- #1

- 127

- 5

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.

But isn't this plain wrong just by common sense? Because 'All truths are knowable' certainly doesn't mean 'All truths are already known'. Because consider a universe in which there's a house in which only one person lives. There is nothing else in the universe. There are only two truths about the universe. Both truths are written on two different pieces of paper, one piece is hidden in the kitchen and the other in the balcony. So, both truths are knowable to the person, they just have to check the kitchen and the balcony, but that clearly does not mean 'both truths are already known to the person. So, something MUST be wrong with the proof, right?