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Wittgenstein set out in particular to subvert the seductive theories about mind and consciousness that philosophers since Descartes had puzzled and battled over. Again and again in Philosophical Investigations, he catches his interlocutors in the act of being suckered by their overconfident intuitions about what their words mean--what their words must mean, they think--when they talk about what's going on in their own minds. As he says, "The decisive moment in the conjuring trick has been made, and it was the very one that we thought quite innocent." (Today's neuroscientists fall into these same traps with stunning regularity, now that they have begun trying to think seriously about consciousness. Unfortunately, Wittgenstein's work has not been appreciated by many scientists.) But didn't his own antidote to such theories constitute a theory of the mind? That is just one of many quandaries and paradoxes he has left behind for posterity.
In 1939, Wittgenstein's Cambridge seminar on the foundations of mathematics included a brilliant young mathematician, Alan Turing, who was giving his own course that term on the same topic. Turing too had been excited by the promise of mathematical logic and, like Wittgenstein, had come to see that it had limitations. But in the course of Turing's formal proof that the dream of turning all mathematics into logic was strictly impossible, he had invented a purely conceptual device--now known as a Universal Turing Machine--that provided the logical basis for the digital computer. And whereas Wittgenstein's dream of a universal ideal language for expressing all meanings had been shattered, Turing's device actually achieved a somewhat different sort of universality: it could compute all computable mathematical functions.
Happily, in those days before tape recorders, some of Wittgenstein's disciples took verbatim notes, so we can catch a rare glimpse of two great minds addressing a central problem from opposite points of view: the problem of contradiction in a formal system. For Turing, the problem is a practical one: if you design a bridge using a system that contains a contradiction, "the bridge may fall down." For Wittgenstein, the problem was about the social context in which human beings can be said to "follow the rules" of a mathematical system. What Turing saw, and Wittgenstein did not, was the importance of the fact that a computer doesn't need to understand rules to follow them. Who "won"? Turing comes off as somewhat flatfooted and naive, but he left us the computer, while Wittgenstein left us...Wittgenstein.
Some will say that in the longer run, Wittgenstein's legacy will prove to be the more valuable. Perhaps it will. Wittgenstein, like any other charismatic thinker, continues to attract fanatics who devote their life to disagreeing with one another (and, presumably, with my brief summary) about the ultimate meaning of his words. These disciples cling myopically to their Wittgenstein, not realizing that there are many great Wittgensteins to choose from. My hero is the one who showed us new ways of being suspicious of our own convictions when confronting the mysteries of the mind. The fact remains that one's first exposure to either the Tractatus or Philosophical Investigations is a liberating and exhilarating experience. Here is a model of thinking so intense, so pure, so self-critical that even its mistakes are gifts.