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Възприятие и крайност: феноменологически измерения на доказателството на Декарт за съществуването на „материални неща“
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Възприятие и крайност: феноменологически измерения на доказателството на Декарт за съществуването на „материални неща“

Author(s): Stefan Popov / Language(s): Bulgarian Issue: 6/2015

The critical appraisals of Descartes’s proof of the existence of „material things“ commenced with the first readings of the Meditations and have continued ever since. From Hobbes to the contemporary Anglo-American realists, the proof has provoked confusion and numerous reconstructions, which look into its essential logical moves. A number of critiques have declared it unsuccessful and even somehow preposterous. Descartes’s interest, however, is not in „material things“ per se or in the fact that they exist. Nor is it in the idea that something like a proof of their existence would guarantee both their own being and the being of what is called the external world. The focus of the proof is not on material things in the sense of an external world. Instead, it has a functional significance in a broader context, where Descartes is interested in the possibility of knowledge under the condition of finitude. Understanding the internal meaning of the proof of the existence of material things requires a phenomenological reading of the Cartesian meditation as a whole. From a phenomenological perspective, it is essential to account for and preserve the condition of perception as finite. In its relation to objects and object schemes, thinking discovers concepts in its own realm, within itself. Both thought and its objects thus carry the features of purity and infinity. Perception, on the other hand, is directly connected to finitude, which in turn is articulated in receptivity. Receptivity needs to have what is perceived as given. Descartes proof provides a procedural and schematic expression of this condition of perception, which requires that something be given outside of it and independently of it.

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За една логическа грешка, свързана с термините „познание“, „свобода“ „справедливост“ и „демокрация“
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За една логическа грешка, свързана с термините „познание“, „свобода“ „справедливост“ и „демокрация“

Author(s): Ventseslav Kulov / Language(s): English,Bulgarian Issue: 2/2016

The article consecutively analyzes the different meanings of the terms „knowledge“, „justice“, „freedom“ and „democracy”; the author concludes it is useless to generalize these meanings. To dwell on knowledge, justice, freedom and democracy in general in a text, without specifying the meanings implied in them, results in an insurmountable lack of clarity, which makes the whole text senseless.

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Спектър на логиките на задаване на въпроси
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Спектър на логиките на задаване на въпроси

Author(s): Jaakko Hintikka / Language(s): English,Bulgarian Issue: 2/2016

The leading idea in this essay concerns knowledge-seeking through questioning. Asking a question and receiving an answer (an interrogative move) is radically different from a logical deduction (a logical inference move). However, from a strategic viewpoint, the two steps are parallel, in the sense that the principles guiding the choice of the best questions to ask are analogous with the strategic principles guiding the choice of the best logical inferences that can be drawn from given premises. Another main insight that the interrogative approach yields is the possibility of a rational, and even logical, theory of discovery. In that case, the problem of justification becomes redundant; nevertheless, we can develop an interesting and rich theory of discovery, of which the centerpiece is the problem of optimal question selection.

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Яко Хинтика. Логиката и философията на математиката през втората половина на ХХ век
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Яко Хинтика. Логиката и философията на математиката през втората половина на ХХ век

Author(s): Rosen Lyutskanov / Language(s): English,Bulgarian Issue: 2/2016

The present papers attempts to summarize Jaakko Hintikka's contributions to the development of logic, semantics and philosophy of mathematics.

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ХV международен конгрес по логика, методология и философия на науката
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ХV международен конгрес по логика, методология и философия на науката

Author(s): Anton Donchev,Mila Marinova,Lilia Gurova / Language(s): English,Bulgarian Issue: 2/2016

The article offers an overview of the 15th Congress of Logic, Methodology and Philosophy of Science, held on 3-8 August 2015 in Helsinki. It includes a brief outline of the history of these congresses, with special attention to its trends of development and comparisons between the last five of them. These trends are indicative of the changes taking place in the development of philosophy of science over the last 16 years. A special focus is put on the main topics of the congresses as well as on some of the most significant presentations. Finally, the paper provides information about the Bulgarian participation in the latest congress, which reveals a significant increase compared with the previous ones, which inspires hope that the ascending development of philosophy of science in Bulgaria will continue and its presence at international forums will become increasingly visible.

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Coming to Know by Asking Questions: Exploring the Borderline of Logic and Epistemology

Coming to Know by Asking Questions: Exploring the Borderline of Logic and Epistemology

Author(s): Rosen Lutskanov / Language(s): English Issue: 2/2018

The paper explores the intricate interplay of two parallel developments: on the one hand, the Socratic turn in epistemology with its shifting focus on information retrieval, evidence-based reasoning, and the cognitive relevance of questions; and the advance of dynamic epistemic logic with its accent on knowledge-acquisition. Both are relevant for any realistic model of knowledge which pays due attention to learning. It is argued that the formal models are still wanting in some key respects, but the development of alternative and mutually complementing logical systems marks a promising trend for re-establishing the close links between epistemology and epistemic logic.

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The Basics of Neo-Realist Cosmology: Bertrand Russell against Alfred North Whitehead

The Basics of Neo-Realist Cosmology: Bertrand Russell against Alfred North Whitehead

Author(s): Andrii Synytsia / Language(s): English Issue: 25/2020

The article presents a comparative analysis of neo-realist views of Russell and Whitehead on cosmology in the first decades of the 20th century. It is noted that despite the similarity of the basic theoretical and methodological principles of their philosophizing, these thinkers formulated philosophical-cosmological conceptions that differed significantly from each other. The reason for this was that Russell, at the epistemological level, used the theory of degrees of certainty, and on the logical one he developed the theory of descriptions, but Whitehead, in contrast, was a supporter of the theory of critical realism in epistemology and the method of extensive abstraction in logic. All this influenced the former to pay more attention to the questions of analysis and, accordingly, to use the basic concepts of facts, logical atoms, and propositions, and the latter to focus on the question of synthesis and to consider the structure of being through the prism of concepts of actual entities, eternal objects and prehension. Hence the world for Russell is a static formation (set of events), and we only need to define its laws, and for the Whitehead world is a dynamic formation (set of processes), the laws of which still need to be understood. It is emphasized that as a result, Russell’s cosmology rejected the previous metaphysics, but Whitehead’s cosmology aimed at finding the origins of modern cosmology in the writings of early thinkers. Nevertheless, it is argued that the cosmological teachings of both had a significant influence on the development of analytic philosophy.

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U mrežama normi: Brandomovo razumijevanje racionalnosti

U mrežama normi: Brandomovo razumijevanje racionalnosti

Author(s): Kenan Šljivo / Language(s): Bosnian Issue: 02/158/2020

The paper analyses the concept of rationality as developed in the philosophical considerations of Robert Brandom. It is the analysis of Brandom’s pragmatically-oriented discourse concerning the issue of rationality from the perspective of human being’s linguistic practices, where only upon meeting the other members of specific linguistic community the aspects of human nature we may characterise by the term rationality are manifested. The central part of this paper treats Brandom’s normative idiom that he postulates as explanatorily most suitable for understanding the linguistic practices and the idea of rationality based upon them.

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Mathematics as a love of wisdom: Saunders Mac Lane as philosopher

Mathematics as a love of wisdom: Saunders Mac Lane as philosopher

Author(s): Colin McLarty / Language(s): English Issue: 69/2020

This note describes Saunders Mac Lane as a philosopher, and indeed as a paragon naturalist philosopher. He approaches philosophy as a mathematician. But, more than that, he learned philosophy from David Hilbert’s lectures on it, and by discussing it with Hermann Weyl, as much as he did by studying it with the mathematically informed Göttingen Philosophy professor Moritz Geiger.

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Creating new concepts in mathematics: freedom and limitations. The case of Category Theory

Creating new concepts in mathematics: freedom and limitations. The case of Category Theory

Author(s): Zbigniew Semadeni / Language(s): English Issue: 69/2020

In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning.We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski.

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Abstract logical structuralism

Abstract logical structuralism

Author(s): Jean-Pierre Marquis / Language(s): English Issue: 69/2020

Structuralism has recently moved center stage in philosophy of mathematics. One of the issues discussed is the underlying logic of mathematical structuralism. In this paper, I want to look at the dual question, namely the underlying structures of logic. Indeed, from a mathematical structuralist standpoint, it makes perfect sense to try to identify the abstract structures underlying logic. We claim that one answer to this question is provided by categorical logic. In fact, we claim that the latter can be seen—and probably should be seen—as being a structuralist approach to logic and it is from this angle that categorical logic is best understood.

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No-signaling in topos formulation and a common ontological basis for classical and non-classical physical theories

No-signaling in topos formulation and a common ontological basis for classical and non-classical physical theories

Author(s): Marek Kuś / Language(s): English Issue: 69/2020

Starting from logical structures of classical and quantum mechanics we reconstruct the logic of so-called no-signaling theories, where the correlations among subsystems of a composite system are restricted only by a simplest form of causality forbidding an instantaneous communication. Although such theories are, as it seems, irrelevant for the description of physical reality, they are helpful in understanding the relevance of quantum mechanics. The logical structure of each theory has an epistemological flavor, as it is based on analysis of possible results of experiments. In this note we emphasize that not only logical structures of classical, quantum and no-signaling theory may be treated on the same ground but it is also possible to give to all of them a common ontological basis by constructing a “phase space” in all cases. In non-classical cases the phase space is not a set, as in classical theory, but a more general object obtained by means of category theory, but conceptually it plays the same role as the phase space in classical physics.

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Quantum geometry, logic and probability

Quantum geometry, logic and probability

Author(s): Shahn Majid / Language(s): English Issue: 69/2020

Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂+f = (−Δθ + q − p)f for the graph Laplacian Δθ, potential functions q, p built from the probabilities, and finite difference ∂+ in the time direction. Motivated by this new point of view, we introduce a ‘discrete Schrödinger process’ as ∂+ψ = ı(−Δ + V )ψ for the Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘generalised Markov process’ for f = |ψ|2 in which there is an additional source current built from ψ. We also mention our recent work on the quantum geometry of logic in ‘digital’ form over the field F2 = {0, 1}, including de Morgan duality and its possible generalisations.

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Information and physics

Information and physics

Author(s): Radosław Kycia,Agnieszka Niemczynowicz / Language(s): English Issue: 69/2020

This is an overview article that contains the discussion of the connection between information and physics at the elementary level. We present a derivation of Lindauer’s bound for heat emission during irreversible logical operation. In this computation the Szilard’s version of Maxwell’s demon paradox is used as a model to design thermodynamic implementation of a single bit of computer memory. Lindauer’s principle also motivates the discussion on the practical and emergent nature of the information. Apart from physics, the principle has implications in philosophy.

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The homunculus brain and categorical logic

The homunculus brain and categorical logic

Author(s): Steve Awodey,Michał Heller / Language(s): English Issue: 69/2020

The interaction between syntax (formal language) and its semantics (meanings of language) is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the brain is able to create meanings. To emphasize the toy character of the proposed model, we prefer to speak of the homunculus brain rather than the brain per se. The homunculus brain consists of neurons, each of which is modeled by a category, and axons between neurons, which are modeled by functors between the corresponding neuron-categories. Each neuron (category) has its own program enabling its working, i.e. a theory of this neuron. In analogy to what is known from categorical logic, we postulate the existence of a pair of adjoint functors, called Lang and Syn, from a category, now called BRAIN, of categories, to a category, now called MIND, of theories. Our homunculus is a kind of “mathematical robot”, the neuronal architecture of which is not important. Its only aim is to provide us with the opportunity to study how such a simple brain-like structure could “create meanings” and perform abstraction operations out of its purely syntactic program. The pair of adjoint functors Lang and Syn model the mutual dependencies between the syntactical structure of a given theory of MIND and the internal logic of its semantics given by a category of BRAIN. In this way, a formal language (syntax) and its meanings (semantics) are interwoven with each other in a manner corresponding to the adjointness of the functors Lang and Syn. Higher cognitive functions of abstraction and realization of concepts are also modelled by a corresponding pair of adjoint functors. The categories BRAIN and MIND interact with each other with their entire structures and, at the same time, these very structures are shaped by this interaction.

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Category Theory in the hands of physicists, mathematicians, and philosophers

Category Theory in the hands of physicists, mathematicians, and philosophers

Author(s): Mariusz Stopa / Language(s): English Issue: 69/2020

Book review: Category Theory in Physics, Mathematics, and Philosophy, Kuś M., Skowron B. (eds.), Springer Proc. Phys. 235, 2019, pp.xii+134.

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“Is logic a physical variable?” Introduction to the Special Issue

“Is logic a physical variable?” Introduction to the Special Issue

Author(s): Michał Eckstein,Bartłomiej Skowron / Language(s): English Issue: 69/2020

“Is logic a physical variable?” This thought-provoking question was put forward by Michael Heller during the public lecture “Category Theory and Mathematical Structures of the Universe” delivered on 30th March 2017 at the National Quantum Information Center in Sopot. It touches upon the intimate relationship between the foundations of physics, mathematics and philosophy. To address this question one needs a conceptual framework, which is on the one hand rigorous and, on the other hand capacious enough to grasp the diversity of modern theoretical physics. Category theory is here a natural choice. It is not only an independent, well-developed and very advanced mathematical theory, but also a holistic, process-oriented way of thinking.

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Conjoining and the Weak/Strong Quantifier Distinction
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Conjoining and the Weak/Strong Quantifier Distinction

Author(s): John Collins / Language(s): English Issue: 60/2020

Pietroski’s model of semantic composition is introduced and compared to the standard type hierarchy. Particular focus is then given to Pietroski’s account of quantification. The question is raised of how the model might account for the weak/strong distinction in natural language quantification. A number of options are addressed and one proposal is tentatively recommended.

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Generative Linguistics Meets Normative Inferentialism: Part 1
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Generative Linguistics Meets Normative Inferentialism: Part 1

Author(s): David Pereplyotchik / Language(s): English Issue: 60/2020

This is the first installment of a two-part essay. Limitations of space prevented the publication of the full essay in present issue of the Journal. The second installment will appear in the next issue, 2021 (1). My overall goal is to outline a strategy for integrating generative linguistics with a broadly pragmatist approach to meaning and communication. Two immensely useful guides in this venture are Robert Brandom and Paul Pietroski. Squarely in the Chomskyan tradition, Pietroski’s recent book, Conjoining Meanings, offers an approach to natural-language semantics that rejects foundational assumptions widely held amongst philosophers and linguists. In particular, he argues against extensionalism— the view that meanings are (or determine) truth and satisfaction conditions. Having arrived at the same conclusion by way of Brandom’s deflationist account of truth and reference, I’ll argue that both theorists have important contributions to make to a broader anti-extensionalist approach to language. What appears here as Part 1 of the essay is largely exegetical, laying out what I see as the core aspects of Brandom’s normative inferentialism (§1) and Pietroski’s naturalistic semantics (§2). In Part 2 (next issue), I argue that there are many convergences between these two theoretical frameworks and, contrary to first appearances, very few points of substantive disagreement between them. If the integration strategy that I propose is correct, then what appear to be sharply contrasting commitments are better seen as interrelated verbal differences that come down to different—but complementary—explanatory goals. The residual disputes are, however, stubborn. I end by discussing how to square Pietroski’s commitment to predicativism with Brandom’s argument that a predicativist language is in principle incapable of expressing ordinary conditionals.

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WE WILL FIGURE IT OUT. KNOW-HOW, HYBRID WAYS, AND COMMUNICATIVE (INTER)ACTIONS

WE WILL FIGURE IT OUT. KNOW-HOW, HYBRID WAYS, AND COMMUNICATIVE (INTER)ACTIONS

Author(s): Ion Copoeru,Adrian Luduşan / Language(s): English Issue: 3/2020

The goal of this paper is primarily to pinpoint some substantial analytical and conceptual difficulties with the account of knowledge how proposed by (Stanley & Williamson, Knowing How, 2001) [henceforth S&W] and (Stanley, Knowing (How), 2011), (Stanley, Know How, 2011) based on (Groenendijk & Stokhof, 1984) [henceforth G&S] semantic analysis of embedded questions. In light of such difficulties, (1) we propose supplementing their account with an integrated approach of knowledge how, and suggest adding a mereological layer to the semantic framework of embedded questions (2) we argue that the characteristics of what we call ‘hybrid ways’ and ‘hybrid knowledge’ strongly indicate reopening the issue of the proper account of questions towards the complementary relevant account of interrogation in communicative interactions, and the role of the context (in)forming knowledge-how. As a methodological principle, we remain neutral on the intellectualist vs anti-intellectualist debate. We also remain silent on the nature and explanation of the modes of presentations or ways of thinking that should be developed in order to adequately account for hybrid ways and hybrid knowledge.

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