ccording
as the things known are particulars or universals. Among particulars, we
have acquaintance with sense-data and (probably) with ourselves. Among
universals, there seems to be no principle by which we can decide which
can be known by acquaintance, but it is clear that among those that
can be so known are sensible qualities, relations of space and time,
similarity, and certain abstract logical universals. Our derivative
knowledge of things, which we call knowledge by _description_, always
involves both acquaintance with something and knowledge of truths. Our
immediate knowledge of _truths_ may be called _intuitive_ knowledge,
and the truths so known may be called _self-evident_ truths. Among such
truths are included those which merely state what is given in sense, and
also certain abstract logical and arithmetical principles, and (though
with less certainty) some ethical propositions. Our _derivative_
knowledge of truths consists of everything that we can deduce from
self-evident truths by the use of self-evident principles of deduction.

If the above account is correct, all our knowledge of truths depends
upon our intuitive knowledge. It therefore becomes important to consider
the nature and scope of intuitive knowledge, in much the same way as,
at an earlier stage, we considered the nature and scope of knowledge by
acquaintance. But knowledge of truths raises a further problem, which
does not arise in regard to knowledge of things, namely the problem of
_error_. Some of our beliefs turn out to be erroneous, and therefore
it becomes necessary to consider how, if at all, we can distinguish
knowledge from error. This problem does not arise with regard
to knowledge by acquaintance, for, whatever may be the object of
acquaintance, even in dreams and hallucinations, there is no error
involved so long as we do not go beyond the immediate object: error can
only arise when we regard the immediate object, i.e. the sense-datum,
as the mark of some physical object. Thus the problems connected
with knowledge of truths are more difficult than those connected
with knowledge of things. As the first of the problems connected
with knowledge of truths, let us examine the nature and scope of our
intuitive judgements.

CHAPTER XI. ON INTUITIVE KNOWLEDGE

There is a common impression that everything that we believe ought to be
capable of proof, or at least of being shown to be highly probable. It
is felt by many that a belief