> 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?
There is no way to know that the scenario described is not true. If something has tampered with our ability to reason, or for that matter, if our thinking is defective in the first place, then we are screwed!
Actually, we don't need to resort to hypothetical pixies for this. How do you know that when you think "4 + 3 is 7" that you are not dreaming? Maybe you will wake up and realize that 4 + 3 was 8 all along!
Worse yet, history is replete with examples of crazy ideas being accepted as indisputable fact, even by the "experts."