LOGICAL TRUTH AND TRUTH-VALUE GAPS

Elementary microphysical statements can be neither true nor false without violating the classical codification of statement logic. The existence of such a possibility depends upon a revision in the standard explication of logical truth, a revision more harmonious with the idea of argument validity as merely truth-preserving. The revision in question, in turn, depends upon Bas van Fraassen's investigations into the semantical foundations of positive free logic, a species of logical system whose philosophical significance was first made plain in Henry Leonard's pioneering study of 1956, ‘The Logic of Existence’.

Students who steadfastly refuse to accept an argument as valid unless all of the component statements are in fact true frustrate teachers of logic. “Now look!” the teacher may heatedly emphasize, “the validity of an argument has to do with its form alone. So to say that an argument is valid is to say only that if its premises were true its conclusion would also be true!” But, then, not only is the argument from the pair of false statements

and

to the false statement

valid, but so is the argument from the pair of (allegedly) truth-valueless statements

and

to the (allegedly) truth-valueless statement