There is no way to know the truth
Is this true? Because if so it is a contradiction.
Knowledge and truth are two different things, although I should have written it better. There's no way to know the truth on this particular subject. (Well, there is a way to know theoretically, if a god exists. There isn't a way to know if one doesn't exist though. You can't prove that something that doesn't exist doesn't exist. You can only prove that something exists.)
This is just another way of making a truth claim even though you can't know the truth.
No, you can use logic to prove certain things can't exist. If there's a contradiction, it can't be correct, for example.
Who says seeking truth is something we ought to do? Particularly if knowing the truth is an impossibility. These are all assertions as to what we should do without any justification as to why we should do them.
I'm not making a universal statement. I'm making the statement that someone who values truth should seek truth. That seems self-evident.