As is yours that there are three types of knowlege that must must remain separate.
Faith has no basis in fact.
It may be defined that way, but most faith is based upon positive statements, either in language or in physical reality. Even people who believe in the Tooth Fairy have at least received some communication implying the Tooth Fairy's existence. And if you can imagine a Tooth Fairy, shall we say what is in your imagination does not exist? It most certainly exists as a thought. Are thoughts outside the realm of science? How can they be when all of science is dependent upon thought in the first place?
Thats not a opinion. Its stated, defined and practiced by each field of knowledge. You should call all the philosophy, science, and mathematics department and advise them that your opinion is that they are interchangeable, definitions should be changed, they should not remain separate and faith and belief should run the show. Get back to me when you have a response from them.
A better summation of FesterWorld could hardly be stated.