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Relativism and Classical Logic

Published online by Cambridge University Press:  12 April 2010

Crispin Wright
St Andrews and Columbia Universities


Let me begin with a reminder of the crude but intuitive distinction from which the relativistic impulse springs. Any of the following claims would be likely to find both supporters and dissenters:

That snails are delicious

That cockroaches are disgusting

That marital infidelity is alright provided nobody gets hurt

That a Pacific sunset trumps any Impressionist canvas

and perhaps

That Philosophy is pointless if it is not widely intelligible

That the belief that there is life elsewhere in the universe is justified

That death is nothing to fear

Disputes about such claims may or may not involve quite strongly held convictions and attitudes. Sometimes they may be tractable disputes: there may be some other matter about which one of the disputing parties is mistaken or ignorant, where such a mistake or ignorance can perhaps be easily remedied, with the result of a change of heart about the original claim; or there may be a type of experience of which one of the disputing parties is innocent, and such that the effect of initiation into that experience is, once again, a change of view.

Copyright © The Royal Institute of Philosophy and the contributors 2002

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1 See especially Williamson (1992) and (1994) and Sorensen (1988).

2 I shall capitalize—‘Epistemicist’, ‘Epistemicism’, etc.—whenever referring to views which, like those of Sorensen and Williamson, combine a conception of vagueness as, broadly, a matter of ignorance with the retention of classical logic and its associated Bivalent metaphysics.

3 Experience shows that Epistemicists incline to protest at this. Suppose ‘tall’, say, as a predicate of human beings, applies to an individual just if they are precisely 5'11“ tall or more—that 5' 11“ tall or more is the property denoted by the vague, “tall”, as actually used. Then why, in saying that an individual is tall, should I be regarded as understanding what I have said to any lesser an extent than when, in circumstances where I do not know the identity of the culprit, I say that whoever broke the clock had better own up? Why should ignorance of what, in fact, I am talking about be described as an imperfection of understanding?

Although it is not my purpose here to develop criticisms of the Epistemic conception, I'll take a moment to try to justify the charge. The foregoing protest assumes that the epistemicist is entitled to regard us as knowing what type of sharply bounded property an understood vague expression denotes, and as ignorant only of which property of that type its use ascribes. I know of no justification for that assumption. What type of sharply bounded property does ‘red’ denote? Something physical? Or a manifest but sharply bounded segment of the ‘colour wheel’? Or something else again? On what basis might one decide? And if the understanding of some common-or-garden vague expressions gives rise to no favoured intuitive type of candidate for their putative bounded denotations, why should we favour the obvious candidates in cases—like ‘tall’— where there are such?

Intuitively, to understand e.g. a simple, subject-predicate sentence is to know what object is being talked about and what property is being ascribed to it. To be sure, the purport of that platitude should not be taken to require that one invariably has an identifying knowledge of the former: I can fully understand an utterance of ‘Smith's murderer is insane’ without knowing who the murderer is. But it is different with predication. Here what is demanded of one who understands is, at least in the overwhelming majority of cases, that they know—in a sense parallel to the possession of identifying knowledge of the referent of a singular term—what property the use of a particular predicate ascribes. Since the overwhelming majority of natural language predicates are vague, that is what the Epistemicist denies us. It would be no good for her to reply: ‘But you do know what property ‘red’ denotes—it is the property of being red!’. On the Epistemic account, I know neither which property that is, nor what type of property it is, nor even—in contrast to, say, my understanding of ‘… has Alex’s favourite property' where while ignorant in both ways, I at least know what a property has to do in order to fit the bill—what would make it true that a particular property was indeed ascribed by the normal predicative use of ‘red’. It is the last point that clinches the observation in the text; if you were comparably ignorant in all three respects about the content of a definite description—thus ignorant, in particular, of what condition its bearer, if any, would have to meet—it would be absolutely proper to describe you as failing fully to understand it.

4 Harman has been, of course, a long-standing champion of the idea. The most recent extended defence of his views is inHarman, Gilbert and Jarvis Thomson, JudithMoral Relativism and Moral Objectivity (Oxford: Basil Blackwell, 1996)Google Scholar, Part One. For a many-handed discussion, seeHarman, Thomson and others ‘Book Symposium on Harman and Thomson‘, Philosophy and Phenomenological Research LVIII, 1998, pp. 161213CrossRefGoogle Scholar.

5 Blackburn, Simon, Spreading the Word (Oxford: Clarendon Press, 1984)Google Scholar, Ch. 6: ‘Evaluations, Projections and Quasi-realism’, still remains the best introduction to his view, but the most recent official incarnation is Blackburn, Simon, Ruling Passions (Oxford: Clarendon Press, 1998)Google Scholar; Gibbard's, Alan ideas are developed systematically in his magisterial Wise Choices, Apt Feelings (Cambridge, Mass: Harvard University Press, 1990)Google Scholar.

6 For exposition and development of some of the basic difficulties, see Hale, Bob, ‘The Compleat Projectivist’, The Philosophical Quarterly 36, 1986. pp. 6584CrossRefGoogle Scholar; ‘Can there be a logic of attitudes?’ in John, Haldane and Crispin, Wright (eds), Reality, Representation and Projection (Oxford: Oxford University Press, 1992), pp. 337–63; and ‘Can arboreal knotwork help Blackburn out of Frege's abyss?’ Forthcoming in a Philosophy and Phenomenological Research book symposium on Blackburn's (1988).Google Scholar

7 Wright (1992).

8 A fuller list might include

: the transparency of truth—that to assert is to present as true and, more generally, that any attitude to a proposition is an attitude to its truth— that to believe, doubt or fear, for example, that P is to believe, doubt or fear that P is true. (Transparency)

: the opacity of truth—incorporating a variety of weaker and stronger principles: that a thinker may be so situated that a particular truth is beyond her ken, that some truths may never be known, that some truths may be unknowable in principle, etc. (Opacity)

: the conservation of truth-aptitude under embedding: aptitude for truth is preserved under a variety of operations—in particular, truth-apt propositions have negations, conjunctions, disjunctions, etc. which are likewise truth-apt. (Embedding)

: the Correspondence Platitude—for a proposition to be true is for it to correspond to reality, accurately reflect how matters stand, ‘tell it like it is’, etc. (Correspondence)

: the contrast of truth with justification—a proposition may be true without being justified, and vice-versa. (Contrast)

: the timelessness of truth—if a proposition is ever true, then it always is, so that whatever may, at any particular time, be truly asserted may—perhaps by appropriate transformations of mood, or tense—be truly asserted at any time. (Timelessness)

: that truth is absolute—there is, strictly, no such thing as a proposition's being more or less true; propositions are completely true if true at all. (Absoluteness)

The list might be enlarged, and some of these principles may anyway seem controversial. Moreover it can be argued that the Equivalence Schema underlies not merely the first of the platitudes listed—Transparency—but the Correspondence and Contrast Platitudes as well. For elaboration of this claim, see Wright (1992) pp. 24–7. For further discussion of the minimalist conception, and adjacent issues, see Wright (1998).

9 A partial development of them is offered in Wright (1992) Chs. 1–2.

10 Wright (1992), p. 144.

11 It may be rejoined (and was, by Mark Sainsbury, in correspondence) that we could accept the Simple Deduction without commitment to the stark bivalence espoused by the Epistemic Conception if we are prepared to allow that A‘s and B’s respective opinions may indeed both reflect cognitive shortcoming where P's truth-status is borderline—on the ground that, in such circumstances, both ought to be agnostic about P. The point is fair, as far as it goes, against the preceding paragraph in the text. However I believe—and this will be a central plank of the discussion to follow—that it is a profound mistake to regard positive or negative verdicts about borderline cases as eo ipso defective. If that were right, a borderline case of P should simply rank as a special kind of case in which—because things are other than P says—it's negation ought to hold. In any case the Simple Deduction will run no less effectively if what B accepts is not ‘Not- P’ when understood narrowly, as holding only in some types of case where P fails to hold, but rather as holding in all kinds of case where things are not as described by P—all kinds of ways in which P can fail of truth, including being borderline (if, contra my remark above, that is how being borderline is conceived). So even if Bivalence is rejected, the Simple Deduction still seems to commit us to the more general principle Dummett once called Determinacy: that P always has a determinate truthstatus— of which Truth and Falsity may be only two among more than two possibilities—and that at least one of any pair of conflicting opinions about P must involve a mistake about this status, whatever it is. That is still absolutely in keeping with the realist spirit of the Epistemic Conception, to which it still appears—at least in spirit—the Simple Deduction commits us if unchallenged.

12 This point was first observed inShapiro, Stewart and Taschek, William, ‘Intuitionism, Pluralism and Cognitive Command,’ Journal of Philosophy 93, 1996, pp. 7488Google Scholar.

13 See footnote 3 above,

14 One substitution instance, of course, is:

Not-P → it is feasible to know that not-P,

15 To forestall confusion, let me quickly address the quite natural thought that, where EC applies, cognitive command should be assured— since any difference, of opinion will concern a knowable matter—and hence that any reason to doubt cognitive command for a given discourse should raise a doubt about EC too. This, if correct, would certainly augur badly for any attempt to locate disputes of inclination within discourses where cognitive command failed but EC held! But it is not correct. What the holding of EC for a discourse ensures is, just as stated, that each of the conditionals

P → it is feasible to know that P

Not-P → it is feasible to know that not-P,

is good for each proposition P expressible in that discourse. That would ensure that any difference of opinion about P would concern a knowable matter, and hence involve cognitive shortcoming, only if in any such dispute it would have to be determinate that one of P or not-P would hold. But of course it is of the essence of (true) relativism to reject precisely that—(and to do so for reasons unconnected with any vagueness in the proposition that P.)

16 The modality involved in feasible knowledge is to be understood, of course, as constrained by the distribution of truth values in the actual world. The proposition that, as I write this, I am in Australia is one which it is merely (logically or conceptually) possible to know—the possible world in question is one in which the proposition in question is true, and someone is appropriately placed to recognise its being so. By contrast, the range of what it is feasible for us to know goes no further than what is actually the case: we are talking about those propositions whose actual truth could be recognised by the implementation of some humanly feasible process. (Of course there are further parameters: recognisable when? where? under what if any sort of idealisation of our actual powers? etc. But these are not relevant to present concerns.)

17 To stress: it is not merely Truth and Objectivity's implicit proposal about relativism that is put in jeopardy by the EC-Deduction. According to the project of that book, cognitive command is a significant watershed but is assured for all discourses where epistemic constraint fails and realism, in Dummett's sense, is the appropriate view. Thus it appears that if the EC-Deduction were to succeed, cognitive command would hold universally and thus fail to mark a realism-relevant crux at all.

18 I draw here on a suggestion of Patrick Greenough.

19 There will be no cause to question the converse conditional, which is needed for the derivation of the uncontroversial T ¬ P → ¬ TP.

20 Only ‘approximates’. Intuitionistically, we have no a priori reason to suppose that there is a fact of the matter to which Goldbach's conjecture answers. But pure arithmetic is plausibly a region of discourse exhibiting cognitive command nonetheless, so not one fit for relativism according to the present proposal. (A dispute about Goldbach's conjecture will involve one form of cognitive shortcoming—prejudice—if it occurs in the absence of any purported proof; and if there is a purported proof, the dispute will involve ignorance if the proof is good, or error if it is not.)

21 This paper presents a self-contained and somewhat elaborated treatment of one strand from my larger On being in a Quandary: Relativism, Vagueness, Logical Revisionism,’ Mind CX, 2001, pp. 4598Google Scholar. I am grateful to John Broome, Patrick Greenough, Richard Heck, Fraser MacBride, Sven Rosenkranz, Mark Sainsbury, Joe Salerno, Stephen Schiffer, and Tim Williamson for valuable comments and discussion. The research for the paper has been conducted during my tenure of a Leverhulme Research Professorship; I gratefully acknowledge the support of the Leverhulme Trust.

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