Adding a Conditional to Kripke’s Theory of Truth
Tóm tắt
Kripke’s theory of truth (Kripke, The Journal of Philosophy
72(19), 690–716; 1975) has been very successful but shows well-known expressive difficulties; recently, Field has proposed to overcome them by adding a new conditional connective to it. In Field’s theories, desirable conditional and truth-theoretic principles are validated that Kripke’s theory does not yield. Some authors, however, are dissatisfied with certain aspects of Field’s theories, in particular the high complexity. I analyze Field’s models and pin down some reasons for discontent with them, focusing on the meaning of the new conditional and on the status of the principles so successfully recovered. Subsequently, I develop a semantics that improves on Kripke’s theory following Field’s program of adding a conditional to it, using some inductive constructions that include Kripke’s one and feature a strong evaluation for conditionals. The new theory overcomes several problems of Kripke’s one and, although weaker than Field’s proposals, it avoids the difficulties that affect them; at the same time, the new theory turns out to be quite simple. Moreover, the new construction can be used to model various conceptions of what a conditional connective is, in ways that are precluded to both Kripke’s and Field’s theories.
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