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.
That part of a proposition whose function it is to ‘indicate,’ or denote, what it is of which the proposition is a sign […], and which it signifies, or indirectly images, in the predicate.
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.
If a sign, A, only denotes real objects that are a part or the whole of the objects denoted by another sign, B, then A is said to be a subject (or substantial part) of B.