Max BlackMax Black was an analytic language philosopher who worked with Peter Geach to translate the philosophical writings of Gottlob Frege. Both Geach and Black were taken by the question of what constitutes identity. Black wrote a somewhat cryptic dialogue between A and B, perhaps ironically questioning whether A can ever be said to be identical with any B? They cannot, because A always has the property of being A, of being itself, which can never be true of B, while being B. They can, however, be identical with respect to their intrinsic internal information, which neglects the extrinsic properties This requires ignoring the object’s position in space and time, which is the only remaining distinction between the two spheres in Black’s construct of identical spheres in otherwise empty space.
A. The principle of the Identity of Indiscernibles seems to me obviously true. And I don't see how we are going to define identity or establish the connexion between mathematics and logic without using it. B. It seems to me obviously false. And your troubles as a mathematical logician are beside the point. If the principle is false you have no right to use it. A. You simply say it's false - and even if you said so three times that wouldn't make it so. B. Well, you haven't done anything more yourself than assert the principle to be true. As Bradley once said, "assertion can demand no more than counter-assertion; and what is affirmed on the one side, we on the other can simply deny ". A. How will this do for an argument? If two things, a and b, are given, the first has the property of being identical with a. Now b cannot have this property, for else b would be a, and we should have only one thing, not two as assumed. Hence a has at least one property, which b does not have, that is to say the property of being identical with a. B. This is a roundabout way of saying nothing, for "a has the property of being identical with a" means no more than "a is a" When you begin to say " a is . . . " I am supposed to know what thing you are referring to as 'a' and I expect to be told something about that thing. But when you end the sentence with the words " . . . is a " I am left still waiting. The sentence "a is a" is a useless tautology. A. Are you as scornful about difference as about identity? For a also has, and b does not have, the property of being different from b. This is a second property that the one thing has but not the other. B. All you are saying is that b is different from a. I think the form of words "a is different from b" does have the advantage over "a is a" that it might be used to give information. I might learn from hearing it used that 'a' and 'b' were applied to different things. But this is not what you want to say, since you are trying to use the names, not mention them. When I already know what 'a' and 'b' stand for, "a is different from b" tells me nothing. It, too, is a useless tautology.Black's paper was titled The Identity of Indiscernibles, taken from Leibniz's Law, which also has a converse or contrapositive as the Indiscernibility of Identicals. The Indiscernibility of Identicals can be described as "for every x and for every y, if x is identical to y, then every property F that is possessed by x is also possessed by y, and every property F that is possessed by y is also possessed by x" or in symbolic logic, (x)(y) [x=y → (F)(Fx ↔ Fy)]. Note that given two truly identical things, by definition there can be no discernible differences between them. The Indiscernibility of Identicals may be simply an ideal concept, unrealizable for two distinct material objects. Black's version (the identity of indiscernibles) may be described as "for every x and for every y, if every property F that is possessed by x is also possessed by y, and every property F that is possessed by y is also possessed by x, then x is identical to y." Again, in symbolic logic terms, (x)(y) [(F )(Fx ↔ Fy) → x=y]. Black's basic argument is if two things were identical, then they would be only one thing, and not two. This is correct in information philosophy. Only a unique individual has exactly the same information as itself. If we say a is identical to b, Black says that we are using two different names to refer to the same thing. (Cf., the "Hesperus is Phosphorus" example from Frege) If a and b are merely two different names for the same thing, then when we say that "a is identical to b," we are merely saying that "a is a," which is a tautology. According to Black, the idea is trivial that "If there is no difference between a and b, then they are the same." Black imagines a universe consisting of just two things, two exactly similar perfect spheres. These two spheres could share the same properties and still not be the same, (because they have different dispositional properties, they are in two different places) challenging the identity of indiscernibles. What we have in Black's simple case of two similar spheres is what Peter Geach and David Wiggins call "relative identity."
Frege TranslationIn 1948, Black translated the classic Frege work "Sinn und Bedeutung" as "Sense and Reference," thus establishing the term "reference," where John Stuart Mill and Bertrand Russell had used "denotation." Denotation and connotation nicely fit the difference between naming and meaning. Black also mistranslated Gleichheit ("Sameness") as "Identity." Frege said in a footnote that he was using Gleichheit "in the sense of Identität, but Black changed the footnote, saying Frege used the word "strictly," adding to the confusion. See our bilingual version of Sinn und Bedeutung