Saturday, July 23, 2011

Reading Wittgenstein

It's always an adventure, primarily, I think, because the texts we have are mostly in the form of notes Wittgenstein was jotting to himself. They are not put together into a continuous stream of thought, so it can be difficult to discern the gestalt of what Wittgenstein is up to. Nevertheless, even while struggling with the issue of the big picture, one finds many little gems scattered throughout.

For instance, one of my favourites is Wittgenstein's demonstration of why, in order to determine that someone is wrong about some specific thing, we must recognize him as being mostly right in that area. Let's say, for instance, my friend says to me, "Snakes are mammals." Well, I ask him to show me a snake, and he points out a garter snake in the grass. He generally is right about snakes, but wrong about in which order they belong.

But imagine that he says to me, instead, "Snakes are four-dimensional, vermillion hypercubes." Well, in this case, I hardly know what to say, except that whatever he is talking about, it's not the snakes I am talking about.

Or imagine two students taking a math quiz. One has written down numbers for her answers, generally near the range of the correct answer. This student might have gotten every answer wrong, but we can say that only because she was in the ballpark: she, in general, understood what was going on.

But another student, where the answers should be, has written a number of sonnets. It would be misleading to say this student answered the math problems incorrectly: instead, she was doing something other than answering math problems!


  1. This doesn't at all disprove your point (which is, of course, correct), but it would certainly be possible, if one were so inclined, to write correct answers in sonnet form on some of the math exams I've given.

  2. .. not sure if you are aware of this Wittgenstein discussion group.



"If your approach to mathematics is mechanical not mystical, you're not going to go anywhere." -- Nassim Nicholas Taleb