On 15 Sep 2011, at 04:24, meekerdb wrote:

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On 9/14/2011 5:51 PM, Mindey wrote:"Nothingness" (as absence of things) is more than a concept. It is a mathematical concept - an empty set. It is easy to give an example of an empty setI'm not so sure about that. Usually you would give some definitionlike "The present king of France" = { }. But if you think theuniverse is infinite and 'everything' exists, then there is apresent king of France...somewhere. Bruno of course would saysomething like "The even divisors of three" = { }, but that would becircular since the definition of three is the successor of thesuccessor of the successor of { }. And in any case he assumesarithmetic exists.

`Not really. I have define three as the successor of successor of`

`successor of 0. Which is a primitive symbol. I don't rely on set theory.`

`Of course I could have use an axiomatic of hereditarily finite sets,`

`instead of PA, like I could use combinators or java programs, but we`

`have to stick on the definition, once chosen. Simple sets of numbers`

`can be handled in PA by arithmetical definition, indeed we can define`

`in arithmetic all recursively enumerable set, and we can talk about`

`non recursively enumerable set too, although not always define them.`

`Also, it is slightly misleading to say that I assume arithmetic`

`exists. Arithmetic exists like physics exists, like music exists, etc.`

`What I assume is that arithmetical statements are true independently`

`of me, and of the physical laws (which is a very common assumption`

`implicitly used in theoretical physics, analysis, etc.). (and then I`

`assume the "yes doctor" and Church thesis).`

`To just understand CT we need at least the believe that the excluded`

`middle applies on the sigma_1 sentences: a machine stops or does not`

`stop. I don't need much more.`

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.