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Computing, Modelling, And Scientific Practice: Foundational Analyses And Limitations, Filippos A. Papagiannopoulos

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This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic computation and to offer foundations for scientific computing.

The dissertation consists of three parts. In the first part, we …