[70]  (1) Whence it follows that there is in ideas something real,
whereby the true are distinguished from the false.  (2) This reality
must be inquired into, if we are to find the best standard of truth
(we have said that we ought to determine our thoughts by the given
standard of a true idea, and that method is reflective knowledge),
and to know the properties of our understanding.  (70:3) Neither must
we say that the difference between true and false arises from the
fact, that true knowledge consists in knowing things through their
primary causes, wherein it is totally different from false knowledge,
as I have just explained it: for thought is said to be true, if
it involves subjectively the essence of any principle which has no
cause, and is known through itself and in itself. 

[71]  (1) Wherefore the reality (forma) of true thought must exist
in the thought itself, without reference to other thoughts; it does
not acknowledge the object as its cause, but must depend on the
actual power and nature of the understanding.  (2) For, if we
suppose that the understanding has perceived some new entity which
has never existed, as some conceive the understanding of God before
He created thing (a perception which certainly could not arise 
any object), and has legitimately deduced other thoughts from said
perception, all such thoughts would be true, without being
determined by any external object; they would depend solely on the
power and nature of the understanding.  (71:3) Thus, that which
constitutes the reality of a true thought must be sought in the
thought itself, and deduced from the nature of the understanding.

[72]  (1) In order to pursue our investigation, let us confront
ourselves with some true idea, whose object we know for
certain to be dependent on our power of thinking, and to have
nothing corresponding to it in nature.  (2) With an idea of this
kind before us, we shall, as appears from what has just been said,
be more easily able to carry on the research we have in view.
(72:3) For instance, in order to form the conception of a sphere,
I invent a cause at my pleasure - namely, a semicircle revolving
round its center, and thus producing a sphere.  (4) This is
indisputably a true idea; and, although we know that no sphere in
nature has ever actually been so formed, the perception remains
true, and is the easiest manner of conceiving a sphere.
(72:5) We must observe that this perception asserts the rotation
of a semicircle - which assertion would be false, if it were not
associated with the conception of a sphere, or of a cause
determining a motion of the kind, or absolutely, if the assertion
were isolated.  (6) The mind would then only tend to the
affirmation of the sole motion of a semicircle, which is not
contained in the conception of a semicircle, and does not arise
from the conception of any cause capable of producing such motion.
    (72:7) Thus falsity consists only in this, that something is
affirmed of a thing, which is not contained in the conception
we have formed of that thing, as motion or rest of a semicircle.
(8) Whence it follows that simple ideas cannot be other than
true - e.g., the simple idea of a semicircle, of motion, of rest,
of quantity, &c.
    (72:9) Whatsoever affirmation such ideas contain is equal to the
concept formed, and does not extend further.  (10) Wherefore we
form as many simple ideas as we please, without any fear of error.

[73]  (1) It only remains for us to inquire by what power our mind
can form true ideas, and how far such power extends.  (2) It is
certain that such power cannot extend itself infinitely.  (3) For
when we affirm somewhat of a thing, which is not contained in the
concept we have formed of that thing, such an affirmation shows a
defect of our perception, or that we have formed fragmentary or
mutilated ideas.  (4) Thus we have seen that the notion of a
semicircle is false when it is isolated in the mind, but true when
it is associated with the concept of a sphere, or of some cause
determining such a motion.  (73:5) But if it be the nature of a
thinking being, as seems, prima facie, to be the case, to form true
or adequate thoughts, it is plain that inadequate ideas arise in us
only because we are parts of a thinking being, whose thoughts - some
in their entirety, others in fragments only - constitute our mind.

[74]  (1) But there is another point to be considered, which was not
worth raising in the case of fiction, but which give rise to complete
deception - namely, that certain things presented to the imagination
also exist in the understanding - in other words, are conceived
clearly and distinctly.  (2) Hence, so long as we do not separate that
which is distinct from that which is confused, certainty, or the true
idea, becomes mixed with indistinct ideas.  (3) For instance, certain
Stoics heard, perhaps, the term "soul," and also that the soul is
immortal, yet imagined it only confusedly; they imaged, also, and
understood that very subtle bodies penetrate all others, and are
penetrated by none.  (74:4) By combining these ideas, and being at the
same time certain of the truth of the axiom, they forthwith became
convinced that the mind consists of very subtle bodies; that these
very subtle bodies cannot be divided &c.

[75]  (1) But we are freed from mistakes of this kind, so long as we
endeavor to examine all our perceptions by the standard of the given
true idea.  (2) We must take care, as has been said, to separate such
perceptions from all those which arise from hearsay or unclassified
experience.  (3) Moreover, such mistakes arise from things being
conceived too much in the abstract; for it is sufficiently self-evident
that what I conceive as in its true object I cannot apply to anything
else.  (75:4) Lastly, they arise from a want of understanding of the
primary elements of nature as a whole; whence we proceed without due
order, and confound nature with abstract rules, which, although they
be true enough in their sphere, yet, when misapplied, confound
themselves, and pervert the order of nature.  (5) However, if we
proceed with as little abstraction as possible, and begin from primary
elements - that is, from the source and origin of nature, as far back
as we can reach, - we need not fear any deceptions of this kind.

[76] (1) As far as the knowledge of the origin of nature is concerned,
there is no danger of our confounding it with abstractions.  (2) For
when a thing is conceived in the abstract, as are all universal
notions, the said universal notions are always more extensive in the
mind than the number of individuals forming their contents really
existing in nature.  (3) Again, there are many things in nature, the
difference between which is so slight as to be hardly perceptible to
the understanding; so that it may readily happen that such things are
confounded together, if they be conceived abstractedly.  (4) But since
the first principle of nature cannot (as we shall see hereafter) be
conceived abstractedly or universally, and cannot extend further in
the understanding than it does in reality, and has no likeness to
mutable things, no confusion need be feared in respect to the idea of
it, provided (as before shown) that we possess a standard of truth.
(5) This is, in fact, a being single and infinite [76z] ; in other
words, it is the sum total of being, beyond which there is no being
found. [76a]

[77]  (1) Thus far we have treated of the false idea. We have now
to investigate the doubtful idea - that is, to inquire what can
cause us to doubt, and how doubt may be removed.  (2) I speak of
real doubt existing in the mind, not of such doubt as we see
exemplified when a man says that he doubts, though his mind does
not really hesitate.  (77:3) The cure of the latter does not fall
within the province of method, it belongs rather to inquiries
concerning obstinacy and its cure.

[78]  (1) Real doubt is never produced in the mind by the thing
doubted of.  (2) In other words, if there were only one idea in
the mind, whether that idea were true or false, there would be no
doubt or certainty present, only a certain sensation.  (3) For an
idea is in itself nothing else than a certain sensation. (4) But
doubt will arise through another idea, not clear and distinct
enough for us to be able to draw any certain conclusions with
regard to the matter under consideration; that is, the idea which
causes us to doubt is not clear and distinct. (5) To take an example.
(78:6) Supposing that a man has never reflected, taught by experience
or by any other means, that our senses sometimes deceive us, he will
never doubt whether the sun be greater or less than it appears.
(7) Thus rustics are generally astonished when they hear that the
sun is much larger than the earth. (8) But from reflection on the
deceitfulness of the senses [78a] doubt arises, and if, after
doubting, we acquire a true knowledge of the senses, and how things
at a distance are represented through their instrumentality, doubt
is again removed. 

[79]  (1) Hence we cannot cast doubt on true ideas by the supposition
that there is a deceitful Deity, who leads us astray even in what is
most certain.  (2) We can only hold such an hypothesis so long as we
have no clear and distinct idea - in other words, until we reflect 
the knowledge which we have of the first principle of all things, and
find that which teaches us that God is not a deceiver, and until we
know this with the same certainty as we know from reflecting on the
are equal to two right angles.  (3) But if we have a knowledge of God
equal to that which we have of a triangle, all doubt is removed.
(79:4) In the same way as we can arrive at the said knowledge of a
triangle, though not absolutely sure that there is not some
arch-deceiver leading us astray, so can we come to a like knowledge
of God under the like condition, and when we have attained to it,
it is sufficient, as I said before, to remove every doubt which we can
possess concerning clear and distinct ideas. 

[80]  (1) Thus, if a man proceeded with our investigations in due
order, inquiring first into those things which should first be
inquired into, never passing over a link in the chain of association,
and with knowledge how to define his questions before seeking to
answer them, he will never have any ideas save such as are very
certain, or, in other words, clear and distinct; for doubt is only a
suspension of the spirit concerning some affirmation or negation
which it would pronounce upon unhesitatingly if it were not in
ignorance of something, without which the knowledge of the matter in
hand must needs be imperfect.  (2) We may, therefore, conclude that
doubt always proceeds from want of due order in investigation.

[81]  (1) These are the points I promised to discuss in the first part
of my treatise on method.  (2) However, in order not to omit anything
which can conduce to the knowledge of the understanding and its
faculties, I will add a few words on the subject of memory and
forgetfulness.
   (81:3) The point most worthy of attention is, that memory is
strengthened both with and without the aid of the understanding.
(4) For the more intelligible a thing is, the more easily is it
remembered, and the less intelligible it is, the more easily do we
forget it.  (5) For instance, a number of unconnected words is much
more difficult to remember than the same number in the form of a
narration.

[82]  (1) The memory is also strengthened without the aid of the
understanding by means of the power wherewith the imagination or
the sense called common, is affected by some particular physical
object.  (2) I say particular, for the imagination is only affected
by particular objects.  (3) If we read, for instance, a single romantic
comedy, we shall remember it very well, so long as we do not read
many others of the same kind, for it will reign alone in the memory
(4) If, however, we read several others of the same kind, we shall
think of them altogether, and easily confuse one with another.
(82:5) I say also, physical.  (6) For the imagination is only
affected by physical objects.  (7) As, then, the memory is
strengthened both with and without the aid of the understanding,
we may conclude that it is different from the understanding,
and that in the latter considered in itself there is neither
memory nor forgetfulness. 

[83] (1) What, then, is memory? (2) It is nothing else than the
actual sensation of impressions on the brain, accompanied with the
thought of a definite duration, [83d] of the sensation.  (3) This
is also shown by reminiscence.  (4) For then we think of the
sensation, but without the notion of continuous duration; thus the
idea of that sensation is not the actual duration of the sensation
or actual memory.  (83:5) Whether ideas are or are not subject to
corruption will be seen in philosophy.  (6) If this seems too
absurd to anyone, it will be sufficient for our purpose, if he
reflect on the fact that a thing is more easily remembered in
proportion to its singularity, as appears from the example of
the comedy just cited.  (83:7) Further, a thing is remembered more
easily in proportion to its intelligibility; therefore we cannot
help remember that which is extremely singular and sufficiently
intelligible.
 

[84]  (1) Thus, then, we have distinguished between a true idea and
other perceptions, and shown that ideas fictitious, false, and the
rest, originate in the imagination - that is, in certain sensations
fortuitous (so to speak) and disconnected, arising not from the power
of the mind, but from external causes, according as the body,
sleeping or waking, receives various motions.
   (2) But one may take any view one likes of the imagination so long
as one acknowledges that it is different from the understanding, and
that the soul is passive with regard to it.  (3) The view taken is
immaterial, if we know that the imagination is something indefinite,
with regard to which the soul is passive, and that we can by some
means or other free ourselves therefrom with the help of the
understanding.  (4) Let no one then be astonished that before proving
the existence of body, and other necessary things, I speak of
imagination of body, and of its composition.  (5) The view taken is,
I repeat, immaterial, so long as we know that imagination is something
indefinite, &c. 

[85] (1) As regards as a true idea, we have shown that it is simple
or compounded of simple ideas; that it shows how and why something
is or has been made; and that its subjective effects in the soul
correspond to the actual reality of its object.  (2) This conclusion
is identical with the saying of the ancients, that true proceeds
from cause to effect; though the ancients, so far as I know,
never formed the conception put forward here that the soul acts
according to fixed laws, and is as it were an immaterial automaton. 

[86]  (1) Hence, as far as is possible at the outset, we have
acquired a knowledge of our understanding, and such a standard of
a true idea that we need no longer fear confounding truth with
falsehood and fiction.  (2) Neither shall we wonder why we
understand some things which in nowise fall within the scope of
the imagination, while other things are in the imagination but
wholly opposed to the understanding, or others, again, which
agree therewith.  (3) We now know that the operations, whereby the
effects of imagination are produced, take place under other laws
quite different from the laws of the understanding, and that the
mind is entirely passive with regard to them. 

[87]  (1) Whence we may also see how easily men may fall into grave
errors through not distinguishing accurately between the imagination
and the understanding; such as believing that extension must be
localized, that it must be finite, that its parts are really distinct
one from the other, that it is the primary and single foundation of
all things, that it occupies more space at one time than at another
and other similar doctrines, all entirely opposed to truth, as we
shall duly show. 

[88] (1) Again, since words are a part of the imagination - that is,
since we form many conceptions in accordance with confused
arrangements of words in the memory, dependent on particular bodily
conditions, - there is no doubt that words may, equally with the
imagination, be the cause of many and great errors, unless we 
strictly on our guard. 

[89] (1) Moreover, words are formed according to popular fancy and
intelligence, and are, therefore, signs of things as existing in the
imagination, not as existing in the understanding.  (2) This is
evident from the fact that to all such things as exist only in the
understanding, not in the imagination, negative names are often
given, such as incorporeal, infinite, &c.  (3) So, also, many
conceptions really affirmative are expressed negatively, and vice
versa, such as uncreate, independent, infinite, immortal, &c.,
inasmuch as their contraries are much more easily imagined, and,
therefore, occurred first to men, and usurped positive names.
(89:4) Many things we affirm and deny, because the nature of words
allows us to do so, though the nature of things does not.  (5) While
we remain unaware of this fact, we may easily mistake falsehood for
truth.

[90] (1) Let us also beware of another great cause of confusion,
which prevents the understanding from reflecting on itself.
(2) Sometimes, while making no distinction between the imagination
and the intellect, we think that what we more readily imagine is
clearer to us; and also we think that what we imagine we understand.
(3) Thus, we put first that which should be last: the true order of
progression is reversed, and no legitimate conclusion is drawn. 

[91]  [91e] (1) Now, in order at length to pass on to the second
part of this method, I shall first set forth the object aimed at,
and next the means for its attainment.  (2) The object aimed at
is the acquisition of clear and distinct ideas, such as are
produced by the pure intellect, and not by chance physical motions.
(3) In order that all ideas may be reduced to unity, we shall
endeavor so to associate and arrange them that our mind may, as far
as possible, reflect subjectively the reality of nature, both as
a whole and as parts. 

[92] (1) As for the first point, it is necessary (as we have said)
for our purpose that everything should be conceived, either solely
through its essence, or through its proximate cause.  (2) If the
thing be self-existent, or, as is commonly said, the cause of
itself, it must be understood through its essence only; if it be
not self-existent, but requires a cause for its existence, it must
be understood through its proximate cause.  (3) For, in reality,
the knowledge, [92f] of an effect is nothing else than the
acquisition of more perfect knowledge of its cause. 

[93] (1) Therefore, we may never, while we are concerned with
inquiries into actual things, draw any conclusion from
abstractions; we shall be extremely careful not to confound that
which is only in the understanding with that which is in the
thing itself. (2) The best basis for drawing a conclusion will
be either some particular affirmative essence, or a true and
legitimate definition.  (93:3) For the understanding cannot descend
from universal axioms by themselves to particular things, since
axioms are of infinite extent, and do not determine the
understanding to contemplate one particular thing more than
another. 

[94] (1) Thus the true method of discovery is to form thoughts
from some given definition.  (2) This process will be the
more fruitful and easy in proportion as the thing given be
better defined.  (3) Wherefore, the cardinal point of all this
second part of method consists in the knowledge of the conditions
of good definition, and the means of finding them.  (4) I will
first treat of the conditions of definition.

[95]  (1) A definition, if it is to be called perfect, must
explain the inmost essence of a thing, and must take care not
to substitute for this any of its properties.  (2) In order
to illustrate my meaning, without taking an example which
would seem to show a desire to expose other people's errors,
I will choose the case of something abstract, the definition
of which is of little moment.  (95:3) Such is a circle.  (4) If
a circle be defined as a figure, such that all straight lines
drawn from the center to the circumference are equal, every
one can see that such a definition does not in the least
explain the essence of a circle, but solely one of its
properties.  (5) Though, as I have said, this is of no
importance in the case of figures and other abstractions,
it is of great importance in the case of physical beings
and realities: for the properties of things are not understood
so long as their essences are unknown. (6) If the latter be
passed over, there is necessarily a perversion of the
succession of ideas which should reflect the succession of
nature, and we go far astray from our object.

[96]  In order to be free from this fault, the following rules
should be observed in definition:-
I.  (1) If the thing in question be created, the definition
   must (as we have said) comprehend the proximate cause.
   (2) For instance, a circle should, according to this rule,
   be defined as follows: the figure described by any line
   whereof one end is fixed and the other free.  (3) This
   definition clearly comprehends the proximate cause.
II.  (4) A conception or definition of a thing should be such
   that all the properties of that thing, in so far as it is
   considered by itself, and not in conjunction with other
   things, can be deduced from it, as may be seen in the
   definition given of a circle: for from that it clearly follows
   that all straight lines drawn from the center to the
   circumference are equal.  (5) That this is a necessary
   characteristic of a definition is so clear to anyone, who
   reflects on the matter, that there is no need to spend time
   in proving it, or in showing that, owing to this second
   condition, every definition should be affirmative.  (6) I
   speak of intellectual affirmation, giving little thought to
   verbal affirmations which, owing to the poverty of language,
   must sometimes, perhaps, be expressed negatively, though
   the idea contained is affirmative.

[97]  The rules for the definition of an uncreated thing
are as follows:--
I.  The exclusion of all idea of cause - that is, the thing
   must not need explanation by Anything outside itself.
II. When the definition of the thing has been given, there must
   be no room for doubt as to whether the thing exists or not.
III. It must contain, as far as the mind is concerned, no
   substantives which could be put into an adjectival form;
   in other words, the object defined must not be explained
   through abstractions.
IV. Lastly, though this is not absolutely necessary, it should
   be possible to deduce from the definition all the properties
   of the thing defined.
All these rules become obvious to anyone giving strict
attention to the matter.

[98]  (1) I have also stated that the best basis for drawing a
conclusion is a particular affirmative essence.  (2) The more
specialized the idea is, the more it is distinct, and therefore
clear.  (3) Wherefore a knowledge of particular things should
be sought for as diligently as possible.

[99]  (1) As regards the order of our perceptions, and the manner
in which they should be arranged and united, it is necessary that,
as soon as is possible and rational, we should inquire whether
there be any being (and, if so, what being), that is the cause
of all things, so that its essence, represented in thought, may
be the cause of all our ideas, and then our mind will to the
utmost possible extent reflect nature. (2) For it will possess,
subjectively, nature's essence, order, and union.  (3) Thus we
can see that it is before all things necessary for us to deduce
all our ideas from physical things - that is, from real entities,
proceeding, as far as may be, according to the series of causes,
from one real entity to another real entity, never passing to
universals and abstractions, either for the purpose of deducing
some real entity from them, or deducing them from some real
entity.  (4) Either of these processes interrupts the true
progress of the understanding.

[100]  (1) But it must be observed that, by the series of causes
and real entities, I do not here mean the series of particular
and mutable things, but only the series of fixed and eternal
things. (2) It would be impossible for human infirmity to follow
up the series of particular mutable things, both on account
their multitude, surpassing all calculation, and on account of
the infinitely diverse circumstances surrounding one and the same
thing, any one of which may be the cause of its existence or
non-existence.  (3) Indeed, their existence has no connection
with their essence, or (as we have said already) is not an
eternal truth.

[101] (1) Neither is there any need that we should understand
their series, for the essences of particular mutable things are
not to be gathered from their series or order of existence,
which would furnish us with nothing beyond their extrinsic
denominations, their relations, or, at most, their circumstances,
all of which are very different from their inmost essence.
(101:2) This inmost essence must be sought solely from fixed and
eternal things, and from the laws, inscribed (so to speak) in
those things as in their true codes, according to which all
particular things take place and are arranged; nay, these mutable
particular things depend so intimately and essentially (so to
phrase it) upon the fixed things, that they cannot either be
conceived without them.

[102]  (1) But, though this be so, there seems to be no small
difficulty in arriving at the knowledge of these particular things,
for to conceive them all at once would far surpass the powers of
the human understanding.  (2) The arrangement whereby one thing is
understood, before another, as we have stated, should not be sought
from their series of existence, nor from eternal things.  (3) For
the latter are all by nature simultaneous.  (4) Other aids are
therefore needed besides those employed for understanding eternal
things and their laws.  (5) However, this is not the place to recount
such aids, nor is there any need to do so, until we have acquired a
sufficient knowledge of eternal things and their infallible laws,
and until the nature of our senses has become plain to us.

[103]  (1) Before betaking ourselves to seek knowledge of particular
things, it will be seasonable to speak of such aids, as all tend to
teach us the mode of employing our senses, and to make certain
experiments under fixed rules and arrangements which may suffice to
determine the object of our inquiry, so that we may therefrom infer
what laws of eternal things it has been produced under, and may gain
an insight into its inmost nature, as I will duly show.  (2) Here,
to return to my purpose, I will only endeavor to set forth what seems
necessary for enabling us to attain to knowledge of eternal things,
and to define them under the conditions laid down above.

[104]  (1) With this end, we must bear in mind what has already been
stated, namely, that when the mind devotes itself to any thought, so
as to examine it, and to deduce therefrom in due order all the
legitimate conclusions possible, any falsehood which may lurk in the
thought will be detected; but if the thought be true, the mind will
readily proceed without interruption to deduce truths from it.
(104:2) This, I say, is necessary for our purpose, for our thoughts
may be brought to a close by the absence of a foundation.

[105]  (1) If, therefore, we wish to investigate the first thing of
all, it will be necessary to supply some foundation which may direct
our thoughts thither.  (2) Further, since method is reflective
knowledge, the foundation which must direct our thoughts can be
nothing else than the knowledge of that which constitutes the reality
of truth, and the knowledge of the understanding, its properties, and
powers.  (3) When this has been acquired we shall possess a foundation
wherefrom we can deduce our thoughts, and a path whereby the intellect,
according to its capacity, may attain the knowledge of eternal things,
allowance being made for the extent of the intellectual powers.

[106]  (1) If, as I stated in the first part, it belongs to the nature
of thought to form true ideas, we must here inquire what is meant by
the faculties and power of the understanding.  (2) The chief part of
our method is to understand as well as possible the powers of the
intellect, and its nature; we are, therefore, compelled (by the
considerations advanced in the second part of the method) necessarily
to draw these conclusions from the definition itself of thought and
understanding.

[107]  (1) But, so far as we have not got any rules for finding
definitions, and, as we cannot set forth such rules without a
previous knowledge of nature, that is without a definition of the
understanding and its power, it follows either that the definition
of the understanding must be clear in itself, or that we can
understand nothing.  (2) Nevertheless this definition is not
absolutely clear in itself; however, since its properties, like
all things that we possess through the understanding, cannot be
known clearly and distinctly, unless its nature be known previously,
understanding makes itself manifest, if we pay attention to its
properties, which we know clearly and distinctly.  (3) Let us,
then, enumerate here 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 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 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
    not to be relied on without great caution; for unless we are
    exceedingly careful we shall forthwith fall into error.
    (2) When things are conceived thus abstractedly, and not
    through their true essence, they are apt to be confused by the
    imagination.  (3) For that which is in itself one, men imagine
    to be multiplex.  (4) To those things which are conceived
    abstractedly, apart, and confusedly, terms are applied which are
    apt to become wrested from their strict meaning, and bestowed on
    things more familiar; whence it results that these latter are
    imagined in the same way as the former to which the terms were
    originally given.
[i] I shall here treat a little more in detail of experience,
    and shall examine the method adopted by the Empirics,
    and by recent philosophers.
[k] By native strength, I mean that not bestowed on us by external
    causes, as I shall afterwards explain in my philosophy.
[l] Here I term them operations: I shall explain their nature
    in my philosophy.
[m] I shall take care not only to demonstrate what I have just
    advanced, but also that we have hitherto proceeded rightly,
    and other things needful to be known.
[33note1] (1) In modern language, "the idea may become the
    subject of another presentation."  (2) Objectivus generally
    corresponds to the modern "subjective," formalis to the
    modern "objective." [Trans.- Note 1]
[n] (1) Observe that we are not here inquiring how the first
    subjective essence is innate in us.  (2) This belongs to an
    investigation into nature, where all these matters are amply
    explained, and it is shown that without ideas neither
    affirmation, nor negation, nor volition are possible.
[o] The nature of mental search is explained in my philosophy.
[p] To be connected with other things is to be produced by them,
    or to produce them.
[q] In the same way as we have here no doubt of the truth of
    our knowledge.
[r] See below the note on hypotheses, whereof we have a clear
    understanding; the fiction consists in saying that such
    hypotheses exist in heavenly bodies.
[s] (1) As a thing, when once it is understood, manifests itself,
    we have need only of an example without further proof.
    (2) In the same way the contrary has only to be presented to
    our minds to be recognized as false, as will forthwith appear
    when we come to discuss fiction concerning essences.
[t] Observe, that although many assert that they doubt whether God
    exists, they have nought but his name in their minds, or else
    some fiction which they call God: this fiction is not in
    harmony with God's real nature, as we will duly show.
[u] (1) I shall presently show that no fiction can concern eternal
    truths. By an eternal truth, I mean that which being positive
    could never become negative.  (2) Thus it is a primary and
    eternal truth that God exists, but it is not an eternal truth
    that Adam thinks.  (3) That the Chimaera does not exist is an
    eternal truth, that Adam does not think is not so.
[x] (1) Afterwards, when we come to speak of fiction that is
    concerned with essences, it will be evident that fiction never
    creates or furnishes the mind with anything new; only such things
    as are already in the brain or imagination are recalled to the
    memory, when the attention is directed to them confusedly and all
    at once.  (2) For instance, we have remembrance of spoken words
    and of a tree; when the mind directs itself to them confusedly,
    it forms the notion of a tree speaking.  (3) The same may be said
    of existence, especially when it is conceived quite generally as
    an entity; it is then readily applied to all things together in
    the memory.  (4) This is specially worthy of remark.
[y] We must understand as much in the case of hypotheses put forward
    to explain certain movements accompanying celestial phenomena;
    but from these, when applied to the celestial motions, we any
    draw conclusions as to the nature of the heavens, whereas this
    last may be quite different, especially as many other causes are
    conceivable which would account for such motions.
[z] (1) It often happens that a man recalls to mind this word soul,
    and forms at the same time some corporeal image: as the two
    representations are simultaneous, he easily thinks that he
    imagines and feigns a corporeal soul: thus confusing the name
    with the thing itself.  (2) I here beg that my readers will not
    be in a hurry to refute this proposition; they will, I hope,
    have no mind to do so, if they pay close attention to the
    examples given and to what follows.
[61a] (1) Though I seem to deduce this from experience, some
    may deny its cogency because I have given no formal proof.
    (2) I therefore append the following for those who may
    desire it.  (3) As there can be nothing in nature contrary
    to nature's laws, since all things come to pass by fixed
    laws, so that each thing must irrefragably produce its own
    proper effect, it follows that the soul, as soon as it
    possesses the true conception of a thing, proceeds to
    reproduce in thought that thing's effects.  (4) See below,
    where I speak of the false idea.
[64b] (1) Observe that fiction regarded in itself, only differs
    from dreams in that in the latter we do not perceive the
    external causes which we perceive through the senses while
    awake.  (2) It has hence been inferred that representations
    occurring in sleep have no connection with objects external
    to us.  (3) We shall presently see that error is the dreaming
    of a waking man: if it reaches a certain pitch it becomes delirium.
[76z] These are not attributes of God displaying His essence,
    as I will show in my philosophy.
[76a] (1) This has been shown already.  (2) For if such a being
    did not exist it would never be produced; therefore the mind
    would be able to understand more than nature could furnish;
    and this has been shown above to be false.
[78a] (1) That is, it is known that the senses sometimes deceive us.
    (2) But it is only known confusedly, for it is not known how
    they deceive us.
[83d] (1) If the duration be indefinite, the recollection is
    imperfect; this everyone seems to have learnt from nature.
    (2) For we often ask, to strengthen our belief in something
    we hear of, when and where it happened; though ideas
    themselves have their own duration in the mind, yet, as we
    are wont to determine duration by the aid of some measure
    of motion which, again, takes place by aid of imagination,
    we preserve no memory connected with pure intellect.
[91e] The chief rule of this part is, as appears from the first
    part, to review all the ideas coming to us through pure
    intellect, so as to distinguish them from such as we imagine:
    the distinction will be shown through the properties of each,
    namely, of the imagination and of the understanding.
[92f] Observe that it is thereby manifest that we cannot understand
    anything of nature without at the same time increasing our
    knowledge of the first cause, or God.





End of "On the Improvement of the Understanding."


Notes by Volunteer.

1. Used, in part, with kind permission from:
   http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/

2. The text is that of the translation of the Tractatus de Intellectus
   Emendatione by R. H. M. Elwes, as printed by Dover Publications
   (NY):1955), ISBN 0-486-20250-X.  This text is "an unabridged and
   unaltered republication of the Bohn Library edition originally
   published by George Bell and Sons in 1883."

3. Paragraph Numbers, shown thus [1], are from Edwin Curley's
   translation in his "The Collected Works of Spinoza", Volume 1, 1985,
   Princeton University Press; ISBN 0-691-07222-1.

4. Sentence Numbers, shown thus (1), have been added by volunteer.

5. Spinoza's endnotes are shown thus [a]. The letter is taken from
   Curley, see Note 3.

6. Search strings are enclosed in square brackets; include brackets.

7. HTML versions of "On the Improvement of the Understanding" are
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       http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/
       http://www.erols.com/jyselman/teielwes.htm