60 
of incapacity with respect to physical axioms, and the mass of 
mankind are so still. . . . But though many are incapable of 
grasping physical axioms, it no more follows that physical 
axioms are not knowable a priori by a developed intelligence 
than it follows that logical relations are not necessary because 
undeveloped intellects cannot perceive their necessity” (p. 176 
of First Principles) . 
23. Now I venture to think that, in this passage, Mr. 
Spencer overlooks the distinction between “ necessary truths, 
knowable a priori ,” and “ axioms.” Many truths are know- 
able a priori which, so far from being self-evident, require a 
long series of arguments to satisfy the mind that they are 
truths. To call such a priori truths axioms seems a new and 
misleading application of the latter term. The 47th Propo- 
sition of the first book of Euclid is a necessary truth, know- 
able a priori, and therefore is an axiom in Mr. Spencer's sense 
of the word ; yet so far from its being self-evident, forty-six 
propositions have to be proved (after the axioms have been 
stated) before the intellect can have become sufficiently 
“developed and disciplined” to see its necessity. Much 
more is this the case with the more advanced truths of 
geometry. Surely then we are justified in asserting that phy- 
sical propositions which “ all mankind ” (including the most 
learned) were incapable of seeing until recently, and which 
the mass of mankind are still unable to recognise, even when 
plainly set before them, have no pretension to be classed 
under the head of axioms. The importance of this remark 
will be seen in the sequel, when we shall have to consider 
propositions which are propounded as possessing the two 
characteristics of axioms, namely, self-evidence and incapa- 
bility of proof, but which in fact only possess the latter. 
24. One of these physical axioms (to use Mr. Spencer's 
phraseology) is the indestructibility of matter. He says 
( First Principles , p. 177) : “ Conceive the space before you to 
be cleared of all bodies save one. Now imagine the remaining 
one not to be removed from its place, but to lapse into nothing 
while standing in that place. You fail. The space which 
was solid you cannot conceive becoming empty, save by trans- 
fer of that which made it solid.” Now, the only way in 
which I, as an individual, can reply to this argument is by 
saying that my intellect is not sufficiently “ developed and 
disciplined” to be able to recognise this as a physical axiom. 
Mr. Spencer would, no doubt, say that this is owing to my 
having imagined, previous to the attainment of better scien- 
tific information, that bodies could be in great part anni- 
hilated by combustion, or that water could be made to boil 
