matter when to-morrow may be.
What is there at the base of this belief? Notice that the belief is more
or less assured, according as the case may be, but that it is forced
upon the mind as an absolute necessity when the microcosm considered
contains only magnitudes. If two numbers be given, I am not free to
choose their difference. If two sides of a triangle and the contained
angle are given, the third side arises of itself and the triangle
completes itself automatically. I can, it matters not where and it
matters not when, trace the same two sides containing the same angle: it
is evident that the new triangles so formed can be superposed on the
first, and that consequently the same third side will come to complete
the system. Now, if my certitude is perfect in the case in which I
reason on pure space determinations, must I not suppose that, in the
other cases, the certitude is greater the nearer it approaches this
extreme case? Indeed, may it not be the limiting case which is seen
through all the others and which colors them, accordingly as they are
more or less transparent, with a more or less pronounced tinge of
geometrical necessity?[82] In fact, when I say that the water on the
fire will boil to-day as it did yesterday, and that this is an absolute
necessity, I feel vaguely that my imagination is placing the stove of
yesterday on that of to-day, kettle on kettle, water on water, duration
on duration, and it seems then that the rest must coincide also, for the
same reason that, when two triangles are superposed and two of their
sides coincide, their third sides coincide also. But my imagination acts
thus only because it shuts its eyes to two essential points. For the
system of to-day actually to be superimposed on that of yesterday, the
latter must have waited for the former, time must have halted, and
everything become simultaneous: that happens in geometry, but in
geometry alone. Induction therefore implies first that, in the world of
the physicist as in that of the geometrician, time does not count. But
it implies also that qualities can be superposed on each other like
magnitudes. If, in imagination, I place the stove and fire of to-day on
that of yesterday, I find indeed that the form has remained the same; it
suffices, for that, that the surfaces and edges coincide; but what is
the coincidence of two qualities, and how can they be superposed one on
another in order to ensure that they are identical? Yet I exten