l, however,
has his own view of 'predication.' 'Man' is a mark of John, Peter,
Thomas, and the rest. When I say 'John is a man,' I mean that 'man is
another mark to that idea of which John is a mark.'[524] I am then
able to make a statement which will apply to all the individuals, and
save the trouble of repeating the assertion about each. 'Predication,'
therefore, is simply a substitution of one name for another. So, for
example, arithmetic is simply naming. What I call two and two, I also
call four. The series of thoughts in this case is merely 'a series of
names applicable to the same thing and meaning the same thing.'[525]
This doctrine, as J. S. Mill remarks, is derived from Hobbes, whom
Leibniz in consequence called _plus quam nominalis_.[526] My belief
that two and two make four explains why I give the same name to
certain numbers; but the giving the name does not explain the belief.
Meanwhile, if a class name be simply the mark which is put upon a
bundle of things, we have got rid of a puzzle. Mill triumphs over the
unfortunate realists who held that a class meant a mysterious entity,
existing somewhere apart from all the individuals in which it is
embodied. There is really nothing mysterious; a name is first the mark
of an individual, the individual corresponding to a 'cluster' or a set
of 'simple ideas, concreted into a complex idea.'[527] Then the name
and the complex idea are associated reciprocally; each 'calls up' the
other. The complex idea is 'associated' with other resembling ideas.
The name becomes a talisman calling up the ideas of an indefinite
number of resembling individuals, and the name applied to one
in the first instance becomes a mark which calls up all, or, as
he says, is the 'name of the whole combination.' Classification,
therefore, 'is merely a process of naming, and is all resolvable into
association.'[528] The peculiarity of this theory, as his commentators
again remark, is that it expressly omits any reference to abstraction.
The class simply means the aggregate of resembling individuals without
any selection of the common attributes which are, in J. S. Mill's
phrase, 'connoted' by the class-name. Abstraction, as James Mill
explains, is a subsidiary process, corresponding to the 'formation of
_sub-species_.'[529]

Mill has now shown how the various forms of language correspond to
ideas, formed into clusters of various orders by the principle of
association. The next step will naturally