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that a dog is a barking animal； man a rational animal； and in fact nearly all
the practical knowledge of life。
＇21＇ （1） We deduce one thing from another as follows： when we
clearly perceive that we feel a certain body and no other； we thence clearly
infer that the mind is united ＇g＇ to the body； and that their union is the
cause of the given sensation； but we cannot thence absolutely understand
＇h＇ the nature of the sensation and the union。 （2） Or； after I have become
acquainted with the nature of vision； and know that it has the property of
making one and the same thing appear smaller when far off than when
near； I can infer that the sun is larger than it appears； and can draw other
conclusions of the same kind。
＇22＇ （1） Lastly； a thing may be perceived solely through its essence；
when； from the fact of knowing something； I know what it is to know that
thing； or when； from knowing the essence of the mind； I know that it is
united to the body。 （2） By the same kind of knowledge we know that two
and three make five； or that two lines each parallel to a third； are parallel
to one another； &c。 （3） The things which I have been able to know by this
kind of knowledge are as yet very few。
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＇23＇ （1） In order that the whole matter may be put in a clearer light； I
will make use of a single illustration as follows。 （2） Three numbers are
given … it is required to find a fourth； which shall be to the third as the
second is to the first。 （23：3） Tradesmen will at once tell us that they know
what is required to find the fourth number； for they have not yet forgotten
the rule which was given to them arbitrarily without proof by their masters；
others construct a universal axiom from their experience with simple
numbers； where the fourth number is self…evident； as in the case of 2； 4； 3；
6； here it is evident that if the second number be multiplied by the third；
and the product divided by the first； the quotient is 6； when they see that
by this process the number is produced which they knew beforehand to be
the proportional； they infer that the process always holds good for finding
a fourth number proportional。
＇24＇ （1） Mathematicians； however； know by the proof of the
nineteenth proposition of the seventh book of Euclid； what numbers are
proportionals； namely； from the nature and property of proportion it
follows that the product of the first and fourth will be equal to the product
of the second and third： still they do not see the adequate proportionality
of the given numbers； or； if they do see it； they see it not by virtue of
Euclid's proposition； but intuitively； without going through any process。
＇25＇ （1） In order that from these modes of perception the best may be
selected； it is well that we should briefly enumerate the means necessary
for attaining our end。
I。 （2） To have an exact knowledge of our nature which we desire to
perfect； and to know as much as is needful of nature in general。
II。 To collect in this way the differences； the agreements； and the
oppositions of things。 III。 To learn thus exactly how far
they can or cannot be modified。 IV。 To compare this result
with the nature and power of man。 （4） We shall thus discern the
highest degree of perfection to which man is capable of attaining。
＇26＇ （1） We shall then be in a position to see which mode of perception
we ought to choose。 （2） As to the first mode； it is evident that from
hearsay our knowledge must always be uncertain； and； moreover； can give
us no insight into the essence of a thing； as is manifest in our illustration；
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now one can only arrive at knowledge of a thing through knowledge of its
essence； as will hereafter appear。 （3） We may； therefore clearly conclude
that the certainty arising from hearsay cannot be scientific in its character。
（4） For simple hearsay cannot affect anyone whose understanding does not；
so to speak； meet it half way。
＇27＇ （1） The second mode of perception ＇i＇ cannot be said to give us
the idea of the proportion of which we are in search。 （2） Moreover its
results are very uncertain and indefinite； for we shall never discover
anything in natural phenomena by its means； except accidental properties；
which are never clearly understood； unless the essence of the things in
question be known first。 （3） Wherefore this mode also must be rejected。
＇28＇ （1） Of the third mode of perception we may say in a manner that
it gives us the idea of the thing sought； and that it us to draw conclusions
without risk of error； yet it is not by itself sufficient to put us in possession
of the perfection we aim at。
＇29＇ （1） The fourth mode alone apprehends the adequate essence of a
thing without danger of error。 （2） This mode； therefore； must be the one
which we chiefly employ。 （3） How； then； should we avail ourselves of it
so as to gain the fourth kind of knowledge with the least delay concerning
things previously unknown？ （4） I will proceed to explain。
＇30＇ （1） Now that we know what kind of knowledge is necessary for us；
we must indicate the way and the method whereby we may gain the said
knowledge concerning the things needful to be known。 （2） In order to
accomplish this； we must first take care not to commit ourselves to a
search； going back to infinity … that is； in order to discover the best method
of finding truth； there is no need of another method to discover such
method； nor of a third method for discovering the second； and so on to
infinity。 （3） By such proceedings； we should never arrive at the
knowledge of the truth； or； indeed； at any knowledge at all。 （30：4） The
matter stands on the same footing as the making of material tools； which
might be argued about in a similar way。 （5） For； in order to work iron； a
hammer is needed； and the hammer cannot be forthcoming unless it has
been made； but； in order to make it； there was need of another hammer and
other tools； and so on to infinity。 （6） We might thus vainly endeavor to
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prove that men have no power of working iron。
＇31＇ （1） But as men at first made use of the instruments supplied by
nature to accomplish very easy pieces of workmanship； laboriously and
imperfectly； and then； when these were finished； wrought other things
more difficult with less labour and greater perfection； and so gradually
mounted from the simplest operations to the making of tools； and from the
making of tools to the making of more complex tools； and fresh feats of
workmanship； till they arrived at making； complicated mechanisms which
they now possess。 （31：2） So； in like manner； the intellect；