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Systematicity, Accessibility, and Universal Properties
William H. Wilson1 and Steven Phillips2
1School of Computer Science and Engineering, The University of New South Wales, Australia
billw@cse.unsw.edu.au
2Mathematical Neuroinformatics Group Human Technology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, Japan
steve@ni.aist.go.jp
Abstract. Human cognition is a mixture of the systematic and the non-systematic. One thing we can do systematically can be described as follows. If we know about multiplication, and the facts of basic multiplication, and we know conceptually what division is, then we can utilise the facts of multiplication that we know in order to solve division problems that correspond to those facts. For example, once children know that 4 ×7 = 28, and once they understand about division, they can work out that 28 / 4 = 7. Aizawa has defined standards for what counts as an explanation of systematicity. In this paper, in accordance with Aizawa’s framework, we apply concepts from category theory to this problem, and resolve it by identifying the unique natural transformation that underpins this example of systematicity, and others in the same class.
LNAI 7691, p. 555 ff.
lncs@springer.com
© Springer-Verlag Berlin Heidelberg 2012