Take a piece of Swiss cheese: it has "cheese" and "holes". Weight the piece, count the holes. Write down the numbers. Start making more holes. Notice that the more holes you make, the higher the hole count, the lower the weight of the piece. Now ask yourself a very silly question: "how many holes do I have when the weight of the cheese is zero?"

Obviously no one is silly enough to waste time with a question like that, right? Right...

While mathematics seems to require sentient beings, does the mathematical relation "2+2=4" continue to be true if no one was around to perform the computation?

That's a simple question. Imagine, for a moment, that you are the only sentient creature in the whole universe. That's not a difficult thing to do, as we often have just that feeling. So, while you are the only sentient being around, stop performing computations and ask yourself the question: "is '2 + 2 = 4' true?"

The answer is as obvious to me as it should be to you: "no one knows"

Does mathematics exist independent of humanity ...

The above gedanken experiment should make it clear that that question has no known answer.

... or does it exist entirely in our heads?

It's only possible to know the answer the latter question if you could answer the former. Since the former has no known answer, this one doesn't either.

What you have to understand is that your question about math is as ill-founded as the question about the number of holes in a piece of cheese that doesn't exist. It's a powerful feature of human language that you can use it not only to express truths, but also falsehoods and nonsense. You have to watch out for it, as it can be very difficult to tell falsehoods and, especially, nonsense from truth. There is, in fact, a whole field of human activity dedicated to the pursuit of nonsense: it's called metaphysics.

Good luck!

• Here's the problem... - harvey1 - July 17, 2003 - 14:33 UTC
  • On knowledge - mikelev - July 17, 2003 - 14:47 UTC
• Rational thought is Welcome - doctordick - July 18, 2003 - 00:08 UTC
  • LOL - harvey1 - July 18, 2003 - 01:41 UTC
  • Doctor Dick, you were my Igor ! - sillyuniverse - July 18, 2003 - 01:43 UTC
• michael levine: "What you have to understand" - sillyuniverse - July 18, 2003 - 02:00 UTC