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This is a simple reference request, for the origin of a particular type of paradoxical statement. The example I remember is

Roger Penrose can't consistently claim this statement to be true.

It's a true statement, but if you happen to be Roger Penrose you can't say so without contradicting yourself. I have a feeling it might be due to (or popularised by) Douglas Hofstadter, but I'm not sure.

Note: it's a different statement from

Roger Penrose can't consistently believe this statement to be true.

It would be helpful to know the origin of both statements, but I'm particularly interested in the first, in which the target person can know the statement to be true but can't consistently say so.

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    Sure feels like a GEB-ism 😆 – Rusi Jul 8 at 12:48
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    What the above formulation adds to the "usual" Liar paradox? – Mauro ALLEGRANZA Jul 8 at 12:54
  • @MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it? – Nathaniel Jul 8 at 13:16
  • @MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example. – Nathaniel Jul 8 at 14:04
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    @MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points. – Nathaniel Jul 8 at 15:31
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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 cannot be consistently asserted by Lucas'.

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