David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Axiomathes 20 (2-3):347-355 (2010)
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.
|Keywords||Standard Non-standard Model Inconsistency|
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References found in this work BETA
Per Lindström (1999). Aspects of Incompleteness. Studia Logica 63 (3):438-439.
Andrzej Grzegorczyk (1974). An Outline of Mathematical Logic: Fundamental Results and Notions Explained with All Details. D. Reidel Pub. Co..
Richard Kaye (1991). Models of Peano Arithmetic. Clarendon Press.
Citations of this work BETA
Walter Carnielli (2011). The Single-Minded Pursuit of Consistency and its Weakness. Studia Logica 97 (1):81 - 100.
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