Peter Smith on “Church’s Thesis After 70 Years”

Church’s Thesis After 70 Years is a very expensive collection of new papers on the Church-Turing thesis.  It was published by Ontos Verelag a few months ago.  It is edited by Adam Olszewski and Jan Wolenski.

An Introduction to Gödel’s Theorems is a fairly affordable, sophisticated introduction and discussion of Gödel’s Incompleteness Theorems and related topics, including the Church-Turing thesis.  It just came out from CUP.  The author is Peter Smith.

Beyond the overlap in topic, there is a further link between these two books.  Smith has put together a website for his book, on which he has posted a commentary (almost a review) on most of the papers in Church’s Thesis After 70 Years.  He trashes it.  Out of 22 papers in the collection, he only recommends reading those by Copeland, Shagrir, and Shapiro (and Sieg, though Sieg’s paper is a reprint).  (Smith’s review previously appeared in Smith’s blog, Logic Matters.)


  1. Well, I’m reading the book right now. I haven’t read Simons’ review but I found many more interesting papers (e.g., Krajewski’s paper with a reference to his wonderful book on Goedel, where he proved that Lucas and Penrose arguments are either unsound or inconsistent; English version in preparation, stay tuned), a very interesting paper by Hartmut Fitz on realizing computations, and a paper by Blass & Gurevich (this one is definitely too short!). Mycka’s paper on analog computation is also interesting. The worst one is Odifreddi’s paper on Kreisel’s views on CT.

  2. Those who are interested in “An Introduction to Gödel’s Theorems” might also be interested in “Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse” by Torkel Franzen. I just received it a few days ago, so I’ve only read the first couple of chapters, but so far I’m impressed.

  3. I’m not sure that “trashes” s quite the right word — though some of the papers are very poor indeed (and far too many are very badly written). I should perhaps have made it clear — and I’ll make some changes when I have a moment! — that my recommendations about what was worth reading were addressed to people whose main interests were philosophical and the status of CTT. Some of the other papers may well be of more interest to those coming from a different angle.

  4. Well, I’ve read the review, and I can second many opinions (Woleński and Murawski paper on the status of CTT is poor, as well as Olszewski’s one is also not really so interesting). Yet CTT is not purely a logical point, and some of the problems of hypercomputation, analog computation and interactive computation do show up in many papers, as they should.
    But the bottom line is that I wouldn’t ever buy the book. I just found it in my library a couple of weeks ago 😉

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