Comment author:Marcello
07 November 2007 05:39:37PM
5 points
[-]

Venu: You definitely can do that in Mathematics, but that's because reasoning about Mathematics has some special properties that most reasoning about the real world does not.
1. Math is black and white
If you find a proof for something, it's true. Until you do, you can't really call your hunch math.
However, in the real world, it's very easy to find arguments for things that are false.
2. Math has monotonicity
What this means is, that if you use Lemma A and Lemma B to prove Theorem Z, then whether or not Lemma C is true has nothing to do with whether your proof of Z still stands. The real world isn't like this, in that you can't arbitrarily pick a subset of the things you know to reason from. If A, B, C and Z were causally related events in the world, ignoring C would be cherry-picking your evidence.

The upshot is, if you try to backward chain from a conclusion in our non-monotone probabilistic world, you're quite likely to find a nice sounding but possibly flawed argument starting from cherry-picked premises. In fact, if your conclusion is wrong, you pretty much have to, unless your argument generator is so awesome that it *fails* to come up with arguments when you try to find one for a wrong conclusion. Sadly, we know from experience that the human argument generator isn't that awesome.

## Comments (88)

OldVenu: You definitely can do that in Mathematics, but that's because reasoning about Mathematics has some special properties that most reasoning about the real world does not. 1. Math is black and white If you find a proof for something, it's true. Until you do, you can't really call your hunch math. However, in the real world, it's very easy to find arguments for things that are false. 2. Math has monotonicity What this means is, that if you use Lemma A and Lemma B to prove Theorem Z, then whether or not Lemma C is true has nothing to do with whether your proof of Z still stands. The real world isn't like this, in that you can't arbitrarily pick a subset of the things you know to reason from. If A, B, C and Z were causally related events in the world, ignoring C would be cherry-picking your evidence.

The upshot is, if you try to backward chain from a conclusion in our non-monotone probabilistic world, you're quite likely to find a nice sounding but possibly flawed argument starting from cherry-picked premises. In fact, if your conclusion is wrong, you pretty much have to, unless your argument generator is so awesome that it *fails* to come up with arguments when you try to find one for a wrong conclusion. Sadly, we know from experience that the human argument generator isn't that awesome.