Allowing, Forbidding, but not Requiring: A Mathematic for a Human World

In Morris Kline’s extraordinarily thoughtful Mathematics: The Loss of Certainty (Kline, 1980), one aspect emerges clearly: over by far the greatest part of its history, mathematics has been driven by the need to describe the physical world of things. The distinction between pure and applied mathematics did not emerge until comparatively recently; no sharp distinction was made between mathematics and science in the seventeenth and eighteenth centuries, and all the great names contributed to the vast overlapping area between the two. In brief “there was some pure mathematics but no pure mathematicians” (Kline, 1980, p 281). It is unfortunate that, just as the biological and human sciences started to hive off from philosophy as separate fields of inquiry, so mathematics began to detach itself from the physical sciences. First, this means that few mathematicians today have ever been truly challenged by the biological and human sciences, with the result that old and inappropriate forms of mathemetics have been borrowed from the realm of the physical world to distort descriptions of the biological and human worlds. Second, the possibilities for creating new and appropriate qualitative mathematics have been diminished as mathematicians look increasingly to mathematics itself, rather than to the challenges beyond their distressingly private realm of discourse.