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Understanding, Expression and Unwelcome Logic

100%
Holub Š.
Studia Semiotyczne
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2020
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vol. 34
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issue 1
EN
In this paper I will attempt to explain why the controversy surrounding the alleged refutation of Mechanism by Gödel’s theorem is continuing even after its unanimous refutation by logicians. I will argue that the philosophical point its proponents want to establish is a necessary gap between the intended meaning and its formulation. Such a gap is the main tenet of philosophical hermeneutics. While Gödel’s theorem does not disprove Mechanism, it is nevertheless an important illustration of the hermeneutic principle. The ongoing misunderstanding is therefore based in a distinction between a metalogical illustration of a crucial feature of human understanding, and a logically precise, but wrong claim. The main reason for the confusion is the fact that in order to make the claim logically precise, it must be transformed in a way which destroys its informal value. Part of this transformation is a clear distinction between the Turing Machine as a mathematical object and a machine as a physical device.
2
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O różnych sposobach rozumienia analogowości w informatyce

71%
Stacewicz P.
Semina Scientiarum
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2017
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vol. 16
EN
Two different types of analog computations are discussed in the paper: 1)analog-continuous computations (performed physically upon continuous signals),2) analog-analogical computations (performed naturally by means of socalled natural analogons of mathematical operations). They are analyzed withregard to such questions like: a) are continuous computations physically implementable?b) what is the actual computational power of different analogtechniques? c) can natural (empirical) computations be such reliable as digital?d) is it possible to develop universal analog computers (assuming that theyshould be functionally similar to universal Turing machine)? Presented analysesare rather methodological than formal.
3
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Von Neumann, Turing a Gödel: o mysli a strojích

63%
Jurková B., Zámečník L. H.
Teorie vědy (Theory of Science)
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2023
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vol. 45
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issue 1
3-36
EN
The paper discusses some of the poorly explored links between the conceptual systems of logic in Kurt Gödel, the theory of automata in Alan Turing, and the theory of self-reproducing automata in John von Neumann. Traditional controversies are left aside (especially the opposition of Gödel and Turing in the view of mind) and attention is focused on the similarities between all three authors. In individual chapters, the text deals with: the form of differentiation of syntax and semantics in formal system in Gödel, Turing and von Neumann; von Neumann’s variant of Gödel’s theorem and von Neumann’s and Gödel’s conception of Turing machine; and finally the same basis of the view of the relation between mind and automaton in all three authors.
CS
Stať pojednává o některých nedostatečně prozkoumaných vazbách mezi pojmovými systémy logiky u Kurta Gödela, teorie automatů u Alana Turinga a teorie sebe-reprodukujících se automatů u Johna von Neumanna. Stranou jsou ponechány tradiční polemiky (především opozice Gödela a Turinga v pojetí mysli) a pozornost je soustředěna na podobnosti mezi všemi třemi autory. V jednotlivých kapitolách se text věnuje postupně: podobě odlišení syntaxe a sémantiky formálního systému u Gödela, Turinga a von Neumanna; von Neumannově variantě Gödelova důkazu a von Neumannově a Gödelově pojetí Turingova stroje; a konečně stejnému základu pojetí vztahu mezi myslí a strojem u všech tří autorů.
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Indistinctness and Disunion

63%
Hogrebe W.
Dialogue and Universalism
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2016
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issue 3
183-192
EN
In the paper the concept of indistinctness is examined. In the author’s view, indis-tinctness is present in all the aspects of the world. The problem of indistinctness is ap-prehended in four steps, namely, by 1. claiming and proving that the world of indis-tinctness and vagueness enhances our creative intelligence; 2. examining who and when discovered the advantages of indistinctness; 3. maintaining that precision is usually of advantage, but not always; 4. proving the misery of reductionistic programmes.
5
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Semantics and symbol grounding in Turing machine processes

62%
Sarosiek A.
Semina Scientiarum
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2017
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vol. 16
EN
The aim of the paper is to present the underlying reason of the unsolved symbolgrounding problem. The Church-Turing Thesis states that a physical problem,for which there is an algorithm of solution, can be solved by a Turingmachine, but machine operations neglect the semantic relationship betweensymbols and their meaning. Symbols are objects that are manipulated on rulesbased on their shapes. The computations are independent of the context, mentalstates, emotions, or feelings. The symbol processing operations are interpretedby the machine in a way quite different from the cognitive processes.Cognitive activities of living organisms and computation differ from each other,because of the way they act in the real word. The result is the problem ofmutual understanding of symbol grounding.
6
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Liczby nieobliczalne a granice kodowania w informatyce

51%
Stacewicz P.
Studia Semiotyczne
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2018
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vol. 32
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issue 2
131-152
PL
Opis danych i programów komputerowych za pomocą liczb jest epistemologicznie użyteczny, ponieważ pozwala określać granice różnego typu obliczeń. Dotyczy to w szczególności obliczeń dyskretnych (cyfrowych), opisywalnych za pomocą liczb obliczalnych w sensie Turinga. Matematyczny fakt istnienia liczb rzeczywistych innego typu, tj. nieobliczalnych, wyznacza minimalne ograniczenia technik cyfrowych; z drugiej strony jednak, wskazuje na możliwość teoretycznego opracowania i fizycznej implementacji technik obliczeniowo silniejszych, takich jak obliczenia analogowe-ciągłe. Przedstawione w artykule analizy prowadzą do wniosku, że fizyczne implementacje obliczeń niekonwencjonalnych (niecyfrowych) wymagają występowania w przyrodzie wielkości nieskończonych aktualnie (a nie tylko potencjalnie). Za fizycznym istnieniem takich wielkości przemawiają wprawdzie pewne argumenty fizyki teoretycznej, nie są one jednak ostateczne.
EN
The description of data and computer programs with the use of numbers is epistemologically valuable, because it allows the definition of the limits of different types of computations. This applies in particular to discrete (digital) computations, which can be described by means of computable numbers in the Turing sense. The mathematical fact that there are other types of real numbers, i.e. uncomputable numbers, determines the minimal limitations of digital techniques; on the other hand, however, it points to the possibility of theoretical development and physical implementation of computationally stronger techniques, such as analogue-continuous computations. Analyses presented in this article lead to the conclusion that physical implementations of unconventional (non-digital) computations require the occurrence of actually infinite entities in nature. Although some arguments of theoretical physics support the physical existence of such entities, they are not definitive.
7
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The Computational and Pragmatic Approach to the Dynamics of Science

51%
Marciszewski W.
Filozofia i Nauka
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2020
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vol. 8
8
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The Computational and Pragmatic Approach to the Dynamics of Science

51%
Marciszewski W.
Filozofia i nauka. Studia filozoficzne i interdyscyplinarne
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2020
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vol. 8/1
31-67
EN
Sciencemeans here mathematics and those empirical disciplines which avail themselves of mathematical models. The pragmaticapproachis conceived in Karl R. Popper’s The Logic of Scientific Discovery(p.276) sense: a logical appraisal of the success of a theory amounts to the appraisal of its corroboration. This kind of appraisal is exemplified in section 6 by a case study—on how Isaac Newton justified his theory of gravitation. The computationalapproach in problem-solving processes consists in considering them in terms of computability: either as being performed according to a model of computation in a narrower sense, e.g., the Turing machine, or in a wider perspective—of machines associated with a non-mechanical device called “oracle”by Alan Turing (1939). Oracle can be interpreted as computer-theoretic representation of intuitionor invention. Computational approach in an-other sense means considering problem-solving processes in terms of logical gates, supposed to be a physical basis for solving problems with a reasoning.Pragmatic rationalismabout science, seen at the background of classical ration-alism (Descartes, Gottfried Leibniz etc.), claims that any scientific idea, either in empirical theories or in mathematics, should be checked through applications to problem-solving processes. Both the versions claim the existence of abstract objects, available to intellectual intuition. The difference concerns the dynamics of science: (i) the classical rationalism regards science as a stationary system that does not need improvements after having reached an optimal state, while (ii) the pragmatical ver-sion conceives science as evolving dynamically due to fertile interactions between creative intuitions, or inventions, with mechanical procedures.The dynamics of science is featured with various models, like Derek J.de Solla Price’sexponential and Thomas Kuhn’s paradigm model (the most familiar instanc-es). This essay suggests considering Turing’s idea of oracle as a complementary model to explain most adequately, in terms of exceptional inventiveness, the dynam-ics of mathematics and mathematizable empirical sciences.
9
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Konekcjonistyczne modele wyjaśniania procesów poznawczych w kognitywistyce.

51%
Pacholik-Żuromska A.
Humanistyka i Przyrodoznawstwo
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2017
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issue 23
43-55
XX
Celem artykułu jest przegląd i analiza modeli konekcjonistycznych na tle faz rozwoju kognitywistyki. Konekcjonizm, jako druga faza rozwoju kognitywistyki, zaoferował najlepsze narzędzia wyjaśniania i modelowania procesów poznawczych. Został on przedstawiony w relacji do wcześniejszej i późniejszej fazy rozwoju kognitywistyki. Wykazuje się tu również kompatybilność konekcjonizmu z enaktywizmem (trzecią fazą) na gruncie proponowanego modelu wyjaśniania, jak kształtuje się poznanie.
EN
The aim of this paper is an overview and analysis of the connectionist models on the basis of the milestones in the development of cognitive science. It is claimed that connectionism, as the second phase of cognitive science, offers the best tools of explanation and modelling of cognition. There is also indicated the compatibility of connectionism and enactivism (the third phase) on the basis of the proposed models of explanation.
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