Please correct me if I am wrong:
Bruno believes that information, for example mathematical concepts and theorems, exist independently of their encoding in some physicsl systems (arithmetic realism); in other words, that the number 4 esists independently of the presence in the physical world of sets of 4 separate objects, or that 2+2=4 is true independently of the possibility to physically verify this with 4 bottlecaps.
Eugen believes that mathematics is the physics of bottlecaps, and that information cannot be said to exist if it is not carried by a physical system in the actual world.
Are we sure that both mean the same thing by "existence"?
I guess it is clear that in the following sentences "pi exists" and "the moon exists"
the meaning of "exists" is different. But the point was the question of knowing
or betting which "existence" is more fundamental. We differ on which one is reducible to
Eugen seems to pretend that it is obvious that "physical existence" is more
fundamental than "mathematical existence", and I guess he was meaning that
the existence of pi is a sort of psychological existence, that is pi exists "in" the brain
of the mathematician, so that the existence of pi could be reduce to the physical existence
of brain and the like. I of course respect completely that opinion; but I point on the fact
that once you make the computationnalist hypothesis then it is the reverse which becomes
true: even if locally pi is a production of the human brain, globally the laws of physics logically
develop on the set of all possible beliefs of all possible universal and immaterial (mathematical)
machines embedded in all possible computations (computationnal histories). That's all my thesis
is about. I don't pretend it is obvious, for sure.
By the way I am reading Bruno's thesis, the few pages that I have read are very interesting.
Thanks for saying, don't hesitate to ask questions.