225 
rejects the hypothesis put forth in a book which many, nay I 
believe a large majority of sound-thinking men, consider a 
Vivine Revelation,— is more consistent with observed facts, 
““f 3 difficulties and requires fewer assumptions, than 
that which he endeavoured to enforce, with all his skill, on 
his auditors at the meeting of the British Association. 
JNot only do I believe this, but by the same laws of thought 
by winch I am compelled to accept those axioms which I 
- aS scieiltlfic traths > or rather as the bases upon 
! ch ‘, e sciences are built, -I feel constrained to believe 
that all things, whether organic or inorganic, with which my 
senses make me conversant, were the works of a Divine Creator. 
Mathematical axioms are not the only self-evident truths, 
r ’, no * ■ self-evident, truths which must, nevertheless, be accepted 
without demonstration, before we can raise the structure of any 
science Before we make any progress in science, whethe"r 
abstract or applied, we must lay the foundations of our science 
on axioms. The man who will not admit these puts himself 
beyond the pale of science. The man who tells me that he 
cannot believe that “ the whole is greater than the part,” or 
that things which are equal to the same are equal to one 
another, cannot step over the very threshold of geometry. 
JNor ^re these axioms confined to self-evident truths Even in 
the abstract science of geometry, the eleventh axiom of the 
J!. ,° -E lll jhd is an undemonstrable proposition, as 
difficult to be received as any proposition for which Euclid has 
produced a demonstration. 
If I were required to show what claims pure science makes 
on man s capacity for faith, I might refer you to the algebraist 
who says thatanythingmultiplied by nothing is nothing, but that 
anything divided by nothing is infinite, while nothing divided 
by nothing may be something 1 If not satisfied by these calls 
on his faith I might go a step further, and mystify him with 
the astounding metaphysical assumptions required by the 
different 1 ** 1 and integral calculus. When, however, we take a 
tilde from the abstract sciences to the concrete or applied 
ones, what do we meet with ! The same foundation on 
axiomatic truths. Are not the three laws of motion axioms 
n which the whole structure of astronomical and dynamical 
science rest? These axioms apply to the motion of physical, 
tangible matter, yet an experimental, a true convmcino- 
cnonTT^ 1 dem0n ® tratl011 of an 7 one of these three law! 
f.w P b f V6n ' lh<3y are deduoed from a vast crowd of 
tacts, by making some special deduction, or excepting some 
particular P^ en uinenon from each experimental fact.° They 
aie then added to the science of abstract mathematics, as 
