On 21 Sep 2011, at 20:51, meekerdb wrote:

On 9/21/2011 9:20 AM, Jason Resch wrote:
The Mandelbrot set has a definition which we can use to explore it's properties. Would you say the set was non-existent before Mandelbrot found it? If we have to define something for it to exist, then what was this universe before there were conscious beings in it?

"To exist" just means to occur in the ontology of some model. We have a model of enumeration, which we call "the integers" and a model of combining them, which we call "arithmetic". In this model prime numbers "exist" because they satisfy the rules for the ontology. But this kind of "exist" is quite different from the way my chair "exists" and the way dinosaurs "existed".

Yes. Now assuming mechanism, we can understand that in fine we have to explain the appearance of the existence of chair and dinosaurs from the existence of the numbers.

Whenever one is tempted to write "exist" he should first count to ten.

Ten? I think eight is enough :)

With mechanism the question is rather simple. You have the primitive existence. It is the usual existence of the numbers, or combinatores, java program etc. This does not need to be conceived in any material way, and should not be confused with any of their physical, or human minded instantiation. Then all other existence are epistemological. So you have

1) the existence of the number. Symbolically Ex(x = <that number>) like Ex(x = 0), Ex(x = s(0)), Ex(x = s(s(s0))), etc.

2) the seven+ notion of existences with the forms: BExB(x = <that number with such or such property), and B being defined by Bp, Bp & p, etc. Each hypostase defines its own notion of existence, completely defined in arithmetic or at the meta-level of arithmetic. For example, chairs exist in the sense: BDEx(BD(x = <that number with such or such property). The "BD", and its arithmetical property account of the appearance of the physical aspect (including the quantum, and the quale) of the chairs, up to now.



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