On 4/25/2013 3:53 AM, WM wrote: > > Nobody can read, write or use an infinite string. > Real numbers are represented by *finite names*
The names might be COMPACT (WM really should learn the difference), but what is presupposed by Leibniz principle of identity of indiscernibles is a different matter:
"All existential propositions, though true, are not necessary, for they cannot be proved unless an infinity of propositions is used, i.e., unless an analysis is carried to infinity. That is, they can be proved only from the complete concept of an individual, which involves infinite existents. Thus, if I say, "Peter denies", understanding this of a certain time, then there is presupposed also the nature of that time, which also involves all that exists at that time. If I say "Peter denies" indefinitely, abstracting from time, then for this to be true -- whether he has denied, or is about to deny -- it must nevertheless be proved from the concept of Peter. But the concept of Peter is complete, and so involves infinite things; so one can never arrive at a perfect proof, but one always approaches it more and more, so that the difference is less than any given difference."
WM has been asked to provide coherent systems of logic against which to judge his statements. Instead, he uses the axioms he denies and the principles he rejects.