“Objective truth” - I’d love to know how one goes about this, feels like a Nietzsche reading here would be helpful
With contradictions you know what is not true, and through knowing what is not true, you can approach what is true. Truth is expressed in consistency, not completeness.
That's why anyone should be extremely suspicious of anyone who is not, or doesn't care about, being internally consistent.
I also love SMBC's explanation of this: https://smbc-wiki.com/index.php/2010-09-23