a. Jane believes with justification that John is a bachelor
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then a) is true and b) is true and John is a bachelor — Michael

The part in bold makes no sense. (a) is the premise "Jane believes with justification that John is a bachelor". A premise is treated as true, so why make it the consequent of a conditional?

Then the other part of the conclusion is vacuous - it just repeats the antecedent of the conditional (If John is a bachelor, then John is a bachelor).

The part in bold makes no sense. (a) is the premise "Jane believes with justification that John is a bachelor". A premise is treated as true, so why make it the consequent of a conditional?

Then the other part of the conclusion is vacuous - it just repeats the antecedent of the conditional (If John is a bachelor, then John is a bachelor). — Relativist

a) I am a man
b) I am British
c) Therefore, if I am 30 years old then I am a man and I am British and I am 30 years old

It makes perfect sense. It's valid.

So in this case:

a. Jane's belief that John is a bachelor is justified
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's belief that John is a bachelor is justified and Jane's belief might be wrong and John is a bachelor

We can combine "Jane's belief that John is a bachelor is justified" and "John is a bachelor" to make "Jane's belief is justified and true":

a. Jane's belief that John is a bachelor is justified
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's belief is justified and true and Jane's belief might be wrong

We can combine "Jane's belief is justified and true" and "Jane's belief might be wrong" to make "Jane's belief is justified and true and might be wrong":

a. Jane's belief that John is a bachelor is justified
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's belief is justified and true and might be wrong

When I said it makes no sense, I wasn't indicating it was invalid. It's just that the argument is vacuous, so I see no sense in posting it on a philosophy forum.

Initially, I was trying to help you understand the modal scope issues that were present. I suspected you were confused about this, so was trying to politely help. Sorry if I offended you.

This is painful to watch.

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.
...

It's just that the argument is vacuous, so I see no sense in posting it on a philosophy forum. — Relativist

And yet the conclusion has been met with such resistance. Why is that? Perhaps others are equivocating and reading something into the "might be wrong" in the conclusion that isn't read into the "might be wrong" in the premise.

And if it's "vacuously" true that Jane's knowledge might be wrong then it seems worthy of posting to me, but to each their own.

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

1. P.
2. (1) might be wrong.
... — Srap Tasmaner

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 (which is not the same as saying that that there is this belief might be wrong, as would be suggested by your wording above).

But I do think it has to do with the meaning of "might be wrong", which is why here I addressed various interpretations and here set out the paradox in that when we translate "might be wrong" using one of these interpretations there is no issue, but when we consider it untranslated it is rejected. Why is that? As above, perhaps others are equivocating and reading something into the "might be wrong" in the conclusion that isn't read into the "might be wrong" in the premise.

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

1. P.
2. (1) might be wrong. — Srap Tasmaner

Such as

(p ∧ ¬□p) → ◇¬p

To be fair.

Or even

1. p
2. ¬□(p)

Or

1. p
2. ¬□(1)

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.)

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.

I agree, although I don't see how that is relevant to what I am arguing. In a stripped down form:

Argument 1
Jane's belief might actually be wrong
Therefore, Jane's belief is false

If Argument 1 is invalid then Argument 2 is valid

Argument 2
Jane's belief might actually be wrong
Therefore, if Jane's belief is true then Jane's belief might actually be wrong and Jane's belief is true

The consequent of the conclusion of Argument 2 is simply the conjunction of the premise and the antecedent, and so the meaning of "Jane's belief might actually be wrong" in the conclusion means whatever it means in the premise.

So which is valid?

The only way in which they can both be invalid is if "Jane's belief might actually be wrong" is necessarily false.

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.

(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. — Srap Tasmaner

Then there's an issue with the claim "I believe p but I might be wrong".

It shouldn't be interpreted simply as "I believe p and I'm not wrong but there is some other possible world that isn't the actual world where I'm 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?

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."

But see this is not an argument. — Srap Tasmaner

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

So which of arguments 1 and 2 is valid?

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.

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.

And yet the conclusion has been met with such resistance. Why is that? — Michael

I haven't read every post, but the posts I read seem due to a lack of understanding of modal logic. I explained the problem in my first post.

And no, it isn't, and it isn't. — Srap Tasmaner

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."

If you don't like me referring to it as an "argument" then I'll call it a "sentence" and say that either it is true or Argument 2 is valid.

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

It's not "deliberately misleading" if I explicitly say "the meaning of 'Jane's belief might actually be wrong' in the conclusion means whatever it means in the premise".

If you want to say "Jane's belief might actually be wrong" in the conclusion means something like "Jane's belief might have been wrong had things been different" then you are saying that this is what it means in the premise, which I think is false.

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.

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.

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.

I was still (am still!) trying to figure out what's going on here. — Srap Tasmaner

I am trying to make sense of this:

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.

To understand the issue we need to understand what the premise is saying. One interpretation is:

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. The premise "Jane's belief might be wrong" isn't just saying that there is a possible world where Jane's belief is false; it's suggesting that the actual world might be such world, and so we need something like:

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 might be adding a second layer of possible world semantics, but I don't know how else to phrase it. I know that there have been attempts to make sense of modal logic without possible world semantics, so maybe that is what is needed for claims like these.

Perhaps, as you suggested, this is now an epistemic matter, and the interpretation is something like:

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 interpretation of Argument 3.

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?

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.

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." — Srap Tasmaner

Yet something like this seems to be what we are saying when we say "I believe this but I might be wrong". We are claiming that the actual world might be other than how we believe it to be.

So if Argument 3 is invalid then either "if I might be wrong then I am wrong" is true or "I might be wrong" is necessarily false.

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.

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.

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. — Srap Tasmaner

It's the meaning of the phrase that matters here, not what its assertion implies about the speaker.

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"?

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 — Srap Tasmaner

Then I don't understand the issue you have. 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?

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

Throw in justification to the above.

If Jane's belief is justified and if Jane's belief might be wrong and if Jane's belief is true then Jane's belief is justified and true and might be wrong. Again, why do you disagree so much with this contraction?

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.

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. — Srap Tasmaner

I don't understand your modality.

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? That something isn't false isn't that it can't be false (unless it's necessarily true).

You seem to have this notion of modality that sits somewhere between p and ◇p?