I agree that you can't empirically prove the existance of mathematical objects. Mathematical objects (numbers, sets etc.) are not physical objects. The ontological status of such things is pretty tricky. For me anyway. I know Quine regarded himself as a physicalist, but also had a place in his ontology for these kinds of non-physical things.
There are really two sepperate issues here. It is perfectly possible to say that mathematical objects are non-physical (in that they are eternal, non spatial and do not enter in to causal relationships etc.) but also take the line that they are confirmed by science. Science makes reference to theoretical unobservable entities all the time. Like subatomic particles. If the theories work, the unobservables can be considered proven to exist. The same kind of deal could be used to confirm the existence of these weird non-physical objects, based on the success of science as a whole. I'm not sure about this tact myself, since it kind of suggests that some weird scientific discovery could prove that 2+2 does not in fact equal 4. But even you're like me, and you dont really buy the physics confirms mathematics line, I'm not sure it matters. Yeah, so there are these mathematical objects, which are abstract, non-physical, and eternal, which we have an intuitive grasp of and we use them to do science. What are the implications for anything?
Also, kinda nitpicky maybe, but, physicalism is a philosophical position, and not a scientific paradigm.
There are really two sepperate issues here. It is perfectly possible to say that mathematical objects are non-physical (in that they are eternal, non spatial and do not enter in to causal relationships etc.) but also take the line that they are confirmed by science. Science makes reference to theoretical unobservable entities all the time. Like subatomic particles. If the theories work, the unobservables can be considered proven to exist. The same kind of deal could be used to confirm the existence of these weird non-physical objects, based on the success of science as a whole. I'm not sure about this tact myself, since it kind of suggests that some weird scientific discovery could prove that 2+2 does not in fact equal 4. But even you're like me, and you dont really buy the physics confirms mathematics line, I'm not sure it matters. Yeah, so there are these mathematical objects, which are abstract, non-physical, and eternal, which we have an intuitive grasp of and we use them to do science. What are the implications for anything?
Also, kinda nitpicky maybe, but, physicalism is a philosophical position, and not a scientific paradigm.
