The Symbol-Grounding Problem in Numerical Cognition: A Review of Theory, Evidence, and Outstanding Questions

Tali Leibovich, Daniel Ansari

Research output: Contribution to journalArticlepeer-review


How do numerical symbols, such as number words, acquire semantic meaning? This question, also referred to as the "symbol-grounding problem," is a central problem in the field of numerical cognition. Present theories suggest that symbols acquire their meaning by being mapped onto an approximate system for the nonsymbolic representation of number (Approximate Number System or ANS). In the present literature review, we first asked to which extent current behavioural and neuroimaging data support this theory, and second, to which extent the ANS, upon which symbolic numbers are assumed to be grounded, is numerical in nature. We conclude that (a) current evidence that has examined the association between the ANS and number symbols does not support the notion that number symbols are grounded in the ANS and (b) given the strong correlation between numerosity and continuous variables in nonsymbolic number processing tasks, it is next to impossible to measure the pure association between symbolic and nonsymbolic numerosity. Instead, it is clear that significant cognitive control resources are required to disambiguate numerical from continuous variables during nonsymbolic number processing. Thus, if there exists any mapping between the ANS and symbolic number, then this process of association must be mediated by cognitive control. Taken together, we suggest that studying the role of both cognitive control and continuous variables in numerosity comparison tasks will provide a more complete picture of the symbol-grounding problem.

Original languageAmerican English
Pages (from-to)12-23
Number of pages12
JournalCanadian Journal of Experimental Psychology
Issue number1
StatePublished - 1 Mar 2016
Externally publishedYes


  • approximate number system
  • nonnumerical magnitudes
  • numerical cognition
  • numerical magnitudes
  • symbol-grounding problem

All Science Journal Classification (ASJC) codes

  • Experimental and Cognitive Psychology


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