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Frederick Williams wrote:
> vfilipch wrote:
> >
> > Frederick Williams wrote:
> > > vfilipch wrote:
> > > >
> > > > I would like to hear a opinion of prfessionals (because I am not one)
> > > > on the following question:
> > > >
> > > > Is it possible to apply Set Theory for an elment which I would like to
> > > > define as an "unobserved object"? In other words, for an element for
> > > > which there is no way to know ANY properties.
> > >
> > > Do you at least know if your "unobserved object" is a set or not? If it
> > > is, then the usual set theories will deal with it--the sets have no
> > > properties other than those implied by the axioms. If it is not, then
> > > you'll need a set theory with urelemente.
> > >
> > > --
> > > Remove "antispam" and ".invalid" for e-mail address.
> >
> > Thank you for a reply!
> >
> > I would say that since my element was/is "unobserved", I don't know if
> > it is a set or not a set.
> >
> > "Urelemente" is a new word for me, I have no clue what would be the
> > implication of "set theory with urelemente" on my question.
> >
> > Does it meant some kind of "informal" (obvious) description of
> > elements? If "yes" I would think that such set theory cannot be applied
> > to my question, because "obvious" elements should be previously
> > observed (some property is known).
>
> The objects that traditional set theories talk about are all sets:
> everything is built up from the empty set. But some set theories start
> from a set of individuals that are not sets: those individuals are
> called urelemente (German) or urelements (English).
>
> --
> Remove "antispam" and ".invalid" for e-mail address.
So, in my case I can say that I have a set with a urelement "unobserved
object", right?
And Set Theory claims that all its axioms must be perfectly applicable
for such set, right?
But I cannot agree, because since nothing is known about a member of
this set, there is a possibility for my urelemnet to have a property
that specifcally invlidates all axioms of Set Theory.
Don't you think we need to put some restrictions on urelemnts in order
to avoid such situation?
Thanks for your thoughts.
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