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instance； that man is a laughing animal； a two…footed animal
without feathers； a rational animal； and thus； in other cases；
everyone will form general images of things according to the
habit of his body。
It is thus not to be wondered at； that among philosophers； who
seek to explain things in nature merely by the images formed of
them； so many controversies should have arisen。
*****Note IIFrom all that has been said above it is clear； that
we； in many cases； perceive and form our general notions：（1。）
From particular things represented to our intellect
fragmentarily； confusedly； and without order through our senses
（II。 xxix。 Cor。）； I have settled to call such perceptions by the
name of knowledge from the mere suggestions of experience。 （2。）
From symbols； e。g。； from the fact of having read or heard
certain words we remember things and form certain ideas
concerning them； similar to those through which we imagine
things （II。 xviii。 Note）。 I shall call both these ways of
regarding things 〃knowledge of the first kind；〃 〃opinion；〃 or
〃imagination。〃 （3。） From the fact that we have notions common
to all men； and adequate ideas of the properties of things （II。
xxxviii。 Cor。； xxxix。 and Cor。； and xl。）； this I call 〃reason〃
and 〃knowledge of the second kind。〃 Besides these two kinds of
knowledge； there is； as I will hereafter show； a third kind of
knowledge； which we will call intuition。 This kind of knowledge
proceeds from an adequate idea of the absolute essence of
certain attributes of God to the adequate knowledge of the
essence of things。 I will illustrate all three kinds of
knowledge by a single example。 Three numbers are given for
finding a fourth； which shall be to the third as the second is
to the first。 Tradesmen without hesitation multiply the second
by the third； and divide the product by the first； either
because they have not forgotten the rule which they received
from a master without any proof； or because they have often made
trial of it with simple numbers； or by virtue of the proof of
the nineteenth proposition of the seventh book of Euclid；
namely； in virtue of the general property of proportionals。
But with very simple numbers there is no need of this。 For
instance； one； two； three being given； everyone can see that the
fourth proportional is six； and this is much clearer； because
we infer the fourth number from an intuitive grasping of the
ratio； which the first bears to the second。
XLI。 Knowledge of the first kind is the only source of falsity；
knowledge of the second and third kinds is necessarily true。
》》》》》ProofTo knowledge of the first kind we have （in the
foregoing note） assigned all those ideas； which are inadequate
and confused； therefore this kind of knowledge is the only
source of falsity （II。 xxxv。）。 Furthermore； we assigned to the
second and third kinds of knowledge those ideas which are
adequate； therefore these kinds are necessarily true （II。
xxxiv。）。 Q。E。D。
XLII。 Knowledge of the second and third kinds； not knowledge of
the first kind； teaches us to distinguish the true from the
false。
》》》》》ProofThis proposition is self…evident。 He； who knows how
to distinguish between true and false； must have an adequate
idea of true and false。 That is （II。 xl。； note ii。）； he must
know the true and the false by the second or third kind of
knowledge。
XLIII。 He； who has a true idea； simultaneously knows that he has
a true idea； and cannot doubt of the truth of the thing
perceived。
》》》》》ProofA true idea in us is an idea which is adequate in
God； in so far as he is displayed through the nature of the
human mind （II。 xi。 Cor。）。 Let us suppose that there is in God；
in so far as he is displayed through the human mind； an adequate
idea； A。 The idea of this idea must also necessarily be in God；
and be referred to him in the same way as the idea A （by II。
xx。； whereof the proof is of universal application）。 But the
idea A is supposed to be referred to God； in so far as he is
displayed through the human mind； therefore； the idea of the
idea A must be referred to God in the same manner； that is （by
II。 xi。 Cor。）； the adequate idea of the idea A will be in the
mind； which has the adequate idea A； therefore he； who has an
adequate idea or knows a thing truly （II。 xxxiv。）； must at the
same time have an adequate idea or true knowledge of his
knowledge； that is； obviously； he must be assured。 Q。E。D。
*****NoteI explained in the note to II。 xxi。 what is meant by
the idea of an idea； but we may remark that the foregoing
proposition is in itself sufficiently plain。 No one； who has a
true idea； is ignorant that a true idea involves the highest
certainty。 For to have a true idea is only another expression
for knowing a thing perfectly； or as well as possible。 No one；
indeed； can doubt of this； unless he thinks that an idea is
something lifeless； like a picture on a panel； and not a mode of
thinkingnamely； the very act of understanding。 And who； I
ask； can know that he understands anything； unless he do first
understand it？ In other words； who can know that he is sure of
a thing； unless he be first sure of that thing？ Further； what
can there be more clear； and more certain； than a true idea as a
standard of truth？ Even as light displays both itself and
darkness； so is truth a standard both of itself and of falsity。
I think I have thus sufficiently answered these
questionsnamely； if a true idea is distinguished from a false
idea； only in so far as it is said to agree with its object； a
true idea has no more reality or perfection than a false idea
（since the two are only distinguished by an extrinsic mark）；
consequently； neither will a man who has a true idea have any
advantage over him who has only false ideas。 Further； how comes
it that men have false ideas？ Lastly； how can anyone be sure；
that he has ideas which agree with their objects？ These
questions； I repeat； I have； in my opinion； sufficiently
answered。 The difference between a true idea and a false idea
is plain： from what was said in II。 xxxv。； the former is
related to the latter as being is to not…being。 The causes of
falsity I have set forth very clearly in II。 xix。 and II。 xxxv。
with the note。 From what is there stated； the difference
between a man who has true ideas； and a man who has only false
ideas； is made apparent。 As for the last questionas to how a