Paula Quinon and Barbara Sarnecka
“Number concept”, “placeholder structure”, “bootstrapping”. Conceptual differences in cognitive science and philosophy
Abstract
Natural numbers are studied in different disciplines from different perspectives, but there is little cross- or interdisciplinary work on this topic. In this presentation, we consider two fields that study natural numbers: philosophy of mathematics and cognitive-developmental psychology. We believe that each field could benefit from insights generated by the other, but that mutual understanding is often hampered by differences in background assumptions, as well as by terms that are used in both fields, but to mean different things. Our objective is to facilitate future collaborations between philosophers and psychologists by clarifying similarities and differences in the background assumptions with which each field approaches the study of natural numbers, as well as in how each field typically uses the terms “number concept,’’ “bootstrapping,” and “placeholder structure.’’
Workshop: Mathematical cognition and its relevance for the philosophy of mathematics
August 30, 2014, University of Bucharest
Program
Chair: Markus Pantsar
9:00 – 10:00 – Jessica Carter: The role of visualisation in mathematics
10:00 – 11:00 – Sorin Bangu: Dolls and Drumbeats: Experiments on Infant Mathematical Cognition
11:00 – 11:30 Coffee Break
Chair: Jessica Carter
11:30 – 12:30 – Paula Quinon & Barbara Sarbecka: “Number concept”, “placeholder structure”, “bootstrapping”. Conceptual differences in cognitive science and philosophy
12:30 – 13:30 – Kai Büttner & David Dolby: Numbers as Pictures of Extensions
13:30 – 14:30 Lunch Break
Chair: Sorin Bangu:
16:30 – 17:30 – Markus Pantsar: Origins of Numerical Cognition and the Epistemology of Arithmetic
