Abstract
The aim of this paper is to think through a raft of issues that the view known as ‘dialetheism’ raises. In particular, it is concerned with three inter-related questions: (1) Are the contradictions involved simply in our conceptual/linguistic representations, or are they in reality? And what exactly does this distinction amount to anyway? (2) Assuming that it is only in the former, can we get rid of them simply by changing these? (3) If we can, should we do so? The paper takes up these issues in the three parts of his paper. The journey takes us through a number of important issues in metaphysics, semantics, and epistemology.
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Much of the paper has been provoked by many years of enjoyable discussion with Diderik Batens—including his generous comments on some earlier drafts of this paper. I thank him for all of this. The paper was originally written for a conference in honour of his 60th birthday. The conference did not eventuate; but I’m delighted to dedicate the paper to him anyway. Diderik and I come at dialetheism from very different general perspectives. In particular, he gives much more importance to the role of context in semantics and epistemology than I do. See, e.g., Batens (1985, 1992) and Meheus and Batens (1996). Some of the matters I discuss here are difficult disengaged from these differences. I do my best.
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Quineans would, of course, reject the distinction being made here between semantic and worldly factors. This is not the place to defend the notion of analyticity. I do so in Priest (1979).
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The example comes from Priest (1987, 13.2).
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Take A(x) to be x∉x, and r to be {x: x∉x}. Then we have y ∈ r iff y∉y. Hence, r ∈ r iff r∉r, and so r ∈ r and r∉r.
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An example of a similar kind, which does have an explicit element of fiat, is that of the Secretaries’ Liberation League, given by Chihara in Chihara (1979).
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A number of people have taken me (mistakenly) to be committed to this kind of dialetheism. See Priest (1987, 20.6).
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The point is made in Priest (1987, 11.1).
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This isn’t quite right. Facts may not themselves be intrinsically negative: the relation between the facts that A and that ¬A must be intrinsic. But this does not change matters much: there must still be some kind of negativity in reality. There are other ways of making sense of the idea that the world itself is contradictory. For example, it may be held that reality is composed of properties, and that objects are bundles of properties. Then a contadictory world would be one in which there are property-bundles which contain the properties P and ¬P, for some P. Again, there must be some kind of negativity in reality. This time, negative properties.
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In situation semantics, states of affairs come with an internal “polarity bit”, 1 or 0. Facts with a 0 bit are negative. Alternatively, a positive fact may be a whole comprising objects and a positive property/relation; whilst a negative fact may be a whole comprising objects and a negative property/relation. For a fuller discussion of a dialetheic theory of facts, see Priest (2006, Chap. 2).
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This assumes that all truths correspond to facts. In principle, anyway, one could endorse a view to the effect that some kinds of sentence are true in virtue of the existence of corresponding facts, whilst others may have different kinds of truth-makers.
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Actually, I think that the change here is not so much a change of concepts as a change of the world. Arguably, the change of the law does not affect the meanings of ‘vote’, ‘right’, etc. The statement ‘Pat has the right to vote’ may simply change its truth value, in virtue of a change in the legal “facts”.
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Batens (1999, p. 267) suggests that a denial of this conjecture is the best way to understand a claim to the effect that the world is inconsistent. ‘[I]f one claims that the world is consistent, one can only intend to claim that, whatever the world looks like, there is a language L and a [correspondence] relation R such that the true description of the world as determined by L and R is consistent.’ He maintains an agnostic view on the matter. See also Batens (2002, p. 131).
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I note that Batens (2002, p. 131, fn. 7) suggests that a consistent replacement for an inconsistent language might well be required to have a non-denumerable number of constants, which would make it humanly unusable.
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Note that, if it is not, the same procedure can be used to get rid of truth value gaps.
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As a matter of fact, Diderik (an amateur beekeeper) tells me, this is false. Bees have a heart, but no kidneys.
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More generally, relations relevant to confirmation are well known not to be invariant under linguistic transformations. See, e.g., Miller (1974).
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A detailed discussion of all this can be found in Priest (1995).
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And can we? If one has such an ability, how can one lose it, short of some brain trauma?
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I change his notation to bring it into line with the rest of this essay.
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The text actually interchanges ‘second’ and ‘third’, but I take this to be a slip. The union of the first and third sets in Batens’ enumeration is characterised by P.
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Clarified by Batens in correspondence.
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The conditional (**) is not a logical truth; one can think of it as part of the theory of P. (Classical logic, in effect, promotes this contingent truth into a necessary (logical) one.) This is beside the point, though; what is at issue is whether triviality can be triggered in a paraconsistent context.
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The objection is given under the rubric ‘objections to dialetheism’. This is misleading, for he himself is a dialetheist. He holds that there are inconsistent concepts, and so dialetheias.
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One of these criteria may well be consistency. See Priest (2006, Part 3) for a full account of the details.
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Of course, in consistent contexts, a paraconsistent negation may behave indistinguisably from classical negation. That does not mean that it is classical negation that is being used.
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A number of people have suggested to me that tonk is perfectly meaningful. Its meaning is just defective. I have no objection to this if one can give a satisfactory account of defective meaning (which I don’t know how to do). The point is that, whatever one says about tonk, the same applies to Boolean negation.
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Batens’ own views about meaning depend heavily on his contextualism, and he would dispute my whole approach to meaning, but that is far too big an issue to take on here. In what follows, his objections may be taken to be ad hominem.
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There is, in fact, a small industry of people (not including Batens) who have attempted to produce arguments to this effect, based on “strengthened paradoxes”. The arguments are discussed and rejected in Priest (1987, 20.3).
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Versions of this paper, or parts of it, have been given under various titles at a number of philosophy departments and conferences over the last few years: the University of Melbourne, the University of Queensland, the Australasian Association of Philosophy (Australian National University), the University of Chapel Hill (North Carolina), the University of Connecticut, the Massachusetts Institute for Technology, Logic and Reality (Universities of Namur and Louvain la Neuve), the University of Gent, the City University of New York (Graduate Center), the Fourth Cambridge Graduate Conference on the Philosophy of Logic and Mathematics. I thank the participants for many lively discussions and helpful comments. Thanks for comments go also to two referees for the volume in which this essay appears.
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Priest, G. (2014). Contradictory Concepts. In: Weber, E., Wouters, D., Meheus, J. (eds) Logic, Reasoning, and Rationality. Logic, Argumentation & Reasoning, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9011-6_10
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