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I agree with all of the above. Except there are isolated cases of philosophy actually pushing forward the frontiers of knowledge. Arguably Russell & Whitehead d
by derrida 14y ago
I agree with all of the above. Except there are isolated cases of philosophy actually pushing forward the frontiers of knowledge. Arguably Russell & Whitehead did in the Principia Mathematica, which attempted to put the foundation of mathematics in terms of logic. That system is the system where Godel found a paradox, which lead to Godels theorems. I'm sure Turing had it in the back of his mind that the Turing machine was a useful way of reasoning about those propositions which are 'true and provable'. Russell/Whitehead --> Godel --> Turing.
Another area where there have arguably been successes (even through failure), is in the attempts to formalise natural languages into logic (Frege, Russell, Wittgenstein). This is the tradition that informed Chomsky, whose theories of grammar inform modern compiler design.
There are philosophers alive that I believe have advanced the frontier of knowledge, but as with some areas of pure mathematics it's hard to say practically what that means. I have in mind Kripke.
- derleth 14y ago> Chomsky, whose theories of grammar inform modern compiler design That's math, though, not philosophy. The difference: Math is a symbol game that occasionally produces useful tools for other fields, whereas philosophy is a discussion of human problems.
- deleted 14y ago[deleted]
- derrida 14y ago"Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything." _ Leibniz > Math is a symbol game So is logic. > philosophy is a discussion of human problems. No. It's not.
- DannoHung 14y agoHow is logic not mathematics?
- Confusion 14y agoUsually logic is considered part of mathematics. However, in an important sense, logic precedes mathematics. You can't do mathematics without using logic.
- derrida 14y agoMany have, take the sort of mathematics done in order to understand physics. Logic is the study of formal reasoning. Mathematics is the study of form and structure. It took R&W's Principia Mathematica to attempt to show that the entirety of mathematics was rested on a logical foundation. That's pretty recent on the scene if you think about the history of mathematics! To me, the idea you expressed, seems like a very 20th century thing.
- _delirium 14y agoThere is mathematics in it, but it's not just mathematics; it was originated, and is still used in areas like AI, as an attempt to formalize thought, i.e. a kind of formal philosophy. A good portion of the foundational work was done by philosophers (e.g. Frege, Russell), and a lot of current work (especially in modal logic) is done by philosophers as well.
- andrewcooke 14y agoit's more like philosophy is the dumping ground for stuff that we don't understand well enough to formalize and place in its own little box. that means that it changes with time. so there was a point when foundational issues in maths and logic were philosophy. the importance of frege, and then later peano, russel, etc, is that they were the ones that found a way to attack that set of problems, letting us isolate a chunk of knowledge as logic, set theory, etc. a similar process is probably happening now with consciousness - we're starting to develop the tools to answer questions that are currently "philosophical".
- yxhuvud 14y agoYou can go back even further. The impact of Descartes and Leibniz on math is not small.
- bitdiddle 14y agoabsolutely, it's at the boundary. I think Brouwer's work in topology and intuitionistic logic is a good example of this interplay
- chrisdevereux 14y agoExactly. Claiming that Philosophy never answers anything makes one hell of a selection bias. When Philosophy answers something, it ceases to be Philosophy.
- bitdiddle 14y agoMath is a symbol game? I'm sure you don't believe that any more than you believe music is a symbol game.
- derleth 14y agoYou have no idea what I believe and I wonder why you think I do.
- ktizo 14y agoUnless you are a true original in every sphere, then we can make a reasonable guess that the majority of what you believe lies within the known sets of human beliefs. Then from observing your actions and reactions to stimuli, (ie, your interaction on this board), we could extrapolate from there and make a reasonable guess on your beliefs on a wide variety of subjects. It won't be absolutely correct, obviously, but it won't be a complete shot in the dark either.
- bitdiddle 14y agoyou're absolutely correct, I can only go by what you say.