Re: Epistemology 201: The Science of Science
From: robert j. kolker (nowhere_at_nowhere.net)
Date: 03/22/05
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Date: Mon, 21 Mar 2005 19:41:04 -0500
Allan C Cybulskie wrote:
>
>
> Would we agree that there are two elements in the set {a, b}?
Yes.
>
> Would we agree that there are at least three elements in the set of
> integers?
Yes
>
> What more do you need?
What happens when you have two infinite sets. What does more mean then.
When one of the sets if finite there is no problem. Given a finite set
and an infinite set it is not contoversial to say the infinite set has
more elements. This is true, when cardinality is intended by "more".
Given two finite sets the comparison of number of elements IS the
cardinality definition. If A and B are finite and you match each element
of A with an element of B and A runs out before B, then B has more. But
this is the cardinality comparison again. The interesting case is when
both A and B are infinite. So tell us what "more" means other than in
the cardinality sense?
Bob Kolker
>
>
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