Tuesday, April 21st, 2015, 13.15-15.00
Philosophy Department, Lund University
Philosophy of arithmetic and number cognition: re-assessing the basis of interdisciplinarity.
Case study: Approximate Number System.
Frege in Grundlagen formulated a severe criticism of ‘psychological influence’ in foundations of mathematics. My general objective is to reconsider Frege’s position and re-examine possible mutual influences between the research on the concept of natural numbers in philosophy of mathematics and the results from developmental cognitive science. In this talk I will focus on one of the basic cognitive systems of number-cognition, called Approximate Number System.
Paula Quinon and Barbara Sarnecka
“Number concept”, “placeholder structure”, “bootstrapping”. Conceptual differences in cognitive science and philosophy
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
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
In Spring semester 2014 I visited Sarnecka Cognitive Development Lab at University of California at Irvine. The main research line in the Lab is a study of number cognition in preschool children. My objective was to understand specificity of cognitive scientists approach to number concept and to study the possible use of their results in philosophy of mathematics.