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How Computationally Relevant is Definability?

Barry Cooper ( Leeds )

Barry Cooper: A large part of the scientific enterprise is bringing plausible descriptions of reality within practical computational frameworks. Mathematically, it is easy to describe classically incomputable objects from algorithmic ingredients. And the technical links between definability and computability have been extensively mapped out. What is far from clear is the extent to which the hierarchies and fine-structure theories built from simple computational ingredients are mirrored in the material world. On the other hand, the recognition of the real-world computational content of definability does seem to offer a widely applicable explanatory potential.



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