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25 Years In Contradiction (University of Glasgow, 7-9/12/2012)
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50th Anniversary of the Department of Logic and Methodology of Sciences, Faculty of Philosophy, Comenius University in Bratislava
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Social and cultural peculiarities of "ignominious" period in the history of the university philosophy of 50-60th of XIX century are opened in the article. It was the time when philosophy lecturing in universities was stopped and lecturing of logic and psychology was replaced. The functioning of university professorate was displaced on the teachers and disciples of spiritual academies.
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This article examines the main characteristics of the concepts of implication in relevant, connexive and paraconsistent logics and discusses the origins of these concepts in Antiquity. It is made a comparative analysis between the meaning of this connective in the three logics in regard to their correspondence to the conditional “if…., then….” used in natural language and presents arguments that the notion of implication, proposed by relevant logic, provides the most adequate formal explication of the conditional connective in the mentioned sense.
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The diverse and complex cultural consequences of the present time have been subject to various studies. The new non-material digital forms of communication make the global cultural flows to move easier and more freely around the globe, a phenomenon that has been associated with many cultural consequences. Major theses, such as homogenization (standardization around a Western or American pattern), polarization (resistance to cultural conformity or standardization and emergence of cultural alternatives), and hybridization have been used as relevant analysis criteria. Having in mind the final objective (respectful contact with other cultures and successful intercultural communication), the present study, as part of a larger enterprise, is an introduction to a critical thinking approach to cultural awareness and the need for a cultural paradigm shift.
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This paper discusses an experiment in cognitive psychology called the Linda problem. Firstly, some natural conditions for the correctness of the interpretation of psychological experiments (such as the Linda problem) are formulated. The article is essentially a critique of the interpretation of the results of the Linda problem experiment provided by Kahneman and Tversky as well as – indirectly – their concept of heuristics. It is shown that the interpretation provided by Kahneman and Tversky does not meet the aforementioned conditions for correctness. The main argument is justified utilizing such rules of rationality as conditional probability and Grice’s conversational maxims. It is also pointed out that this argument can be reformulated in terms of the intuitive system of reasoning.
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The paper deals with the problem of the fuzzy data clustering. In other words, objects attributes can be represented by fuzzy numbers or fuzzy intervals. A direct algorithm of possibilistic clustering is the basis of an approach to the fuzzy data clustering. The paper provides the basic ideas of the method of clustering and a plan of the direct possibilistic clustering algorithm. Definitions of fuzzy intervals and fuzzy numbers are presented and distances for fuzzy numbers are considered. A concept of a vector of fuzzy numbers is introduced and the fuzzy data preprocessing methodology for constructing of a fuzzy tolerance matrix is described. A numerical example is given and results of application of the direct possibilistic clustering algorithm to a set of vectors of triangular fuzzy numbers are considered in the example. Some preliminary conclusions are stated.
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Souhlasím s kritikou Bělohradovy argumentace, kterou provedl výše Pavel Materna a chtěla bych doplnit, že ve zmíněném (jinak velice kvalitním příspěvku) je ještě jedna nepřesnost.
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There are two fundamental questions concerning the choice and presence of objects in various formal systems: (1) Where do these objects come from? (2) What do (can) we know about them? To answer these questions I introduce the notion of a proto-ontology as the pre-theoretic realm of (unspecified) entities from which the basic objects – individuals – of the formal system S are postulated. The pragmatic aspects of such choices are investigated with regard to first-order logic, both pure and applied, set theory and mereology. It is claimed that the postulated (chosen, constructed) objects enter the formal system S with a package of properties and relationships, the recognition of which depends on the interpretation and application of the available predicates of S. If these properties and relationships are not made explicit, a possible clash may arise between them and the properties and relationships “assigned” to the individuals of S by the interpreted predicates of S. As regards the relationship between logic and metaphysics, I contend that logic can perhaps be viewed as the articulation of the fundamental features of proto-ontological objects without which no discourse or theory would be possible. In this sense logic could also be viewed as a theory and method of the construction of a well-articulated metaphysical theory.
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The challenges of the global time require new solutions and up-to-date ways of thinking and communication. These challenges call for the ability to use critical thinking to face the ever-changing world and the ability to maintain a dialog based on the effective skills of communication. Studies in the fields of logic and argumentation theory are of particular importance in this regard. Nowadays they can be presented as a mix of theoretical and practical approaches.In this paper, I will present my reflections on informal logic, which was formed in the late 1970s. Unfortunately, in spite of numerous papers, books, and text-books published over the last forty years,consensus on many issues in this field has not been achieved so far. Therefore, it is difficult to treat informal logic as one of the well-defined approaches to argumentation. The goal of this paper is to take a look at the place of informal logic in state-of-the art study of argumentation by clarifying its subject matter and figuring out the realm to which informal logic belongs
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A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And as a result, inferences such as ‘Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle’ are shown to be first-order.
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We contend that a very seductive argument for theological fatalism fails. In the course of our discussion we point out that theological fatalism is incompatible with the existence of a being who is omnipotent, omniscient and infallible. We suggest that ‘possible’ formalized as ‘‘ is to be understood as ‘can or could have been’ and not simply as ‘can’. The argument we discuss conflates the two. We end by rounding out, hopefully, some left over corners of serious concern to the theist.
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P. Tichý finished, and probably also began to write, this paper in 1973. At that time, he was affiliated at the University of Otago, New Zealand, for already three years. From there he sent the paper to Pavel Materna and me. The paper ‘On Describing’ is connected to, in its content, Tichý’s paper ‘An Approach to Intensional Analysis’ which appeared in Noûs 5, 1971, 273 – 297. The former paper was intended by Tichý to make the public familiar with some ideas published in the technically more demanding Noûs paper. In so doing, he pays particular attention to prospects his conceptual apparatus has for solutions of certain philosophical problems. In the second half of the paper, he utilizes a slightly modified language of Chuch’s theory of types (enriched with possible world variables) that Tichý had introduced already in the paper ‘An Approach to Intensional Analysis’. The study ‘On Describing’ is an excellent introduction into Tichý’s work, in particular his semantics. Fundamental intuitive ideas involved in the paper go throughout, in modified forms, all his work.
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The present note corrects an error made by the au- thor in answering an open problem of axiomatizing an expansion of Nelson's logic introduced by Heinrich Wansing. It also gives a correct axiomatization that answers the problem by importing some results on subintuitionistic logics presented by Greg Restall.
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Review of: Frederik Stjernfelt - Review of Peirce’s Speculative Grammar: Logic as Semiotics by Francesco Bellucci. New York, London: Routledge, 2017, 388 pages
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In this paper I defend a pluralistic approach in understanding function, both in biological and other contexts. Talks about function are ubiquitous and crucial in biology, and it might be the key to bridge the “manifest image” and the “scientific image” identified by Sellars (1962). However, analysis of function has proven to be extremely difficult. The major puzzle is to make sense of “time-reversed causality”: how can property P be the cause of its realizer R? For example, “pumping blood” is a property of hearts, but a property of hearts cannot be the cause of the presence of hearts, since properties cannot predate their realizers and be causes of them. In section 2 I discuss Wright’s etiological analysis, Cummins’ causal-role analysis, and their critics. In section 3 I defend a version of the “consensus without unity” strategy proposed by Godfrey-Smith from Christopher Boorse’s recent critique (2002). In Section 4 I conclude by reflecting on the relation between functional discourses and physicalism.
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The article discusses a new theory — that the dimensions of space and time areaccompanied by a non dimensional expanse, primordial void, or zero dimension. Thiszero dimension would have existed 'before' and would have remained after the big bang.And just as the expanse of space-time dimensions results in separation between allthings — so would an expanse lacking dimensions result in a lack of separation betweenall things. A zero dimension would therefore have a unifying nature, causing all thing tobecome at-one with each other within such a realm. A zero-dimensional realm that lacksdimensions would also be infinite and eternal. This and other attributes developed in thearticle, show that an underlying/invisible expanse of zero dimensions would besynonymous with an infinite-eternal realm of heaven — providing an eternal home forconsciousness or soul — and providing a universal and scientific basis for at least 42tenets of religion and principles of spirituality.
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The goal of this paper is to examine the conditions of validity for the rule of β-conversion in TIL, which is a hyperintensional, typed λ-calculus of partial functions. The rule of β-reduction is a fundamental computational rule of the λ-calculi and functional programming languages. However, it is a well-known fact that the specification of this rule is ambiguous (see, e.g., Plotkin 1975 or Chang & Felleisen 2012). There are two procedurally non-equivalent ways of executing the rule, namely β-conversion ‘by name’ and β-conversion ‘by value’. In the λ-calculi conversion by name is usually applied, though it is known that such a conversion is not unconditionally valid when partial functions are involved. If a procedure that is typed to produce an argument value is improper by failing to produce one, conversion by name cannot be validly applied. On the other hand, conversion by value is valid even in the case of improperness. Moreover, we show that in a typed λ-calculus the specification of λ-closure is also not unambiguous. There is an interpretation of this specification under which β-reduction by name is not valid even when the argument procedure does not fail to produce a value. As a result, we present a universally valid rule of β-reduction by value.
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In the article, while differentiating between the resistance theories of Badiou, Deleuze, and Guattari, the attempt is made to emphasize Badiou’s critique of the theory of asubjective becoming and desire as well as his attempt to develop it into the dialectics between the insurgent students and what Deleuze and Guattari call the “missing people”. Badiou’s theory of the subject, based on the works of Hegel, Lenin and Mao, is regarded as a counterpoint to the theories of revolutionary desire. The revolutionary strategies of Lenin and Mao, based on Hegel’s philosophy, allow them to create the concepts of totality as the unity of the opposites, as the split One, as well as to determine the conflictual dialectical process that conditions the rise and existence of a revolutionary subject – party. While relating the dialectical concepts of the above mentioned authors with Badiou’s concepts of scission, torsion and periodization, Badiou’s logic of the subject is explained. It allows revolutionary forces to constantly resist the institutional practices of placement, destroy stability and immerse into the new cycles of struggle instead of undergoing the process of recuperation and return to the system. The above mentioned concepts meaningfully supplement the vocabulary of social movements and minor politics. Allowing them to spread beyond their comfort zones and to aim at what for them is still a “noumenon”: the sphere of everyday struggles for dignity and survival. We, not the “missing people”, have to be the protagonists of such struggles.
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