On 06 Aug 2011, at 22:00, Stephen P. King wrote to Craig Weinberg:

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Craig: Natural numbers are an invention of an entity that thinks,

Bruno: The existence of numbers, with the laws of addition and multiplication, entails the existence of universal numbers. They can introspect themselves and discover, for themselves, the numbers andtheir laws. They can even discover themselves in there, and thison avariety of levels.Craig: I don't think that you can say that they do that without a mathematician being there to watch and understand, or a silicon chip to prove it. What numbers help you discover is the logic behind sense and the sense behind logic, but they don't necessarily reveal a logic independent of sense. (That may be my main point right there).Stephen: I think that you are both wrong! Numbers as independentprimitives can do nothing without the schemata of ordering andrelations that even allows the notion of "introspection" and"discovery" to be meaningful.

`I said numbers *with the laws of addition and multiplication*. You`

`can define the order x < y by Ez(not(z = 0) & (x + z = y)).`

`In fact with addition and multiplication, you have the dreams and`

`their coherence property leading to physics.`

OTOH, requiring the physical presence of a mathematician is missingthe point that the relationships upon which 'introspection' and'discovery' supervene are not limited some just some particularkinds of things. You are missing the true part of functionalism.

OK. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "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.