lid, or whatever
his modern substitute may be, has to be taught; but that does not show
that Geometry is an arbitrary system {65} invented by the ingenious and
interested devices of those who want to get money by teaching it.
Arithmetic was invented largely as an instrument of commerce; but it
could not have been invented if there were really no such things as
number and quantity, or if the human mind had no original capacity for
recognizing them. Our scientific ideas, our political ideas, our ideas
upon a thousand subjects have been partly developed, partly thwarted
and distorted in their growth, by similar influences. But, however
great the difficulty of getting rid of these distorting influences and
facing such questions in a perfectly dry light, nobody suggests that
objective truth on such matters is non-existent or for ever
unattainable. A claim for objective validity for the moral judgement
does not mean a claim for infallibility on behalf of any individual
Conscience. We may make mistakes in Morals just as we may make
mistakes in Science, or even in pure Mathematics. If a class of forty
small boys are asked to do a sum, they will probably not all bring out
the same answer: but nobody doubts that one answer alone is right,
though arithmetical capacity is a variable quantity. What is meant is
merely that, if I am right in affirming that this is good, you cannot
be likewise right in saying that it is bad: and that we have some
capacity--though doubtless a variable capacity--of judging which is the
true {66} view. Hence our moral judgements, in so far as they are true
judgements, must be taken to be reproductions in us of the thought of
God. To show that an idea has been gradually developed, tells us
nothing as to its truth or falsehood--one way or the other.

(3) In comparing the self-evidence of moral to that of mathematical
judgements, it is not suggested that our moral judgements in detail are
as certain, as clear and sharply defined, as mathematical judgements,
or that they can claim so universal a consensus among the competent.
What is meant is merely (_a_) that the notion of good in general is an
ultimate category of thought; that it contains a meaning intelligible
not perhaps to every individual human soul, but to the normal,
developed, human consciousness; and (_b_) that the ultimate truth of
morals, if it is seen at all, must be seen immediately. An ultimate
moral truth cannot be deduced from, or p