Could you rephrase the question?

"The present King of France is bald" is another statement to which we cannot (easily) allocate a truth value. — Banno

And obviously what I had in mind when I said 'presupposition'. Now consider statements that have presuppositions that aren't contingently but necessarily false. It's not the statement itself you need to deny, but the presupposition.

I'm not seeing the immediate connection between the Liar Paradox and the incompleteness theorems — Kornelius

By way of gossip, I'm almost certain Godel himself said as much, and may even have suggested he wasn't thrilled about how close the arguments were. To be googled.

For 'claims' here and there above, perhaps 'presupposes' is what we need.

'This is the prettiest square circle anyone has ever drawn.'

Should add: by predicating 'not true' of itself, the Liar claims to be a member of the class of sentences that are true or false, and perhaps it is this claim that turns out to be false, making the conjunction of its claims false.

I've been thinking, if we're going to (what we needn't) treat True(...) as a predicate applicable to sentences, then we should also be able to talk about classes. (There are of course problems with enumerating sentences, but in natural language we do use class talk that might present technical problems or resist formalization.)

The Liar, then, claims -- speaking a little loosely here -- that it is not true, which is equivalent to claiming that it is true iff it is false, claims thus to be a member of a class that is by definition empty, and claims further that said class is not empty because it itself is a member. Thus the Liar is false.

That assumption is discharged at step 5 — Kornelius

Ugh, the Liar is such a pain. I was about to slap my forehead and say you're absolutely right, but are you? I'm genuinely not sure now. The discharge step would have this form:

4.5. P → P & Q

Can we say that P has been discharged if it's on the right hand side here? That doesn't seem right.

(This is the consideration I dismissed, in so many words, above. 'It doesn't matter that (Li) is part of the expression (Li) & ~(Li).' Geez.)

Whether we can discharge (Li) this way truly doesn't matter though because (4.5) is just P → Q, which is clearly fine, and we can have that even before getting to 4:

3.5. True( Liar) → ~True( Liar )

and that's just equivalent to ~True( Liar ).

So, yes, no question, by the time we get to applying [T-in], (1) has been discharged, either by forming the contradiction, as you did, or by forming (Li)→~(Li).

And so you are, finally, absolutely right we get ~(Li) as a theorem and then (Li) as a theorem from that, so we end up proving outright (Li) & ~(Li). Thanks for setting me straight!


(Not sure which of the logical equivalences I used are intuitionist-safe, but I so don't care at the moment.)

But notice that the rule you mention here doesn't get us from [(Li) is true and (Li) is not true] is false to (Li) is not true. If a conjunction is false, either of its conjuncts could be false, so the inference here is invalid. — Kornelius

Sorry -- knew that would be confusing. It's valid because it doesn't matter that (Li) is part of the expression (Li) & ~(Li); what matters is that that's a contradiction and it's false, and therefore one of the premises from which we derived it is false. Since there was only one premise...

Here's your original presentation:

1. Assume (Li) is true
2. Then '(Li) is not true' is true (substitution).
3. Then (Li) is not true (T-out)
4. Then (Li) is true and (Li) is not true (from 1 and 3. Contradiction)
5. Then (Li) is not true (reductio 1-4) — Kornelius

What I was pointing out is just step (5) in your (or Scharp's) presentation. The inference rule I referred to is just the reductio rule.

What we really want is for steps 5-8 to be a separate argument, using [ T-in ] instead of [ T-out ] and showing that ~(Li) is also false. By continuing on past the reductio, we just rederive the premise in step 1, rederive step 4 as step 8, all of which still only gets you ~(Li) because it's the only premise.

5. Then (Li) is not true (reductio 1-4)
6. Then '(Li) is not true' is true (T-in)
7. Then (Li) is true (substitution)
8. Then (Li) is true and (Li) is not true (from 5 and 7. Contradiction). — Kornelius

This presentation only shows, with some repetition, that the Liar is false. (If the idea was to sweep up intuitionist logic along with classical logic, by avoiding appeals to the LEM and to double negation elimination, it does not appear to me successful.)

What we have is [(Li) is true and (Li) is not true] is not true.

Agreed. But by what rule of inference would it follow that (Li) is not true? — Kornelius

The usual one: if P entails a contradiction, P is false.* If you want, you could say the problem is that both the Liar and its negation are false, which in turn violates the LEM.

It's simply a case of my suggestion not being very good! — fdrake

Disagree.


* It's not uncommon to just define $\neg P$ as $P\to\bot$. Even in systems that don't, this is an introduction rule for $\neg$.

I do think you are right in pressing against the view I was arguing here, namely that we should assume it is meaningful. — Kornelius

I'm not sure it amounts to anything.

@SophistiCat and I have ended up having a discussion that's hard to distinguish from an argument about whether the Liar is meaningful. And there's just no point to that, because of revenge.

Even the other idea I had in mind amounts to the same thing. (If you ask what 3+5 is, there's a single right answer and an infinite number of wrong answers. This kind of thing shows up in a few places and there's a reason I'll bet @fdrake knows.) In essence it just amounts to having a designated value, and again we know this won't help because of revenge.

I almost gave 'Its syntax is fine' as an example of a rule for assuming a sentence is meaningful! But--

That's kinda like saying the semantic problems of a sentence are semantic problems.

Worse: doesn't this amount to saying that if a sentence has even a very severe semantic problem, such as being meaningless even if its syntax is fine, then you only find this out by looking at its semantics, and therefore it's meaningful?

But that's too general. You're right that we have to make enough sense of the Liar to understand that it empowers us to use it to infer 'I'm false' from 'I'm true' and vice versa. I can't dispute that.

But, as I tried to express above, that's pretty weird. If you think of the Liar as an introduction rule, then its semantic content is, in one sense anyway, syntactic. And that's all it has. But that's not supposed to happen. It's why we distinguish them.

I want to follow this but I can't.

Reporter: 'So Canada is a terrorist state?'
President: 'Yes.'
R: 'But you don't believe Canada is a terrorist state.'
P: 'Of course not.'

It's just a counterexample to the claim that no one would ever say 'P but I don't believe P.' It's not a restatement of Moore's paradox.

It is only once we trace the logical implications that we realize that something is wrong, but in order to be able to do that, didn't we have to first understand what the sentence is saying? — SophistiCat

On the one hand, sure, you can imagine having to explain to someone who doesn't get it what the problem here is, and that might feel like guiding them through a formal deduction.

On the other hand, the Liar is introduced as a premise, but then behaves like an inference rule. ('Given me, you may introduce not-me.') You have to understand the inference rule to use it, that is true. But that's understanding-how, not understanding-that. Inference rules are deliberately empty, have no 'that' content. They don't say anything themselves; it's premises that actually say stuff.

When we trace the logical implications of the Liar, we stop at contradiction, as @Kornelius did, because that's one of our things, a proof-doing practice. But I've also demonstrated it to people by starting at true and then saying, 'But if it's true, then it's false, but if it's false then it's true, but if it's true ...' and doing the same thing starting with false. You never 'finish' so you never get to a point where you've figured out what it says. The completion of the statement is always deferred.

Since I don't see any problems in the argument I presented, it follows that your objection must revolve around L and P. — TheMadFool

It's not just my objection; it's the revenge pattern: if you hope to avoid the Liar by using some other semantic predicate also available in your language, we'll just construct a new Liar-like sentence that is just as bad as the original.

'... is a proposition' is such a predicate: you absolutely can use it to block the Liar, just as you did, but it's no help with the revenge sentence, 'This sentence is not true or is not a proposition.' You might as well not have bothered.

i'm a month late, but this is timeless:

But there's no need for anything meta, right? — TheMadFool

In a natural language, even in philosophical English, the object language and the meta-language are one. I do not understand your point.

If you have the patience for it, I'd like to set aside my position and just examine yours for now. My goal at the moment is just to understand your position better than I do now. I'm not even looking for arguments against it, though I will have questions.

Here's how I understand your position:

(1) The sentences 'Dewey has defeated Truman' and 'I believe Dewey has defeated Truman' mean the same, have the same use.

(Thus Moore's paradox is only an apparent paradox; the speaker who utters 'Dewey has defeated Truman, and I do not believe Dewey has defeated Truman' is uttering a contradiction.)

The idea behind (1) is that 'Dewey has defeated Truman' is really 'I believe that Dewey has defeated Truman' but elides or suppresses the 'I believe ...' It is nevertheless an expression of belief, or of purported belief, if we have to account for insincerity at some point.

This is so because we can only talk about the world as we understand it, and we understand it entirely in terms provided us by the mental model of the world our brain constructs and continually updates.

Our words refer to artifacts of this model, not to objects in the world.

Everything we say is, in a sense, a 'report' on the latest iteration of the model we are aware of.

If I have this right so far, this is where I'm a little unsure. Certainly, as you've said, there are those occasions where we might speak about our beliefs as an outsider would, observing ourselves as an object, but this is not the usual case, so 'report' there sounds a little wrong. We want a clear way of saying that the sentences we utter are informed by the mental model, entirely dependent on it, but for speech acts to be something other than comments about it.

Certainly we'll continue from here with a pragmatist account of speech acts, but we have to backtrack a little because 'belief' is being used in two ways here. On the one hand, it's kind of kind of pragmatist shorthand -- 'Jim believes there's beer in the fridge' just unifies descriptions of actions Jim is taking or might take, things he says or won't say, and so on. A belief is nearly a theoretical posit -- what we're really interested in is behavior. But above we claim that 'Dewey has defeated Truman' is something a lot like a description of my mental state, that it's about my beliefs in a sense not too different from the way people generally understand beliefs, just somewhat broader. That claim doesn't seem to rely directly on some idea of utility as a pragmatist account might; it's an argument about what the semantic content of our speech acts must be.

So my question is roughly this: do we argue here that the pragmatist account actually kicks in a little earlier, in the model taken as a sort of Bayesian inference engine, that this is where we find the idea of utility? But then are we also looking for pragmatist account of semantics? Do we even need one, or do we sort of get it for free by focusing on how the model (whence all our speech acts originate) works?

Not too clear, but I hope you get the gist of what I'm asking. If not I'll take another run at it.

I was arguing without using a specific criterion of meaning. This is just to say that I was arguing by referencing speakers' intuitions and was anticipating with the other side may say to argue it is meaningless (i.e. ungrammatical, issue with self-reference). I think that (Li) is intuitively meaningful in this sense. Most competent speakers of English will not react to (Li) as they would to the sentence "the runner runs runningly run running". — Kornelius

I'm not so sure. 'Whether an ideal speaker would consider P meaningful' looks to me like a separate criterion of meaningfulness -- that is, not just asking whether P is truth-apt.

Also, '... is meaningful' feels like a weasel-predicate. That is, '... is meaningful' deliberately avoids asking, for instance, 'What does it mean?' or 'What does it say?' Ask an average person about the Liar, and you can expect them to reply, 'Well that's stupid. It doesn't say anything.' (This applies to 'This sentence is true' as well!) Surely if you find a sentence meaningful, you could say what it means. There hasn't been 2000 years of debate over what the Liar means, what it says, because it evidently fails to quite mean anything.

Anyway, for the assumption angle, I was trying to think of something like that principle -- the name escapes me, has to do with entropy -- that there are always more ways of being wrong than right. Not exactly that, but something like it. A justification for assuming that a sentence, even a grammatical sentence, is nonsense until it is demonstrated that you can assign a truth value to it. (If it's a question or a command, say, so you fail to assign a value, then we need convincing arguments to bring them in anyway. For the 'always takes both values' case of the Liar, I can't imagine what a convincing argument would be -- we do generally prefer our sentences to take at most one truth value at a time -- but if there is one, then this approach fails anyway and we're back to the meaningfulness arguments.)

I've been keeping in my back pocket an example of this that comes straight out of speech act theory.

Suppose the US has information that some very high level Canadian official, who's traveling through a US airport, is connected to a terrorist group, and for whatever reason Canada can't change his status in time for the US to apprehend him. You could imagine the President declaring Canada a terrorist state to provide a legal basis for the action, and announcing it by saying, "I do not in fact believe Canada to be a terrorist state and will revoke this declaration in about three hours, but for legal reasons I am officially declaring Canada to be a terrorist state."

What you have here is in the form of a proof but of course it is not a proof because we're not talking about a formal system -- Tarski told us long ago that you just don't include predicates like '... is true' and '... is a proposition' in your language and you're fine. If you want them, they have to be in the next language up, the meta- to this object. What to do when it comes to natural languages -- there's the rub.

And while I sympathize with your approach, what happens with this sentence?

(L') 'This is not a proposition.'

If it's true, then it can't be true because it can't take a truth value. If it's false, then it can take a truth value and so assigning it "false" in all models is fine. So it looks like the predicate '... is a proposition' should be fine and L' is necessarily false. Cool.

But then what about this one?

(L'') 'This sentence is not true or is not a proposition.'

If it's true, it's either not true or it's not a proposition, so it's not a proposition, so it can't be true. If it's not true, it's true and a proposition.

This is the revenge paradox, and you could do the same thing with '... is meaningful' in my post above. In a sense, even formalizing truth the minimum amount that Scharp describes blocks you from formalizing other semantic predicates like '... is meaningful' or '... is a proposition' on pain of revenge. That would leave you with a formalized truth predicate you can't actually use in a formalized way. On the other hand, if you decide to give up on bivalence and roll the other semantic predicate you want into "truth", so you have three values, then you just get revenge immediately. This is the point @Kornelius is making here.

The Liar always argues its way out of any argumentative box you try to put it in. To deal with it once and for all you have to give up on formalizing your semantics even a little, formalize it differently from the way we have so far (and there are always such proposals around, some of which are nice), or protect the old semantics from having to deal with it in some other way. (Whether this last is even an option is unclear, and it's the approach I was suggesting be explored, just for funsies.)

It's hard not to see it, but splitting the Liar in half allows you to assign truth values, so you can end up with a sentence that is arguably true but cannot be asserted in the first person in the present tense. (Moore had a nose for the problems indexicals raise.)

What makes it a paradox is, as you say, it appears analogous to many other sentences that are just fine, but when we try to assign it a truth value, something goes wrong; we have two ways of deciding whether the Liar is meaningful and they give different answers.

I suggested we need an argument for why we should consider it meaningful. (I was thinking of the analogous efforts in support of treating questions, commands and the like -- over on the 'gap' side' -- as meaningful, despite starting from a model clearly designed for simple indicative statements.)

You suggest we need an argument for why we shouldn't treat it as meaningful.

We have an extra layer here now. There are arguments (M) that the Liar is or isn't meaningful; there are also arguments (A) that the Liar should or shouldn't be assumed to be meaningful, so that a convincing argument is required to overcome this assumption. A convincing M-argument would allow you to ignore the A-arguments, but we already know we're in paradox land and the Liar comes equipped with arguments on both sides. I'm not much moved by the 'apparently meaningful' argument, but I have to admit that many people are, you among them, so there's some reason to think the arguments against meaningfulness aren't that strong, or that the arguments for meaningfulness are just as strong.

So what about the A-arguments? Can we imagine a way to decide whether to assume meaningfulness or not without rehearsing the arguments for and against meaningfulness? What would we need for such a decision?

the science of Linguistics uses truth-conditional semantics for natural languages. Since liar sentences can be formed in natural languages, then the linguist must provide a semantics for these sentences (on the assumption they are meaningful). But we cannot give such a semantics for such sentences, despite their being meaningful. — Kornelius

We're skipping a step though, aren't we? Even if we're not going to reach for a separate criterion of meaningfulness (not relying on truth conditions), we have to argue for the meaningfulness of gaps (won't take a truth value) and gluts (takes too many, like the Liar).

You know it's funny you spotted that in this necro-thread because lately I've started warming to the general idea of dialectic -- though I don't know that I'll live long enough to develop an interest in Hegel. Don't tell apo.

Agreed across the board.

Do you have a way of fleshing out 'commitment'?

Tiny additional point: folk psychology freely mixes reasons and explanations, especially when the mental state in question includes emotions as well as beliefs.

'Say, Lefty -- why does Tex hate Canadians so much?'
'Canadian killed his pa.'
'Mmm. I still say, that's no justification for judging a whole country.'

"I believe it's raining" (taken as a psychological statement) is not in the same model as "It's raining", it's talking about how the model of 'raining' is being formed - by my believing it to be the case. — Isaac

We do get to choose though, and some choices may be better grounded than others in particular circumstances. Where you say '(taken as a psychological statement)', you're simply announcing your choice. I announced mine a few pages ago when I said 'meaning, referring and believing are part of our frame not yours, part of folk psychology, not neuroscience.'

Compare these answers to 'Why do you think it's going to rain?':

(1) Because Channel 5 said ...
(2) Because my neurons ...

In everyday life, and in philosophy, we talk about beliefs having or lacking reasons; in psychology, you're headed for causes or explanations.

If we're in the shared model where "It's raining" just means that in-world clouds are dropping in-world water, then "I believe it's raining" is not truth-evaluable by me. My beliefs about this model are assumed to be the case, that's the game we're playing when we talk about stuff in-world. — Isaac

The presuppositions of our shared model are assumed -- that there's objects, that time passes, that people have beliefs and intentions, and so on -- but obviously people worry all the time about whether their beliefs are true, and they do so within the shared model, accepting those presuppositions.

Our beliefs about whether it's raining are the authors of the story in which it's raining. — Isaac

Our shared beliefs are the author of the story in which it is possible for it to be raining, but an individual can clearly believe it's raining when it isn't. The world in this game is persistent: we change what stories we tell as individuals within it without rebooting the whole shared world every few milliseconds.

So in what sense is my at this moment belief not truth-evaluable by me, just assumed to be the case? Are we all prisoners of our own beliefs? If you believe something, you can do other than assume you're right, deluded though you may be?

This is just to say that you actually believe what you believe. I also actually bend at the waist and allow the chair to support me when I sit. That's neither a consequence nor an explanation; it's just what sitting is. Your at this moment belief is not truth-evaluable by you not because you are prisoner of your at this moment mental model, but because you have already evaluated its truth. You've already put a check in the T box, so your pencil is no longer hovering between the T and the F. And you might change that, but at this moment the T box does have a check. That's just what believing is.

Even in isolation the utterances have quite different pragmatics – 'I believe it's raining' is weaker, in that it implies a hedge, and puts less pressure on the audience on the uptake. Cf. 'I believe it's raining, but I'm not sure if it is,' versus 'It's raining, but I'm not sure if it is.' — Snakes Alive

Obviously I agree with everything in your post, and have said as much, but I've avoided leaning on this particular point because, while it's true that in everyday usage people reach for 'believe' precisely when they want to deny claiming knowledge or certainty, around here 'believe' is usually shoptalk that's just neutral on the confidence with which you believe. The latter is not so much a 'weaker' cognitive verb, as just a limited one. In everyday usage, your first example there ('I believe it's raining, but I'm not sure') is almost redundant. In everyday usage, certainty is sometimes an implicature that can be canceled. ('How many are left?' 'Seventeen -- but don't quote me on that.')

This is all very long-winded, but there is a methodological worry at the end: earlier-days ordinary language philosophy often marshalled evidence for a claim by saying things like 'If that were true, you'd be able to say this, but you can't.' As OLP birthed or transformed into pragmatics, it became clear that reading those cases as questions of 'what makes sense' is not so simple: what makes sense is sometimes what fits the pragmatics rather than what is truth-apt or something.

A bit of philosophy that has passed into general usage is, given a fictional world such as a novel or a movie or a video game, to distinguish between the perspective of fictional characters who (in their fictional way) dwell in that world and our own perspective as outsiders. This isn't hard but I'm going to give an example anyway. Here are two answers to the question, 'Does Santa fly around the world in a helicopter delivering toys on Christmas Eve?':

(1) No, it's a sleigh pulled by eight (sometimes nine) magic reindeer who can fly;
(2) No, because Santa Claus doesn't exist, so he doesn't fly around in anything.

Both are defensible answers, and which is preferred depends on circumstances.

*

Now, you have a story about how the world doesn't really include objects we refer to and talk about using words; these so-called 'objects' are all artifacts of our mental models of reality, created and continually updated by our brains automatically, without our awareness much less our intervention.

Let's say you're right -- it's the standard view in the cognitive sciences these days, I hear, and I have no cause to challenge it. We all inhabit a virtual reality.

But this is not what you and I, or you and @Luke, have been disagreeing about, I believe. It's that when (in-world) I (in-world) asks (in-world) you to (in-world) put the (in-world) book (in-world) on the (in-world) table, you're inclined to tell me that there isn't really a 'table', that the 'table' is in-world and that what I'm talking about is part of a model of reality instantiated in my brain somehow.

Well that's true, right? And didn't I just admit as much?

No. Because in-world I lives in a world that has actual tables and actual books to put on them. In-world, these things are all quite real. It's the whole point of having the model. It's the whole reason our brains generate the virtual reality to start with. The tables in in-world-I's world aren't artifacts of the in-world-model of the in-world-world in in-world-I's in-world brain; they're just tables.

And you accept this too, not just in unguarded or non-philosophical moments, but even here in this discussion every time you say 'brain' instead of saying 'more or less invariant features of reality that we keep track of using the label "brain".' But even that wouldn't do -- look how many words there were used with their in-world meanings! It's all of them.

Actually, I'll make one little point on my way out.

I think the Problem of the Criterion is slightly more interesting than the Church-Fitch paradox or the Münchhausen trilemma because it invites solution, and possible solutions have something interesting in common. Robert Stalnaker, at the beginning of his Locke lectures, put it this way: that the right place to begin philosophy is not at the beginning, but in the middle.

Well good luck to you.
— Srap Tasmaner

Thanks but I suppose you were being sarcastic. — TheMadFool

Poor choice of words on my part. Just bowing out of the discussion.

A proposition is a speech act. — Isaac

This is all very helpful. (At the moment, I'm really just trying to figure out how we can stop talking past each other.) We're still having serious terminological problems -- in my world, the above is either a contradiction or just nonsense! -- but that can be remedied. And I know perfectly well that Ramsey had truth-deflationist leanings, which is why it seemed odd to me that what we land on as "assertion" is claiming, of some proposition, that it is true.

I think what you want to say is something like this: I have enough confidence in some of my beliefs that among the actions I am willing to take on the basis of those beliefs is, in the appropriate circumstances, to say out loud that this is how things stand, to agree with someone else who says it, to answer in the affirmative when asked if this is how things stand. Speaking is a way of acting upon a belief.

But something is getting garbled when you also tell the causal story of how we produce an utterance, and then call what caused the utterance what the utterance is 'about'. I'm just not getting the connection you see between the causal chain or process that results in an utterance and 'aboutness.' If I assert, by making an utterance, that this is how things stand, what I'm talking about is how things stand. Your occasional use of 'about' to mean something else has me befuddled.

Not all beliefs can be properly expressed as propositions. — Isaac

Example?

This is clearly what LW was up to -- without even going back to the Investigations, you could guess that what's going to interest him here is the grammar of "I believe ..."

What is lovely is the observation that a belief is not like a sense impression. Sense impressions have this sort of authority, like scouts or emissaries who actually come from the lands beyond to report how things stand. Beliefs aren't like that at all.

When I tried to think of counterexamples, I kept finding things much more like sense impressions. Say you're looking for your car keys, and suddenly remember seeing them on the kitchen table; you can indeed take your own mental state as evidence that your keys are on the kitchen table, but you wouldn't describe this as suddenly remembering that you believe they're on the kitchen table and had merely forgotten that you believe this. That's cool.

the assertion can be about nothing else but the belief (not the fact of their belief, the content of it) — Isaac

A belief in the sense I'm talking about, is an inference about the state of the world. — Isaac

Just to connect some dots here -- what you called the belief's 'content' above, that's the inference about the state of the world. (And 'inference' you're using here not in the sense of 'an act of inferring' but in the sense of 'a conclusion reached by an act of inferring,' a proposition, yes? Not trying to be pedantic here, but that word's ambiguous and we're already having enough trouble.)

So beliefs are about the world and assertions are about the content of beliefs, namely, inferences that have been made about the world.

Alright, suppose I have inferred that Dewey defeated Truman, and I hold a belief the content of which is 'Dewey defeated Truman.' If I were to assert that Dewey defeated Truman, for instance by saying, 'Dewey defeated Truman,' I would be, as I understand it, saying something about the proposition (expressed here as) 'Dewey defeated Truman,' the content of a belief I hold. What would I be saying about it? That it is true?

Well good luck to you.

(1) 'Dewey defeated Truman' is true iff [ insert theory of truth ]
(2) Alice knows that Dewey defeated Truman iff [ insert theory of knowledge ]
(2a) Alice knows that 'Dewey defeated Truman' is true iff [ same kind of theory as in (2) not as in (1) ]

(1) is about what happened, maybe about what properties that sentence must have and what other properties the world must have for that sentence to be true; (2) is probably about whether Alice believes that it happened and whether we by-and-large approve of how she came to believe that, but maybe something else; (2a) is a recasting of (2) to emphasize that (this sort of) knowledge is propositional.

No.

According to the Internet Encyclopedia Of Philosophy: — TheMadFool

it is important to be clear about the nature of (1) and (2). These are not questions about the nature of truth itself. Rather, these are epistemological questions concerning which propositions we should think are true and what the correct criteria are for determining whether a proposition should be accepted as true or false. It is possible that one could have answers to these questions without possessing any particular theory of truth, or even taking a stand at all as to the correct theory of truth. Additionally, it is possible to have a well-developed theory of the nature of truth without having an answer to either (1) or (2). So, the issue at the heart of the Problem of the Criterion is how to start our epistemological theorizing in the correct way, not how to discover a theory of the nature of truth.

So what do you mean here:

1. Propositions can't be true prior to the existence of a criterion (hence the need for a criterion) — TheMadFool

Are you talking about what makes a proposition true, or about how we know that it is true?

Suppose you study a messy but widely used concept like "fascism," and your research results in a formula, something like 'all fascist regimes have at least five of the following seven properties ...'; your formula selects the regimes we all agree are fascist, rejects the ones we all agree aren't, and gets you booked on cable news shows to tell us whether the borderline cases we're concerned about are or aren't, and how we'll know when they 'cross the line,' if they do.

This is just business as usual for determining a criterion: you take your data as already partially sorted since no one is claiming that maybe we don't know which regimes are 'really' fascist. We notice some natural variation and try to tighten things up a bit, and then we let "fascist Mk 2" deal with new data and corner cases. (If convincing objections are raised to how it handles these, it's on to Mk 3.)

Sadly this procedure has an obvious shortcoming as an approach to the theory of knowledge.

(If you don't like that answer, consider that you would have to know at least one thing before you deploy your criterion and start sorting statements into "true" and "false," namely what the criterion is.

In neither case do we need or expect a complete partition of statements, just some starting point, something already known.)