> He sketches out a hypothetical “Turing Machine,” proving that, if something is computable at all, a machine (in principle) can handle it.
That's not what Turing proved. Instead, what he proved in his paper was that there are some problems which aren't solvable by Turing Machines (and therefore presumably by any machine). That's the Entscheidungsproblem (decision problem) referenced in the title.
What TFA references is the so-called Church-Turing-Thesis, which is exactly that, a thesis. It can't really be proven although we have very strong reason to believe it given that in almost 100 years nobody has found a system of computation more powerful than Turing Machines.
That's not what Turing proved. Instead, what he proved in his paper was that there are some problems which aren't solvable by Turing Machines (and therefore presumably by any machine). That's the Entscheidungsproblem (decision problem) referenced in the title.
What TFA references is the so-called Church-Turing-Thesis, which is exactly that, a thesis. It can't really be proven although we have very strong reason to believe it given that in almost 100 years nobody has found a system of computation more powerful than Turing Machines.