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I'm a mathematics student interested in philosophy. We don't have philosophy courses at our university. But I want to learn some stuff. I'm inspired by Bertrand Russell, Ludwig Wittgenstein and such philosophers. I've read Wittgenstein's Tractatus once but I couldn't understand half of it. Now my questions are the following.

How would one sum up "Analytic philosophy"? What are the prerequisites for analytic philosophy? How would one go on to study philosophy by his own without attending any formal lectures at an established university?

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    Some formal logic is useful; and obviously at least an overview on the history of philosophy. – Mauro ALLEGRANZA May 14 '17 at 18:24
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    Some good books: M.Dummett, Origins of Analytical Philosophy and J.Floyd (editor), Future Pasts: The Analytic Tradition in Twentieth-century Philosophy. – Mauro ALLEGRANZA May 14 '17 at 18:25
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    You can start with IEP survey of analytic philosophy, but in truth there is no summing it up, the label covers almost all of Anglo-American philosophy since 1930-s. For reading It would help if you tell what aspect appeals most to you: philosohy of science, language, mind, etc.? – Conifold May 14 '17 at 19:31
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    @Conifold Thanks for citing that IEP page. In addition to its references, I've also very much enjoyed Quine's very accessible introduction, books.google.com/books?id=GxlUEyI-6JoC&pg=PA35 I'm pointing you to page 35 for his cute, pithy aphorism, "Logic chases truth up the tree of grammar." And somewhat more detailed is Romanos' mitpress.mit.edu/books/quine-and-analytic-philosophy And one of IEP's cited references, Carnap's so-called "Aufbau" books.google.com/books?id=WgY2ZMsJtQgC I found extremely interesting but ultimately dissatisfying. The first 100 or so pages... – John Forkosh May 15 '17 at 5:52
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    ...[preceding comment continued] reads (to me) very much like the introduction section of a formal mathematical paper, where he motivates the rigorous development to follow. And I was waiting with bated breath for him to introduce an axiomatization of his brilliant but only semi-rigorous introductory discussion. But that just never comes. Do you know if anybody has subsequently tried axiomatizing his "framework", or something as close as possible? – John Forkosh May 15 '17 at 6:01
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I think the error here is that Analytic Philosophy can be succinctly summed up as though it was this tangible specific concept. There was a reaction against Hegel's grand, sweeping yet obscure proclamations about reality.

Such abstraction made philosophers realize just how much we take for granted regarding language and words. This led them to examine words and their relationships to meaning and truth much more closely.

However, it would be wrong to think that Wittgenstein's specificity and focus on the mechanics of language meant that this is 'the aim of analytic philosophy'. What he found was that language isn't logical and concrete, he found the opposite-- that language is absolutely not some objective thing to figure out. Words mean different things to different people at different times used in different ways. Essentially, even though language is complex, regarding ideas and concepts, we essentially use the same combination of a handful of rudimentary tools to accomplish almost everything regarding language and words.

You're a math guy huh? Which did you like better, geometry or algebra? Mathematics are kind of a good analogy of different 'levels of reality' in philosophy...they each have their own kind of internal coherent logic, which is what math essentially is too, wouldn't you say?-- different levels and forms of coherent systems of logic?

As a mathematician I can see why philosophy a la Wittgenstein would be particularly appealing to you. . . math guys can sometimes

Just don't forget; Wittgenstein's nitpicking wasn't the point of what he was doing, it was merely the starting point of trying to always ensure as much clarity as possible. We don't do math for maths sake, we use math to create things and understand things, we don't own cars to work on our cars

Just as we find that on the very basic, smallest, most fundamental quantum levels of reality, everything(including the math) gets really weird and abstract, there are deep truths of life that don't neatly fit into a dense newtonian logic..

I hope I'm not being too vague here.

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