The real problem here is philosophical. Most people have no knowledge of the elementary distinction between a priori and a posteriori knowledge. One is obvious logically and the other is derived from experience.
One is deductive and the other is inductive, if you prefer.
2 + 2 can never, ever equal 5, no matter how many times you hear it or see it written or look at actual objects to try to make it different.
“a posteriori knowledge”
That reads more like pulling it out of your butt, so to speak.