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1

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.

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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.

3

On the Anti-Mechanist Arguments Based on Gödel’s Theorem

63%

Krajewski S.

Studia Semiotyczne

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2020

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vol. 34

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issue 1

EN

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.

4

Can a Robot Be Grateful? Beyond Logic, Towards Religion

63%

Krajewski S.

Eidos. A Journal for Philosophy of Culture

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2018

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vol. 2

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issue 4(6)

4–13

EN

Philosophy should seriously take into account the presence of computers. Computer enthusiasts point towards a new Pythagoreanism, a far reaching generalization of logical or mathematical views of the world. Most of us try to retain a belief in the permanence of human superiority over robots. To justify this superiority, Gödel’s theorem has been invoked, but it can be demonstrated that this is not sufficient. Other attempts are based on the scope and fullness of our perception and feelings. Yet the fact is that more and more can be computer simulated. In order to secure human superiority over robots, reference to the realm of human relations and attitudes seems more promising. Insights provided by philosophy of dialogue can help. They suggest an ultimate extension of the Turing test. In addition, it seems that in order to justify the belief in human superiority one must rely on the individual experiences that indicate a realm that is not merely subjective. It makes sense to call it religious.

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2 Studia Semiotyczne

1 Eidos. A Journal for Philosophy of Culture

1 Teorie vědy (Theory of Science)

2 Krajewski S.

1 Holub Š.

1 Jurková B.

1 Zámečník L. H.

1 2023

2 2020

1 2018

Understanding, Expression and Unwelcome Logic

Von Neumann, Turing a Gödel: o mysli a strojích

On the Anti-Mechanist Arguments Based on Gödel’s Theorem

Can a Robot Be Grateful? Beyond Logic, Towards Religion