IUSS Philosophy Seminars
Epistemology of Mathematics and Logic
OBJECTIVITY IN MATHEMATICS, WITHOUT MATHEMATICAL OBJECTS
June 11th, 2020, 14-16
Claims of objectivity in mathematics come in many forms, ranging from the reports of mathematicians who feel that they are discovering a universe of mathematical objects to philosophical arguments that only the objectivity of mathematical truths can account for mathematical applications in natural sciences. In the general spirit of ontological parsimony, however, the existence of causally inefficacious mathematical objects is a notoriously problematic position. In this talk, I pursue the possibility of explaining the claims of objectivity without assuming an ontology of mathematical objects. Focusing on arithmetic, I will argue that the core cognitive abilities for treating quantitative information can form the basis for the apparent mathematical objectivity. However, the numerical abilities based on the core systems need to be developed in ontogeny in a specific, consistent and culturally shared fashion. I conclude that analysing this enculturated process of developing mathematical cognition beyond the core abilities is enough to explain the apparent objectivity of mathematics. In explaining that process, there is no need for the hypothesis that mathematical objects have a mind-independent existence.
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PhD Program in Neurocognitive Science and Philosophy of Mind