Symmetries as grounds for induction: the case of the Ω− baryon

• Published in: Synthese (Dordrecht) 2023-10, Vol.202 (4), p.126, Article 126
• Main Author: Tricard, Julien
• Format: Article
• Language: English
• Subjects: Education; Epistemology; Function words; Heuristic; Humanities and Social Sciences; Logic; Metaphysics; Original Research; Philosophy; Philosophy of Language; Philosophy of Science; Physics; Reasoning; Symmetry
• ISSN: 1573-0964; 0039-7857; 1573-0964
• DOI: 10.1007/s11229-023-04344-7

By analyzing the successful prediction of the Ω − particle by M. Gell-Mann and Y. Ne'eman (in 1962), I bring to light a so far unexamined role of symmetries in physics. Symmetries within a family of objects or states (here, strongly interacting particles) may be used not only to classify the discovered ones, but also to predict the existence of unobserved ones, as instances of a nomological conjecture. To this end, I criticize previous accounts of Ω − ’s episode as involving abductive reasoning or a very problematic, Pythagorean “Reification Principle” (Bangu, 2008), or as a case of heuristic reasoning (Ginammi, 2016; Bueno & French, 2018). I show that an adequate reconstruction of the episode relies on a principle according to which symmetric elements of a mathematical representation must be jointly interpreted, provided that a structuralist, background assumption is made on the represented physical system. I finally show that this rule reveals a nomological use of symmetries, which are used to bring together different states or objects as instances of the same law and to predict unobserved instances, such that mathematics—here, Group Theory—provides us with induction instruments to expand our knowledge of the physical world.