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Published online by Cambridge University Press: 23 January 2009
A standard method for refuting a set of claims is to show that it implies a contradiction. Stephen Clark questions this method on the grounds that the Law of Non-Contradiction, together with the other fundamental laws of logic do not accord with everyday reality. He accounts for vagueness by suggesting that, for any vague predicate ‘F’, an ordinary object is typically to some extent both F and not-F, and that objects do not change abruptly from being F to being not-F. I challenge Clark's ‘deconstruction’ of logic, and show that, in characterizing vagueness and dealing with the associated Sorites paradox, we can accommodate his observation that change from being F to being not-F is ineradically continuous without tampering with any fundamental logical laws.
1 Here and subsequently, page references given in parentheses are to Clark, Stephen R.L., ‘Deconstructing the Laws of Logic’, Philosophy, 83 (2008), 25–53CrossRefGoogle Scholar.
2 One alternative formulation of the Sorites employs just the Principle of Mathematical Induction, another just the Law of Identity. These formulations, like the one cited in the text which features repeated applications of modus ponens, involve only fundamental logical principles.
3 An experiment with a series of colour patches is reported by Parikh, Rohit in ‘The Problem of Vague Predicates’, in Language, Logic and Method: Vol. 31 of Boston Studies in the Philosophy of Science, Cohen, R.S. and Wartofsky, M.W. (Eds.) (Dordrecht: Reidel, 1983), 241–261CrossRefGoogle Scholar. Felicia Ackermann has conducted another experiment demonstrating no precise borderline for ‘absolutely clearly middle aged’. She records reversals of judgment, where a subject backtracks, revising some judgments made earlier in the experiment. See her ‘A Vagueness Paradox and its Solution’, Midwest Studies in Philosophy, 14 (1989), 395–398.
4 I am grateful to Peter Cave for suggesting this comparison.
5 See Gold, Joshua and Shadlen, Michael, ‘Banburismus and the Brain: Decoding the Relationship between Sensory Stimuli, Decisions and Reward’, Neuron, 36 (2002), 299–308CrossRefGoogle ScholarPubMed.
6 See the experiments reported in Malkoc, G., Kay, P. and Webster, M.A., ‘Variations in Normal Color Vision. IV. Binary Hues and Hue Scaling’, Journal of the Optical Society of America A, 22 (2005), 2154–2168CrossRefGoogle ScholarPubMed.
7 An interesting difference between the pure blue and the red/orange cases is that individual experimental subjects are normally stable and reliable over time in their judgments of pure hues. See Hardin, C.L., Color for Philosophers (Indianapolis: Hackett, 1988), 169–170Google Scholar. Of course, individual subjects do not fluctuate wildly in their judgments of borderline colours.
8 Ackerman (1989), 397. For an independent argument for the conclusion that there is no fact of the matter as to whether to label as red rather than reddish orange an object about which there is irresoluble disagreement between competent observers as to its hue, see Hardin (1988), 186–187. Hardin comments, ‘To recognize that there is, in such a situation, no fact of the matter is to abandon neither realism nor hope of formulating semantic rules, but simply to realize that the nature of our purposes and the capabilities of our natures impose limits on the precision of our utterances’.
9 What a given individual rates as borderline can be verified by a standard 2AFC (Two Alternative Forced Choice) test. See, for example, Green, D. and Swets, J.A., Signal Detection Theory and Psychophysics (New York: Wiley, 1966)Google Scholar and, for a refinement, Katkov, M., Tsodyks, M. and Sagi, D., ‘Singularities in the Inverse Modeling of 2AFC Contrast Discrimination Data’, Vision Research, 46 (2006), 259–266CrossRefGoogle ScholarPubMed. Erratum, ibid p. 2157. For a useful discussion of colour boundaries, see Hardin (1988), 169–186.
10 Hanfling, Oswald ‘What is Wrong with Sorites Arguments?’, Analysis, 61 (2001), 29–35CrossRefGoogle Scholar.