So there are unknown truths? — Luke
Not according to Fitch's argument. — Luke
Technically speaking Fitch's argument shows that the knowability principle entails that all truths are known — Michael
BTW, I just realized that my above statement was wrong. And you had the opportunity to easily refute it, if you had paid attention to a detail instead of wondering about what is the type of logic that this statement belongs to. The detail is the word "something". Because one might simply ask: "An apple is 'something'. Can we say that an apple is true or false?" Of course not. It makes no sense. Only a statement or an assertion or a report and that sort of things can be true or false. So my statement was clearly wrong.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 ... — Banno
By everyone always, or by someone at some time? — Luke
I take it all truths are known implies that no truths are knowable (because they are known)? — Luke
But if they are known only by someone at some time, would that imply they can be knowable by others, in order to save KP? — Luke
There are paradoxes that are not self-referential. — Banno
This is true, but Fitch's paradox is self-referential. Actually, after looking at it more, including SEP, I'm not sure it is. It seems more like a tautology, or at least a trivial statement, a language game. Calling a particular statement a truth means the same thing as saying it is true. If I know something is true, it isn't unknown. — T Clark
7. q ∧ ¬Kq → ◊K(q ∧ ¬Kq) (from 1)
8. r ∧ ¬Kr → ◊K(r ∧ ¬Kr) (from 1)
9. ◊K(q ∧ ¬Kq) ∨ ◊K(r ∧ ¬Kr) (from 6, 7, and 8) — Michael
That's right.This has no bearing on Fitch's paradox. — Michael
Fitch's paradox is self-referential. — T Clark
The detail is the word "something — Alkis Piskas
If a conclusion is reached via formal logic which cannot be translated back into plain language and shown to be valid, then something has gone wrong somewhere... — Janus
But the conclusion of Fitch's argument can be "translated back" into plain english - and has been, multiple times, in both articles and in this thread. :roll: — Banno
many arguments are clearer when presented formally. — Banno
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