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Topic: Is it possible that 3+4=8?
Replies: 21   Last Post: Jan 29, 2011 9:06 AM

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Tim Little

Posts: 1,793
Registered: 2/7/09
Re: Is it possible that 3+4=8?
Posted: Jan 23, 2011 7:29 PM
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On 2011-01-23, Craig Feinstein <> wrote:
> 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.

Let's write this as 3' + 4' = 8', where the primed numerals represent
numbers in pixie-world which don't behave the same way as our numbers.
It only takes a moments thought to see that a' = a+1 makes them
equivalent: e.g. 3' + 4' = 4 + 5 = 9 = 8'.

So it would be indistinguishable from a world where people just used
different names for numbers. The arithmetic structure of natural
numbers would be identical.

> 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?

Mathematics is not a science at all, as has been pointed out many
times in a recent thread. Your question is founded on a false


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