Philosophy and Mathematics

Mathematicians work forward; philosophers backward. The ideas come into the head, and you have to go backward to explain them to others. This is a tedious process. Philosophy is like one who stumbles upon the end of a journey, but has to go back into the woods to find those who are lost in order to show them what was found. It requires showing the person this wrong turn, that wrong turn, then, finally, the house in the woods (the end of the trip). But here is the key: philosophers themselves do not initially find their house by following maps or rules, they find it by solving puzzles along the venture. They find it in bursts of thoughts. They can see a pathway before others can, but they don’t know exactly where it goes. They know that the house is somewhere near – this path or that one – but they can never be certain until they have found it. Once found, however, they can never be credited without finding the others who remain lost and showing them. The final expressed product, therefore – what is known as X’s philosophy – is a work that backtracks. I do not think this is true with mathematics. Mathematics always works forwards. Mathematics takes its people along the venture together, with it. When it is successful, all have arrived at the same house through the same vehicle. The work product is not defined by “back tracking.”