Philosophy Lexicon of Arguments

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II 213
Goedel/Incompleteness/Hilbert/Genz: In 1917 Hilbert had drawn up the program to summarize all mathematics in a scheme in the logic of the 1st level, Goedel proved in 1931 that this was not possible. It works well for Euclidean and non-Euclidean geometry, but not for addition and multiplication, if you take their derivation rules together.
It is always about sentences that are formulated in a language, but cannot be derived or refuted.
Abundance/Genz: in poor languages, all statements that can be formulated in them can either be derived or disproved. The richer they are, the more statements can be formulated that do not succeed.
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II 214
These sentences make a statement about themselves, namely that they cannot be derived.
Solution: Extension of the language. For example, to accept his negation as an axiom.
Problem: In every extension there are new non-derivable sentences.
Deductibility: A language in which any sensible phrase at all could be derived would allow to derive contradictions.


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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.

Gz I
H. Genz
Gedankenexperimente Weinheim 1999

Gz II
Henning Genz
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002


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Ed. Martin Schulz, access date 2017-12-17