His argument is self-defeating. Ultimately, it amounts to: "There is no such thing as truth." But that is a statement about the truth. The law of noncontradict

His argument is self-defeating. Ultimately, it amounts to: "There is no such thing as truth." But that is a statement about the truth. The law of noncontradiction is one of several axioms that are presupposed by any proposition. Such axioms can't be "proven," because any proof would presume their correctness, but it is proper to accept them.