We can at once see that a pair, having a structure, must present a variety of features; and this is a character in which the dyad differs markedly from the monad, which having no structure nor parts in any sense, is bare of all features except that each one is something peculiar. [—]
A monad has no units. [—]
In the beginning was nullity, or absolute indetermination, which, considered as the possibility of all determination, is being. A monad is a determination per se.
A non-relative name with a substantive verb, as “– is a man,” or “man that is –,” or “–‘s manhood” has one blank; it is a monad, or monadic relative.
…let a number of the proper designations of individual subjects be omitted, so that the assertion becomes a mere blank form for an assertion which can be reconverted into an assertion by filling all the blanks with proper names. I term such a blank form a rheme. [—] If the number of blanks is one, I term the rheme a monad.
A rhema which has one blank is called a monad; a rhema of two blanks, a dyad; a rhema of three blanks, a triad; etc.
In the present application, a medad must mean an indecomposable idea altogether severed logically from every other; a monad will mean an element which, except that it is thought as applying to some subject, has no other characters than those which are complete in it without any reference to anything else; a dyad will be an elementary idea of something that would possess such characters as it does possess relatively to something else but regardless of any third object of any category; a triad would be an elementary idea of something which should be such as it were relatively to two others in different ways, but regardless of any fourth; and so on.