Date: Apr 25, 2013 8:49 PM
Author: fom
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."

Leibniz

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.

http://en.wikipedia.org/wiki/Doxastic#Types_of_reasoners

see "peculiar reasoner"