โ Scribed by Donald Perlis
No coin nor oath required. For personal study only.
I am sympathetic to the work in paraconsistent logics that Priest describes, but I think it should be viewed more in the form of an interesting alternative rather than a definitive improvement on what has been done before. Here I respond partly in defense of my I position, but also partly in an attempt to assess the picture in terms of these two approaches that in some respects have much in common. I will present my comments in five pieces: general ideas about paradox and commonsense; metalanguage issues; an apparent disadvantage of paraconsistent logics; an apparent advantage of paraconsistent logics; and a related line of research. Throughout I use T as a truth predicate and L as a liar sentence: L is provably equivalent to the denial of its truth: (L iff 7 TL). I also take Fa as an abbreviation for T-~a.
The issue can be seen in terms of a choice between the T-scheme and excluded middle (T v F: every wff is either true or false) on the one hand, and ex contradictione quodlibet and what we might call excluded straddle 2 (not T & F: no wff can be both true and false) on the other. Both excluded middle and excluded straddle (as well as the T-scheme) are part of naive pre-paradoxical intuition. But together they produce a seemingly intolerable conflict. For in the 11 hasten to remind the reader that "my" approach was really started by Gilmore [5] and Kripke [8] and then pursued by Feferman [4] and myself [12]. Also, many of these matters have been hotly debated in the literature for the past several years, especially in the Journal of Philosophy and the Journal of Philosophical Logic, and a number of Priest's criticisms have been made before. See Martin [9], Reinhardt [14,15], and Goodman [7] for a glimpse of some positions.
2This terminology was suggested to me by Mark Fulk.
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