Wittgenstein is often represented as a kind of one-man transition from logical positivism to the present era of philosophy. While this is a bit of an overstatement, in my view, it certainly does give you an idea of the shape of Wittgenstein’s corpus.
The Tractatus Logico-Philosophicus was written, so-to-speak, under the influence of Russell. The logical atomism that Russell propounded forms the basis for Witty’s worldview there. This video has some digressions, but the guy speaking therein (who is kind of a douchebag) seems to explain the picture theory of meaning found in the Tractatus in a vaguely satisfactory fashion:
Now, the story as it is commonly told is that, after writing the Tractatus, Wittgenstein had some kind of existential crisis, trashed his old worldview, and wrote the Philosophical Investigations, which were, in some sense, the work of an entirely different man. Before I offer my opinion on that, I’m going to explain what the big deal is.
The two most salient parts of Wittgenstein’s later work, it seems to me, are the use theory of meaning and the private language argument. The use theory of meaning is the idea that the meaning of a word is the way that it is used in particular context, what Wittgenstein calls a “language game.” The reason that “check” means something different in hockey than it does in chess is because hockey and chess are two different situations. You don’t “check” someone in chess the way you do in hockey (which may lead to you being thrown out of the chess tournament…) because they’re two different games. This might seem like a banal, commonsensical thing to say, but think of it this way: suppose that the dictionary defines “check” in a manner that is different from the way people use the word. In that case, the dictionary is wrong. Language is defined by practice. The best that grammar books and dictionaries can do is try to record the manner in which words are used. Indeed, you pick up most of your vocabulary by imitation, by hearing people use words and then using them the same way. It’s not an intellectual thing where you look the word up and then use it correctly, or deduce its meaning rationally. It’s more like training. It’s a monkey-see, monkey-do type of thing. You learn words by seeing other people using them and then imitating those people by using the word the same way. If you get it wrong, they correct you.
The use theory of meaning is not original to Wittgenstein, which is why I said that it’s an overstatement to view him as a one-man transition from logical positivism to the next phase; J.L. Austin offered a use theory of meaning in his book How To Do Things With Words. What is unique to Wittgenstein — one of the things unique to him, at any rate — is the way he employs his use theory of meaning, which is for his private language argument.
The private language argument is so recondite that it’s hard to even explain without busting out a few technical terms, which I would then have to define, so I’ll try to explain it without doing that. Here goes nothing…
Suppose that you can talk to yourself, which you can. Now, here’s the question: could you make up a language that, in principle, only you can understand? The “in principle” part is important, and a lot of people misunderstand this about the private language argument. Sure, you can make up a language and keep it in your head, and, in practice, nobody else can understand it. However, if you so chose, you could explain that language to someone else. You could translate it for them and teach them how to speak it.
But could you make up a language that only you can understand, in principle? Something that is so personal, so unique to you, that you couldn’t explain it to someone else even if you wanted to? Wittgenstein’s answer is “no,” because his use theory of meaning dictates that, without a social context in which words can take on meaning, what you’ve created is not a language at all. It’s as if someone were to say, “But I know how tall I am!” and lay their hand on top of their head to prove it! It’s not that ineffable, private phenomena are nonexistent, per se; Wittgenstein’s famous “beetle in a box” argument says that whatever is in the box (representing ineffable private experience) is not a nothing, but not a something either. It’s more that — and this is my interpretation — Wittgenstein wants to construct a framework where he has a justification for dismissing certain kinds of question. If you ask Wittgenstein something about qualia or ineffable private experience, he wants to be able to say, “That’s not a sensible question,” and his philosophy gives him a framework for doing that. It gives him a justification for dismissing certain kinds of question.
This is an informal essay not a piece of philosophical analysis, so I’ll end with a little personal aside: I once had a dream in which I saw Wittgenstein’s philosophy in front of me. It was a machine on the ground, with cranks and levers and switches. A voice in my head said, “Wittgenstein invites philosophers to turn the wheel and dissolve any philosophical problem whatsoever.” I turned the wheel, and saw that the machine worked perfectly. However, I had a very strange, sneaking suspicion that I had somehow been duped into using the machine, that this was all a lie.
Perhaps the reason for that dream can be found in one of Wittgenstein’s own remarks:
The idea of an unbridgeable gulf between consciousness and brain-process: how does it come about that this does not come into the considerations of our ordinary life? This idea of a difference in kind is accompanies by slight giddiness,—which occurs when we are performing a piece of logical sleight-of-hand.
Philosophical Investigations, remark 412
I think that much of the suspicion of Wittgenstein comes from the fact that, when reading his own remarks, philosophers are assaulted by that same giddiness. To many people, for whatever reason, Wittgenstein’s work just smells wrong, as if there’s some subtle legerdemain doing on that is not prima facie apparent to us. And perhaps, after another 50 years of exegesis on his work, we’ll find out what that is.