'Leibniz's Law': A Useless Expression

Pedant and quibbler that I am, it annoys me when I hear professional philosophers use the phrase 'Leibniz's Law.'  My reason is that it is used by said philosophers in three mutually incompatible ways.  That makes it a junk phrase, a wastebasket expression, one to be avoided.  Some use it as Dale Tuggy does, here, to refer to the Indiscernibility of Identicals, a principle than which no more luminous can be conceived.  (Roughly, if a = b, then whatever is true of a is true of b, and vice versa.)  Fred Sommers, referencing Benson Mates, also uses it in this way.  (See The Logic of Natural Language,  p. 127)

Others, such as the distinguished Australian philosopher Peter Forrest, use it to refer to the Identity of Indiscernibles, a principle rather less luminous to the intellect and, in my humble opinion, false.  (Roughly, if whatever is true of a is true of b and vice versa, then a = b.)  And there are those who use it as to refer to the conjunction  of the Indiscernibility of Identicals and the Identity of Indiscernibles.

So 'Leibniz's Law' has no standardly accepted usage and is insofar forth useless.  And unnecessary.  You mean 'Indiscernibility of Identicals'?  Then say that.  If you mean its converse, say that. Ditto for their conjunction.

There is also the problem of using a great philosopher's name to label a principle that the philosopher may not even have held.  Analytic philosophers are notorious for being lousy historians.  Not all of them, of course, but the run-of-the-mill.  If Sommers is right, Leibniz was a traditional logician who did not think of identity as a relation as Frege and Russell do.  (p. 127) Accordingly, 'a = b' as this formula is understood in modern predicate logic does not occur in Leibniz.

 

Comments

[Mister Wolf]

Professor,

I must admit, I'm quite new to the philosophizing game(I only had one course through the philosophy department during my undergrad and that was basically a survey of eastern philosophy) but, concerning the "Identity of Indiscernibles", I would like to know why you consider it false.

If I were to venture a guess, I would assume that one variable could in fact be a subset of the other. Therefore making every quality in variable "a" also a qualities in variable "b". However, "b" can have far more qualities not present in "a" and therefore, they're not equal.

I could be quite off though, hence the comment.

[Bill Vallicella]

Very briefly, since my post is not about the Identity of Indiscernibles, but about phil. terminology:

The principle says, roughly, that if a and b share all properties, then a = b. If intended as a necessary truth, then to refute it all I need is one merely possible counterexample. Well, is it not possible that there be just two iron spheres that share all relational and nonrelational properties?

[Mister Wolf]

I would say so Professor. Hence uniform ball bearings that we find in a number of machines.

I'm also sorry for the tangent. I simply did not want to error in my understanding(being the beginner that I am).

[Dale]

Hi Bill,

Good points, all.

But here's another: 3 syllables vs. 12 syllables.

Accuracy be damned!

:-)

[Bill Vallicella]

Hi Dale,

Sorry to use you as an example, but I did like your post!

Coming to Tucson this summer?

[Dale]

No problem, friend.

No - can't come out this summer. Hoping to visit the inlaws around Christmas time. Will surely email you if that happens. Really enjoyed hanging out with ya'll.