On 12/8/2012 8:02 AM, Roger Clough wrote:
Hi Stephen P. King
For what it's worth, I think Richard referred to
Indra's Beads in connection with this problem.  Every monad
has its own myriad set of perceptions of the other monads,
but these are indirect (are constantly updated by the Supreme
Monad).
The Supreme Monad is needed to keep all of these perceptions
correct, each from their own viewpoint. Each monad is different.
Dear Roger,

The analogy of monads to Indra's beads (or jewels) is exact. Each monad's perception (it is a singular integration not fragmented plurality) is identical to a set of perceptions of other monad's, in the sense that one of the Jewels in Indra's net 'reflects all others'. But we have to be careful. If the word "all" is absolute, then the jewels (monads) are identical to each other and thus all monads are One. It is only then the 'all' of the reflections is not absolute that we obtain distinctions between monads. We cannot just consider the ideal case, we must also consider the non-idea cases, such as when monads do not have complete images of each other and thus do not have a global harmony. We are considering here something known as mereology.

See:  http://plato.stanford.edu/entries/mereology/

A good formal mathematical consideration of this mereology is found in Non-Well founded sets, where the special case of a well founded set appears. The well founded set plays the role of the special absolute case of the absolute 'all' , as in "one of the Jewels in Indra's net 'reflects all others' ". This is the ideal case only such as the case where we can consider monads to have a global pre-established harmony! There is a difference between assuming that a harmony exists and thinking about how it is that such a harmony is possible. Leibniz did only the former, I am asking questions of the latter: How is a pre-ordained harmony possible?! Julian Barbour made the same mistake as Leibniz and had no idea, in the conversation that I had with him, why I was asking him "how it is that Time Capsules came to have a best-matching?". When I told him that his best-matching was an example of a computation of an NP-hard problem, he seemed to be dumbfounded, not having any idea what I was talking about and yet he explicitly bemoaned how long it took for his computer to run a Best-matching for a simple example of a time capsule. Geee!


--
Onward!

Stephen


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