[FOM] iterative conception/cumulative hierarchy

Nik Weaver nweaver at math.wustl.edu
Mon Mar 5 11:47:32 EST 2012

d_obrien wrote:

> A so called  "naive" idea that "sets are extensions of concepts and
> every concept has an extension" is entirely bogus

Maybe you just don't understand it?

What I am getting out of this thread is how invested people are in
quasi-physical ideas about sets: sets are "formed" in stages, or as
you put it, "every plurality can be unified in a totality".  Of course
these images are incompatible with the idea of sets as atemporal abstract
objects (how exactly does one go about unifying a plurality?), so we have
to say that language like this is merely a colorful metaphor for some
abstract static notion of metaphysical dependence.  But this suggestion
doesn't pan out.  It turns out that all of the work is being done by
aspects of the iterative conception that get lost in translation.

So much effort is put into legitimizing talk of "abstract objects" as if
having such things would be an unqualified good.  The harm is that thinking
about sets as abstract objects invites us to speak, nonsensically, about
"forming" and "unifying" them as if they were physical objects.

Concepts do not have to be understood as metaphysical entities.  We are
really just talking about language, specifically, predicates.  When we
decide not to distinguish between two predicates that are tautologically
equivalent, we are talking about concepts.  If we go further and decide
not to distinguish between concepts that are intersubstitutable (can
replace each other without affecting truth values) we are talking about
extensions.  There's no magic about "forming" anything.


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