It is a paradox if you believe there are omniscient beings. If there are no omniscient beings, there is no paradox. The sentence is either true or false. If the sentence is true, we have an omniscient being that lacks knowledge about a true statement. Contradiction. If it is false, there is an omniscient being that knows it to be true. This means that the statement is true, but the statement itself says that no omniscient being knows it to be true. Contradiction.
“This sentence contains 2 words” is a sensible sentence. It has 5 words, so what the sentence says is false.
The self-reference in the sentence is similar to that of the Liar’s paradox. Cousins of that paradox have been used to prove major limitative results in mathematical logic such as
It is a paradox if you believe there are omniscient beings. If there are no omniscient beings, there is no paradox. The sentence is either true or false. If the sentence is true, we have an omniscient being that lacks knowledge about a true statement. Contradiction. If it is false, there is an omniscient being that knows it to be true. This means that the statement is true, but the statement itself says that no omniscient being knows it to be true. Contradiction.
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It’s not a paradox, it’s a dumb logic puzzle. It’s no different than saying something nonsensical like “This sentence contains 2 words”.
No, if it is false, then it is simply wrong. A wrong sentence doesn’t imply something else is right, it’s just wrong.
“This sentence contains 2 words” is a sensible sentence. It has 5 words, so what the sentence says is false.
The self-reference in the sentence is similar to that of the Liar’s paradox. Cousins of that paradox have been used to prove major limitative results in mathematical logic such as
https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
In usual logic, a false sentence implies every sentence.
https://en.wikipedia.org/wiki/Material_conditional
Also, if sentence P is false, then “P is false” is true
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