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

Brent

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