Numbers, Minds, and Magnitudes

The study of the cognitive systems underlying our arithmetical abilities has become a thriving domain of research, producing mountains of data detailing how magnitude representations could allow humans to develop mathematically-viable mental content. For some, it is tempting to see the tremendous progress of the study of the cognitive bases of our arithmetical practices as a step towards a return to mathematical psychologism. However, such an optimistic outlook for psychologism fails to acknowledge that the metaphysical implications of the empirical study of numerical cognition have received little attention, and that platonism is still a dominant position in the foundations of mathematics. The aim of this conference is to bring together philosophers and psychologists interested in magnitudes and their representation to allow them to take a fresh look at the question of whether psychology can inform the ontology of numbers and magnitudes. In particular, this conference will explore the extent to which the psychological study of magnitude representations can shed light on the metaphysics of magnitudes like space, time and number.