proposition will convey as much information as a real one. To say 'The
sun is in mid-heaven at noon,' though a merely verbal proposition,
will convey information to a person who is being taught to attach a
meaning to the word 'noon.' We use so many terms without knowing their
meaning, that a merely verbal proposition appears a revelation to many
minds. Thus there are people who are surprised to hear that the lion
is a cat, though in its definition 'lion' is referred to the class
'cat.' The reason of this is that we know material objects far better
in their extension than in their intension, that is to say, we know
what things a name applies to without knowing the attributes which
those things possess in common.

230. There is nothing in the mere look of a proposition to inform us
whether it is verbal or real; the difference is wholly relative to,
and constituted by, the definition of the subject. When we have
accepted as the definition of a triangle that it is 'a figure
contained by three sides,' the statement of the further fact that it
has three angles becomes a real proposition. Again the proposition
'Man is progressive' is a real proposition. For though his
progressiveness is a consequence of his rationality, still there is no
actual reference to progressiveness contained in the usually accepted
definition, 'Man is a rational animal.'

231. If we were to admit, under the term 'verbal proposition,' all
statements which, though not actually contained in the definition of
the subject, are implied by it, the whole body of necessary truth
would have to be pronounced merely verbal, and the most penetrating
conclusions of mathematicians set down as only another way of stating
the simplest axioms from which they started. For the propositions of
which necessary truth is composed are so linked together that, given