In order to grasp the full extent of Wittgenstein’s contribution, you can’t read the Tractatus without also reading Philosophical Investigations. For starters, a lot of the latter is a critique of the former, so perhaps the best thing to do with the pair of them is throw both books into into a sack and and let them fight it out. Even if you’re interested in the narrower question of what relevance Wittgenstein has for the current state of computational linguistics, and even if you have the sense that the latter is more right than the former, you still can’t have one without the other. So if I’m going to start with a quick flyby, I might as well do a quick flyby of them both.
Stylistically the two books are worlds apart. Ostensibly Philosophical Investigations is the more accessible. Where Tractatus is like a math book woefully bereft of examples and having a lot of formal logic prerequisites, Philosophical Investigations is a chatty, discursive set of examples written in everyday prose. But this transparency is deceiving. If the Tractatus is too dense, Philosophical Investigations is too easy. Each individual paragraph seems completely lucid, but it can be difficult to keep enough of them in your head at once to string together the argument.
“String together” is the wrong metaphor here anyway. The paragraphs aren’t beads, they’re glimpses. There are a few common threads, but no specific conclusions. For a computational linguist, the meaning-is-use thread (roughly paragraphs 1 through 142) is the most relevant. The other threads that discuses private language, express skepticism about our ability to meaningfully describe sensations, or a challenge to the notion that we can focus our attention internally–all that is independent of state-of-the-art Natural Language Processing. Not that it might not be relevant at some point in the future, but at the moment, there isn’t any particular theory of the mind baked into the field’s worldview. Contemporary language engineers are content to just observe linguistic phenomena from the outside, remaining agnostic on issues of internal representation and therefore willing to grant nodding acquiescence to Wittgenstein’s strong claims in this area.
As for the “meaning-is-use” business–there’s definitely a sense in which this could be a slogan of contemporary NLP inasmuch as statistical models of surface phenomena count as a reasonable account of “use”. Unlike the Tractatus, which seems to have inspired a particular program which has informed theoretical linguistics and at least some approaches to NLP, it’s not clear if the less programmatic Philosophical Investigations has relevance beyond this slogan. Notions of probability, for instance, make no appearance.
Here’s my takeaway so far: the Tractatus specifies a model of language. In it, Wittgenstein claims this model can handle certain empirical facts but not ethics, aesthetics, lots of other things people like to talk about. Therefore these are things whereof we cannot speak. An alternate explanation is that we can speak of these things, it’s just that the system laid out in the Tractatus isn’t up to the task. Since that system got roughly translated into theoretical semantics and early NLP, identifying the ways it is not up to the task will help us spot inadequacies in its descendants. Philosophical Investigations will assist us inasmuch as it will provide a set of snappy counterexamples of Wittgenstein’s earlier work. The meat of it still isn’t relevant to NLP, which is too bad, because it strikes me as the more interesting book.