Wouldn't it then just be "it might be known that there are truths that are not known" rather than " It might be known that there is a truth that is not known" ? Is there a salient difference? — Janus
(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 (1) into KP) — Banno
It seems to me that 'an unknown truth' cannot legitimately be formalised as p but only as (p or ~p) Is that right? does it make sense? — unenlightened
It seems to me that 'an unknown truth' cannot legitimately be formalised as p but only as (p or ~p) Is that right? does it make sense? — unenlightened
There exists some proposition p that is both true and not known to be true — Michael
I am questioning the legitimacy of that. — unenlightened
It seems to be stating a contradiction by asserting p and claiming it to be unknown. — unenlightened
But that's the non-omniscience principle? Without it we must accept that every true proposition is known to be true – which is what Fitch's paradox shows follows from the knowability principle. — Michael
It's not a contradiction to say "there is intelligent alien life but I don't know that there is." Such a statement is possibly true. — Michael
I don't think so. I think the principle needs to be formalised differently, as I indicated. — unenlightened
I think it is a contradiction, because it asserts something and denies that it is known. "Either there is intelligent alien life or there isn't, but I don't know which." -- that makes sense. — unenlightened
(p or ~p) and ~Kp and ~K~p.
Can you work with that a little and see how it goes? — unenlightened
In fact from this I'm pretty sure it follows that ∃q(q ∧ ¬Kq) — Michael
Fitch's paradox shows that if all truths are knowable then all truths are known. Some truths aren't known, therefore some truths aren't knowable.
— Michael
Can you lay out the argument clearly in plain English? — Janus
Why not just accept unknowable truths? — Tate
The paradox is of concern for verificationist or anti-realist accounts of truth, for which the knowability thesis is very plausible,[1] but the omniscience principle is very implausible. — Fitch's paradox of knowability - Wikipedia
More seriously, presumably people who have considered Fitch's paradox do accept that. But from Wikipedia:
The paradox is of concern for verificationist or anti-realist accounts of truth, for which the knowability thesis is very plausible,[1 — Andrew M
A typical deflationist will say that truth only serves a social function. Is someone disagreeing with that? — Tate
She would say we shouldn't be bewitched by language. — Tate
A deflationist does not have a problem with using the word "true" in the normal way. She just resists piling unwarranted projects on top of that normal usage. — Tate
If truth is a property of statements, talk of "unknown truths" might give us unstated statements. Not good. — Tate
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