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You do need faith that the axioms you work with are consistent, unless you're working in one of the few provably consistent systems.
by mannerheim 5y ago
You do need faith that the axioms you work with are consistent, unless you're working in one of the few provably consistent systems.
- eru 5y agoThat's somewhat true. Though in practice, you can just accept it provisionally as an empirical observation. (Math is just as applicable even if you have your doubts and are missing absolute certainty.)
- necovek 5y agoEmpirical observation is not considered much proof of abstract principles because of the measuring errors. I.e. Newtonian mechanics is empiricaly observed to be true with a certain error margin during measurements. As you lower measurement errors, you start to notice things that are not consistent with it. Newtonian physics was and still is very much applicable for many use cases, just like mathematics is. You seem set on "defending" mathematics where nobody is attacking it. My comment is not to discredit mathematics: it is the ultimate expression of the human mind, showing the limits of our comprehension. Limits that clearly show that we can start reasoning only if we accept a few things as a given (what I simplified to "faith"). It is beautiful and transcendent in its expression, and while people consider it the most complex of human expression, I consider it the simplest full expression, worked down to the smallest ambiguities our brain will let us have. It is a reflection of what our mind can understand and grasp, and we should accept it as such so we can both grow our understanding of the world, and test limits of our understanding.