The Sorites Paradox and Higher-Order Vagueness
Burgess (J.A.)
Source: Synthese, Vol. 85, No. 3 (Dec., 1990), pp. 417-474
Paper - Abstract

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Author’s Introduction

  1. One thousand stones, suitably arranged, might form a heap. If we remove a single stone from a heap of stones we still have a heap; at no point will the removal of just one stone make sufficient difference to transform a heap into something which is not a heap. But, if this is so, we still have a heap, even when we have removed the last stone composing our original structure.
  2. So runs the Sorites1 paradox. Similar paradoxes can be constructed with any predicate which, like 'heap', displays borderline vagueness. Although I have frequently heard it said that there is no completely credible and satisfying dissolution of the paradoxes of the Sorites2 family, and although there is no possible approach to dissolution which has not been at least partially explored, philosophers continue glibly to use vague language as though it were entirely unproblematic. Since no argument has ever been produced which would justify our ignoring the paradoxes, this situation is extremely unsatisfactory.
  3. Whilst I think that we are right to be dissatisfied with the currently available dissolutions of the paradoxes, the tendency to adopt this attitude whilst continuing uncritically to employ the paradox-prone expressions is widespread and greatly in need of explanation. Perhaps under the influence of G. E. Moore, some philosophers have surely thought that our familiar vague expressions must be coherent, so the paradox must be a sophism. There must be a dissolution lurking, and, furthermore, it must turn on simple and obvious considerations which are fully comprehensible to someone who is innocent of technical developments in semantics. These philosophers are bound to be disappointed. No problem survives for thousands of years which has a simple and obvious solution. Moorean intuitions, even if applicable, are not decisive. At most they indicate that there must be a dissolution; not that it must be simple and non-technical. So, one reason for dissatisfaction with current dissolutions is a desire for simplicity and philosophical innocence to which we have not been freely entitled since sceptics and nihilists first produced arguments to confound the would-be philosophical primitive.
  4. There is another more reputable reason for dissatisfaction with current dissolutions of the paradoxes. It might be thought that the technical ideas so far advanced treat only the symptoms and not the disease. I am partially in agreement with this reaction. All of the most promising approaches to the dissolution of the paradoxes adopt, in some form, or presuppose, in some form, the intuitive idea that vague concepts are bounded by border areas rather than borderlines. In this regard, my approach will be no exception. But this is only the barest, most austerely skeletal, framework for a dissolution.

Author’s Final Paragraph
  1. It is a question of considerable social and, perhaps, moral, importance, when a human being first comes into existence. It would be ludicrous to propose a democratic resolution of the differences between those who favour the period (not point, note) of conception and those who require a degree of brain development sufficient to support some (primitive) level of mental activity. But it is far from ludicrous to propose that minor differences between those who agree in accepting one of the above proposals might well best be resolved intersubjectively. For there might in fact be nothing objective on the basis of which to choose one boundary rather than another.
  2. This is always the case with neighbouring cases in convincing Sorites-series3, and reflecting on it gives rise to the paradox. Were there something objective really lurking in the background, in these cases, just waiting to be discovered, we should not really be bothered by Sorites4 paradoxes at all.
  3. I think that a refusal to face up to these considerations is the product of an irrational fear of recognising the, in my view, inescapable connection between intersubjectivity and the coherence of vague predicates. That there is such a connection is a view that I have been at pains to establish here quite generally, whilst contenting myself with exploring the connection in some detail, only for the special, but highly suggestive, case of the secondary qualities.

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