On 19 Sep 2012, at 13:16, Roger Clough wrote:

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Leibniz's characteristic numbersI apologize if this is just a can of worms, but it seems related tocomp:All of his life, Leibniz sought to be able to develop a universalcalculus,in which (as I understand it) ideas could be discussed and debatedunambiguously. Issues could be settled arithmetically oralgebraically.Here is a comment on Leibniz' presumed goal: http://www.rbjones.com/rbjpub/philos/classics/leibniz/meth_math.htm "Towards a Universal CharacteristicAn ancient saying has it that God created everything according toweight, measure, and number.However, there are many things which cannot be weighed, namely,whatever isnot affected by force or power; and anything which is not divisibleinto parts escapes measurement.On the other hand, there is nothing which is not subsumable undernumber. Number is therefore, so to speak,a fundamental metaphysical form, and arithmetic a sort of staticsof the universe,in which the powers of things are revealed.'

`OK. But the idea of a universal language to settle all problems is`

`also close to Hilbert idea of settling the math foundation in such a`

`language.`

`That very dream of Hilbert is what Gödel, but I would say more deeply`

`just the existence of the universal numbers or machines refutes, even`

`effectively, that dream.`

`Hilbert's dream had been qualified as Hilbert's nightmare and in that`

`sense, it is a relief that it is inconsistent, as it prevents`

`normative theory for the possible beings (notably the Löbian one and`

`above).`

`There is a universal language for computability, (CT), and a universal`

`machine understanding it, but this entails, in two diagonalizations,`

`that there are no general theories in which we can settle all`

`questions, notably due to the presence of all those universal entities.`

`Was Leibniz closer than Hilbert to the universal machine? Question for`

`future historians.`

`The universal machine needed Boole, Frege, Post, Turing, Church,`

`Markov, Kleene, ...`

`Babbage got it, I think, from the study of an amazing book of 1936 by`

`Jacques Lafitte "La Science des machines". He got the concept and`

`understood that the snake eats its own tail.`

Bruno

I appologize it this is just a can of worms, but in relation to thatprojectLeibniz developed a set of "characteristic numbers", (put leibniz characteristic numbers into Google.) which to me, a non-mathematician, appears to be a form of set theory, such as, if I got it right, all a is b some a is b no a is b some a is not b so each number a is actually a pair of numbers (or IMO terms) logically related by Aristotle's logic. It has been applied (apparently with some problems) to cognitivism by Dreyfus: http://www.springerlink.com/content/gk5115u747772604/ Roger Clough, rclo...@verizon.net 9/19/2012 "Forever is a long time, especially near the end." -Woody Allen --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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