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Honestly, Wittgenstein's philosophical critiques of set theory in relation to the foundations of mathematics still hold true today. Shame he doesn't get more re
by robobro 11y ago
Honestly, Wittgenstein's philosophical critiques of set theory in relation to the foundations of mathematics still hold true today. Shame he doesn't get more recognition for his great work in logic.
- shadytrees 11y agoI'm intrigued but, upon Googling, pretty at sea with all the vocabulary. Is there an explain-like-I'm-slightly-above-five for Wittgenstein's critique of set theory? It seems like he doesn't like infinity very much?
- valera_rozuvan 11y agoHave you seen Victor Rodych's entry at the plato.stanford.edu site entitled "Wittgenstein's Philosophy of Mathematics"? Direct link: http://plato.stanford.edu/entries/wittgenstein-mathematics/ http://plato.stanford.edu/entries/wittgenstein-mathematics/ .
- valera_rozuvan 11y ago2.6 Wittgenstein's Intermediate Critique of Set Theory http://plato.stanford.edu/entries/wittgenstein-mathematics/#WitIntCriSetThe http://plato.stanford.edu/entries/wittgenstein-mathematics/#...
- dvt 11y agoWittgenstein was primarily interested in the linguistic applications of logic. IMO, he wasn't on the same level as Whitehead, Russell, or Curry; let alone Hilbert, Gödel, and Zermelo. And maybe it's just my experience, but Wittgenstein was always shoved down our throats in my undergraduate and graduate classes, whereas people may have never even heard of Jan Łukasiewicz or Stephen Kleene.
- tikhonj 11y agoAh, different communities with different goals. In CS, I've run into Kleene a lot and Wittgenstein never. (Although I'm sure people have heard of him!)
- amelius 11y agoI guess it is mostly a matter of taste, like whether one favors functional programming or imperative programming. Set theory is being used successfully in formal systems, so in principle there is nothing wrong with it.
- mafribe 11y agoShame [Wittgenstein] doesn't get more recognition for his great work in logic. Which great work in logic did W. produce? He is known for some inchoate criticisms, e.g. he doesn't like Cantor's diagonal proof, but none of his criticisms have -- as far as I'm aware, lead anywhere interesting in logic.
- dvt 11y agoThe Tractatus Logico-Philosophicus. In it, Wittgenstein touts his logical atomism. I don't put much stock in the Tractatus, but some people build entire academic careers on it. So who knows, maybe I'm missing something.
- mafribe 11y agoI don't see any particular contributions to logic in the Tractatus.