this post was submitted on 24 Oct 2024
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Science Memes

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submitted 13 hours ago by [email protected] to c/[email protected]
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[–] [email protected] 0 points 5 hours ago (2 children)

Self-referential paradoxes are at the heart of limitative results in mathematical logic on what is provable, so it seems plausible a similar self-referential statement rules out omniscience.

Greek gods are gods in a different sense than the monotheistic conception of god that is omniscient, omnipotent and omnibenevolent. Sure, so the argument I give only applies to the latter sense.

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[–] [email protected] 1 points 4 hours ago (1 children)

Man I don't know if I'll ever get over seeing Mastodon toots on Lemmy and all of the other wild cross-fediverse fun the Fediverse enables

[–] [email protected] 0 points 1 hour ago

I didn't notice until you said something. Wild.

[–] [email protected] 0 points 2 hours ago (1 children)

That's not a paradox though, it's a silly logic puzzle that isn't hard to solve. It doesn't prove or disprove anything about omniscience or gods.

[–] [email protected] 0 points 2 hours ago (1 children)

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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[–] [email protected] 0 points 1 hour ago (1 children)

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".

If it is false, there is an omniscient being that knows it to be true

No, if it is false, then it is simply wrong. A wrong sentence doesn't imply something else is right, it's just wrong.

[–] [email protected] 1 points 56 minutes ago

"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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