Max Black
(1909-1988)
In information philosophy, only a unique individual has exactly the same information as itself.
Max 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.
("The Identity of Indiscernibles," Mind, New Series, Vol. 61, No. 242 (Apr., 1952), pp. 153-164p.153-4)
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 Translation
In 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
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