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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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