I take it all truths are known implies that no truths are knowable (because they are known)?
— Luke
In fact the opposite: Kp → ◊Kp. — Michael
Suppose Tom wants to go to the party, but he doesn't know what time it begins. Furthermore, he doesn't even know anyone who does know. So he asks Bill, who doesn't know when the party begins, but he does know that Mary knows. So Bill tells Tom that Mary knows when the party begins. Now Tom knows something, too—that Mary knows when the party begins.
So Tom knows what Mary knows (he knows that she knows when the party begins). Now consider the following argument:
Tom knows what Mary knows.
What Mary knows is that the party begins at 9 pm.
What Mary knows = that the party begins at 9 pm.
Therefore, Tom knows that the party begins at 9 pm.
What is wrong with this argument? It commits the fallacy of equivocation.
In (A), “what Mary knows” means what question she can answer. But in (B) and (C), “what Mary knows” means the information she can provide in answer to that question. — Meno's paradox ambiguity
(1) There is a truth that is not known (instantiation from NonO)
(2) If there is a truth that is not known, then it might be known that there is a truth that is not known
....(sub (2) into KP)
(3) It might be known that there is a truth that is not known — Banno
Can you lay out the argument clearly in plain English? — Janus
The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known [i.e. an unknowable truth]. — Archived SEP article
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Can you lay out the argument clearly in plain English? — Luke
If one of all of the knowable truths (KP) is that we are non-omniscient or that there is an unknown truth (NonO) - in other words, if it is possible to know that there is an unknown truth - then it follows that an unknown truth is knowable.
However, it can be independently shown that an unknown truth is unknowable. — Luke
I don't see how it follows from the fact that we know (if we do know) there are unknown truths that an unknown truth is knowable — Janus
the fact that there are unknown truths (if there are) is not itself an unknown truth (if it is known). — Janus
(1) There are truths that are not known (instantiation from NonO) — Janus
Oliver5, are you proposing that the argument suffers a modal fallacy? Can you set it out explicitly? — Banno
It isn't that we do know there are unknown truths, it is that it is possible to know there is an unknown truth. If it is possible to know, then it is knowable. These terms are simply synonymous. — Luke
the fact that there are unknown truths (if there are) is not itself an unknown truth (if it is known). — Janus
No, but why do you think it should be? — Luke
That's not an instantiation. — Banno
I'm sure you did. And I'm sure you also aware that assumptions can be big traps. :smile:I just assumed your were adopting the convention of restricting that "something" to propositions. And I understood your "simple logic" to be classical logic. — Banno
Thank you for your kindness, Banno. :smile:The principle of charity at work. — Banno
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