War of Intuition: A Platonistic, Non-Foundational Approach to Maths

So I have a title (for my big nasty essay). It's far too pretentious to keep but I like it for now. My thought is that maths as we know it is just a shadow of the truth, that we can use different and overlapping theories (pluralities, sets etc) as analogies but that we can never fully get the right picture and that is because the truth is outside of our "set" or "language" and so we cannot fully comprehend. Like with Plato and his good old shadows of Forms or, I don't know, say Paul and his poor reflections.

Analogies, allegories, parables... they all seem to serve a good purpose. It's kinda the way of the world and not just a communication tool. Maybe it's just me "seeing" semblances of truth in everything I do and the stretching it to a contentious metaphor but it seems that everywhere there are signs of something else, something bigger: hair cuts, Disney songs, a moment with a friend, a great picture, a poem, a cool proof, a new political appointment (OK I am a bit Obama-happy right now!), a mundane task or a speed limit on the motorway. We can see some great truth in a million different tiny things and it's like some kind of set hierarchy when the little extends to the big. Or a fractal where it just keeps getting reiterated larger and larger but always the same basic form. Or when, maybe you glimpse eternity 'cause of a perfect shopping trip or well-timed doctors appointment. All these things are made of something bigger.

Now. All I have to do is express this without relying on the bible to backup what I say. More to the point, I have to rely on stuff that is far more complicated and bizarre (which is saying something) and show some kind of pretense that I know what any of that jazz is about, without talking too much about Cheerios or saying "well, Duh, it's obvious...". Which is hard 'cause that seems to be all that the proper Philosophers do.

But I do have a temporary title, which is sort-of progress.