] and [SAY 04]. This is done by proving a representation theorem preserving given countable sets of infinite meets for certain reducts of ?- dimensional polyadic algebras, the so-called G polyadic algebras (Theorem 5). Here G is a special subsemigroup of (?, ? o) that specifies the signature of the algebras in question. We state and prove an independence result connecting our (...) representation theorem to Martin's axiom (Theorem 6). Also we show that the countable atomic G polyadic algebras are completely representable (Corollary 16) contrasting results on cylindric algebras. Several related results are surveyed. (shrink)

In 1963 Duchamp described his vertical installation of three Readymades at the Pasadena Art Museum as “readymade talk of what goes on in the Large Glass.” Elsewhere, he spoke of the Readymades as “vehicles for unloading ideas,” and during the years 1912-15 his mind was filled with ideas as he invented the “playful physics” for his techno-scientific allegory of quest, The Bride Stripped Bare by Her Bachelors, Even [The Large Glass]. This essay argues that the “ideas” being unloaded in the (...) Readymades were rooted in his extensive study of contemporary science and technology as well as the biographical experience of his stay at Herne Bay on the English seacoast during August 1913. Readymades addressed include the Bicycle Wheel, With Hidden Noise, Paris Air, and Fresh Widow. Central themes include string or thread, traced from his preoccupation with tennis during his holiday, and the impact of the electrical spectacle of the illuminated Pier Pavilion at Herne Bay. (shrink)

This chapter presents Connecting Scotland as a case study, highlighting the correlation between current research into digital inequality to identify those most in need of support, and the practical application of work to address this at scale through third sector organisations working directly with those at greatest risk of digital exclusion. The chapter also considers the vital role of the ‘trusted intermediary’ acting as digital champion for device recipients, and, using the data gathered via sessions with hundreds of frontline staff, (...) explore immediate challenges and opportunities for engagement. It will also reflect on the application of research in the creation of training and resources to support the programme. Finally, the chapter will reflect on some of the many lessons learned, and consider implications for both policy-makers and fieldworkers seeking to address digital inequality at scale. All three authors were involved extensively in the development and delivery of this work. (shrink)

IntroductionIncivility is defined as an interpersonal misconduct involving disregard for others and a violation of norms of respect . This phenomenon has been extensively investigated in workplaces . However, only a few studies have focused their attention on the academic setting, investigating both student and faculty general incivilities .While previous studies’ theoretical framework was mainly informed by organizational and psychosocial theories , this study suggests viewing incivility through the lens of justice psychology, which examines individual justice concerns . According to (...) this theory, in order to understand psychological processes, individual experiences should be considered alongside objective environmental conditions . Drawing on justice psychology, the way students in .. (shrink)

Extensive research has demonstrated that rs1360780, a common single nucleotide polymorphism within the FKBP5 gene, interacts with early-life stress in predicting psychopathology. Previous results suggest that carriers of the TT genotype of rs1360780 who were exposed to child abuse show differences in structure and functional activation of emotion-processing brain areas belonging to the salience network. Extending these findings on intermediate phenotypes of psychopathology, we examined if the interaction between rs1360780 and child abuse predicts resting-state functional connectivity (rsFC) between the (...) amygdala and other areas of the salience network. We analyzed data of young European adults from the general population (N = 774; mean age = 18.76 years) who took part in the IMAGEN study. In the absence of main effects of genotype and abuse, a significant interaction effect was observed for rsFC between the right centromedial amygdala and right posterior insula (p <.025, FWE-corrected), which was driven by stronger rsFC in TT allele carriers with a history of abuse. Our results suggest that the TT genotype of rs1360780 may render individuals with a history of abuse more vulnerable to functional changes in communication between brain areas processing emotions and bodily sensations, which could underlie or increase the risk for psychopathology. (shrink)

Drawing on 49 oral-history interviews with Scottish family business owner-managers, six key-informant interviews, and secondary sources, this interdisciplinary study analyses the decline of kinship-based connections and the emergence of new kinds of elite networks around the 1980s. As the socioeconomic context changed rapidly during this time, cooperation built primarily around literal family ties could not survive unaltered. Instead of finding unity through bio-legal family connections, elite networks now came to redefine their ‘family businesses’ in terms of affectively loaded ‘family values’ (...) such as loyalty, care, commitment, and even ‘love’. Consciously nurturing ‘as-if-family’ emotional and ethical connections arose as a psychologically effective way to bring together network members who did not necessarily share pre-existing connections of bio-legal kinship. The social-psychological processes involved in this extension of the ‘family’ can be understood using theories of the moral sentiments first developed in the Scottish Enlightenment. These theories suggest that, when the context is amenable, family-like emotional bonds can be extended via sympathy to those to whom one is not literally related. As a result of this ‘progress of sentiments’, one now earns his/her place in a Scottish family business, not by inheriting or marrying into it, but by performing family-like behaviours motivated by shared ethics and affects. (shrink)

This article examines Wilfrid Sellars's views on the epistemic status of philosophical propositions. It suggests that according to Sellars philosophical propositions are normative and practically oriented. They do not form a theory for the description of reality; their function is, rather, that of motivating actions which aim at changing reality. The article argues that the role of philosophical propositions can be illuminated if they are understood as a special kind of (proposed) “material” rules of inference, provided that the latter are (...) construed as being firmly entrenched in practice. To this end, a distinction between “theoretical” and “practical” anomalies is drawn to better elucidate—and in some cases criticize and further expand—Sellars's position on the relation between the theoretical and practical dimensions of philosophical activity. In this connection, the Weberian notion of the “disenchantment of the world” is used to throw light on the relation between these two dimensions. (shrink)

Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but also on what we (...) call Gentzen-regular connectives. For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations. (shrink)

In the years spanning the first half of the 20th century Bertrand Russell wavered between two incompatible accounts of physical reality. On one account, physical objects were taken to be logical constructs of phenomenal entities, the immediate data of sense experience. Such a view roughly fits the familiar characterization of being a combination of “Hume plus mathematical logic.” This type of phenomenalism, in the empiricist tradition, contrasted starkly with a variant of scientific realism, including a realistic account of causal connections (...) as relations between universals, that Russell developed between 1912 and 1927, and which was derived from Kant’s distinction between a noumenal and a phenomenal world. My concern in this paper is with the viability of the unique form of scientific realism Russell developed, the role of universals and causal explanation in it, and criticisms that have been directed at it. I will argue that an early refutation of Russell’s realism by the mathematician M. Newman and a recent revival of that refutation by W. Demopoulos and M. Friedman ignore the critical role universals play in Russell’s scientific realism and hence fail to refute his view. I will also briefly consider a recent “anti-realist” argument that repeats Newman’s mistake: interpreting predicates in terms of extensions and not as referring to universal properties and relations. (shrink)

We show that the lattices of the normal extensions of four well-known logics—propositional intuitionistic logic \, Grzegorczyk logic \, modalized Heyting calculus \ and \—can be joined in a commutative diagram. One connection of this diagram is an isomorphism between the lattices of the normal extensions of \ and \; we show some preservation properties of this isomorphism. Two other connections are join semilattice epimorphims of the lattice of the normal extensions of \ onto that of \ and of (...) the lattice of the normal extensions of \ onto that of \. The link between \ and \ is a well-known isomorphism established by the Blok–Esakia theorem. (shrink)

We prove that for a finitely generated infinite nilpotent group $G$ with structure $(G,\cdot,\dots)$, the connected component ${G^*}^0$ of a sufficiently saturated extension $G^*$ of $G$ exists and equals \[ \bigcap_{n\in\N} \{g^n\colon g\in G^*\}. \] We construct an expansion of ${\mathbb Z}$ by a predicate $({\mathbb Z},+,P)$ such that the type-connected component ${{\mathbb Z}^*}^{00}_{\emptyset}$ is strictly smaller than ${{\mathbb Z}^*}^0$. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for (...) the van der Waerden theorem for finite partitions of groups. (shrink)

_This paper will explore two strands of Vilhjálmur Árnason’s extensive body of work: his analysis of dialogue ethics within medical ethics and his analysis of ethics in the Icelandic sagas. The central thesis is that combining these two strands, bioethics and literary analysis, can provide valuable insights to further the discussion of ethics among citizens in multicultural communities. _ _Vilhjálmur’s 1 analysis of the Icelandic sagas shows that the sagas have a specific value foundation, specific virtues as well as (...) narrative in how to present the ethical aspects. In the field of bioethics, he has developed the study of dialogue ethics in several aspects, such as between patient and professional, in interdisciplinary research, and in public deliberation. By integrating insights from historic literary studies with contemporary bioethical research we gain an interesting platform for a discussion on Western assumptions of what constitutes a good dialogue. One of the core aspects in dialogue ethics is how to develop the procedure for a fair, open-minded, and oppression-free discussion in ethical issues. Vilhjálmur’s contributions are summarized here, but could they also be extended beyond the Icelandic and Western horizon?_ _I will compare his ethical framework to a recent parallel discussion on the claims of indigenous peoples for a fair dialogue. That is, a dialogue that must be inclusive with a carefulness about deciding the foundation of inherent values and the procedure of how to perform the dialogue. Finally, I draw conclusions on what dialogue ethics will gain from this explorative work._ _Keywords: _dialogue ethics, one health approaches, Indigenous peoples, bioethics, interdisciplinarity, ethics in the Icelandic sagas, medical ethics, literary analysis, multicultural communities. (shrink)

The work is concerned with the so called display property of display logic. The motivation behind it is discussed and challenged. It is shown using one display calculus for intuitionistic logic as an example that the display property can be abandoned without losing subformula, cut elimination and completeness properties in such a way that results in additional expressive power of the system. This is done by disentangling structural connectives so that they are no longer context-sensitive. A recipe for characterizing structural (...) extensions of display calculi is provided. (shrink)

Automated theorem proving amounts to solving search problems in usually tremendous search spaces. A lot of research therefore focuses on search space reductions. Our approach reduces the search space which arises when using so-called connection tableau calculi for first-order automated theorem proving. It uses disjunctive constraints over first-order equations to compress certain parts of this search space. We present the basics of our constrained-connection-tableau calculi, a constraint extension of connection tableau calculi, and deal with the efficient handling (...) of constraints during the search process. The new techniques are integrated into the automated connection tableau prover Setheo. (shrink)

The most favourable explanation pertaining to the Yoruba origin is that of the Oduduwa tradition according to which he is the original ancestor of the Yoruba people. Although the Yorubas have reached a settlement on Oduduwa as their ancestor, they disagree on the origin of Oduduwa. Whilst some associated his origin with Mecca or Arabia, others say Egypt or Israel. Samuel Johnson, the most prominent writer of the Yoruba history, discussed various theories that pertained to the origin of Oduduwa. He (...) argued that Oduduwa or the original ancestors of the Yoruba people were Coptic Christians. Writers of Yoruba history from the 20th and 21st centuries had continued to build upon Johnson’s view of the Yoruba origin in connection with Oduduwa. This research is a study of the Yoruba and Johnson’s perspectives of Oduduwa in connection with the Yoruba origins. The research elucidates the circumstances of Johnson’s Christianisation of the Egyptian origin of the Yoruba.Contribution: This article shall contribute to a distinct understanding of the origin of the Yoruba in connection with the identity and the personality of Oduduwa. Students of history and cultural studies will find this research of utmost benefit because it explains the origin of the Yoruba from the perspective of Samuel Johnson, the first Yoruba man to document extensively on the Yoruba history, language, its culture and its people in a single document or collection. (shrink)

It was meaningful to predict the customers' decision-making behavior in the field of market. However, due to individual differences and complex, non-linear natures of the electroencephalogram signals, it was hard to classify the EEG signals and to predict customers' decisions by using traditional classification methods. To solve the aforementioned problems, a recurrent t-distributed stochastic neighbor embedding neural network was proposed in current study to classify the EEG signals in the designed brand extension paradigm and to predict the participants' decisions. The (...) recurrent t-SNE neural network contained two steps. In the first step, t-SNE algorithm was performed to extract features from EEG signals. Second, a recurrent neural network with long short-term memory layer, fully connected layer, and SoftMax layer was established to train the features, classify the EEG signals, as well as predict the cognitive performance. The proposed network could give a good prediction with accuracy around 87%. Its superior in prediction accuracy as compared to a recurrent principal component analysis network, a recurrent independent component correlation algorithm [independent component analysis ] network, a t-SNE support vector machine network, a t-SNE back propagation neural network, a deep LSTM neural network, and a convolutional neural network were also demonstrated. Moreover, the performance of the proposed network with different activated channels were also investigated and compared. The results showed that the proposed network could make a relatively good prediction with only 16 channels. The proposed network would become a potentially useful tool to help a company in making marketing decisions and to help uncover the neural mechanisms behind individuals' decision-making behavior with low cost and high efficiency. (shrink)

Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.