Sometimes,a s a discussion unfolds, the only thing to do is to laugh and walk away. — Banno

But that's no fun unless you come back occasionally and make snide comments from the ivory tower.

I think you're conflating two different senses of "meaning" — Michael

I'm really not. If I candidly assert an indicative sentence, I imply that the content of my belief is represented by that sentence. It's simply false that I have to preface everything I say with "I believe."

I'm concerned with meaning in the sense of definition. — Michael

I get that. But I'm not sure invoking the word "definition" is going to get you very far.

"I believe that the book is in my room" and "the book is in my room" do not share a definition. — Michael

Neither one of them has a definition; they have semantic content. Which I think is the right thing to be talking about.

Otherwise how do you make sense of the "the book is in my room" part of "I believe that the book is in my room"? The latter isn't to be interpreted as "I believe that I believe that the book is in my room". — Michael

Well that's a question. The biconditionals I offered look circular, don't they? What are we to do about that?

I think you're just taking meaning-as-use to an irrational extreme. — Michael

You're confusing me with what I want to argue against, but we can't ignore that there is insight underlying the doctrine of meaning as use.

"It can be true that I believe something even if what I believe is false" is something I believe. — Michael

Now try it with a specific belief. You can't assert that the book is in your room, or that you believe the book is in your room, and that it is not true that the book is in your room. Someone else, let's say "George", can say it of you, and then there's nothing to stop a third party from saying that you believe the book is in your room and George doesn't, full-stop.

I think the right strategy is to block the supposed dependence of semantic content on beliefs.

↪TonesInDeepFreeze The sad thing is that your clear explanation will not correct the confusion here. — Banno

It's not that simple.

For instance, I had a look at the SEP article about revision theory, and I was puzzled that we're treated to what amounts to a wholesale reconstruction of model theory to allow the proposed extension, complete with new versions of interpretation and everything else, and then I realized that you have to do this if you accept that Tarski's machinery is not up to the task.

I don't think we even have a complete syntax for any natural language; lacking that, there's no hope for a complete semantics.

So while I'm deeply sympathetic to the formal approach, and in particular with model-theoretic truth-conditional semantics, we can't claim to have managed more than some fragments of some natural languages. And formal semantics takes lexical semantics as just given, somehow, which means it is never going to address issues of reference; that's a non-issue for mathematics, where reference is essentially stipulative all the way down, but it's a big damn deal with natural languages.



I obviously don't have any problem with the specifics of what you posted, but I'm not clear on what you expect to achieve by posting it. The box and diamond operators are defined as they are because of our pre-existing intuitions about alethic modality. And similarly for the axioms of various modal logics. You're surely not arguing that someone's intuitions can be refuted by the definitions and axioms we've chosen... If those definitions and axioms don't match our intuitions, so much the worse for them.

I'm also not clear what kind of mileage you hope to get out of talking about models. What models? How do you construct them? Again, I'm all for this, but I don't think we get to assume this is all settled for natural languages.

If the point you wanted to make was "quit doing that, because you can do this instead," I'd endorse that!

I'm not clear on what you expect to achieve by posting it — Srap Tasmaner

I don't expect to achieve anything other than giving a simple starting point, since there had been confusion in the thread.

You're surely not arguing that someone's intuitions can be refuted by the definitions and axioms we've chosen — Srap Tasmaner

Of course not.

What models? — Srap Tasmaner

Whatever models one likes.

How do you construct them? — Srap Tasmaner

Most formally in the usual methods of mathematical logic and/or formal modal logic. Less formally, in whatever informal way one likes.

I don't think we get to assume this is all settled for natural languages. — Srap Tasmaner

Of course not.

It's not that simple. — Srap Tasmaner

It's simple that the poster is nuts to think that "Possibly P" implies "Not P".

If the point you wanted to make was "quit doing that, because you can do this instead," I'd endorse that! — Srap Tasmaner

That'll do.

The task at hand is choosing between different grammars. If a grammar leads to a confusion, such as

"Possibly P" implies "Not P" — TonesInDeepFreeze

...then best reject it. Quit doing that, and do this instead.

It is that simple.

...or snide comments about my snide comments...

"Possibly P" implies "Not P" — TonesInDeepFreeze

Just to be clear, I don't propose that.

Yes they can breed...surprised? Perhaps better to apply a prophylactic...

Of course.

You appear to be equivocating on the meaning of "means". We're using it in the sense of a definition, not in the sense of entailment. — Michael

Unless someone provides a definition, "meaning" is not being used in the sense of a definition. So in common usage, which is what we seemed to be talking about with the example "the book is in my room", people do not provide definitions for the words they use, therefore the meaning of those words is not "meaning" in the sense of a definition. It is meaning in the sense of how they are used.

The T-schema doesn't say that asserting the proposition "the book is in my room" entails that the book is in my room. It only says that the book being in my room is the truth-condition of the proposition "the book is in my room", and according to Davidson the definition of a proposition is given by its truth-conditions. — Michael

Yes, but don't you see that when someone says "the book is in my room", this can only imply that the book is in that room, if we add the premise that the statement is true (in that sense of "true"). And, the statement only "means" (as in what is meant by the speaker) that the book is in my room, if the person speaks truthfully (honestly). So if you are not talking about what is implied logically through definition, nor what is meant by the language in its use, what other sense of "meaning" are you appealing to?

What you mean by "possible" is that the future holds more than one possibility; that there are several possible worlds and one of those becomes the actual world. — Luke

What was meant in the quoted passage, was that "possible worlds" referred to logical possibilities for what is the case. If we do not know precisely what is the case in a specific situation, we allow for many different possibilities. So it's not really about future possibilities here, but logical possibilities. That was the reason for the use of "possible worlds". Srap introduced that, to try and get a handle on the meaning of "possible".

If there is more than one possible world at t0 and one of those becomes the actual world at t1, then the actual world at t1 is still one of those possible worlds that was at t0; one of the possibilities that could have been. — Luke

The particular possibilities at 10, are no longer possibilities at 11. That's the nature of passing time, things change as time passes

If you had many possibilities prior to the act, then the one that became actual remains one of those possibilities. — Luke

No, none of them are possibilities after the act, not even the one you chose, that's the point. You can't have your cake and eat it too. Once you eat the cake, eating it is no longer a possibility.

Ok. What is communion as you’re using the word? — Mww

Communion would be all forms of participating in and sharing of thoughts, and activities, like communication and working together. What I explained is that logic has a foundation in imagination and is supported by usefulness. So it is, in its foundation, a private activity, like strategy. Since usefulness is defined relative to particular goals, which are personal, and this is what supports these rules, the rules of logic are fundamentally inconsistent with the rules of communion (human interaction), which are moral rules.

What was meant in the quoted passage, was that "possible worlds" referred to logical possibilities for what is the case. If we do not know precisely what is the case in a specific situation, we allow for many different possibilities. — Metaphysician Undercover

Those different possibilities are regarding a future situation, not the current situation. We do not know whether there will be a sea battle tomorrow, and it is possible today that there will be a sea battle tomorrow or there won't be a sea battle tomorrow. But. come tomorrow, there will be no other possibilities regarding the sea battle except for the one that becomes the actual situation.

The particular possibilities at 10, are no longer possibilities at 11. That's the nature of passing time, things change as time passes — Metaphysician Undercover

Exactly. The particular possibilities at t0 are possibilities regarding the future situation at t1; they are not possibilities regarding the present situation at t0. There are no other possibilities (for t0) at t0 other than the actual situation.

No, none of them are possibilities after the act, not even the one you chose, that's the point. You can't have your cake and eat it too. Once you eat the cake, eating it is no longer a possibility. — Metaphysician Undercover

You either had other possibilities (prior to eating the cake) at t0 besides eating the cake at t1, or you didn't have other possibilities at t0 besides eating the cake at t1. If you had other possibilities at t0, then eating the cake at t1 was possible. If you didn't have other possibilities at t0, then eating the cake at t1 was necessary. I don't agree that eating the cake at t1 was necessary if you had other possibilities at t0. This a misuse of the term "necessary".

Those different possibilities are regarding a future situation, not the current situation. — Luke

That's really not how Srap was using "possible worlds". We were talking about hypotheticals, counterfactuals, and whether or not it is raining out. Here is where Srap Used "possible worlds" in an example.

For example, the hypothetical assumption “Suppose I have lost my copy of Lewis 1973” picks out a set of possible worlds at which I have indeed lost my copy of Lewis 1973. If I determine that in any such world (or only in nearby worlds, or in sufficiently similar worlds, etc., whatever the appropriate restriction is) I would be a miserable cuss, and I would prefer not to be, then I can discharge the assumption by concluding, for example, “If I were to lose my copy of Lewis 1973, I would have to replace it.” — Srap Tasmaner

We do not know whether there will be a sea battle tomorrow, and it is possible today that there will be a sea battle tomorrow or there won't be a sea battle tomorrow. But. come tomorrow, there will be no other possibilities regarding the sea battle except for the one that becomes the actual situation. — Luke

I will follow this example though, if you like.

Exactly. The particular possibilities at t0 are possibilities regarding the future situation at t1; they are not possibilities regarding the present situation at t0. There are no other possibilities (for t0) at t0 other than the actual situation. — Luke

No, the possibilities are the ones which are present, at the current time. Yes, they are derived from our view toward the future, but they are stated as the possibilities which are present. They are an aspect of one's knowledge. So, "that there will be a sea battle tomorrow", is a possibiltiy present right now in my mind, if I believe this. That's why the action involved in this possibility which exists now, is stated as "tomorrow", because the possibility exists prior in time to the act, i.e. today. At the current time, there are many possibilities for the future, within my mind, and yours too I assume.

ou either had other possibilities (prior to eating the cake) at t0 besides eating the cake at t1, or you didn't have other possibilities at t0 besides eating the cake at t1. If you had other possibilities at t0, then eating the cake at t1 was possible. If you didn't have other possibilities at t0, then eating the cake at t1 was necessary. I don't agree that eating the cake at t1 was necessary if you had other possibilities at t0. This a misuse of the term "necessary". — Luke

I'm saying that after the act is carried out it is no longer a possibility in my mind, it is necessary, as what has been carried out, what is actual. Example: Yesterday there was a sea battle. I believe that this actually occurred, therefore there are no other possibilities in my mind. In my mind, by my knowledge, it is a fact, something necessary, impossible to be otherwise, not a possibility.

Seems to me that we're perfectly capable of understanding what sorts of thoughts are exclusive to humans and what sorts are not.
— creativesoul

You seem to think I have disagreed with this
— Janus

That's how to avoid anthropomorphism. — creativesoul

Do you not understand that understanding what sorts of thoughts are exclusive to humans and what sorts are not is how to avoid anthropomorphism?

You are talking with a poster not capable of making sense. — TonesInDeepFreeze

What that poster says makes sense. But some who are taught that something contrary to what the poster says makes sense, refuse to allow the possibility that what the poster says also makes sense. Those are the closed minded.

The sad thing is that your clear explanation will not correct the confusion here. That confusion is wilful. — Banno

See, even Banno recognizes that it makes sense, to the poster at least, as it is said to be willful. It is the others, who see things differently from the poster, and see them as clear, who are closed minded to the views of others. The poster in question sees the ambiguity and therefore does not see the things as clear. Yet ambiguity makes sense to that poster because ambiguity is as much a part of reality as the people who see ambiguous propositions as something clear are a part of reality.

"I'm the only one here who is right. Everyone else is wrong. I have an open mind. They don't". Thus spake the crank.

The particular possibilities at t0 are possibilities regarding the future situation at t1; they are not possibilities regarding the present situation at t0. There are no other possibilities (for t0) at t0 other than the actual situation.
— Luke

No, the possibilities are the ones which are present, at the current time. Yes, they are derived from our view toward the future, but they are stated as the possibilities which are present. They are an aspect of one's knowledge. So, "that there will be a sea battle tomorrow", is a possibiltiy present right now in my mind, if I believe this. — Metaphysician Undercover

As I said, the possibilities which are present, at the current time (at t0), are possibilities regarding the future situation (at t1). You acknowledge this with the example about today's possibility of tomorrow's sea battle - the possibilities are regarding the future situation, not the present situation. The possibilities are not about themselves; they are about the future potential sea battle.

I'm saying that after the act is carried out it is no longer a possibility in my mind, it is necessary, as what has been carried out, what is actual. — Metaphysician Undercover

And I am saying that if there were other genuine possibilities prior to the act being carried out, then it was not necessary, because one of those alternative possibilities could actually have been carried out instead. It is only if there had been no other genuine possibilities that could actually have been carried out instead, that the act being carried out would be necessary.

Your assertion that all actual situations are necessary negates that there are ever any genuinely alternative possibilities, and thus precludes free will.

It's simple that the poster is nuts to think that "Possibly P" implies "Not P". — TonesInDeepFreeze

Certainly it is not the case that ◇P ⊃ ~P.

But it is also the case that "It might be in the car" implicates (but does not entail) "I don't know for sure where it is" — and, to connect the dots, if I don't know where it is I am not in a position to assert something like "It is in the car," some simple declarative statement P, but only a weaker ◇P — and it is a locution people resort to precisely to avoid admitting that they know exactly where it is and how it got there.

For all that, I will still say that P ⊃ ◇P is a solid axiom (or however you arrive at it) that captures some of what we have in mind when we reason about what's possible.

Side note: I recently had occasion to read this page about the Wason selection task, which I had forgotten all about. It seems often to have been counted as evidence against the everyday conception of logical consequence being captured by the material conditional, but there's further work that makes this less clear, and more interestingly there's this report:

A psychologist, not very well disposed toward logic, once confessed to me that despite all problems in short-term inferences like the Wason Card Task, there was also the undeniable fact that he had never met an experimental subject who did not understand the logical solution when it was explained to him, and then agreed that it was correct. — same wiki page

Now that's really curious, and leaves considerable room for the likes of logic, set theory, arithmetic, geometry, modal logic, and the rest to continue in the effort to axiomatize our intuitions, with the expectation that, even though ordinary folks don't think in precisely these terms, when explained to them, such systems will make sense and they will agree this is a good way to go about things.

This, @Banno, is how I would justify what we're up to. If this counts as "choosing a grammar that doesn't lead to confusion," okay. But I'm never going to put it that way because I think that way of putting it leads to confusion.

I have no idea what you are trying to say. — Janus

Earlier I asked how you/we avoided anthropomorphism. You basically questioned whether or not we could. I claimed that we can in both principle and practice. You then said you did not share my optimism. Then...

I expressed that we understand the difference between thought and belief that is exclusive to humans and thought and belief that is not.

You then acted as if you had not disagreed with that, but you had, evidently unbeknownst to yourself, because you disagreed that we could avoid anthropomorphism. The problem(for you) is that if we can understand that much, then we can avoid anthropomorphism, for that is the key for doing so. That's how. If you agree with that then it ought be easy enough for you to realize that we can avoid anthropomorphism in both principle and practice. That's one of the things I am getting at.

Secondly, you invoked the notions of 'language capable beings' and 'linguistically mediated thoughts' in order to make a claim that you later judged as trivial/uninformative. You were arguing with yourself, because I never invoked those notions. In fact, neither can draw and maintain the distinction necessary to avoid anthropomorphism because some animals have language.

I have no idea what you are trying to say. — Janus

I suppose I could make the broader point now. Perhaps the reason you do not share my optimism regarding avoiding anthropomorphism is because you have difficulty yourself in understanding what sorts of thought and belief are exclusive to humans and what sorts are not. The notions of 'language capable beings' and 'linguistically mediated thought' only discriminate between language users and language less creatures, so, they are unhelpful for avoiding misattributing some of our thought and belief to other language using creatures. We see this often in nature shows.

Yes, for any rational being it is not plausible that for all q we have Pq -> ~q.

But — Srap Tasmaner

And that 'but' is not going refute that it is not the case that for all q we have Pq -> ~q.

it is also the case that "It might be in the car" implicates (but does not entail) "I don't know for sure where it is" — Srap Tasmaner

No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the car". If I was looking for the book, then I would not appreciate my friend being coy that way, but he would not be logically incorrect.

Or, let 'Kq' stand for 'q is known'. Let 'L' stand for '~K~q'.

For any rational being it is not plausible that for all q we have Lq -> ~q.

Or, let 'Bq' stand for 'q is believed'. Let 'Cq' stand for '~B~q'.

For any rational being it is not plausible that for all q we have Cq -> ~q.

Anyway, the point stands, only a nutcase says that "Possibly the book is in the car" implies that the book is not in the car.

Let's make it a life and death situation:

A young boy is lost in treacherous terrain. The county sheriff's search and rescue expert tells the parents, "Possibly he's in the canyon. So he's not in the canyon." I don't think there is any parent in the world who would say, "Okay, I understand your logic perfectly. Let's not waste time looking in the canyon."

/

Unrelated but poignant is Sartre's "The Wall". SPOILER ALERT. In the Spanish Civil war, Pablo is a prisoner of the fascists. His imprisoners will execute him if he doesn't give up the hiding place of his comrade Ramon. Pablo believes Ramon is not hiding in the nearby graveyard. As a joke on his imprisoners, Pablo lies to them that Ramon is hiding in the graveyard. But Ramon is hiding in the graveyard. And later Pablo learns that Ramon was caught in the graveyard and killed.

If I candidly assert an indicative sentence, I imply that the content of my belief is represented by that sentence — Srap Tasmaner

Yes, you imply it. But that asserting a sentence implies something isn't that that sentence (or assertion) means that thing. The sentence (even as an assertion) "I am going to vote in the next election, and I believe that Joe Biden is the best candidate" implies that I am going to vote for Joe Biden in the next election, but that's not what the sentence means.

This is where I think you're conflating different senses of "meaning" or "expression". I can assert something that expresses my anger or my love or my disapproval, but that's not the same thing as the assertion meaning "I am angry" or "I love you" or "I disapprove of this".

You can't assert that the book is in your room, or that you believe the book is in your room, and that it is not true that the book is in your room. — Srap Tasmaner

Sure I can: I believe that the book is in my room but the book isn't in my room. I can assert anything I like.

But I don't really see the relevance of this. If we accept that we are fallible then what left is there to discuss? We accept the distinction between truth and belief; between the book being in my room and believing that the book is in my room.

@Srap Tasmaner

Consider this exchange:

John: The book is in my room
Jane: What you say is wrong because the book is not in your room

Should this be interpreted as the below?

John: I believe that the book is in my room
Jane: I believe that what you say is wrong because the book is not in your room

So Jane believes that John doesn't believe that the book is in his room because the book isn't in his room? That doesn't seem right.

Even if John's assertion that the book is in his room implies that he believes that the book is in his room, his assertion being true or false has nothing to do with what he believes (or what Jane believes), and everything to do with whether or not the book is in his room.

This level of analysis doesn't work. You start from an assumption that the meaning of a proposition can be questioned "X exists", but then you analyse the felicity of that meaning by assuming that another proposition " X is wrong" stands with a priori clarity.

If the meaning of "X exists" is in question, then the question cannot be resolved by assuming the meaning of "X is wrong" is not similarly in question.

As I said, the possibilities which are present, at the current time (at t0), are possibilities regarding the future situation (at t1). You acknowledge this with the example about today's possibility of tomorrow's sea battle - the possibilities are regarding the future situation, not the present situation. The possibilities are not about themselves; they are about the future potential sea battle. — Luke

Yes, those possibilities are how we think "about" the future, just like we can say something "about" the future.

And I am saying that if there were other genuine possibilities prior to the act being carried out, then it was not necessary, because one of those alternative possibilities could actually have been carried out instead. It is only if there had been no other genuine possibilities that could actually have been carried out instead, that the act being carried out would be necessary. — Luke

Sure, but at this time, after the act, one of the other "genuine possibilities" (whatever that means) was not actually carried out instead. And, it no longer is a possibility because the act chosen was carried out instead. And, this cannot be changed, there is no possibility of going back in time to alter it, therefore it is necessary.

You do not seem to be properly accounting for the temporal perspective. Prior to the act it is a possibility which can be chosen. Posterior to the act it is an actuality which has already occurred, and therefore necessary rather than possible. This is obvious in our day to day experience. We know that we cannot change the past so we describe it as what has actually occurred, and we also believe that we can describe the future as possibilities. To deny this difference is to deny the reality of time.

So, prior to the act we describe it as a possibility. The possibility is "about the future", as you say. After the act we describe it as an actuality, something which has actually occurred. It is now a fact, not a possibility, and is therefore treated as a necessity in the logical proceeding. Therefore the same act has a different type of description depending on one's temporal perspective, before or after it.

We can apply this to the act of counting the coins in the jar. Prior to counting the coins, the number of coins in the jar is described as a possibility. Posterior to counting the coins, the number of coins in the jar is described as an actuality. This is a true representation of what we believe about the number of coins in the jar. Prior to counting we do not know the number, and we understand it as a possibility. Posterior to counting, we know the number and understand it as an actuality.

Your assertion that all actual situations are necessary negates that there are ever any genuinely alternative possibilities, and thus precludes free will. — Luke

Obviously this is not true. It is a simple aspect of our experience, as human beings, that we view events of the past differently from events of the future. So the very same event is spoken about differently when it is in the future than when it is in the past. This is the result of the difference in temporal perspective. Clearly understanding this aspect of our experience does not negate genuine possibilities. It just provides a healthy respect for the reality of time and its role in relation to "genuine possibilities".

No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the car". If I was looking for the book, then I would not appreciate my friend being coy that way, but he would not be logically incorrect. — TonesInDeepFreeze

Of course you would not appreciate your friend behaving like this, because unless you are engaged in some sort of guessing game, it is dishonesty. And, your claim that it is "literally honest and correct" is very much refuted by your own admission that you would not appreciate it, even though you would assert that the friend is not logically incorrect.

What is at issue here is the inconsistency between what is logically correct, and what is morally correct, honest. Since you accept that this type of behaviour, which is asserted to be logically correct, is in general not appreciated (because it is clearly dishonest I would say), you seem to recognize this inconsistency.

John: The book is in my room — Michael

Our upcoming discourse on this topic will be safely and perpetually interpretable as pointing all appropriate paraphrases of "the book" and of "is in my room" at the same region of space-time.

Jane: What you say is wrong because the book is not in your room — Michael

I predict that our discourse will either reject that basis for interpretation or become far less agreeable.

his assertion being true or false has nothing to do with what he believes (or what Jane believes), and everything to do with whether or not the book is in his room. — Michael

But it has everything to do with agreement about the reference of words in the discourse, as well as the things thereby referred to. No truth without language.

Communion would be (....) communication and working together. — Metaphysician Undercover

Oh. Social anthropology. Not interested.

(...) logic (...) is (...) in its foundation, a private activity, like strategy. — Metaphysician Undercover

Yes. Sort of.

usefulness is defined relative to particular goals, which are personal, and this is what supports these rules — Metaphysician Undercover

Is it the same to say logical rules are useful in support of the attainment of personal goals?

the rules of logic are fundamentally inconsistent with the rules of communion (human interaction), which are moral rules. — Metaphysician Undercover

If the most personal one can be, is demonstrated by his moral convictions, and if logical rules are the ground for particular personal goals, then it follows that logical rules are not so much merely consistent with, as in fact necessary for, the dispensation of him toward his moral activities.

All rules developed and used by us, in private, rational decision-making, re: judgment, without exception, are reducible to logical rules.

it is also the case that "It might be in the car" implicates (but does not entail) "I don't know for sure where it is"
— Srap Tasmaner

No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the car". If I was looking for the book, then I would not appreciate my friend being coy that way, but he would not be logically incorrect. — TonesInDeepFreeze

Indeed. That would be why I said "does not entail." This being coy, it's a violation of Grice's maxims — quantity I think, because you are sharing less information than you have.

Look, I'm only talking about this because I want to wall off these sorts of considerations: it is a fact that if you know that something is the case, then there are circumstances in which saying only that it is possible is misleading. I'm pointing at that phenomenon so that I can block it from undermining our claim that actuality entails possibility. If it's only a conversational implicature, it has no bearing on the relevant entailments.

If I candidly assert an indicative sentence, I imply that the content of my belief is represented by that sentence
— Srap Tasmaner

Yes, you imply it. But that asserting a sentence implies something isn't that that sentence (or assertion) means that thing. [ ... ]

This is where I think you're conflating different senses of "meaning" or "expression". — Michael

Except for the part where I'm clearly not, because I've been at pains to say that we're only talking about implication not literal meaning. It's right there. What what you say means is one thing, sentence meaning, and what you mean by it is something else, speaker's meaning. I'm not conflating them at all; I am acknowledging that there is more to our utterances than the literal meaning of what we say so that it doesn't interfere with the logical analysis.

You can't assert that the book is in your room, or that you believe the book is in your room, and that it is not true that the book is in your room.
— Srap Tasmaner

Sure I can: I believe that the book is in my room but the book isn't in my room. I can assert anything I like. — Michael

Sorry, yes, I should have said "without falling into Moore's paradox," and so on.

Both @Isaac and @Metaphysician Undercover are going to consistently deny that there is anything at all to your asserting P than that you believe (using various accounts and locutions for this) that P, in every instance. Notably, that includes any hypothetical. If you say "Suppose the book is in my room, but I believe it is not ..." they will ask who holds the belief that it is in your room, whose judgment that is, and so on. translates claims of fact into predictions about the agreeability of our discourse. (Is that Lewis's scorekeeping, or Goodman's worldmaking?)

We proceed on the assumption that we can analyze "naked" propositions with no speaker; they do not. Every proposition is an utterance of someone, for a purpose, even if that someone is only virtual or something. Think of it as a sort of Nietzschean perspectivism. The kicker, of course, is that the "naked" view is linguistically indefensible. You have to invoke a generalized competent speaker of English. The right question is whether you can "factor out" linguistic competence through your analysis of semantic content...

We don't have to take this position into account; we can just go about our business. But if you want to engage with the loyal opposition here, you have to find some way of making the point that is not simply question-begging. I'm working on it. ;)

I've been at pains to say that we're only talking about implication not literal meaning. — Srap Tasmaner

Then I'm not sure what relevance it has to the discussion. Are you saying that the truth of an assertion is concerned with its implication and not its literal meaning? Such that "I am going to vote in the next election, and I believe that Joe Biden is the best candidate" is false if I'm not going to vote for Joe Biden in the next election?

Also, I don't think anyone, including me, has given an adequate response to what I take to be @Metaphysician Undercover's position, that alethic modality reduces — or, rather, should reduce — entirely to temporal modality. I don't think that position is prima facie wrong.

I've been at pains to say that we're only talking about implication not literal meaning.
— Srap Tasmaner

Then I'm not sure what relevance it has to the discussion. — Michael

Consider:

But we’re not just interested in what people mean by what they say.
— Srap Tasmaner

Why not? If "I'm not certain" means "I don't know" then "I know but I'm not certain" means "I know but I don't know" which is, of course, a contradiction. So it doesn't make sense to say "I know but I'm not certain".

And if it doesn't make sense to say "I know but I'm not certain" then it shouldn't make sense to say "I can know without being certain". — Michael

Here you are, trying to decide whether an agent S can simultaneously be in a state of knowledge and in a state of uncertainty, but you choose to test this possibility by figuring out whether it would "make sense" for an individual to say, of themselves, that they are in both these states.

Not a great plan.

The case is perfectly clear when it's a third party saying it: you and a friend are watching your daughter at a spelling bee, she's floundering, looking overwhelmed; you can straightforwardly say, "She knows this one — we reviewed it last night and she had it cold — she's just flustered and second-guessing herself." There is no general problem attributing both knowledge and uncertainty to someone; there seems to be some weirdness when that someone is yourself. If I talk about implicatures and such, it is only to block mistaken reliance on "what it makes sense to say."