PROF. DANIEL NOLAN
(AUSTRALIAN NATIONAL UNIVERSITY)
Conditionals and Curry
Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. Once we have a sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that an independently motivated treatment of conditionals provides a philosophically satisfactory explanation of the status of Curry sentences. (Or to be less coy, the closest-worlds approach to counterpossible conditionals I prefer offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, to give the verdict that standard Curry conditionals are false, along with related "contraction conditionals".)
DR. MARK JAGO
(UNIVERSITY OF NOTTINGHAM)
Three Roads to the Impossible
I discuss three kinds of impossible content: the structured approach, the impossible worlds approach, and the state space approach. On the face of it, each approach seems very different to the others, with applications in different areas. But, once the approaches have been developed to avoid the objections they face, they start to look a lot more like one another. The question arises: are the three views notational variants of one another? Can one translate freely between the three approaches? In this talk, I’ll discuss and develop each of the three views on offer. I’ll indicate the options open to a defender of one of the views, and discuss why one might prefer one to the others. And I’ll discuss whether there are three genuinely distinct views on offer, or whether they should be thought of as variants on a theme.
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