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Extended mathematical cognition: external representations with non-derived content.

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Summary
This summary is machine-generated.

Vehicle externalism suggests mental representations can exist outside the brain. This study argues that novel mathematical symbols, introduced through enculturation, possess genuine non-derived content, challenging the idea that only biological representations are original.

Keywords:
Cognitive integrationEnculturationMathematical cognitionMental contentRepresentational vehiclesVehicle externalism

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Area of Science:

  • Cognitive Science
  • Philosophy of Mind
  • Neuroscience

Background:

  • Vehicle externalism posits that cognitive representations can be instantiated outside the brain.
  • A key objection is that external representations only have derived content, unlike original, biologically instantiated content.
  • This challenges the scope of vehicle externalism in cognitive science.

Purpose of the Study:

  • To respond to the objection that external vehicles only have derived content.
  • To develop Menary's theory of cognitive integration, specifically enculturation.
  • To argue for the existence of non-derived content in external representational vehicles.

Main Methods:

  • Analysis of Menary's vehicle externalist theory.
  • Examination of the enculturation process in cognitive integration.
  • Case studies of expert mathematicians creating new symbols for novel mathematical possibilities.

Main Results:

  • Expert mathematicians introduce new symbols for not-yet-understood mathematical possibilities.
  • These novel symbols possess genuine non-derived content.
  • This content is not dependent on interpretation or conventional associations.

Conclusions:

  • Enculturation can lead to external representational vehicles with non-derived content.
  • This supports vehicle externalism by demonstrating original content in non-biological representations.
  • The study reframes the debate on the nature of cognitive content and its external instantiation.