Lessons for Vagueness from Scrambled Sorites


Vagueness demands many boundaries. Each is permissible, in that a thinker may without error use it to distinguish objects, though none is mandatory. This is revealed by a thought experiment—scrambled sorites—in which objects from a sorites series are presented in a random order, and subjects are required to make their judgments without access to any previous objects or their judgments concerning them.

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  1. 1.

    Expressed more carefully: for some i, the ith object in the sorites series of objects is red, and the ith judgment in the soritical series of judgments is N.

  2. 2.

    Epistemicists will think there is exactly one such series, though we can never know which it is. This view has to be set aside in this paper, though it concurs with one main point: vagueness does not preclude sharp cuts.

  3. 3.

    See Kölbel (2003).

  4. 4.

    Lewis uses this example in various writings (1972, 1979). Kamp (1981: 245–6) illustrates the contextual dependence he has in mind by examples of cross-sentence anaphor.

  5. 5.

    In Roy Sorensen’s elegant formulation (2012): “Hans Kamp, the founder of contextualism, maintained that the extension of vague words orbits the speaker's store of conversational commitments”. The founding is best attributed to Kamp (1975).

  6. 6.

    As Geert Keil has pointed out (personal communication), much depends on exactly how the forced march is presented, and philosophers’ accounts are generally not very detailed. One possibility is that the subject is presented with the whole series of patches, and then asked to attend to the two leftmost ones, #1 and #2, then to #2 and #3, and so on. In such a case, one would expect some sort of anxiety to begin from the start, well before a borderline case has been reached. At another extreme, a subject might be presented with two adjacent panels, and asked to make a color judgment about each in turn. The panels will be arranged so as to make it clear that the panel most recently judged remains visibly the same when the next judgment is solicited: only the color in the other panel is changed. (Judgments relate alternately to left and right panels.) One could insert distracting elements, to help conceal the soritical nature of the arrangement. The crucial feature of forced marches remains: when making a judgment about patch #i, both it and the patch #i − 1 that has previously been judged are present to the subject, and the subject knows this, and knows what she has judged about #i − 1. In this setup, anxiety is likely to begin later, since the subject is not directly confronted with the soritical character of the experiment.

  7. 7.

    The example is suggested by one given by Williamson (1994: 217), though for a different purpose.

  8. 8.

    There are further contextual effects: tall for a child is different from tall for an adult, and nearby delivers different distances depending as foot travel or car travel is envisaged. These effects are not what scoreboard contextualism relies upon.

  9. 9.

    An alternative approach would be to retain an absolute conception of truth, and regard a nonmandatory ruling as effecting a local semantic change (thanks to Geert Keil for reminding me of this). Which approach to adopt is a substantive issue, beyond the scope of this paper.


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This paper emerged from a class given jointly with Hans Kamp at NASSLLI 2012. Many thanks to Hans for help and comments at every stage. We plan a joint paper on the various ways in which context relates to vagueness. I would also like to thank the following for valuable comments: audiences at NASSLLI 2012, at the LOGOS conference Departing from Sainsbury, Barcleona 2012, and the Editor of this volume.

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Sainsbury, M. Lessons for Vagueness from Scrambled Sorites. Int Ontology Metaphysics 14, 225–237 (2013). https://doi.org/10.1007/s12133-013-0123-4

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  • Vagueness
  • Sorites
  • Sharp boundaries
  • Forced march
  • Contextualism