1 Citing several unanticipated implications of sorites reasoning in the work of Derek Parfit, Goodenough observes that “[p]erhaps it is better to leave the sorites to the logicians after all.” See Goodenough, J. M.'s “Parfit and the Sorites Paradox,” Philosophical Studies, 83 (1994): 113–20.CrossRefGoogle Scholar

2 See Schwartz, Stephen P., “Why It Is Impossible to Be Moral,” American Philosophical Quarterly, 36 (1999): 351–60Google Scholar. Schwartz's version of the proof appeals to the vagueness of moral properties, but the argument can also be formulated with the assumption that moral predicates are vague. So, no metaphysical commitment to vague properties is necessary to the Impossibility Proof.

3 The principle of utility might constitute an exception to this claim. Suppose a simple version of the principle of utility is offered as a principle of justice rather than (or in addition to) a principle of beneficence. Simple utilitarian principles permit an unequal distribution of goods in the absence of morally relevant reasons in cases where the specific distribution of goods makes no difference to overall utility.

4 In personal communication, Schwartz has advanced various versions of the Impossibility Proof. The most serious problem the proof presents for moral reasoning is the rejection of PE or PDT.

5 One further clarification. The claim that B and A are morally indistinguishable, as it is used in the Impossibility Proof, is the metaphysical claim that there is no moral difference between B and A. It is not the weaker epistemic claim that we can discern no moral difference between B and A.

6 Let us underscore the difference between (i) and (iii) below. Given the vagueness of moral properties, propositions (i) and (ii) are consistent, but (iii) and (ii) are not.

(i) It is not false that A and B are morally indistinguishable.

(ii) It is not true that A and B are morally indistinguishable.

(iii) It is true that A and B are morally indistinguishable.

7 Colour properties offer good examples of vague properties and it might be useful to consider a non-moral example. Suppose the question were whether A and B differ with respect to colour (specifically the colour red). The proposition that A and B are indistinguishable with respect to colour might express the proposition that it is true that there is no colour difference between A and B. That is so just in case it is true that A is red and it is true that B is red. But suppose the colour of B falls in that part of the spectrum that is on the borderline between red and non-red. In this case it is not true that B is red, but it is also not false that B is red. We might still wish to say that A and B are indistinguishable with respect to colour. But we would then be expressing the prop- osition that it is not false that there is no colour difference between A and B. It is true that A is red and it is not false that B is red. If there were an aesthetic principle analogous to the Principle of Equality (which required that if A and B are the same in every aesthetically relevant respect, then A and B must be in the same aesthetic category), then the principle would properly apply to A and B only if it is true that A and B are the same in every aesthetically relevant respect (including colour).

8 Schwartz, “Why It Is Impossible to Be Moral,” pp. 353ff. He assumes in the proof that moral properties observe what he calls the” “non-transitivity of similarity.” This is the observation that moral properties are vague. But, as noted above, the entire discussion could be couched in terms of vague moral predicates instead.

9 This is equivalent to denying bivalence for “x is a person” which is a typical approach to the logic of vagueness. But there are differences in these logics worth noting. The “gap” view in the logic of vagueness states that there are some propositions that lack a truth-value—they are not true, false, or any other value. The degree approach includes (at least) three truth-values: True, False, and Indeterminate. The now discarded “glut” approach states that some propositions are both true and false—there is, in short, a glut of truth-values for some propositions. The glut approach is the result of confusing underdetermination with overdetermination and is a non-starter for those of us unprepared to countenance true contradictions. I also note that, as is generally required of vague predicates, there is also a higher-order vagueness for “being a person.” Between those beings that are in the range of neither persons nor non-persons and those beings that are in the range of persons there are countless beings concerning which it is neither true nor false that they are neither persons nor non-persons. Effectively it is undetermined whether it is undetermined whether they are persons.

10 I have argued elsewhere that the Principle of Equality and the Principle of Differential Treatment together entail that the relation “same moral treatment” is intransitive. See Michael J. Almeida and Mark H. Bernstein, “Is It Impossible to Relieve Suffering?” (Philosophic, forthcoming).

11 Schwartz makes the stronger claim that all moral properties are vague. See “Why It Is Impossible to Be Moral,” pp. 353ff.

12 Whatever is on the borderline of being a person is equally on the borderline of being a non-person. It is this symmetry that prevents us from including the borderline persons in the range of determinate non-persons and vice versa. See Keefe, R. and Smith, P., eds., Vagueness: A Reader (Cambridge: MIT Press, 1996), pp. 6ff.Google Scholar

13 It is a different question altogether whether the theoretical difference we are discussing makes a practical difference here. It is likely that persons and near-persons will—as a matter of practical convenience—be treated in the same way. But that practical point is consistent with the theoretical position that there is no moral requirement to treat persons and near-persons in precisely the same way.

14 In his “Vagueness, Truth, and Logic,” Kit Fine observed very early a similar mistake in reasoning with vague predicates: “Some have thought that a vague sentence is both true and false and that a vague predicate is both true and false of some object. However, this is part of the general confusion of under- and over-determinacy. A vague sentence can be made more precise; and this operation should preserve truth-value. But a vague sentence can be made either true or false and therefore the original sentence can be neither” (in Keefe and Smith, eds., Vagueness: A Reader, p. 121; my emphasis). The confusion of (3″) and (4″) with (3') and (4') is the result of assuming that “being a person” is both true and false of B.

15 See Parfit, Derek, Reasons and Persons (Oxford: Oxford University Press, 1984), esp. Part 3, chap. 11Google Scholar. For a compelling series of objections to Parfit's use of the sorites argument, see Goodenough's “Parfit and the Sorites Paradox,” pp. 113–20.

16 For examples of each of these responses, see Keefe and Smith, eds., Vagueness: A Reader.

17 Many thanks to Mark Bernstein, Stephen Schwartz, and two Dialogue referees for insightful discussion and comments.