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According to Thagard and Stewart (Cogn Sci 35(1):1–33, 2011), creativity results from the combination of neural representations (an idea which Thagard calls ‘the combinatorial conjecture’), and combination results from convolution, an operation on vectors defined in the holographic reduced representation (HRR) framework (Plate, Holographic reduced representation: distributed representation for cognitive structures, 2003). They use these ideas to understand creativity as it occurs in many domains, and in particular in science. We argue that, because of its algebraic properties, convolution alone is ill-suited to the role proposed by Thagard and Stewart. The semantic pointer concept (Eliasmith, How to build a brain, 2013) allows us to see how we can apply the full range of HRR operations while keeping the modal representations so central to Thagard and Stewart’s theory. By adding another combination operation and using semantic pointers as the combinatorial basis, this modified version overcomes the limitations of the original theory and perhaps helps us explain aspects of creativity not covered by the original theory. While a priori reasons cast doubts on the use of HRR operations with modal representations (Fisher et al., Appl Opt 26(23):5039–5054, 1987) such as semantic pointers, recent models point in the other direction, allowing us to be optimistic about the success of the revised version.

DOI: 10.1007/s11229-015-0934-7

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