Temat: Gödel - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Skocz do pozycji: 2.

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

Skocz do pozycji: 3.

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

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