quote  Proved" in this case is only appropriate for mathematics or logics. This is a psychology/epistemology-related claim. And, no, it's not a matter of "agreeing" or "disagreeing" with it!) 
 I will answear to this.If you use logic in a discussion who seems to be philosophical more than mathematical , you use the same "mathematical implication".It's not a claim , it's a proof.A Ph D proof in a scientific domain (theoretical informatics) not a philosophical discussion.Read the text.