I have a mathematical mind. It is the curse of being a philosopher, or rather, having a philosophical bent. I studied mathematics and philosophy in college. Then, I went back and studied computer science. I’ve had more logic than I know what to do with. And sometimes that is a severe disadvantage. Because a mathematical mind is often an inflexible mind.
In my case, I look at things as either true or false. In mathematics, for example, most problems have definitive answers. If you do the work and follow it, you can establish the truthfulness or falsity of an assertion with certainty. When the answer to a mathematical question is found, it is established and irrefutable. Math is the only science like that; math is the only science in which the term “proof” has its truest meaning. Unfortunately, it is an open question whether or not the field of mathematics actually applies to the world. Back when I was studying philosophy, there were basically three (or was it five?) theories on what mathematics actual is. There was Plato’s view of mathematics; that is, it is about the eternal relationships between real properties (Plato’s Theory of Forms). There was Kant’s view of mathematics; that is, it is really the result of the structure of the human mind. And there were three other theories, I think, although I remember only one: that mathematics is just a game. In my view, the solution is either Kant or Plato. Either two plus two equals four because the property of twoness always leads to four when it is doubled (Plato), or because we can’t see the relationship any other way, because our minds are structured that way and limited. As far as math being a game … that never satisfied me. I’ve gone off on a tangent here; let me try to get back. The original point was: How does math apply to the world? If Plato is right, it is a part of the world. If Kant is right, it’s a part of our minds. If the game theory is right, it is an invention of our own making.
Once I was in a stock room trying to put together a shelf. The shelves didn’t quite fit right. I could tell by looking at the shelf that the angle was off slightly, and that geometrically, the shelves would never fit. Hence, it was no use trying to make them fit and I gave up the cause as hopeless. Whereupon, my boss and another individual promptly forced the shelf into place through brute force and completed the shelf. As rigid as metal is, it does bend; it is not as rigid as a perfect geometrical line. Metal can be distorted. Errors can be forced. So what was the geometry of the situation? It could describe the shelf effectively, but in a manner that led one to believe the problem had no solution. In such a situation, it doesn’t seem that the mathematics was “real.” Brute force could conquer it. The real world could resolve the problem where math indicated there was no solution. Upon reflection it appears that geometry, my Euclidean understanding of it, anyway, was derived from the real world; that pure math exists only in the human mind. That said, if pushed, I can give you a few examples from Number Theory where the opposite is true; situations that absolutely can’t be forced, where a mathematical determination of “the solution is impossible” guarantees that the solution is, in fact, impossible. So, what is mathematics? I don’t know. All I know is that I tend to think along mathematical lines.
It’s great to have an analytical mathematical mind, but it also stinks like a rotten egg; I have the common sense of a stone. I’ve spent most of my life proving that last and it’s something I don’t think I can change.