Goedel and Caratheodory Theorems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F17%3A43913129" target="_blank" >RIV/60461373:22340/17:43913129 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.researchgate.net/publication/319618405_Goedel_and_Caratheodory_Theorems" target="_blank" >https://www.researchgate.net/publication/319618405_Goedel_and_Caratheodory_Theorems</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Goedel and Caratheodory Theorems

Popis výsledku v původním jazyce

We show that the Caratheodory I. and II. theorems and his formulation the II. Law of Thermodynamics are physically analogous with the real sense of the Goedel?s wording of his I. and II. incompleteness theorems. By using physical terms the Caratheodory theorems express the properties of the Peano Aritmetic inferential process (and even properties of any deductive and recursively axiomatic inference at all); as such they set physical and then the logical limits of any real inference (of the sound, not paradoxical thinking) which can run only on a physical/thermodynamic basis. Then the real/physical sense of the Goedel?s wording of his incompleteness theorems, just having been expressed in the form of the Caratheodory theorems and their common formulation as the II. Law of Thermodynamics, is in the very base of the physics. Then it is obvious that the Caratheodory&apos;s formulations about the adiabatic changes, having been compared with, or translated into, the formulations of the Goedel&apos;s proof, represent the first historical and clear statement of gnoseological limitations of the deductive and recursively axiomatic inference and sound thinking at all. And that the very real sense of the Goedel incompleteness theorems is the metaarithmetic-logical analog of the II. Law of Thermodynamics.

Název v anglickém jazyce

Goedel and Caratheodory Theorems

Popis výsledku anglicky

We show that the Caratheodory I. and II. theorems and his formulation the II. Law of Thermodynamics are physically analogous with the real sense of the Goedel?s wording of his I. and II. incompleteness theorems. By using physical terms the Caratheodory theorems express the properties of the Peano Aritmetic inferential process (and even properties of any deductive and recursively axiomatic inference at all); as such they set physical and then the logical limits of any real inference (of the sound, not paradoxical thinking) which can run only on a physical/thermodynamic basis. Then the real/physical sense of the Goedel?s wording of his incompleteness theorems, just having been expressed in the form of the Caratheodory theorems and their common formulation as the II. Law of Thermodynamics, is in the very base of the physics. Then it is obvious that the Caratheodory&apos;s formulations about the adiabatic changes, having been compared with, or translated into, the formulations of the Goedel&apos;s proof, represent the first historical and clear statement of gnoseological limitations of the deductive and recursively axiomatic inference and sound thinking at all. And that the very real sense of the Goedel incompleteness theorems is the metaarithmetic-logical analog of the II. Law of Thermodynamics.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

IIAS-Transactions on System Research and Cybernetics

ISSN

1609-8625

e-ISSN

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Svazek periodika

15

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

11

Strana od-do

1-10

Kód UT WoS článku

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EID výsledku v databázi Scopus

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