There are two branches of reasoning, one is called Logic, and the other is Analogic.
In order to understand the difference between them one has to understand the Two-Element Metaphysics which disappeared in history. The work of Plato was based on it, and Aristotle has preserved observations on it, however, Aristotle did not understand it and made a mess of things.
As aristotle pointed out, there is a way to think of “part” differently than what normal people do. We can think of parts of a thing as a things form and the material in that form. This gives everything two parts, or two elements.
To make anything then we need material and form. How often have you heard that the statue was always in the stone, etc.
Now this gives us the two branches of reasoning, Logics and Analogics. In logics the forms are a given, ie, the symbol set and conventions of generating strings of symbols to make in names the material for those names is acquired by participating in the naming covention, by direct abstraction from the environment or what Aristotle called induction, and Analogics where the material is a given and one learns how to divided it, to form it shape it. The convention for applying forms are standards. For example, in geometry, any tool that provide one and only one difference between two points, generally believed to be the compass, straight edge and ellipse. With these one can solve the Delian Problem as I did.
Now, it stands to reason that each branch of reasoning must produce the same thing. It does not matter if you start with form and apply material or start with material and apply form. This does not mean that because they can produce the same things, and must, that one can produce as well in the one as the other. For example, take the Logic arithmetic. One cannot always, due to the naming convention, produce the name of a thing, whereas in the analogic of geometry one can. Irrationality is the inability to produce a name in accordance with a grammars naming convention. So, where arithmetic one cannot be rational, in algebra they can.
A formal system is as the Greeks demanded. One says the same thing in a logic that they have said in an analogic, this format was demonstrated by Euclid. I also demonstrate it in all my works, the Delian Quest and Jacob’s Ladder series.
So, a formal system must present both branches of reasoning side by side in order to construct something. That something was once called wisdom.
So, as in the Delian Quest, the geometric figure is an analogic, and is to be read just as much as the equations with the figure that say the same thing.
It also means that if one cannot produce the complimentary grammar they really do have a lot more work to do before they start crowing about how wise they are.
Now it has become a popular thing to retreat into so called systems and run from common logics like common grammar arithmetic etc, as a means not of promoting reasoning, but of promoting one’s ignorance of linguistic facts being explored by a few ancient Greeks.