In saying “A is the same as B” or “A is identical with B” must we always add a “sortal” or modifier: “the same F as” or “relative to F,” where F is a property? When we say that A = B, we need not necessarily know what A and B are — what their essence is. John Perry argues that “the role of the general term [F] is to identify the referents — not to identify the ‘kind of identity asserted’.” (Metaphysics: An Anthology, 92) The kind of identity means identity relative to something, such as F.
Let’s look at some examples. Consider the following list of words:
A. Bull
B. Bull
C. Cow
There are three “tokens” here of two “types.” Peter Geach, whom Perry criticizes, argues that “there are not two kinds of objects to be counted, but two different ways of counting the same object. And the reason there are two ways of counting the objects is that there are two different ‘criteria of relative identity’.” (93) So it seems that we can claim that
(1) A is the same word type as B, but A and B are different word tokens.
In addition, it is uninformative to say that A is the same as B simpliciter. Perry replies that “If ‘A’ and ‘B’ refer to the same objects throughout (1), the first conjunct of (1) is not an identity statement, and the counterexample fails. If both conjuncts are identity statements in the required sense, ‘A’ and ‘B’ must refer to word types in the first conjunct and word tokens in the second, and the counterexample fails.” (94) In other words, if A and B are taken to refer to tokens, then with respect to their type A is not numerically identical with B, but rather both share a property, “being of the same type” or “being equiform.”
And this will be our pattern. Having all their properties in common is at least a necessary condition for some two objects to be numerically one (or for two names to refer to the same object). (For a defense of insufficiency of this criterion see Max Black’s paper “The Identity of Indiscernibles,” 66) Now if A is identical with B, then for any property F that A has we can say, if we care to, that A is the same F as B. But if there exists a property which A has and B doesn’t or vice versa, then the two objects are guaranteed not to be the same, and so it may be valuable to find out which properties they do share. In this case we are justified in saying “A is the same F as B but not the same G as B.”
Geach’s worry is that we might conclude that A is identical with B prematurely. As we learn more about these things our “ideology” may well change and so may our judgment of identity between A and B, if, e.g., we discover new properties not shared by A and B. But identity relative to any particular property will never be challenged by new information. So, we would be well advised not to make rush decisions and speak only of kinds of identity rather than identity as such. It is an odd argument, to be sure. And I think it can be countered by saying that it is useful to take a risk and act with the belief that A and B are identical, if all evidence points to it. We may have to revise this claim as time goes by, but we can’t escape the imperative to make such judgments, more or less contingent though they may be.
Another example: let there be “a certain set of predicables that are true of men but do not discriminate between two men of the same surname. If the ideology of a theory T is restricted to such predicables, the ontology of T calls into being a universe of androids… who differ from men in just this respect, that two different ones cannot share the same surname. I call these androids surmen…” (96) Then two people, A and B, can be the same surman yet different men. Well, “being the same surman” can be cashed out as “having the same surname,” again sharing one property and failing to share another, “being the same man.” Thus our A and B are not numerically identical. It is not meaningless or dangerous or in any way improper to say so.
Continuing in this manner,
Suppose Smith offered Jones $5,000 for a clay statue of George Washington. Jones delivers a statue of Warren Harding he has since molded from the same clay, and demands payment, saying, “This is the same thing you bought last week.”
It is the same piece of clay, but a different statue. It seems that we can form the awkward but true conjunction “This is the same piece of clay as the one you bought last week, but this is a different statue from the one you bought last week.” (97)
The statue is form-in-matter or informed matter. We can look at it in its aspect of its material cause or in its aspect of its formal cause. The former is the same; the latter is different. So the two objects, the future and as yet unmade statue Smith bought and the actual statue that was delivered are not identical. They share a property of “having the same matter” or “being made of the same clay,” but they are different in the value of the property “what the statue is” or “of whom the statue is.” Similarly, suppose both the formal and material causes of the statue are the same, but Smith wanted it to be made by Jones, a famous sculptor, himself, whereas Jones had one of his apprentices make it. We see that the efficient cause is different, and therefore the statue ordered and the statue received are, once again, not identical. Lastly, let all three of the foregoing causes be the same; except that Smith intended to re-sell the statue at a profit but found out a few days after making his purchase that he could not do so. Now the final causes are different, and so are the statue’s temporal stages. (Update: in the last case Smith considered the statue to be equivalent to, via exchange of property titles, some amount of money, but events proved him wrong. Is it a change in the statue or in Smith or in what?)
Finally, let A and B be in genus G, though A is species S1, and B is species S2 within that genus. It will be correct to say that A and B are the same genus but different species. But again, it can be asserted that A is not the same as B, because they don’t share all of their properties.
As a consequence of A’s being identical with B, for any F that A has, A is the same F as B, and B is the same F as A. But “A is the same as B” asserts more than merely the convergence of all their properties, both known and unknown, as pointed out also by Black. It is a stronger statement, and for that reason it is true that we should be cautious in asserting it. But assert it we surely can. My final point is that our counterexamples are fairly contrived. If A and B are the same apple, penny, poem, etc., then we can safely conclude that they are identical simply.