1+1=2 if our standard is "a preponderance of the evidence," the same standard that a court used to find OJ Simpson "responsible for the deaths" of his ex-wife and an associate of hers. But using a higher standard of proof a different court found him not guilty of their murders. There are many other factors involved that make that a less than ideal example, but it's well known. It illustrates that a thing can be "proven" by one standard but fail to be proven by another standard.
1+1= 2 can be proven by the lesser standard which is basically saying it is more likely than not to be true.
But to actually prove it would be difficult. If we started calling expert witnesses in the fields of mathematics, physics, philosophy and other fields, depending on the budget and the time allowed for the trial, we might begin to doubt that 1 = 1.
Doubt is good!
But what is doubt? A method to establish if something is true or not and using the outcome to create a certainty, a base from which you can use to accomplish " something ". To create things, visible, factual, things that are now part of technology. When I look outside my window I can see many of those things, like cars, houses, and I'm using a tablet to type things, that couldn't be made if 1+1 wasn't 2. Mind you before that, there had to be an imagination, a fantasy, of a house, a car, a phone.
That, for me is evidence based logical reasoning. In principal.
It's a bit like a scientifical method.
The supposition: The terrible snowman exist is a useful one cause you can prove it by finding him.
The supposition: The terrible snowman does not exist is not useful cause by not finding him you didn't prove, can't prove, he doesn't exist.
In science the only question that can be answered is a logical question.
Illogical questions can be answered but the answers are bound to be illogical too.
There are many standards, I agree. But the only one based on hard, coldstone facts and useful is a logical standard in the scientific sense.
I agree the jurisdictional system is a system based on another type of so-called logic. The Aristotelian one.
But that is not based on mathematics, like 1+1=2. And therefore not scientific.
I like to think, suppose, that creating art, like music, literature, prose, poetry, films, photography, painting, architecture, is like researching science but without prove. Without evidence. It uses the same method. Is it therefore of a lesser value? Not to me, but I know there are different opinion on that.
By the way I found out that not that many years ago but before my time, the entity Academy consisted of 3 territories; Education, Science and Arts. They were for a long time considered to be belonging to the same environment in a classical sense. Deriving from the Greec and Roman culture.
Due to developments like specialisation this is no longer the case although I read 2 articles promoting it, and reasoning there would be great or greater benefits from it. I don't know, not an expert but it sounded great.
Because they are not there. Logically speaking, and as far as we know. You could say 1+1= 3. And assume synergy. But that has noting to do with logic itself. 
