Diagonal Arguments

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F17%3A00483331" target="_blank" >RIV/67985955:_____/17:00483331 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.14712/24647055.2017.14" target="_blank" >http://dx.doi.org/10.14712/24647055.2017.14</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14712/24647055.2017.14" target="_blank" >10.14712/24647055.2017.14</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Diagonal Arguments

Popis výsledku v původním jazyce

It is a trivial fact that if we have a square table filled with numbers, we can always form a column which is not yet contained in the table. Despite its apparent triviality, this fact can lead us the most of the path-breaking results of logic in the second half of the nineteenth and the first half of the twentieth century. We explain how this fact can be used to show that there are more sequences of natural numbers than there are natural numbers, that there are more real numbers than natural numbers and that every set has more subsets than elements (all results due to Cantor), we indicate how this fact can be seen as underlying the celebrated Russell’s paradox, and we show how it can be employed to expose the most fundamental result of mathematical logic of the twentieth century, Gödel’s incompleteness theorem. Finally, we show how this fact yields the unsolvability of the halting problem for Turing machines.

Název v anglickém jazyce

Diagonal Arguments

Popis výsledku anglicky

It is a trivial fact that if we have a square table filled with numbers, we can always form a column which is not yet contained in the table. Despite its apparent triviality, this fact can lead us the most of the path-breaking results of logic in the second half of the nineteenth and the first half of the twentieth century. We explain how this fact can be used to show that there are more sequences of natural numbers than there are natural numbers, that there are more real numbers than natural numbers and that every set has more subsets than elements (all results due to Cantor), we indicate how this fact can be seen as underlying the celebrated Russell’s paradox, and we show how it can be employed to expose the most fundamental result of mathematical logic of the twentieth century, Gödel’s incompleteness theorem. Finally, we show how this fact yields the unsolvability of the halting problem for Turing machines.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

<a href="/cs/project/GA17-15645S" target="_blank" >GA17-15645S: Logické modely usuzování a argumentace v přirozeném jazyce</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Acta Universitatis Carolinae. Philosophica et Historica

ISSN

0567-8293

e-ISSN

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Svazek periodika

—

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

20

Strana od-do

33-43

Kód UT WoS článku

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EID výsledku v databázi Scopus

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