Abstract
This paper investigates relations between truth and consistency. The basic intuition is that truth implies consistency, but the reverse dependence fails. However, this simple account leads to some troubles, due to some metalogical results, in particular the Gödel-Malcev completeness theorem. Thus, a more advanced analysis is required. This is done by employing the concept of ω-consistency and ω-inconsistency. Both concepts motivate that the concept of the standard truth should be introduced as well. The results are illustrated by an interpretation of the well-known logical square and its generalization.
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References
Gaifman H (2003) Non-standard models in a broader perspective. In: Enayat A, Kossak R (eds) Nonstandard models of arithmetic and set theory. American Mathematical Society, Providence, pp 1–22
Grzegorczyk A (1974) An outline of mathematical logic. Fundamental results and notions explained in all details. Kluwer Academic Publishers, Dordrecht
Kaye R (1991) Models of Peano arithmetic. Clarendon Press, Oxford
Kossak R, Schmerl J (2006) The structure of models of Peano arithmetic. Clarendon Press, Oxford
Lindström P (2003) Aspects of incompleteness. A K Peters, Matick
Woleński J (1996) Logical squares: generalizations and interpretations. In: Childers T, Kolár P, Majer O (eds) Logica ‘95. Proceedings of the 9th international symposium. Praha, Filosofia, 1996, pp 67–75
Woleński J (1999) Semantic conception of truth as a philosophical theory. In: Peregrin J (ed) Truth and its nature (If Any). Kluwer Academic Publishers, Dordrecht
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Woleński, J. Truth and Consistency. Axiomathes 20, 347–355 (2010). https://doi.org/10.1007/s10516-010-9112-1
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DOI: https://doi.org/10.1007/s10516-010-9112-1