Pretense, Mathematics, and Cognitive Neuroscience
Abstract
A pretense theory of a given discourse is a theory that claims that we do not believe or assert the propositions expressed by the sentences we token (speak, write, and so on) when taking part in that discourse. Instead, according to pretense theory, we are speaking from within a pretense. According to pretense theories of mathematics, we engage with mathematics as we do a pretense. We do not use mathematical language to make claims that express propositions and, thus, we do not use mathematical discourse to make claims that are either true or false. In this paper I make use of recent findings from cognitive neuroscience and developmental science to suggest that pretense theories of mathematics fail.
1 Introduction
2 The Autism Objection
2.1 Autism and pretense
2.2 Autistic engagement with mathematics
2.2.1 Cortical folding
2.2.2 The language of mathematics
3 The Onset of the Number Sense and the Recognition of Pretense
3.1 A difference in neurology
3.2 Young and no numbers
3.2.1 When and where is the difference?
3.2.2 Damaged HIPS without impairment to engagement with fiction
4 Concluding Remarks
