CFA: 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.

Confirmed speakers include

• Christopher Peacocke (NCH, Columbia)

• Jacob Beck (Y ork)

• Ophelia Deroy (LMU Munich) and

• Zee Perry (Boulder)

In addition to the four confirmed speakers, organizers are seeking contributions from early career researchers (PhD students or postdocs) on questions such as:

• Can the study of magnitude representations shed new light on how humans interact with – that is, think about, refer to, and gain knowledge of - quintessentially abstract objects like numbers?

• Are some magnitude representations primitive while others are derived from these? If so, is numerical magnitude primitive?

• If representations of number are derived from more basic magnitude representations, as some (e.g. Walsh 2003, 2009) have suggested, does this mean that it is possible to construct numerical content from other mental content?

• Given that numerical magnitude is discrete while other magnitudes are continuous, does numerical magnitude have a different status from other magnitudes?

• What is the relationship between numerosity and number?

• To what extent do data on magnitude representations carry philosophical currency regarding realism or anti-realism about numerical magnitude? For example, do relations between magnitudes reflect how our minds work, or does metaphysical investigation into the nature of magnitudes precede how our minds conceive them, as Peacocke (2015) has argued? Can empirical data help to decide this issue?

• Some have argued that magnitude representations have nonconceptual content. If this is true and numerical content is built from magnitude representations, then how can we account for the construction of conceptual content out of nonconceptual content?

Any submission that addresses similar questions related to the nature of numerical magnitudes and their relationship to mental content will be considered.Those interested in participating should send an anonymized extended abstract (between 700 and 1000 words) to Jean-Charles Pelland at [email protected] before April 1st 2019.