Abstract
Mathematical cognition has become an interesting case study for wider theories of cognition. Menary (Open MIND 25(T):1–20, 2015) argues that arithmetical cognition not only shows that internalist theories of cognition are wrong, but that it also shows that the Hypothesis of Extended Cognition is right. I examine this argument in more detail, to see if arithmetical cognition can support such conclusions. Specifically, I look at how the use of numerals extends our arithmetical abilities from quantity-related innate systems to systems that can deal with exact numbers of arbitrary size. I then argue that the system underlying our grasp of small numbers is an unhelpful case study for Menary; it doesn’t support an argument for externalism over internalism. The system for large numbers, on the other hand, clearly displays important interactions between public numeral systems and our cognitive processes. I argue that the large number system supports an argument against internalist theories of arithmetical cognition, but that one cannot conclude that the Hypothesis of Extended Cognition is correct. In other words, the large number case doesn’t decide (on the basis of an inference to the best explanation) between the Hypothesis of Extended Cognition and the Hypothesis of EMbedded Cognition.
Highlights
The goal of this paper is to look at the Discrete Number System (DNS) case study in more detail, combining literature from cognitive science on the functioning of the brain with more theoretical studies of numeral systems [such as Zhang and Norman (1995) and Schlimm and Neth (2008)]. This has not yet been done in the context where the DNS is used in an argument for Hypothesis of Extended Cognition (HEC) over Hypotesis of Embedded Cognition (HEMC), though details resulting from this combination of approaches are relevant: the small number DNS is, I argue, not a good basis for an argument for externalism, whereas the large number DNS at least decides in favour of EXT
The cognitive processes that make up the large number DNS are structured in a way that builds on the structure of the numeral system we use
Performance is clearly influenced by contingent features of the numeral system, and it seems that the underlying cognitive processes are at least combined in different ways depending on the kind of numeral system one uses
Summary
The goal of this paper is to look at the DNS case study in more detail, combining literature from cognitive science on the functioning of the brain with more theoretical studies of numeral systems [such as Zhang and Norman (1995) and Schlimm and Neth (2008)] This has not yet been done in the context where the DNS is used in an argument for HEC over HEMC, though details resulting from this combination of approaches are relevant: the small number DNS is, I argue, not a good basis for an argument for externalism, whereas the large number DNS at least decides in favour of EXT. I, argue that the large number DNS does not decide between HEC and HEMC (on the basis of an inference to the best explanation)
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