Effective Procedures

Round 1

Reviewer 1 Report

Please see the attached review.

Comments for author File: Comments.pdf

Author Response

I appreciate the reviewer's careful and thoughtful review. The reviewer has two substantive comments. It should be noted in response to the first that the original submission included the full proof. In response to the first-round and second-round reviews, the editors asked me to remove the technicalities and to provide instead a non-technical overview. The technical details are provided in a version that will be published in the logic journal, Logica Universalis. In light of the reviewer's worry, I have now included a brief remark about the proof strategy (which is primarily Cantorian diagonalization). The reviewer also insists that at the very least, a particular footnote should be moved instead into the text. I am not convinced that this improves the paper, but I have now done as the reviewer requires. Nothing more can be done in this direction without reintroducing the very technicalities that the editors explicitly asked me to omit. The interested reader who is unable reconstruct the proof on the basis of these largely nontechnical remarks can consult the more technical version of the paper in Logica Universalis. I agree with the editors that the typical reader will be content to accept that there exists a proof which is accessible somewhere.

The reviewer's second comment is a largely terminological matter. The word 'algorithm' may be polysemous. It has a definite meaning in computability theory (which used to be called 'recursive-function theory'). It might additionally have a broader meaning in computer science. In the former sense, an algorithm is, by definition, an effective valuation procedure, nothing more and (to the point) nothing less. Cf. for example the entry in Wikipedia on 'algorithm', as well as the sub-entry on 'algorithms' within the entry for 'effective method'. These entries follow the usage from recursive-function/computability theory. As the reviewer admits, the point about the possible alternative use of 'algorithm' need not be addressed in the paper. For the purposes of the paper, I propose to deal with the matter by explicitly specifying that the word 'algorithm' is used here in the sense of an effective valuation procedure.

Reviewer 2 Report

I think this paper is highly controversial but is coming from a highly knowledgeable author that is making a fine contribution to the debate even when I strongly disagree with their conclusion as I don’t think it follows whatsoever what the author is proposing from its premises.  I do think there is no way to exhibit all realizable models of computation to proof the CT thesis and it even seems to miss several aspects of the thesis that other authors have dissected before.

Author Response

Younger generation reviewers in philosophy and logic do not understand the role of a reviewer, which is not to assess whether they themselves are in agreement with the author's conclusions, but to assess suitability for publication in the relevant venue. This is an old-school type of review, in that it recommends publication even while expressing disagreement with my conclusions. As the author, I very much appreciate the reviewer's intellectual maturity and judgment, and especially their balanced understanding of the purpose of academic review.