Psychology Dictionary of Arguments

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Kurt Gödel: Kurt Gödel (1906 – 1978) was a logician, mathematician, and philosopher. He is best known for his incompleteness theorems, which show that within any axiomatic system powerful enough to express basic arithmetic, there will always be statements that can neither be proven nor disproven within that system. Major works are "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" (1931), "Consistency-Proof for the Generally Covariant Gravitational Field Equations" (1939), "What is Cantor's Continuum Problem?" (1947), "Russell's Mathematical Logic" (1951), "On Undecidable Propositions of Formal Mathematical Systems" (1956). See also Incompleteness, Completeness, Proofs, Provability.
Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Concept Summary/Quotes Sources

David Deutsch on Goedel - Dictionary of Arguments

I 221
Penrose claims that the very existence of a kind of open mathematical intuition is incompatible with the existing structure of physics and in particular with the Turing principle.
If the Turing principle is true, we can conceive the brain (like any other object) as a computer executing a certain program. Such a program embodies a set of Hilbert's rules of proof, which cannot be complete according to Gödel's theorem.
Therefore, the mathematician whose mind is a computer can also never accept this statement as proven.
Penrose then suggests to present the statement to this mathematician. The mathematician understands the proof. It is, after all, self-evidently valid, and therefore the mathematician can presumably see that it is valid. But that would contradict Gödel's theorem. So there must be a mistake here somewhere. And this is, according to Penrose" opinion, the Turing principle.
I 222
DeutschVsPenrose: E.g.

Deutsch cannot consistently prove the truth of this statement.

I cannot, although I see that it is true. And I also understand the proposition. So it is at least possible that a statement that is inconceivable for a person, can of course be true, however for any other person.
Cf. >Turing machine
, >Evidence, >Understanding.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Deutsch I
D. Deutsch
Fabric of Reality, Harmondsworth 1997
German Edition:
Die Physik der Welterkenntnis München 2000

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