It is impossible to know an unknown sentence — Luke

There might be a teapot in orbit around Jupiter.

You know the sentence "there might be a teapot in orbit around Jupiter"

You do not know if there is a teapot in orbit around Jupiter.

Hence you know an unknown sentence.

IF you don't like the teapot example, substitute any other unknown assertion.

self-referential "paradoxes" are just word games with no intellectual or philosophical significance. — T Clark

There are paradoxes that are not self-referential.

Further, paradoxes show problems with the grammar of our expressions. If the grammar is inconsistent, we might be able to improve on it. In this case, logic has developed in multiple directions as a result of puzzling over the paradox - the SEP article lists them in some detail.

Logic is really bad at doing time. — unenlightened

In 4.3 of the SEP article there is an a account of an attempt to take the timeliness of knowledge into account. The discussion is ongoing.

I agree. @Luke seems to have the parsing wrong. The argument shows that if every statement is knowable, then every statement is known. The obvious conclusion is that not every statement is knowable.

It's not the truth value of p which is unknown, because we know that p is true. — Luke

I don't see that we do. In the proof, p is only ever presented as part of a conditional.

So, either we know that something is true or false or we cannot say anything about its truthness or falseness. — Alkis Piskas

So you are going with the rejection of classical logic - you are happy to introduce statements which are neither true nor false?

Are you accepting intuitionist logic or are you moving to paraconsistent logic?

Then I will offer a specific example of p:

1. if the Riemann hypothesis is true then it is possible to know that the Riemann hypothesis is true
2. we don't know that the Riemann hypothesis is true
3. if the Riemann hypothesis is true and we don't know that the Riemann hypothesis is true then it is possible to know that the Riemann hypothesis is true and that we don't know that the Riemann hypothesis is true

It is a fact that we don't know that the Riemann hypothesis is true – it's one of the more significant unproven problems in mathematics. Therefore, we must reject the knowability principle. — Michael

What if the Riemann hypothesis is false? Then we do not reject 1. It is not enough that we don't know whether p is true; it must also be true. "p" means/entails "p is true". This is where the equivocation lies.

¬Kp could mean that we don't know the content/meaning of p and/or that we don't know the truth of p; that we don't know the Riemann hypothesis and/or that we don't know that it is true.

There might be a teapot in orbit around Jupiter.

You know the sentence "there might be a teapot in orbit around Jupiter"

You do not know if there is a teapot in orbit around Jupiter.

Hence you know an unknown sentence. — Banno

If I know the sentence, then how is it an unknown sentence?

IF you don't like the teapot example, substitute any other unknown assertion. — Banno

No such example can be given. As the Wiki article tells us:

...if all truths are knowable, the set of "all truths" must not include any of the form "something is an unknown truth" — Fitch's paradox of knowability

What are your views on K(P) → KP? — Agent Smith

I don't disagree with the conclusion of Fitch's argument, but I don't interpret it to mean that knowability implies the superhuman knowledge of all (known and unknown) true statements, either.

You agree, I assume, that there is a difference between knowing the sentence "There is a teapot in orbit around Jupiter" and knowing that there is a teapot in orbit around Jupiter?

Yes, I agree.

Was there a point to your question?

Only to check a piece of background. Now it's clear I don't understand your point.

Oh I see. I take it you're no longer arguing that it's possible to know an unknown sentence?

Suppose p is a sentence that is an unknown truth; that is, the sentence p is true, but it is not known that p is true. In such a case, the sentence "the sentence p is an unknown truth" is true; and, if all truths are knowable, it should be possible to know that "p is an unknown truth". — Fitch's paradox of knowability

Right, we are supposing, stipulating that the sentence p is an unknown truth, not knowing it, obviously, so what's the problem, where's the paradox? If we come to know that the sentence p is true. then it would no longer be an unknown truth. We would then know that the sentence p was an unknown truth, but is no longer. It seems that changes through time have not been accounted for in this purported paradox of knowability.

rather, I don't see where you think this fits into the Fitch argument.

The premiss is

∀p (p → Kp)

That's not "it's possible to know an unknown sentence".


Edit: Ah - I see; it's the Wiki rendering that sets the assumption out like that. Have a look at the version in SEP, which avoids this problem.

ditto,

rather, I don't see where you think this fits into the Fitch argument. — Banno

Read the OP and see the Wikipedia proof given there (or see Janus' partial quote above). I am following its use of an unknown p.

Yeah, and that is why the proof is problematic. Wiki's is a poor rendering. Fitch's paradox is that if all truths are knowable then all truths are known. The Wiki rendering is dreadful.

So if the thread is about the argument in the Wiki article, it is not about Fitch's paradox.

SEP's proof is much clearer, and does not use the problematic assumption.

What does "¬Kp" refer to there?

p is unknown.

SO the proof works with ∃p( p & ~Kp) in place of the problematic assumption.

And what about ◊K(p∧¬Kp)?

Line 3. It's a conclusion, not an assumption. Hence the paradox.

However, it can be shown independently that it is impossible to know this conjunction. Line 3 is false.

Yes, I had misunderstood the way the sentence was being used, because I was looking at the SEP proof. I was mistakenly trying to make sense of it as a confusion of use and mention. My bad.

Line 3. It's a conclusion, not an assumption. Hence the paradox. — Banno

You said that it wasn't part of Fitch's paradox. Anyway, I agree that it is impossible to know an unknown sentence. You appeared to be arguing that it was possible only a few posts back. I'm not disputing the argument or its conclusion. I am only disputing the assumption regarding its conclusion: that knowability implies knowledge of all (known and unknown) true statements.

Hence you know an unknown sentence. — Banno

Is it the sentence or it's truth value that is unknown?

In truth, I had failed to notice that the Wiki argument uses the wrong assumption. Too much faith in Wiki, I guess.

SO you accept the assumption ∀p (p → ♢Kp) but not the conclusion ∀p (p → Kp)?

Yes, that was what I was thinking, too. But see my error, above.

I think it would be best to stick to the SEP proof.

I do not see any paradox described in your OP.

Wikipedia is written by people who typically do not fully understand what they're confidently pronouncing on.

Suppose p is a sentence that is an unknown truth; that is, the sentence p is true, but it is not known that p is true. In such a case, the sentence "the sentence p is an unknown truth" is true; and, if all truths are knowable, it should be possible to know that "p is an unknown truth". But this isn't possible, because as soon as we know "p is an unknown truth", we know that p is true, rendering p no longer an unknown truth, so the statement "p is an unknown truth" becomes a falsity. Hence, the statement "p is an unknown truth" cannot be both known and true at the same time. Therefore, if all truths are knowable, the set of "all truths" must not include any of the form "something is an unknown truth"; thus there must be no unknown truths, and thus all truths must be known. — Fitch's paradox of knowability

It is just asserted above that all truths are knowable.

Well, no they're not. Demonstrably. For instance, take the proposition 'X is the case and nobody believes X'. Well, that can be true. But it can't be known to be true.

Or take the view that there are no justifications. It's possibly true. But it could never be known to be, for to know something is to have a 'justified' true belief.

So it would appear demonstrable that not all truths are knowable.

Where's the problem? Is the idea that all truths are knowable supposed to be self-evident or something? It isn't.

In truth, I had failed to notice that the Wiki argument uses the wrong assumption. Too much faith in Wiki, I guess. — Banno

Where does it use the wrong assumption?

SO you accept the assumption ∀p (p → ♢Kp) but not the conclusion ∀p (p → Kp)? — Banno

I accept the conclusion, but there is an equivocation whether Kp means knowledge of the sentence or knowledge that the sentence is true.

Well, no they're not. Demonstrably. For instance, take the proposition 'X is the case and nobody believes X'. Well, that can be true. But it can't be known to be true. — Bartricks

It can be true, but is it true? The argument speaks only of possible knowledge (of true statements), not of possible truth.

but there is an equivocation whether Kp means knowledge of the sentence or knowledge that the sentence is true. — Luke

...not in the SEP version...

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