Grounding Concepts

Grounding Concepts and The Origin of Concepts are two new and important books. The first is by Carrie Jenkins, a philosopher of mathematics very much in the analytic tradition; the second is by Susan Carey, a psychologist who is well connected to philosophy. Both are deeply concerned with how we acquire our arithmetical concepts, and both are empiricist‐minded (perhaps naturalist‐minded is a better description of Carey). Yet their approaches are strikingly different. Jenkins aims to reconcile three conflicting beliefs: (i) our knowledge of arithmetic is a priori; (ii) the facts of arithmetic are objectively true (realism, which she characterizes as mathematics being independent of our mental lives); (iii) sensory input is the only source of knowledge. Her solution, in brief, is to say that we acquire arithmetic concepts through empirical experience, but we learn mathematical truths through the analysis of those concepts

A priori and a posteriori · Analogical reasoning · Analogy · Analytic philosophy · Arithmetic function · Cognitive science · Contemporary philosophy · Discrete mathematics · Empiricism · Epistemology · Mental arithmetic · Naturalism · Realism · Computer Science · Mathematics · Philosophy · Philosophy and History of Science · Psychology