So you need to have knowledge about the rules.
SO doesnt this makes maths knowledge.
Here you yourself say tha you have to apply The rules of mathemathics ,so you already have the knowledge of the rules.
Im aint saying that through logic you cannot get to know more knowledge by testing, experiments etc.
Im just saying that just like in your maths problem your mind will solve and find the answer based on the knowledge it possess.
Now you are going to apply some logic that krishna cannot be basis of brahman since brahman is etc. etc. but that is because you have limited knowlede about brahman.
Though that is a different thing both are beyond mind and intelligence..
Just take another example.
Bhoothnath - Wikipedia, the free encyclopedia
ANother example-
Just take the mind of a five year old child.Now
he is scared of going to dark room because he had heard some ghost story from his brother, so his mother just to remove his fear will say that there is no such things as ghost and there are only devtas.Now because he believes in his mother, in his mind he has decided that ghosts dont exist.
And now even if he sees a ghost he will not beleive that it is a ghost but consider it a devta since his logic is that ghosts dont exist which come from the knowledge that his mother has given him.