PatrickPowers said:
So would a completely alien intelligence come up with similar mathematics or not? Perhaps some day we shall find out. Not that that would end the debate :-)
Right, it would not, because even if some other alien that seemed very different from us formulated similar mathematical theorems that we do, and even if they found similar ways that their mathematics resonated with a certain order to their reality, it would not prove anything other than what we already know-- the
resonances between our mathematics and our physical reality do exist. The real question persists: what are we to gather from the existence of such resonances? A dog creates some concept of what its master is, and achieves certain resonances by it, but would we not be shocked by how far from our own picture of ourselves is a dog's picture of its master? If a cat creates a picture of its master that resembles the picture the dog creates, all it means is the picture encompasses the pet/owner relationship in some way, it does not convince us that somehow the dog and cat know us better than we know ourselves.
In that light, earlier you argued that the existence of the resonances requires that there be an objective reality, but I don't see what axioms you take as true that can lead to that conclusion. We can say there needs to be
something, but what do we mean by "objective reality", and what claims can we make on it? One approach you might take is to simply
define the concept of objective reality around the empirically demonstrated resonances between mathematics and common experience, and I'd say that is more or less the standard approach used in physics. But that's also pretty much what
Len Moran is talking about-- we cannot choose a philosophical definition of objective reality that is somehow separate from the methods of science, and then use science to discover how such a reality works, because science doesn't exist on the side of that philosophical construct, it exists on the side of the scientific approaches to answering questions. As Bohr said, physics is not about nature, it is about what we can
say about nature. That might be a lot more like what a dog or cat can say about its master than what its master can say about themself.
So science is always forced to create its own concept of objective reality, around the patterns of common experience that resonates with our mathematics. We have no access to any other concept of objective reality in physics, so it is purely tautological to claim that science has somehow shown that objective reality exists. What it really shows is that the scientific concept of objective reality affords us some power over, and understanding of, our environment. That power and understanding is all the scientist means by objective reality, just as our models of gravity are all we ever mean by the term gravity. But of course this always begs the question as to whether or not there "really is" any such thing as gravity outside of our scientific models of it, or whether any elements of our models exist anywhere but in those models.
Now, some say, there must be some real kind of gravity or else we couldn't model it successfully, but to them I would point out that the real kind of gravity they have in mind does not need to actually involve
any of the attributes of our models. Similarly, if you demand that there be a thing called objective reality, I would point out that it need not actually involve a single one of the aspects that you attribute to it. So it is a kind of objective reality that need not be either objective or real, the instant you provide meanings to those words, and so calling it "objective reality" doesn't really mean a whole heck of a lot. Instead, what has meaning is saying "let's enter into a kind of pretense that there is a thing called objective reality with the following attributes, and let's just see how far it gets us, under no illusions that it is actually true." I would say that science works best when framed in just that way, and it certainly saves a lot of embarrassment hundreds or thousands of years later.
, we just have to avoid intellectual shortcuts on the nature of matter : as to say it's unknowable per se, it doesn't exist at all or that science is not about it any way but about paradigms and interpretations... The outcome of "empiricism" would be completely "idealist" if not...
OMGLOL!
Also, if I'm not mistaken, subjects in quantum level cannot be separated from the measuring device, and the measuring device cannot be separated from the environment around it etc etc (Quantum non-locality and uncertainty principle). 
