Experience And Mathematical Knowledge

Experience and Mathematical Knowledge by Rodolfo Gaeta

According to a very common view, the main tenet of empiricism is the conviction that all human knowledge derives from sensory experience. But classic philosophers representing empiricism hold that mathematical knowledge is a priori. Mill intended to demonstrate that the laws of arithmetic and geometry have inductive origins. But Frege and others authors showed that Mill’s arguments were wrong. Benacerraf held that, since mathematical objects are abstract entities, they could not have any causal relationship with human beings, so they cannot be known by us. On the other hand, biology and psychology show that in animals and human creatures we can find innate behaviours, in accordance with the theory on natural selection. Experiments performed by Wynn and by other psychologists strongly support that very young babies can determine the results of simple arithmetical operations without any previous learning. We conclude that there are convincing reasons to accept the rationalist thesis about the a priori character of mathematical knowledge.

I seem to remember that Quine once said that if irreproachable experiences showed that some people are clairvoyant, it would be necessary to recognize the phenomenon (recall Rhine’s and others’ controversial experiments on extrasensory perception). Well, the aforementioned empirical research about babies proves nothing about the ontological status of numbers, the truth of mathematical propositions or their foundation. But, on the basis of several types of different experiments, several authors find plausible the hypothesis that certain cog-nitive phenomena, and among them some very simple — logical or mathematical operations include important elements of innate origin, something like an a priori component.

See also the old Skeptiko Resources Thread on Platonism and Mathematics.