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?

Seriously? — Srap Tasmaner

Actually, no. I think I can still accept 6. Because it means one of these two things:

1. There is a possible world where my true belief is false
2. I am not certain that my true belief is true

e) I am not certain that the number 2 is even

Which may, in fact, be false.

How do you think this is resolved? — Michael

By recognizing that it's due to identity ignorance.

Which is to say, Alice knows that the number 2 is even, but not that the number written on the hidden piece of paper is even, even though it is 2. The difference is due to Alice not having identified the written number as 2.

Similarly, we know that blue balls are blue and true statements are true by understanding the identities involved. But Alice may not know that this particular blue ball is blue, or that this particular true statement is true because she hasn't yet identified the ball as blue or the statement as true.

There doesn't seem to be any identity ignorance here:

a) If I know that John is a bachelor then John might not be a bachelor

This can be interpreted as:

b) If I know that John is a bachelor then there is a possible world where John is not a bachelor
c) If I know that John is a bachelor then I am not certain that John is a bachelor

Do you believe that either of (b) and (c) is false? Or do you believe that neither of these is the correct interpretation of (a)?

We then conclude that I could be wrong even if I know everything — Michael

As far as I can tell that's a contradiction: know and wrong are mutually exclusive, oui?

As far as I can tell that's a contradiction: know and wrong are mutually exclusive, oui? — Agent Smith

Knowing and being wrong are contradictions, but knowing and possibly being wrong are not.

For example, it is possible that I am wrong in believing that you are American. It doesn't follow from this that you are not American. Therefore, it could be the case that both a) it is possible that I am wrong, and b) I am not wrong.

In my book, "possibly being wrong" is fallibilism which precludes omniscience sensu strictissimo.

In my book, "possibly being wrong" is fallibilism which precludes omniscience sensu strictissimo. — Agent Smith

Why does fallibilism preclude omniscience? Doesn't omniscience just mean knowing everything? If fallibilism is true then I can know everything even if I am not certain about anything (assuming, for the sake of argument, it is possible to know everything). Call it fallible omniscience if you like.

Or does omniscience mean knowing everything with certainty?

I'm stumped Michael. It appears that the time has come for more nuanced acceptance of facts.

Or does omniscience mean knowing everything with certainty? — Michael

By logical implication, yes.

By logical implication, yes. — universeness

And what does certainty require? I suspect that what is true is necessarily true. In which case knowing everything with certainty (omniscience) requires that everything which is true is necessarily true. Therefore, if there is something which is true but not necessarily true then omniscience is impossible.

And what does certainty require? — Michael

Empirical evidence/proof. Proof that remains irrefutable in all past/current and future scenario's is impossible, therefore omniscience is impossible as are all the omnis as are omnigods.
It's impossible that nothing is impossible. Paradox is simple impasse. It's just a logic hamster wheel.
I think you and @Srap Tasmaner should be :clap: :clap: ed and be given the TPF award for the most tenacious exchange on any thread I have read so far. I admire tenacity but I feel exhausted for both of you with 0 progress made imo.

f there is something which is true but not necessarily true then omniscience is impossible. — Michael

OK, but its impossible either way because necessity is subjective and circumstantial. All possible circumstances cannot be predicted. So even if all truths were necessarily true, omniscience would still be impossible. So, we are left with the immovable object meeting the irresistible force impasse. An impossible scenario.

a) If I know that John is a bachelor then John might not be a bachelor — Michael

I think that is false.

This can be interpreted as:

b) If I know that John is a bachelor then there is a possible world where John is not a bachelor
c) If I know that John is a bachelor then I am not certain that John is a bachelor

Do you believe that either of (b) and (c) is false? — Michael

I do. We don't doubt what we know.

I do. — Andrew M

p ⊬ □p

Therefore (b) is true if there is a possible world where John is not a bachelor.

And if fallibilism is true then knowledge does not require certainty, and so knowledge does not entail certainty. I can know and not be certain. Therefore (c) is true if I am not certain that John is a bachelor.

et al,

Just my thoughts...

Unless you can define what a deity is, and what it has in strengths and weaknesses, you cannot compare human frailties to a deity. You cannot define a deity, therefore you cannot compare it to mortal humans.

No one in this forum can define a deity.

While it s the case that man cannot change the laws of the universe, a deity, instrumental in the creation of the universe, can tweak, adjust, change or modify any law because the Supreme Being established the Laws of the Universe.

Respectfully,
R

No one in this forum can define a deity. — Rocco Rosano

That's normally the case with nonexistents.

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.

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." — Srap Tasmaner

I think you're describing the lottery paradox there?

There are 1,000 tickets and one of them is a winner and you are not certain which. For each ticket n it is rational to say, given the 0.1% chance of being the winner, that ticket n is a loser.

And, of course, for each ticket one can say "it might be the winner" and "it might be a loser".

For each ticket n it is rational to say that this ticket might be (even most likely is) a loser. — Michael

They could all be loser's ie, a rollover!

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.

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.

It just is or isn't. — Srap Tasmaner

It just is or isn't the case that aliens exist, and yet I can say "aliens might exist" and you can say "aliens might not exist" and we'd both be right. How do we make sense of what it means that things might be a certain way, given that they just are a certain way? I offered two explanations here:

a) There is a possible world where aliens (do not) exist
b) I am not certain that aliens (do not) exist

Does "aliens might (not) exist" mean something other than (a) or (b)?

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.

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. — Srap Tasmaner

Certainty describes our epistemic condition as well and that was one of my examples. I agree that we say "I might be wrong" when we don't know, but I don't know if "I might be wrong" means "I don't know". I think "I'm not certain" (or "it is not certain") is more accurate.

But even if we use your meaning, we still have:

a) if aliens exist then aliens might not exist

Which is intuitively false and yet possibly true.

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

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

How is it mixing modalities? You just said that "aliens might not exist" means "I do not know if aliens exist" and so the claim above is:

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

This claim is true. Therefore, "if aliens exist then aliens might not exist" is true.

Perhaps mixing modalities is what you and others do when you misinterpret this claim as something like "it's possible that if aliens exist then aliens do not exist", and that would explain why it's intuitively false; we intuitively misinterpret the claim.

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.

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? — Srap Tasmaner

It's a material conditional, which is true if the consequent is true. Given that "I do not know if aliens exist" is true it then follows that "if aliens exist then I do not know if aliens exist" is true.

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. — Srap Tasmaner

It shows that both "aliens exist" and "I do not know if aliens exist" can both be true. And so, given your definition of "might be" it shows that "aliens exist" and "aliens might not exist" can both be true.

And it's not supposed to be informative, just as Moore's paradox isn't supposed to be informative. It's just supposed to show, like Moore's paradox, that there is a claim (whether that be "if aliens exist then aliens might not exist" or "aliens exist and aliens might not exist") which is possibly true and yet intuitively contradictory.

If you don't like the material conditional then we can go back to using premises and a conclusion.

Aliens exist
Aliens might not exist (≔ I do not know if aliens exist)
Therefore, aliens exist and aliens might not exist

The argument is valid (even if vacuous). The second premise is true. The first premise is possibly true. The conclusion appears to be a contradiction but it isn't, and it's possibly true.

It shows that both "aliens exist" and "I do not know if aliens exist" can both be true. — Michael

How does it do that?

It's a material conditional, which is true if the consequent is true. — Michael

Meaning the conditional is true whether the antecedent is true or not.

So how do you think the truth of this conditional shows that the antecedent and the consequent can both be true? It would still be true even if it is necessarily false that aliens exist. What are you even talking about?

Aliens exist
Aliens might not exist (≔ I do not know if aliens exist)
Therefore, aliens exist and aliens might not exist — Michael

It is clearly possible for aliens to exist and for me not to know it. That's not only uncontroversial, for all I know it's true.

But what you've been chasing in this thread is me knowing aliens exist even though they might not. To get there you have to allow premise 1 to be the epistemic claim and force premise 2 to be something else.

If you've nothing new, I'm hopping off this particular hamster wheel.