igure, got by reduction, are really the same as the original ones, and
as the only arguments of great scientific importance, viz. those in
which the conclusion is a universal affirmative, can be proved in the
first figure alone, it is best to hold that the two elementary forms of
the first figure are the universal types, the one in affirmatives, the
other in negatives, of all correct ratiocination.

The _dictum de omni et nullo_, viz. that whatever can be affirmed or
denied of a class can be affirmed or denied of everything included in
the class, which is a true account generalised of the constituent parts
of the syllogism in the first figure, was thought the basis of the
syllogistic theory. The fact is, that when universals were supposed to
have an independent objective existence, this dictum stated a supposed
law, viz. that the _substantia secunda_ formed part of the properties of
each individual substance bearing the name. But, now that we know that a
class or universal is nothing but the individuals in the class, the
dictum is nothing but the identical proposition, that whatever is true
of certain objects is true of each of them, and, to mean anything, must
be considered, not as an axiom, but as a circuitous definition of the
word _class_.

It was the attempt to combine the nominalist view of the signification
of general terms with the retention of the dictum as the basis of all
reasoning, that led to the self-contradictory theories disguised under
the ultra-nominalism of Hobbes and Condillac, the ontology of the later
Kantians, and (in a less degree) the abstract ideas of Locke. It was
fancied that the process of inferring new truths was only the
substitution of one arbitrary sign for another; and Condillac even
described science as _une langue bien faite_. But language merely
enables us to remember and impart our thoughts; it strengthens, like an
artificial memory, our power of thought, and is thought's powerful
instrument, but not its exclusive subject. If, indeed, propositions in a
syllogism did nothing but refer something to or exclude it from a class,
then certainly syllogisms might have the dictum for their basis, and
import only that the classification is consistent with itself. But such
is not the primary object of propositions (and it is on this account, as
well as because men will never be persuaded in common discourse to
_quantify_ the predicate, that Mr. De Morgan's or Sir William Hamilton's
_quantific