If p is necessarily true it is not possible that p could have been false. If p is true is it is not possible that p is false, but it is possible that p could have been false. — Janus

I think you should read up on modal logic. Here is how possibility and necessity are actually defined:

□p ≔ ¬◇¬p
◇p ≔ ¬□¬p

I don't think you've answered the question. — Janus

I did. That it is necessary that p is true is that it is not possible that p is false.

But what does "necessarily true" mean? — Janus

Necessity and possibility are defined by each other:

□p (necessarily p) is equivalent to ¬◇¬p ("not possible that not-p")
◇p (possibly p) is equivalent to ¬□¬p ("not necessarily not-p")

Then just look to the ordinary understanding of the words "possibly" and "necessarily" to inject some actual substance into the meaning.

I think it is "could have been wrong" not "could be wrong" the latter is a contradiction. — Janus

It's not a contradiction.

p ⊬ □p
¬□p
∴ p → ◇¬p

p being true does not entail that p is necessarily true
p is not necessarily true
Therefore, if p is true then p is possibly false

This is a valid argument.

The 'possibility' of something is a measure of our uncertainty about it, so once we know x is the case, the possibility P(x)=1 which is the same as just x. — Isaac

So you reject fallibilism and claim that knowledge requires certainty?

Remember also that "I am possibly wrong" can also imply "I am possibly right".

The problem here is with using modal logic terms together with knowledge — Isaac

I'm not even talking about knowledge at this point.

I'm just talking about claims like "I believe that you are American but it's possible that I'm wrong". My claim is true if my belief is right and my claim is true if my belief is wrong.

I don't have any knowledge of your nationality whatsoever.

You don't seem to understand what "possibly" means.

Because of the law of excluded middle, this is true:

1. ◇p ∧ (¬p ⊻ p)
It's possible that I'm wrong and I'm either right or wrong.

This then means that for any given p, one of these is true:

2. ◇p ∧ p
It's possible that I'm wrong and I'm wrong

3. ◇p ∧ ¬p
It's possible that I'm wrong and I'm right

If you say that 3 is false for all p then you are saying that 2 is true for all p. If 2 is true for all p then:

4. ◇p → p

I don't see how. — Isaac

Because you say that ◇p ∧ ¬p can never be true. If you say that ◇p ∧ ¬p can never be true then you say that ◇p ∧ p is always true. If ◇p ∧ p is always true then ◇p → p.

2 and 4 are false at any given time. — Isaac

Then you agree with this:

1. ◇p → p
2. If it is possible that I am wrong then I am wrong

Are you saying it's possible to be x at the same time as not being x? — Isaac

These are two different claims:

1. ◇(¬p ∧ p)
2. ¬p ∧ ◇p

Translated:

3. It it is possible that I am both not wrong and wrong
4. I am not wrong and it is possible that I am wrong

1 and 3 are false, 2 and 4 are true.

Returning back to this to explain it:

5. ◇p → p
6. If it is possible that I am wrong then I am wrong

You seem to disagree with 5 and 6. If you disagree with 5 and 6 then you accept that there is some situation where ◇p is true and p is false. In other words, you accept that there is some situation where 2 and 4 are true.

If I'm not a cat, I can't possibly be a cat. I could have been, but I cannot actually be at the same time as I'm not. — Isaac

You conflate "it is possible that I am wrong" and "I am wrong". These two mean different things:

1. ◇p (it is possible that I am wrong)
2. p (I am wrong)

And so the two similar, but different, claims are:

3. ¬p ∧ ◇p (I am not wrong and it is possible that I am wrong)
4. ¬p ∧ p (I am not wrong and I am wrong)

When you say "but I cannot actually be at the same time" you are referring to 4 being false, not 3. 3 is true if ¬p is not necessarily true.

Consider the conclusion.

◇p → p

If it is possible that I am wrong then I am wrong

Do you believe that this is false?

It doesn't seem to matter what we put into that syllogism (right term?), it seems to come out wrong. — Isaac

Because premises of that form are almost always false. You cannot go from "not p" to "not possibly p".

The only time the premise is true is when p is necessarily true.

https://truthsocial.com/@realDonaldTrump/108828041518355960

Wow! In the raid by the FBI of Mar-a-Lago, they stole my three Passports (one expired), along with everything else. This is an assault on a political opponent at a level never seen before in our Country. Third World!

They took his passports?

I understand "I can be wrong" as "it is possible that I am wrong". So:

p ≔ I am wrong

¬p → ¬◇p
∴ ◇p → p

If I am not wrong then it is not possible that I am wrong
Therefore, if it is possible that I am wrong then I am wrong

I think the conclusion is false, therefore I think the premise is false.

Which part do you disagree with? Do you think that the conclusion is true or do you think that the premise is true even though the conclusion is false?

Draw that out for me...? — Isaac

p ≔ I am wrong
q ≔ I can be wrong

¬p → ¬q
∴ q → p

If I'm not wrong then I can't be wrong
Therefore, if I can be wrong then I am wrong

I think the conclusion is false, therefore I think the premise is false.

Again, it's just not clear how you're getting here. The "...I could be wrong" cannot be true if the proposition is it's referring to is true. — Isaac

Are you saying that "I believe this but I could be wrong" is only true if I am wrong (as per the above conclusion)? Then what's the difference between "I am wrong" and "I could be wrong"?

When I say "I believe that you are American but I could be wrong" I'm not saying "I believe that you are American but I am wrong" and I'm not just saying "I believe that you are American but in some other possible world I am wrong".

"I believe that you are American but I could be wrong" is true even if you are in fact an American.

There seems to be this assumption made by some that if I'm not wrong then I can't be wrong, but then via modus tollens it then follows that if I can be wrong then I am wrong. This obviously isn't right.

Salman Rushdie: Iran blames writer and supporters for stabbing

But on Monday, Iran's foreign ministry spokesperson Nasser Kanaani - giving the country's first official reaction - said Tehran "categorically" denied any link, adding "no-one has the right to accuse the Islamic Republic of Iran".

However, he said freedom of speech did not justify Mr Rushdie insulting religion in his writing.

"In this attack, we do not consider anyone other than Salman Rushdie and his supporters worthy of blame and even condemnation," the spokesman said during his weekly press conference in Tehran.

"By insulting the sacred matters of Islam and crossing the red lines of more than 1.5 billion Muslims and all followers of the divine religions, Salman Rushdie has exposed himself to the anger and rage of the people."

So they say the attack is justified.

Can you give a real-life example or does this have to firmly stay in propositional logic?
Say about your own attributes for example. I know I am male, could I be wrong? I know I am caucasian, could I be wrong? etc. — universeness

It's better understood with belief.

1. I believe that you are a mathematician, but I could be wrong.

Even if my belief is true it is still the case that it could be false. There is a difference between "I am wrong" and "I could be wrong". I could be wrong even if I'm not wrong.

If 1 is true of a true belief then it's also true of knowledge because knowledge just is true belief (with sufficient justification).

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.

Not about things you know - they are true. — Banno

Some of the things I believe but don't know are true as well. When I say "I believe p but I could be wrong" I'm not saying "I believe p but I am wrong". And when I say "I know p but I could be wrong" I'm not saying "I know p but I am wrong".

"I could be wrong" can be true even if I'm not wrong. So that I'm not wrong if I know isn't that I can't be wrong if I know.

I think the mistake is in conflating modal logic with possible world semantics. You can have the former without the latter. I'm just using modal logic here.

It is possible that I am wrong about what is the case in the actual world. That seems to me to be the ordinary meaning of "I could be wrong".

A better would be something like "I believe that in the actual worlds, p, although in other possible worlds, ~p" — Banno

The literal translation of 4 is "I believe that this thing is true and it is possible that this thing is not true" which is just what I understand "I could be wrong" means.

Because, as above, when I say "I believe p but I could be wrong" I'm not saying "I believe p and in the actual world I'm right and in some other possible world I'm wrong". I'm saying "I believe p and in the actual world I could be wrong".

When I see a philosophical thread with the words Omniscient or God, I think "that's not philosophy". — Banno

I regret using that term now. Too many can't seem to get past it. That's why I offered this as an alternative.

But the actual world is a possible world...

So when you say that she might be 30 in the actual world, you are saying she might be 30 in some possible world... — Banno

That's why I said "I'm not just saying that."

The point is that when I say "I believe p but I could be wrong" I'm not saying "I believe p and in the actual world I'm right and in some other possible world I'm wrong". I'm saying "I believe p and in the actual world I could be wrong".

(2) is only true when the modality of 'possible' is alethic, or if we know that p fallibly. — Kuro

Yes, that's what I said here:

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. — Michael

Omniscience aside, if we're fallibilists then we could be wrong even if we have knowledge.

Well, yes, you are saying that in some possible world here age might not be 30. — Banno

I'm not just saying that. I'm saying that she might not be 30 in the actual world. 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.

2. I believe p but I could be wrong
But suppose also that in the actual world, p, but in other possible worlds, ~p; then we have

2. (In the actual world, p and Bp) ^ (in other possible worlds, ~p) — Banno

I don’t think that’s right because when I say “I believe she’s 30 years old but I might be wrong” I’m not saying that in some alternate world she might not be 30 years old, I’m saying that she might not be 30 years old in the actual world.

If it helps, think of it in the third person instead. John believes that p is true and it is possible that p is not true.

Good point, maybe I should have had it as if p then Kp and the conclusion as if p then Bp ∧ ◇¬p.

Or consider the simplified argument here.

Edit: I’ve edited that in.

10. ∃p: Bp ∧ ◇¬p (from 6, 8, and 9)
Which means you believe some propositions that are true, but are metaphysically contingent. Not really a problem. — Relativist

Do you not think this means “I believe p but it’s possible that I’m wrong”?

It seems to be paradox whether it's about omniscience or our everyday, limited knowledge.

I know that my name is Michael but it's possible that I'm wrong.

For those of you who can't seem to get past "omniscience", consider instead this simplified paradox of knowledge:

Kp ≔ x knows that p is true
Bp ≔ x believes that p is true

1. Kp ⊨ Bp (premise)
2. Kp (premise)
3. ¬□p (premise)
4. Bp ∧ ◇¬p (from 1, 2, and 3)

In ordinary language:

1. Knowing that something is true entails believing that this thing is true (premise)
2. I know that something is true (premise)
3. This thing is not necessarily true (premise)
4. I believe that this thing is true and it is possible that this thing is not true (from 1, 2, and 3)

The counterintuitive conclusion is that I could be wrong in believing that something is true even though I know that this thing is true.

Prima facie, this seems ridiculous. I know Crowley's religion , Thelema, but I do not believe it. — jgill

Sorry, I wasn’t precise. If I know that p is true then I believe that p is true.

Not when those same agencies are engaged in reckless or criminal behavior. — NOS4A2

Of course, everyone except Trump is reckless and criminal.

Why is it against the law to posses declassified documents? — NOS4A2

Because Congress passed such a law which was then signed by the President of the time?

See here

it is without precedent — NOS4A2

Yes. There's never been a President quite as criminal as Trump (although maybe Nixon).

None of this has been proven and all of it is without precedent. None of us have seen the affidavit. So your claim he broke the law is without merit, and given a long and poor history of such claims, just another conspiracy in my books. — NOS4A2

Possessing those documents is against the law. So are you saying that he didn't possess them? Then what were these non-existent things that he supposedly declassified?

And on a side note, that he would declassify documents just to take them home shows how incompetent he was and how dangerous it was for him to be President.

Can presidents declassify matters directly?
Yes, because it is ultimately their constitutional authority.
…

Do presidents have to obey the usual procedures?
There is no Supreme Court precedent definitively answering that question. — NOS4A2

That's about procedures. Some people say that a President just has to say "it's declassified", others say that it actually has to go through a process where the classification markings are changed and the relevant departments are made aware of this.

Such information is called “restricted data.” Legally, it is not the same thing as being “classified” under the executive order — NOS4A2

So you want to argue over semantics? Regardless of what word you use, Trump broke the law by possessing the documents and by not returning them when subpoenaed. That's why they raided his home. It wasn't a political hit job as per your conspiracy theory.

Tell me if I am getting anywhere with: — universeness

1. Knowledge entails belief. In other words, if I know p then I believe p.
2. For everything that is the case, this hypothetical person knows that it is the case. In other words, our hypothetical person is omniscient.
3. At least one thing that is the case is not necessarily the case. In other words, it is possibly not the case.
4. For at least one thing that is the case, this hypothetical person believes that it is the case and it is possibly not the case. In other words, he could be wrong.

The counterintuitive conclusion is that an omniscient being could be wrong about something.