Here's an overview of my position, with the three propositions related to the Turing Test listed first.
Why do I think the other four propositions are true? Well, actually, no one should dispute P TM. After all, persons regularly build TMs in order to solve problems, and they also engage in cognition which is intended to perfectly map to TM processing (e.g., the logic tasks Fetzer recounts having tackled at Princeton). (It may be worth remembering here that Turing and Post started not with the concept of a computer, but rather with the concept of a computist: a human who carries out -- or perhaps just is -- an effective procedure.) What about the remaining three propositions? Specifying my arguments for this trio requires more space than I have in three books (What Robots Can and Can't Be and two forthcoming ones,  and ); accordingly, here I only intimate my rationale.
I haven't read Carol Cleland's attack on Church's Thesis, to which Fetzer draws our attention in . But I gather that my own attack is radically different, as it is based on what I think is a victorious instantiation of the valid argument-schema Arg shown below. In this schema (which was part of a paper I presented at Eastern APA 1993 on Church's Thesis), and , recall, represent (in the Arithmetic Hierarchy) that which can be solved by any of the techniques open to standard computationalism. It is an easy and well-known theorem that successfully deciding some set A can be adapted to successfully enumerate A; Arg exploits this elementary theorem, a move that is inspired by Peter Kugel . In order to refute CTT one needs to set A to some set that makes all the premises in question true. I think the set of all ``interesting" stories, , fits the bill, as I explain in . The core of this argument is really quite straightforward: People who can decide , that is, people who can decide whether something is an interesting story, can't necessarily generate interesting stories. Put baldly, it's easy to see that stories like King Lear are interesting, but it's not so easy to write drama of this caliber. The more explicit version of the argument looks like this:
P axM is something I've defended in What Robots Can and Can't Be. For example, in Chapter IX I argue that a very circumspect variety of incorrigibilism (so-called hyper-weak incorrigibilism) is something at the heart of personhood, but also something that no computer hardware whatsoever can support. Although proposition P ZM is also defended in What Robots Can and Can't Be, the main arguments for this thesis will appear in In Defense of Uncomputable Cognition . A key chapter in that book specifies this reasoning: ``Computation is reversible; cognition isn't; ergo, cognition isn't computation." (Machines more powerful than TMs are irreversible.) Another chapter unpacks and defends the claim that mathematical expertise involving infinitary logic is uncomputable.