Can a sentence be both true and false in the same sense? - Dialetheism
It might seem nonsensical until one sees the liar’s paradox:
This sentence is false.
Using classical logic, this sentence seems to be both true and false. Due to the explosion rule, that implies every sentence. This is absurd, but philosophers don’t agree on what has gone wrong here.
Dialetheism is the solution that accepts that it is both true and false and modifies logic to exclude the principle of explosion
I think there are two problems that make this hard to answer:
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Not all sentences that can be parsed grammatically can also be parsed logically.
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Human-language sentences do not contain all the information needed to evaluate them.
It is impossible to fully separate context from human language in general. The sentence “it is cold” is perfectly valid, and logically coherent, but in order to evaluate it you’d need to draw external information from the context. What is “it”? Maybe we can assume “it” refers to the weather, as that is common usage, but that information does not come from the sentence itself. And since the context here is on the Internet, where there is no understanding of location, we can’t really evaluate it that way.
It’s hot somewhere, and it’s cold somewhere. Does that mean the statement “it is cold” is both true and false, or does that mean there is insufficient information to evaluate it in the first place? I think this is largely a matter of convention. I have no doubt that you could construct a coherent system that would classify such statements as being in a superposition of truth and falsehood. Whether that would be useful is another matter. You might also need a probabilistic model instead of a simple three-state evaluation of true/false/both. I mean, if we’re talking about human language, we’re talking about things that are at least a little subjective.
So I don’t think the question can be evaluated properly without defining a more restrictive category of “sentences”. It seems to me like the question uses “sentence” to mean “logical statements”, but without a clearer definition I don’t know how to approach that. Sentences are not the same as logical statements. If they were, we wouldn’t need programming languages :)
Apologies for the half-baked ideas. I think it would take a lifetime to fully bake this.
Under classical logic, a paradox is a result of faulty premises, and proof that the premises cannot be true. It’s how you make any logical proof, by assuming the null hypothesis, and showing how it implies A and ¬A. It’s true for the liar’s paradox, and for Russell’s paradox (sorry Russell).
So my conclusion is “This sentence is false” is false. If it was true, then the sentence would be both true and not true. By the contrapositive, “This sentence is false” cannot be true, and cannot be a logical premise.
Never heard of dialetheism.
It’s not a logical issue because the sentence itself is nonsense. There’s no information in it and isn’t proper English. If you have to break a language to invent a paradox, then it likely isn’t worthy of consideration to begin with.
Nothing you said is true.
- Nonsense. False.
- No information. False.
- Improper English. False.
This is a very well known sentence that leads to things like Gödel’s Incompleteness Theoreom.
If you don’t enjoy the philosophy of logic, that’s fine, but don’t go saying a very famous sentence is improper English.
There is information in it. Namely, that it itself is false. It is fully grammatical. Similar sentence are obviously valid such as:
This sentence has five words.
That is a true valid grammatical sentence.
I didn’t invent the paradox. Philosophers have been contemplating this paradox for a long time.
The problem it gestures at is very deep and similar paradoxes showed up in the foundations of mathematics in the 20th century. It can’t be dismissed easily.
“My name is Bradley” is true when spoken by people named Bradley, but false when spoken by people named Amy
When I consider if the sentence is true, it claims to be false which is exclusive with truth, therefore the sentence is not true.
When I consider if the sentence is false, the claim is inverted, so the sentence has to be not false.
I arrived at a conclusion that is the opposite of Dialetheism, with the sentence being neither true nor false.