Mathematical Explanation as Part of an (Im)perfect Scientific Explanation: An Analysis of Two Examples

Abstract

Alan Baker argues that mathematical objects play an indispensable explanatory role in science. There are several examples cited in the literature as solid candidates for such a role. We discuss two such examples and show that they are very different in their strength and (im)perfection, although both are recognized by the scientific community as examples of the best scientific explanations of particular phenomena. More specifically, it will be shown that the explanation of the cicada case has serious shortcomings compared with the explanation of the case of Königsberg's bridges. We will argue that the latter is a perfectly reliable scientific explanation that employs mathematical reasoning whereas the former is not.

The Role of Mathematical Tools in Scientific Phenomenon Explanation – A Guarantee of Reliability or a Pillar of False Credibility?

“…A probability for the occurrence of such a random event is extremely small. 11 One of the explanations of this biological phenomenon includes elementary facts from number theory. Namely, since prime number is divisible only by 1 and by itself, the cicada whose life-cycle is stated by a prime number has better chances to survive than the cicada whose life-cycle is stated by a composite number.…”

“…SeeHoward (1937) andBaker (2005) 11. Probability that a randomly chosen natural number from, say, segment[8,20] will be prime number is approximately 0.3.…”