3 ms·

I completely agree with you. It's a difficult subject. I have proposed the following two definitions: 1. Philosophers in the original article: best understood

I completely agree with you. It's a difficult subject. I have proposed the following two definitions: 1. Philosophers in the original article: best understood as acedemic philosopers. 2. Progress in AI/maths/hard science: comes from those who actually "do the maths/implementation/repeatable measurement" as opposed to using natural language only for discussing their ideas. In my opinion the purpose of all science is truth, and truth (pace Socrates and the slave boy) must -- among other things -- be reproducable by others, ideally by every human. Technology for truth has improved over time, with mathematisation (and edge case programming and exectuion on a computer) as the current state of the art in reproducibility. When Frege succeeded in formalising first-order logic, the sacred heart of rationality, informal methods became second-class. All substantial progress in subjects formerly restricted to informal methods has since come from formalisation and empirical experiment. If you don't agree with my (1, 2) above, than that's fine, we are talking abotu (slightly) different things.

foldr 8y ago
You seem to be assuming that philosophers are somehow restricted to using natural language only, but * the formalization and regimentation of natural language has always been a fairly central concern in philosophy (that's where formal logic comes from); * mathematics can be, and used to be, done in largely natural language.
- YorkshireSeason 8y ago
  What was a good definition of philosopher then is not what is a good definition now. Meaning evolves! I invite you to think historically, and in terms of ongoing differentiation of science: the drive towards formalising/axiomatising mathematics which was started in earnest at the end of the 19th, beginning of the 20th century, has been accelerating. These days mathematics is partly verified in interactive theorem provers like Isabelle/HOL, Coq, Agda and Lean. A Fields medallist (Voevodsky) dedicated his post-Fields career towards more mechanisation of Mathematics. I predict that in 100 years from now, mathematics that is not formalised in a mechanical tool will not be publishable in reputable venues.
  - foldr 8y ago
    Philosophy is also much more formal than it was 1000 years ago (e.g. compare [1] to [2]). Indeed, the formalization of mathematics was driven by philosophers trying to put mathematical reasoning on an adequate foundation. [1] https://mally.stanford.edu/Papers/ontological.pdf https://mally.stanford.edu/Papers/ontological.pdf [2] https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp

foldr 8y ago

You seem to be assuming that philosophers are somehow restricted to using natural language only, but * the formalization and regimentation of natural language has always been a fairly central concern in philosophy (that's where formal logic comes from); * mathematics can be, and used to be, done in largely natural language.

YorkshireSeason 8y ago
What was a good definition of philosopher then is not what is a good definition now. Meaning evolves! I invite you to think historically, and in terms of ongoing differentiation of science: the drive towards formalising/axiomatising mathematics which was started in earnest at the end of the 19th, beginning of the 20th century, has been accelerating. These days mathematics is partly verified in interactive theorem provers like Isabelle/HOL, Coq, Agda and Lean. A Fields medallist (Voevodsky) dedicated his post-Fields career towards more mechanisation of Mathematics. I predict that in 100 years from now, mathematics that is not formalised in a mechanical tool will not be publishable in reputable venues.
- foldr 8y ago
  Philosophy is also much more formal than it was 1000 years ago (e.g. compare [1] to [2]). Indeed, the formalization of mathematics was driven by philosophers trying to put mathematical reasoning on an adequate foundation. [1] https://mally.stanford.edu/Papers/ontological.pdf https://mally.stanford.edu/Papers/ontological.pdf [2] https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp