out introducing the "Self." Further, the "Self," as defined, can be nothing but a bundle of
perceptions, not a new simple "thing." In this I think that any thoroughgoing empiricist must agree
with Hume.
It does not follow that there is no simple Self; it only follows that we cannot know whether there
is or not, and that the Self, except as a bundle of perceptions, cannot enter into any part of our
knowledge. This conclusion is important in metaphysics, as getting rid of the last surviving use of
"substance." It is important in theology, as abolishing all supposed knowledge of the "soul." It is
important in the analysis of knowledge, since it shows that the category of subject and object is
not fundamental. In this matter of the ego Hume made an important advance on Berkeley.
The most important part of the whole Treatise is the section called "Of Knowledge and
Probability." Hume does not mean by "probability" the sort of knowledge contained in the
mathematical theory of probability, such as that the chance of throwing double sixes with two dice
is one thirty-sixth. This knowledge is not itself probable in any special sense; it has as much
certainty as knowledge can have. What Hume is concerned with is uncertain knowledge, such as is
obtained from empirical data by inferences that are not demonstrative. This includes all our
knowledge as to the future, and as to unobserved portions of the past and present. In fact, it
includes everything except, on the one hand, direct observation, and, on the other, logic and
mathematics. The analysis of such "probable" knowledge led Hume to certain sceptical
conclusions, which are equally difficult to refute and to accept. The result was a challenge to
philosophers, which, in my opinion, has still not been adequately met.
Hume begins by distinguishing seven kinds of philosophical relation: resemblance, identity,
relations of time and place, proportion in quantity or number, degrees in any quality, contrariety,
and causation. These, he says, may be divided into two kinds: those that depend only on the ideas,
and those that can be changed without any change in the ideas. Of the first kind are resemblance,
contrariety, degrees in quality, and proportions in quantity or number. But spatio-temporal and
causal relations are of the second kind. Only relations of the first kind give certain knowledge; our
knowledge concerning the others is only probable. Algebra and arithmetic are the only sciences in
which we can carry on a long chain of reasoning without losing certainty.