## FROM DESCARTES TO TURING: THE COMPUTATIONAL CONTENT OF SUPERVENIENCE

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@MISC{Cooper_fromdescartes,

author = {S. Barry Cooper},

title = {FROM DESCARTES TO TURING: THE COMPUTATIONAL CONTENT OF SUPERVENIENCE},

year = {}

}

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### Abstract

Mathematics can provide precise formulations of relatively vague concepts and problems from the real world, and bring out underlying structure common to diverse scientific areas. Sometimes very natural mathematical concepts lie neglected and not widely understood for many years, before their fundamental relevance is recognised and their explanatory power is fully exploited. The notion of definability in a structure is such a concept, and Turing’s [77] 1939 model of interactive computation provides a fruitful context in which to exercise the usefulness of definability as a powerful and widely applicable source of understanding. In this article we set out to relate this simple idea to one of the oldest and apparently least scientifically approachable of problems — that of realistically modelling how mental properties supervene on physical ones.