Re: Relation between sets and their elements


"Paul Holbach" <paulholbachSPAMBAN@xxxxxxxxxx> wrote in message
news:1114657172.056244.74250@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> > Paul Holbach wrote:
>
> > What is the relation between sets and their elements
> > (provided, of course, they have any)?
> >
> > Is it the relation of identity or of parthood, or in some
> > sense both of
> > identity and of parthood?
>
> I have come across an argument against the idea that the relation
> between sets and their elements is a part-whole-relation.
> It concerns transitivity:
>
> If A is part of B, and B is part of C, then A is part of C.
> But if A is an element of {A}, and {A} is an element of {{A}}, then A
> is not an element of {{A}}.

With a certain viewpoint though, we can have a mereology-like relationship
between a set and its elements that is transitive.

By "dom", we mean "degree of membership" in the following sense:

given a 2 set X and Y, if there exist n number of sets S1, S2, ..., Sn
such that:

S1 = {X}, S2 = {S1}, S3 = {S2}, ..., Sn = {Sn-1} = Y

then n is said to be a dom of X w.r.t. Y. Now by the relation xRy, we mean k
is
a dom of x w.r.t y, for at least one k >= 1. Then xRy is transitive.


>
> Regards
> PH
>


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