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    Wyświetlanie 1-9 z 9
    Tytuł:
    Remarks on the Gödelian Anti-Mechanist Arguments
    Autorzy:
    Raatikainen, Panu
    Powiązania:
    https://bibliotekanauki.pl/articles/1796974.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Gödel
    incompleteness
    mechanism
    Opis:
    Certain selected issues around the Gödelian anti-mechanist arguments which have received less attention are discussed.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 267-278
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Gödel’s Incompleteness Theorem and the Anti-Mechanist Argument: Revisited
    Autorzy:
    Cheng, Yong
    Powiązania:
    https://bibliotekanauki.pl/articles/1796969.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Gödel’s incompleteness theorem
    the Anti-Mechanist Argument
    Gödel’s Disjunctive Thesis
    intensionality
    Opis:
    This is a paper for a special issue of Semiotic Studies devoted to Stanislaw Krajewski’s paper (2020). This paper gives some supplementary notes to Krajewski’s (2020) on the Anti-Mechanist Arguments based on Gödel’s incompleteness theorem. In Section 3, we give some additional explanations to Section 4–6 in Krajewski’s (2020) and classify some misunderstandings of Gödel’s incompleteness theorem related to AntiMechanist Arguments. In Section 4 and 5, we give a more detailed discussion of Gödel’s Disjunctive Thesis, Gödel’s Undemonstrability of Consistency Thesis and the definability of natural numbers as in Section 7–8 in Krajewski’s (2020), describing how recent advances bear on these issues.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 159-182
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Understanding, Expression and Unwelcome Logic
    Autorzy:
    Holub, Štěpán
    Powiązania:
    https://bibliotekanauki.pl/articles/1796970.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    mechanism
    Gödel’s theorem
    Turing machine
    hermeneutics
    Opis:
    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.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 183-202
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Martin-Löf’s Constructive Optimism
    Autorzy:
    Peluce, V. Alexis
    Powiązania:
    https://bibliotekanauki.pl/articles/1796975.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    optimism
    pessimism
    Martin-Löf
    Gödel’s disjunction
    Opis:
    In his 1951 Gibbs Memorial Lecture, Kurt Gödel put forth his famous disjunction that either the power of the mind outstrips that of any machine or there are absolutely unsolvable problems. The view that there are no absolutely unsolvable problems is optimism, the view that there are such problems is pessimism. In his 1995—and, revised in 2013—Verificationism Then and Now, Per Martin-Löf presents an illustrative argument for a constructivist form of optimism. In response to that argument, Solomon Feferman points out that Martin-Löf’s reasoning relies upon constructive understandings of key philosophical notions. In the vein of Feferman’s analysis, one might be object to Martin-Löf’s argument for either its reliance upon constructivist (as opposed to classical) considerations, or for its appeal to non-unproblematically mathematical premises. We argue that both of these responses fall short. On one hand, to be critical of Martin-Löf’s reasoning for its constructiveness is to reject what would otherwise be a scientific advance on the basis of the assumption of constructivism’s falsehood or implausibility, which is of course uncharitable at best. On the other hand, to object to the argument for its use of non-unproblematically mathematical premises is to assume that there is some philosophically neutral mathematics, which is implausible. Martin-Löf’s argument relies upon his third law, the claim that from the impossibility of a proof of a proposition we can construct a proof of its negation. We close with a discussion of some ways in which this claim can be criticized from the constructive point of view. Specifically, we contend that Martin-Löf’s third law is incompatible with what has been called “Poincaré’s Principle of Epistemic Conservation”, the thesis that genuine increase in mathematical knowledge requires subject-specific insight.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 233-242
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Problematic Nature of Gödel’s Disjunctions and Lucas-Penrose’s Theses
    Autorzy:
    Avron, Arnon
    Powiązania:
    https://bibliotekanauki.pl/articles/1796961.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Gödel disjunction
    Lucas-Penrose argument
    mechanism
    mind
    computationalism
    Opis:
    We show that the name “Lucas-Penrose thesis” encompasses several different theses. All these theses refer to extremely vague concepts, and so are either practically meaningless, or obviously false. The arguments for the various theses, in turn, are based on confusions with regard to the meaning(s) of these vague notions, and on unjustified hidden assumptions concerning them. All these observations are true also for all interesting versions of the much weaker (and by far more widely accepted) thesis known as “Gö- del disjunction”. Our main conclusions are that pure mathematical theorems cannot decide alone any question which is not purely mathematical, and that an argument that cannot be fully formalized cannot be taken as a mathematical proof.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 83-108
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Syntax-Semantics Interaction in Mathematics
    Autorzy:
    Heller, Michael
    Powiązania:
    https://bibliotekanauki.pl/articles/561342.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    philosophy of mathematics
    categorical logic
    syntax-semantic interaction
    Bell’s program
    Gödel-like limitations
    Opis:
    Mathematical tools of category theory are employed to study the syntaxsemantics problem in the philosophy of mathematics. Every category has its internal logic, and if this logic is sufficiently rich, a given category provides semantics for a certain formal theory and, vice versa, for each (suitably defined) formal theory one can construct a category, providing a semantics for it. There exists a pair of adjoint functors, Lang and Syn, between a category (belonging to a certain class of categories) and a category of theories. These functors describe, in a formal way, mutual dependencies between the syntactical structure of a formal theory and the internal logic of its semantics. Bell’s program to regard the world of topoi as the univers de discours of mathematics and as a tool of its local interpretation, is extended to a collection of categories and all functors between them, called “categorical field”. This informal idea serves to study the interaction between syntax and semantics of mathematical theories, in an analogy to functors Lang and Syn. With the help of these concepts, the role of Gödel-like limitations in the categorical field is briefly discussed. Some suggestions are made concerning the syntax-semantics interaction as far as physical theories are concerned.
    Źródło:
    Studia Semiotyczne; 2018, 32, 2; 87-105
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Anti-Mechanist Arguments Based on Gödel’s Theorem
    Autorzy:
    Krajewski, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/1796977.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Gödel’s theorem
    mechanism
    Lucas’s argument
    Penrose’s argument
    computationalism
    mind
    consistency
    algorithm
    artificial intelligence
    natural number
    Opis:
    The alleged proof of the non-mechanical, or non-computational, character of the human mind based on Gödel’s incompleteness theorem is revisited. Its history is reviewed. The proof, also known as the Lucas argument and the Penrose argument, is refuted. It is claimed, following Gödel himself and other leading logicians, that antimechanism is not implied by Gödel’s theorems alone. The present paper sets out this refutation in its strongest form, demonstrating general theorems implying the inconsistency of Lucas’s arithmetic and the semantic inadequacy of Penrose’s arithmetic. On the other hand, the limitations to our capacity for mechanizing or programming the mind are also indicated, together with two other corollaries of Gödel’s theorems: that we cannot prove that we are consistent (Gödel’s Unknowability Thesis), and that we cannot fully describe our notion of a natural number.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 9-56
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Diagonal Anti-Mechanist Arguments
    Autorzy:
    Kashtan, David
    Powiązania:
    https://bibliotekanauki.pl/articles/1796972.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    mechanism
    mind
    computability
    incompleteness theorems
    computation-al theory of mind
    the cogito
    diagonal arguments
    Gödel
    Descartes
    Tarski
    Turing
    Chomsky
    Opis:
    Gödel’s first incompleteness theorem is sometimes said to refute mechanism about the mind. §1 contains a discussion of mechanism. We look into its origins, motivations and commitments, both in general and with regard to the human mind, and ask about the place of modern computers and modern cognitive science within the general mechanistic paradigm. In §2 we give a sharp formulation of a mechanistic thesis about the mind in terms of the mathematical notion of computability. We present the argument from Gödel’s theorem against mechanism in terms of this formulation and raise two objections, one of which is known but is here given a more precise formulation, and the other is new and based on the discussion in §1.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 203-232
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Using Kreisel’s Way Out to Refute Lucas-Penrose-Putnam Anti-Functionalist Arguments
    Autorzy:
    Buechner, Jeff
    Powiązania:
    https://bibliotekanauki.pl/articles/1796962.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    functionalism
    Computational Liar
    Gödel incompleteness theorems
    finitary computational machine
    mathematical certainty
    finitary reasoning
    epistemic refutation
    metaphysical refutation
    epistemic justification
    recursively unsolvable
    epistemic modality
    finitary computational description
    Opis:
    Georg Kreisel (1972) suggested various ways out of the Gödel incompleteness theorems. His remarks on ways out were somewhat parenthetical, and suggestive. He did not develop them in subsequent papers. One aim of this paper is not to develop those remarks, but to show how the basic idea that they express can be used to reason about the Lucas-Penrose-Putnam arguments that human minds are not (entirely) finitary computational machines. Another aim is to show how one of Putnam’s two anti-functionalist arguments (that use the Gödel incompleteness theorems) avoids the logical error in the Lucas-Penrose arguments, extends those arguments, but succumbs to an absurdity. A third aim is to provide a categorization of the Lucas-Penrose-Putnam anti-functionalist arguments.
    Źródło:
    Studia Semiotyczne; 2020, 34, 1; 109-158
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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