al grounds for thinking that an
organism such as a man's body must sooner or later wear out. Neglecting
the second ground, and considering merely our experience of men's
mortality, it is plain that we should not be content with one quite
clearly understood instance of a man dying, whereas, in the case of 'two
and two are four', one instance does suffice, when carefully considered,
to persuade us that the same must happen in any other instance. Also
we can be forced to admit, on reflection, that there may be some doubt,
however slight, as to whether _all_ men are mortal. This may be made
plain by the attempt to imagine two different worlds, in one of which
there are men who are not mortal, while in the other two and two make
five. When Swift invites us to consider the race of Struldbugs who never
die, we are able to acquiesce in imagination. But a world where two
and two make five seems quite on a different level. We feel that such a
world, if there were one, would upset the whole fabric of our knowledge
and reduce us to utter doubt.

The fact is that, in simple mathematical judgements such as 'two and two
are four', and also in many judgements of logic, we can know the general
proposition without inferring it from instances, although some instance
is usually necessary to make clear to us what the general proposition
means. This is why there is real utility in the process of _deduction_,
which goes from the general to the general, or from the general to the
particular, as well as in the process of _induction_, which goes from
the particular to the particular, or from the particular to the general.
It is an old debate among philosophers whether deduction ever gives
_new_ knowledge. We can now see that in certain cases, at least, it does
do so. If we already know that two and two always make four, and we
know that Brown and Jones are two, and so are Robinson and Smith, we can
deduce that Brown and Jones and Robinson and Smith are four. This is
new knowledge, not contained in our premisses, because the general
proposition, 'two and two are four', never told us there were such
people as Brown and Jones and Robinson and Smith, and the particular
premisses do not tell us that there were four of them, whereas the
particular proposition deduced does tell us both these things.

But the newness of the knowledge is much less certain if we take the
stock instance of deduction that is always given in books on logic,
namely, 'All men