premisses and indeterminable by relation to them, we must say of an idea
that moves among relations of necessary determination, through premisses
which contain their conclusion in advance, that it follows the inverse
direction, that of materiality. What appears, from the point of view of
the intellect, as an effort, is in itself a letting go. And while, from
the point of view of the intellect, there is a _petitio principii_ in
making geometry arise automatically from space, and logic from
geometry--on the contrary, if space is the ultimate goal of the mind's
movement of _detension_, space cannot be given without positing also
logic and geometry, which are along the course of the movement of which
pure spatial intuition is the goal.

It has not been enough noticed how feeble is the reach of deduction in
the psychological and moral sciences. From a proposition verified by
facts, verifiable consequences can here be drawn only up to a certain
point, only in a certain measure. Very soon appeal has to be made to
common sense, that is to say, to the continuous experience of the real,
in order to inflect the consequences deduced and bend them along the
sinuosities of life. Deduction succeeds in things moral only
metaphorically, so to speak, and just in the measure in which the moral
is transposable into the physical, I should say translatable into
spatial symbols. The metaphor never goes very far, any more than a curve
can long be confused with its tangent. Must we not be struck by this
feebleness of deduction as something very strange and even paradoxical?
Here is a pure operation of the mind, accomplished solely by the power
of the mind. It seems that, if anywhere it should feel at home and
evolve at ease, it would be among the things of the mind, in the domain
of the mind. Not at all; it is there that it is immediately at the end
of its tether. On the contrary, in geometry, in astronomy, in physics,
where we have to do with things external to us, deduction is
all-powerful! Observation and experience are undoubtedly necessary in
these sciences to arrive at the principle, that is, to discover the
aspect under which things must be regarded; but, strictly speaking, we
might, by good luck, have hit upon it at once; and, as soon as we
possess this principle, we may draw from it, at any length, consequences
which experience will always verify. Must we not conclude, therefore,
that deduction is an operation governed by the properties