Kinds of Simple and Compound Propositions

In one line

Simple propositions are divided by what they assert of what, and compound propositions by the connective that joins their components.

In the wording a student can write in an examination: a simple proposition contains no component proposition, and is either subject-predicate or relational in form. A compound proposition contains at least one component, and is classified by its connective as negative, conjunctive, disjunctive, implicative or equivalent.

The notation, once and for all

Simple propositions are written as single letters, p, q, r. Brackets group, exactly as in arithmetic: ~(p • q) is the denial of the conjunction, while ~p • q is the conjunction of a denial with q, and the two are different propositions.

Kinds of simple proposition

Subject-predicate propositions, also called attributive. A quality is asserted of a thing. "Ravi is a minor." "The document is registered." This is the only form traditional logic recognised.

Relational propositions. A relation is asserted to hold between two or more things. "Ravi owes Meena two lakh rupees." "The mortgagee is entitled to redeem from the mortgagor." "A paid B on behalf of C." Modern logic treats the relation as the predicate and the things related as its arguments, of which there may be two, three or more. This is the answer to failure one of sequence 320.

Class-membership and class-inclusion propositions. "Ravi is a lawyer" puts an individual into a class. "All lawyers are graduates" puts one class inside another. Traditional logic ran the two together, because both look like "S is P", and the difference matters: the first has an individual as its subject and the second a class.

The two terms of a relation have names, and MU asks for them. The term from which the relation proceeds is the referent; the term to which it proceeds is the relatum. In "Ravi owes Meena two lakh rupees", Ravi is the referent and Meena the relatum. In "the mortgagor redeemed from the mortgagee", the mortgagor is the referent. Inference by converse relation, at sequence 530, is the operation that exchanges the two.

A caution about relational propositions. The order of the terms is part of the proposition, which is to say that referent and relatum cannot be swapped without changing what is asserted. "Ravi owes Meena" and "Meena owes Ravi" are different propositions, and no rearrangement of one gives the other. This is obvious and it is exactly what the traditional form could not record, since both would reduce to a subject with a predicate attached.