What you describe as not having occurred in your particular case does happen though. — Hanover

I think the wording was ambiguous. This is closer to what I meant:

It's not like I recognized that I am English and live in England and then concluded that I therefore must already be a supporter of the English football team.

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.

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.

Fanhood isn't immutable. From point A to Point B, what causes you to change into a fan? — Hanover

Perhaps being English and living in England. Or perhaps a family member is a supporter and so I adopted the team as my own.

But it's a mistake to say that the cause of that self-identity is the characteristic that constitutes the self-identity. It's not like I recognized that I am English and live in England and then concluded that I therefore must be a supporter of the English football team.

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.

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.

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)?

Something makes you a fan. — Hanover

Identifying as a fan.

Your love of the team, your undying commitment to your land, the excitement of singing stupid songs, getting drunk with hooligans — Hanover

I think you're getting it backwards. I'm not a supporter because I wear the shirt or watch the games; rather I wear the shirt or watch the games because I'm a supporter.

You tell me what doesn't count as an attribute of a MU supporter, but can't tell me what does. — Hanover

Identifying as a Manchester United supporter.

My position is that wearing the shirt and attending the matches is part of what it means to be a MU fan. As with the trans issue, I similarly would expect a trans MtF to wear women's clothes. That's part of it. Saying the expression isn't part of the identity seems too brittle a distinction. The behavior isn't all you are, but is part. — Hanover

I support England when they play. I don't wear the shirt and most of the times I don't even watch the games.

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".

Then part of your identity links to your appearance. — Hanover

Not in the sense that the appearance is what determines identity. Wearing a Manchester United shirt isn’t what it means to be a Manchester United supporter.

I read him as denying any discernable definition of gender other than generally thinking himself a man, offering no characteristic of what a man would be.

If we dissociate gender entirely from physical attributes, the concept of physical transition becomes incoherent. How can you physically transition from male to female if you are already a female and your body has nothing to do with that? — Hanover

I'm sure a Manchester United supporter would feel uncomfortable wearing a Manchester City shirt. It's not incoherent for them to want to change their clothes.

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.

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.

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?

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.

The T-schema ... formulates the logic of correspondence — Janus

I don't think it does. @bongo fury quoted this earlier which is worth revisiting:

Some of the trouble traces back to Alfred Tarski's unfortunate suggestion that the formula " 'Snow is white' is true if and only if snow is white" commits us to a correspondence theory of truth. Actually it leaves us free to adopt any theory (correspondence, coherence, or other) that gives " 'Snow is white' is true" and "snow is white" the same truth-value. — Goodman, Of Mind and Other Matters

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)?

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

But to argue that even animals don't behave in predictably natural ways seems a stretch that doesn't need to be made. — Hanover

I'm not saying they don't. I just don't think animal behaviour has anything to do with gender.

Animals don't have genders, just biological sexes.

Very clever, there is a possible world where both of these are true:

a) the number in the box might be odd
b) the number in the box is 2

Which contracts to:

c) the number in the box is 2 and might be odd

And even:

d) the number 2 might be odd

However, 2 is necessarily even and so we have a contradiction. And even if we understand "might be" in terms of one's own certainty rather than logical possibility we have:

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

Which may, in fact, be false.

How do you think this is resolved? I wonder if perhaps these don't mean the same thing?

1. The ball is blue and might be red
2. The blue ball might be red

3. The number in the box is 2 and might be odd
4. The number 2 might be odd

I'm happy to reject 2 and 4.

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

Do you think that the number 2 might be (or could be) odd? — Andrew M

No, because the number 2 is necessarily even. My examples are only ever where the truth of the claim is not necessarily true. Hence in the OP:

1. Kp (premise)
2. ¬□p (premise)
3. Kp ∧ ◇¬p (from 1 and 2)

And men are not able to. No one alive or dead was born of a man. — NOS4A2

That's an empirical claim that requires first knowing what it means to be a man or woman and then looking to see if anyone meeting these conditions has given birth or breastfed.

So you first need to tell me what it means to be a man or a woman.

Whereas you seem to be interpreting them in a Moorean sentence sense. While such sentences can be true, no-one would ever assert them. People would either say the ball is blue (when they knew it was blue) OR say the ball might be red (when they didn't know it was blue), but not both together. — Andrew M

Yes, exactly that. Moore's paradox was the inspiration for this discussion.

"I believe it is raining and it is not raining" is logically consistent and possibly true, but not something we would ever assert.

"Jane's knowledge might be wrong" is logically consistent (unless knowledge requires certainty) and possibly true, but not something we would ever assert.

I’m saying that people who give birth and breastfeed are women. — NOS4A2

They're women because they give birth and breastfeed? Or only women are able to give birth and breastfeed?

So you're saying that someone is a woman iff they can give birth and breastfeed?

No, I'm saying that it is false that "the blue ball might be red", just as it is false that "The number 2 might be odd". There's a difference between conceptual and empirical claims. — Andrew M

a) The ball might be red

If you accept that a) is true even if the ball is blue then you accept that there is a possible world where the ball is blue and a) is true.

And then I don't see a difference between these phrasings:

1. The ball is blue and a) is true
2. The ball is blue and the ball might be red
3. The ball is blue and might be red
4. The blue ball might be red

Do these mean different things to you, and so have different truth-conditions?

There is a ball hidden in a box. That ball is either red or blue.

a) The ball might be red.

This proposition is true whatever the colour of the ball in the box. It is true if the ball is red and it is true if the ball is blue.

If you want to say that a) is false if the ball is blue then you are saying that if the ball might be red then it is red.

If you accept that a) is true even if the ball is blue then you accept that there is a possible world where the ball is blue and a) is true; you accept that there is a possible world where the ball is blue and the ball might be red.

But there are no possible worlds where John is a bachelor and married. — Andrew M

I know, but "bachelor John could be married" doesn't mean "there is a possible world where John is a bachelor and married".

There is a difference between:

a) John is a bachelor and could be married
b) John could be a bachelor and married

Why? To me all it entails or suggests is that for every actuality a true corresponding proposition can be formulated. — Janus

I showed why in that post.

q ≔ the proposition that p
T(q) ≔ q is true

1. T(q) ↔ p
2. T(q) → ∃x(x=q)
3. p → ∃x(x=q)
4. ¬T(q) ↔ ¬p
5. ¬T(q) → ∃x(x=q)
6. ¬p → ∃x(x=q)
7. ∃x(x=q)

In ordinary English:

1. the proposition that p is true if and only if p
2. if the proposition that p is true then the proposition that p exists
3. if p then the proposition that p exists (from 1 and 2)
4. the proposition that p is false if and only if not p (from 1)
5. if the proposition that p is false then the proposition that p exists
6. if not p then the proposition that p exists (from 4 and 5)
7. the proposition that p exists (from 3 and 6)

If that's a problem then we can simply rephrase the T-schema as saying something like if the proposition "p" exists then "p" is true iff p, and so the T-schema will say nothing about states of affairs that aren't talked about.

The first option is fine when understood as an expression of uncertainty as in, "I believe it is raining but I'm not certain". But not in the sense of, "My true beliefs could be false". — Andrew M

What does "could be false" mean? Either "there is a possible world where it is false" or "I am not certain that it is true". In both cases "My true belief could be false" can be true.

If you just mean that my true belief could not be both true and false then I agree, but "my true belief could be false" doesn't mean "my true belief could be both true and false".

The "could be false" in "my true belief could be false" means the same thing it does in "my belief could be false". Therefore, if "my belief could be false" being true does not entail that my belief is false then "my true belief could be false" could be true.

Seems to me that the problem stems from sport using the wrong criteria to group athletes. It's a congenital problem with the notion of "fair" competition.

Why gender, as opposed to height or bodyweight or muscle mass index or blood testosterone levels? — Banno

Is it gender that sports uses to group athletes? Or is it sex?

If I know it's raining outside then I can't be wrong that it's raining outside. Knowledge entails truth. — Andrew M

A true belief entails truth as well. I guess that it's raining outside and I might be wrong. Even if I guessed correctly. Otherwise "I might be wrong" is only true if I guessed incorrectly, i.e. if I am wrong.

So, either "I might be wrong" can be true even if I have a true belief or "I might be wrong" is only true if I have a false belief.

You said that if we have a justified belief it might be wrong, which is true; but a justified belief is not knowledge, since knowledge is defined as a justified true belief. It is not the case that a justified true belief might be wrong. — Janus

See above.

Isn't a person's self identity largely thrust upon them by society? — sime

I believe so. I suspect I identify as a man because I've been told that I'm a man as I grew up and it stuck.

For society to automatically respect self-identification seems morally problematic, because it would mean for society to automatically reinforce the social treatment a person receives, however dysfunctional and situational. — sime

Do you have specific examples of why it is morally problematic to respect gender self-identity?

So in terms of meaning being use, I rely upon what usage to know if you're a man? That you tell me you are? Is that the only public usage manifestation? — Hanover

You can make an assumption based on appearances if you like, and in most cases you'd be right, but then if you hear me or someone who knows me say otherwise then you'll be corrected.

That strikes me as essentialism. To be a man, it is essential that one believe they are — Hanover

I suppose if you want to say that the essential characteristic of being a man is identifying as a man then it's a kind of essentialism, but I was thinking of essentialism as involving a little more than that when I asserted my rejection of it.

A usage theory requires variability of characteristics and a public meaning, not just an internal state. — Hanover

I'm not convinced by a usage theory of meaning, but maybe that's a topic for another discussion.

It applies to being a man (and woman). I don't know off the top of my head what other things are like this. Maybe being a supporter of Manchester United?

That is, there is something characteristically a man about you, which might not be the same characteristic I have that makes me a man, but some characteristic must be placing you in the man category. — Hanover

I don’t know what any such characteristics would be. I can imagine waking up in a woman’s body, whether by magic or a brain transplant, and yet I’d continue to identify as a man, so it certainly doesn’t have anything to do with my body. And I can’t think of what psychological traits I have, except the obvious of identifying as a man, that would count as being such characteristics.

Again from the first page, but amended to not be about omniscience:

Maybe the problem is with the interpretation of the English sentence. These two don’t mean the same thing:

a) It is possible that I know something and am wrong about that thing
b) I know something and it is possible that I am wrong about that thing

The former is false but the latter seems possible as the arguments show.

I suppose the latter is the implication of fallibilism. If knowledge does not require certainty then I can know and not be certain.

It seems you and others are misinterpreting my position as saying something like a).