Tuesday, February 23, 2010

Using Logic to prove a negative

You hear a lot of blather about people trying to prove that they can prove a negative.

To prove a negative you have to prove that you have documented all the conditions.

For example, say you want to prove there is not a weasel in your pocket.

First you have to define the boundaries of "you pocket" and the tolerance range of those boundaries.

Then you have to define exactly what a "weasel" is, the boundary conditions and tolerance range of "weaselness".

Then you have to define the time frame in which you are working, from the moment that you start to the moment that you finish, essentially the boundary conditions and tolerance range of that time frame.

Once you have done all that you have not proved that there is no weasel in your pocket, you have only proved what is in your pocket that falls within the boundary conditions that you have set.

Here is the kicker and it kicks a lot of scientists in the ass. Proving something is true does not prove something else is false.

You have only proved what is in your pocket, within specific boundaries and tolerance ranges.

You can not prove, for example, that the weasel did not jump out of your pocket and run away between the moment the time frame started and the moment you began removing things from your pocket.

Did the weasel disparate as they say in Harry Potter? Did it shift dimensions? Did it hide somehow? Unless you can prove that weasels cannot shift dimensions either at will or by accident you can't prove that there was no weasel in your pocket during the boundaries of the test.

We can assume some things, and in science we should make some assumptions. In logic people often make illogical assumptions related to knowing everything (the boundaries of the experiment). That would be a bad assumption to make, unless, like me you really do know everything.