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comment by avturchin · 2023-06-18T10:32:47.642Z · LW(p) · GW(p)

I think you are right that the class "sentence" can't have truth value, but what if we replace it with another word, like: "This claim is false".

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comment by [deleted] · 2023-06-18T16:07:42.361Z · LW(p) · GW(p)

I would still argue the same. If it is not coherent, it is not a proposition.

comment by Dagon · 2023-06-18T15:37:24.409Z · LW(p) · GW(p)

redefine "false" in A as designed to decieve or confuse;

Umm, if you're going to redefine the key words, you rather miss the point.  Whatever word you prefer for "matches reality" can be put into the sentence to restore the paradox.  

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comment by [deleted] · 2023-06-18T16:11:07.844Z · LW(p) · GW(p)

I was just saying that "This sentence/claim is false" is incoherent and therefore can't be a proposition.

comment by Ariel Kwiatkowski (ariel-kwiatkowski) · 2023-06-18T14:38:10.431Z · LW(p) · GW(p)

When you say "X is not a paradox", how do you define a paradox?

comment by benjamincosman · 2023-06-18T14:24:34.800Z · LW(p) · GW(p)

"All models are wrong but some are useful" - George Box

First for my less important point: I submit that your framing is a bit weird, in a way that I think stems from a non-standard and somewhat silly definition for the word "paradox". (The primary purpose here will be to build a framework useful in the next part, not to argue about the 'true definition of paradox' since such a thing does not exist.) We live in (as far as we know) a consistent universe; at the base reality layer, nothing self-contradictory or impossible ever occurs. But it is easy to (accidentally or intentionally) construct models in our heads that contain contradictions, and then it is quite useful to have a word meaning roughly "a concise statement/demonstration/etc which lays bare a contradiction in a model". I'm going to use the word "paradox" for that; feel free to pick a different word if you want. Since the contradiction is always in the model and not in reality, a paradox can always be resolved by figuring out where exactly the model was wrong. Once you do that, it is still reasonable to keep using the word "paradox" (or, again, whatever word you've chosen for this useful concept) to keep referring to the thing that just got resolved, since it is still a thing that lays bare a contradiction in that model. Continuing to use that word is not a "misnomer", otherwise every paradox is a misnomer (since we just haven't finished finding the flaws in the models yet, but you know we must eventually).

Now for the more important part: your resolution of these particular paradoxes kind of misses the point. There is a model of math/logic which basically says that every statement which sounds like it could have a truth value does have a truth value. This is a very convenient model, because it means that when I want to make a logical argument, I can just start saying English sentences and focus on how each logically follows from the ones before it, while not spending time convincing you that each is also a thing that can validly have a truth value at all. And most of the time this model actually works pretty well, to the point that it still has a place in widely accepted math proofs, even though we know the model is wrong. But part of why it remains usable is that we know when we can use it and when we must not, because we have things like the Liar's Paradox which concisely demonstrate where its flaws are. Your analysis resolves the paradoxes without showing where these important flaws are by instead exploiting 'gotchas' in the exact ways you chose to word them. As a result, the resolutions aren't particularly useful because someone with only those resolutions would still not know why the model is ultimately unfixably wrong, and also not very robust because I can break them using small variations on the original paradoxes which retain the underlying contradiction while avoiding your semantic weaseling - for example, replace "I am lying" by "I am lying or did lie", and "This sentence is false" by "The logical claim represented by this sentence is false".

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comment by [deleted] · 2023-06-18T16:13:47.403Z · LW(p) · GW(p)

"The logical claim represented by this sentence is false" is incoherent. 

Replies from: benjamincosman
comment by benjamincosman · 2023-06-18T16:30:36.101Z · LW(p) · GW(p)

Ultimately yes that is the resolution, but the point is that you usefully get there not by playing a never-ending game of whack-a-mole arguing that each variant is still somehow incoherent or has a truth value though some weird quirk of the English tense used, but rather by switching from a blacklist system to a whitelist system: everything is presumed invalid unless build up from axiomatic building blocks.

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comment by [deleted] · 2023-06-18T16:38:54.857Z · LW(p) · GW(p)

I don't get it. The reason I say "The logical claim represented by this sentence is false" isn't coherent is because there is no end when trying to understand that sentence/claim.

"The logical claim" refers to "The logical claim represented by this sentence is false" and trying to understand the referent would lead to same process where you endlessly try to understand the subject. Since it can never be understood it is incoherent. Do you see? I didn't do any building up from axiomatic building blocks.