(But philosophical natter won’t help with making actual progress, won’t get you anywhere. Having concluded that physical world and the domain of decision theory are fundamentally mathematical, the next step is to master what people know about mathematical thinking, and perhaps physics. Fluency in commonly useful mental tools, just short of becoming specialized in anything in particular in order to complete this stage in reasonable time, like 10 years.)
Sans les mathématiques on ne pénètre point au fond de la philosophie. Sans la philosophie on ne pénètre point au fond des mathématiques. Sans les deux on ne pénètre au fond de rien. — Leibniz [Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything.]
(Perhaps we should taboo “philosophical”. Speculative technical discussion often leads to actual progress. I don’t yet believe in math, but I know that I need to hang out a lot with people who do believe in math if I’m to stay on track, and that’s what I do. (Though not enough.))
(But philosophical natter won’t help with making actual progress, won’t get you anywhere. Having concluded that physical world and the domain of decision theory are fundamentally mathematical, the next step is to master what people know about mathematical thinking, and perhaps physics. Fluency in commonly useful mental tools, just short of becoming specialized in anything in particular in order to complete this stage in reasonable time, like 10 years.)
(From Chaitin’s home page:
)
What did “philosophie” mean in Leibniz’s time? (For Newton, e.g., “natural philosophy” was the usual term for what we now call “physics”.)
(Perhaps we should taboo “philosophical”. Speculative technical discussion often leads to actual progress. I don’t yet believe in math, but I know that I need to hang out a lot with people who do believe in math if I’m to stay on track, and that’s what I do. (Though not enough.))