14 Feb '18 11:316 edits

I am trying to understand Fitch's paradox of knowability but don't understand it because I don't see any paradox there!

The 'paradox' is supposed to be a challenge to the 'knowability thesis', which states that every truth is, in principle, knowable.

But is that "knowable" only in the present or does that include the future? I initially naturally assumed obviously it must mean the latter but then later got confused into thinking from what wiki says that it may mean only in the present!

Wiki says;

https://en.wikipedia.org/wiki/Fitch%27s_paradox_of_knowability

"...

Proof (of the paradox);

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; ..."

OK, so far so good.

But then it says;

"...and, if all truths are knowable, it should be possible to know that "p is an unknown truth". ..."

OK, But is that supposed to be "possible to know that "p is an unknown truth" in the present or in the future?

Then it says;

"...But this isn't possible, because as soon as we know "p is an unknown truth", we know that p is true, ..."

At this point it looses me completely;

How does us knowing "p is an unknown truth" logically imply that "we know that p is true"?

Where is the contradiction in us knowing "p is an unknown truth" and "we DON'T know that p is true"?

Please somebody enlighten me...

The 'paradox' is supposed to be a challenge to the 'knowability thesis', which states that every truth is, in principle, knowable.

But is that "knowable" only in the present or does that include the future? I initially naturally assumed obviously it must mean the latter but then later got confused into thinking from what wiki says that it may mean only in the present!

Wiki says;

https://en.wikipedia.org/wiki/Fitch%27s_paradox_of_knowability

"...

Proof (of the paradox);

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; ..."

OK, so far so good.

But then it says;

"...and, if all truths are knowable, it should be possible to know that "p is an unknown truth". ..."

OK, But is that supposed to be "possible to know that "p is an unknown truth" in the present or in the future?

Then it says;

"...But this isn't possible, because as soon as we know "p is an unknown truth", we know that p is true, ..."

At this point it looses me completely;

How does us knowing "p is an unknown truth" logically imply that "we know that p is true"?

Where is the contradiction in us knowing "p is an unknown truth" and "we DON'T know that p is true"?

Please somebody enlighten me...