Richard at Philosophy Sucks! gave this example of how math truths might be empirically justified:
Suppose that you had two pens of sheep; one with 6 and one with 7 sheep. Now suppose that you counted the sheep individually in each pen (and got 6 and 7) and then you counted all of the sheep and got 14. Suppose you did it again. 1. 2. 3. 4. 5. 6. Yep six sheep in that pen. 1. 2. 3. 4. 5. 6. 7. Yep seven sheep in that pen. Then all the sheep. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Suppose that this was repeated by all of your friends with the same results. Suppose that it was on the news and tested scientifically and confirmed. Suppose that this phenomenon was wide spread, observable, and repeatable. If this were the case we would be forced to admit that 7+6=14 is true therefore mathematics is empirically justified.
I got to say I’m little disappointed with this example, because it doesn’t work at all… In the comment there I said that to make things fair for the rationalist, we should after counting the sheep from first pen, do both those things in same time: a)continue counting the sheep in both pens and b)count the sheep from the second pen.
So, we count the sheep from the first pen, 1. 2. 3. 4. 5. 6, and then for each sheep in the second pen we continue both countings – – so (7. 1.) , (8. 2.) , (9. 3.), (10. 4.), (11. 5.), (12. 6.), (13. 7).
What we did is then, that we counted all the sheep (13), and counted the number of sheep in both pen (6 and 7).
But anyway, I still have trouble figuring out what would it mean for math claims to be empirically justified. It is not like as if we can find mathematical entities in the world, so that we can test them. We could do this kind of counting and be surprised that everytime when we get 6 and 7 we get 13, but surely it is weird thing to do – given the we agree of how we count, it can’t be otherwise!