Hi Stephen P. King 

Ah so.  I can point leibniz's critics to Godel.

And to the contingency of the world. What did you expect ? 
A rose garden ?

Leibniz sort of sensed Godel's theorem  by his recognition that while things 
must be perfect in Heaven,
down here things were contingent, iffy, troublesome, imperfectly fitting and 
imperfect in the small,
but optimal in the large. 

There were reaslons behind each event, but they needn't entirely jibe with
one another. And even the reasons were mutually contingent. What a mess.

Roger , rclo...@verizon.net
Leibniz would say, "If there's no God, we'd have to invent him so everything 
could function."
----- Receiving the following content ----- 
From: Stephen P. King 
Receiver: everything-list 
Time: 2012-08-18, 17:37:52
Subject: Re: Russell's possibly defective understanding of Leibniz. Or was 
itLeibniz's fault ?

On 8/18/2012 2:56 PM, Bruno Marchal wrote:

On 18 Aug 2012, at 16:41, Roger wrote:

Hi Bruno Marchal 
Admittedly, the more I dig into Leibniz, the more questions I have. 
But I won't abandon him yet, thinking I misunderstood one of his
statements.? Or perhaps Russell misunderstood what Leibniz meant.
According to Russell, "Complete set of predicates" means?"sufficient,?omplete?n 
a minimal sense".
Like "sufficient reason" I suppose. Or Occam's razor. Or the truth should
be simple. Thus "Socrates was a man"?s? proposition which is, as a proposition, 
thus a substance. This is tied into necessary reason, always either true or 
So I think the better definition is "Complete and unchanging set of predicates" 
So because "The horse was lame" may not always have been true,
it is possibly contingent (is only a current fact), so?s a proposition 
it cannot be a substance as far as we know.?
None of this can be true, however, since?ost things will change with time.
The conclusion is that Russell may be wrong,?hat nothing?be a substance.? 
Yet Leibniz says the universe is made up 
entirely of monads, and monads are substances by definition.
"For Leibniz, the universe is made up of an infinite number of simple 
substances ... "
Perhaps Leibniz meant "the world I refer to in my philosophy..."
He did not count time and space for excample as monads.

Russell was still believing that the mathematical reality was axiomatizable.?

G?el did not just destroyed Hilbert's program, but also a large part of the 
antic conception of platonism, including a large part of Russelm's conception. 
After G?el and Turing, after Post and Kleene, we know that the arithmetical 
Platonia is *full* of life, but also typhoons, black holes, and many things.?

There is a "Skolem paradox", which needs model theory to be made precise: 
arithmetic is enumerable, nevertheless, when seen by machines from inside, it 
is not. It is *very* big.

I respect a lot people like Leibniz and Russell. Leibniz, by many token, was 
closer to the discovery of the universal numbers/machines than Russell, despite 
Comp is still close to Russell's philosophy of numbers but departs from his 
philosophy of sets.
Leibniz needs just to be relativized, imo, by allowing accessibilty relations, 
or neighborhood relations between worlds/realities (shared dream/vido-game, 
somehow). Comp does not let much choice in the matter, anyway. We are 
confronted with a big problem, but we can, actually we have to, translate it in 
arithmetic, once we assume comp.


Dear Bruno,

?? I think that Leibniz' Monads can be relativized by defining the equivalence 
relation in their mereology with a bisimulation function. 



"Nature, to be commanded, must be obeyed." 
~ Francis Bacon

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