Wiggershaus, Nick
(2023)
Towards a Unified Theory of Implementation.
[Preprint]
Abstract
Various conceptual approaches to the notion of implementation can currently be traced in the foundations of computing. This paper articulates a unified theory of implementation based on agential and use-based notions of physical computation. Two hitherto largely independently treated notions of implementation are juxtaposed: type-(A), dealing with the notion of correctness through the ascription of teleological functions to ‘computational artifacts’; and type-(B), concerned with bridging the abstract/concrete dichotomy for providing an account of concrete computation. While little research has been conducted on their relationship, my analysis shows that their scope overlaps at the abstract-physical interface. Considering recent developments in the respective discourses, I show that both accounts may mutually enrich each other considerably through unification. Specifically, I submit that (A) and (B) can be unified by appealing to the conceptual machinery of use-based accounts of computation informed by the literature on material models and scientific representation. On this view, agents use putative computational systems as epistemic tools by imputing mathematical functions and ascribing teleological functions.
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