Belie

Contradict (v.)

Gottolb Frege, a well-respected and prolific philosopher and mathematician, tried to show that math is really just a kind of logic. He wrote a big book of proofs and explanations showing this. Frege's proofs were based on several "Basic Laws" that he laid at the foundation of his arguments.
It should be noted that people who do things logically are uncomfortable with inconsistencies. Classically, a contradiction is an indication of logical sin. If something is both true and not true in a logician's theory, there falls within him a collapse of mind and heart that is barely imaginable.

(But try to imagine it: A man spends years and years constructing a fantastic castle. After putting the last flag on the final parapet, he rests his eyes. But when he opens them, instead of a vast horizon, he sees the ceiling above his small bed and he feels a dirty sweat settled on his tired, emaciated body. After many seconds of shock he sits up in bed, alone, and finds that he has woken from a long, realistic dream and that he has built nothing.)

A few weeks after the book came out, Frege received a letter from a student named Bertrand Russell. The letter was only a few pages long. In it, Russell gave a proof showing that Basic Law 5, a law upon which Frege's entire system depended, led to a contradiction.
After some discussion with Russell and others about this, Frege found that he could not fix Basic Law 5.
He did not publish anything for the next 14 years.