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Abstract
This paper provides a tutorial introduction to numerical cognition, with a review
of essential findings and current points of debate. A tacit hypothesis in cognitive
arithmetic is that numerical abilities derive from human linguistic competence. One
aim of this special issue is to confront this hypothesis with current knowledge of
number representations in animals, infants, normal and gifted adults, and brain-lesioned
patients. First, the historical evolution of number notations is presented, together
with the mental processes for calculating and transcoding from one notation to another.
While these domains are well described by formal symbol-processing models, this paper
argues that such is not the case for two other domains of numerical competence: quantification
and approximation. The evidence for counting, subitizing and numerosity estimation
in infants, children, adults and animals is critically examined. Data are also presented
which suggest a specialization for processing approximate numerical quantities in
animals and humans. A synthesis of these findings is proposed in the form of a triple-code
model, which assumes that numbers are mentally manipulated in an arabic, verbal or
analogical magnitude code depending on the requested mental operation. Only the analogical
magnitude representation seems available to animals and preverbal infants.