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Monday, October 31, A.D. 2011
Painting in the Dark

Happy Halloween!

I do not have anything to add about our favorite less than Christianized pagan feast that I did not already mention in “All Hallow’s Eve.” Enjoy your All Saints’, your All Souls’, and even your Samhain.

However, the shadowy character of the holiday reminds me of an image that came to me during a recent discussion about mathematics. Nominalism is so rampant in the spiritual air that we breathe that I frequently find myself arguing with folks who hold that men created mathematics—ex nihilo, I suppose. In my last quixotic attempt to open the eyes of the blind to realism, my interlocutor suggested that mathematical concepts were entirely conventional. If that were true, then we should be able to dispose of them and to create another system of mathematics from scratch. Yet, even when we tweak various axioms that underly a particular mathematical approach, as in non-Euclidean geometry, the fundamental logic of mathematical relations continues to operate. There is much controversy in the philosophy of mathematics regarding the relationship between mathematics and formal logic, and I do not understand the problem enough to have any conviction on the matter. Yet, I cannot see how we could maintain logic or an understanding of mathematical relations without the other. I do not know if one implies the other, but, intuitively, they seem to coexist, at least in our thought process. To say that mathematics is entirely conventional is to say that we can think independently of what we mean by mathematical relations, and I do not see how such is possible. It is like asking a computer to function without programming or like asking a painter to copy a visible setting in the absence of light. We cannot think beyond the confines of thought. Could we have thought without mathematical reasoning? I am not sure if the simplest act of recognizing identity involves a mathematical judgment, but I am not comfortable in maintaining that we could still keep reason without such a significant constituent of it. We may manipulate which principles we apply in a given situation or thought experiment, but we do so still knowing and thinking with the suppressed principles in mind. Can we do violence to νοῦς without losing our mind entirely?

Posted by Joseph on Monday, October 31, Anno Domini 2011
Philosophy | EpistemologyMetaphysicsComments
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