less than 100 have been actually
multiplied together, and the value of the product recorded in the
multiplication table. But we also know that the number of integers is
infinite, and that only a finite number of pairs of integers ever have
been or ever will be thought of by human beings. Hence it follows that
there are pairs of integers which never have been and never will be
thought of by human beings, and that all of them deal with integers the
product of which is over 100. Hence we arrive at the proposition:
'All products of two integers, which never have been and never will
be thought of by any human being, are over 100.' Here is a general
proposition of which the truth is undeniable, and yet, from the very
nature of the case, we can never give an instance; because any two
numbers we may think of are excluded by the terms of the proposition.

This possibility, of knowledge of general propositions of which no
instance can be given, is often denied, because it is not perceived
that the knowledge of such propositions only requires a knowledge of the
relations of universals, and does not require any knowledge of instances
of the universals in question. Yet the knowledge of such general
propositions is quite vital to a great deal of what is generally
admitted to be known. For example, we saw, in our early chapters,
that knowledge of physical objects, as opposed to sense-data, is only
obtained by an inference, and that they are not things with which we are
acquainted. Hence we can never know any proposition of the form 'this
is a physical object', where 'this' is something immediately known. It
follows that all our knowledge concerning physical objects is such that
no actual instance can be given. We can give instances of the associated
sense-data, but we cannot give instances of the actual physical objects.
Hence our knowledge as to physical objects depends throughout upon this
possibility of general knowledge where no instance can be given. And the
same applies to our knowledge of other people's minds, or of any other
class of things of which no instance is known to us by acquaintance.

We may now take a survey of the sources of our knowledge, as they have
appeared in the course of our analysis. We have first to distinguish
knowledge of things and knowledge of truths. In each there are two
kinds, one immediate and one derivative. Our immediate knowledge of
things, which we called _acquaintance_, consists of two sorts, a