14 
But, though we can conceive their alarm, we cannot image it ; by 
the depravation of a word we can imagine it. He says that it is 
not very easy to find in philosophical writings either admission 
or refusal of the distinction between imaged and unimaged con- 
cepts ; there is occasionally what can only be construed as implied 
admission or implied refusal ; and very often there is such con- 
fusion of phraseology as would lead to the supposition that the 
distinction is not seen. In his view there is subjective reality, 
both of the infinite and the infinitesimal. I have lately come 
across an important remark of Arago, which, as not occurring in 
a metaphysical work, will have the greater weight. Arago 
notices that the angle at which its tangent meets the circle is an 
infinitesimal angle. How, this being so, we see that if matter be 
continuous, and if we had adequate tools, we could construct an 
infinitesimal angle. Thus we should have not merely an imaged, 
but an actually modelled infinitesimal. Here Arago confirms He 
Morgan. Bor if an infinitesimal may be an imaged concept, an 
infinite may be an intellectual concept, though unimaged. He 
Morgan says that by Hamilton the concept and the image were 
not distinguished. I am not so sure of this. I think that he 
saw # the distinction, but failed to see its full significance. 
11. In Boole’s opinion, a too great addiction to metaphy- 
sical speculation seems, in some instances, to have produced a 
tendency towards this species of illusion — viz., that, of the two 
systems of Thought and Hature, one is the mere product of the 
other. I hope not to be deemed presumptuous if I add that, 
even admitting that every physical question, probed to the 
bottom, opens into a metaphysical one, still the metaphysical 
exploration of physical ideas does not seem likely to lead to very 
important results In dealing with material phenomena, the 
physicist presumes the uniformity of nature and, for the rest, 
resorts to his observations or his calculations. When we say 
that such and such a thing possesses such and such a property 
we are, no doubt, impliedly saying that our expectation is that 
the presence of the thing, under such and such circumstances, 
will be followed by certain results. And so far, it may be said, 
a metaphysical element enters into physics. But it does not 
follow that the metaphysician is competent to give final opinions 
upon such questions as the indestructibility, or ultimate in- 
compressibility of matter, or its geometrical or mechanical 
divisibility, or the laws of its motion, or whether its atoms, if 
such things be, are extended or unextended ; whether, if they 
are small bodies, atoms are infinitesimally small, or whether they 
are geometrical points. Surely, on such questions the metaphy- 
sician can only transmit opinions which, if they be sound ones, 
he, must himself, have obtained from the chemist, or the 
physicist, or the geometer. 
# See Hamilton, Discussions, p. 13 (in his footnotes). 
