Because every speech must contain two elements one indicative, the other symbolic, there is a logical foundation for the separation of a proposition into a subject and predicate. The subject is the part containing the indicative constituent, and from which it cannot conveniently be detached, while the predicate is the part purely symbolic.
In any proposition, i.e., any statement which must be true or false, let some parts be struck out so that the remnant is not a proposition, but is such that it becomes a proposition when each blank is filled by a proper name. The erasures are not to be made in a mechanical way, but with such modifications as may be necessary to preserve the partial sense of the fragment. Such a residue is a predicate. The same proposition may be mutilated in various ways so that different fragments will appear as predicates.
Let a heavy dot or dash be used in place of a noun which has been erased from a proposition. A blank form of proposition produced by such erasures as can be filled, each with a proper name, to make a proposition again, is called a rhema, or, relatively to the proposition of which it is conceived to be a part, the predicate of that proposition.
A dicisign is a sign whose proper interpretant represents the object of the sign to be different from the sign itself, but ignores the distinction between the sign and its interpretant. In order that the proper interpretant may distinguish between the object and the sign itself, it is requisite that the sign should have separate parts representing the sign and its object. [—] The part representing the sign itself is, in propositions, the predicate, while the part representing the object is called the subject.
An ordinary Proposition ingeniously contrives to convey novel information through Signs whose significance depends entirely on the interpreter’s familiarity with them; and this it does by means of a “Predicate,” i.e., a term explicitly indefinite in breadth, and defining its breadth by means of “Subjects,” or terms whose breadths are somewhat definite, but whose informative depth (i.e., all the depth except an essential superficies) is indefinite, while conversely the depth of the Subjects is in a measure defined by the Predicate. A Predicate is either non-relative, or a monad, that is, is explicitly indefinite in one extensive respect, as is “black”; or it is a dyadic relative, or dyad, such as “kills,” or it is a polyadic relative, such as “gives.”