X-Message-Number: 26684
Date: Sun, 24 Jul 2005 10:07:20 -0400
From: Thomas Donaldson <>
Subject: a bit more for Mike Perry

More for Mike Perry:

In your example of identity for sets you are not really defining
what identity might mean here. You say that 2 sets are identical if
their members are the same, and thus give a circular definition.
What constitutes being "the same"? Well, it is being "identical".

Nothing prevents us from considering a set of sets which are
"identical" in the sense that they differ only on a set of measure
0, where "measure" is the Lebesgue measure on the real line.
Well, you might say, such sets do not have the same elements.
Why don't they have the same elements? After all, the Lebesgue
measure of their set difference is 0, isn't it?

If we set up a system in which some set of objects, "points",
are assumed to be minimal, then that's fine as a theoretical
entity. If we want to apply such a system to something in the
real world, we have the same problem of "identity" once more.
Is it appropriate to apply such a system? Well, that depends.

However as it stands, your notion of identity remains circular.
Do you also wish to add a postulate that the points you are
using are minimal? Go ahead. Whether you will be saying anything
useful about the world depends on just what you're discussing ---
as I said above, that depends.

          Best wishes and long long life for all, again,

               Thomas Donaldson

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