The copula is a mere sign of predication, though it is often confounded with to be, the verb of existence (and that not merely by Greeks, but even by moderns, whose larger experience how one word in one language often answers to several in another, should have saved them from thinking that things with a common name must have a common nature). The first division of propositions is into Affirmative and Negative, the copula in the latter being is not. Hobbes and others, by joining the not to the predicate, made the latter what they call a negative name. But as a negative name is one expressing the absence of an attribute, we thus in fact merely deny its presence, and therefore the affirmative guise these thinkers give to negative propositions is only a fiction. Again, modal propositions cannot be reduced to the common form by joining the modality to the predicate, and turning, e.g. The sun did rise, into, The sun is a thing having risen; for the past time is not a particular kind of rising, and it affects not the predicate, but the predication, i.e. the applicability of the predicate to the subject. There are, however, certain cases in which the qualification may be detached from the copula; e.g. in such expressions as, may be, is perhaps; for, then we really do not mean to assert anything about the fact, but only about the state of our mind about it, so that it is not the predication which is affected: e.g. CÆsar may be dead, may properly be rendered, I am not sure that he is alive.

The second division is into Simple and Complex. Several propositions joined by a conjunction do not make a complex proposition. The conjunction, so far from making the two one, adds another, as being an abbreviation generally of an additional proposition: e.g. and is an abbreviation of one additional proposition, viz. We must think of the two together; while but is an abbreviation of two additional propositions, viz. We must think of them together, and we must recollect there is a contrast between them. But hypothetical propositions, i.e. both disjunctives and conditionals, are true complex propositions, since with several terms they contain but a single assertion. Thus, in, If the Koran comes from God, Mahomet is God's prophet, we do not assert the truth of either of the simple propositions therein contained (viz. the Koran comes from God, and Mahomet is God's prophet), but only the inferribility of one from the other. The only difference, then, between a hypothetical and a categorical proposition, is that the former is always an assertion about an assertion (though some categoricals are so likewise; e.g. That the whole is greater than its parts, is an axiom). Their conspicuous place in treatises on Logic arises from this attribute which they predicate of a proposition (for a proposition, like other things, has attributes), viz. its being an inference from something else, being, with reference to Logic, its chief attribute.

The third common division is into Universal, Particular, Indefinite, and Singular. A proposition whose subject is an individual name, even if not a proper name, is singular, e.g. The founder of Rome was killed. In particular propositions, if the part of the class meant by the some were specified, the proposition would become either singular, or universal with a different subject including all the part. Indefinite in Logic is a solecism like doubtful gender in grammar, for the speaker must mean to make either a particular or a universal assertion.