a) if aliens exist then I do not know if aliens exist

This claim is true. — Michael

Is it? It does not look true. What is the connection you're positing between the existence of aliens and my ignorance of that fact? An equivalent English sentence is "Aliens exist only if I don't know whether aliens exist." Does that sound remotely plausible?

What you mean is that you're taking "I don't know whether aliens exist" (P) as a premise, in which case, you can claim any conditional with P as the consequent is true, but all of them are uninformative, so this "argument" is abusive.

And mixes modalities. I don't want to go through all this again.

And yet you resist the world's favorite choice for such a situation: "I do not know whether aliens exist," because you have an agenda. The word "might" in "Aliens might exist" describes our epistemic condition, not the state of the world.

This de dicto / de re sort of problem applies to facts as well as beliefs, which is similar to what you and @Andrew M were discussing. Drawing balls from an urn, it's fine to say "The next one might be red," but it doesn't really make sense to say of either a red or a blue ball that it might be red, even if it's the next ball. It just is or isn't.

Obviously.

The usual sort of probabilistic analysis is well-known, and you can say, with enough hand waving, that there's a definition of "reasonable" in here somewhere, but that might not be true. And it's not what we were looking for.

In a sense I was suggesting that you might try to layer this probabilistic approach on top of a set of beliefs that are not themselves probabilistic (which beliefs about a lottery inherently are). I don't find that very satisfying because you are then forced into taking an attitude toward your own beliefs that inadvertently changes them. There are things I hold probabilistic beliefs about, but I don't think I must treat each of my beliefs as probabilistic because some largely unrelated beliefs are false. That's very weird. ("There's a chance that's not milk because my keys might not be in my jacket." What?)

So I'm still unhappy with the move from "Some of my beliefs are false" to "Each of my beliefs might be false." For a whole bunch of reasons, some of which have been on display in this thread.

fallibilism — Michael

Suppose reason and experience suggest to me that it is almost certain that some of what I believe is in fact false, but that I am not in a position to know which of my beliefs will turn out to have been wrong.

The conjunction of all of my beliefs is thus false, but only because at least one of them is false; the claim that I believe something false is an existential claim, and ranges over my beliefs disjunctively.

Put another way, I must believe that my beliefs taken together, in sensu composito, are false, while at the same time believing of each, in sensu diviso, that it is true, since these are after all my beliefs. If someone were to enumerate my beliefs, and question me about them one by one, at the end they would announce that I do not after all believe that one of my beliefs is false, because "my beliefs" is just the conjunction of a great many things I believe are true. This is a quandary.

A tempting approach is to say that since I believe a certain number of my beliefs are false, without knowing which ones, my attitude toward each of my beliefs should be that it might be one of the false ones. But this is problematic because a conjunction of all of these "might be false"'s leads to the conclusion that all of my beliefs might be false, which is not what I think at all. Quandary unresolved.

And the problem isn't restricted to these universal conjunctions. If I believe there is a needle in a haystack, I need not believe, of any subset of the haystack, that it contains the needle; the overwhelming majority of moderately sized "substacks" will not contain the needle. But I must at the same time believe that there is a substack that does contain the needle.

And all of this applies to facts, though I've been presenting it in terms of beliefs. Most subsets of my beliefs have conjunctions that are true, and most substacks of the haystack do not contain the needle.

We can also, in a sense, reverse our analysis: I could hold that my beliefs are generally true (de dicto) while refusing to endorse unreservedly any one of them taken individually (de re). As a matter of simplistic probability, if I figure 99% of my beliefs are true, I could say of each that the chances of it being true are 99 out of 100 and leave it at that.

Is there a way out of this?

I'm not sure. One thing that looks a bit suspicious to me is the temptation to treat our beliefs as a countable (either finite or countably infinite) set, something like a haystack that we really could examine member by member. It could be argued that in reasoning, we only deal with such finite or countably infinite sets, but I'm not sure that's true either, because reasoning always takes place within a context of quite vaguely defined background knowledge. I find the idea that beliefs could be enumerated as implausible as enumerating the real numbers. If that view is correct, the model relied on here is faulty. But I'm not certain. Despite my reservations about background knowledge, deliberate reasoning does consist in part of trying to restrict which of our beliefs are in play and which are not, so perhaps that objection misses the point, while quite rightly drawing attention to the fact that whether we reason successfully is sometimes down to whether we have properly drawn the boundary between what we include and what we exclude. (That is, have we kept out everything we should, and let in everything we should?)

There is some fuzziness in the analogies here too. If I know there is a needle in a haystack, then I know there is some subset of the haystack that contains the needle, but would I really claim to know, of any given substack, that it does or does not contain the needle? I have probability on my side, so there's justification about, but if I claim to know of each substack that it does not contain the needle, I am (1) effectively claiming there is no needle, and (2) I am wrong on at least one occasion. And here it begins to look like not so much a case of the occasion when we're wrong being unfortunate, as we usually think, as all the cases in which we were right being lucky. (Which suggests we were doing some part of the analysis backwards, that we have the wrong designated term.)

I haven't solved it yet. My real suspicion is that there is mistake in moving from "Somewhere among my beliefs there is a falsehood" to "I should think, of each of my beliefs, that it might be false." There's something wrong there, which is what motivated this ramble, but I don't have an alternative model to offer yet.

So in terms of my original argument, I'll still commit to 5 but reject 6:

5. My belief is true and might be wrong
6. My true belief might be wrong — Michael

Seriously?

It's something like ~(P & ~P). It's really that simple.

3. There are possible worlds in which we are brains in vats, and we do not (or, perhaps, "cannot") know that this world is not one of those.
— Srap Tasmaner

This is acceptable except your use of the word “know”. — Michael

And I think you should have raised an eyebrow at "cannot". That would pretty much force us to start sorting worlds by our epistemic condition and then determining (1) whether worlds in which we know we're brains in vats are possible, and (2) whether worlds in which we are brains in vats but don't know it are possible, and so on and on. There is, I understand, quite a bit of literature along exactly these lines, none of which I've spent any time with.

I don’t understand what you’ve been arguing against. — Michael

I think that's true.

Some of what I've been saying has become clearer to me, but not to you, as we went along. Some of it is just subtle enough that I think I've expressed myself poorly at least a couple times, but I have been trying to be more precise with each post.

I think I have been mistaken, even in that last post, in how I imagined we would keep the issues of how the world is and our knowledge of it separate. I still think we should keep them separate, but it's becoming clearer to me that they are both ways of sorting and partitioning sets of worlds -- different ways, yes, but the only way forward is to treat them similarly if separately. Otherwise there are too many things I can't say without serious cheating.

As far as I can tell, and you'll correct me if I'm wrong, your position and your understanding of the issues involved has changed not at all since the OP, despite everything I and others have posted. You still appear to be baffled that anyone would disagree with anything you've posted and just post it again, as here.

If you have something new to say, I'll listen, but for now I've put as much work into this as I intend to, and I'm not going down the rabbit hole of modal conditions on knowledge without very good reason.

The skeptic claims that we might be brains in a vat. There are two different ways to interpret this claim:

1. There is a possible world where "we are brains in a vat" is true
2. It is possible that "we are brains in a vat" is true in the actual world

I think it obvious in context that they are making a claim such as 2). So with that in mind, I will rephrase the above: — Michael

3. There are possible worlds in which we are brains in vats, and we do not (or, perhaps, "cannot") know that this world is not one of those.

See how that separates the concerns you have mashed together in (2)? You must first argue that brains-in-vats worlds are possible (that it is coherent, and maybe a bunch of other stuff), and then further argue that we have and possibly can have no knowledge that our world is not one of those.

"Possibly true in W" is not nearly clear enough, not for this kind of discussion, and I'm tired of disentangling the various strands of meaning.

Not gonna address your worlds that "might be" this or that. Clarify your terminology or I'm done.

No. If Jane's belief is actually true, it can only be counterfactually false, not actually false. It's what "counterfactual" means.
— Srap Tasmaner

You accepted here that "Jane's belief might be false" and "Jane's belief is true" can both be true, so I don't understand your objection. Do these two phrasings mean something fundamentally different to you? Obviously the second phrasing combines the premise and conclusion of the first phrasing into a material conditional, but the meaning of "Jane's belief might be false" is identical in every occurrence. — Michael

I doubt either of us has been perfectly consistent about this, but I can explain what I'm thinking.

When we say "P is true," for instance, I am taking that as "P is true in the actual world." I think that's generally what's intended with an unadorned "true" or "false." When it matters, I'm saying "actually true" or "true in W," something like that.

When we say "P is possibly true," with no other restriction, I am taking that as "true in some possible world," and the set of possible worlds in which P is true may or may not include the actual world.

So, in our earlier exchange, I took "Jane's belief is true" to mean true in the actual world, and "Jane's belief might be false" to mean false in some (other) possible world. They can both clearly be true, on this reading, even though JB being actually true means the actual world is not one of the worlds in which JB is false.

Phrasing 1:
Jane's belief might be false
Jane's belief is true
Therefore, Jane's belief might be false

Phrasing 2:
Jane's belief might be false
Therefore, if Jane's belief is true then Jane's belief might be false — Michael

Phrasing 2 is a degenerate argument in which JB's truth plays no role.

Phrasing 1 is fine because I'm reading "might be" as counterfactual. If you change that to "Jane's belief might actually be false," I'll say no.

Maybe I need to be even simpler. — Michael

I'd rather you be more explicit. It is absurd that in this sort of conversation we are not in every case saying "true in W" instead of unadorned "true." It would make many points much clearer.

Do you accept that both of these are possible worlds?

World 1
Jane's belief might be false
Jane's belief is true

World 2
Jane's belief might be false
Jane's belief is false — Michael

Worlds? Not sets of worlds?

For the first, if JB is true in W1, no it cannot be false in W1. How could it be?

For the second, I'll address the bit I skipped over with W1. What exactly do you mean by "might be"? I cheated a little in W1, because the second premise allowed me to construe it as "not violating the law of noncontradiction." But really what is "might be" supposed to mean within a given world?

If you want these claims to be true within a single world, I think we have to take "might be" as indicating our epistemic position, because it makes no sense at all to count a world as its own counterfactual. Worlds are collections of facts, not possibilities. Sets of worlds represent possibilities, depending on how the facts are distributed among them.

I can continue to read W2 as I read W1, that it does not violate the law of noncontradiction for JB to be false. But these "worlds" are specified using unnecessarily ambiguous language. I wish this language were just nonsensical, but it happens that there are things we want to say that can be made to fit (the logical and epistemic issues), and that are sometimes what people mean when they talk this way. Since we know there are several different types issues in play, there's no reason for us not to be much clearer.

Is anyone besides Michael checking my math?

I am barely qualified to be explaining this stuff and feel like I'm on the verge of making a hash of it.

Would really appreciate it if someone more knowledgeable chimed in.

You are right that Jane's belief, which is true in the actual world, isn't false in the actual world, but what do you mean by saying that it can't be false in the actual world? — Michael

Only the law of of noncontradiction. It's a matter of, let's say, "logical" necessity. What is true cannot be false, even if it might have been false. No such law prevents a sentence from being both true and English, say. But by the same token an English sentence cannot be a Russian sentence.

Option 1
It is possible that Jane's belief is actually false
Therefore, if Jane's belief is true then it is possible that Jane's belief is actually false — Michael

No. If Jane's belief is actually true, it can only be counterfactually false, not actually false. It's what "counterfactual" means.

Option 2
It is possible that Jane's belief is actually false
Therefore, Jane's belief is actually false — Michael

No. We do not know that Jane's belief is necessarily false, so we do not know that it is not possible that Jane's belief is actually true.

This is tricky though, and can be put a little more clearly the other way around. There are worlds in which Jane's belief is false; the actual world might be one of those worlds. "Might be" here is epistemic; it's about our knowledge of what sort of world this one is, not about what sort of world it is. There are two steps: determining what sorts of possible worlds there are, and then determining which of those we happen to live in. We simply do not have enough here to conclude that this world is the sort of world in which Jane's belief is false. The other kind of world may be possible, and this might be one of those.

(For what it's worth, the epistemic issue is forcing me to talk about possibilities that might or might not be, which is terribly uncomfortable, but I'm not sure how to get around it. I wondered aloud once before whether we could just capture the epistemic options in more sets of possible worlds, but that's more work than I feel like doing unless I have to, and I don't even know that it works. Again, very likely reinventing the wheel here, as this sort of stuff is a very hot topic today in epistemology.)

Option 3
It is not possible that Jane's belief is actually false — Michael

So this is not freestanding but the fallback if I reject 1 and 2.

Option 1 I have a problem with because even if JB is only contingently actually true, it cannot be actually but only counterfactually false. I am not committed to JB being necessarily true.

Option 2 tries to take the logical necessity of Option 1 and turn it into metaphysical necessity. That is, there are conditions under which I have said JB cannot be actually false (namely JB being actually true), therefore if JB can be actually false, those conditions must not be met (JB is not actually true). But JB need only be contingently actually true to block JB being actually (rather than counterfactually) false, so I am still not committed to JB being necessarily true.

If JB were necessarily true, it would not be possible for it to be actually false. Since I am not committed to JB being necessarily true, am I committed to anything else that would make it impossible for JB to be actually false? Nothing I can think of, so it's "no" to option 3 as well.

Which option is correct? It must be one of them. — Michael

Also no.

I understand your quandary here, I think, but it's mainly down to use of modal sounding terms in different senses. The fact that whenever P is true in W, it cannot be false in W, comes right out of the definition of W, which includes P carrying a value of "true". That's just not the same thing as saying that P is true in all possible worlds; it's only saying that the worlds in which it is true are defined by its being true there, and if you need it to be false then you're in another set of worlds.

If Jane's belief might be wrong and if Jane's belief is true then Jane's belief is true and might be wrong. Why do you disagree so much with this contraction? — Michael

Because you have been very clear that you mean Jane's belief, which is true in the actual world, might be false in the actual world, and that's not an option. If it's true in ℋ, it cannot be false in ℋ; if it's possibly false, in addition to being true in ℋ, it's false counterfactually in some ℳ where ℳ ≠ ℋ.

Do you at least understand the difference between "the actual world might be other than I believe it to be" and "there is a possible world that is other than how I believe the actual world to be"? — Michael

I think I do.

For instance, there could be a possible world that is other than how I believe the actual world to be because I am wrong about how the world is, and this world is that "other" world.

The actual world is a possible world. There are possible worlds I know I don't live in, and possible worlds I can contemplate that, for all I know, are this one.

No, it doesn't "mean the same thing," but it might or might not be different from how I think it is implies that I do not know whether it is how I think it is.

Unless of course you're being abusive. I listen to a quiz show sometimes in which the host says things amounting to "Well the answer might be C ..." in order to get the guest to give the correct answer of C. (It's a friendly show. If it weren't, he might say something like that to trick the guest into giving the wrong answer.)

If we have actuality in hand, if we know the facts, what would motivate us to talk instead in terms of possibility? There are good and bad reasons for doing so ...

If we do not know the facts, it is obvious what our motivation for considering possibilities is.

Your reasoning here seems to be that "Jane's belief might be wrong" and "Jane's belief is true" cannot both be true — Michael

They can both be true, yes, but you have to be careful. If Jane's belief is true in ℋ, which it is by stipulation, it cannot be false in ℋ. If it can be false, also stipulated, it must be false in some ℳ, where ℳ ≠ ℋ. That is to say, counterfactually.

But there's a way to say this that is misleading or even abusive. The magician tells you the coin is in his left hand or in his right, even when he knows which is the case, because he intends not to inform you. I could say, "Michael, honey, I might have overdrawn our checking account," when I know perfectly well that I have, but don't quite want to admit it. *

I don't think we have much use for arguments that rely on degenerate cases like "If Caesar was a goat then today is Thursday," today being Thursday.

We are suggesting that the actual world might be other than how we believe it to be. — Michael

I have offered, I think half a dozen times, a distinction between the world being different from how we think it is and counterfactually different from how it is.

What's different about your version here is that the world might be different from how we think. And that's to say we don't know how the world is, else we would be in a position to judge whether we had been mistaken, and in a position to contemplate counterfactual worlds.

And this gets us no closer to your goal of fallibilist knowledge, so far as I can tell.


* Should have added: I know that I might have, because I've done it. Actuality entails possibility.

Argument 1
Jane's belief might be wrong
Therefore, if Jane's belief is true then Jane's belief might be wrong

The argument is valid but the conclusion is counterintuitive despite its consequent simply being a restatement of the premise — Michael

Right. This is
1. P
2. (anything at all, true or false) → P

But, it is now "misleading" because if Jane's belief is true, its being false is no longer a real possibility in this world, only elsewhere. What's more, we only say things like "Jane's belief might be false" when we don't know whether Jane's belief is true or false, so it is very odd to take it as a consequent of Jane's belief being true.

There's also this general counterintuitiveness about unnecessary disjunctions: "Today is Thursday" entails "Today is Thursday or Caesar was a goat." Uh huh. And we have that here: "P is true, so it might be true or it might be false." (Twirls mustache.)

Argument 2
There is a possible world where Jane's belief is false
Therefore, if Jane's belief is true then there is a possible world where Jane's belief is false

The conclusion is acceptable, but I think that the premise is an inaccurate interpretation of the original. — Michael

And it doesn't say much and it's not what you're actually interested in.

Argument 3
It is possible that Jane's belief is actually false
Therefore, if Jane's belief is true then it is possible that Jane's belief is actually false

I understand that this is adding a second layer of possible world semantics, but I don't know how else to phrase it. — Michael

Yeah, I don't think you can or want to do that, and if you can't then you still can't say a proposition that is true in W can be false in W. It's just the way true and false work, and the whole point of introducing W as, in essence, a set of assignments of truth-values to propositions.

I get what you're going for, I do. But if Jane's belief is true, Jane's belief can only be false counterfactually. We already know how to say that, and it's "Jane's belief might have been false," or "could have been false."

Argument 4
Jane's belief is not certain
Therefore, if Jane's belief is true then Jane's belief is not certain

This, at least, appears to have an acceptable premise and conclusion, although I'm not sure if it's an accurate translation of Argument 3. — Michael

Maybe I'm missing the boat, but as I indicated before I don't think we're wedded to falling back on degrees of confidence or certainty or any of that. Despite the popularity of that approach these days, my gut is that this is a different issue. What about the shy schoolboy who does in fact know what the capital of Arkansas is, but doubts himself?

The paradox, though, is that whereas we may be willing to accept Arguments 2 and 4, we appear unwilling to accept Argument 1 (as shown by the resistance I am getting). Why is that? — Michael

Yes, 2 says nothing and is not what you want anyway. 4 is another issue, I think, though lots would disagree. 1 and 3 are what matter.

1 is fucked up in various ways that amount to abuse. 3 ends up not being what you want because the epistemic issue you were after has been swallowed up by counterfactuals. Your options are to give in and treat "might be false" as "don't know", for whatever that gets you, or try to develop 3 into something coherent about knowledge and counterfactuals. Don't reinvent the wheel though. Look at sensitivity and safety, for instance here, if you really want to throw your life away on this.

A favorite joke of mine from M*A*S*H:

Colonel Flagg joins the poker game in the swamp and sits down next to Klinger.
Flagg: Hey, up close you're a guy.
Klinger: Far away too.

In a context like this, "might be" is deliberately misleading. — Srap Tasmaner

To clarify, the context I was referring to was saying that something I know to be false "might be true," as in the example about my legal name.

That first argument was a reference to your claim here. When I asked you if that meant that "I might be wrong" entails "I am wrong" you responded with "I think that's the converse of what I was at least trying to say." — Michael

The converse would be that "I am wrong" entails "It is possible that I am wrong", which of course is true. Actuality entails possibility. Possibility doesn't entail actuality.

As for the rest, I believe the posts you're talking about may not have been the clearest I've written, because I was still (am still!) trying to figure out what's going on here. There seems regularly to be a problem with the sense in which truth excludes falsehood -- the truth of P in W makes it "impossible" that P is false in W, but that "impossibility" is not modal, only logical. There are no available possibilities within W.

If my keys are in my pocket, they cannot not be in my pocket, can't be on the dresser or on the table, even though they only happen to be in my pocket and might not have been. See how that works?

Is any of this even related to what you want? "I might be wrong," "I could be wrong," and similar formulations are about me, about the limits of my knowledge, and my knowledge in turn is knowledge of the actual world, but if I'm wrong it's because the world is different from what I thought, not because of some counterfactual something or other.

Maybe that's putting it too strong. It's how the world is or isn't we're interested in. If you ask me to guess the next card you're going to deal and I say "ace" but it's a 2, I can truly say, "If it had been an ace, I would have been right." And there has been work on knowledge that relies on that sort of thing. I'm just not sure any of this is in the neighborhood of your interest in fallibilism.

It is. It’s like saying “I’m a bachelor, therefore I’m not married”. — Michael

And no, it isn't, and it isn't.

My legal name might be "Srap Tasmaner" but it isn't.

That's logically the same form as the conclusion to your argument 2, and it's fine, so long as we know what we're about. In a context like this, "might be" is deliberately misleading. I don't think that's what you want. You want something that expresses epistemic modesty.

I might wire you £1,000 today but I won't.

Jane's belief might actually be wrong
Therefore, Jane's belief is false — Michael

But see this is not an argument.

If Jane's belief that P may be false in the actual world, that only says it is not necessary that P and P's truth-value is, at this point, unknown. It doesn't even get us the possibility that P in this or any world.

Then there's an issue with the claim "I believe p but it's possible that I'm wrong".

It shouldn't be interpreted simply as "I believe p and I'm not wrong but there is some other possible world where I am wrong".

And I don't think it should be interpreted simply as "I believe p but I'm not certain" as the claim prima facie says something about the subject matter of the belief rather than one's reasons for holding it.

So how do we make sense of such a claim? — Michael

I believe that P but I do not know that P.

If you acknowledge right off the bat that you might be mistaken, you pre-emptively abandon the claim to know, without waiting for the evidence to decide things either way.

You might even claim to have high confidence that P, but not, as you note, certainty. That really could be treated as a different issue, because there are cognitive claims we are inclined to make even assigning low confidence, given the totality of the evidence, but swayed by some sort of salience. I'm thinking of things like "I suspect it was Billy that left the refrigerator open, but really have no idea how it happened."

Here, I'll address this one directly, for all the good it will do.

I think our conflict is in regards to the prima facie difference between saying:

a. There is a possible world where my belief is false
b. It is possible that my belief is actually false

Given Kp ∧ ◇¬p I trust that you accept (a) is true even if my belief is true? — Michael

Absolutely.

But I suspect that you claim that (b) is false if my belief is true?

(b) is a misuse of "possible" in this context, because of the "actually" there.

There are no leftover possibilities in the actual world. It is defined by which possibilities it actualizes and which it doesn't. A statement that has a different truth value from the one it has in the actual world, is a statement that belongs to and partly defines a different possible world.

I tried to work around this issue by suggesting that the epistemic dilemma can be cast as trying to figure out which sort of world the actual world is. That might work, for all I know, but I suspect it's reinventing the wheel. @Kuro seems to be much more knowledgeable about this stuff than me.

Not quite, as it's not asserting p and then asserting that p might be wrong. It's asserting that there is this belief and then asserting that this belief might be wrong — Michael

Bob has a belief, called "Bob's belief", that it's Thursday.

Bob's belief is right if and only if it's Thursday.

Bob's belief is wrong if and only if it's not Thursday.

Such as

(p ∧ ¬□p) → ◇¬p — bongo fury

You would think, right? I did. But @Michael has been very clear that this is not what he means.

This says, perfectly clearly, that p holds in the actual world, and there is at least one possible world in which ~p. The second conjunct on the LHS says "p need not be true". What Michael wants is for p to "maybe" be false in the actual world, even though there's a premise that says it's true.

It's also clear that Michael wants wants p as a premise in addition to some premise along the lines of "S believes that P" because he wants to say something about true beliefs, about knowledge "possibly" being wrong. Even in recent formulations that don't have p as a premise, it's in the conclusion as a discharged assumption.

I think it turns out modal logic is not the right tool for this job and its introduction has just confused things. It may be possible to formalize the argument neatly, but it'll be in some sort of epistemic logic, and I don't know those. (That is, even less than the tiny bit I know of modal logic.)

The principal issue, so far as I can tell, has nothing to do with omniscience, nothing to do with knowledge, nothing to do with fallibilism, and nothing to do with modal logic.

The issue is what to make of arguments that go like this:

1. P.
2. (1) might be wrong.
...

No one raises an eyebrow on hearing "I think there are three left, but I could be wrong," or "I'm pretty sure there are three left, but I could be wrong," or even "I'm almost certain there are three left, but I could be wrong."

But no one ever says "I know for a fact there are three left, but I could be wrong."

Why not?

This entire thread has been devoted to confusing "I have knowledge of something that need not be the case" with "I have knowledge of something that may not be the case."

3. It is acceptable to say that we can have knowledge that is not necessarily true — Michael

The ambiguity here is crippling.

Let's say there need not be aliens, but there are. That they exist is a contingent fact, not necessary, and we can know this contingent fact.

• This is what (3) seems to say that most of us would agree with.

If you accept that Kp → p, then given Kp, you "must" conclude p, by modus ponens. That "must" is a sort of necessity, but it's logical necessity; it is different from the sort of necessity that the existence of aliens lacks. (Perhaps it would be more modern only to say that you may introduce p. In place of logical necessity, we would have logical permission or logical entitlement. In epistemic lands, that might be close to "warrant" or even "justification".)

If you define knowledge that p to include a stipulation that p is true, then it is analytic that when you know that p, p is true, and that's yet another sense of "necessity", very close to logical necessity, but perhaps different, as no specific logical principle is invoked.

• Something around here is what (3) seems to want to deny.

And of course, if you have P in hand, either as a premise, or derived, perhaps from your knowledge that P, then at that point we can apply the law of noncontradiction to deny that P is also false, and we'll usually say, P "cannot" be false, or that it cannot not be true, which is either a case of logical necessity, or the law of noncontradiction (perhaps also double negation) merely expressing the meaning of "true", "false", and "not", in which case this is analytic. Whatever.

• And this is the part of (3) I've been trying to make clear: once you have, perhaps even as a premise, that there are aliens, then there are, really and truly, here in the actual world, and it no longer makes sense to say maybe there aren't, even though their presence is entirely contingent. It still makes sense, as others have pointed out, to say, in English, "there might not have been", but that's not a temporal usage, that's the English past subjunctive, expressing contingency. We all agree, in some cases, that what is might not have been, but none of us agree, for any case, that what is might not be.

(2) breaks down into cases, right?

(2a) I'm not wrong, and aliens do exist here.
(2b) I am wrong, and aliens do not exist here.

Are both of those cases consistent with premise (3)?

No, they are not. By disjunctive inference, we are forced into the (2a) branch.

I should add: if you don't like my translation of (2), and would prefer it to be something like "It is possible there are no aliens here, in this world" then, in the presence of a further premise that there are or are not aliens here, this can only be understood as an epistemic possibility -- that is, as a way of saying I don't happen to know.

"I might be wrong" here means, it is possible that aliens do not exist. That is, there is a possible world in which aliens do not exist.

If you add the further premise that aliens do exist in this world, you can draw two conclusions: (1) they are possible; (2) this is not one of the worlds in which they do not exist. That's it. If I suggested otherwise, I must have expressed myself poorly.

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

Let's suppose aliens might not exist. Then there is at least one possible world in which they don't.

Can the possible world in which aliens do not exist be a world in which aliens exist? No.

Can it be true, in a world in which aliens do exist, that there are other worlds in which they don't?

That's the same as asking if there are worlds in which aliens don't exist. We are supposing that aliens might not exist, so by stipulation, yes, there is at least one world in which they don't, and that continues to be true even in a world in which they do.

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.

The actual world cannot "possibly" be a different one. It simply is whichever one it is, just as all the others are. It is not a matter of which name goes on which world, because "actual" is not a name but an indexical.

If aliens exist, then it follows that you are not wrong to think they do.

Not being wrong won't stop you from thinking you might be, but it quite definitely stops you from actually being wrong.

If aliens exist, neither you nor anyone else can be mistaken in thinking they exist. That possibility is blocked by them existing.

You can still think they might not all you like. You'll always be wrong, though.

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

Are you trying to equivocate? Why not distinguish the issue of what sort of world you happen to be in from the issue of what sort of world you think you're in?

is the below true?

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

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

But if you know aliens are actual, then they are actual, and you know this is not a world where they're not.

If aliens don't exist in this world, then this is one of the worlds in which they don't exist, whether you know it or not. If aliens are possible, then they are possible whether you happen to be in a world where they are actual or not, and whether you know they're possible or not.

I think you're trying to ask if this world could conceivably be a different world, but that's already baked in. All the possible worlds are already there; the question for you, the epistemic question, is which one you're in.