Modal logic can be used in epistemic terms as well, where ◻ means "certain" and ◇ means "not certainly not".

And also from close to the start of this discussion:

I suppose the latter is the implication of fallibilism. If knowledge does not require certainty then I can know everything even if I am not certain about anything. In this case I have fallible omniscience.

And I think certainty is only possible if the truth is necessary, so infallible omniscience requires that all truths are necessary.

I believe this but I might be wrong — Michael

as just saying that one is not certain of one's beliefs. — Banno

That's exactly what I'm saying as I made clear here:

To avoid the conclusion you must be an infallibilist and claim that knowledge requires certainty. In which case if I am certain that aliens exist then "I might be wrong" is false, and so I can't have knowledge that might be wrong.

I think a mistake that some fallibilists here are making is that they switch to infallibilism. They say that we don't require certainty to have knowledge but then imply that if we have knowledge then we're certain.

I think that's the converse of what I was at least trying to say. — Srap Tasmaner

Yes, and I think it's false, and so I think your premise is false.

When I say "I believe this but I might be wrong" I'm not saying, in a roundabout way, "I believe this but I am wrong". That I might be wrong has nothing to do with whether or not I am wrong. I'm just admitting to the possibility of being wrong (and not in Banno's "I'm actually right, but there's a possible world where I'm wrong" sense but in the "I might actually be wrong" sense). ◇¬p does not entail ¬p.

I think what's happening is that you're misinterpreting "it's possible that I have a true belief that might be wrong" as something like ◇(p ∧ Bp ∧ ¬p), but this symbolism actually say "it's possible that I have a true belief that is wrong" and is, of course, false. You should be interpreting it as "◇(p ∧ Bp ∧ ◇¬p)" which is true if ¬□p.

Again, these two are true:

1. I believe that aliens exist
2. I might be wrong

One of these is true:

3. Aliens exist
4. Aliens do not exist — Michael

These premises are not independent. The truth-value of (2) depends on which of (3) and (4) is true. If aliens exist, you cannot be wrong to think they do; if they don't, you cannot be wrong to think they don't. — Srap Tasmaner

So if I might be wrong then I am wrong?

Continuing on from the above, what is the difference between a true belief and knowledge? If we're fallibilists and agree with the JTB definition of knowledge then knowledge is justified true belief, so let's amend the above:

These two are true:

1. I believe with justification that aliens exist
2. I might be wrong

One of these is true:

3. Aliens exist
4. Aliens do not exist

Therefore, either these 3 are true:

1. I believe with justification that aliens exist
2. I might be wrong
3. Aliens exist

Or these 3 are true:

1. I believe with justification that aliens exist
2. I might be wrong
4. Aliens do not exist

If the first set is true then I have knowledge that might be wrong.

To avoid the conclusion you must be an infallibilist and claim that knowledge requires certainty. In which case if I am certain that aliens exist then "I might be wrong" is false, and so I can't have knowledge that might be wrong.

I think a mistake that some fallibilists here are making is that they switch to infallibilism. They say that we don't require certainty to have knowledge but then imply that if we have knowledge then we're certain.

I'm not saying that if aliens exist then I have a true belief and am wrong. I'm saying that if aliens exist then I have a true belief and I might be wrong.

Again, these two are true:

1. I believe that aliens exist
2. I might be wrong

One of these is true:

3. Aliens exist
4. Aliens do not exist

Therefore, either these 3 are true:

1. I believe that aliens exist
2. I might be wrong
3. Aliens exist

Or these 3 are true:

1. I believe that aliens exist
2. I might be wrong
4. Aliens do not exist

If the first set is true then I have a true belief that might be wrong.

Except you seem also to want to say that your true belief "might be" false. — Srap Tasmaner

Yes.

1. I believe that aliens exist
2. I might be wrong

These are both true.

Can I derive “aliens don’t exist” from 2? No, because aliens can still exist even though 2 is true. It then follows that if aliens exist then I have a true belief and I might be wrong.

To deny the conclusion you must argue that you can derive “aliens don’t exist” from the truth of 2. You must argue that if I might be wrong then I am wrong.

I don’t understand what you’re asking. I’m simply saying that I believe that aliens exist but I might actually be wrong. Do you agree?

If that's a way of saying, I don't know which sort of world I'm in, sure. — Srap Tasmaner

So returning to my original wording, my claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.

So I might actually be wrong even if I have a true belief.

All the possible worlds are already there; the question for you, the epistemic question, is which one you're in. — Srap Tasmaner

Sure, so is the below true?

This world might be one of the ones in which aliens don't exist

Trump’s claim that FBI “stole” his three passports turns out to be “nothing like what Trump said”

"In executing search warrants, the FBI follows search and seizure procedures ordered by courts, then returns items that do not need to be retained for law enforcement purposes," an FBI spokesperson told NBC.

So exactly what I said. They take the boxes then check the contents and return what they need to.

This world might ... be one of the ones in which aliens don't exist, even if it is one of the ones in which aliens exist. — Srap Tasmaner

Yes, and do you accept that this is true?

To make it simpler to understand, if necessary:

1. This world might be one of the ones in which aliens don't exist

Is this true? If yes then does it entail that aliens don't exist? If no then it is true even if aliens exist

The problem here is that we still have subjunctives, because we're layering the epistemic issue on top of the, let's say, metaphysical one. — Srap Tasmaner

I'm not sure what's problematic about the sentence above. It seems straightforward to me?

I'm not talking about knowledge at this point, just belief.

1. I believe that aliens exist but I don't know that aliens exist.
2. I claim that I might actually be wrong.
3. My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.

Then why did they return the passports? Because they shouldn’t have taken them. — NOS4A2

Because they shouldn't keep them. This really is quite straightforward stuff.

Legal or not, it just goes to show their incompetence or corruption. They were there for classified documents and walked out with personal documents. Pretty basic stupidity — NOS4A2

It's not incompetence, corruption, or stupidity. The search warrant told them to take the box and so they take the box. They're carrying out proper procedure. Your rhetoric here is neither reasonable nor convincing.

No I think it was ironic and wrong to take Trump’s passports. — NOS4A2

If it's not an unconstitutional search warrant then they had the legal right (and so it isn't stealing) to take Trump's passports if they were contained within a box that contained documents marked as classified.

This really isn't difficult to understand.

The parenthesis “and all contents therein” is simply a way to weasel out of constitutional violations and other incompetent or corrupt moves, such as taking Trump’s passports. — NOS4A2

So you think the search warrant itself is unconstitutional. Well, Trump's legal team can try to appeal it if they want, not that it will do any good now.

You’re defending the FBI taking things they ought not to have. — NOS4A2

What they ought to have taken is what the search warrant told them to take. The search warrant told them to take "any containers/boxes (including any other contents) in which such documents are located". Therefore, they ought to have taken any containers/boxes (including any other contents) in which such documents are located. And if Trump's passports were in such a box then they ought to have taken Trump's passports.

Did they raid the house for Donald Trump’s passports? The answer is “no”. There is no need to weasel for their incompetence or corruption. — NOS4A2

Jesus, do you really think such poor reasoning is going to work on me? You're embarrassing yourself.

I’m not sure why you’re leaving out the first sentence, but passports aren’t “physical documents with classification markings”. — NOS4A2

Is your reading comprehension that bad?

"any containers/boxes (including any other contents) in which such documents are located"

This means that if a box contains a document that has classified markings then you take the box and everything in it. It doesn't say that you take out all the documents marked as classified and then leave the box.

The 4th amendment demands that law enforcement know what they’re taking before they take it. — NOS4A2

A judge signed off on the warrant that included the phrase "any containers/boxes (including any other contents) in which such documents are located". If you think the warrant itself is unconstitutional then I suppose Trump's legal team can appeal it. Although it's a little late for that now. Maybe they can at least get a moral victory.

It’s not reasonable to take people’s passports when you’re there to seize government classified documents. The FBI ought to know what they’re taking before they take it, and if they don’t, they are either incompetent or corrupt. — NOS4A2

They take what the search warrant tells them to take, which included "any containers/boxes (including any other contents) in which such documents are located, as well as any other containers/boxes that are collectively stored or found together with the aforementioned documents and containers/boxes."

You'd only be right if the passports were just sitting on the table out in the open.

The search warrant says:

a. Any physical documents with classification markings, along with any containers/boxes (including any other contents) in which such documents are located, as well as any other containers/boxes that are collectively stored or found together with the aforementioned documents and containers/boxes

So it seems reasonable to assume that Trump's passports were mixed in with documents marked as classified. And that after all the documents were properly examined, stuff that wasn't relevant was returned.

I don't see how that's irony?

@Banno

Incidentally your reasoning entails that everyone lies when they admit that they might be wrong. If they’re not wrong then they can’t be wrong (according to your reasoning). They believe that they’re not wrong. Therefore they believe that they can’t be wrong (if they accept your reasoning). When they admit that they might be wrong they’re saying something they believe to be false.

Not if it is a true belief. — Banno

1. I believe that aliens exist but I don't know that aliens exist.
2. I claim that I might actually be wrong.
3. My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.

Are you now saying that the third claim is false?

See the word "actually"? It sneaks in a misplaced modal quantifier. — Banno

I am using that word to account for what I explained here:

When we admit to the possibility of being wrong we're not saying "I'm actually right, but in some possible world I'm wrong". We're saying "I might actually be wrong." That's fallibilism

So what? — Banno

Exactly what I said above. I have a true belief and yet "I might actually be wrong" is true.

IF your belief is true in reality, it cannot be false, and so you could not in reality be wrong. — Banno

If my belief is true in reality, it isn't false, and so I am not wrong.

You're making the same mistake as others. "it isn't" doesn't mean the same thing as "it cannot". "I am not" doesn't mean the same thing as "I could not be".

Again, these three claims are true:

I believe that aliens exist but I don't know that aliens exist.
I claim that I might actually be wrong.
My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.

SO what's the problem? — Banno

I have a true belief and yet "I might actually be wrong" is true.

If you know, you cannot actually be wrong. — Banno

I'm not talking about knowledge at this point. I explicitly said that I don't know that aliens exist:

I believe that aliens exist but I don't know that aliens exist.
I claim that I might actually be wrong.
My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.

What? — Banno

What's the problem? I can't explain that any simpler than I already did.

I believe that aliens exist but I don't know that aliens exist. I claim that I might actually be wrong. My claim that I might actually be wrong is true even if aliens exist and I'm not wrong.

And the way to make this consistent is to observer that if you know something to be the case in reality, you cannot be wrongin reality; but there might be an alternate state of affairs in which you thought you knew, but you were wrong. — Banno

If it's true of a true belief then, if we're fallibilists, it's also true of knowledge.

But when you know something, you are not wrong. — Banno

My claim that I might actually be wrong is true even if I'm not wrong. If it's true of a true belief then, if we're fallibilists, it's also true of knowledge.

I think I was on the mark here:

I think the reason that this conclusion seems counterintuitive is that even if we claim to be fallibilists there is this intuitive sense that knowledge entails certainty. — Michael

See here.

When we admit to the possibility of being wrong we're not saying "I'm actually right, but in some possible world I'm wrong". We're saying "I might actually be wrong." That's fallibilism.

So I am entertaining possible worlds. I'm simply explaining that this is the incorrect translation of our claims.

You're not addressing what I'm saying.

Again, seems as the modals are being muddled. What we can conclude is that omniscience can know everything and yet things might have been other than they are; not that the omniscience might be wrong.

There's nothing more here. — Banno

When I say that I believe that you are Australian but that it's possible that I'm wrong I'm not just saying that there is some possible world where you're not Australian and I'm wrong. I'm saying that it's possible that you're not actually Australian and I am actually wrong.

And what I say is true even if I am not wrong.

If "aliens exist" is true, then "aliens exist" cannot be false — Janus

If "aliens exists" is true then "aliens exist" is not false.

"is not" does not mean "is not possibly". ¬p does not mean ¬◇p.

Again, see the valid modal logic:

p ⊬ □p
¬□p
∴ p → ◇¬p

Both of these are true:

1. "aliens exist" is possible true
2. "aliens exist" is possibly false

One of these is true:
3. "aliens exist" is true
4. "aliens exist" is false

Therefore, either these three are true:

1. "aliens exist" is possible true
2. "aliens exist" is possibly false
3. "aliens exist" is true

Or these three are true:

1. "aliens exist" is possible true
2. "aliens exist" is possibly false
4. "aliens exist" is false

I thought the very basis of modal logic is that contingent truths, which cannot be false (obviously) could have been false (which means could be false in other possible worlds). — Janus

No, it's just saying something like "aliens exist" is not necessarily true and not necessarily false, therefore it's possibly true and possibly false.

You're introducing temporal logic. Temporal logic isn't modal logic.