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> Denials of an objective reality are, in the opinion of the author, and also of the reviewer, aberrations of human thought, plain and simple. I found this sen

> Denials of an objective reality are, in the opinion of the author, and also of the reviewer, aberrations of human thought, plain and simple. I found this sentence rather disappointing, although I can sympathize. It really does seem like there is an objective reality out there, and humanity has certainly benefited greatly from our collective power over the natural world. However, if this "reality" is mathematical in nature, and mathematics is incomplete, then I don't see what is the big deal with giving up the idea of an objective reality. The founders of QM seemed to be much more open to these ideas, eg. Heisenberg and Bohr.

jamesrcole 9y ago
Why do you think incompleteness means non-objectivity? One reason I ask is that, as I understand it, incompleteness concerns the ability to prove certain characteristics rather than meaning a system has/hasn't got those characteristics.
- antonvs 9y ago
  > incompleteness concerns the ability to prove certain characteristics rather than meaning a system has/hasn't got those characteristics. That's right. I like the way Gregory Chaitin puts it, "some mathematical facts are true for no reason, they are true by accident, or at random." I also don't see any connection to objective reality. Ignoring mathematics, we know that the universe contains things that are true by accident, but that doesn't undermine the idea of objective reality.
- mathgenius 9y ago
  You can go on adding new axioms to your incomplete system, in an attempt to complete it. This to me looks like measurement processes in quantum mechanics. Mathematicians gave up on the idea of the "one true" mathematics, but it seems physicists still hope for the "one true" reality. Maybe this is a facile analogy. I'm still pondering if there are deeper things to be said about this.
soVeryTired 9y ago
I think the biggest problem with the “objective reality is mathematical” point of view is that there are many non-equivalent ways of interpreting the mathematics (e.g. wavefunction collapse vs. many worlds). It’s also the case that two non-equivalent mathematical formalisms can describe the same phenomenon. I’m not a physicist, but I think classical vs. Hamiltonian mechanics fits the bill there. Also possibly quantum vs. Bohmian mechanics (but I’m far too naïve in physics to be able to judge that one properly).
tpeo 9y ago
"Incomplete" in what sense? In the sense that our description of the world always seems to fall short of what it's trying describe? Or in the Gödelian sense of some theorems not being provable in finitely many steps in some particular language? Because as far as I know, the latter isn't really an issue.
renox 9y ago
> However, if this "reality" is mathematical in nature Uh? Einstein's quote seems quite appropriate here: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

jamesrcole 9y ago

Why do you think incompleteness means non-objectivity? One reason I ask is that, as I understand it, incompleteness concerns the ability to prove certain characteristics rather than meaning a system has/hasn't got those characteristics.

antonvs 9y ago
> incompleteness concerns the ability to prove certain characteristics rather than meaning a system has/hasn't got those characteristics. That's right. I like the way Gregory Chaitin puts it, "some mathematical facts are true for no reason, they are true by accident, or at random." I also don't see any connection to objective reality. Ignoring mathematics, we know that the universe contains things that are true by accident, but that doesn't undermine the idea of objective reality.
mathgenius 9y ago
You can go on adding new axioms to your incomplete system, in an attempt to complete it. This to me looks like measurement processes in quantum mechanics. Mathematicians gave up on the idea of the "one true" mathematics, but it seems physicists still hope for the "one true" reality. Maybe this is a facile analogy. I'm still pondering if there are deeper things to be said about this.

soVeryTired 9y ago

I think the biggest problem with the “objective reality is mathematical” point of view is that there are many non-equivalent ways of interpreting the mathematics (e.g. wavefunction collapse vs. many worlds). It’s also the case that two non-equivalent mathematical formalisms can describe the same phenomenon. I’m not a physicist, but I think classical vs. Hamiltonian mechanics fits the bill there. Also possibly quantum vs. Bohmian mechanics (but I’m far too naïve in physics to be able to judge that one properly).

tpeo 9y ago

"Incomplete" in what sense? In the sense that our description of the world always seems to fall short of what it's trying describe? Or in the Gödelian sense of some theorems not being provable in finitely many steps in some particular language? Because as far as I know, the latter isn't really an issue.

renox 9y ago

> However, if this "reality" is mathematical in nature Uh? Einstein's quote seems quite appropriate here: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."