504 INTELLECTUAL SYMBOLISM. 
CHAPTER V. 
KNOWLEDGE AND FAITH. 
“ Ave those who would make man the measure of all things, sure that they have found man’s true measure ?” 
The Patience of Hope: Boston ed., p. 84. 
163. THE object of every science is the discovery of truth. 
164. In many investigations, as for instance in the propositions of Geometry, we arrive 
at results which it is impossible to doubt,—results which are recognized as necessary by 
every one who can understand the train of reasoning by which they were obtained. The 
argument which conveys this necessary and universal conviction, is called demonstration, 
~ and the sciences which are built upon demonstration are called exact sciences. 
165. But in the inquiries which are of the most general interest, such as the character 
of our own being, our relation to our fellow-men and to the universe in which we are 
placed, our duties and the proper mode of determining them, conflicting opinions are held 
and zealously maintained. Demonstration of mental and of moral truth seems unattain- 
able, and if we seek for illumination from the writings of metaphysical philosophers, we 
can hardly fail of being led into skepticism or universal doubt, and we may esteem our- 
selves fortunate, if we are able to pass over the abyss of doubt into settled conviction, or 
even into partial belief. ' 
166. Two and two make four. The three angles of a triangle are equal to two right 
angles. 
167. These two propositions are mathematical truths, the first being an axiom or self- 
evident proposition, the other a theorem or demonstrable proposition. Every intelligent 
person accepts them without hesitation, and without requiring a strict definition of all the 
terms employed. The meaning of two, three, and four, of angle, right angle, and triangle, 
is supposed to be sufficiently obvious, and such questions as ‘“‘ How do you know that two 
is always two?’ ‘ How do you know what an angle is?” would be generally regarded as 
indications of impertinence, or insanity. 
168. Every effect must have a cause. God is. The soul is immortal. 
169. These three propositions are all metaphysical. We may not perhaps be able to 
decide upon their truth or falsity, until we have obtained satisfactory answers to questions 
like the following. What is an effect? What is a cause? What is God? What is the 
soul? What is immortality? How do we know that an effect must have a cause,—that 
there is a God,—that the soul is immortal ? 
