object of Logic is to find how propositions are to be proved. As
preliminary to this, it has been already shown that the Conceptualist
view of propositions, viz. that they assert a relation between two
ideas, and the Nominalist, that they assert agreement or disagreement
between the meanings of two names, are both wrong as general theories:
for that _generally_ the import of propositions is, to affirm or deny
respecting a phenomenon, or its hidden source, one of five kinds of
facts. There is, however, a class of propositions which relate not to
matter of fact, but to the meaning of names, and which, therefore, as
names and their meanings are arbitrary, admit not of truth or falsity,
but only of agreement or disagreement with usage. These _verbal_
propositions are not only those in which both terms are proper names,
but also some, viz. _essential_ propositions, thought to be more closely
related to things than any others. The Aristotelians' belief that
objects are made what they are called by the inherence of a certain
_general substance_ in the individuals which get from it all their
essential properties, prevented even Porphyry (though more reasonable
than the mediaeval Realists) from seeing that the only difference between
altering a non-essential (or _accidental_) property, which, he says,
makes the thing [Greek: alloion], and altering an essential one, which
makes it [Greek: allo] (i.e. a different thing), is, that the latter
change makes the object change its name. But even when it was no longer
believed that there are real entities answering to general terms, the
doctrine based upon it, viz. that a thing's essence is that without
which the thing could neither be, nor be conceived to be, was still
generally held, till Locke convinced most thinkers that the supposed
essences of classes are simply the significations of their _names_. Yet
even Locke supposed that, though the essences of classes are _nominal_,
_individuals_ have _real_ essences, which, though unknown, are the
causes of their sensible properties.

An accidental proposition (i.e. in which a property not connoted by the
subject is predicated of it) tacitly asserts the existence of a thing
corresponding to the subject; otherwise, such a proposition, as it does
not explain the name, would assert nothing at all. But an essential
proposition (i.e. in which a property connoted by the subject is
predicated of it) is identical. The only use of such propositions i