Formal Logic its legitimate place among the essentials of scientific
procedure, Sir W. Hamilton was at the same time enlarging it on its
technical side, in two modes which are highly esteemed both by himself
and by others: 1. The recognition of two kinds of Syllogisms; one in
Extension, the other in Comprehension: 2. The doctrine of the
Quantification of the Predicate.--Both these novelties are here
criticised by Mr Mill in chapter xxii., which we recommend the reader to
peruse conjointly with Lectures 15 and 16 of Sir W. Hamilton on Logic.

Now whereas the main objection, by which the study of the syllogistic
logic has been weighed down and discredited in modern times, is this,
that it encumbers the memory with formal distinctions, having no useful
application to the real process and purposes of reasoning--the procedure
of Sir W. Hamilton might almost lead us to imagine that he himself was
trying to aggravate that objection to the uttermost. He introduces a
variety of new canons (classifying Syllogisms as Extensive and
Intensive, by a distinction founded on the double quantity of notions,
in Extension and in Comprehension) which he intimates that all former
logicians have neglected--while it plainly appears, even on his own
showing, that the difference between syllogisms, in respect to these two
sorts of quantity, is of no practical value; and that 'we can always
change a categorical syllogism of the one quantity into a categorical
syllogism of the other, by reversing the order of the two premises, and
by reversing the meaning of the copula' (Lect. xvi. p. 296); nay, that
every syllogism is already a syllogism in both quantities (Mill, p.
431). Against these useless ceremonial reforms of Sir W. Hamilton, we
may set the truly philosophical explanation here given by Mr Mill of the
meaning of propositions.

'All judgments' (he says--p. 423), 'except where both the
terms are proper names, are really judgments in
Comprehension; though it is customary, and the natural
tendency of the mind, to express most of them in terms of
Extension. In other words, we never really predicate
anything but attributes; though, in the usage of language,
we commonly predicate them by means of words which are names
of concrete objects--because' (p. 426)--'we have no other
convenient and compact mode of speaking. Most attributes,
and nearly all large bundles of attributes, have no names of