some preliminary roughings out of my thesis


since the very dawn of philosophy, man has looked to mathematics to describe the world accurately. we rely on math for certainty. 


in chimes the frenchman. 
"we are not merely skeptics, nor only mathematicians. we are Christians. we can not only doubt, we may not only affirm. we must, somewhere, submit." - pascal, in a rough paraphrase of pensée 201.

 in the Christian cosmos, then, what abides? where can we stand? what abides? 


the jew. 
"So now faith, hope, and love abide, these three; but the greatest of these is love." - st. paul, 1 cor. 13:13
              
faith                 hope                          love                          -- normative aspect: philosophy of math
   |                       |                                 |
knowledge      truth                         wisdom                      -- situational aspect: physics (math applied)
   |                       |                                 |
grammar         logic                         rhetoric                     -- existential aspect: teaching math
   |                       |                                 |
   |                       |                                 |
   |                       |                                 |
arithmetic     algebra              quantum theory                   -- the kinds of mathematics we learn
                     calculus      non-euclidean geometries


math, at its foundation, is faith
               we have faith in God as the Creator, as the Constant One, the Righteous one. math is trustworthy not because it is self-evident, it is trustworthy because God is; because He loves us and does not lie to us. 2+2=4 because He is forever 1 which is always 3. 

math next is hope
               we hope to one day have dominion over creation. the Creator has hidden glories everywhere for us to search out. this means that when we do a calculus problem involving a decreasing mass, increasing acceleration, highly variable friction, and decreasing gravitational force, we simply hope that our rocket will actually escape the atmosphere. we have faith in the numbers working out, but there is only hope that it will actually describe the world. we hope in the righteousness, the trustworthiness of our God. 


and the greatest of these is love. 
               mathematics is the meter of creation, which was sung by God. and He is love. mathematics, then, is the meter chosen by love. and so, to choose the right meter, we must be loving. i declare to you a mystery. force is nothing more or less than the mass of a thing times its acceleration. always. most of the time. unless you're not on earth. then, at least you can be sure that the energy is equal to the mass of the thing counted as many times as light is fast squared. except, that's not really how it works all the time. because turns out there's something faster than light on the universe. truly, a great mystery, yet i give you a greater. my mother's forehead wrinkled between her eyebrows. it was a wednesday. my father says, "come on, let's grab lunch quick. you're getting a headache from not eating, aren't you?" my mother's forehead wrinkled between her eyebrows. this time it was a thursday. my father says, "hey let's get out of here. you're worried about eating too much. so let's go." 
               here is the riddle's heart, here the knot of the mystery: for the creation is our bride, and we are her husband. we must know her parts well enough to know which language we use to speak to her. we should love creation enough to know that the language of newton's calculus is wonderful, but creation doesn't like that language when we're speaking about black holes and electrons. what will happen on the day that we actually love the handiwork of our Creator? i daresay we'll fly faster than light, fall upwards, and burn things without them being consumed. i dare, even, to say that we shall be creators ourselves. that we shall give life at last, and not death. then, death, thou too shall die. 

If we were first of all to take stock of ourselves, we would realize how incapable we were of progressing further. How could a part possibly know the whole? But we will perhaps aspire to knowing at least those parts on our own level. But the parts of the world are so connected and interlinked with each other that I think it would be impossible to know one without the rest.

pascal, pensée 230, pp.70-71

That is our true state. That is what makes us incapable of certain knowledge or absolute ignorance.

pascal, pensée 230, p.70


man is incapable of certainty. there it is. 

We must  know where to doubt, where to affirm and where to submit when necessary. Whoever does not do this does not understand the force of reason. There are some who fall short of these three principles, either by affirming that everything can be demonstrated, lacking all knowledge of the demonstration, or doubting everything, lacking the knowledge of where to submit, or by submitting to everything, lack the knowledge of where to discriminate.

pascal, pensée 201


and just like that, pascal wipes away the arguments of descartes and most of modern/postmodern mathematical theory. beautiful.