On 3/14/2013 2:30 PM, WM wrote: > > It is so simple: > > Here it is again.
It is not possible to advance to a logic of parts of individuals as individuals without the (correct, geometric) version of Leibniz' principle of the identity of indiscernibles interpreted with Cantor's intersection theorem pertaining to nested sequences of closed sets having vanishing diameter.
It is not possible to "quantize" the tails of those infinite sequences with a general distinction between "closed" and "open" sets in a topology without being informed through the situation described above.
Naming by virtue of definite description is an inherently infinitary process because of the epistemic nature of definition. So, any use of a singular term in any language act subject to the Fregean or Russellian analyses presupposes a completed infinity.
And, that includes references to infinity via potential infinity.