Abstract
The history of thinking about thinking is populated by numerous attempts to model reason in topological terms. Amongst them, the prominent place is occupied by Immanuel Kant’s explanation of thought’s need to restrain its own exercise by means of an analogy between geographical orientation (modeled on the human body) and orientation in thinking. As natural as his analogy might seem, the first part of this chapter aims at deconstructing Kant’s attempt as both replaceable and constraining, and at proposing a possibility of alternative topological accounts of thinking. Hence, while endorsing the utility of spatial models, we call for an unbinding of the parochial connection between thinking and the form of the human body implicit in historical topological models of reason. For this reason, in the second part of the chapter we suggest that the topological framework embodied by Artificial Neural Networks (ANNs) can be used as an alternative to formulate such a model of thinking, based on their commitment to dimensionality and use of space as an active, dynamic and transitory element. Rather than arguing that ANNs somehow think, we suggest that they offer a mirror that lets humans look back at themselves and construct their thinking differently. We conclude by proposing that the benefit of looking in this mirror is open-ended and twofold: (1) It divorces our image of thinking from anthropomorphism, and (2) it offers a normative model of reason with potentially practical consequences for how humans act.

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