42 
TRANSACTIONS OF THE TEXAS ACADEMY OF SCIENCE. 
found and even radical. For it has caused a different mode of reason¬ 
ing to take the place of that which formerly prevailed in all classes, and 
which still prevails among the least intelligent classes of the present 
time. I have already explained one great difference in the logic of the 
ancient civilized peoples as contrasted with modern scientific logic, and 
which consisted in the assumption of fixed and arbitrary premises. The 
logical forms and processes were syllogistic, and they were highly elabo¬ 
rated by the Greek philosophers and sophists, who often used them with 
great ingenuity. But with premises which were usually either wholly 
false or incomplete, the conclusions were either invalid or imperfect. 
The scanty results thus obtained were just what might have been ex¬ 
pected. With the decay of Greek philosophy the art of reasoning be¬ 
came degraded to lawless, incoherent disputation, which reached its lowest 
state of depravity in the scholasticism of the middle ages. In the dark 
ages nothing was so dark as the reasoning of those who claimed it to be 
their province to enlighten the world. But this was only the proverbial 
darkest hour before the dawn. With the beginnings of modern science 
came the beginnings of new modes of reasoning. Scientific knowledge 
can be reached only by sound methods of research and sound logic, and 
its results must be sustained by their own practical workings in harmony 
with the system of nature. It must begin with the closest possible scru¬ 
tiny of facts; its observations must be accurate, and the observing mind 
must be trained to candor and freedom from bias. The modern art of 
observation calls to its assistance a highly developed system of measure¬ 
ments in all things which are susceptible of measure, to the end that the 
highest attainable accuracy of observation may be secured. Then fol¬ 
lows comparison. Its object is to ascertain what are the natural relations 
existing among observed facts. Here the chief quality of mind demanded 
is candor, or the freedom from any prejudice in favor of one relation 
rather than another, or in favor of any relation except such as the observed 
facts themselves appear to indicate. Next in order comes the generaliza¬ 
tion, or the statement of the natural law. By natural law is meant the 
statement of the relations which natural phenomena bear towards one 
another, as disclosed by observation. The last step is the test of the 
natural law, so formulated, by experiment, whether in the laboratory, or 
in the workshop, or in the daily incidents of human life and human 
action. Those which are sustained by all the tests to which they are 
subjected are ultimately received as true, and those which fail are either 
rejected or amended. 
In dealing with material phenomena, i. e. with the relations of matter to 
time and space and force, most of the relations are quantitative. In deal¬ 
ing with such quantities as mass, time, force and space, modern science has 
developed a logical machinery unknown to the ancients, though some par- 
