Neither the non-recognition of the truth that 7 and 5 are 12, which inthe savage results from undeveloped mental structure, nor the assertion,due to the boy's careless mental action, that they make 11, leads us to doubtthe necessity of the relation between these two separately-existing numbersand the sum they make when existing together. Nor does failure from eithercause to apprehend the necessity of this relation, make us hesitate to saythat when its terms are distinctly represented in thought, its necessitywill be seen; and that, apart from multiplied experiences, this necessitybecomes cognizable when structures and functions are so far developed thatgroups of 7 and 5 and 12 can be mentally grasped.
Manifestly, then, there are recognitions of necessary truths, as such,which accompany mental evolution. And there are ascending gradations in theserecognitions. A boy who has intelligence enough to see that things whichare equal to the same thing are equal to one another, may be unable to seethat ratios which are severally equal to certain other ratios that are unequalto each other, are themselves unequal; though to a more-developed mind thislast axiom is no less obviously necessary than the first.
All this which holds of logical and mathematical truths, holds, with changeof terms, of physical truths. There are necessary truths in Physics for theapprehension of which, also, a developed and disciplined intelligence isrequired; and before such intelligence arises, not only may there be failureto apprehend the necessity of them, but there may be vague beliefs in theircontraries. Up to comparatively-recent times, all mankind were in this stateof incapacity respecting physical axioms; and the mass of mankind are sostill. Effects are expected without causes of fit kinds; or effects extremelydisproportionate to causes are looked for; or causes are supposed to endwithout effects.(*)
But though many are unable to grasp physical axioms, it no more follows thatphysical axioms are not knowable a priori by a developed intellect, thanit follows that logical relations are not necessary, because undevelopedintellects cannot perceive their necessity.
It is thus with the notions which have been current respecting the creationand annihilation of Matter. In the first place, there has been a confoundingof two radically-different things -- disappearance of Matter from a visibleform, say by evaporation, and passage of Matter from existence into non-existence.
Until this confusion is avoided, the belief that Matter can be annihilatedreadily obtains currency. In the second place, the currency of it continuesso long as there is not power of introspection enough to make manifest whatresults from the attempt to annihilate Matter in thought. But when the vagueideas arising in a nervous structure imperfectly organized, are replacedby the clear ideas arising in a definite nervous structure; this definitestructure, moulded by experience into correspondence with external things,makes necessary in thought the relations answering to uniformities in things.
Hence, among others, the conception of the Indestructibility of Matter.
