294 
The Mean- 
ing of “ Ax. 
ioms. 1 * 
see, that any other proposition, not obviously false, might be 
substituted with equal logic for “ persistence of force” in 
that sentence ? What would he say if we substituted the 
“existence of a Creator” for it? Yet that is a vast deal 
more self-evident than the conservation of force. 
Perhaps he or his followers may say that it is the very 
nature of axioms or self-evident truths not to be demon- 
strable by reasoning. And yet I see that one of them, 
the editor of Knowledge , in a depreciatory notice of the 
article on the Spencerian philosophy in the last Edinburgh 
Review , gives exactly the opposite definition of an axiom. 
He says that “in its proper sense it means a fact or law 
established by experience, and known to be worthy (a^oc) 
of acceptance ” : a truly fortunate pair of “ proper mean- 
ings ” ! For (1) all truths are worthy to be received, and 
yet there are an infinity of truths for one axiom. And (2) 
so far from a^'uoga, or axiom (which are the same word 
in Greek and English writing), according to dictionaries and 
Aristotle, the great authority on such matters, always meant 
in philosophy “ a self-evident truth, or basis of demon- 
stration, or a truth which cannot be made plainer by 
demonstration ” ; in short, the very opposite of what requires 
experience to prove it. Euclid’s axioms meant the same, 
and so did Newton’s “ Axioms or Laws of Motion,” though 
he illustrated them by a few experiences and experiments, 
which alone were quite inadequate to prove them, if they had 
been at all doubtful in themselves. It is impossible to con- 
ceive action and reaction not being equal and opposite. And 
if bodies did not persist in the same direction and velocity, or 
rest, unless some new force disturbs them, to which side could 
they turn, and why should they either retard or accelerate 
themselves ? The second law would require more discussion 
than this third and first ; but I have no doubt Newton thought 
that also self-evident. If he did not, I have only to say that 
he was wrong, according to established use in Greek and 
English, to call his Laws of Motion “ Axioms.” Indeed they 
never are so called now, but always simply “ The Laws of 
Motion,” either for shortness or to avoid the ambiguity. But 
that is a mere verbal question. 
I suppose that even Spencerian disciples will admit that 
something more than mere assertion is requisite to establish a 
new axiom ; especially when a series of eminent philosophers 
had been for years trying to prove the thing in question by 
elaborate experiments, and have at last succeeded, so far as any 
law of nature can be said to be absolutely proved. Real axioms 
