It is impossible to know an unknown sentence — Luke
self-referential "paradoxes" are just word games with no intellectual or philosophical significance. — T Clark
Logic is really bad at doing time. — unenlightened
So, either we know that something is true or false or we cannot say anything about its truthness or falseness. — Alkis Piskas
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
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 you don't like the teapot example, substitute any other unknown assertion. — Banno
...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
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
However, it can be shown independently that it is impossible to know this conjunction. Line 3 is false.
Line 3. It's a conclusion, not an assumption. Hence the paradox. — Banno
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
In truth, I had failed to notice that the Wiki argument uses the wrong assumption. Too much faith in Wiki, I guess. — Banno
SO you accept the assumption ∀p (p → ♢Kp) but not the conclusion ∀p (p → Kp)? — Banno
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
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