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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 chara
by 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 agoYou 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.