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the properties of the understanding； let us examine them； and begin by
discussing the instruments for research which we find innate in us。 See
＇31＇
＇108＇ （1） The properties of the understanding which I have chiefly
remarked； and which I clearly understand； are the following：… I。 （2） It
involves certainty … in other words； it knows that a thing exists in
reality as it is reflected subjectively。 II。 （108：3） That it perceives certain
things； or forms some ideas absolutely； some ideas from others。 （4）
Thus it forms the idea of quantity absolutely； without reference to any
other thoughts； but ideas of motion it only forms after taking into
consideration the idea of quantity。 III。 （108：5） Those ideas which the
understanding forms absolutely express infinity； determinate ideas are
derived from other ideas。 （6） Thus in the idea of quantity； perceived
by means of a cause； the quantity is determined； as when a body is
perceived to be formed by the motion of a plane； a plane by the
motion of a line； or； again； a line by the motion of a point。 （7） All
these are perceptions which do not serve towards understanding
quantity； but only towards determining it。 （108：8） This is proved by
the fact that we conceive them as formed as it were by motion； yet this
motion is not perceived unless the quantity be perceived also； we can
even prolong the motion to form an infinite line； which we certainly
could not do unless we had an idea of infinite quantity。 IV。 （9） The
understanding forms positive ideas before forming negative ideas。 V。
（108：10） It perceives things not so much under the condition of
duration as under a certain form of eternity； and in an infinite number；
or rather in perceiving things it does not consider either their number
or duration； whereas； in imagining them； it perceives them in a
determinate number； duration； and quantity。 VI。 （108：11） The ideas
which we form as clear and distinct； seem to follow from the sole
necessity of our nature； that they appear to depend absolutely on our
sole power； with confused ideas the contrary is the case。 （12） They
are often formed against our will。 VII。 （108：13） The mind can
determine in many ways the ideas of things； which the understanding
forms from other ideas： thus； for instance； in order to define the plane of
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an ellipse； it supposes a point adhering to a cord to be moved around two
centers； or； again； it conceives an infinity of points； always in the same
fixed relation to a given straight line； angle of the vertex of the cone； or in
an infinity of other ways。 VIII。 （108：14） The more ideas express perfection
of any object； the more perfect are they themselves； for we do not admire
the architect who has planned a chapel so much as the architect who has
planned a splendid temple。
＇109＇ （1） I do not stop to consider the rest of what is referred to
thought； such as love； joy； &c。 （2） They are nothing to our present
purpose； and cannot even be conceived unless the understanding be
perceived previously。 （3） When perception is removed； all these go with it。
＇110＇ （1） False and fictitious ideas have nothing positive about them
（as we have abundantly shown）； which causes them to be called false or
fictitious； they are only considered as such through the defectiveness of
knowledge。 （2） Therefore； false and fictitious ideas as such can teach us
nothing concerning the essence of thought； this must be sought from the
positive properties just enumerated； in other words； we must lay down
some common basis from which these properties necessarily follow； so
that when this is given； the properties are necessarily given also； and when
it is removed； they too vanish with it。
The rest of the treatise is wanting。
Spinoza's Endnotes： Marks as per Curley； see Note 5 above。 ＇a＇ （1） This
might be explained more at large and more clearly： I mean by
distinguishing riches according as they are pursued for their own
sake； in or furtherance of fame； or sensual pleasure； or the
advancement of science and art。 （2） But this subject is reserved to its
own place； for it is not here proper to investigate the matter more
accurately。 ＇b＇ These considerations should be set forth more precisely。 ＇c＇
These matters are explained more at length elsewhere。 ＇d＇ N。B。 I do no
more here than enumerate the sciences necessary for our purpose； I
lay no stress on their order。 ＇e＇ There is for the sciences but one end； to
which they should all be directed。 ＇f＇ （1） In this case we do not
understand anything of the cause from the consideration of it in the
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On the Improvement of the Understanding
effect。 （2） This is sufficiently evident from the fact that the cause is
only spoken of in very general terms； such as … there exists then
something； there exists then some power； &c。； or from the that we
only express it in a negative manner … it is not or that； &c。 （3） In
the second case something is ascribed to the cause because of the
effect； as we shall show in an example； but only a property； never an
essence。 ＇g＇ （1） From this example may be clearly seen what I have just
drawn attention to。 （2） For through this union we understand
nothing beyond the sensation； the effect； to wit； from which we
inferred the cause of which we understand nothing。 ＇h＇ （1） A conclusion of
this sort； though it be certain； is yet