...not in the SEP version...

it seems to me to use Kp as knowing p, not knowing of p... — Banno

That's the assumption that I'm challenging. Simply asserting that assumption is not an argument.

Is there any reason/argument why "¬Kp" can only mean that p's truth value is unknown, and not that the sentence p is unknown?

Doesn't "p" entail that p is true?

You've missed the point. There are lots of propositions that can be true - and may well be true as we speak - but which can't be known to be true when or if they are. They're known as 'blindspot' propositions.

There's a number of blades of grass in the world. So make that X. Now I am fairly certain that nobody currently believes that there are that number of blades of grass in the world. So this proposition: "there are x number of blades of grass in the world and nobody believes it" is true. Yet it can't be known to be true.

And I gave you another example. It is entirely possible that no justifications exist. Well, if that's true - if, right now, there are no justifications for any beliefs at all - then it is true that there are no justifications, yet nobody can know it as knowledge requires justification.

So again, what's the problem?

So this proposition: "there are x number of blades of grass in the world and nobody believes it" is true. Yet it can't be known to be true. — Bartricks

Then how do you know that "there are x number of blades of grass in the world and nobody believes it" is true?

Then how do you know that "there are x number of blades of grass in the world and nobody believes it" is true? — Luke

I don't. No one can. That's the point.

'True' does not mean 'known'.

So there's no problem with there being true propositions that are unknown. I mean, there is a number of blades of grass in the world. And no one knows it. So we already know that there are truths that no one knows.

And it would seem that there are some true propositions that, by their nature, cannot be known.

What's the problem?

Like I say, there's no contradiction involved for 'knowledge' involves truth, but truth does not involve knowledge.

So I don't see any puzzle.

Is there any reason/argument why "¬Kp" can only mean that p's truth value is unknown, and not that the sentence p is unknown? — Luke

Yep. The interpetation directly after K principle:

which says, formally, for all propositions p, if p then it is possible to know that p.

It's "know that P", not "know of p".

So this proposition: "there are x number of blades of grass in the world and nobody believes it" is true. Yet it can't be known to be true.
— Bartricks

Then how do you know that "there are x number of blades of grass in the world and nobody believes it" is true?
— Luke

I don't. No one can. That's the point. — Bartricks

But you said that it was true? I'm asking how you know that in the first place before you tell me that it can't be known to be true.

It's "know that P", not "know of p". — Banno

I don't see that it matters.

Is there any reason/argument why "¬Kp" can only mean that p's truth value is unknown, and not that the sentence p is unknown? — Luke

But you said that it was true? — Luke

Yes. So? That a proposition is true does not entail that it is known to be.

Look, this is very simple: this proposition "X is true and no one believes it" can be true. But when or if it is true, it could not be known. Why? Because to know a proposition is to believe it. And if you believe that in that proposition's truth, then it is false. So, when it is true, no one believes it. And thus it is never known to be true.

You're just confusing truth and knowledge, it seems to me. There's no puzzle here.

Yes. So? That a proposition is true does not entail that it is known to be. — Bartricks

But you said that it was true. You both know and don't know that it's true?

Hm. I think I answered that.

You've lost me.

But you said that it was true. You both know and don't know that it's true? — Luke

No. Here are tonight's lottery numbers: 1,2, 3,4,5,6.

Imagine they are. Do I know that those are tonight's lottery numbers? No, for my belief was wholly unjustifed.

So, there's a case of a true proposition that I believe to be true and that is not known.

Anyway, as I keep saying, there are countless examples of propositions that are true and not known, and propositions that do not seem capable of being known.

You've yet to explain to me what the problem is supposed to be. You just keep conflating truth and knowledge.

Knowing that P could equally mean knowing the meaning of the sentence. If you don't know the meaning of the sentence then neither can you know that P is true. That is the reason why P's knowability implies P must be known. The truth value of P is beside the point and merely gets conflated with the meaning of P.

So, there's a case of a true proposition that I believe to be true and that is not known. — Bartricks

I thought you were making a point about (not) all truths being knowable?

Yes. I gave you some examples of such unknowable truths.

Yes. I gave you some examples of such unknowable truths. — Bartricks

But you cannot justify that they are true. Neither can you justify that "there are no justifications" is true.

That does not appear anywhere in the argument. — Banno

Oh! I must be mistaken then. It's been a long time since I read about the paradox. This must be early-onset Alzheimer's. :fear:

Yes, that's why they're not knowable! Sheesh.

There are no justifications.

There. That proposition might be true. Assume it is. Now, we don't know it to be true, do we? We can't. Because if it is true - and assume it is - then no belief is justified.

That proposition might be true. Assume it is. — Bartricks

The knowability thesis is that all truths (i.e. all true statements) are, in principle, knowable.

In order to disprove this, you want me to assume something that might or might not be true? The knowability thesis is about true statements only. If you want to disprove it then use a true statement. You can't just assert that some true statements are unknowable.

The knowability thesis is that all truths (i.e. all true statements) are, in principle, knowable. — Luke

That thesis is demonstrably false. I am demonstrating its falsity by providing you with examples of truths that, if true - and it's metaphysically possible that they are - could not be known.

Note, the existence of such truths is not controversial. They've got a name! They're known as 'blindspot propositions'.

Now, again, what is the problem you're trying to raise?

Knowing that P could equally mean knowing the meaning of the sentence. — Luke

I don't think so. Logic deals in sentences, not meanings of sentences, whatever they are.

Think I'll leave you to it.

That thesis is demonstrably false. I am demonstrating its falsity by providing you with examples of truths that, if true - and it's metaphysically possible that they are - could not be known. — Bartricks

My point is that you don't know whether those statements are true or not; they are only possibly true statements. Therefore, they cannot be used to disprove the claim that all true statements are, in principle, knowable. The knowability thesis is not about possibly true statements. You are claiming that if those statements are true, then not all true statements are knowable. That's a big IF. Unless you can show that they are true, then you have not disproven the knowability thesis.

My point is that you don't know whether those statements are true or not; — Luke

I know! That's the point!

The thesis that every truth is in principle knowable is not, note, the thesis that every truth is actually known. It is that every truth can - in principle - be known.

And it's demonstrably false. There are all manner of propositions that, if true, could not be known. I keep giving you examples. There are LOADS. "No one knows anything" for example.

Now don't reply 'how do you know it's true" - that's the point!! I don't and can't - no one can (save God, of course).

So what problem are you trying to raise? Do you think the knowability thesis has some prima facie plausiblity? It doesn't. It has nothing to be said for it. It's just a false thesis. It may not be obviously false, but it's false upon a bit of reflection.

So what's the problem? Why on earth would one ever think that all truths could be known? It's like thinking all flour is in cakes. No it isn't. There's flour in cakes. But there's no reason to think all flour is cake bound.

I don't think so. Logic deals in sentences, not meanings of sentences, whatever they are. — Banno

The meaning of a sentence is irrelevant to its truth value?

So what problem are you trying to raise? — Bartricks

See the OP and the rest of the discussion.

Do you think the knowability thesis has some prima facie plausiblity? — Bartricks

I can see no reason why any true statement might be unknowable. Let's agree to disagree.

I did read the OP and I explained why it does not raise a problem.

I have asked you umpteen times now to raise a problem. You haven't.

Here are some more problems for us to discuss: the cat/shape problem. My cat has a shape. But some shapes aren't cats. Puzzling.

The hair head problem. My head has hair. But there is some hair that is not on my head. Puzzling.

The language/speak problem. I speak a language. But no language speaks me. Puzzling.

The addition problem. Adding 2 to 2 makes 4. But adding 2 to 3 makes 5. Puzzling.

Sure, if you like. As I said, I'm not following your argument.

Cheers.

When can we assert p? When we have a sound argument that p.

When can we say we don't know p, a truth? When we're not aware of the justification for p and/or we don't believe p (re JTB theory of knowledge).

p is an unknown truth = p & ~Kp = there are good reasons that p is true but either we're in the dark about those reasons and/or we don't believe p or both.

K(p & ~Kp): Since p is an unknown truth is itself a proposition and we know that, K(p & ~Kp).

The rule that's now applied in Fitch's argument is K(r & s) $\to$ Kr & Ks. That's to say K(p & ~Kp) $\to$ Kp & K~Kp.

Kp = We know p i.e. we believe p, p is justified, and p is true.

K~Kp = We know that we don't know p (Socrates).

K~Kp $\to$ ~Kp (the rule here is Kp $\to$ p)

~Kp means that we don't believe p and/or we're not aware of the justifications for p and/or p is false.

Kp & ~Kp isn't a contradiction, appearances can be deceptive (not all the conditions of Kp are negated by ~Kp. p is true in both. Coming to justifications it's not that p doesn't have good ones, we just don't know 'em; etc.)

I'm not following your argument. — Banno

The crux of my argument is that "Kp" conflates the knowledge that:

(a) p (where "p" represents a meaningful proposition); and
(b) p is true

These are both entailed by "Kp".

Note that this is the same distinction that you emphasised earlier between knowing a sentence (e.g. "There is a teapot in orbit around Jupiter") and knowing the truth of that sentence.

Hence, "¬Kp" could mean either that:

(a) p (the meaningful proposition) is unknown; or
(b) p is true is unknown.

Upon further reflection, and thanks in large part to the responses from @Michael, I believe that I am disputing the non-omniscience supposition of the argument:

And suppose that collectively we are non-omniscient, that there is an unknown truth:

(NonO) ∃p(p∧¬Kp) — SEP article on Fitch's paradox

However, I do not claim omniscience. Instead, I would argue that truth implies knowledge. This is the conclusion of the argument, after all: for all p, if p is true, then it is known that p is true. The reason that the (NonO) statement is false is because p is true implies p is known, so there cannot be any p for which p is true and p is unknown. The reason that p is true implies p is known is because p cannot be true without knowing the meaningful proposition represented by p. Again, this results from the equivocation over the meaning of p and the truth of p.

This is just criticism, @Banno. You only present characterizations (names and adjectives). No argumentation. If you want to disprove my statement-position, you must do it with plausible arguments and/or examples. Can you?