Ok, I think I can clarify what people generally mean when they consider that the logic Church-Turing thesis is correct.
There is an intuitive notion of computation that is somewhat consensual. It doesn’t account for limits on time (beyond the fact that everything must be finitely long) and does not account for limits in space / memory.
It is also somewhat equivalent to “what a rigorous idiot could be made to do, given immortality and infinite paper/pen”.
Many people / most computer scientist share this intuitive idea and at some point people thought they should make more rigorous what it is exactly.
Whenever people tried to come up with formal processes that only allow “obviously acceptable” operations with regard to this intuitive notion, they produced frameworks that are either weaker or equivalent to the turing machine.
The Church-Turing thesis is that the turing machine formalism fully captures this intuitive notion of computation. It seems to be true.
With time, the word “computable” itself has come to be defined on the basis of this idea. So when we read or hear the word in a theoretical computer-science context, it now refers to the turing machine.
Beyond this, it is indeed the case that the word “computation” has also come to be applied to other formalisms that look like the initial notion to some degree. In general with an adjective in front to distinguish them from just “computation”. We can think for example of “quantum computing”, which does not match the initial intuition for “computation” (though it is not necessarily stronger). These other applications of the word “computation” are not what the Church-Turing thesis is about, so they are not counterexamples.
Also, all of this is for the “logic” Church-Turing thesis, to which what can be built in real life is irrelevant.
PS: I take it for granted that computer scientists, including those knowledgeable on the notions at hand, usually consider the thesis correct. That’s my experience, but maybe you disagree.
Ok, I think I can clarify what people generally mean when they consider that the logic Church-Turing thesis is correct.
There is an intuitive notion of computation that is somewhat consensual. It doesn’t account for limits on time (beyond the fact that everything must be finitely long) and does not account for limits in space / memory. It is also somewhat equivalent to “what a rigorous idiot could be made to do, given immortality and infinite paper/pen”. Many people / most computer scientist share this intuitive idea and at some point people thought they should make more rigorous what it is exactly.
Whenever people tried to come up with formal processes that only allow “obviously acceptable” operations with regard to this intuitive notion, they produced frameworks that are either weaker or equivalent to the turing machine.
The Church-Turing thesis is that the turing machine formalism fully captures this intuitive notion of computation. It seems to be true.
With time, the word “computable” itself has come to be defined on the basis of this idea. So when we read or hear the word in a theoretical computer-science context, it now refers to the turing machine.
Beyond this, it is indeed the case that the word “computation” has also come to be applied to other formalisms that look like the initial notion to some degree. In general with an adjective in front to distinguish them from just “computation”. We can think for example of “quantum computing”, which does not match the initial intuition for “computation” (though it is not necessarily stronger). These other applications of the word “computation” are not what the Church-Turing thesis is about, so they are not counterexamples. Also, all of this is for the “logic” Church-Turing thesis, to which what can be built in real life is irrelevant.
PS: I take it for granted that computer scientists, including those knowledgeable on the notions at hand, usually consider the thesis correct. That’s my experience, but maybe you disagree.