KNOWLEDGE AND FAITH. 505 
170. There is, then, a difference in the character of propositions that may be presented for 
our consideration. In what does this difference consist? Why do we require a greater 
amount of information, and a closer investigation in one instance than in another? What 
are the characteristics of truth, and on what authority can we rely as the arbiter of cer- 
tainty? What is the nature of fundamental truth, and in what manner should we pro- 
ceed to increase our knowledge, by the comparison of fundamental truths? 
171. The most obvious knowledge is that which is purely sensual. 
172. Whatever views we may hold with regard to our spiritual nature, or the object of 
our being, we cannot overlook our intimate connection with the material universe. That 
connection is maintained and recognized by the five senses, which we possess in common 
with many of the inferior animals. The evidence of the senses is purely personal. We 
neither require any higher authority than ourselves to decide whether we really see and 
feel, nor can we admit any right or possibility inherent in any superior being, to give 
validity to our sensations. Ifa ball is placed in my hand, I may question as to its nature, - 
the nature and attributes of matter, the relation which exists between the ball and my 
perceptions, the mode in which a knowledge of its existence is conveyed to my brain, but 
I cannot doubt,—in other words, I know that I see and feel,—that there is a something, 
—call it matter, force, spirit, or whatever you will,—that produces sensations, the aggre- 
gate of which I define by the term sphere. 
173. Among the most obvious ideas suggested to us by the senses of touch and sight, 
are those of form and proportion. ‘The idea of proportion is also conveyed by the ear, 
since all harmony requires that a determinable mathematical relation shall exist between 
different vibrations. We have also other sensual ideas, such as those of light, color, heat, 
taste, smell, between which it is more difficult to discern any general connection. But even 
in some of these the laws of proportion are traceable, and if the undulatory theories of light 
and heat are correct, nearly all the impressions of our senses may be subjected to mathe- 
matical calculation. 
174. Mathematics may be defined as “the science of form and proportion,” proportion 
including the idea of number. Its demonstrations are obtained by observing the relations 
between certain axioms, or self-evident truths. The relations, as well as the axioms them- 
selves, must be self-evident, and they are self-evident because all sensual perceptions are 
self-evident, there being no tribunal conceivable higher than ourselves to which they can 
be referred for decision. 
175. It is true that most of the propositions of pure mathematics are abstract and 
general. There is therefore a mental effort superadded to the sensible impression. But 
this effort is made by ourselves, in our own right, and constitutes a part of the judgment 
from which no appeal is either possible or desirable. ‘Thus the abstract idea of two, is 
