- Despite the varied authors and approaches the articles of this group build up to a considerable measure of agreement:
- The principle of the identity of indiscernibles1 is philosophically uninteresting unless it is taken as necessary.
- Two reasonably correct statements of the principle are as follows:
- If two objects are numerically different there is at least one property possessed by one of them that is not possessed by the other.
- There cannot be mere numerical difference without qualitative difference (i.e., difference in some quality, property, or relation.)
- Unless certain relational properties, e.g. identity and difference, are excluded by a suitable restriction the principle becomes trivially true.
- A suitable restriction is provided by the requirement that nothing is to count as a property unless it can be specified in general descriptive terms without the use of any references to individuals.
- If this qualification is put in it seems to be possible to conceive of consistent universes in which the principle is contingently false, e.g.,
- a radially symmetric universe,
- a universe entirely composed of an infinite series of qualitatively identical sounds.
- In such universes it is impossible to distinguish the qualitatively identical things in purely predicative terms.
- The above principle, namely (6), is itself trivial.
- Even in a universe such as one described in (5), it would be possible to distinguish qualitatively identical items by non-descriptive individual reference expressions such as "This" and "That."
- Noteworthy additions or departures from this general agreement are the following:
- Bergmann distrusts appeals to what can and cannot be conceived, and holds that an adequate explication of 'analytic' can be given which would show the principle of the identity of indiscernibles2 to be analytic.
- Ayer fears that the denial of the necessity of the principle rests on adherence to a belief in "bare" substances, and hence, though he finds no answer to Black's symmetrical universes, he is inclined to cling to the identity of indiscernibles3.
- Wilson suggests an alternative to the restriction listed in (4) above, viz., Properties such as bearing R to Smith, and bearing R to Smith2, though numerically distinct are qualitatively identical.
- O'Connor urges that the issues involved cannot be settled without developing a fairly full metaphysics, in- cluding satisfactory answers to the problems about the nature of space, time, proper- ties, relations, etc.
- Rescher prefers to state the principle in terms of linguistic reference adequacy. But living natural languages, he agrees, can always be extended, presumably by adding a suitable individual referring expression, so that they are referentially adequate and can thus pick out any object in the intended domain of reference.
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