A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. I
John Stuart Mill · en
to account for the feeling of infinity inherent in our conceptions of
space and time; that apparent infinity is sufficiently accounted for by
simpler and universally acknowledged laws.
Now, in the case of a geometrical axiom, such, for example, as that two
straight lines cannot inclose a space,--a truth which is testified to us
by our very earliest impressions of the external world,--how is it
possible (whether those external impressions be or be not the ground of
our belief) that the reverse of the proposition _could_ be otherwise
than inconceivable to us? What analogy have we, what similar order of
facts in any other branch of our experience, to facilitate to us the
conception of two straight lines inclosing a space? Nor is even this
all. I have already called attention to the peculiar property of our
impressions of form, that the ideas or mental images exactly resemble
their prototypes, and adequately represent them for the purposes of
scientific observation. From this, and from the intuitive character of
the observation, which in this case reduces itself to simple inspection,
we cannot so much as call up in our imagination two straight lines, in
order to attempt to conceive them inclosing a space, without by that
very act repeating the scientific experiment which establishes the
contrary. Will it really be contended that the inconceivableness of the
thing, in such circumstances, proves anything against the experimental
origin of the conviction? Is it not clear that in whichever mode our
belief in the proposition may have originated, the impossibility of our
conceiving the negative of it must, on either hypothesis, be the same?
As, then, Dr. Whewell exhorts those who have any difficulty in
recognising the distinction held by him between necessary and contingent
truths, to study geometry,--a condition which I can assure him I have
conscientiously fulfilled,--I, in return, with equal confidence, exhort
those who agree with him, to study the general laws of association;
being convinced that nothing more is requisite than a moderate
familiarity with those laws, to dispel the illusion which ascribes a
peculiar necessity to our earliest inductions from experience, and
measures the possibility of things in themselves, by the human capacity
of conceiving them.