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Old 10-09-2008, 03:09 AM   #24
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Originally Posted by Achilles View Post
Originally Posted by Samuel Dravis View Post
It's true that 2+2=4 is confirmed by observation, but the generality of the equation is not justified by those observations (this is part of Bahnsen's argument, actually).
At the risk of sounding contrarian, I think I'm going to have to disagree once again. An alien species might have other words for "two", "plus", "equals", and "four", however I find it very difficult to believe that the idea itself would be in any way, shape, or form, foreign to them.
I agree with Achilles here. Bahnsen here is trying to claim that mathematics and logic is inductive and cannot be known to be true. Unfortunately, if you allow me to use logic here, that is a contradiction.

Originally Posted by Samuel Dravis View Post
However, the proposition 2+2=4 is a part of our language and used in a certain way within it, and that use is intertwined with how we can talk about it. So, if an alien were to come and learn how we use it - see the context in which we apply it - then they'd know what we meant by 2+2=4. It's universal in that anyone who uses our methods of solving mathematical problems will inevitably come up with 4 as the answer to 2+2. Of course, there's no warranty for the results coming from anyone using some other method!
What method? The method of defining numbers? If the quantity denoted by '2' is increased by another quantity of '2' the final quantity is defined as '4' (for any base > 4).

Perhaps we should question whether the idea of any 'number' is has any real meaning outside the human experience as well. It's just as abstract as logic and even more simple. I suppose Bahnsen would suggest that numbers are inductive as well and hold no universality to them or that God is required for them to be reliable?

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