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I know that the Liar Paradox has been discussed a fair bit on here, but I have a question about it that seems a bit more fundamental. Perhaps it has been asked and answered here in more proper terminology and as such I just wasn't able to recognize it as my question, or perhaps I have fundamentally misunderstood the issue, but heregoes:

I say something untrue. Then I tell you that I did. So in that case, in the second sentence, I have told the truth. But if it is true, then I actually lied. Is that the gist?

Can one not just say that I told the truth about lying, in the second sentence, but actually lied in the first? And so there is no contradiction? I am assuming I have misunderstood, but I can't quite figure it out on my own.

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    Usually, the paradox is formulated using just ONE sentence, viz. a sentence that talks about itself: ‘This very sentence is false’ is one way to do it, where the demonstrative ‘this very sentence’ denotes the sentence itself. If the sentence is false, then what the sentence says is the case; so, the sentence is true. Yet if the sentence is true, what it says must be the case; so, the sentence is false. Contradiction. If you instead say: ‘Grass is blue. That last sentence is false’, no paradox arises: the first sentence is false, the second true. (Whether you lied is a different question.) – MarkOxford Mar 14 '18 at 8:16
  • See Liar Paradox for "variations" of the basic structure: single-sentence, circular, etc. – Mauro ALLEGRANZA Mar 14 '18 at 8:34
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    There are "situations" involving self-reference that produce a contradiction: we call it paradoxical. The fact that you can manufacture a similar situation taht produces no contradiction, does not imply that you have removed the paradoxical cases. – Mauro ALLEGRANZA Mar 14 '18 at 8:37
  • Classical example (probably in @MauroALLEGRANZA's link). Plato: Socrates is lying, Socrates: Plato is telling the truth. – barrycarter Mar 16 '18 at 17:14
  • Thanks guys! Especially Mark, I think that's where I was getting confused. – freigz Mar 17 '18 at 19:26
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Usually, the Liar Paradox can be formed of one sentence, where the paradox arises from self-reference; essentially, the sentence "This sentence is not true" says of itself that it is not true.

Take a sentence D such that D = ~Tr(D), where Tr(x) is our truth predicate. ~Tr(D) says that D is not true, and since D = ~Tr(D), it says of itself that it is not true.

This shows the paradox to be an issue of impredicativity, where the content of the sentence depends on the content of a set of sentences of which that sentences is a member. The very truth conditions for the sentence's being true derive a contradiction:

D is true if and only iff its not true that D; formally: Tr(D) ⟷ ~Tr(D)

Tarski uses this to show that an object language cannot contain a truth-predicate that can be used to talk about the language itself. Either the truth-predicate exists as part of a meta-language above the object and talks about sentences of the object language, or the object language contains a truth-predicate but that truth-predicate can only be used to talk about the truth of sentences in lower-level languages (According to Tarski).

The reason for this is that when a sentence of a given language is uttered, it is assumed that when we utter that sentences, we are also making the equivalent claim that the sentence is true: I.e. to say "snow is white" is also to say "the sentence "snow is white" is true". Terence Parsons (1984) calls this principle [T], where for any sentence, X, expressed in a derivation, we can assume Tr(X). This is how we form the biconditional from earlier: Tr(D) ⟷ ~Tr(D).

When this is done, we can derive a contradiction very easily. Parsons gives the following intuitive derivation:

Parsons, 1984

As this derives a contradiction, if we still want the starting assumption to be assertible, we better deny one of the steps in the derivation. Hence, Tarski looks to remove principle [T], such that no object language can express propositions about the semantic values of its own sentences.

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Lying is saying something false against better knowledge. If you believed what you said the first time then you were not lying.

Then somehow you understood you were mistaken in your first statement. And tells us you were wrong ... this is honorable.

I dont really understand what your problem is? What you have said so far has no connection to the Liar Paradox.

What would you think if I said to you:

What I now say is not as I say it is!

Whould I be lying or wouldnt I?

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