This of interest to me, because I would like to know, if I have a coded message, if I can tell if the coded message is true, even if I can't decode the message.

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LoginAny message can be converted into a long positive integer per Godel numbering. Tarski is all about ... how can we apply the logical notion of truth (a limited definition) to Godel numbered logical statements. Tarski's theorem is that we cannot define truth within an object language, you have to have a metalanguage to assess true statements. Given that, logic cannot be used to prove the truth of logical statements (aka depends on the truth of the premises, unless you have a tautology or a contradiction). This is a problem for logic, a logical paradox within logic itself, that is not tied to natural language paradox like "liar's paradox". It only assumes the validity of the arithmetic of the positive integers ... not even zero or negative numbers need be used). Addition, multiplication, powers, roots are defined. Negation, subtraction and division are undefined. Primes are defined however.

So given that I can Godel number a natural language statement, converting that statement into a long integer, can I use the Tarski Theorem to state that ... the truth of the natural language statement is undefined, unless I uses a meta-language? Well that is a paradox, same as happens with mere pure logic statements. I would have to have a supernatural language to assess the truth of a natural language ... but that is impossible, if everything is defined as natural. Any meta-language devised by people, would still qualify as natural.