Defining formalism and related concepts

I use the term “formal” quite a bit, and to me it has always represented a specific notion. I also identify several variants of the term in various telling contexts. Here I define and articulate this pattern of meaning, just to finally put it down in writing and to have something to reference. I may write this up into a paper one day.

Form: a (pre-)defined shape or structure, the verb is a bit more ambiguous but this is appropriate because forks as nouns are not created, they already exist.

Therefore the noun to form is akin to a nominalization, which may be counter-intuitibe because a nominal form is turning a verb into a noun. Formation is also similar to the nominalizaton, as in a continental formation being the product of a think having been formed.

Form also as a document whose variables are defined and potential values expected.

Formulaic is following a series of rules or functions. Formula is the noun of formulaic. Formula is also an abstraction or procedural representation of a method, ie the formula to create a chemical compound or to derive a value mathematically is like a recipe.

Form as in proper form, as in according to professional expectations or etiquette.

Formal as in according to institutional expectations.