Date: Jan 23, 2011 2:47 PM
Author: Craig Feinstein
Subject: Is it possible that 3+4=8?
Let's pretend that we live in a world where there are invisible pixies

running around messing everything up. Let's say you have 3 balls in

your left hand and 4 balls in your right hand. Whenever you combine

the balls together, one of these invisible pixies secretly throws in

another ball, so that whenever you count the balls, you come up with 8

balls. So in this pretend world, it is a known fact that 3+4=8. Anyone

who disputes this fact in our pretend world is considered either crazy

or stupid.

In our real world, it is a known fact that 3+4=7. But how can we be

sure that there are no invisible pixies running around taking balls

away from us causing us to think that 3+4=7 when really 3+4=8?

My point is that mathematics is considered a deductive science, in

which everything is absolutely certain. But how can mathematics prove

that the above scenario cannot be true?