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• 306
Consider the sentence, "'Snow' has four letters and is cold". Snow is mentioned, but that mention is not something that can be cold, only the snow itself is. So the "is cold" predication is a category mistake (specifically, a use-mention error). However we could apply an interpretive rule and say that in such circumstances, the "is cold" predication disquotes the mention and so is really saying that snow is cold. This would unpack as, "'Snow' has four letters and snow is cold". Such a rule would tolerate the above sentence and allow it to be truth-apt.

That's not really the sort of sentence I used. I didn't say the Liar was " 'This sentence' is false". "This sentence" cannot have the property of truth. But I think it's worse for your approach if you apply that interpretive rule. Then the expression just becomes the Liar sentence because the falsity-predicate disquotes the phrase "this sentence" and transforms it into " 'This sentence' is false is false and this sentence is false." That's just a conjunction of Liar Paradoxes.

Now compare that with "'2+2=4' has three numbers in it and is true". My claim is that the mention of '2+2=4' is not something that can be true, but the expression (or use) of '2+2=4' is. If so, then the truth-predication disquotes the mentioned expression and uses it. This would unpack as, "'2+2=4' has three numbers in it and 2+2=4".

I know that's the contention but you haven't explained why truth and falsity predicates are subject to a different set of rules than other predicates which can apply to quoted sentences. We both agree the expression that is quoted can be attributed truth. The difference seems to be (correct me if I'm wrong) that you think the following quote cannot be predicated truth while I think it can:

" '2+2=4' is true"

On your view, does this work? Can you predicate truth of a mentioned expression? I think you can, provided the mentioned expression is the sort of thing that can bear truth. Some mentions are truth-y, the expression mentioned just has to have the right kind of structure. The Liar has that structure. This solution is the same sort of solution Kripke tried and I don't think it works.

Since "This sentence is an English sentence" doesn't contain a truth-predicate, the referring expression is only mentioned, not used (i.e., only the surface aspects of the sentence are referred to). Whereas in the liar sentence, the truth-predication disquotes the mention and uses the referring expression. Thus it is cyclic.

OK, I think this runs into an issue I mentioned earlier to another user (assuming that user wasn't you, too lazy to check). Take the following:

This sentence is true.

Now that's an odd sentence, but it doesn't even have the appearance of a paradox, unlike the Liar. Under the rule you mentioned, it comes out as

"The sentence 'This sentence is true' is true and this sentence is true"

Well, that conjunction is obviously true under this interpretive rule, both conjuncts come out as true because the mentioned sentence is transformed into a use of the quoted expression. But that means that impredicative truth assignment cannot be sufficient to say the Liar is a category mistake. And note, Ryle specifically calls out impredication as the issue here (just look at the passage you quoted, he names "Impredicability").
• 449
I know that's the contention but you haven't explained why truth and falsity predicates are subject to a different set of rules than other predicates which can apply to quoted sentences.

There needs to be a way to convert a mention to a use and using the subject-predicate form is an efficient way to do that.

" '2+2=4' is true"

On your view, does this work?

Yes. To say "'2+2=4' is true" is to say "2+2=4". That is, truth predication of a mentioned expression uses the expression. So it's the inverse of quoting.

This sentence is true.

The truth-teller sentence cycles for the same reason as the liar sentence. Here's the iterative unpacking (the => is just an arrow to indicate the transformation steps):

"This sentence is true" => "'This sentence is true' is true" => "This sentence is true" (truth predication rule). So we have a cycle.

Compare with unpacking the liar sentence:

"This sentence is false" => "'This sentence is false' is false" => "Not ('This sentence is false' is true)" => "Not (This sentence is false)" => "Not ('This sentence is false' is false)" => "'This sentence is false' is true)" => "This sentence is false". So we also have a cycle.

And compare with the English sentence:

"This sentence is an English sentence" => "'This sentence is an English sentence' is an English sentence" => true. So it's truth-apt.
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