5

The origin is with the so-called Whiteley Sentence. See C.Whiteley, “Minds, Machines and Gödel: A Reply to Mr. Lucas (1962)”, Philosophy 37:61-62 : It is possible to devise a formula which will trap a human mind —say, Mr Lucas's— in the same way that his application of Gödel traps the machine. Take, for instance, the formula 'This formula ...


2

See e.g. Gödel’s Incompleteness Theorems : Diagonalization: it is a general result of FOL that : Let A(x) be an arbitrary formula of the language of F with only one free variable. Then a sentence D can be mechanically constructed such that F ⊢ D ≡ A(⌈D⌉). In Heck's paper, page 2, the author applies this general result to formula (9) above (of system PA)...


1

I'm not an expert, but I'd like to venture a response. In classical logic, "this statement is always false" is equivalent to "this statement is false" because there's no intermediate truth value -- "true" in classical logic means the same thing as "always true". There's more nuance here under the model theoretic interpretation of such statements: A ...


1

Could we therefore argue that what he calls his 'self' is nothing but these sets of experiences and their mental deductions that led him to form a boundary between him and the world?< Is not this assertion objectionable on the same ground as the assertion that is attributed to science at the beginning of the question? I mean, one could ask : " what ...


1

It seems to me this is a useful paradox in the sense that where it arises we know we must be thinking incorrectly. But as phrased it seems easy to overcome. I feel there is a more interesting and real paradox underlying this one. It is not thoughts that think. If you drop this idea and rephrase the paradox then it might have more bite.


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