Re: set of a set etc.

On 19 Jul 2005 09:24:32 -0700, "Jasper" <vfiddlestix@xxxxxxx> wrote:

>
> Bad attempt at illustration on my part. The question still remains
> however, as to the conceptual difference between a thing ...x.. and its
> set {x} , the set of its set{{x}} etc. If they aren't the same then it
> sould be possible to say what the difference actually is.
>

Actually, your question has already been answered (for x = {}) by
Jean-Claude Arbaut and Dave Seaman.

Another try:

"The distinction between x and {x} is one of the merits of Peano's
symbolic logic, as well as Frege's. On the basis of our theory of
classes, the necessity for the distinction is of course obvious. But
apart from this, the following consideration makes the necessity
apparent. Let /a/ be a class; then the class whose only member is /a/
has only one member, namely /a/, while /a/ may have many members. Hence
the class whose only member is /a/ cannot be identical with /a/.*"

"* This argument is due to Frege. See his article "Kritische
Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra
der Logik" [...] (1895)"

(Russell & Whitehead, Principia Mathematica, 1910)


F.

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