A maxim, or principle, allows us to achieve the highest grade of clarity about the concepts we use. This definition was introduced by Charles Sander Pierce in the 1878 paper “How To Make Our Ideas Clear, says the [Internet Encyclopedia of Philosophy](https://iep.utm.edu/peircepr/#H2).
Peirce identifies three grades of clarity or understanding.
> The first grade of clarity about a concept is to have an unreflective grasp of it in everyday experience. > * For instance, my inclination to keep some part of my body in stable contact with a supported horizontal surface at all times suggests that I have an underlying grasp of gravity. > The second grade of clarity is to have, or be capable of providing, a definition of the concept. > * This definition should also be abstracted from any particular experience, i.e., it should be general. > * So, my ability to provide a definition of gravity (as, say, a force which attracts objects to a point, like the center of the earth) represents a grade of clarity or understanding over and above my unreflective use of that concept in walking, remaining upright, etc. For the third grade of clarity, we would have > ... to have a full understanding of some concept we must not only be familiar with it in day to day encounters, and be able to offer a definition of it, we must also know what effects to expect from holding that concept to be true.
The example is extended with three grades of understanding of "vinegar".
For a first grade of clarity, ... > "I am able to identify vinegar and use the concept appropriately in my everyday experiences". A second grade of clarity is demonstrated through ... > an "ability to define 'vinegar' as a diluted form of acetic acid, which is sharp to the taste," For a third grade of clarity, a list of definitional propositions which indicate what to expect from actions upon, and interactions with, could be derived. Thus, > the second degree of clarity “vinegar is acetic acid” leads to form an explanation that ... > “If vinegar is acetic acid, then if I dip litmus paper into it, it will turn red.”
"The pragmatic maxim, then, is the means for achieving the third grade of clarity in our understanding of a concept".
The maxims on Root Metaphors in World Hypotheses: A Study in Evidence (1942) also come with corollaries.
* A corollary is "something that results from something else", says the [Cambridge Dictionary](https://dictionary.cambridge.org/dictionary/english/corollary)
* By the later 14th century, a corollary is "a proposition inadvertently proved in proving another", says the [Online Etymology Dictionary](https://www.etymonline.com/word/corollary)