I understand this but they all must adhere to intra-field principles of logic and not contradictory systems of logic as you would have to agree.
I see where you are coming from, but the funny thing is that there literally is no intra-field all-compassing form of logic.
There simply are separate forms of logic, each with it's own application (as you would understand, some are more useful than others, hence why I gave the mathematical logic example).
You call these different kinds contradictory systems I guess, but they are not comparable. Often they do not really exclude the other forms of logic, because they are more like apples and oranges.
What do you do by the way when logicians and philosophers disagree fundamentally on logic?
Well, here you are generalizing a bit too much again. When logicians and philosophers disagree fundamentally on logic, it's still likely, or probably even inevitable, that one of them simply refers to a non-classical kind of logic and the other to a different kind.
I mostly read Bertrand Russell because Einstein recommends him. But I read Kant and Hume also; who do you recommend?
There are a bunch of books you could look into. I take it you've already read Betrand Russel's Principia Mathematica, but I'd also recommend "Logic and Ontology", Stanford Encyclopedia of Philosophy. There's more, but I'd have to dig in my bookshelf for a bit to find them I think,
Cheers
