proposition nothing more than a certain synthesis of words; or, is it
meant to correspond with something further, a synthesis of ideas, or a
relation of facts?

Conceptualist logicians, who speak of judgments instead of
propositions, of course define the judgment in their own language.
According to Hamilton, it is "a recognition of the relation of
congruence or confliction in which two concepts stand to each other." To
lighten the sentence, I have omitted one or two qualifications
(Hamilton's _Lectures on Logic_, xiii.). "Thus," he goes on "if we
compare the thoughts _water_, _iron_, and _rusting_, we find them
congruent, and connect them into a single thought, thus: _water rusts
iron_--in that case we form a judgment." When a judgment is expressed in
words, he says, it is called a proposition.

But has a proposition no meaning beyond the judgment it expresses? Mill,
who defines it as "a portion of discourse in which a predicate is
affirmed or denied of a subject" (_Logic_, Book 1., chap. iv. § 1.),
proceeds to inquire into the import of propositions (Book 1., chap. v.),
and finds three classes of them: (a) those in which one proper name is
predicated of another; and of these Hobbes's Nominalist definition is
adequate, namely, that a proposition asserts or denies that the
predicate is a name for the same thing as the subject, as _Tully is
Cicero_.

(b) Propositions in which the predicate means a part (or the whole) of
what the subject means, as _Horses are animals_, _Man is a rational
animal_. These are Verbal Propositions (see below: chap. v. § 6), and
their import consists in affirming or denying a coincidence between the
meanings of names, as _The meaning of 'animal' is part of the meaning of