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Notes
The main chapters of When Truth Gives Out speak interchangeably of ‘denial’ and ‘rejection’, but the latter also features as a term for a third sui generis form of speech act in Appendix 1. I’ll frame the discussion to follow in terms of ‘rejection’ reserving ‘denial’—I’ll usually say: “proper denial”—for a form of illocution of P appropriate when P is false in the same way and to just the extent that the assertion of P is appropriate when P is true.
pp. 49–50—(all page references to When Truth Gives Out unless otherwise stated).
Where falsity is truth of negation.
Wright (2003) and elsewhere.
This characterisation will need qualification to encompass the ‘glutty’ conception of borderline cases embraced by dialetheic conceptions of vagueness. On such views, the material characteristics of a borderline case are such as to exclude both the truth simpliciter and the falsity simpliciter of the relevant predication. We needn’t worry here about the question whether the dialetheist can coherently say what truth/falsity simpliciter is.
I have argued this in some detail elsewhere; see especially Wright (2007) and (2010).
I do not know if the attribution can be supported by direct quotation. But Frege does most explicitly see its pervasive vagueness as a deficit of natural language that it is to be remedied, in a language ‘fit for scientific purposes’, by a practice of total definition wherever possible. However I anticipate.
For further discussion of the distress of the Fregean conception around higher-order vagueness, see Wright (2010). Let me stress that, as explained in that paper, there is no commitment, in lodging the criticisms to follow, to an endorsement of the reality of higher-order vagueness, as it is normally understood.
—Because, Dear Reader, these second-order cases are closer to the nearer polar verdict, F, than are the first-order borderline cases of the F–G distinction, and there was already mandate to reject the verdict G as applied to the latter.
—Since the appropriateness of the first two rejections is what characterises the first-order borderline cases, and second-order borderline cases ought to be cases where the claim of first-order borderline status should be rejected.
The example doesn’t actually make my point as nicely as possible, since the distinction between bald and non-bald men is more like that between red and blue than between red and purple (or red and reddish purple).
There is no explicit attention to the Curry Paradox in Richard’s book. I’ll say a little more about this omission in a moment.
Others who have made recent play with a notion of rejection in this context include Beall (2009), Field (2008), and Priest (2006). A very useful discussion of many of the issues is Restall, in progress. It is doubtful, though, that all these authors have the same notion of rejection in mind. Actually, there are two different questions in play in recent philosophy of logic. One is whether denial—that is, proper denial: the statement of how things are not—should be explained (is mastered via grasp of) a primary notion of assertion and the operator of negation. That it should not is the central contention in e.g. Rumfitt (2000). The other is whether we should recognise a mode of illocutionary repudiation, as it were, contrasting with both assertion and proper denial (if they are distinct): one that involves no claim of falsity. Richard’s willingness to allow that both lack of truth-value and falsity mandate rejection, in his sense, presumably represents either contest or confusion of this distinction.
Page 4.
—unless they are both! But Richard reserves no space for consideration of a dialetheic response to the paradoxes.
—indeed without commitment to asserting anything about the alethic status of L (since any true such assertion will presumably be inconsistent with the truth of L, and hence sufficient for ‘L is not true’).
I am not sure why Richard takes it that the ‘unforced’ conditional of English is a material conditional. But I do not think that anything hangs on this for present purposes.
Richard’s introduction and explanation of force-embedding connectives is central to his discussion of expressivism, and is one of the most important and interesting ideas developed in the book. Constraints of space prevent me from discussing it here, but I hope to do so on another occasion.
Cf. p. 56.
Or “S is F(Bad)”, ‘F’ some open second-order sentence.
—without moreover any employment of the T-schema, or other rules for truth, though as the reader will find if he formulates the following paradoxical reasoning rigorously, analogous principles feature for the ‘release’ and ‘capture’ of acceptable.
See pp. 163–164.
Thanks to Jc Beall, Aaron Cotnoir and Hartry Field for comments on an earlier draft. Unfortunately the time ran out when more of their helpful observations might have helped me improve the discussion.
References
Beall, Jc. (2009). Spandrels of truth. Oxford: Oxford University Press.
Field, H. (2008). Saving truth from paradox. Oxford: Oxford University Press.
Priest, G. (2006). In contradiction. Oxford: Oxford University Press.
Restall, G. (2006). In progress, assertion, denial, accepting, rejecting, symmetry, paradox and all that. http://consequently.org/papers/assertiondenialparadox.pdf
Rumfitt, I. (2000). “Yes” and “no”. Mind, 109(436), 781–823.
Wright, C. (2001). On being in a quandary: Relativism, vagueness, logical revisionism. Mind, CX, 45–98; reprinted in The Philosopher’s Annual, volume 24 (2001).
Wright, C. (2003). Vagueness: A fifth column approach. In J. C. Beall & M. Glanzberg (Eds.), Liars & heaps: New essays on paradox. Oxford: Oxford University press.
Wright, C. (2007). Wang’s paradox. In R. Auxier & L. Hahn (Eds.), The philosophy of Michael Dummett: the library of living philosophers (Vol. XXXI). Open Court: Chicago and La Salle.
Wright, C. (2010). The illusion of higher-order vagueness. In R. Dietz & S. Morruzzi (Eds.), Cuts and clouds. Oxford: Oxford University Press.
Wright, C. (forthcoming). On the characterisation of borderline cases. In G. Ostertag (Ed.), Meanings and other things: essays on Stephen Schiffer. Cambridge: MIT press.
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Wright, C. The pain of rejection, the sweetness of revenge. Philos Stud 160, 465–476 (2012). https://doi.org/10.1007/s11098-011-9794-2
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DOI: https://doi.org/10.1007/s11098-011-9794-2