Is mathematics purely a human creation, or does it exist independent of us and we have ‘discovered’ it?

From what I’ve briefly read on Russell, Frege and the history of mathematics is that it seems there is no solid ground that mathematics can depend upon without us (humanity) having accepted a long series of axioms that may or may not be consistent. In other words, we can never be certain that (or at least as far as we know today) what we take to be self evidently true, is actually true. Further, it seems apparent that the principle of logic is a process of linguistic analysis rather than mode of arriving at certainty.

This is an area of philosophy I’ve never really considered before. In fact, I assumed that mathematics was independent of human thought. Now, I don’t think it is and there’s a majority of philosophers who have already came to the same conclusion. This needs further investigation, methinks!

Adam

Does this mean aliens can’t add up?

🙂

Who knows?! Might explain why we don’t see many alien spaceships in the sky*

Adam

* This is not the place to cite any sightings of UFOs!

I think I would answer “yes” to that question. In one sense it is a human creation, but there are at least some aspects (numbers?, geometric concepts such as “point” and “line”?) that seem to be external “givens” and must

exist in any conceivable physical reality.

MathsMan

I see what you are saying. However, how sure can we be about these external givens? It seems to me that we have to accept them just as they appear, and not be certain. That is, our accepted axioms are based on observation. I’m reminded here of the what happens when one tries to draw a triangle* on a sphere. Here, the sum of the angles are less than 360Â° – this is not a ‘triangle’ in the observable sense, merely a representation of the concept. In fact, it’s probably fair to say, that we cannot draw a ‘perfect’ triangle, no matter how hard we try. We will always have the problems of earth curvature and even space/time curvature. This is just one example of the many axioms we accept to be correct, but all we really have is a concept.

I must admit, I was somewhat naive, or ambitious, with the thought that mathematics could lead to a system of guaranteed knowledge. I thought that it was a priori and that it could be relied upon without fail. Or, in other words, a self-contained system guaranteed to produce certainty.

Adam

Adam

You are being manipulated by the red herings of some philosophers about the nature of mathematics – if I state for example that ‘the sum of the internal angles of any triangle drawn on a single plane is always the same’, this is a true statement. It does not depend on the existence of a human mind for it to be true.

I have claimed on my blog (http://religious-tolerance.blogspot.com) that mathematics belongs to the supernatural realm since it is not subject to science. The example of the triangle is an example of the interaction of the supernatural with the natural since this particular branch of maths has to be expressed in terms of space. Another branch I call simple arithmatic (1+2=3) is independent of the space and time. There is no superstition about this at all!

“You are being manipulated by the red herings of some philosophers about the nature of mathematics – if I state for example that â€˜the sum of the internal angles of any triangle drawn on a single plane is always the sameâ€™, this is a true statement. It does not depend on the existence of a human mind for it to be true.”

Isn’t this what I said? OK, perhaps your’s is a little more eloquent 😉

Mike and notaphilosopher,

I understand your position in that you believe mathematics is independent of the human mind. I disagree but I donâ€™t at this moment have the time to give a full explanation why.

Your position is technically known as

. I claim, and will show (later!), that there are problems with this position. For now you will have to bear with me as Iâ€™m away for a few days.mathematical realismAdam