Church’s Thesis 5: Effective computability, machine computability

The sixth paper in the Olszewski collection is Jack Copeland’s “Turing Thesis”. Readers who know Copeland’s previous writings in this area won’t be surprised by the general line: but truth trumps novelty, and this is all done with great good sense. To take up a theme in my last posting, Copeland insists that ‘effective’ is a term of art, and that

The Entscheidungsproblem for the predicate calculus [i.e. the problem of finding an effective decision procedure] is the problem of finding a humanly executable procedure of a certain sort, and the fact that there is none is consistent with the claim that some machine may nevertheless be able to decide arbitrary formulae of the calculus; all that follows is that such a machine, if it exists, cannot be mimicked by a human computer.

And he goes on to identify Turing’s Thesis as a claim about what can be done ‘effectively’, meaning by finite step-by-step procedure where each step is available to a cognitive agent of limited (human-like) abilities, etc. Which seems dead right to me (right historically, but also right philosophically in drawing a key conceptual distinction correctly, as I’ve said in previous posts).

Copeland goes on to reiterate chapter and verse from Turing’s writings to verify his reading, and he critically mangles Andrew Hodges’s claims (later in this volume and elsewhere) that Turing originally had a wider thesis about mechanism and also that Turing changed his views after the war about minds and mechanisms. I’m not one for historical minutiae, but Copeland seems clearly to get the best of this exchange.

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