e
present state of the world than we have to inquire into the causes of
those causes, and again the still earlier causes, and so on to infinity.
But, this being impossible, we must be content, wherever we stop, to
contemplate the uncaused, that is, the unexplained; and then all that
follows is only relatively explained.

Besides this difficulty, however, there is another that prevents the
perfecting of any theory of the abstract material world, namely (b),
that it involves more than one first principle. For we have seen that
the Uniformity of Nature is not really a principle, but a merely nominal
generalisation, since it cannot be definitely stated; and, therefore,
the principles of Contradiction, Mediate Equality, and Causation remain
incapable of subsumption; nor can any one of them be reduced to another:
so that they remain unexplained.

(3) Another limit to explanation lies in the infinite character of every
particular fact; so that we may know the laws of many of its properties
and yet come far short of understanding it as a whole. A lump of
sandstone in the road: we may know a good deal about its specific
gravity, temperature, chemical composition, geological conditions; but
if we inquire the causes of the particular modifications it exhibits of
these properties, and further why it is just so big, containing so many
molecules, neither more nor less, disposed in just such relations to one
another as to give it this particular figure, why it lies exactly there
rather than a yard off, and so forth, we shall get no explanation of all
this. The causes determining each particular phenomenon are infinite,
and can never be computed; and, therefore, it can never be fully
explained.

Sec. 8. Analogy is used in two senses: (1) for the resemblance of relations
between terms that have little or no resemblance--as _The wind drives
the clouds as a shepherd drives his sheep_--where wind and shepherd,
clouds and sheep are totally unlike. Such analogies are a favourite
figure in poetry and rhetoric, but cannot prove anything. For valid
reasoning there must be parallel cases, according to substance and
attribute, or cause and effect, or proportion: e.g. _As cattle and deer
are to herbivorousness, so are camels; As bodies near the earth fall
toward it, so does the moon; As 2 is to 3 so is 4 to 6._

(2) Analogy is discussed in Logic as a kind of probable proof based upon
imperfect similarity (as the best that can be discovered) be