Jack Copeland gave an interesting lecture on the Church-Turing thesis today. The CT thesis is apparently much misunderstood. Historically, it's the claim that any algorithm can be computed by a Turing machine. But even well-respected philosophers (Jack offered quotes from Fodor, Dreyfus, etc.) sometimes label a much stronger claim - that no information-processing machine can do anything that Turing machines can't - the "Church-Turing thesis", even though neither Church nor Turing ever made such a claim. Note the difference: whereas the real version merely relates Turing machines and algorithms, the stronger version places restrictions on all information processing devices. For example, the latter version implies that no machine can solve the Halting problem. More generally, it can be seen as the claim that hypercomputation is impossible, and that standard (Turing) computation is the pinnacle of information processing. The original Church-Turing thesis made no such grand claims.
An especially extravagant elaboration was made by the Churchlands. They claimed that Turing's results entail that "a Turing machine can display any systematic pattern of responses to the environment whatsoever." Jack pointed out that this was a rather outrageous claim, since some uncomputable 'patterns of response' are perfectly systematic. Consider an environment which presents integer inputs. We can assign each Turing machine a number. Now, here is a perfectly systematic pattern of responses to this environment: the info-processor take the input n, and outputs a '1' if the nth Turing machine halts, and a '0' if it does not halt. But no computer can display this pattern of responses, or else they could solve the Halting problem (which we can prove no computer can do). So there are systematic patterns of response that no computer - i.e. Turing machine - can possibly display.