Keith’s Conundrums: Leibnizian Principles

Keith Douglas

Last time I provided 20 examples of sentences using “if” in ordinary language. Reader Alex had an unusual take on the Kennedy assassination item, which I will not comment further on as it is off my topic, which is the logic, semantics, and pragmatics of “if.” 

On that note, reader Steve tried to use some classical logic, like the equivalence of a certain “or” usage and a certain “if” usage. He also raises the question of subjunctive conditionals, which I drew attention to as well. Most philosophers who wind up studying them do seem to think that breaking them up into antecedent and consequent as Steve did is actually correct. I have never seen a good argument for this, given that it seems clear to me that they have no such items as ordinarily understood. His reluctance in item 13 is related: though “A would have been B” is arguably (standard) English, something like “Armstrong were a great Australian philosopher” is not. The technique of universalizing may work, but then one deals with the problem of “vacuous universals.” (Classical logic makes “All X are Y” true if there are no Xs.)

Leibnizian Principles

Two famous principles are attributed to Leibniz: that of a) the “identity of indiscernibles” and b) the “indiscernibility of identicals.” Modern glosses are:

1. For any X and Y, if X is identical to Y, X and Y have all the same properties.
2. For any X and Y, if X and Y have all the same properties, X and Y are identical.

A few notes: The “identity of indiscernibles” is often regarded as a tautology. Is it? The “indiscernibility of identicals” has sometimes been regarded as false. Why? Consider two spheres, of identical composition and size. Those have all their properties (right?) and yet there are two of them. How can they be one?

Thus, overall: Are these Leibnizian principles true?

HINT: What’s a property?

HINT 2: My “(right?)” might be important.

HINT 3: Why did the great physicist J-A Wheeler propose that there is only one electron?