It’s Not Like That!

Some big thinkers have gotten their reputation for bigness by saying things are not the way people think they are.  For example: Socrates said everything we think might be the definition of “courage” is wrong, but he proposed no alternative, better definition.   Others (Kant, Nagarjuna, the Upanishads, the pseudo-Dionysus) have done their work by saying no as well.

A worry I’ve always had is — what’s the difference between negating a sentence and affirming a sentence?  Why should it be deep?   Take a simple case: I have written an integer from one to three on a paper and not shown it to you.  If you ask “Is it 2” and I say “No” you have learned that it’s either 1 or 3.  If you asked “Is it 1 or 3” and I said “Yes” you would have learned exactly the same thing.  So in this case negation and affirmation supply precisely the same information.

Why then do thinkers like Socrates et. al. seem deep?

Imagine a different game.  I have told you that I have hidden a pawn on a chessboard which you do not see.  If you ask me “Is it on square A1” and I say “No” it might seem that I have told you the same as if I had affirmed the pawn is on one of the other 63 squares of the chessboard.

However that’s not true.  In fact, in this example, it is a very, very tiny pawn and I have placed it on the black line that separates square A1 from square A2.

Negation may negate our accustomed categories in other words and point towards a solution that we have not imagined yet.  You assumed in this case that the pawn hidden on the chessboard had to be on one of the 64 squares.  But you were wrong to do so.  The negation of your guess — A1 — was correct.  But the affirmation that you thought was logically equivalent to it — it is on one of the other 63 squares — was also incorrect.

Of course if the negator offers us literally no help at all at imagining these other possibilities he is not so helpful.  But he’s still right.




2 thoughts on “It’s Not Like That!

  1. An interesting meditation on the issue. I would add two things, perhaps obvious.

    First, philosophers often make their mark not merely by arguing that some definition is wrong, but by arguing that some widely-accepted definition is wrong. One of the tricks of the trade, quite popular in Ph.D. dissertations, is to define an ordinary term in a very precise and idiosyncratic way, from which the writer deduces that the normal understanding of the term is wrong. Many arguments for skepticism start in just that way: define “knowledge” by criteria that are impossible to fulfill, and then deduce to everyone’s astonishment that knowledge is impossible.

    Second, it seems to me that situations involving negation often have an implied universe of discourse that limits the possible answers to a question. You point out, correctly, that we can make mistakes unless we know the universe of discourse. In a game of 20 questions, allowed answers are animal, vegetable, or mineral. If someone is thinking of a number or scientific theory, he or she isn’t playing that game. In chess, pieces and pawns are on squares if they are on the board at all, and the error came from assuming that the rules of chess still applied when nobody was playing chess.

  2. It’s not so much that it is deep but that it illustrates a potential to be somewhere that is far more deep and vast than we think. Take away a word, a little life raft, and suddenly what arises is a sense of potentially being lost in a massive sea, legs kicking above whatever stirs in the darkness below. What to cling to now? What compass do you have, when all is at sea?

    It is a little shallow, but then again so is plato’s cave. Information that was unimagined (an unknown unknown) always has a sort of magic show feel to it when revealed.

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