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