2022/04/12 by Francesco Nappo, Nappo, Francesco, Nicolò Cangiotti +3
Arts and Humanities · Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #00A30 #Bayesian Modeling and Causal Inference #Biomedical Text Mining and Ontologies #FOS: Mathematics #History and Overview (math.HO) #Philosophy and History of Science #math.HO #msc:00A30
paper · pdf · doi:10.48550/arxiv.2204.05643
25 pages, 2 figures
openalex publication_date 2022/04/12 · arxiv created 2022/06/15 · arxiv updated 2022/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an incremental and a non-incremental form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting 'hybrid' framework captures many important aspects of the use of analogical inference in the realm of pure mathematics.