The discovery and comparison of symbolic magnitudes

•A model of the discovery and comparison of symbolic magnitudes is proposed.•Magnitudes can be computed from more elementary features.•The precision of magnitudes in working memory increases with proximity to a reference point.•The model accounts for phenomena including symbolic distance, semantic congruity, and markedness.•The model is applied to two sets of independently-generated inputs.

Humans and other primates are able to make relative magnitude comparisons, both with perceptual stimuli and with symbolic inputs that convey magnitude information. Although numerous models of magnitude comparison have been proposed, the basic question of how symbolic magnitudes (e.g., size or intelligence of animals) are derived and represented in memory has received little attention. We argue that symbolic magnitudes often will not correspond directly to elementary features of individual concepts. Rather, magnitudes may be formed in working memory based on computations over more basic features stored in long-term memory. We present a model of how magnitudes can be acquired and compared based on BARTlet, a representationally simpler version of Bayesian Analogy with Relational Transformations (BART; Lu, Chen, & Holyoak, 2012). BARTlet operates on distributions of magnitude variables created by applying dimension-specific weights (learned with the aid of empirical priors derived from pre-categorical comparisons) to more primitive features of objects. The resulting magnitude distributions, formed and maintained in working memory, are sensitive to contextual influences such as the range of stimuli and polarity of the question. By incorporating psychological reference points that control the precision of magnitudes in working memory and applying the tools of signal detection theory, BARTlet is able to account for a wide range of empirical phenomena involving magnitude comparisons, including the symbolic distance effect and the semantic congruity effect. We discuss the role of reference points in cognitive and social decision-making, and implications for the evolution of relational representations.