Abstract
Transitive inference, class inclusion and a variety of other inferential abilities have strikingly similar developmental profiles—all are acquired around the age of five. Yet, little is known about the reasons for this correspondence. Category theory was invented as a formal means of establishing commonalities between various mathematical structures. We use category theory to show that transitive inference and class inclusion involve dual mathematical structures, called product and coproduct. Other inferential tasks with similar developmental profiles, including matrix completion, cardinality, dimensional changed card sorting, balance-scale (weight-distance integration), and Theory of Mind also involve these structures. By contrast, (co)products are not involved in the behaviours exhibited by younger children on these tasks, or simplified versions that are within their ability. These results point to a fundamental cognitive principle under development during childhood that is the capacity to compute (co)products in the categorical sense.
Highlights
Children acquire various reasoning skills over remarkably similar periods of development
Two examples are Transitive Inference and Class Inclusion, which develop around five years of age
Older children understand that if John is taller than Mary, and Mary is taller than Sue, John is taller than Sue
Summary
Children acquire various reasoning skills over remarkably similar periods of development. Transitive Inference and Class Inclusion are two behaviours among a suite of inferential abilities that have strikingly similar developmental profiles—all are acquired around the age of five years [1]. The number of items belonging to the superclass is greater than the number of items in any one of its subclasses. This form of reasoning is called Class Inclusion. These two types of inference appear to have little in common. Explicit tests of these and other inferences for a range of age groups revealed that success was attained from about the median age of five years [1]
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