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.
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References
Fodor, J., Pylyshyn, Z.: Connectionism and cognitive architecture: A critical analysis. Cognition 28, 3–71 (1988)
Smolensky, P.: The constituent structure of mental states: A reply to Fodor and Pylyshyn. The Southern Journal of Philosophy 26(suppl.), 137–161 (1987)
McLaughlin, B.: Systematicity redux. Synthese 170, 251–274 (2009)
Phillips, S., Wilson, W.H.: Categorial compositionality III: F-(co)algebras and the systematicity of recursive capacities in human cognition. PLoS ONE 7(4), e35028 (2012)
Aizawa, K.: The systematicity arguments. Kluwer Academic, New York (2003)
Phillips, S., Wilson, W.H.: Categorial compositionality: A category theory explanation for the systematicity of human cognition. PLoS Computational Biology 6(7), e1000858 (2010)
Halford, G.S., Wilson, W.H., Phillips, S.: Processing capacity defined by relational complexity: Implications for comparative, developmental and cognitive psychology. Behavioral and Brain Sciences 21(6), 803–831 (1998)
Bird, R., de Moor, O.: Algebra of programming. Prentice-Hall (1997)
Arbib, M.A., Manes, E.G.: Arrows, structures, functors: the categorical imperative. Academic Press, New York (1975)
Goldblatt, R.: Topoi: the categorical analysis of logic, revised edn. Dover, New York (2006); Original ed. Elsevier (1984)
Suppes, P., Zinnes, J.L.: Basic measurement theory. In: Luce, R.D. (ed.) Handbook of Mathematical Psychology, pp. 1–76. Wiley (1963)
Halford, G.S., Wilson, W.H.: A category theory approach to cognitive development. Cognitive Psychology 12, 356–411 (1980)
Mac Lane, S.: Categories for the working mathematician, 2nd edn. Springer, New York (2000)
Barr, M., Wells, C.: Category theory for computing science, 1st edn. Prentice Hall, New York (1990)
Awodey, S.: Category theory, 2nd edn. Oxford University Press (2010)
Phillips, S., Wilson, W.H.: Categorial Compositionality II: Universal Constructions and a General Theory of (Quasi-) Systematicity in Human Cognition. PLoS Computational Biology 7(8), e1002102 (2011)
van Gelder, T.: Compositionality: A connectionist variation on a classical theme. Cognitive Science 14, 355–384 (1990)
Phillips, S., Wilson, W.H., Halford, G.S.: What do Transitive Inference and Class Inclusion have in common? Categorical (co)products and cognitive development. PLoS Computational Biology 5(12), e1000599 (2009)
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Wilson, W.H., Phillips, S. (2012). Systematicity, Accessibility, and Universal Properties. In: Thielscher, M., Zhang, D. (eds) AI 2012: Advances in Artificial Intelligence. AI 2012. Lecture Notes in Computer Science(), vol 7691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35101-3_47
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DOI: https://doi.org/10.1007/978-3-642-35101-3_47
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