Plato wrote on the door of his academy, "Let no one enter here that is ignorant of geometry". Aristotle is known for studying the sciences and even putting them into categories and giving them names. Other famous philosophers were also known for their work in mathematics such as Descartes, Leibnitz, and Pascal. A lot of philosophers came into philosophy through mathematics.
Mathematics was back then, and even now, still one of the most important means of gaining knowledge and understanding in this world. What is it about mathematics that makes it so reliable? Why do we think that we can trust mathematics in so many areas of study and everyday life? I don't know what a professor, mathematician, or a scientist would say but my answer is that mathematics makes the world go round. Without mathematics we would still be living like cavemen. So, I guess mathematics was the beginning of civilization, or the beginning of "thinking".
I think what mathematics represents is a kind of truth. Through deductive reasoning you get to an answer based on facts that you have. We get to the truth based on what there is and the way things are. Then there is another factor, the human mind. How the mind takes facts and interprets everything is also important.
I think I'm going to stop at this point because after throwing the human mind in the situation I feel that I'm not sure of anything else beyond that point.
The connection seems odd to those who come to Philosophy through the current disciplinary divisions of the university because mathematics seems so closely aligned with experimental science and "wordier" disciplines like Philosophy seem to belong with English Literature and History.
ReplyDeletePhilosophy is immersed in language, reading and writing well are essential to philosophical literacy, and philosophers find excellent fellow travelers in the ranks of other humanities disciplines; but, philosophy has much in common with folks on the other side of campus, as well.
In the Republic, Plato lists mathematics as one of those activities that accustom the mind to apprehending the forms of things. Mathematics insists that we lift our thinking from concrete things to more universal concepts. And, Plato argues, opens the intellectual door for us to move toward thinking of ideas more universal than those considered by mathematicians. In that sense, mathematical thinking becomes for philosophers a middle term between apprehending concrete things and apprehending the true forms of things.
All of this sounds very hifalutin (and it is!), but one can think of it in far less intimidating terms: Mathematical thinking is Philosophical gymnastics. Mathematics teaches the philosopher to have a clear, organized mind, to demand evidence and valid proof, and to take seriously things that might not present themselves directly to our senses. Good stuff, that.
So . . . go take some math, Philosophers! You'll be the better for it.
-ct
"Mathematical thinking is Philosophical gymnastics". Dr. Thomas, that was awesome.
ReplyDeleteSomething that's shaped my thinking in this area is the [phenomenological] cognition that mathematics historically functions as Being's manifestation in the arithmetical --- in other words that the mathematical is really a specific orientation we have toward the world, a lens we have for examination that perhaps was issued to us on loan for a while.
ReplyDeleteA good example of how this plays out in the history of ideas is Descartes' suggestion in the Discourse on Method that we can compare our lived-in world to one of perfect regularity and law-governed order. We *can* imagine that the universe and the earth came to be as the product of a swirl of physical matter subject to mathematical physics. It is *possible* to conceive anything on earth as having x,y,z coordinates and observable properties that exhibit mathematical patterns.
Beyond these observations however the mathematical can be viewed as more of a hypothetical language that we've stipulated to possess some analogy to the world.
I would suggest that the journey from math to philosophy comes more from how mathematical truth opens our eyes more broadly to the wonder of logical truth. This idea relates to how a lot of analytic philosophers liken philosophical logic to mathematics (where it's not clear which of these actually is more primary).