HERBERT PAUL GRICE AND PETER CATHCART WASON ON THE HORSESHOE

Speranza

It has been suggested by Peter Cathcart Wason (Oxford-educated, etc.) that the truth table for the horseshoe ('if') is "defective". This defectiveness is provided a rough conceptual analysis by Wason: a table is defective iff the values of certain cells could be indeterminate (particularly the cells corresponding to a false antecedent in the truth table for the horseshoe) because an 'if' utterance is alleged to be 'irrelevant' under such circumstances.

This seems to be tantamount to proposing a determinate THREE-valued logic, alas, since there is no lack of specification here. The indeterminate cells are NOT awaiting a value. They already have one (viz., ‘indeterminate’, in the sense of, shall we say, irrelevant).

This point is particularly important, because the Wason's remark about the "defective truth table" of the horseshoe has been alleged to have certain pretty highly implausible implications, especially from a philosophical point of view!