The Weirdness of If
Over on Imago Dei, much is being made of the unfairness of logical asymmetry.
Once again, how can we have scientific evidence against the presence of something when we are not allowed to have scientific evidence supporting the presence of something?
This takes me back to teaching an artificial intelligence class some years ago. The answer to the conundrum lies in a basic asymmetry in propositional logic. One runs into it very quickly, because it has to do with that most basic of relations, implication. It is all about “if”.
If I make a statement A, and I say that when A is true, then statement B is true, I have just asserted that if A, then B.
OK, so what does a truth table for this look like?
A B (if A then B) --------------------------- 0 0 1 0 1 1 1 0 0 1 1 1
If we observe that B is actually true, that is consistent with A being true, but it is just as consistent with A being false. On the other hand, if we observe that B is in fact false, then we know that A cannot be true.
This is the basis for Popper’s procedure of falsification, and the reason why Popper so strongly asserted that no scientific theory could obtain absolute proof: while our observations can tell us which things are false, they cannot reliably inform us as to which things are true.