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, complete in a minimal sense".
Like "sufficient reason" I suppose. Or Occam's razor. Or the truth should
be simple. Thus "Socrates was a man" is a proposition which is, as a proposition, thus a substance. This is tied into necessary reason, always either true or false. 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 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 with time. The conclusion is that Russell may be wrong, that 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.

Gôdel 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 Gödel 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 Babbage. 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.

Bruno



Dear Bruno,

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

--
Onward!

Stephen

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

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