the
principle, and then we realize that the particularity is irrelevant, and
that there is a generality which may equally truly be affirmed. This is
of course familiar in such matters as teaching arithmetic: 'two and
two are four' is first learnt in the case of some particular pair of
couples, and then in some other particular case, and so on, until at
last it becomes possible to see that it is true of any pair of couples.
The same thing happens with logical principles. Suppose two men are
discussing what day of the month it is. One of them says, 'At least you
will admit that _if_ yesterday was the 15th to-day must be the 16th.'
'Yes', says the other, 'I admit that.' 'And you know', the first
continues, 'that yesterday was the 15th, because you dined with Jones,
and your diary will tell you that was on the 15th.' 'Yes', says the
second; 'therefore to-day _is_ the 16th.'

Now such an argument is not hard to follow; and if it is granted that
its premisses are true in fact, no one will deny that the conclusion
must also be true. But it depends for its truth upon an instance of a
general logical principle. The logical principle is as follows: 'Suppose
it known that _if_ this is true, then that is true. Suppose it also
known that this _is_ true, then it follows that that is true.' When it
is the case that if this is true, that is true, we shall say that this
'implies' that, and that that 'follows from' this. Thus our principle
states that if this implies that, and this is true, then that is true.
In other words, 'anything implied by a true proposition is true', or
'whatever follows from a true proposition is true'.

This principle is really involved--at least, concrete instances of it
are involved--in all demonstrations. Whenever one thing which we believe
is used to prove something else, which we consequently believe, this
principle is relevant. If any one asks: 'Why should I accept the results
of valid arguments based on true premisses?' we can only answer by
appealing to our principle. In fact, the truth of the principle is
impossible to doubt, and its obviousness is so great that at first sight
it seems almost trivial. Such principles, however, are not trivial to
the philosopher, for they show that we may have indubitable knowledge
which is in no way derived from objects of sense.

The above principle is merely one of a certain number of self-evident
logical principles. Some at least of these principles must be grante