The first reading really reminds of the class a couple weeks ago when we looked up a copy of Newton's Principalia to see how much it was worth. It really makes you wonder how can we put price on things like that? How do we determine how much a piece of artwork is worth, is it based on the technical difficulty, on the virtue of who made it, or do we put more weight into how the artwork makes us feel? This can then be extended to trying to figure out how much a human life is worth in the case of accidents where someone gets killed? How can insurance companies put a monetary value on a human life, how can you quantify the value of a soul? It is these types of questions that mathematicians quickly realize they couldn't answer, and that they were also questions they had no reason to answer.
It was then interesting to see how mathematics try then to formalize itself into what it is today, as a set of rules and symbols. That as mathematics came out from behind the shadows it had to restructure itself so that it could hold up to scrutiny as it went beyond this world, and transverse into the realm of hypothetical. It was interesting to see how as the more formalized and "modern" math got, the more it took on the shape of philosophy. It would ask questions that you would not normally think to ask, then it would set out to find the answers. To me mathematics are one in the same, in that both aim to try to unravel the mysteries of the universe. The only difference is that mathematics deals with the quantitative questions while philosophy tackles the qualitative answers. That is how I view them, but what do you guys think? Is math and philosophy two sides of the same coin working in unison to unravel the mysterious complexities of the universe, or are they mortal enemies in an eternal struggle for dominance over each other till the end of time?
I don't think that philosophy and math are enemies, they've given far to much to each other for that to be real. In fact, having never taken calculus when it was described briefly to me yesterday (especially zeno's paradox and whether or not infinity exists), it seemed (to me) remarkably philosophic. I'm not sure I would so as far as to call them separate heads of a coin either, I think I would call them two branches of the same tree, with the same roots and trunk, and where if one succeeds it aids the health of the other.
ReplyDeleteThis is best exemplified when you use a mathematical solution to prove a theory you arrived at through philosophy (I'm just thinking of how we use statistics in International Relations, but I'm positive many other fields do this too).
I don;t know if I could comfortably assume that math and philosophy are one in the same or that they are mortal enemies. Sure, they may have many things in common and the thought process may be very similar with regards to proofs and what not but I think they are too different to consider being the same. Math is a way of describing the world around us with a set of quantities where as philosophy is a way of thinking about abstract intangibles. At least the rudimentary math that I've been exposed to has had at least been mostly grounded by physical quantities in space. Philosophy however doesn't share that same grounding.
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ReplyDeleteWhile I agree with the above two commenters in that philosophy and math are not mortal enemies, after all for many years the two were one and the same, I have a hard time viewing math and philosophy as "two sides of the same coin." Math produces tangible, useful, provable results that have changed the world. Philosophy on the other hand, while important in creating a well rounded person, seems to me the be pretty much the same discipline as it was five hundred years ago. When you ask questions that have no answer, it is hard to move forward rather than getting bogged down in arguments.
ReplyDeleteMath and philosophy are not one in the same or two sides of a coin. They both try to define the world around them. They both have a system where they use proofs to validity or falsify the ideas created. Both have to use high levels of logic to be able to understand concepts. I believe in order to be a great mathematician you would also have to be able to think philosophically. Mathematics is, like previously commented is a more tangible approach to defining the world around us. Philosophy is more abstract and not at all a tangible thought. Math is viewed as more of an absolute truth because it is tangible.
ReplyDeleteTo me, it seems as though math and philosophy have similarities to each other (in some ways), but at the same time, they are also different. I remember when I was younger (like in elementary school), I used to think of mathematics as “just numbers” and philosophy as “asking big questions” (keeping in mind that at this point in time, I didn’t formally take any philosophy courses, most of my thoughts on philosophy came from TV shows). It was only after I took Math 310 and Philosophy 107 when I first began drawing some connections to the two fields of study. Despite the fact that my thoughts on philosophy didn’t really change that much, I came to realize that mathematics also dealt with asking big questions.
ReplyDeleteHowever, the difference that I found was that the questions that math and philosophy asks is pretty different. Furthermore, the ways that math and philosophy tackle the way they answer the questions are different. I once read in a textbook about Euclidean and Non-Euclidean Geometry that the only things that can be “proved” are mathematics and pure logic. Everything else can only be highly speculated. I think that this is why people believe that mathematics is “absolute truth”, because there are things to back up people’s claims. For philosophy, (with the exception of logic questions) none of the questions asked can ever be “proven” true or false. However, despite this, I think that both fields uses the same type of thinking, and, as you said, “[works] in unison to unravel the mysterious complexities of the universe”.