Abstract
In J Philos Logic 34:155–192, 2005, Leitgeb provides a theory of truth which is based on a theory of semantic dependence. We argue here that the conceptual thrust of this approach provides us with the best way of dealing with semantic paradoxes in a manner that is acceptable to a classical logician. However, in investigating a problem that was raised at the end of J Philos Logic 34:155–192, 2005, we discover that something is missing from Leitgeb’s original definition. Moreover, we show that once the appropriate repairs have been made, the resultant definition is equivalent to a version of the supervaluation definition suggested in J Philos 72:690–716, 1975 and discussed in detail in J Symb Log 51(3):663–681, 1986. The upshot of this is a philosophical justification for the simple supervaluation approach and fresh insight into its workings.
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References
Belnap, N. (1982). Gupta’s rule of revision theory of truth. Journal of Philosophical Logic, 11, 103–116.
Burgess, J. P. (1986). The truth is never simple. The Journal of Symbolic Logic, 51(3), 663–681.
Cantini, A. (1990). A theory of truth arithmetically equivalent to \({ID}^1_1\). The Journal of Symbolic Logic, 55(1), 244–259.
Feferman, S. (1991). Reflecting on incompleteness. Journal of Symbolic Logic, 56(1), 1–49.
Field, H. (2008). Saving Truth from Paradox. Oxfoed: OUP.
Fitting,M. (1986). Notes on the mathematical aspects of Kripke’s theory of truth. Notre Dame Journal of Formal Logic, 27(1), 75–88.
Gupta, A., & Belnap, N. (1993). The revision theory of truth. Cambridge: MIT Press.
Hodges, W. (1997). A shorter model theory. Cambridge: CUP.
Kaye, R. (1991). Models of peano arithmetic. Oxford: Oxford University Press.
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.
Leitgeb, H. (2005). What truth depends on. The Journal of Philosophical Logic, 34, 155–192.
Leitgeb, H., & Welch, P. (2009). A theory of propositional functions and truth. unpublished manuscript.
Moschovakis, Y. (1974). Elementary induction on abstract structures. Mineola: Dover.
van Fraassen, B. C. (1971). Formal semantics and logic. New York: Macmillan.
Vugt, F., & Bonnay, D. (2009). What makes a sentence be about the world? towards a unified account of groundedness. Unpublished.
Welch, P. D. (2003). On revision operators. The Journal of Symbolic Logic, 68, 689–711.
Welch, P. (2009). Games for truth. Bulletin of Symbolic Logic, 15(4), 410–427.
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Meadows, T. Truth, Dependence and Supervaluation: Living with the Ghost. J Philos Logic 42, 221–240 (2013). https://doi.org/10.1007/s10992-011-9219-x
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DOI: https://doi.org/10.1007/s10992-011-9219-x