506 INTELLECTUAL SYMBOLISM. 
part of the impression conveyed to the mind by the sight of two objects, and we can 
employ that idea in any train of reasoning, with the same unhesitating confidence as we 
give to the simple original perception of two distinct objects. 
176. From these considerations we may discover a sufficient reason for the implicit 
faith that we place in mathematical axioms. Without stopping for the present to inquire 
whence the power is derived, we know that there is a power inherent in our own nature, 
by which we perceive their truth. They constitute a part of our immediate perceptions, 
and each individual is necessarily the only judge of what he himself perceives. 
177. It is often said that our senses deceive us. Is this assertion true, or is it our judg- 
ment that deceives us, and are we led into error by a hasty or improper exercise of our 
own powers ¢ 
178. Let us suppose the following question propounded to a person of sound faculties 
and mature judgment, but one who is entirely ignorant of chemistry, and of the results 
-produced by the mixture of different ingredients. 
“Tf I were to mix two quarts of one fluid, with two quarts of another fluid, how much 
would there be in the whole ?” 
The answer would probably be, “‘ Four quarts.” 
“How do you know that there would be four quarts?” 
“« Because two and two always make four.” 
179. But it could be easily shown, by mixing two quarts of sulphuric acid and two 
quarts of water, that in consequence of the chemical affinity existing between the liquids, 
a condensation would take place, so that there would be less than four quarts of the mix- 
ture. Whence then did the error of opinion arise ? 
180. Certainly not from the mathematical axiom, for our confidence in its truth would 
still be unshaken, but from a hasty judgment, and from losing sight of the precise meaning 
and extent of the axiom. 
181. Suppose again the following conversation with a man well versed in plane geome- 
try, but entirely ignorant of the nature of spherical triangles. 
“To what is the sum of the three angles of a triangle always equal ?” 
“To two right angles.” . 
“Would it be possible to construct a triangle, in which the sum of the angles would be 
either greater or less than two right angles?” 
“Tt would not ?” 
‘«¢ Are you sure of this?” 
“T am, as sure as I am that two and two make four.” 
“And yet, as I will show you upon this sphere, we may describe a triangle, in which 
