FOM: misunderstandings?

Fred Richman richman at
Mon Jun 5 16:54:25 EDT 2000

Cristian Cocos wrote:

> As for the reasons of his [David Lewis] aversion to the membership
> relation, I am still not very clear... I have never considered it
> problematic, nor have I come across mathematicians that do.

Mathematicians don't find anything problematic.

It seems to me that the membership relation, like the equality
relation, may be problematic because it is thought of without a
context. Contrast this with the relation a < b in the real numbers. We
have to add the phrase "in the real numbers" to supply a context.
Nobody is going to ask whether some real number is less than some
abelian group, so the relation is limited in scope. 

That does not seem to be the typical attitude toward the membership
relation or the equality relation, at least among set theorists.
Presumably we can ask of any object whether or not it is a real
number. I don't think a mathematician would do that, outside a context
like the complex numbers. *A* membership relation applies between
elements of a set and subsets of that set. That seems unproblematic to
me. But *the* membership relation is a bit mysterious.


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