Tagged: Philosophy of Mathematics

John Von Neumann: The Mathematician. 1947

John von Neumann wrote The Mathematician which was published in Works of the Mind Vol. I no. 1 (University of Chicago Press, Chicago, 1947), 180-196. It has also been published in von Neumann’s Collected Works. A discussion of the nature of intellectual work is a difficult task in any field, even in fields which are not so far removed from the central area of our common human intellectual effort as mathematics still is. A discussion of the nature of any intellectual effort is difficult per se – at any rate, more difficult than the mere exercise of that particular intellectual...

Mathematical Realism

How does mathematics and reality relate to each other? Some mathematicians believe that mathematical entities are “real”, and this view can be characterized as a version of Platonic philosophy. Quine and Putnam developed an argument in support of mathematical realism, which starts with the observation that mathematics is indispensable for almost every other science. Here is a short description of these indispensability arguments in the philosophy of mathematics. It is quoted from the  Stanford Encyclopedia of Philosophy, the entry is written by Mark Colyvan: “One of the most intriguing features of mathematics is its applicability to empirical science. Every branch...