Pluralism ignored: The Church-Turing thesis and philosophical practice

Abstract

The Church-Turing thesis is widely stated in terms of three equivalent models of computation (Turing machines, the lambda calculus, and rewrite systems), and it says that the intuitive notion of a computable function is what is defined by any one of these models. Despite this well-established equivalence, the philosophical literature concentrates almost exclusively on the Turing machine model. We argue that this has been to the detriment of the philosophy of computation, and specifically that it ignores two issues: firstly, equivalence in the Church-Turing sense is extensional equivalence, whereas many of the delicate issues in the philosophy of mind, and in theoretical computer science, are to do with fine-grained intensional equivalence of algorithms. Secondly, real computers are not in any meaningful sense Turing machines: they are nondeterministic, their memory may fail to be in a determinate state due to cache coherence issues, and the boundaries between inside and outside are ill-defined and permeable. We explore the philosophical significance of these issues and give some examples. © 2014 Springer International Publishing.