David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 49 (1):87 - 104 (1990)
Three views on definite descriptions are summarized and discussed, including that of P. F. Strawson in which reference failure results in lack of truth value. When reference failure is allowed, a problem arises concerning Universal Instantiation. Van Fraassen solves the problem by the use of supervaluations, preserving as well such theorems as a=a, and Fa or ~Fa, even when the term a fails to refer. In the present paper a form of relevant, quasi-analytic implication is set out which allows reference failure to infect even a=a and Fa or ~Fa with lack of truth-value. Reference failure causes lack of truth-value in a subwff to spread throughout any wff built up by the classical connectives. As a result none of the classical first-order axiom schemes remain as axiom schemes in the system presented.
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References found in this work BETA
W. V. Quine (1953/1980). From a Logical Point of View. Harvard University Press.
Ludwig Wittgenstein (1922/1999). Tractatus Logico-Philosophicus. Dover Publications.
P. F. Strawson (1952). Introduction to Logical Theory. New York, Wiley.
P. F. Strawson (1950). On Referring. Mind 59 (235):320-344.
Bas C. van Fraassen (1966). Singular Terms, Truth-Value Gaps, and Free Logic. Journal of Philosophy 63 (17):481-495.
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