Mathematical logic has more freedom then classical logic. I personally describe classical logic, that when its intuitive logical for you, its classical. Everybo

Mathematical logic has more freedom then classical logic. I personally describe classical logic, that when its intuitive logical for you, its classical. Everybody into real logician would scream now, because that is not the definition of course, but I think that classical logic is they way our neural network learns the rules of the universe, because it's logical and we therefor inherit this logic through observation. If things would appear and disappear from thin air in front of our eyes, we would learn this is part of how the world works and therefor would be part of our logic, nobody would say its illogical that something just appeared. I give you an example: You take a equation and you substitute x1 through s1. In mathematical logic, this is always allowed and you can define s1 with whatever as long as it fulfills the rules of math. In classical logic you can't. You have to explain where s1 comes from and in case of physics, what natural law this s1 implements. Hope that helped a bit to clarify, but from my philosophy study I can assure you, logic is a very large field with many different logics and not everything is so clear then most of us think. Very often mathematicians teach logic in the courses, but they are very biased by their mathematical one, while in reality general logic is part of philosophy and much more diverse.