Goedel: certain ">
|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. |
Daniel Dennett on Goedel - Dictionary of Arguments
Mind/Goedel/Dennett: Goedel himself seemed to deem the "sky hook" necessary as an explanation for the human mind.
Goedel: certain truths can be "seen" but never proved. (> Proof).
Goedel Figure: it is possible to arrange all sorts of axiomatic systems in alphabetical order.
DennettVsGoedel: Problem: how can you find out whether a mathematician proved a sentence or has only made a sound like a parrot? (Behavior).
J.R.Lucas, 1961(1): the crucial property should be "to represent a sentence as true".
DennettVsLucas: but this faces insurmountable problems of interpretation.
Goedel/Toshiba Library/Dennett: "there is no single algorithm that can prove all the truths of arithmetics". Dennett: Goedel says nothing about all the other algorithms in the library.
1. J.R.Lucas, Minds, Machines, and Gödel. Etica E Politica 5 (1):1 (1961)_____________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.
Darwin’s Dangerous Idea, New York 1995
Darwins gefährliches Erbe Hamburg 1997
Kinds of Minds, New York 1996
Spielarten des Geistes Gütersloh 1999
"COG: Steps towards consciousness in robots"
Bewusstein, Thomas Metzinger, Paderborn/München/Wien/Zürich 1996
"Animal Consciousness. What Matters and Why?", in: D. C. Dennett, Brainchildren. Essays on Designing Minds, Cambridge/MA 1998, pp. 337-350
Der Geist der Tiere, D Perler/M. Wild, Frankfurt/M. 2005