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219. Let us now declare the means whereby our understand-
ing can rise to knowledge without fear of error. There are two
such means: intuition and deduction. By intuition I mean not
the varying testimony of the senses, nor the deductive judgment
of imagination naturally extravagant, but the conception of an
attentive mind so distinct and so clear that no doubt remains
to it with regard to that which it comprehends; or, what amounts
to the same thing, the self-evidencing conception of a sound and
attentive mind, a conception which springs from the light of
reason alone, and is more certain, because more simple, than
deduction itself. . . .

It may perhaps be asked why to intuition we add this other
mode of knowing, by deduction, that is to say, the process
which, from something of which we have certain knowledge,
draws consequences which necessarily follow therefrom. But
we are obliged to admit this second step; for there are a great
many things which, without being evident of themselves, never-
theless bear the marks of certainty if only they are deduced from
true and incontestable principles by a continuous and uninterrupted
movement of thought, with distinct intuition of each
thing; just as we know that the last link of a long chain holds to
the first, although we can not take in with one glance of the eye
the intermediate links, provided that, after having run over
them in succession, we can recall them all, each as being joined to
its fellows, from the first up to the last. Thus we distinguish
intuition from deduction, inasmuch as in the latter case there is
conceived a certain progress or succession, while it is not so in
the former; . . . whence it follows that primary propositions,
derived immediately from principles, may be said to be known,
according to the way we view them, now by intuition, now by
deduction; although the principles themselves can be known
only by intuition, the remote consequences only by deduction.

DESCARTES.

Rules for the Direction of the Mind, Philosophy
of D. [Torrey] (New York, 1892), pp. 64, 65.

Source: Memorabilia mathematica; or, The philomath's quotation-book - Moritz, Robert Édouard, 1868-1940

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