Comments on: Limits of Mathematics http://www.reason42.com/2007/08/07/limits-of-mathematics/ The more I know the less I understand - Tao Le Ching Fri, 30 Dec 2011 23:52:37 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: reason42 http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-128 reason42 Mon, 13 Aug 2007 17:10:52 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-128 Mike and notaphilosopher, I understand your position in that you believe mathematics is independent of the human mind. I disagree but I don’t at this moment have the time to give a full explanation why. Your position is technically known as <strong><em>mathematical realism</em></strong>. I claim, and will show (later!), that there are problems with this position. For now you will have to bear with me as I’m away for a few days. Adam Mike and notaphilosopher,

I understand your position in that you believe mathematics is independent of the human mind. I disagree but I don’t at this moment have the time to give a full explanation why.

Your position is technically known as mathematical realism. I claim, and will show (later!), that there are problems with this position. For now you will have to bear with me as I’m away for a few days.

Adam

]]> By: notaphilosopher http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-127 notaphilosopher Mon, 13 Aug 2007 12:58:05 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-127 "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." Isn't this what I said? OK, perhaps your's is a little more eloquent ;) “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.”

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

]]> By: mikereflects http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-126 mikereflects Sat, 11 Aug 2007 12:23:12 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-126 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! 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!

]]> By: reason42 http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-125 reason42 Wed, 08 Aug 2007 16:47:25 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-125 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 360° - 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 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 360° – 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

]]> By: MathsMan http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-124 MathsMan Wed, 08 Aug 2007 13:24:36 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-124 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 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

]]> By: reason42 http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-123 reason42 Tue, 07 Aug 2007 20:47:32 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-123 :) 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! :)

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!

]]> By: notaphilosopher http://www.reason42.com/2007/08/07/limits-of-mathematics/comment-page-1/#comment-122 notaphilosopher Tue, 07 Aug 2007 20:27:28 +0000 http://www.reason42.com/2007/08/07/limits-of-mathematics/#comment-122 Does this mean aliens can't add up? Does this mean aliens can’t add up?

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