About: Gödel, Truth and Proof

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Gödel, Truth and Proof Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The usual way of interpreting Gödel's incompleteness result is as showing that there is a gap between truth and provability, i.e. that we can never prove everything that is true. However, this result is supposed to show that there are unprovable truths which we can know to be true. This, so the story goes, shows that we are more than machines that are restricted to acting as proof systems. Hence our minds are 'not mechanical'. In this paper I would like to indicate that this interpretation of Gödel goes far beyond what he really proved. I would like to show that to get from his result to a conclusion of the above kind requires a train of thought which is fuelled by much more than Gödel's result itself, and that a great deal of the excessive fuel should be utilized with an extra care. The usual way of interpreting Gödel's incompleteness result is as showing that there is a gap between truth and provability, i.e. that we can never prove everything that is true. However, this result is supposed to show that there are unprovable truths which we can know to be true. This, so the story goes, shows that we are more than machines that are restricted to acting as proof systems. Hence our minds are 'not mechanical'. In this paper I would like to indicate that this interpretation of Gödel goes far beyond what he really proved. I would like to show that to get from his result to a conclusion of the above kind requires a train of thought which is fuelled by much more than Gödel's result itself, and that a great deal of the excessive fuel should be utilized with an extra care. (en) Obvyklý způsob interpretace Gödelova výsledku ohledně neúplnosti je taková, že ukazuje, že mezi pravdivostí a dokazatelností zeje mezera, to jest že nikdy nemůžeme dokázat vše, co je pravdivé. O tomto výsledku se však má za to, že ukazuje, že existují nedokazatelné pravdy, o nichž můžeme vědět, že jsou to pravdy. A tohle údajně ukazuje, že my jsme více nežli stroje odsouzené k fungování jako důkazové systémy. Takže naše mysli 'nejsou mechanické'. V tomto článku bych chtěl naznačit, že tato interpretace Gödela daleko přesahuje to, co skutečně dokázal. Chtěl bych ukázat, že dostat se od jeho výsledků k uvedeným závěrům vyžaduje myšlenkové pochody předpokládající mnohem více než samotný Gödelův výsledek, a že k podstatné části z toho, co předpokládají navíc, bychom měli být velice rezervovaní. (cs)
Title	Gödel, Truth and Proof Gödel, Truth and Proof (en) Gödel, pravda a důkaz (cs)
skos:prefLabel	Gödel, Truth and Proof Gödel, Truth and Proof (en) Gödel, pravda a důkaz (cs)
skos:notation	RIV/67985955:_____/07:00308906!RIV08-AV0-67985955
http://linked.open.../vavai/riv/strany	1;10
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA401/04/0117), Z(AV0Z90090514)
http://linked.open...iv/cisloPeriodika	82
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Peregrin, Jaroslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Filosofický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	423518
http://linked.open...ai/riv/idVysledku	RIV/67985955:_____/07:00308906
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Gödel; incompleteness of arithmetic; proof vs. truth (en)
http://linked.open.../riv/klicoveSlovo	Gödel incompleteness of arithmetic proof vs. truth
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[1B248DF77FD8]
http://linked.open...i/riv/nazevZdroje	Journal of Physics, Conference Series
http://linked.open...in/vavai/riv/obor	AA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	LOGICA 2004-2006: a comprehensive project combining research, organisation and publication programmes in lpgic
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	-
http://linked.open...iv/tvurceVysledku	Peregrin, Jaroslav
http://linked.open...n/vavai/riv/zamer	Transdisciplinary research into selected key areas of philosophy and related disciplines, in particular, logic, classical and medieval studies, and the theory of science. Editions and publications of corresponding texts and electronic databases.
issn	1742-6596
number of pages	10 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Gödel, Truth and Proof Gödel, Truth and Proof Gödel, Truth and Proof

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 110 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software