Seminar Series in Analytic Philosophy 2025-26: Session 9

Prime Numbers and Periodical Cicadas: The Case for Mathematical Platonism?

Luca Caiti (LanCog, University of Lisbon)

21 November 2025, 16:00 (Lisbon Time – WET)

Faculdade de Letras de Lisboa

Sala Mattos Romão [C201.J] (Departamento de Filosofia)

Abstract: In his “Are There Genuine Mathematical Explanations of Physical Phenomena?” (2005), Alan Baker proposed an indispensable mathematical explanation for a peculiar biological case: the prime-numbered life-cycles of North American periodical cicadas. Following his “Explanatory Indispensability Argument” (EIA), we should then be ontologically committed to mathematical entities. In this paper, I criticize that view on two main grounds. First, I show that both the alleged indispensability and the explanatory structure Baker offers are fundamentally flawed. In doing so, I draw upon recent biological findings and analyze the discussion in the scientific literature, including a new theory for the phenomenon in question—the so-called “internal-clock theory”. Accordingly, if we take the cicada case study and the EIA, it actually follows the exact opposite of what Baker argued: that his mathematical explanation is not indispensable and that we should not be committed to the existence of mathematical objects. Second, I examine the EIA’s general stance and outline possible ways to reject it, regardless of the indispensability of Baker’s mathematical explanation. Consequently, we shouldn’t endorse such an ontological commitment, even if Baker’s mathematical explanation were indispensable—let alone given that it is not.