Gödelova věta a relace logického důsledku

• Authors: Zouhar Jaroslav

Title variants

EN

GOEDEL'S INCOMPLETENESS THEOREM AND THE RELATION OF LOGICAL CONSEQUENCE

• Languages of publication: CS

Abstracts

EN

In his proof of the first incompleteness theorem, Kurt Goedel provided a method of showing the truth of specific arithmetical statements on the condition that all the axioms of a certain formal theory of arithmetic are true. Furthermore, the statement whose truth is shown in this way cannot be proved in the theory in question. Thus it may seem that the relation of logical consequence is wider than the relation of derivability by a pre-defined set of rules. The aim of this paper is to explore under which assumptions the Goedelian statement can rightly be considered a logical consequence of the axioms of the theory in question. It is argued that this is the case only when the all the theorems of the theory in question are understood as statements of the same kind (and true in the same sense) as statements of arithmetic and statements about provability in the theory, and only if the language of the theory contains logical expressions allowing to include certain predicates of meta-language in the language of the theory.

Keywords

EN

AXIOMATIC THEORY; GOEDEL'S THEOREM; INCOMPLETENESS; LOGIC

Discipline

• PHILOSOPHY: PHILOSOPHY

• Publisher: Institute of Philosophy, Czech Academy of Sciences
• Journal: Teorie vědy (Theory of Science)
• Year: 2010
• Volume: 32
• Issue: 1
• Pages: 59-95
• Document type: ARTICLE

Contributors

author

Zouhar Jaroslav

• Jaroslav Zouhar, Filosoficka fakulta, Univerzita Karlova v Praze, Celetna 20, 116 42 Praha 2, Czech Republic

Identifiers

CEJSH db identifier

11CZAAAA094922