Number concepts for the concept empiricist

Abstract

Dove (2009) and Machery (2007) both argue that recent findings about the nature of numerical representation present problems for Concept Empiricism (CE). I shall argue that, whilst this evidence does challenge certain versions of CE, such as Prinz (2002), it needn’t be seen as problematic to the general CE approach. Recent research can arguably be seen to support a CE account of number concepts. Neurological and behavioral evidence suggests that systems involved in the perception of numerical properties are also implicated in numerical cognition. Furthermore, the discovery of associations between spatial and numerical representations also lends independent support to a CE approach. Although these findings support CE in general, certain versions of the theory may need revising in order to accommodate them. In particular, it may be necessary to either jettison Prinz's (2002) Modal Specificity Hypothesis or to revise one’s method for individuating modal representational formats.

Keywords:

• Cognition
• concept empiricism
• concepts
• embodied cognition
• mathematical cognition
• number concepts
• perception
• representation

Acknowledgements

Many thanks to Richard Pettigrew, Finn Spicer, Guy Dove, Jesse Prinz, and Hannes Leitgeib for their useful feedback and interesting discussions regarding earlier versions and presentations of this paper. Many thanks too to all of those that contributed to discussions at presentations of previous versions of this paper at the 9th International Symposium of Cognition, Logic and Communication in Riga; the Bristol-Munich Workshop; and the 17th Oxford Philosophy Graduate Conference.

Notes

¹ Abbreviations: CE = Concept Empiricism, SCE = Strong Concept Empiricism, MSH = Modal Specificity Hypothesis, ANS = Approximate Number System, hIPS = Horizontal Intraparietal Sulcus, SNA = Spatial-Numerical Association, IPS = Intraparietal Sulcus.

² A consequence of this is that proponents of CE need not be committed to the kind of anti-nativism that is associated with traditional empiricism. It may be the case that cognition involves innate representations that are, nonetheless, couched in perceptual or motor representational formats.

³ It should be noted that the notion of “embodied” representations has been used in a variety of different contexts to mean a number of different things. Here, it is used to emphasize that conceptual representations involve representations of the body used in perception and action, rather than the more radical claim that parts of the body are active constituents of mental representations.

⁴ It should be noted that many proponents of Embodied Cognition that support the claim that I am here calling CE might not actively identify as supporters of Concept Empiricism. I refer to the main claim as CE, rather than Embodied Cognition, in order to pick out a particular strand of the Embodied Cognition approach, since the term Embodied Cognition has been used to refer to a range of different interrelated claims (Shapiro, 2011, p. 2).

⁵ Though Machery and Dove present similar arguments for the problematic nature of numerical cognition for CE, they do so in the service of different conclusions. Machery’s critique of CE is presumably best seen as providing support for his more general rejection of unified accounts of concepts (Machery, 2009). Dove (2009, 2011), on the other hand, offers a more positive account, advocating the need for both modal and amodal representations in an account of concepts.

⁶ It may be possible to question whether the ANS really meets all of Fodor’s criteria. However, even if its qualification for a few of the criteria can be called into question, this is not sufficient to rule out the ANS’s modularity, since modularity is presented as a “cluster concept” (Fodor, 1985, p. 3).

⁷ A number of proponents of CE have pointed to evidence that suggests that modal representations play a significant role in linguistic comprehension (Glenberg & Kaschak, 2002; Pulvermüller, 2008; Zwaan, 2004). Some have criticized these approaches, arguing that linguistic comprehension requires amodal symbols (Weiskopf, 2010). The question of whether a CE account of number concepts is tenable is presumably prior to considerations about comprehension, since most would assume that concepts are a precursor for comprehension. Thus, if linguistic comprehension is problematic for CE in general then this is not a problem that is specific to the case of number concepts.

⁸ There are some obvious exceptions to this general trend. For example, ‘1.0001’ contains more digits that ‘1,001’. However, cases such as this tend to arise in the context of more advanced, and therefore developmentally less basic, mathematics. Furthermore, the presence of various counterexamples to the iconicity of numerical language should not detract from the fact that widespread iconicity distinguishes numerical language from ordinary language which is rarely, if ever, iconic.