Numbers: Their Tales, Types, and Treasures.
Chapter 11: Numbers and Philosophy
11.3.AN ONGOING DISCUSSION
In 2007, an article titled “Let Platonism Die,” by British mathematician E. Brian Davies (1944–), revived the discussion. Davies points out that the belief in the independent existence of an abstract mathematical world makes implicit assumptions about the working of our brain. Platonists seem to believe that the brain can make a connection to the Platonic realm and thus reach beyond the confines of space and time into an abstract cosmos. For Davies, this view “has more in common with mystical religion than with modern science.”4 He points out that scientific studies about how the brain creates mathematics indicate that mathematical thought processes have a purely physiological basis, and that these studies “owe nothing to Platonism, whose main function is to contribute a feeling of security in those who are believers. Its other function has been to provide employment for hundreds of philosophers, vainly trying to reconcile it with everything we know about the world. It is about time that we recognized that mathematics is not different in type from all our other, equally remarkable, mental skills and ditched the last remnant of this ancient religion.”5
In 2008, two follow-up articles by American mathematicians Reuben Hersh (1927–) and Barry Mazur (1937–) took the discussion further. The question of the reality of mathematical objects has nothing to do with the fact that mathematics is a human and culturally dependent pursuit. Thus, numbers could well have an independent existence, even if a basic understanding of numbers was provided by evolution, and even if the mental images of numbers created in our mind depend on sociological factors. Dr. Mazur gives the following example: If we were not interested in numbers, but in “writing a description of the Grand Canyon, and if a Navajo, an Irishman, and a Zoroastrian were each to set about writing their descriptions, you can bet that these descriptions will be culturally dependent, and even dependent upon the moods and education and the language of the three describers.”6 But this does not “undermine our firm faith in the existence of the Grand Canyon.”
According to Reuben Hersh, Platonism “expresses a correct recognition that there are mathematical facts and entities, that these are not subject to the will or whim of the individual mathematician but are forced on him as objective facts and entities.”7 But in his opinion, the “fallacy of Platonism is in the misinterpretation of this objective reality, putting it outside of human culture and consciousness. Like many other cultural realities, it is external, objective, from the viewpoint of any individual, but internal, historical, socially conditioned, from the viewpoint of the society or the culture as a whole.”