“My cat ate my house” makes sense, you understand the full concept, but it is nonsense. It won’t happen in reality. Language is a great tool for conveying our thoughts to one another, great until it is used as a device to trick you. Many find themselves losing an argument and rather than conceding, they resort to manipulating the language to ‘prove’ they are correct instead.
“This sentence is false” is one more of the countless language twists that has stoked a bit of fun.
Replace ‘this sentence’ with x and “x is false” is no big deal. However, as ‘this sentence’ includes ‘this sentence is false’ it becomes recursive.
(this sentence is false) is false.
((this sentence is false) is false) is false.
To avoid being labelled a politician / pedantic pain / prat / estate agent, you can stick to going by what people mean rather than rearrange the things they say.
This (prison) sentence is false, spoils the point also. (Sentence is not spelt with an 'a' if used as jail time)
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