On 10/29/2012 1:15 AM, Roger Clough wrote:
Hi Bruno
Still waiting for the storm to shut things down.
Numbers are not discussed specifically as far as I can find yet,
in my books on Leibniz. Which probably means that
they are simply numbers, with no ontological status.
Sort of like space or time. Inextended and everywhere.
Numbers are definitely not monads, because no
corporeal body is attached. Although they can
whenever thought of appear in the minds of
particular men in the intellects of their monads.
Hi Roger,
Physical bodies and, by extension, physical worlds follow from
mutually consistent aspects of the individual 1p of monads; they are not
"attached". Leibniz, IMHO, bungled this badly in his discussions of the
Monadology. Given that "monads have no windows", it logically follows
that /they do not have any external aspect/. Monads do not see the
outsides of each other in any direct way. All that monads have as
percepts of that which is other than themselves are those aspects of
their own 1p that cannot be reconsidered as belonging to their identity
in the moment of the observation/appearance.
Leibniz does refer to a proposed "universal"
language, which is simply everywhere
as well as possibly in each head. Numbers would
no doubt be the same, both everywhere and
in individual minds at times.
Yes, this is the Pre-Established Harmony, but as I have argued
before this concept is deeply flawed because it tries to claim that the
solution to NP-Hard problem (of choosing the best possible world) is
somehow accessible (for the creation of the monads by God) prior to the
availability of resources with which to actually perform the computation
of the solution. One cannot know the content of a solution before one
computes it, even if one is omniscient!
So numbers are universal and can be treated
mathematically as always.
I agree, but the concept of numbers has no meaning prior to the
existence of objects that can be counted. To think otherwise is
equivalent to claiming that unspecified statements are true or false
even in the absence of the possibility of discovering the fact.
--
Onward!
Stephen
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