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Rupert 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.
> >
> > Thanks in advance.
>
> Set theory usually doesn't care much about the nature of the objects.
> There are versions of set theory in which everything is a set, and
> there are versions in which there are objects which are not sets (known
> as individuals). In the latter case, we usually don't care much about
> the properties of the individuals. We just study the sets of them, the
> sets of sets of them, and so on.
Thank you very much for a reply!
I asked this question because I was thinking about a following
possibility:
Since an "unobserved object" may have (I can imagine) a specific
"property" which would make all axioms of Set Theory to be invalid, I
would guess that it would be improper to use Set Theory on such wierdly
defined elements as "unobserved object."
Is there something in Set Theory which would prevent situations like
that? Is there any restrictions on elements in the Set Theory ?
BTW, I couldn't find anywhere a definition of "element" in the Set
Theory. Is there a such definition besides "member of set", which
sounds to me like a tautaulogy.
I hope I am clear in my questions :) and hope to read more replies.
Thanks for your thoughts.
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