The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Tim Little

Posts: 1,793
Registered: 2/7/09
Re: Is it possible that 3+4=8?
Posted: Jan 23, 2011 7:29 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.