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)

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)

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)

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)

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.

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)

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)

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.

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)

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)

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 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)

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)

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.

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)

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)

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)

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)

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)

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)

Some scholars working on the ethics of paternalism are interested in whether there is a systematic normative connection between hard paternalism and people’s moral rights. One affirmative view is that hard paternalism is pro tanto wrong inasmuch as it always involves a rights infringement. Daniel Groll defends this view on the grounds that hard paternalism always infringes a competent adult’s right to be the only one to act only for his own good. I call this right the right to (...) self-beneficence. In this note, I argue that Groll misidentifies a right that competent adults have. Rather than the right to self-beneficence, I argue that if hard paternalism infringes any particular right, it is a right that a competent adult has against others “taking over” matters that fall within his sphere of legitimate agency or, by extension, the legitimate exercise of his agency. I call this right the right against legitimate agency interference. (shrink)

This thoughtful, learned, well-written, extensively illustrated, and heavily documented study deserves to be regarded as a landmark in art history. Traditional art history has dealt for the most part with the “fine arts” (chiefly painting, drawing, sculpture, and architecture), whereas other human creations that take physical form (such as furniture, ceramics, textiles, and metal and glass items), whether utilitarian or decorative (or both at once), are considered “craft” or “applied art” and are studied by folklorists, anthropologists, and archaeologists and often (...) displayed in different museums. Cooke wishes to break down this “hierarchical taxonomy,” this “fragmented, hierarchical field,” that emerged from Western Europe's “misunderstanding of art,” which valued “the cerebral over the manual.” His goal, in other words, is to outline “a more inclusive human history of art”— “a connected art history.” This phrase from his subtitle refers not simply to connecting “fine art” with “applied art” but also to crossing temporal and regional boundaries. Still another act of connecting is to examine all parts of an object's life history, and thus the three main divisions of the book deal with the making of objects, their circulation from one person and place to another (and “their ability to transmit ideas” in the process), and their meaning for the persons who possessed or encountered them.Over the years I have repeatedly said that all objects made by human beings are worthy of preservation and study because they bring us into direct contact with the past and, as part of our surroundings, affect our thoughts in the present. Every object, I have argued, including copies of a single printed edition of a book (so-called duplicates), is an independent witness to the past. I am particularly pleased, therefore, to welcome a major book that explores in detail, with a wealth of examples from many centuries and cultures, the place of objects in human history. Cooke's pursuit is “object-driven,” beginning with the nature of the materials and finally coming to “the inherent power of the object itself to influence human thought and action.” (Compare the subtitle of Sherry Turkle's 2007 anthology Evocative Objects: Things We Think With.) Cooke's refusal to separate “materials” from “people,” or “technologies” from “values,” reminds me of John Szarkowski's approach to photographs. In Photography until Now (1989), Szarkowski points out that histories of photography generally treat technical matters separately from artistic ones—a split between the “empirical” and the “intuitive” that he finds indefensible, for “these two ways of knowing meet in the process of making things.” He adds, “The meeting can be cordially symbiotic or aggressively competitive, but its resolution defines the character and meaning of the thing that is made.” This statement has been a favorite of mine as an elegant characterization of the nature of art, and it is one that Cooke would clearly agree with.Cooke does not discuss photography, but he makes clear that he is not attempting a “comprehensive history that charts the complete ebb and flow of objects over time.” Rather, his book is meant to be a “suggestive guide” to the “principles of material literacy,” a “kit of tools for future complex constructions of history.” Even so, I find some of the omissions puzzling. Why, for example, are glass objects not taken up, when he so thoroughly deals with other common materials? More serious, in my opinion, is the exclusion of the fine arts. (Of the 215 illustrations, five are of oil paintings and one is of a Japanese print, but they are present only as the sources for information drawn from their pictorial content; one Hogarth engraving is shown because its image was often reproduced on punch bowls; and there is a very brief passage on the “uneasy relationship” between sculpture and material culture, but no sculptures are illustrated or used as examples for discussion.) Presumably Cooke felt it was unnecessary for his book to encompass the fine arts after demonstrating that functional objects are just as sophisticated artistically and culturally as products of the fine arts are. Yet those products also belong to the universe of “entangled objects” (How could they not?), and it would have been illuminating to see them adduced among the examples Cooke cites. One could argue that by excluding them—and by referring to the makers of the objects he does discuss as “artisans” and “craftspeople”—he comes close to reinforcing the division he wishes to eliminate.Less easy to explain is Cooke's omission of books, for they have been one of the largest and most widely circulated classes of utilitarian objects. Most people never think about books as objects, treating them only as disposable receptacles for transmitting verbal texts in tangible form (which is why so many books are destroyed when their texts supposedly become available in another form). Such people do not realize that texts have connections with their physical embodiments. (For example, books, whether manuscript or printed, often contain clues revealing how their texts were affected by the production process; and readers’ attitudes toward texts can be influenced by their presentation.) Cooke, however, with his deep understanding of the way objects function and his impressive knowledge of the scholarship, cannot be one of these uninformed people. He would obviously be aware of the vast literature devoted to leather and cloth bookbindings and their decoration, as well as to the myriad styles of letters and the varieties of paper and parchment; he would also know how letterforms and binding designs reflect a complex interplay of social, political, and artistic forces. Bibliographers have long studied books as Cooke advocates studying other objects: “working from the inside out,” beginning with the evidence in books themselves for reconstructing the routines that were followed in their creation. And book historians are recognizing the necessity for an international approach like Cooke's, since many of the books circulating in one country originated in other countries. Books would have been a prolific additional source for illustrating Cooke's analyses.My admiration for Cooke's book is not altered by these few disappointments. Even without discussions of paintings, sculptures, and books, it is still exhilarating in its scope and depth. One hopes that art and material-culture historians will pay attention to it. But it ought to have a wider audience, for the daily lives of all of us would be enriched by a greater appreciation of the objects that make up a significant part of our environment. (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)

The late J. D. Bernal's lectures given to first-year students in physics at Birkbeck College, University of London, are presented here in their entirety, tracing the history of physics up to the end of the classical era at the end of 19th century, just before the discoveries of the subatom and relatively were made. In view of the prestige and profundity of the newer discoveries, Bernal felt that the classical era was being largely forgotten. In this book, he attributes a (...) greater relevance to the work of men from the distant past than is usually given. For instance, the idea of "atom" not only retains the language of the Greek, Democritus, who first postulated it, but there is also an absolutely unbroken connection between the atom of the Greek and that of the modern physicist. Bernal felt that the historical method would be a suitable introduction to the fundamental concepts of physics, and it is hoped that the readers of the book will be able to see something of the interplay between the theoretical and practical aspects of the subject. (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)

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)

In contrast to rigid conceptions of nonhuman animals, several philosophers have put forth ideas that suggest a more flexible and extended vision of other animals. In articulating the condition of humans in the world, philosophers have referenced ideas that necessarily bring other beings in common with humanity. Significantly, conceptions of movement and biological transformation have played a central role in these ruminations, thereby suggesting the importance of geographical variables in human/nonhuman relations. By drawing out the connections between these perspectives, this (...) paper outlines an ethics of extension. (shrink)

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)

A major and timely re-examination of key areas in the social and political thought of Hegel and Marx. The editors' extensive introduction surveys the development of the connection from the Young Hegelians through the main Marxist thinkers to contemporary debates. Leading scholars including Terrell Carver, Chris Arthur, and Gary Browning debate themes such as: the nature of the connection itself scientific method political economy the Hegelian basis to Marxs' "Doctoral Dissertation" human needs history and international relations.

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)

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)

In trying to characterize the relationship between psychology and neuroscience, the trend has been to argue that reductionism does not work without suggesting a suitable substitute. I offer explanatory extension as a good model for elucidating the complex relationship among disciplines which are obviously connected but which do not share pragmatic explanatory features. Explanatory extension rests on the idea that one field can "illuminate" issues that were incompletely treated in another. In this paper, I explain how this "illumination" would work (...) between psychology and neuroscience. (shrink)

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)

This article elucidates some connections and divergences between S.N. Eisenstadt’s work on multiple modernities and critical reflections on ‘African modernity’ presented by Africanist scholars. It argues that there is more cross-over between these discussions than is commonly thought when both are seen as parallel responses to the shortcomings of post-war modernization theory. Eisenstadt’s work can inform debates in African Studies concerning the effective power of tradition in postcolonial African societies, and on African interpretations of the ‘cultural programme’ of modernity. The (...) article also discusses some weaknesses in Eisenstadt’s theorizing which arise from an extension of the multiple modernities framework to African societies, namely, an underappreciation of the various modalities of colonial imperialism and racialization, as well as the institutional constraints placed on postcolonial societal elites. It claims that these can be offset via a dialogue with the work of scholars in African Studies. Moreover, it is argued that the paradigm of multiple modernities can more satisfactorily shed light on African trajectories of modernity via the retrieval of tenets of Eisenstadt’s ‘heterodox’ modernization theory and work on post-traditionality, outlined in the 1960s and the 1970s, which include specific reflections on African societies. (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)

We consider a number of statements involving restrictions and extensions of algebras, and derive connections with large cardinal axioms.

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)

Interpretations of Nietzsche as a virtue theorist have proliferated in recent years as commentators have sought to read him as a modern eudaimonistic philosopher while also attempting to show what makes his contribution to this tradition valuable and distinctive.1While some commentators still contend that interpreting Nietzsche as a eudaimonist is antithetical to his overtly-stated philosophical aims,2 over the last decade there has been a upsurge of support for such readings, especially from commentators who emphasise what they claim is the pervasive (...) influence of the Hellenistic tradition on his work. Keith Ansell-Pearson has argued that Epicurus was a key influence on Nietzsche’s middle period, for example; whereas Michael Ure has claimed that the Stoic thought of Seneca and Epictetus was also highly influential.3 Nevertheless, even those commentators who agree that Nietzsche can be informatively situated, or is even best situated, within the Hellenistic tradition cannot agree on two seemingly-intractable puzzles which any virtue-theoretical reading must solve in order to give a full account of his moral philosophy. The puzzles can be stated as follows: Puzzle 1: Which character traits does Nietzsche endorse as virtues? Puzzle 2: What is Nietzsche’s ethical ideal? This article offers an exegetical strategy to shed light on both puzzles, especially the first one regarding which character traits Nietzsche endorses as virtues which, as we shall see, is tougher to answer by a straightforward appeal to his texts. To elucidate this puzzle, I will propose that his approving comments regarding excellence-based moral philosophy indicate that his own ethics is also structured in terms of an ethical ideal with a requisite set of virtues which, following his ancient philosophical influences, he views as fundamentally connected. As Julia Annas notes, one the most distinctive ‘assumptions which ancient theories make [is] the relationship of [our] virtues to our final end’,4 and given Nietzsche’s interest in, and apparent endorsement of, ancient eudaimonism – especially compared to his invariably scathing remarks on the modern deontological and utilitarian traditions – we have reason to think that he shares this view.5 What is significant for this article, however, is that Nietzsche’s commitment to a kind of eudaimonism modelled on the ancient world offers a potential way to solve both puzzles. If his virtues and ethical ideal are connected in a similar way to ancient eudaimonistic theories, then understanding his ethical ideal allows us to infer which character traits he endorses as virtues, and vice versa. Although it might be objected that a method tackling both puzzles in tandem would be unworkable if their solutions were contained in each other, in what follows I will show that Nietzsche’s extensive comments on his ethical ideal of ‘becoming what one is’ positions us in a strong position to infer which character traits he prizes most highly. I will call these character traits ‘virtues of self-cultivation’. (shrink)

This is an exploratory paper whose aim is to investigate the potentialities of bilattice theory for an adequate definition of the deduction apparatus for multi-valued logic. We argue that bilattice theory enables us to obtain a nice extension of the graded approach to fuzzy logic. To give an example, a completeness theorem for a logic based on Boolean algebras is proved.

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.

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)

The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the \ calculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. In (...) terms of the \ calculus, we first introduce two different interpolation methods, each of which uniformly shows that the Dunn logics have the interpolation property. One of the methods is closely related to Maehara’s method but the other method, which we call the pruned tableau method, is novel to this paper. We provide various reasons to prefer the pruned tableau method to the Maehara-style method. We then turn our attention to extensions of Dunn logics with so-called appropriate implication connectives. Although these logics have been considered at various places in the literature, a study of the interpolation properties of these logics is lacking. We use the pruned tableau method to uniformly show that these extended Dunn logics have the interpolation property and explain that the same result cannot be obtained via the Maehara-style method. Finally, we show how the pruned tableau method constructs interpolants for functionally complete extensions of the Dunn logics. (shrink)

Problem: The article seeks to tackle three problems of Mitterer's non-dualistic philosophy. Firstly, the key term description remains not only rather unclear and rudimentary but also isolated from relevant neighboring terms and theories of other disciplines. Secondly, a logical reconstruction and formal model of non-dualism is still lacking. Thirdly, there are hardly any extensions of philosophical non-dualism to non-philosophical disciplines and fields. Findings: The three main findings of the article are based on the abovementioned problems. Firstly, the non-dualistic term description (...) will be connected to the sociological and semiotic term meaning by emphasizing their semantic-pragmatic similarities. Moreover, a common and distinction-theoretic conceptualization of both terms will be proposed. Secondly, a non-dualistic formalization and logical reconstruction will be elaborated by deducing non-dualism from dualism using the operation of re-entry. Thirdly, the non-dualistic formalization will be applied to the classical semiotic triangle, resulting in the elaboration of a non-dualistic semiotic triangle. Benefits: The aforementioned findings have two possible benefits. Firstly, the compatibility between the terms description and meaning makes philosophical non-dualism connectable to social science approaches, especially to sociology and semiotics. This may be an important avenue for interdisciplinary cross-fertilization and co-operation. Secondly, the formalization and logical deduction may help to clarify and explicitize non-dualism's main arguments and implicit assumptions. (shrink)

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms (...) of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructed. (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)

In the present paper we prove that the poset of all extensions of the logic defined by a class of matrices whose sets of distinguished values are equationally definable by their algebra reducts is the retract, under a Galois connection, of the poset of all subprevarieties of the prevariety generated by the class of the algebra reducts of the matrices involved. We apply this general result to the problem of finding and studying all extensions of the logic of paradox. (...) In order to solve this problem, we first study the structure of prevarieties of Kleene lattices. Then, we show that the poset of extensions of the logic of paradox forms a four-element chain, all the extensions being finitely many-valued and finitely-axiomatizable logics. There are just two proper consistent extensions of the logic of paradox. The first is the classical logic that is relatively axiomatized by the Modus ponens rule for the material implication. The second extension, being intermediate between the logic of paradox and the classical logic, is the one relatively axiomatized by the Ex Contradictione Quodlibet rule. (shrink)