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‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.Find out more about the Kindle Personal Document Service.And if you trawl through both of our papers, you may well find a speech act of denial which employs the worlds ‘indeterminate’ (for Field) or ‘false only’ (for me).
Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate.
In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, , §§21–23) and argue that it does not offer a way out of the revenge problem.
Thanks also go to JC Beall and Stephen Read for written comments on an earlier draft.
Especial thanks go to Hartry Field himself for extended email discussions on a number of matters dealt with here – and for many other fun discussions over the years and bottles of wine.
However, I will argue that this distinction does not provide an acceptable ground to distinguish between genuine and non-genuine semantic notions, and thus it does not offer a way out of the revenge problem.
More generally, I will argue that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should ultimately be abandoned.
Such paradoxes often make use of notions employed in the theories they are directed against, and are argued to be similar to the ‘standard’ semantic paradoxes, such as the Liar and Curry’s paradox (see e.g.
Field Revenge arguments are typically used to conclude that revenge-prone theories do not solve the semantic paradoxes in general: even though they avoid the ‘standard’ semantic paradoxes, they suffer from new, structurally similar antinomies, that can only be avoided at the cost of significant expressive limitations. The inexpressibility of the model-theoretical notion of ‘determinateness’ provides an example of an MT-revenge paradox.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your To give just two examples from the first couple of pages of the book: ‘None of this seems terribly attractive’ (7), ‘which I find very hard to get my head around’ (10–11). Brady's proof uses a double recursion of the same kind employed by Field.
All page and section references are to Field's book, unless otherwise specified. As far as I know, Brady was the first person to show that it was possible to apply persistence methods of this kind to non-monotonic connectives. Since Field takes the ground model to contain the standard model of arithmetic, of course it is not axiomatizable.