We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.

This book discusses deep problems about our place in the world with a minimum of jargon. It argues that 'absolutist' ideas dating back to Plato continue to mislead generations of mathematicians, physicists and theologians, and reveals the underlying reasons for the current conflicts between science and religion.

A number of those actively involved in the physical sciences anticipate the creation of a unified approach to all human knowledge based on reductionism in physics and Platonism in mathematics. We argue that it is implausible that this goal will ever be achieved, and argue instead for a pluralistic approach to human understanding, in which mathematically expressed laws of nature are merely one way among several of describing a world that is too complex for our minds to be able to (...) grasp in its entirety. (shrink)

Many of those actively involved in the physical sciences adopt a reductionist point of view, in which all aspects of the world are ultimately controlled by physical laws that are expressed in terms of mathematical equations. In this article we adopt a pluralistic approach to human understanding in which mathematically expressed laws of nature are merely one way among several of describing a world that is too vast and complex for our minds to be able to grasp in its entirety.

We study the state of mechanics and astronomy between 1660 and 1675 in order to understand the extent of the commitment to the mechanical philosophy of Kepler prior to the writing of Principia.