ol4 INTELLECTUAL SYMBOLISM. 
OISh Ay IP a0 1d Jay |W Ie 
CHARACTER AND LIMITS OF BELIEF AND CERTAINTY. 
212. WE must be careful to distinguish between /nowledge and belief, for whatever we 
know can never be denied by any one else, but our belief may be modified by errors that 
have been inadvertently admitted. Knowledge is uniform,—belief is manifestly various ; 
the knowledge of one age can neither be falsified nor weakened by the discoveries of 
a subsequent age, but systems of belief have their rise and fall, and are constantly under- 
going modification. 
213. Is such knowledge as I include in my definition possible? Are there any facts 
which we can assert with absolute certainty,—without reference to our own constitution, 
or the constitution of things around us,—truths independent of all accidental circum- 
stances, independent even of the power of Omnipotence, necessary, indubitable, incontro- 
vertible? Most assuredly there are. We know that we have an existence, a personal 
being,—that we have certain sensations, thoughts, impulses,—that there is an existence 
exterior to ourselves, exerting an influence upon us, and capable of being influenced to 
some extent by us. If we are asked how we know all this, we can only answer that we 
know it,—that we have a faculty given to us by our Creator, which can perceive truth, 
and know it to be truth. Could that faculty receive any greater authority than it already 
has? We feel that it could not. We know that it could not. We may prove that it 
could not. Even without paying any regard to the source of its authority, we see that if 
any higher tribunal should attempt to strengthen our conviction, it must do so by appeal- 
ing to this very faculty. In order to have any confidence in the teacher, we must know 
that he is authorized to teach; the final appeal is therefore necessarily to ourselves,—to 
our own power of knowing. 
214. We are apt to confound certainty with demonstrability,—to think that some doubt 
attaches to all that cannot be proved. We hear much said, and deservedly said, in favor 
of mathematical science, and the rigorous exactness of mathematical reasoning.* We 
* On the other hand, many writers have disparaged the study of mathematics. Hamilton says (Discussions, 
pp: 267-312), “If we consult reason, experience, and the common testimony of ancient and modern times, none 
of our intellectual] studies tend to cultivate a smaller number of the faculties, in a more partial or feeble manner 
than mathematics. . . . The first authority is that of Bernhardt, one of the most intelligent and experienced 
authorities on education to be found in Prussia. 
“¢Tt is asked, Do mathematics awaken the judgment, the reasoning faculty, and the understanding in general 
