The most general meaning of “formal” is “concerned with form”,
but the Latin “forma” can mean “beauty” in addition to “form”,
so perhaps a normative “goodness of form” enters at this root.
The Latin word “norma” literally means a “carpenter’s square”.
The Greek “gnomon” is a sundial pointer taking a similar form.
The most general meaning of “normative” is “having to do with
what a person ought to do”, but a pragmatic interpretation of
ethical imperatives tends to treat that as “having to do with
what a person ought to do in order to achieve a given object”,
so another formula might be “relating to the good that befits
a being of our kind, what must be done in order to bring that
good into being, and how to tell the signs that show the way”.
Defining logic as formal or normative semiotic differentiates
logic from other species of semiotic under the general theory
of signs, leaving a niche open for descriptive semiotic, just
to mention the obvious branch. This brings us to the question:
How does a concern with form, or goodness of form, along with
the question of what is required to achieve an object, modify
our perspective on sign relations in a way that duly marks it
as a logical point of view?