(January 5, 2016 at 10:22 am)Faith No More Wrote: … I do lean towards mathematics being a fundamental property of nature as opposed to simply being a human construct…Where I take umbrage, however, is when the supernatural is applied to math. There's no need to apply magical explanations to something when nature appears to be perfectly capable of being responsible.
Now we are getting somewhere. I imagine that with just a little better understanding of definitions, perhaps I can persuade you that maybe, just maybe, what you call my ‘pompous blustering’ may actually point to a somewhat defensible position, one that even an atheist could hold. As I see it, dicohotomies like natural/supernatural and scientific/spiritual serve more as terms of art than precise distinctions. In my preceding posts, I made a clumsy efforts to reveal these ambiguities.
The position of OP is that knowledge is either scientific OR spiritual. Now anyone can see that ancient civilizations had knowledge of mathematics even without the benefit of the scientific method. According the OP’s way of classifying things the mathematical truths know from antiquity are ‘spiritual’. In the West defining knowledge as “Justified True Belief” goes back at least as far back in time as Plato. Modern science, as a means of acquiring knowledge, is only about 500 years old. The OP’s author appears to be ignorant of this. I don’t blame anyone from using terms of art. I use them all the time. It is only natural that many errors and misunderstandings follow when the same word can covey multiple meanings. ‘Natural’ is itself one such adjective. Some people think that natural and reality are the same. I do not. Nature refers only to physical objects, their features and attributes. Reality includes both physical and non-physical objects, like circles and triangles. Nor does non-physical necessarily mean magical, depending of course on what you mean by magic.
My rudeness reflects my impatience with the inane notion that only empirically verified facts count as knowledge. Mathematical facts, like the value of pi, are certain and perfectly accurate. Empirical facts, like the speed of light, are tentative and approximate (though they may be very very precise). The value of pi is not an average based on measurements of roughly circular objects.
Like you I am not an expert. At the same time someone doesn’t need to know every detail of a subject in great detail to know something. Subjective facts depend on the perceptions and judgments of a knowing subject. The validity of objective facts do not.
The value of pi, is what it is, regardless of what anyone thinks about it. Now some will say that things like values and equations are descriptive and not prescriptive. We can say the same about the laws of nature. And that is true as far as it goes. But the question remains: to what do these descriptions refer? The laws of nature do not prescribe how natural objects will behave but there is a tacit understanding that such laws adequately represent the nature of real physical objects. Likewise the mathematical truths do not prescribe the value of pi; but rather, describe the nature of real non-physical objects, i.e. circles. I see no magic in any of this.
