Yesterday's workshop on Semantic Paradox was enjoyable. Here is a nice photo of the workshop participants taken by Simon Prosser.
One of the many interesting questions that came up concerned "model-theoretic revenge" for approaches like Hartry Field's. I was interested by some of the stuff which appears around p. 23 of the written version of Field's paper. Here Field claims that his model theory 'plays at best a very indirect role in explaining truth. Rather, truth is directly explained by Schema (T), and model theory enters only in helping us understand more fully the logical connectives that occur in instances of Schema (T)'. Validity is not necessary truth-preservation, but is (co-extensive with) preservation of designation in all models. Apparent 'revenge' sentences of the form of:
(Q*) Q* is not designated in model M
(see p. 27) are supposed to be unproblematic precisely because designation in M is not truth but merely a model-relative notion, which means that Q* can consistently be either designated or undesignated in M.
I'm uneasy, but reasons why will have to wait till my next post, as I'm dashing off now to the Vagueness workshop ...