Re: The Difference between a Set and an Element

Chris Menzel wrote:
Paul Holbach wrote:

Gödel: "A plausible conjecture is: Every set is the extension of a concept."

It would take a *very* robust and fine-grained notion of "concept" for
that to be so, e.g., one on which there are infinite disjunctive
concepts whose disjuncts are of the form "being identical with A" for
arbitary objects A. I don't see any other way of justifying the claim
that, e.g., every arbitrary subset of N is the extension of a concept.

As far as arbitrary infinite collections are concerned, we would indeed
have to posit infinite disjunctive concepts.
But that's a matter of theoretical preference, isn't it?

Gödel's notion of concept is very robust:

"We don' t make concepts, they are there."
"Concepts have an objective existence."

[Kurt Gödel--quoted in: Wang, Hao (1996). /A logical journey: From
Gödel to philosophy/. Cambridge, MA: The MIT Press. (pp. 273+316)]

So why not let those infinite disjunctive concepts simply be there?
Isn't the unrestricted principle <for every set there is a concept
whose extension it is> worth it?

#PH

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