You find yourself in an unknown land. One thing you ask is who rules there. Everyone except one man says they have a king, named Xerxes. The one man who denies this, a filthy man lying in the street, says he is king.
IS IT AN IRRATIONAL FALLACY TO BELIEVE “This land is ruled by King Xerxes” on the basis of “everyone but one man here says so”?
It’s a sound argument to the best explanation.
But no one can live by demanding deductive certainty about everything. You don’t KNOW with deductive certainty that most of the things you do every day won’t kill you.
1 Almost everyone believes that P is true.
2 The best explanation why almost everyone believes that P is true, is that P is true.
3 So, P is very probably true.
And formal systems have axioms.
And axioms cannot be proven, and so can be disputed.
2 No axioms can be proven
3 So no deductive system as a whole can itself be deductively proven
4 So if you only accept deductive proof, you’ll have none, since you can’t prove your deductive system via deductive proof