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Extended mathematical cognition: external representations with non-derived content

Published version
Peer-reviewed

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Authors

Schlimm, Dirk 

Abstract

Abstract: Vehicle externalism maintains that the vehicles of our mental representations can be located outside of the head, that is, they need not be instantiated by neurons located inside the brain of the cogniser. But some disagree, insisting that ‘non-derived’, or ‘original’, content is the mark of the cognitive and that only biologically instantiated representational vehicles can have non-derived content, while the contents of all extra-neural representational vehicles are derived and thus lie outside the scope of the cognitive. In this paper we develop one aspect of Menary’s vehicle externalist theory of cognitive integration—the process of enculturation—to respond to this longstanding objection. We offer examples of how expert mathematicians introduce new symbols to represent new mathematical possibilities that are not yet understood, and we argue that these new symbols have genuine non-derived content, that is, content that is not dependent on an act of interpretation by a cognitive agent and that does not derive from conventional associations, as many linguistic representations do.

Description

Funder: Social Sciences and Humanities Research Council of Canada; doi: http://dx.doi.org/10.13039/501100000155

Keywords

S.I. : MathCogEncul, Mental content, Representational vehicles, Vehicle externalism, Cognitive integration, Enculturation, Mathematical cognition

Journal Title

Synthese

Conference Name

Journal ISSN

0039-7857
1573-0964

Volume Title

197

Publisher

Springer Netherlands
Sponsorship
Leverhulme Trust (Leverhulme Centre for the Future of Intelligence under Grant RC-2015-067)