See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/295910425 The symbol-grounding problem in numerical cognition: A review of theory, evidence, and outstanding questions Article in Canadian Journal of Experimental Psychology · February 2016 DOI: 10.1037/cep0000070 CITATIONS READS 8 534 2 authors, including: Daniel Ansari The University of Western Ontario 144 PUBLICATIONS 5,569 CITATIONS SEE PROFILE All content following this page was uploaded by Daniel Ansari on 01 March 2016. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. APA NLM tapraid5/cae-cae/cae-cae/cae00415/cae0277d15z xppws Sϭ1 10/1/15 15:45 Art: 2015-1231 Canadian Journal of Experimental Psychology / Revue canadienne de psychologie expérimentale © 2015 Canadian Psychological Association 2015, Vol. 69, No. 4, 000 1196-1961/15/$12.00 http://dx.doi.org/10.1037/cep0000070 The Symbol-Grounding Problem in Numerical Cognition: A Review of Theory, Evidence, and Outstanding Questions AQ: au Tali Leibovich and Daniel Ansari AQ: 1 The University of Western Ontario 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 as to the symbol-grounding problem. Keywords: numerical cognition, symbol-grounding problem, approximate number system, numerical magnitudes, nonnumerical magnitudes Whether it is to estimate the distance to the nearest bus stop, to of number that we share with other species (the so-called “Approx- choose the shortest line in the supermarket or to calculate the imate Number System” or ANS). Against this background, the change given to you, we use numbers constantly in our everyday present literature review will examine (a) the extent to which the lives. How we represent and process numbers has been studied available behavioural and neuroscientific evidence supports extensively in humans at different developmental stages, as well as the theory that number symbols are grounded in the ANS and (b) in a variety of animal species. One of the key questions in the the extent to which the purported ANS is numerical in nature. The literature concerns how humans learn the meaning of numerical review will close by outlining questions for future theory and symbols (sometimes referred to as the “symbol-grounding prob- research. lem”), such as Arabic numerals, which are uniquely human cul- tural representation of numerosity that children need to learn over The Number Sense/ANS Account of the the course of development. The present article begins by reviewing Symbol-Grounding Problem the most prominent proposal for the resolution of the symbol- One of the most prominent theories in the field of numerical grounding problem in numerical cognition, which postulates that cognition was put forward by several researchers (e.g., Dehaene, symbols are grounded in a system for the approximate representation 1997; Gallistel & Gelman, 1992). According to this theory, the ability to process numerical quantities (i.e., the total number of items in a set or its numerosity) is a basic, automatic, and innate ability that can be found across species. In other words, humans Tali Leibovich and Daniel Ansari, Numerical Cognition Laboratory, are born with a capacity to process nonsymbolic numerosities (e.g., Department of Psychology & Brain and Mind Institute, The University of dot arrays, groups of objects, number of sounds, etc.). Further- Western Ontario. more, according to this theory, symbolic representations of num- This work was supported by operating grants from the Natural Sciences ber, such as Arabic numerals and number words, which children and Engineering Council of Canada (NSERC), the Canadian Institutes of learn over the course of development, are thought to acquire their Health Research (CIHR), the Canada Research Chairs Program, an E.W.R meaning by being mapped onto the preexisting, nonsymbolic rep- Steacie Memorial Fellowship from the Natural Sciences and Engineering resentations of number. Council of Canada (NSERC) to Daniel Ansari, as well as a Brain & Mind Institute (Western University) Postdoctoral Scholarship to Tali Leibovich. This theory is supported by studies demonstrating that preverbal Correspondence concerning this article should be addressed to Daniel babies and animals are able to spontaneously discriminate between Ansari, Department of Psychology & Brain and Mind Institute, The Uni- numerosities (e.g., Libertus & Brannon, 2009; Nieder, 2005). For versity of Western Ontario, Westminster Hall, Room 325, London, ON example, in a habituation study (repeated presentation of a partic- N6A 3K7, Canada. E-mail: [email protected] ular stimuli followed by the presentation of a stimuli that differs in 1 APA NLM tapraid5/cae-cae/cae-cae/cae00415/cae0277d15z xppws Sϭ1 10/1/15 15:45 Art: 2015-1231 2 LEIBOVICH AND ANSARI the variable of interest) by Xu and Spelke (2000), infants were habituated to groups of dots in different sizes but that contained the same numerosity. In the test stage, the infants saw two displays— one display with the same numerosity as in the habituation stimuli and another display containing a novel number of dots. The results OC NO of this experiment revealed that infants looked longer toward the LL novel numerosity compared with the numerosity to which they had IO been habituated. Furthermore, it was found that 6-month-old in- NR fants only exhibited the ability to discriminate between the habit- E uated and novel numerosity when the ratio between the two stimuli was 0.5 (e.g., 8 vs. 16 dots), but not when the ratio was higher Figure 1. Basic effect in numerical cognition. (A) The numerical ratio (e.g., 8 vs. 12 dots). These findings have since been replicated in effect. The plot illustrates the relationship between numerical ratio and a number of different labouratories (Coubart, Izard, Spelke, Marie, response time, in a number comparison task. The x-axis describes the numerical ratio: smaller/larger numerosity. The y-axis represents the time & Streri, 2014; Izard, Sann, Spelke, & Streri, 2009). In addition to it takes to respond to the larger number. Task difficulty increases when the work on infants, it has also been demonstrated that a variety of numerical ratio is closer to 1 (i.e., with an increase in numerical ratio). animals are able to discriminate between different nonsymbolic Inside the plot are examples for symbolic and nonsymbolic stimuli: The numerosities (birds, Bogale, Kamata, Mioko, & Sugita, 2011; numerical ratio of 3 and 8 is ϳ0.37, and the numerical distance is 4; the Watanabe, 1998; fish, Agrillo, Dadda, Serena, & Bisazza, 2008, numerical ratio of 7 and 9 is ϳ0.77, and the numerical distance is 2. It is 2009; rodents, Meck & Church, 1983; lions, McComb, Packer, & also true, then, that task difficulty increases with the decrease in numerical Pusey, 1994; and primates, Cantlon & Brannon, 2006; Nieder, distance. (B) Approximate representation of numerosities. Representation Freedman, & Miller, 2002). of numbers is thought to be represented on a logarithmic scale. This Discrimination between different numerosities shows a similar representation is assumed to be approximate and noisy: Larger numbers are response pattern to that of discriminating between different mag- represented more approximately, and the representation of adjacent num- bers overlap. See the online article for the color version of this figure. nitudes, such as brightness, pitch of sound, physical size, and weight (Cantlon, Platt, & Brannon, 2009; but see also Leibovich, Ashkenazi, Rubinsten, & Henik, 2013; Leibovich, Diesendruck, The ANS and the Symbol-Grounding Problem Rubinsten, & Henik, 2013). In all these cases, the ability to detect change (or to understand that two presented magnitudes are dif- To this point, the discussion of number representations has ferent from each other) depends on the ratio between the to-be- focused on nonsymbolic representations of number. This raises compared magnitudes.