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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； by its native
strength； ＇k＇； makes for itself intellectual instruments； whereby it acquires
strength for performing other intellectual operations； ＇l＇； and from these
operations again fresh instruments； or the power of pushing its
investigations further； and thus gradually proceeds till it reaches the
summit of wisdom。
＇32＇ （1） That this is the path pursued by the understanding may be
readily seen； when we understand the nature of the method for finding out
the truth； and of the natural instruments so necessary complex instruments；
and for the progress of investigation。 I thus proceed with my
demonstration。
＇33＇ （1） A true idea； ＇m＇； （for we possess a true idea） is something
different from its correlate （ideatum）； thus a circle is different from the
idea of a circle。 （2） The idea of a circle is not something having a
circumference and a center； as a circle has； nor is the idea of a body that
body itself。 （3） Now； as it is something different from its correlate； it is
capable of being understood through itself； in other words； the idea； in so
far as its actual essence （essentia formalis） is concerned； may be the
subject of another subjective essence （essentia objectiva）。 ＇33note1＇ （4）
And； again； this second subjective essence will； regarded in itself； be
something real； capable of being understood； and so on； indefinitely。
＇34＇ （1） For instance； the man Peter is something real； the true idea of
Peter is the reality of Peter represented subjectively； and is in itself
something real； and quite distinct from the actual Peter。 （2） Now； as this
true idea of Peter is in itself something real； and has its own individual
existence； it will also be capable of being understood … that is； of being the
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On the Improvement of the Understanding
subject of another idea； which will contain by representation （objective）
all that the idea of Peter contains actually （formaliter）。 （3） And； again；
this idea of the idea of Peter has its own individuality； which may become
the subject of yet another idea； and so on； indefinitely。 （4） This everyone
may make trial of for himself； by reflecting that he knows what Peter is；
and also knows that he knows； and further knows that he knows that he
knows； &c。 （34：5） Hence it is plain that； in order to understand the actual
Peter； it is not necessary first to understand the idea of Peter； and still less
the idea of the idea of Peter。 （6） This is the same as saying that； in order
to know； there is no need to know that we know； much less to know that
we know that we know。 （7） This is no more necessary than to know the
nature of a circle before knowing the nature of a triangle。 ＇n＇。 （8） But；
with these ideas； the contrary is the case： for； in order to know that I know；
I must first know。
＇35＇ （1） Hence it is clear that certainty is nothing else than the
subjective essence of a thing： in other words； the mode in which we
perceive an actual reality is certainty。 （2） Further； it is also evident that；
for the certitude of truth； no further sign is necessary beyond the
possession of a true idea： for； as I have shown； it is not necessary to know
that we know that we know。 （3） Hence； again； it is clear that no one can
know the nature of the highest certainty； unless he possesses an adequate
idea； or