Re: The Difference between a Set and an Element

On Wed, 17 Jan 2007 19:15:28 +0000 (UTC), Chris Menzel
<cmenzel@xxxxxxxxxxxxxxxxxxxx> wrote:


I can see a philosophical role for concepts of some sort, but I can't
imagine what it buys you to have a disjunctive concept
correspondingly uniquely to every set beyond a lot of metaphysical
bloat. But then again, I'm not very imaginative.

Indeed, the universe of concepts becomes "bloated" thereby. This is
already a consequence of Frege's comprehension principle for concepts
[EFAx(Fx <-> phi(x))], which G. Frege uses in his proof

I don't usually think of comprehension as having any implications for
the existence of concepts at all (though of course they played a role in
Frege's own views); the existential quantifier there is ranging over
classes.

I don't think so. We are talking about 2OL here. 2OL is not set
theory.

See:
http://plato.stanford.edu/entries/frege-logic/


But suppose we assume a countable language and that every
formula with at least one free variable signifies a concept.

??? Comprehension just guaranties that for every such formula A[x]
there _is_ an concept F such that for all x: Fx <-> A[x].


On those assumptions, there are at most countably many concepts

I don't think so. Comprehension just guaranties that there are _at
least_ countable many concepts.


F.

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Relevant Pages

  • Re: The Difference between a Set and an Element
    ... I can see a philosophical role for concepts of some sort, ... imagine what it buys you to have a disjunctive concept ... But suppose we assume a countable language and that every ...
    (sci.logic)
  • Re: The Difference between a Set and an Element
    ... indeed have to posit infinite disjunctive concepts. ... matter of theoretical preference, isn't it? ... imagine what it buys you to have a disjunctive concept correspondingly ... This is already a consequence of Frege's comprehension principle for ...
    (sci.logic)