Discourse on the Method of Reasoning | Page 9

it is almost quite as difficult to effect a severance of the
true from the false as it is to extract a Diana or a Minerva from a rough
block of marble. Then as to the analysis of the ancients and the algebra
of the moderns, besides that they embrace only matters highly abstract,
and, to appearance, of no use, the former is so exclusively restricted to
the consideration of figures, that it can exercise the understanding only
on condition of greatly fatiguing the imagination; and, in the latter,
there is so complete a subjection to certain rules and formulas, that
there results an art full of confusion and obscurity calculated to
embarrass, instead of a science fitted to cultivate the mind. By these
considerations I was induced to seek some other method which would
comprise the advantages of the three and be exempt from their defects.
And as a multitude of laws often only hampers justice, so that a state is
best governed when, with few laws, these are rigidly administered; in
like manner, instead of the great number of precepts of which logic is
composed, I believed that the four following would prove perfectly
sufficient for me, provided I took the firm and unwavering resolution
never in a single instance to fail in observing them.
The first was never to accept anything for true which I did not clearly
know to be such; that is to say, carefully to avoid precipitancy and
prejudice, and to comprise nothing more in my judgement than what
was presented to my mind so clearly and distinctly as to exclude all
ground of doubt.
The second, to divide each of the difficulties under examination into as
many parts as possible, and as might be necessary for its adequate
solution.
The third, to conduct my thoughts in such order that, by commencing
with objects the simplest and easiest to know, I might ascend by little
and little, and, as it were, step by step, to the knowledge of the more
complex; assigning in thought a certain order even to those objects
which in their own nature do not stand in a relation of antecedence and
sequence.
And the last, in every case to make enumerations so complete, and
reviews so general, that I might be assured that nothing was omitted.

The long chains of simple and easy reasonings by means of which
geometers are accustomed to reach the conclusions of their most
difficult demonstrations, had led me to imagine that all things, to the
knowledge of which man is competent, are mutually connected in the
same way, and that there is nothing so far removed from us as to be
beyond our reach, or so hidden that we cannot discover it, provided
only we abstain from accepting the false for the true, and always
preserve in our thoughts the order necessary for the deduction of one
truth from another. And I had little difficulty in determining the objects
with which it was necessary to commence, for I was already persuaded
that it must be with the simplest and easiest to know, and, considering
that of all those who have hitherto sought truth in the sciences, the
mathematicians alone have been able to find any demonstrations, that is,
any certain and evident reasons, I did not doubt but that such must have
been the rule of their investigations. I resolved to commence, therefore,
with the examination of the simplest objects, not anticipating, however,
from this any other advantage than that to be found in accustoming my
mind to the love and nourishment of truth, and to a distaste for all such
reasonings as were unsound. But I had no intention on that account of
attempting to master all the particular sciences commonly denominated
mathematics: but observing that, however different their objects, they
all agree in considering only the various relations or proportions
subsisting among those objects, I thought it best for my purpose to
consider these proportions in the most general form possible, without
referring them to any objects in particular, except such as would most
facilitate the knowledge of them, and without by any means restricting
them to these, that afterwards I might thus be the better able to apply
them to every other class of objects to which they are legitimately
applicable. Perceiving further, that in order to understand these
relations I should sometimes have to consider them one by one and
sometimes only to bear them in mind, or embrace them in the aggregate,
I thought that, in order the better to consider them individually, I should
view them as subsisting between straight lines, than which I could find
no objects more simple, or capable of being more distinctly represented
to my imagination and senses; and on the other hand, that in order