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

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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, complete in a minimal sense".Like "sufficient reason" I suppose. Or Occam's razor. Or the truth shouldbe simple. Thus "Socrates was a man" is a proposition which is, as aproposition,thus a substance. This is tied into necessary reason, always eithertrue or false.So I think the better definition is "Complete and unchanging set ofpredicates"So because "The horse was lame" may not always have been true, it is possibly contingent (is only a current fact), so as a proposition it cannot be a substance as far as we know.None of this can be true, however, since most things will change withtime.The conclusion is that Russell may be wrong, that nothing be asubstance.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 ofsimple 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 wasaxiomatizable.Gôdel did not just destroyed Hilbert's program, but also a large partof the antic conception of platonism, including a large part ofRusselm's conception. After Gödel and Turing, after Post and Kleene,we know that the arithmetical Platonia is *full* of life, but alsotyphoons, black holes, and many things.There is a "Skolem paradox", which needs model theory to be madeprecise: arithmetic is enumerable, nevertheless, when seen by machinesfrom inside, it is not. It is *very* big.I respect a lot people like Leibniz and Russell. Leibniz, by manytoken, was closer to the discovery of the universal numbers/machinesthan Russell, despite Babbage.Comp is still close to Russell's philosophy of numbers but departsfrom his philosophy of sets.Leibniz needs just to be relativized, imo, by allowing accessibiltyrelations, or neighborhood relations between worlds/realities (shareddream/vido-game, somehow). Comp does not let much choice in thematter, anyway. We are confronted with a big problem, but we can,actually we have to, translate it in arithmetic, once we assume comp.Bruno

Dear Bruno,

`I think that Leibniz' Monads can be relativized by defining the`

`equivalence relation in their mereology with a bisimulation function.`

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