Abstract
I discuss the problem of whether true contradictions of the form “x is P and not P” might be the expression of an implicit relativization to distinct respects of application of one and the same predicate P. Priest rightly claims that one should not mistake true contradictions for an expression of lexical ambiguity. However, he primarily targets cases of homophony for which lexical meanings do not overlap. There exist more subtle forms of equivocation, such as the relation of privative opposition singled out by Zwicky and Sadock in their study of ambiguity. I argue that this relation, which is basically a relation of general to more specific, underlies the logical form of true contradictions. The generalization appears to be that all true contradictions really mean “x is P in some respects/to some extent, but not in all respects/not to all extent”. I relate this to the strict-tolerant account of vague predicates and outline a variant of the account to cover one-dimensional and multidimensional predicates.
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Notes
- 1.
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Compare with Zwicky and Sadock’s minimal pair: “This dog is not a dog”, versus “*This parent is not a parent”.
- 3.
J. Zehr and I have empirical evidence indicating that polar contradictions of the form “x is P and ant(P)” (where ant(P) is the lexical antonym of P) are less accepted than syntactic contradictions of the form “x is P and not P”, but they are not systematically rejected. See Égré and Zehr (2018) for a brief mention of the finding, and Zehr (2014) for a discussion of antonymous adjectives.
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- 5.
On homogeneity and ways of characterizing the phenomenon, see Križ and Chemla (2015).
- 6.
I am assuming that each of the squares’ color in the alternating blue–red chessboard is clearly perceptible as such. Brentano in his writings considers that one might see a homogeneous purple out of inhomogeneous red and blue tiles if the tiles are small enough. This is not a relevant counterexample to the distinction I am drawing, since I am assuming the tiles to be big enough to the eye. See Massin and Hämmerli (2017) for a discussion of Brentano’s views on mixtures.
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See Fausto-Sterling (1993)’s typology, and her remarks about human intersex that “Although in theory it might be possible for a true hermaphrodite to become both father and mother to a child, in practice, the appropriate ducts and tubes are not configured so that egg and sperm can meet.” Let me add that intersex people who militate for the recognition of a third category distinct from “male” and “female” may possibly be displeased with the description “intersex people are male and not male”, and may prefer the description “intersex people are neither male nor not male”, because they might prefer a description of their status in terms of exclusion of polar opposites (“neither male nor female”) rather than a description in terms of the inclusion of both (“male and female”). If so, this preference could be explained along the pragmatic lines of Égré and Zehr (2018) to account for the overall preference for “neither”-descriptions over “and”-descriptions in relative gradable adjectives (that is by assuming that the default is to interpret “male” and “not male” in the strongest possible sense, see Alxatib and Pelletier 2011; Cobreros et al. 2015a). But this issue lies beyond the scope of the present paper. Incidentally, I note that hermaphrodites too are occasionally described in terms of a “neither”-description. A website on the internet even uses both types of descriptions with polar antonyms in the course of the same paragraph: “Snails are neither male nor female. They are hermaphrodites, which means they are both male and female at the same time”. http://www.educationquizzes.com/nature-matters/2017/04/facts-about-the-slow-paced-and-shelled-snail/.
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We need not suppose that the interval I is the same for every speaker. Similarly, the strict-tolerant account of vague predicates is not committed to the idea that strict and tolerant meaning is the same for all speakers.
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Multiple occurrences of the same predicate are not needed, in particular ellipsis is accommodated here: “x is and isn’t tall” can directly mean “x is (to some extent) and is not (to all extent) tall”, or “x is (to some extent) tall and is (to some extent) not tall”, depending on how negation is handled. This coheres with the discussion given by Ripley (2011b) of inconstant content versus inconstant character in relation to vagueness: “tall” on the present account maintains a constant character.
- 12.
Note that the meaning of the one-dimensional adjective “tall” can be subsumed under that definition. Note also that the above is my rendering of Sassoon’s approach, not literally her approach. I am assuming, in particular, that for all multidimensional predicates, an integration and projection along a single dimension of magnitude is operative. This does not mean that respects won’t need to be accessed separately in the semantics, but I leave a discussion of that aspect for another occasion. See Sassoon (2017) for more on respect accessing.
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See already (McGee 1990, 7–8) on the idea of treating “true” as a vague predicate. McGee, however, does not put emphasis on the gradability of “true” in support of that connection. Note that if “true” is gradable, it has all the features of an absolute gradable adjective, by some of the usual tests. In particular, one can say completely true/perfectly true, but not *completely tall/*perfectly tall (see Kennedy 2007; Burnett 2017). Furthermore, McGee explicitly denies that ““true” is a vague predicate like ordinary vague predicates”, because he sees “true” as overdetermined by conflicting rules, rather than underdetermined. But in my own understanding of ordinary vagueness, vagueness has at least as much to do with overdetermination as it has to do with undertermination.
- 15.
See Douven et al. (2013) for an outline of that view.
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Acknowledgements
I thank Can Başkent and Thomas Ferguson for their invitation and patience in awaiting this manuscript. I am particularly grateful to Olivier Massin, Galit Sassoon, Jeremy Zehr, and to two anonymous reviewers for detailed and helpful comments. Thanks also to Nick Asher, Heather Burnett, and Sam Alxatib for various exchanges, and to my accomplices Pablo, Dave, and Robert, for almost ten years thinking together about true contradictions. Thanks finally to Graham Priest for his inspiration and for enabling us to think so much more broadly and deeply about contradictions. This research was supported by the ANR program “Trivalence and Natural Language Meaning” (ANR-14-CE30-0010), and by the program FrontCog (ANR-17-EURE-0017).
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Égré, P. (2019). Respects for Contradictions. In: Başkent, C., Ferguson, T. (eds) Graham Priest on Dialetheism and Paraconsistency. Outstanding Contributions to Logic, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-25365-3_4
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