On 12 Jul 2012, at 11:34, meekerdb wrote:

On 7/12/2012 1:18 AM, Bruno Marchal wrote:

On 12 Jul 2012, at 00:30, John Mikes wrote:

On Wed, Jul 11, 2012 at 3:27 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

Esse is not percipi. With comp. Esse is more "is a solution to a diophantine polynomial equation".
St.:You have merely replaced the Atoms of the materialists with the Numbers of neo-Platonists. :_(
Study UDA and AUDA, it is exactly the contrary. Universal machines, relatively to the arithmetical truth makes the arithmetical reality into tuburlent unknowns. And matter still exists but is no more primitive as being the condition making collection of universal machines sharing part of the sheaves of all local computations.

UDA is an invitation, or challenge to tell me where you think there is a flaw, for UDA is the point that if we can survive with a digital brain, at some levels, then the physical reality is not the source of the reason why we believe in a physical reality. It is a reasoning Stephen, I repeated it recently on the FOAR list, please tell me a number between 0 and 7, or 8, so that we can agree on what we disagree on.

My question is (my) usual: how do you describe EXIST?
In my view whatever passes the mental royeaume DOES indeed exist. Not the physical world, not the "truth" ideas, ANYTHING. You escaped my earlier question about the "Nature" (or whatever anybody may call it/her) - this one is attached to it with your Latin caveat above exposing the questionable 'percipi' what I indeed included as valid for 'esse'.

Percipi might be valid for esse, but esse is not *just* percipi, like in Berkeley statement.

With comp, and the UDA conclusion things are rather clear. We have ontological existence, and this is given by the sandard meaning we can give to existential proposition, like Ex(x is a prime number). the "E" (it exists) is defined by axioms and inference rule.

So a number with a given property exists only if it can be proven to have that property from axioms by the inference rules?

Not at all. ExP(x) is true if it exists some n such that P(n) is true (provably or not).

Isn't that restrictive?

That would be.

I thought you extended "exist" to all x for which Ex(Px) whether provable or not.

I have perhaps been unclear. We must not confuse ExP(x), which operational meaning is defined by the axiom and rules of inference (telling us when ExP(x) is believed), but which truth might still be unprovable, and the truth of ExP(x), which is the case when it exists some n such that P(n), and which is supposed to be independent of our ability to prove it or not, and which is actually independent of the axioms we chose.



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