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- Title
On Reliability of the Meta-Mathematical Notions Defined by Gödel's Coding Method.
- Authors
Siavashi, Ehsan
- Abstract
It has been taken for granted that Gödel's coding method is a reliable method for defining meta-mathematical notions in every extension of Robinson Arithmetic (Q). However, it could be shown that some formulas defined by the method and interpreted as provability predicate, unprovability predicate or consistency sentence, fail to satisfy some requirements. For example, it is known that some extensions of Robinson Arithmetic prove their own canonical inconsistency sentences, while they are actually consistent. A common response to this problem is that those theories are unsound, and wrong theories might prove wrong things such as their own inconsistency. However, the paper will argue why such responses are not totally convincing. At the end, the paper suggests a reading of the first and the second incompleteness theorems which is free from such interpretations.
- Subjects
METAMATHEMATICS; GODEL'S theorem; MATHEMATICAL logic; DEFINABILITY theory (Mathematical logic); CODING theory; ARITHMETIC
- Publication
Teorema, 2016, Vol 35, Issue 1, p5
- ISSN
0210-1602
- Publication type
Article