Curry’s paradox, Lukasiewicz, and Field


Συγγραφέας: Peter Smith


Peter Smith: Curry’s paradox, Lukasiewicz, and Field (pdf, 9 pages)
In approaching Ch. 4 of Saving Truth from Paradox, it might be helpful first to revisit Curry’s original paper, and to revisit Lukasiewicz too, to provide more of the scenesetting that Field doesn’t himself fill in. So in §1 I’ll say something about Curry, in §2 we’ll look at what Lukasiewicz was up to in his original three-valued logic, and in §3 we’ll look at the move from a three-valued to a many-valued Lukasiewicz logic. In §4, I move on to announce a pair of theorems which kill off any prospect of using a Lukasiewicz logic as a general setting for taming paradoxes. In the light of this, we can regard Field’s chapter as an effort to rescue something from the wreckage. So in §5 we take an outline look at what Field thinks can be rescued, highlight his main result, and wonder very briefly indeed about its significance. It shouldn’t need saying that these remarks are not supposed to be a rounded critical appraisal of Field’s chapter! They were originally written very speedily as a short introductory presentation for a seminar – a spur to further discussion, not a final verdict. And to keep the length of the introduction under control, I in particular don’t here discuss Field’s ‘determinately’ operator.