Abstract
Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.
Highlights
Mathematicians Frege (1879/1967) and Russell (1903/1996) defined number as the class of all classes that shows a one-to-one correspondence with a given class in an attempt to cast number in terms of logic. Piaget (1941/1965) described number as the property of a set that remains invariant when other perceptual characteristics of the set change
ABOUT RELATIVE QUANTITY JUDGMENT When it is advantageous to choose the larger set of discrete things, infants and non-human animals do so, within the limits of their representation systems
The ordinal quantity judgments of both infants and non-human animals indicate an interaction between these two core systems of representation
Summary
Mathematicians Frege (1879/1967) and Russell (1903/1996) defined number as the class of all classes that shows a one-to-one correspondence with a given class in an attempt to cast number in terms of logic. Piaget (1941/1965) described number as the property of a set that remains invariant when other perceptual characteristics (e.g., color, size, and density) of the set change. Piaget (1941/1965) described number as the property of a set that remains invariant when other perceptual characteristics (e.g., color, size, and density) of the set change. What both definitions mean is that “oneness” is the class of all singletons, “twoness” the class of all doubles, and so forth. “threeness” characterizes the number of sides of a triangle, leaves of a shamrock, and notes in a musical triplet Describing number in this way indicates that number is an abstraction – a characteristic based on a single property of stimuli independent of other properties – that conceptualizes a collection of discrete things. Non-human animals like primates, birds, and fish discriminate between sets based on the number of things that each collection contains (Emmerton, 1998; Jordan and Brannon, 2006b; Jordan et al, 2008b; Tomonaga, 2008; Merritt et al, 2009; Agrillo et al, 2010)
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