Comment on Theories on Theories
pfried@reddthat.com 2 weeks agoIt’s not about those specific proofs.
It certainly is about those specific proofs and anything that has been rigorously proven in Lean. We’re discussing techniques that show something is correct forever, and those proofs show that something is correct forever. Philosophical arguments don’t even show that something is correct today.
Furthermore, the kernel still relies on CPU, memory and OS behavior to be bug free.
Only to a point, just like human language proofs require the reviewers brains to be bug free to a point. The repeated verification makes proofs as correct as anything can get.
lemonwood@lemmy.ml 2 weeks ago
Exactly, I’m glad you understand. There’s no epistemological certainty in math, just like in normal language. We have to make do with being pretty certain, as good as it gets. I like lean for it’s intended purpose: advancing math. No one involved in lean is seriously claiming it produces some kind of religious absolute certainty. Neither is anyone trying to replace philosophy.
Math can’t elevate anything above philosophy, because in a sense, it is part of philosophy, one of the parts using specialized language, specifically the part that is concerned with tautologies.
Have you clicked on the links to the philosophy wiki I provided? Maybe read about what a brilliant mathematician and philosopher has written on the philosophy of mathematics to convince yourself, that philosophy of mathematics is valuable and necessary (wether you agree or not). You’re already engaging in philosophical debate yourself. Your claims about the nature of philosophical arguments and mathematical proofs are themselves philosophical in nature.
pfried@reddthat.com 2 weeks ago
That’s my point. Mathematical proofs aren’t generally agreed. Philosophical arguments are generally agreed upon until the tools to take them out of philosophy are developed, and then the philosophical arguments are discarded entirely.
lemonwood@lemmy.ml 2 weeks ago
Yes, they are. Have you seen the controversies around many recent proofs? Proofs are getting so long and topics so specialized, that simply just reading them takes for ever. Some important ones have only been checked by one or two people. Some have been out for years and are still controversial, because no one claims to have some the immense work to actually checked them. That’s one of the reasons why proof assistants are used in the first place. They help, but they come with their own problems and challenges.
This is such a very old idea and you’re not the first one to have it. Just try it yourself as an exercise. Is like to see how you get an ought from an is with pure math. Every one who tried to build ethics on math only failed. Please, just google it or read some of the links I shared. Philosophers are totally familiar with very advanced math and use it. Again read some articles on like set theory or quantum mechanics on plato.stanford.edu to verify yourself. It’s already being used and always has. Even the antique philosophers were mathematicians. They invented logic and geometry. Every philosophy student through antiquity and the middle ages up to the Renaissance was forced to learn them before getting to the more advanced topics.
No matter how smart you are, other smart people probably had very similar ideas before you, tried to formalize them, got challenged, responded, tried again and so on. The history of their work is the history of philosophy. Trying to do better without even reading any of it would fit the definition of being naive.
pfried@reddthat.com 2 weeks ago
And again, the history of philosophy is replacing philosophical arguments with better tools.