163 
are called axioms, because they are self-evident, and must be 
assented to the moment they are placed before the attention. 
No person on earth could persuade a sane man that two straight 
lines may enclose a space. The axiom in this, its generalized 
form, is assumed, because it is a necessary judgment, an afhima- 
tion we are compelled to make by our mental nature, and which 
is independent of observation and experience, and so cannot be 
proved by them. Observation may tell us that no two straight 
lines we ever saw can enclose a space, but what they may ao 
in other worlds and under different schemes of government 
cannot thus be told us. Observation and experience cannot 
generalize that which has never been observed or experienced. 
Mathematical and indeed all reasoning proceeds on principles 
which cannot be proved by reasoning, but must be assumed as 
true. Back of all lies the great universal axiom that whatever 
consciousness says is true. Beyond all controversy, whatever 
consciousness affirms must be assumed as true, otherwise reason- 
in- is a waste of time. Every man, for example, is conscious 
of his own existence ; he would not attempt to deny it, and as 
little would he think of proving it. If he is at liberty to deny 
any one of all its utterances, he is at liberty to deny this; it, 
however, he may not reject this, neither may he reject any 
0t 'rVe have, therefore, certain elementary principles of 
thought, which, being first principles, are incapable ot analysis ; 
are intuitive, not being derived from observation ; and are con- 
sequently universally self-evident. Any proposition which is 
self-evident is axiomatic; it is not necessary that it should be 
intuitive. The axioms of geometry would not be less axioms 
could it be proved that they are derivative, nor would the 
reasoning founded on them be less demonstrative. The dl ff er e“ce 
would be that its truth would be contingent on the truth of the 
axioms. We maintain, however, not only that we demonstrate 
our proposition because we base it on axioms ; but, further, that 
it is necessarily true because the axioms are intuitive. Ihe ; first 
step, therefore, in any demonstration aiming at truth is to 
obtain a starting-point which is known truth, that the mmd, 
beginning with truth, may end with truth. It would manifestly be 
impossible to obtain certain conclusions from uncertain premises, 
as itwould be to erect a firm buildingupon an unstable foundation. 
If it be, however, known that the first proposition is necessarily 
true, and that every succeeding proposition derived from if j* 
also true, then we are assured that the conclusion must be li e- 
wise true. This is the course of a complete demonstration. 
Having obtained the axiomatic foundation, the succeeding pro- 
cess is to reason from it, according to the laws of thought; or, 
