It's misleading because, as you say, it seems like a truth-apt sentence, being that it looks like most other truth-apt sentences, but it isn't.

Again, I'm wondering what the evidence for this is. That it looks no different than other truth-apt sentences would support the claim that it is itself truth-apt.

And it's not that it's a syntactic issue. It's actually a semantic issue. Despite it's structure, it doesn't actually mean anything. Truth-predication is only meaningful when there's some evaluable fact about the world. Liar-like sentences don't have such a thing (much like the sentence "I am a squiloople").

I'm aware that it's a semantic issue, you were the one who said it was an issue of syntax. :P
That solution seems dubious, as many truth-apt sentences have nothing to do with the world (e.g. mathematical and logical truths). Further, that seems subject to an obvious set of Revenge Paradoxes:

"This sentence doesn't mean anything"
"This sentence doesn't involve evaluate to a fact about the world"


Hopefully the contradictions are obvious. And besides which, the idea that sentences containing an empty term (e.g. "squiloople") are somehow meaningless seems clearly false. The sentence you gave wasn't meaningless, it's just that the term "squiloople" has no apparent referent. The sentence is meaningful, I just cannot parse one of the terms. And again, the Liar Sentence does have a referent: Itself. So in don't understand how that constitutes a solution.

It might seem a truth-apt sentence but the claim is that it isn't. Its syntax is misleading.

How so? This is why I mentioned the Williamson quote, because the idea that there is a simple solution to this problem is vitiated by the fact that there is not a standard resolution to these paradoxes amongst logicians. If it were simply a syntactic issue, the problem wouldn't persist. And what do you think that syntactic issue is, anyway?

Do we have to abandon classical logic when we claim that the sentence "go away" is neither true nor false?

No, because that sentence isn't truth-apt, nor can I see how you could attach a truth predicate to it. Its just a command. The Liar sentences seem no different that other truth-apt sentences, in which case, denying it a truth-value would necessitate adopting some type of Non-Classical Logic.

Given the pedigree of the Liar's Paradox, one must be careful in seeking simple, obvious solutions without considering why those solutions haven't gained widespread acceptance amongst logicians and philosophers of logic. To quote Tim Williamson on this issue, "We'll have to be willing to tolerate some pretty strange ideas [to solve the Liar's Paradoxes] because we've tried all the non-strange ideas, and none of them worked."

So the Liar's Paradox (LP) is standardly formulated as follows:

"This [sentence/statement/proposition] is false."

Where's the problem? It's simple. If that Liar Sentence is true, then it follows that it is also false. After all, it says (about itself) that it is false. But if you say that the LP is false, then it follows that it is also true. After all, it says (about itself) that it is false. Giving it either truth-value ends in a contradiction, which people (especially in the Western philosophical tradition) find intolerable.

So a couple of people have voiced their preferred solution, so to address them in brief:

"The Liar Sentence is not Truth-Apt"

The idea here is simple. If giving the LP either the value of "true" or the value of "false" results in an inescapable contradiction, we can avoid the Paradox by saying that the LP has neither value, thus preventing the contradiction. There are many arguable problems here. Firstly, this would seem to require abandoning the Law of the Excluded Middle or else the Principle of Bivalence. Now, I've no qualms with dropping Classical Logic in favor of a Non-Classical Logic, but I get the feeling many people would not like that.
But most importantly, this does *not* actually solve the Liar's Paradox. A so-called Revenge Paradox (RP) can constructed to prove the futility here:

"This proposition is [not true/a valueless proposition]"
"This proposition is neither true nor false"
"This sentence is either false or neither true nor false"
"This sentence is ungrounded."

This RP shows that simply denying the LP a truth-value gets you nowhere. If this RP is truth-valueless (as it must be, if the original LP was valueless), then this Revenge Paradox is *both* True and Truth-Valueless (because it says, about itself, that it lacks a truth-value). And if the RP is not Truth-Valueless, the it is False and Truth-Valueless (because it says of itself, a valueless statement, that it has a truth-value). Again, the contradiction pops up. Revenge Paradoxes are the standard problem with solutions to the Liar's Paradox, and positing truth-value gaps don't have a good track record. And so solutions like Kripke's just don't seem to work. Unless I'm mistaken, Kripke himself posited that his solution would possibly be subject to a Revenge Paradox when he first wrote about his solution.

"The Liar refers to Sentences, when Only Propositions are Truth-Apt"

So the idea here is that sentences aren't the objects which possess the property of truth. But rather, that propositions are the objects which bear truth. Ignoring the debate about what actually bears truth, this seems like a dubious solution to the problem. It seems to be basically Kripke's solution: that the Liar sentences are ungrounded. If that's the case, I don't see how one escapes the Revenge Paradoxes.

"The Liar is an infinite Regress"

The ideas here seem to be a bit odd to me. The Liar doesn't loop endlessly, it can simply be taken to be a proposition which relates to 2 truth-values at the same time. That a program would loop in assessing the Liar's value doesn't mean that the Liar fails to have truth-conditions. Computational processes are (arguably) limited in a number of ways, yet we don't axe logical problems on that basis. For example, so far as I know, no computational process can demonstrate the Incompleteness of logical systems of sufficient complexity, and yet it's plainly obvious to logicians why these systems are Incomplete (see Gödel's Incompleteness theorems & Gödel encoding).

The reason why the Liar sentences are philosophically and logically interesting is because they've played a big role in a number of key areas: the foundations of modern mathematics (Russell’s Paradox), discussions about the nature of truth (Tarski's Theorem, dialetheism), and so on.



Now I personally find the Dialetheist response to these paradoxes compelling. E.g. Accept these as true contradictions, switch to a Paraconsistent Logic, and adopt truth-relational semantics. But that's quite controversial

The "footnote to Plato" thing is mostly accurate, though, at least if we're talking about philosophy posterior to Plato and prior to Descartes

Well so far as I know, Whitehead (from whom the quote originates) was presumably talking about philosophy writ large, not the period between Plato & Descartes. My claim was *never* that there wasn't a clear Platonic influence on (Western) philosophy. It was that Plato is, in my opinion, overrated and that Whitehead's statement should not be taken as being literally true, nor accurate.

1. You are grossly underestimating Plato, mainly because you've probably only read him through modern lenses. Jonathan Barnes and Proclus are not equal interpreters of Plato and Aristotle. Just saying.

2. You are grossly overestimating modern thought and methods.

Well I don't see how I'm underestimating Plato, seeing as my only contention thus far was that the idea that philosophy is but "a footnote to Plato" is just silly.

I think modern thought and methods have, on the whole and quite expectedly, surpassed Plato (and Aristotle) long ago. And by such (echoing another comment), I mean that the diversity, exposition & investigation of virtually all philosophical questions has far surpassed anything that Plato could have imagined. To argue otherwise is to, I think, place certain figures on pedestals that make little sense, and which devalues the actual discourse amongst philosophers. Something which naturally tends to be more fruitful than pinning a single person (or 2) as the eternal master of a discipline. And all of that is to ignore the ridiculous eurocentrism this blog view is predicated on.

Peirce independently and contemporaneously achieved the same thing - the introduction of quantifiers and bound variables.

Well, several years after Frege if you want to get technical (1879 or 80, IIRC).

But while Pierce had better contemporary acknowledgements and influence (poor Frege), I think in the long run it was Frege who had more influence on logic. Like, his (and to a lesser extent, Dedekind's) Logicist program held a lot of sway in philosophy, maths & logic, at least until Gödel's work on incompleteness (although it still has some support, though perhaps no much). A lot of Russell's work was tailored in that direction, after all.

Plato. Especially if you take the old Whitehead "footnote to Plato" quote seriously. In terms of modern philosophical discourse, I don't much see the point in being overly interested in what Plato had to say about some topic.

It's obviously Frege in my opinion. Most logicians (so far as I can tell) agree that modern mathematical logic was a huge improvement on Aristotle's logic. Boole is clearly important too, but Frege's creation of Classical Logic is hard to top, and it was Frege's development of First-Order Predicate Logic that really got mathematical logic going (correct me if I'm wrong).

Although, I wish I could have voted for Priest as well, as he's a bit of a rock star of sorts lately, and wrote perhaps the standard intro text to Non-Classical Logics. I've found him to be quite insightful on logic generally, especially on questions such as how we decide what logics to work with.