[ExI] Meaningless Symbols.

[Gordon Swobe]

--- On Fri, 1/15/10, Stefano Vaj <stefano.vaj at gmail.com> wrote:

> It may surprise you, but I have implemented in my own brain
> at a very young age the algorithm allowing me to multiply integers of
> arbitrary length.

Nobody questions that we can intentionally run algorithms in our brains. But how can you come to know the meanings of symbols merely by virtue of running programs in your mind that manipulate symbols according to syntactic rules as computer programs actually do? You can't.

Less easy to see is that your computer calculates the answers to mathematical questions without understanding the meanings of the numbers.

I think you'll agree that as you count to ten on your fingers, your mind but not your fingers understand the numbers. We invented calculators because we needed to count to eleven. They don't understand numbers either.

-gts