Don't Argue with the Logical Absolutes

The only thing I disagreed with was the bit of set theory that everything is necessarily either “A” or “not A.”

This isn’t something something you should disagree with. It is the foundation of logic: the law of non-contradiction.

“Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”-Avicenna

As trivial as demonstrating 2+2=4, this would be even more trivial. Instead of putting 2 rocks in a pile and then adding 2 more rocks and saying “see,there’s four rocks there;” all one need to do is look at a rock and say “see, its a rock, and if it wasn’t a rock, then it wouldn’t be a rock” If someone still disagrees, Avicenna’s approach looks tempting.