Cog Sci/Philosophy Talk: Paula Quinon (Warsaw) “Cognitive structuralism: Explaining the Regularity of the Natural Numbers”
Paula Quinon (Warsaw University of Technology) will give a talk at Boğaziçi on Friday, April 30th, 2021, 5-7pm.
Respondent: Sam Clarke (Philosophy & Centre for Vision Research, York University, Toronto)
“Cognitive structuralism: Explaining the Regularity of the Natural Numbers”
ABSTRACT: According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. I call the “core cognition paradigm” any framework that commits to the view that the conceptual content of a formal concept is scaffolded on core cognition. It is inspired by work by Spelke in “Core knowledge” (2000) and by Spelke and Kintzler, also called “Core knowledge”, (2007) put forward the idea that complex cognitive skills and concepts can be based on a set of “building block” systems (called also “core knowledge” or “core cognition” systems) that emerge early in human ontogeny, play an important role in phylogeny of concepts, and are detected in non-human animals. Combining representations from these systems enable humans to supervene new complex concepts (which are not a simple combination of the partial concepts, but display original features). Carey (2009) provides a model of the role of core cognition in the creation of mature mathematical concepts, called “bootstrapping”. In my talk, I conduct conceptual analyses of various theories of the acquisition and the development of the concept of natural number that has been formulated within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess an exact quantity of the elements in a collection without counting them), or on the ability to approximate quantities (i.e., to assess an approximate quantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm (Zenter and Eerola 2010; Winkler (2009); Honing 2012).
In order to systematize the previously mentioned research on the acquisition and the development of the concept of natural numbers, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. I suggest that as in the philosophy of mathematics, those positions within the core cognition paradigm that make significant use of the conceptual content responsible for the structural aspect of the natural numbers progression, should be thought of in structuralist terms. Structuralism in philosophy of mathematics is summarized by the famous slogan “mathematics is the science of structure” (Shapiro 1991). I propose to call those positions which both refer in an important way to structural properties and make appeal to core cognitive resources, “cognitive structuralism”.