Methods of thought are various.
Logic is a certain class of methods of thought.
It’s almost like an orthadoxy: human logic.
It’s quite popular, also, because it can be conveyed in an appealing way.
Some people believe that faith is more important than logic,
so not all agree that logic, in one form or another, is good, or
is the best.
You list a few sympathies.
So you are choosing to catagorize.
I don’t bother catagorizing logic much. I just stick to my main method
and observe others.
The reason you do not see them as necessary is because you have always used only one school of philosophy, which is the philosophy of reason
But how do you study literature, or abstract art, and if you do study these subjects, then you realize there is a philosophical school of the heart, which deems that arguments can be made without much to build on, and these arguments are personal to the person
How can you understand Jung, if not through a philosophical school of concepts
or what is called the common sense philosophy of tupac shaker, without the philosophical school of reality
I believe that by first categorizing these schools and defining them, we can begin the process and finding their rules and methods, and can study each school of philosophy, how they are interconnected, and what their potential is to improving the human condition