Re: Cantor's definition of set

On Oct 25, 1:25 pm, John Jones <jonescard...@xxxxxxx> wrote:
On Oct 25, 9:18?pm, Peter_Smith <ps...@xxxxxxxxx> wrote:

On 25 Oct, 20:51, John Jones <jonescard...@xxxxxxx> wrote:

OK. But if the members of a set have nothing in common, then how can
we have a set of numbers, for numbers are derived from each other -
they have something in common.

Where on earth do you get the idea that the members of a set need have
nothing in common?? Take some set of people: the members of the set
have something in common (being human beings, for a start).

OK; then I can have a set of humans. Does this meet the criterion that
a set has unique members? If the answer is yes, then
1) we must presume that all humans are uniquely different. But
wouldn't this make a set dependent not on logical principles but on
material contingencies?

That's ridiculous. Of course differences will be determined by
whatever criteria you prefer. That doesn't mean that the logic of
identity can't then abstract from those particular criteria.

2) a set of humans describes

A set doesn't describe unless that set happens to be linguistic object
too.

what they have in common more than what
is different about them.

A DEFINITION of a particular set will "describe" the common property,
yes.

should we redescribe the set so that it
mirrors the letter of the law as it were, and describes only what is
different about humans?

I can't say what we "should" all do. As long as you're not harming
other creatures, then I suppose my advice is that you should do
whatever tickles your fancy.

3) Can we have a set of differences?

No one is stopping you from defining a 'difference' and then having a
theory about difference combined with a set theory so as to allow sets
of differences, if you're interested enough to do so.

MoeBlee


.

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