Abstract
Philosophers have usually offered a number of ways of describing hypotheses generation, but all aim at demonstrating that the activity of generating hypotheses is paradoxical, illusory or obscure, and then not analysable. Those descriptions are often so far from Peircian pragmatic prescription and so abstract to result completely unknowable and obscure. The “computational turn” gives us a new way to understand creative processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence and cognitive science tools, computational philosophy allows us to test concepts and ideas previously conceived only in abstract terms. It is in the perspective of these actual computational models that I find the central role of abduction in the explanation of creative reasoning in science. Creativity and discovery are no more seen as a mysterious irrational process, but, thanks to constructive accounts, as a complex relationship among different inferential steps that can be clearly analysed and identified. I maintain that the computational philosophy analysis of model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development of programs computationally adequate in rediscovering, or discovering for the first time, for example, scientific hypotheses or mathematical theorems.
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Notes
Magnani (2001a, 2002) introduces the concept of theoretical abduction. He maintains that there are two kinds of theoretical abduction, “sentential”, related to logic and to verbal/symbolic inferences, and “model-based”, related to the exploitation of internalized models of diagrams, pictures, etc., cf. below in this paper.
Manipulative abduction and epistemic mediators are introduced and illustrated in Magnani 2001a.
I derive this expression from the cognitive anthropologist Hutchins, that coins the expression “mediating structure” to refer to various external tools that can be built to cognitively help the activity of navigating in modern but also in “primitive” settings. Any written procedure is a simple example of a cognitive “mediating structure” with possible cognitive aims: “Language, cultural knowledge, mental models, arithmetic procedures, and rules of logic are all mediating structures too. So are traffic lights, supermarkets layouts, and the contexts we arrange for one another’s behaviour. Mediating structures can be embodied in artefacts, in ideas, in systems of social interactions” (Hutchins 1995, pp. 290–291).
It is difficult to preserve precise spatial relationships using mental imagery, especially when one set of them has to be moved relative to another.
It is Hutchins (1995, p. 114) that uses the expression “cognitive ecology” when explaining the role of internal and external cognitive navigation tools. More suggestions on manipulative abduction can be derived by the contributions collected in Morgan and Morrison (eds., 1999), dealing with the mediating role of scientific models between theory and the “real world”.
The epistemic and cognitive role of mirror and unveiling diagrams in the discovery of non-Euclidean geometry is illustrated in Magnani 2002.
This is mathematically justified in Magnani and Dossena 2005.
Of course in the case we are using diagrams to demonstrate already known theorems (for instance in didactic settings), the strategy of manipulations is not necessary unknown and the result is not new.
This approach in computer science, involving the use of diagram manipulations as forms of acceptable methods of reasoning, was opened by Gelernter’s Geometry Machine (1963), but the diagrams played a very secondary role.
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Magnani, L. Symposium on “Cognition and Rationality: Part I” The rationality of scientific discovery: abductive reasoning and epistemic mediators. Mind & Society 5, 213–228 (2006). https://doi.org/10.1007/s11299-006-0018-y
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DOI: https://doi.org/10.1007/s11299-006-0018-y