We then conclude that I could be wrong even if I know everything (and assuming that some p is not necessarily true): — Michael

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.

I believe jgill is a mathematician but is he the best mathematician that has ever existed in human history? — universeness

:rofl:

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: — Michael

Right, if "aliens exist" is true then "aliens exist" is not false, and it could not possibly be false without negating "aliens exist" being true. So. as long as "aliens exist" is true then, "aliens exist" could not possibly be false.

But, in any case "aliens exist" could have been false. I think it's easier to parse this stuff in plain English, and in accordance with common usage. If modal logic yields something contrary to common usage, then there must be something wrong with the modal logic.

if "aliens exist" is true then "aliens exist" is not false, and it could not possibly be false without negating "aliens exist" being true — Janus

Possible-worlds semantics makes this all clearer:

• "Aliens exist" means [ Aliens exist in this world ]
• "Aliens do not exist" means [ Aliens do not exist in this world ]
• "It is possible that aliens exist" means [ There is at least one possible world in which aliens do in fact exist, and in that world it would be true to say "Aliens exist" ]. This might or might not be our ("this", "the actual") world.
• "It is possible that aliens do not exist" means [ There is at least one possible world in which aliens do not in fact exist, and in that world it would be true to say "Aliens do not exist" ]

Therefore

"Aliens exist and it is possible that aliens do not exist" means [ Aliens exist in this world, and there is at least one possible world in which aliens do not exist ]

If you like, you can say, "There exists at least one possible world -- not this one, obviously -- in which aliens don't exist."

It is emphatically not the case that aliens existing makes it impossible that they don't exist. That would mean everything that exists exists necessarily, and every proposition that is true is true necessarily. If you want to claim specifically that, go ahead, but don't get there just by misinterpreting the now generally agreed understanding of the modal operators.

"Necessarily" always includes our world because it always includes all possible worlds. "Possibly" is explicitly non-committal on whether our world is the one described. If aliens are known to exist here, they are known to be possible; they may even be necessary, who's to say? But if you claim their existence is contingent, you're explicitly not claiming that in addition to existing here they don't exist here; you are claiming there is a possible world (maybe nearby, maybe accessible, whatever) in which they do not. Again: in that world, they do not; in this one, they still do. "Possibly not" just isn't about the facts here being different here. That rather misses the whole point.

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

Almost everything you say there makes sense to me, so I am not sure if you were thinking it contradicts anything I had said. I thought I had already covered the "possible world" caveat with the above.

"Necessarily" always includes our world because it always includes all possible worlds. "Possibly" is explicitly non-committal on whether our world is the one described. If aliens are known to exist here, they are known to be possible; they may even be necessary, who's to say? But if you claim their existence is contingent, you're explicitly not claiming that in addition to existing here they don't exist here; you are claiming there is a possible world (maybe nearby, maybe accessible, whatever) in which they do not. Again: in that world, they do not; in this one, they still do. "Possibly not" just isn't about the facts here being different here. That rather misses the whole point. — Srap Tasmaner

That's the way I understood "necessarily" also. When you say "they (aliens) may even be necessary", though, I encounter a difficulty: I assume you can't mean logically necessary, so are you signalling that you are allowing that there may be a physical necessity that must obtain across all possible worlds, just some possible worlds or just this world?

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. — Michael

That is about knowledge, since using 'believe' instead of 'know' is all about making it clear your level of uncertainty is greater than 0. Saying "I believe that you are American but it's possible that I'm wrong" is just a tautology. The expression "I believe..." already means (in most cases) "I could be wrong but..."

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? — Michael

I'm trying to use your terminology here so as not to get into six discussions at once about truth, belief, and knowledge. It has been your claim that if you know something, that something is true. If you merely claim to know something, then you're saying nothing different to "I believe..." with a greater degree of confidence. In that case your conclusion is not at all counterintuitive...

We then conclude that I could be wrong even if I think I know everything (and assuming that some p is not necessarily true): — Michael

It's counterintuitive only if you assume that to know something is to have certainty that that something is the case. Something cannot possibly be the both the case and not the case. therefore, it follows that once we've established that something is the case, it is not possible that it it's not the case (our uncertainty about it is 0).

"It is possible that aliens exist" means [ There is at least one possible world in which aliens do in fact exist, and in that world it would be true to say "Aliens exist" ]. This might or might not be our ("this", "the actual") world. — Srap Tasmaner

Clarity it may have, but accuracy...?

"It is possible that..." clearly does not mean only that "There is at least one possible world in which..." otherwise we end up with silliness like my saying "It is possible that I can jump to the moon" being perfectly right.

"It is possible that..." simply reflects (in most cases) our uncertainty. We're saying that although we believe one thing, we cannot be sure it's opposite is not the case.

Which means that once we can be sure what is the case, we can eliminate the uncertainty about it. Once we are sure aliens exists, claiming it is possible that aliens don't exist is just a contradiction, we've only just established that our uncertainty about their existence is zero.

As @Janus, @Banno and I have all been arguing (I think) the matter is about what could have been, and the temporal aspect makes a difference. Here we are saying that our uncertainty about the present is low, but our uncertainty about hard determinism is higher. We know what is the case, but we're not so sure that it was pre-determined and so could never have been otherwise.

As Janus, @Banno and I have all been arguing (I think) the matter is about what could have been, and the temporal aspect makes a difference. Here we are saying that our uncertainty about the present is low, but our uncertainty about hard determinism is higher. We know what is the case, but we're not so sure that it was pre-determined and so could never have been otherwise. — Isaac

:up:

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.

I've been casually reading this discussion and from my point of view this is the post that most clearly solves the problem. :up:

You're tying yourself in a knot over the term "possible world". All it is, is an alternative state of affairs - like the world being the same except that I live in New Zealand.

Their point is that the truth of a proposition can vary from one possible world to another while maintaining consistency.

You've had the error of your account explained several times, but you reply "Nuh, that's not it!'. You haven't understood the explanation.

But you will get it, sometime.

You're not addressing what I'm saying.

As Janus, @Banno and I have all been arguing (I think) the matter is about what could have been, and the temporal aspect makes a difference. Here we are saying that our uncertainty about the present is low, but our uncertainty about hard determinism is higher. We know what is the case, but we're not so sure that it was pre-determined and so could never have been otherwise. — Isaac

I don't think temporality has much to do with it.

I did, previously, but you refused to entertain possible worlds, and so missed the answer.

Here it is again.

If you know the cat is on the mat in reality, then it is not possible in reality for the car to not be on the mat.

Nevertheless, one can picture a different reality in which the cat is not on the mat.

I know that the cat is on the mat, but it might have been otherwise.

There, I replaced "possible world" with "reality". Does that help?

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.

But when you know something, you are not wrong.

If you were wrong, you didn't know it.

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

My claim that I might actually be wrong is true even if I'm not wrong. — Michael

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

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

What?

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.

I believe that aliens exist but I don't know that aliens exist. — Michael

If you know aliens exist, then aliens exist. (if they do not, then you didn't know...)

Hence, if you know aliens exist, you cannot be wrong. Nor can you actually be wrong.

My claim that I might actually be wrong is true even aliens exist and I'm not wrong. — Michael

What?

What? — Banno

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

My claim that I might actually be wrong is true even aliens exist and I'm not wrong. — Michael

If you actually know, you cannot actually be wrong.

(If you know in this possible world, then in this possible world you cannot be wrong)

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.

SO what's the problem?

SO what's the problem? — Banno

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

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

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

But even if it is true in reality, it may be wrong in some other reality, and in that reality you would be wrong.

See how introducing possible worlds keeps things coherent?

Perhaps not.

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.

"I am not" doesn't mean the same thing as "I could not be". — Michael

No, because the second is modal.

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. — Michael

So what?

So what? — Banno

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