Information Transfer and Thermodynamics Point of View on Goedel Proof
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F18%3A43913131" target="_blank" >RIV/60461373:22340/18:43913131 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.5772/intechopen.68809" target="_blank" >http://dx.doi.org/10.5772/intechopen.68809</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5772/intechopen.68809" target="_blank" >10.5772/intechopen.68809</a>
Alternative languages
Result language
angličtina
Original language name
Information Transfer and Thermodynamics Point of View on Goedel Proof
Original language description
Formula of an arithmetic theory based on Peano Arithmetics (including it) is a chain of symbols of its super-language (in which the theory is formulated). Such a chain is both in convenience with the syntax of the super-language and with the inferential rules of the theory (Modus Ponens, Generalization). Syntactic rules constructing formulas of the theory are not its inferential rules. Although the super-language syntax is defined recursively - by the recursive writing of mathematical-logical claims - only those recursively written super-language's chains which formulate mathematical-logical claims about finite sets of individua of the theory, computable totally (thus recursive) and always true are the formulas of the theory. Formulas of the theory are not those claims which are true as for the individua of the theory, but not inferable within the theory (Great Fermat's Theorem). They are provable but within another theory (with both Peano and further axioms). Also the chains expressing methodological claims, even being written recursively (Goedel Undecidable Formula) are not parts of the theory. The same applies to their negations. We show the Goedel substitution function is not the total one and thus is not recursive. It is not defined for the Goedel Undecidable Formula's construction. For this case, the structure of which is visible clearly, we are adding the zero value. This correction is based on information, thermodynamic and computing considerations, simplifies the Goedel original proof and is valid for the consistent arithmetic theories directly.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Ontology in Information Science
ISBN
978-953-51-5354-2
Number of pages of the result
22
Pages from-to
279-300
Number of pages of the book
310
Publisher name
InTech
Place of publication
Rijeka
UT code for WoS chapter
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