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Computational individuation: Isomorphism, not indeterminacy
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DOI：10.1093/analys/anaf003.png)
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Abstract
En 中文
A pair of arguments for the indeterminacy of physical logic gates play an important role in debates about computational individuation. These arguments purport to show that one needs extrinsic, contextual factors to individuate even simple computations. One of the arguments has a straightforward flaw. Reflection on that flaw shows that there is a (mostly tacit) assumption on both sides of the debate: that computations ought to be understood in a function-theoretic way. I describe an alternative structure-theoretic understanding of the intrinsic mathematical structures instantiated by computations. I show that on a structure-theoretic account, there is no indeterminacy. Instead, any logic gate belongs to a fully determinate equivalence class under isomorphism. Some independent advantages of a structure-theoretic account are also noted.
Keywords:
computation
implementation
indeterminacy
mathematical structure
group theory