CLARENCE E. DUTTON-RELATION OF SCIENCE TO CIVILIZATION. 43 
tial elements of it were contained in their geometry. This logical 
machinery may be called by the name Algebra in the broader sense of 
that word, though it is common to use the more wordy designation of 
analytical mathematics. Algebra in the broader sense is the logic of 
quantity. As a reasoning machine, within the limits of its capacity it is 
logically perfect. But as it is a machine, it is in nowise responsible for 
the data which may be supplied to it to operate upon. As Huxley has 
remarked, the mathematical machine always grinds true, but the grist it 
turns out will depend upon what is fed into the hopper. If the results 
yielded by algebraic analysis are false, we may still know that the error 
is to be sought, not in the algebraic reasoning, but in the data submitted 
to its operation—in other words, in the premises. This is an enormous 
gain. In the old syllogistic and scholastic methods the reasoning might 
be erroneous, indeed, generally was erroneous, at any step in the syl¬ 
logism. In the modern analytical methods the errors may be chased into 
one corner, where they can be hunted for and ferreted out within a nar¬ 
row space. 
This surer and sounder mode of modern reasoning was at first, and 
within two or three centuries, understood and appreciated only by a few 
men of science. But during the present century especially it has diffused 
itself among wider and more numerous classes of men, and is already 
reaching in some measure, though in a very imperfect one, to all classes 
except the most ignorant and uneducated. Would that it were universal! 
But we have to consider the enormous load of prejudice it has been 
obliged to encounter and the fixity of old notions and traditions, old 
habits of thought, which seem to have become hereditary and ingrained 
in all races. Moreover the scientific logic is intrinsically difficult to 
master and is beyond the grasp of minds which are either deficient in 
natural acuteness or else have lacked the training and opportunities to 
master it. Although these modes of thought have thus far diffused them¬ 
selves imperfectly and in diminishing degree as we descend in the scale 
of intelligence, it is absolutely clear that the effects have been great 
and highly beneficial. We have but to look back a few generations to 
recognize the fact that old superstitions, many of them harmful and even 
cruel and all of them ridiculous, have either vanished or become limited 
to the lowest order of intelligence. Among these old and almost extinct 
beliefs are those concerning witchcraft and magic, evil spirits casting 
baneful influences upon mankind, the visitations of ghosts, and attribut¬ 
ing unaccustomed events or striking coincidences to miraculous interven¬ 
tions, the casting of horoscopes, the telling of fortunes, and the use of 
charms against accident or disease. These superstitions are greatly di¬ 
minished though by no means wholly extinct. Nor are they easy to con¬ 
quer even in minds whose intelligence should lead us to expect from 
