272 Prof. Whewell’s Demonstration, Sc. 
our convictions do not re experiment. We learn by _.. 
truths of which we ietvenmes see in necessi This is the case Janitin 
the laws of motion, as I have repeatedly pine ee to shew. The 
same will appear to be the case with the proposition, that bodies of dif- 
ferent kinds have their inertia proportional to their weight. 
“ For bodies of the same kind have their inertia. auanesans to their 
weight, both quantities being proportional to the quantity of matter. 
And if we compress the same quantity of matter into half the space, 
neither the weight nor the inertia is altered, because these depend on 
the quantity of matter alone. But in this way we obtain a body of 
twice the density; and in the same manner we obtain a body of any 
other density. Therefore whatever be the density, the inertia is pro- 
portional.to the quantity of matter. But the mechanical relations of 
bodies cannot depend upon any difference of kind, except a difference 
of density. For if we suppose any fundamental difference of mechan- 
jeal nature in the particles or component elements of bodies, we are 
led to the same conclusion, of arbitrary, and therefore, impossible, re- 
sults, which we deduced from this supposition with regard to weight. 
Therefore all bodies of different density, and hence, all bodies what- 
ever, must have their inertia proportional to their weight. 
‘“‘ Hence we see, that the propositions, that all bodies are heavy, and 
that inertia is proportional to weight, necessarily follow from those fun- 
damental ideas which we unavoidably employ in all attempts to reason 
concerning the mec l relations of bodies. This conclusion may 
perhaps appear the more startling to many, because they have been _ 
accustomed to expect that fundamental ideas and their relations should 
be self-evident at our first contemplation of them. This, however, is 
far from being the case, as I have already shewn. It is not the frst, 
but the most complete and developed condition of our conceptions which 
enables us to see what are axiomatic truths in each province of human 
speculation. Our fundamental ideas are necessary conditions of know- 
ledge, universal forms of intuition, inherent types of mental develop- 
ment; they may even be termed, if any one chooses, results of connate 
intellectual tendencies; but we cannot term them innate ideas, without 
ee up a large array of false opinions. For innate ideas were con- 
d as capable of composition, but by no means of simplification 5 
as. most perfect i in their original condition ; as to be found, if any where, 
in the most uneducated and most uncultivated minds; as the same in 
all ages, nations, and stages of intellectual culture ; as capable of being 
referred. to at once, and. made the basis of our TeASOnINgSs without any 
special acuteness or effort :-in all which ci the fundamental 
ideas of which we have. ok Parone tn, ngatebetn ae eo 
stood. 
5 
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