A friend has just started a Bachelor of Arts degree here at Waikato. As part of her first year study, she’s chosen to do a Philosophy paper. Apparently, one of the questions that has been posed, is "Is maths real?".
Well, what is real? You certainly can’t put ‘maths’ in a box and give it to someone. like you could with a chair or a chicken. But does it have more substance than just some made-up statements about how to add things or describing how large angles are? I’ve often wondered, for example, whether it would be possible to have a universe in which the value of pi was four. In our universe, it isn’t. But is pi, the ratio of the circumference of a circle to its diameter, necessarily 3.14159265…in all universes? I don’t know. I guess it depends on what a circle is.
So is physics real? I would think that it is more real than maths. I mean, physics is supposed to describe reality. Gravity is gravity. Objects attract each other proportional to their masses and inversely proportional to the distance between them. That’s what happens. It’s hard to be a physicist if you’re not a positivist, or at least have strong positivist leanings. In other words, if you don’t believe that there is a real world out there that we can know about, and that we can find out about this world objectively (e.g. by doing experiments), you are going to struggle to be a physicist. (It is true that quantum theory throws a spanner in the works at this point. The quantum world is weird indeed -an example here – and raises big issues about what is real.)
Recently, I was at a teaching seminar that seemed to be populated mostly be social scientists. In social science, a common paradigm is social constructivism, or namby-pamby waffle as it is known by positivists. In social constructivism, what the world is is constructed in one’s mind, and that what you can find out about it inevitably depends upon how go about finding out about it. In other words, everything is relative.
So, back to the point. Where does maths sit in all of this? I’m not sure it does. It’s hard to believe that maths depends on your point of view. It doesn’t matter how you look at it, 1 + 2 doesn’t equal 4, and it never will. But neither does it fit well with reality, either. 1 + 2 would be 4 in any universe, wouldn’t it? Maybe maths sits in some strange space of its own, separate from ties with this universe but not ‘made up’ in anyone’s head. So what is it? Er, that’s getting too close to philosophy for my liking. I await my friend’s response with interest.
Perhaps the best answer is to say that maths is as real as philosophy.