The Mathematical Image

The proof is elegant and the result profound. Still, it is typical mathematics; so, it’s a good example to reflect upon. In doing so, we will begin to see the elements of the mathematical image, the standard conception of what mathematics is. Let’s begin a list of some commonly accepted aspects. By ‘commonly accepted’ I mean that they would be accepted by most working mathematicians, by most educated people, and probably by most philosophers of mathematics, as well. In listing them as...

 Post Modernism Leads to Totalitarianism

There is objective truth to be learned by observation, and the knowledge gained gives power that other "ways of knowing" have not. But the more dangerous problem with postmodernist thinking is its a priori nature. Not truth, but a political goal has to be served—in this particular case the goal of openness, or tolerance without judgment. But without acknowledgi objective truth, all arguments become rhetorical and therefore can go on forever—and we are either paralyzed by it or we must res...

 The Idea of Objective Truth

Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quit...