Me, Math and the Internet (2)

PART TWO:
Integralism OF MATHEMATICS

I would like to tell you a story about a crisis: an intellectual crisis of myself these last few days. The story is like this. When I was retired from the faculty of physics, only then can I wrestle with my hobbies: math. Because I love the philosophy, then I asked where whether the mathematical objects such as numbers and any extension such as functions and mathematical equations is real. Where also lies the geometric space and all geometric shapes in it. In the end I asked where the math world is.

Since I was a theoretical physicist, so I know that the math in nature is only a small part of mathematics. That's why I had the idea that mathematical objects are in a larger world of the living ideas of Plato, which in Islamic philosophy, is then identified with the knowledge of God or the mind of God. Well, the thought of God is realized in the mathematics of nature. The rest of it is in the mind of God, but human beings can try to dive into the mind of God can.

Well, how mathematics is becoming so theological. Sorry, but we could dispose of God and left His Mind as the ideal world of mathematics, and concentrating on the new ideal world can be explored by human. So what is thinking? I got an answer from a Muslim intellectual who has now gone Endang Saifuddin Anshori. According to kang Endang, thinking is arguing with yourself. Usually, we arre arguing with others by using language. The point is the use of language, so the bottom line thinking is having a conversation with yourself.

So, the thinking is the internalization of social discourse. In other words Wittgenstein proposition that mathematics as a language game made sense. As the game of course, there are basic rules of naming and naming-through agreements. The basic rule was none other than logic. Naming was none other than a mutually agreed terms. Naming and regulations are nothing more than social consensus agreement. Thus the real math is socially constructed. This means that the postmodernists have a point.

But postmodernism does not recognize the mathematical ideal as it is assumed by Plato. For those who see mathematics as a social construction, then the whole of mathematics continues to open and flourish elsewhere. But for me the development of constructive mathematics it is directed towards the development of the mathematical ideal of Plato as it's final destination.

This integralism that combines postmodernist relativism with absolutism of the modernist thinkers about the reality of mathematics. The motion of these developments is not an order from a transcendent but a movement of an immanent self-organization. Well, that's the philosophy of integralism about mathematics. But that is not the whole integral philosophy of mathematics.

The movement from the social to the ideal is the continuation of the movement of individual personal to the social. So according integralism, mathematics follows a motion from the social to the personal through a universal ideal. While the personal is the terminal of a cycle from the universal (cosmological) through the collective (biological) to the personal (psychological).

Thus, the overall motion math, in my view, is from the universal to the individual personally, through the collective biological, back to the universal (ontological) through the collective cultural (sociological). Motion back and forth through the collective personal to the universal is the constant process of differentiation /integration which we know as the emanation /creation of the Creator in philosophy integralism.