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begin to know my own powers and the nature which I wish to perfect。
＇19＇ （1） Reflection shows that all modes of perception or knowledge
may be reduced to four：… I。 （2） Perception arising from hearsay or from
some sign which everyone may name as he please。 II。 （3） Perception
arising from mere experience … that is； form experience not yet
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classified by the intellect； and only so called because the given event
has happened to take place； and we have no contradictory fact to set
against it； so that it therefore remains unassailed in our minds。 III。
（19：4） Perception arising when the essence of one thing is inferred
from another thing； but not adequately； this comes when ＇f＇ from some
effect we gather its cause； or when it is inferred from some general
proposition that some property is always present。 IV。 （5） Lastly； there is
the perception arising when a thing is perceived solely through its
essence； or through the knowledge of its proximate cause。
＇20＇ （1） All these kinds of perception I will illustrate by examples。 （2）
By hearsay I know the day of my birth； my parentage； and other matters
about which I have never felt any doubt。 （3） By mere experience I know
that I shall die； for this I can affirm from having seen that others like
myself have died； though all did not live for the same period； or die by the
same disease。 （4） I know by mere experience that oil has the property of
feeding fire； and water of extinguishing it。 （5） In the same way I know
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
a