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re: This Statement is false. Is it so? - [liar's paradox]

Hello and thank you for reading my article - I hope you enjoyed it!

I am not sure that I completely understand what you are saying. Is the problem here the self-reference of the sentence? In that case, consider the sentence: "This sentence has five words." It seems likely that that sentence is both meaningful and true, despite being self-referential. (If, on the other hand, it said that there were six words there instead, it would of course be meaningful but false.)

Is the problem perhaps that the sentence has no meaning? Consider then the sentence: "This sentence has no meaning."

Has something gone wrong with indexicals? In that case, consider the two sentences: "The next sentence is true. The previous sentence is false." In that case, the indexicality is clear. (See also Yablo's paradox for an infinite version, which some - not me - claim has no self-reference.)

In any of the above cases, you end up with similar Trouble. There are many variations on the liar paradox. I am by no means an English grammatician, but there seems to be something compelling about these sorts of propositions. Especially where reasoning (and hence mathematics) is concerned, since there we need to provide a convincing account of how it is that we reason sensibly.

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