## Church’s Thesis 1: CTT, minds and supertasks

I mentioned a few posts ago the collection Church’s Thesis After 70 Years edited by Adam Olszewski et al. Since the editors helpfully refrain from suggesting a sensible reading order, I’m just going to dive in and read the contributed papers in the order they are printed (they are arranged alphabetically by the authors’ names). And to keep my nose to the grindstone, I’ve promised myself to post comments and thoughts here — so it will be embarrassing to stop doing my homework! Here goes, then, starting with Darren Abramson, “Church’s Thesis and Philosophy of Mind”.

Abramson identifies “the Church-Turing Thesis” with the claim “[…] no human computer, or machine that mimics a human computer, can out-compute a universal Turing machine”. That doesn’t strike me as a terribly helpful move, for it runs together two claims, namely (i) no human computer can (in a reasonable sense) compute something that is not effectively computable (by a finite, step-by-step, algorithmic process), and (ii) whatever is effectively computable is Turing-computable/recursive. In fact, in my Gödel book, I call just (ii) “the Church-Turing Thesis”. But irrespective of the historical justification for using the label my way (as many do), this thesis (ii) is surely to be sharply separated from (i). For a start, the two claims have quite different sorts of grounds. For example, (i) depends on the impossibility of the human performance of certain kinds of supertask. And the question whether supertasks are possible is quite independent of the considerations that are relevant to (ii).

I didn’t know, till Abramson told me, that Bringsjord and Arkoudas have argued for (i) by purporting to describe cases where people do in fact hypercompute. Apparently, according to them, in coming to understand the familiar pictorial argument for the claim that lim n → ∞ of 1/2^n is 0 we complete an infinite number of steps in a finite amount of time. Gosh. Really?

Abramson makes short shrift of the arguments from Bringsjord and Arkoudas that he reports. Though I’m not minded to check now whether Abramson has dealt fairly with them. Nor indeed am I minded to bother to think through his discussion of Copeland on Searle’s Chinese Room Argument: frankly, I’ve never felt that that sort of stuff has ever illuminated serious issues in the philosophy of mind that I might care about. So I pass on to the next paper ….