On 9/25/2010 12:38 AM, Bruno Marchal wrote:
Umm, I had no idea that this would be so difficult to understand! I am claiming that if there does not exist a means to determine a difference then no difference can be said to exist. This is just a restatement of the principle of identity of indiscernibles. If the totality of all that exists is such that it does not exclude any possibility then it is infinite and as such would have that property of infinities, namely that any proper subset of that infinity is isomorphic with the infinity itself. This is equivalent to saying that an infinity is such that is cannot distinguish itself as a whole from any "part" of itself. To distinguish objects from each other there must be some form of deviation and/or weakening from this isomorphism relationship.

This is wrong. Proper subsets of infinite sets may well be finite, {1,2} is a proper subset of the integers.


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