Date: Apr 25, 2013 8:49 PM
Subject: Re: Matheology § 258
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.
see "peculiar reasoner"