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The Vagueness of Knowledge

Published online by Cambridge University Press:  01 January 2020

Roy A. Sorensen
New York University, New York, NY 10003, U.S.A.


Epistemologists have profited from studies of the ways in which ‘know’ is ambiguous. We can also profit by studying the ways in which ‘know’ is vague. After classifying sources of vagueness for ‘know,’ I spend the second section examining theories of vagueness. With the exception of the theory that vague predicates are incoherent, which I try to refute, we need not take a stand on a particular theory to show that the vagueness of knowledge has substantive epistemological implications. The third section supports the thesis through a survey of ways in which appeals to vagueness can be applied to the field's issues. First, I show how higher order vagueness is evidence against the KK thesis, the incorrigibility of sense data, and the completability of epistemology. An interesting resemblance between infinity and vagueness provides the point of departure for the next type of application. For this resemblance suggests a new way of handling apparently infinite belief structures. The approach is illustrated with an analysis of common knowledge. The third type of application concerns the ways in which disguised sorites creep into our thinking about knowledge. In addition to brief illustrations concerning naive holism, question begging, and an objection to incorrigibilism, I provide more detailed illustrations involving Jonathan Adler's sceptical appeal to epistemic universalizability, the prediction paradox, and William Lycan's objection to Gilbert Harman's social knowledge cases. I conclude with some general remarks on the lessons to be learned from the vagueness of knowledge.

Research Article
Copyright © The Authors 1987

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1 This paper has benefited from the comments and criticisms of two anonymous referees.

2 Stephen Stich discusses this position in ‘Do Animals Have Beliefs?,’ Australasian Journal of Philosophy (1979) 15-28; quot. from 19.

3 Edmund Gettier presented his counterexamples in ‘Is Justified True Belief Knowledge?,’ Analysis 23 (1963) 121-3.

4 This point was made in Saunders, John Turk and Champawat's, NarayanMr. Clark's Definition of “Knowledge”Analysis 24, 6 (June 1964), 8–9CrossRefGoogle Scholar. They are also responsible for the example of the scientist.

5 Ginet presents this example in his ‘Knowing Less by Knowing More,’ in Midwest Studies in Philosophy 5 (Minneapolis, MN: University of Minnesota Press 1980) 151-61.

6 Lehrer, Keith Knowledge (Oxford: Clarendon Press, 1974) 61–2Google Scholar

7 Radford, Colin“Analysing” “Know(s) That,”Philosophical Quarterly 20 (1970) 222–9CrossRefGoogle Scholar; quot. from 228-9.

8 Lehrer, Keith Knowledge, 67Google Scholar

9 Unger and Wheeler endorse this position in a number of articles. Representative are Unger's ‘There are no Ordinary Things,’ Synthese 41 (1979) 117-54, and Wheeler's ‘On That Which is Not’ (same issue) 253-72.

10 I present the details of this criticism in ‘An Argument for the Vagueness of “Vague,”’ Analysis 45 (1985) 134-7. I also argue that the paradoxes of vagueness cannot be avoided by restricting logic to nonvague terms.

11 An excellent example of the supervaluationist's approach can be found in Kit Fine's ‘Vagueness, Truth, and Logic,’ Synthese 30 (1975) 265-300.

12 The many-valued approach to vagueness originates with Zadeh's, L.A.Fuzzy Sets,’ Information and Control 8 (1965) 338–53CrossRefGoogle Scholar. It seems to have attracted the allegiance of a plurality of the commentators on the sorites paradox. Well developed versions of this position are presented in Sanford's, DavidBorderline Logic,’ American Philosophical Quarterly 18 (1981) 175–84Google Scholar, and Machina's, KentonTruth, Belief and Vagueness,’ Journal of Philosophical Logic 5 (1976) 47–78CrossRefGoogle Scholar.

13 James Cargile was the first to defend the epistemic approach in ‘The Sorites Paradox,’ The British Journal for the Philosophy of Science 20 (1969) 193-202. Other proponents of the view include Richmond Campbell and Isreal Scheffler.

14 Jackson, FrankIs There a Good Argument against the Incorrigibility Thesis?,’ Australasian Journal of Philosophy 51 (1973) 51–62;CrossRefGoogle Scholar quot. from 60.

15 As far as I know, David Sanford provided the first analysis of this resemblance in his excellent piece ‘Infinity and Vagueness,’ The Philosophical Review 84 (1975) 520-35.

16 For a discussion of infinite belief structures in epistemic logic see Hintikka's, Knowledge and Belief (Ithaca: Cornell University Press 1962);Google Scholar for convention, see David Lewis’ appeal to common knowledge in Convention (Cambridge: Harvard University Press 1969); the threat of infinite regress for intentions is discussed by Harman, Gilbert in ‘Practical Reasoning,’ Review of Metaphysics 24 (1976) 431–63Google Scholar. The way infinite belief structures seem to arise for communication is well known from H.P. Grice's theory of meaning. For a perceptual case, see Radford's, ColinReport on Analysis “Problem” No. 19,’ Analysis 43 (1983) 113–15CrossRefGoogle Scholar. For sexual perversion, see Nagel's, ThomasSexual Perversion,’ Journal of Philosophy 66 (1969) 5–17CrossRefGoogle Scholar.

17 Stephen Schiffer appears sympathetic to this position on pp. 31-2 of Meaning (Oxford: Oxford University Press 1972). However, on pp. 34-5 he also seems to support the view that the infinite knowledge is merely potential.

18 Radford, discusses the affair in ‘Knowing and Telling,’ Philosophical Review 78 (1968) 326–36CrossRefGoogle Scholar.

19 See his ‘Utterer's Meaning and Intentions,’ Philosophical Review 78 (1969) 147-77.

20 Heal makes this point on p. 125 of her ‘Common Knowledge,’ Philosophical Quarterly 28 (1978) 116-31.

21 Lewis, David Convention (Cambridge: Harvard University Press 1969) 56Google Scholar

22 Ibid., 56-7

23 Heal, JanCommon Knowledge,’ 128 83117Google Scholar

24 Harman suggests this analysis on pp. 172-4 of ‘Reasoning and Evidence one does not Possess,’ Midwest Studies in Philosophy 5(Minneapolis, MN: University of Minnesota Press 1980) 163-82.

25 For more about these knower paradoxes see Tymoczko's, ThomasAn Unsolved Problem about Knowledge,’ Philosophical Quarterly 34 (1984) 41–52CrossRefGoogle Scholar.

26 The concept of an excluder term is Hall's, Roland as explained in ‘Excluders,’ Analysis 20 (1959) 1–7CrossRefGoogle Scholar.

27 The argument just given is a generalized version of a point made by William G. Lycan and George F. Schumm in an unpublished manuscript ‘A Theory of Question-Begging.’ They observe that the principle’ Any argument trivially equivalent to a question-begging argument is itself question-begging’ can serve as the induction step of a sorites and hence must be restricted.

28 Armstrong, D.M.Is Introspective Knowledge Incorrigible?,’ Philosophical Review 62 (1963) 417–432CrossRefGoogle Scholar; quot. from 420

29 Adler's, Scepticism and Universalizability’ appeared in Journal of Philosophy 77, 3 (March 1981) 143–56CrossRefGoogle Scholar.

30 Ibid., 144-5

31 By ‘justification’ Adler means ‘justification sufficient for knowledge.’ The explanation of ‘defeated’ is: ‘If p justifies q, then the justification is defeated if there is some truth d such that p & d fail to justify q.’ Both of these technical terms are used for convenience. Adler's argument is compatible with alternate terminologies.

32 Ibid., 149

33 Ibid., 155-6

34 Shaw's seminal contribution appeared in ‘The Paradox of the Unexpected Examination,’ Mind 67 (1958) 382-4.

35 I adopt this approach in ‘Conditional Blindspots and the Knowledge Squeeze: A Solution to the Prediction Paradox,’ Australasian Journal of Philosophy 62 (1984) 126-35.

36 Harman presents these cases in Thought (Princeton: Princeton University Press 1973).

37 Lycan, WilliamEvidence One Does Not Possess,’ Australasian Journal of Philosophy 55 (1977) 114–26CrossRefGoogle Scholar; quot. from 119

38 Ibid., 121

39 Ibid.

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