Basic math is another thing that can't be proven. It's known by intuition. Someone once took me to task on this, suggesting he could scientifically prove two plus two equals four. He took two apples and put them together with two more apples to give a total of four. That was his "scientific" proof.

The math wasn't proven in this case, though; it was simply exemplified with different tokens. A token is some physical representation--a sound, a mark of ink on a piece of paper, an object--that represents the unseen type, in this case, a number. Let me illustrate.

I could write "two plus two equals four," or "2 + 2 = 4," or substitute apples as my tokens instead of words or numerals. In each case, the math is demonstrated--restated with different tokens--not actually proven.

We know this to be the case because if this apple demonstration was a true scientific proof, as he attempted, then the experiment would need to be repeated to verify consistent results.

"Repeat the experiment?" one might ask. "That's silly. There's no need to repeat it. The outcome is obvious." That's my point. It's obvious to our intuition. No scientific proof is necessary, nor is it possible.

Math is obvious because of our intuition. As long as one knows what the symbols in the equation 2 + 2 = 4 represent--the numerals and the mathematical signs--a moment's reflection shows that the truth of the equation is self-evident. Indeed, if you disagreed, I would be at a complete loss to prove it to you. Either you see it, or you don't.

The math wasn't proven in this case, though; it was simply exemplified with different tokens. A token is some physical representation--a sound, a mark of ink on a piece of paper, an object--that represents the unseen type, in this case, a number. Let me illustrate.

I could write "two plus two equals four," or "2 + 2 = 4," or substitute apples as my tokens instead of words or numerals. In each case, the math is demonstrated--restated with different tokens--not actually proven.

We know this to be the case because if this apple demonstration was a true scientific proof, as he attempted, then the experiment would need to be repeated to verify consistent results.

"Repeat the experiment?" one might ask. "That's silly. There's no need to repeat it. The outcome is obvious." That's my point. It's obvious to our intuition. No scientific proof is necessary, nor is it possible.

Math is obvious because of our intuition. As long as one knows what the symbols in the equation 2 + 2 = 4 represent--the numerals and the mathematical signs--a moment's reflection shows that the truth of the equation is self-evident. Indeed, if you disagreed, I would be at a complete loss to prove it to you. Either you see it, or you don't.

__Author, Greg Koukl__