By Patrick Hughes

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Extra resources for Vicious Circles and Infinity: A Panoply of Paradoxes

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We are stuck with a cut-off that we cannot accept. And forget the fact that we can give a linguistic description of what goes on in the game. e. a player following the standards of ideal rationality) ought to leave on the table’. 3 But of course this is not the main story. At bottom, the problem is not one of language. It is one of rationality tout court. 4 A pigeon is trained via a regime of reward and punishment to peck to the right on the presentation of red stimuli, and to the left for other (clearly distinct) colors.

This does not necessarily require classical logic. 12 But constructing such proofs is not at all a routine matter. 13 5. Conclusion The issues that I have raised in the last part of the paper all need to be addressed to make the solution to the Sorites that I have suggested fully articulated. Some of these are distinctly non-trivial. For this reason, I do not claim that the solution I have suggested is right. It does, however, seem to me to be one that is both plausible and worthy of further investigation.

And, again, the supervaluationist idea is that truth is super-truth. Since, by hypothesis, Pa is not super-true, it is not correct to assert it—or so argue these supervaluationists. Similarly, those inclined toward a fuzzy approach claim that if a is a borderline case of P, then Pa is less than completely true. Since, strictly speaking, one should assert only full truths, these theorists hold that in strict circumstances, it is not correct to assert Pa, in agreement with our supervaluationists.

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