as such is
really contained in or implied by propositions known. Certainty follows.
Yet there is abundant record of 'proofs' or 'tests' which were
fallacious, and of ostensible demonstrations which were flawed--modes of
squaring the circle, for instance. The ultimate in the matter is the
belief arrived at or evoked; and the significant fact for us is, that
beliefs ostensibly so arrived at may be false, because the cited proof
or evidence is erroneous or the demonstration inconsequent.

Certainty, on the other hand, attaches in the highest degree to certain
beliefs that, in the nature of the case, are 'incapable of proof,' that
is, of being tested. No belief is more certain for all men than the
belief that they will all die, though the event, posited as future,
cannot as such be 'tested.' In this case, the connotation of the word
'proof,' nevertheless, is by common consent transferred to the concept
of mortality: the invariable dying of all previous men is allowed to be
'proof,' or decisive evidence, that all living men will die to the last
generation. In regard to some other certainties, the concept of 'proof'
is wholly irrelevant. You cannot 'prove' that you feel a pain, though it
is one of the most certain of all facts for you while it lasts. If,
then, any general scientific or other belief be shown to be 'incapable
of proof,' in this merely negative sense (as distinguished from 'capable
of disproof'), that is no argument against it for any practical or
philosophic purpose. Such a belief is that in the 'uniformity of
nature,' which is held by the same tenure as that in the mortality of
all men. It cannot be 'proved,' either as to the past or the future, in
the sense of being tested, save as regards past particulars, which are
necessarily a small selection from the totality of phenomena. For the
future, in the terms of the case, there can be no proof. Yet no man has
any more doubt as to the rising of the sun to-morrow than as to his own
ultimate death. Concerning this we are quite certain, which we cannot be
as to many things reasonably held to have been 'proved.' Such and such
are our 'certainties.'

What, then, is Mr. Balfour's case against men of 'science,' and those
whom he calls 'the Freethinkers'? It may be put under three heads.

1. They are lax, he thinks, in their conception of proof. As it happens,
he argues against Mill's criticism of the syllogism, which is that there
can be no real inference from the pr