Copernicus and Axiomatics

Abstract

The debate about the foundations of mathematical sciences traces back to Greek antiquity, with Euclid and the foundations of geometry. Through the flux of history, the debate has appeared in several shapes, places, and cultural contexts. Remarkably, it is a locus where logic, philosophy, and mathematics meet. In mathematical astronomy, Nicolaus Copernicus's axiomatic approach toward a heliocentric theory of the universe has prompted questions about foundations among historians who have studied Copernican axioms in their terminological and logical aspects but never examined them as a question of mathematical practice. Copernicus provides seven unproved assumptions in the introduction of the brief treatise entitled Nicolaus Copernicus's draft on the models of celestial motions established by himself, better known as Commentariolus (ca. 1515), published circa 30 years before the final composition of his heliocentric theory (On the revolutions of the heavenly spheres, 1543). The assumptions deal with the renowned Copernican hypothesis of considering the Earth in motion and the Sun,

The Archimedean Revolution of Nicolaus Copernicus

“…[…] There is no reason to doubt that he also believes these postulates to be true" (Swerdlow 1973, 437). Against Swerdlow, scholars agreed that Copernicus was not referring to axioms as self-evident truths (Goddu 2010; Bardi 2023). Moreover, the notion of self-evidence is not the only feature that mathematicians attach to axioms, which are indeed more versatile and can be employed in many ways in mathematical practice (Schlimm 2013;Bardi 2023).…”

“…Against Swerdlow, scholars agreed that Copernicus was not referring to axioms as self-evident truths (Goddu 2010; Bardi 2023). Moreover, the notion of self-evidence is not the only feature that mathematicians attach to axioms, which are indeed more versatile and can be employed in many ways in mathematical practice (Schlimm 2013;Bardi 2023). To be sure, Copernicus considered his assumptions to be true, because he was certainly not an "instrumentalist".…”