I've been giving this debate my peripheral attention, which explains my short and poorly-worded (and reasoned) posts. Allow me at least a brief attempt at a better explanation of my view.
In a way, Jadam, you're right; almost all things can be explained by mathematics. I still hold that not all things can be. But the explanation that math provides is often the most trivial, superficial kind of explanation.
Let's take up love as an example. You could certainly analyze love mathematically. You can see that love originates as a series of chemical reactions and nerve firings in the brain (although this all seems far more like chemistry and psychology to me, in which math is merely incidental). But that doesn't even begin to scratch the surface of love and its significance for human beings. Have you ever been in love? Have you ever seen someone who is? Do you think that tracking a neutransmitter across a synapse really cuts to the core of that feeling? Do you think that neural firing is all there is to love?
Of course not. Love is incomprehensibly complicated, significant, and vital. You cannot possibly explain love to me in mathematical terms, and I pity the person who thinks he or she can.
You also suggested that notions like 'the good' and 'the just' are merely man-made constructions. Yet do you not think justice would exist without man? Is a concept really dependent on the being that can behold it? Does it simply come into being because we are aware enough to conceptualize it? Surely not.
I don't deny that math is a useful explanatory tool for much of the world around us, but there are certain situations in which math is utterly useless and explains nothing of value. Not least of these is the realm of ideas. You absolutely cannot explain to me certain ideas in terms of math. Explain to me tolerance, or patience, or charity in terms of a formula. Yet would you deny these ideas' fundamental importance in human life?
I've always been a bit troubled by the hubris of science -- that it believes that it can describe anything and everything fully and systematically. You can reach a certain point where systematic science breaks down and renders itself meaningless, or as Nietzsche says, it "coils up... and finally bites its own tail."
Which brings me to the Nietzsche quote that most fully sums up my view: "There is, to be sure, a profound illusion that first saw the light of the world in the person of Socrates: the unshakable faith that thought, using the thread of causality, can penetrate the deepest abysses of being, and that thought is capable not only of knowing being but even of correcting it." This is easily mistakable for anti-science diatribe, but it's not. I don't deny science's incredible value. But just like religious faith, science has been overextended into the sort of dogmatic framework that claims license over everything. That's why I find Nietzsche's characterization of science as an unshakable faith interesting; for me, it parallels neatly the path and perversion of religious faith.
Science has its place, and that place is expansive and important. But when you reach its boundaries, something else altogether is required. For me, that something is 'myth,' loosely termed.
