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Undecidability without Arithmetization.
- Source :
- Studia Logica; Mar2005, Vol. 79 Issue 2, p163-230, 68p
- Publication Year :
- 2005
-
Abstract
- Abstract In the present paper the well-known Gdels Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICS
FUNCTIONAL analysis
MATHEMATICAL analysis
MATHEMATICAL functions
Subjects
Details
- Language :
- English
- ISSN :
- 00393215
- Volume :
- 79
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Studia Logica
- Publication Type :
- Academic Journal
- Accession number :
- 18425642
- Full Text :
- https://doi.org/10.1007/s11225-005-2976-1