Ethics, part 2 (tran Elwes)
by Benedict de Spinoza
Hypertext Meanings and Commentaries
from the Encyclopedia of the Self
by Mark Zimmerman

Benedict de Spinoza, THE ETHICS  
(Ethica Ordine Geometrico Demonstrata)  
  
Translated by R. H. M. Elwes  
  
  
  
  
Part II: ON THE NATURE AND ORIGIN OF THE MIND  
  
  
  
PREFACE I now pass on to explaining the results, which must  
necessarily follow from the essence of  God, or of the eternal  
and infinite being; not, indeed, all of them (for we proved in  
Part i.,  Prop. xvi., that an infinite number must follow in an  
infinite number of ways), but only  those which are able to lead  
us, as it were by the hand, to the knowledge of the human  mind  
and its highest blessedness.
  
DEFINITIONS I. By 'body' I mean a mode which expresses in a  
certain determinate manner the essence  of God, in so far as he  
is considered as an extended thing. (See Pt. i., Prop. xxv.
Cor.)  
  
II. I consider as belonging to the essence of a thing that,  
which being given, the thing is  necessarily given also, and,  
which being removed, the thing is necessarily removed also;  in  
other words, that without which the thing, and which itself  
without the thing, can neither  be nor be conceived.
  
III. By 'idea,' I mean the mental conception which is formed by  
the mind as a thinking  thing.
  
>>>>>Explanation--I say 'conception' rather than perception,  
because the word perception  seems to imply that the mind is  
passive in respect to the object; whereas conception seems  to  
express an activity of the mind.
  
IV. By 'an adequate idea,' I mean an idea which, in so far as  
it is considered in itself,  without relation to the object, has  
all the properties or intrinsic marks of a true idea.
  
>>>>>Explanation--I say 'intrinsic,' in order to exclude that  
mark which is extrinsic,  namely, the agreement between the idea  
and its object (ideatum).
  
V. 'Duration' is the indefinite continuance of existing.
  
>>>>>Explanation--I say 'indefinite,' because it cannot be  
determined through the  existence itself of the existing thing,  
or by its efficient cause, which necessarily gives the  existence  
of the thing, but does not take it away.
  
VI. 'Reality' and 'perfection' I use as synonymous terms.
  
VII. By 'particular things,' I mean things which are finite and  
have a conditioned  existence; but if several individual things  
concur in one action, so as to be all  simultaneously the effect  
of one cause, I consider them all, so far, as one particular   
thing.
  
AXIOMS  I. The essence of man does not involve necessary  
existence, that is, it may, in the order of  nature, come to pass  
that this or that man does or does not exist.
  
II. Man thinks.
  
III. Modes of thinking, such as love, desire, or any other of  
the passions, do not take place,  unless there be in the same  
individual an idea of the thing loved, desired, &c. But the idea   
can exist without the presence of any other mode of thinking.
  
IV. We perceive that a certain body is affected in many ways.
  
V. We feel and perceive no particular things, save bodies and  
modes of thought.
  
N.B. The Postulates are given after the conclusion of Prop.
xiii.
  
PROPOSITIONS  I. Thought is an attribute of God, or God is a  
thinking thing.
  
>>>>>Proof--Particular thoughts, or this and that thought, are  
modes which, in a certain  conditioned manner, express the nature  
of God (Pt. i., Prop. xxv., Cor.). God therefore  possesses the  
attribute (Pt. i., Def. v.) of which the concept is involved in  
all particular  thoughts, which latter are conceived thereby.  
Thought, therefore, is one of the infinite  attributes of God,  
which express God's eternal and infinite essence (Pt. i., Def.
vi.). In  other words, God is a thinking thing. Q.E.D.
  
*****Note--This proposition is also evident from the fact, that  
we are able to conceive  an infinite thinking being. For, in  
proportion as a thinking being is conceived as thinking  more  
thoughts, so is it conceived as containing more reality or  
perfection. Therefore a  being, which can think an infinite  
number of things in an infinite number of ways, is,   
necessarily, in respect of thinking, infinite. As, therefore,  
from the consideration of  thought alone, we conceive an infinite  
being, thought is necessarily (Pt. i., Deff. iv. and vi.)  one of  
the infinite attributes of God, as we were desirous of showing.
  
II. Extension is an attribute of God, or God is an extended  
thing.
  
>>>>>Proof--The proof of this proposition is similar to that of  
the last.
  
III. In God there is necessarily the idea not only of his  
essence, but also of all things which  necessarily follow from  
his essence.
  
>>>>>Proof--God (by the first Prop. of this Part) can think an  
infinite number of things in  infinite ways, or (what is the same  
thing, by Prop. xvi., Part i.) can form the idea of his  essence,  
and of all things which necessarily follow therefrom. Now all  
that is in the power  of God necessarily is (Pt. i., Prop.
xxxv.). Therefore, such an idea as we are considering   
necessarily is, and in God alone. Q.E.D. (Part i., Prop. xv.)  
  
*****Note--The multitude understand by the power of God the free  
will of God, and the  right over all things that exist, which  
latter are accordingly generally considered as  contingent. For  
it is said that God has the power to destroy all things, and to  
reduce them  to nothing. Further, the power of God is very often  
likened to the power of kings. But  this doctrine we have  
refuted (Pt. i., Prop. xxxii., Cors. i. and ii.), and we have  
shown  (Part i., Prop. xvi.) that God acts by the same necessity,  
as that by which he understands  himself; in other words, as it  
follows from the necessity of the divine nature (as all admit),   
that God understands himself, so also does it follow by the same  
necessity, that God  performs infinite acts in infinite ways. We  
further showed (Part i., Prop. xxxiv.), that  God's power is  
identical with God's essence in action; therefore it is as  
impossible for us  to conceive God as not acting, as to conceive  
him as non-existent. If we might pursue  the subject further, I  
could point out, that the power which is commonly attributed to  
God  is not only human (as showing that God is conceived by the  
multitude as a man, or in the  likeness of a man), but involves a  
negation of power. However, I am unwilling to go over  the same  
ground so often. I would only beg the reader again and again, to  
turn over  frequently in his mind what I have said in Part i.
from Prop. xvi. to the end. No one will  be able to follow my  
meaning, unless he is scrupulously careful not to confound the  
power  of God with the human power and right of kings.
  
IV. The idea of God, from which an infinite number of things  
follow in infinite ways, can  only be one.
  
>>>>>Proof--Infinite intellect comprehends nothing save the  
attributes of God and his  modifications (Part i., Prop. xxx.).  
Now God is one (Part i., Prop. xiv., Cor.). Therefore  the idea  
of God, wherefrom an infinite number of things follow in infinite  
ways, can only  be one. Q.E.D.
  
V. The actual being of ideas owns God as its cause, only in so  
far as he is considered as a  thinking thing, not in so far as he  
is unfolded in any other attribute; that is, the ideas both  of  
the attributes of God and of particular things do not own as  
their efficient cause their  objects (ideata) or the things  
perceived, but God himself in so far as he is a thinking thing.
  
>>>>>Proof--This proposition is evident from Prop. iii. of this  
Part. We there drew the  conclusion, that God can form the idea  
of his essence, and of all things which follow  necessarily  
therefrom, solely because he is a thinking thing, and not because  
he is the  object of his own idea. Wherefore the actual being of  
ideas owns for cause God, in so far  as he is a thinking thing.  
It may be differently proved as follows: the actual being of  
ideas  is (obviously) a mode of thought, that is (Part i., Prop.
xxv., Cor.) a mode which expresses  in a certain manner the  
nature of God, in so far as he is a thinking thing, and therefore   
(Part i., Prop. x.) involves the conception of no other attribute  
of God, and consequently  (by Part i., Ax. iv.) is not the effect  
of any attribute save thought. Therefore the actual  being of  
ideas owns God as its cause, in so far as he is considered as a  
thinking thing, &c.  Q.E.D.
  
VI. The modes of any given attribute are caused by God, in so  
far as he is considered  through the attribute of which they are  
modes, and not in so far as he is considered through  any other  
attribute.
  
>>>>>Proof--Each attribute is conceived through itself, without  
any other part (Part i.,  Prop. x.); wherefore the modes of each  
attribute involve the conception of that attribute,  but not of  
any other. Thus (Part i., Ax. iv.) they are caused by God, only  
in so far as he  is considered through the attribute whose modes  
they are, and not in so far as he is  considered through any  
other. Q.E.D.
  
<<<<being of things, which are not  
modes of thought, does  not follow from the divine nature,  
because that nature has prior knowledge of the things.  Things  
represented in ideas follow, and are derived from their  
particular attribute, in the  same manner, and with the same  
necessity as ideas follow (according to what we have  shown) from  
the attribute of thought.
  
VII. The order and connection of ideas is the same as the order  
and connection of things.
  
>>>>>Proof--This proposition is evident from Part i., Ax. iv.  
For the idea of everything  that is caused depends on a  
knowledge of the cause, whereof it is an effect.
  
<<<<thinking is equal to his  
realized power of action-- that is, whatsoever follows from the  
infinite nature of God in the world of extension  (formaliter),  
follows without exception in the same order and connection from  
the idea of  God in the world of thought (objective).
  
*****Note--Before going any further, I wish to recall to mind  
what has been pointed out  above--namely, that whatsoever can be  
perceived by the infinite intellect as constituting the  essence  
of substance, belongs altogether only to one substance:  
consequently, substance  thinking and substance extended are one  
and the same substance, comprehended now  through one attribute,  
now through the other. So, also, a mode of extension and the  
idea  of that mode are one and the same thing, though expressed  
in two ways. This truth seems  to have been dimly recognized by  
those Jews who maintained that God, God's intellect,  and the  
things understood by God are identical. For instance, a circle  
existing in nature,  and the idea of a circle existing, which is  
also in God, are one and the same thing displayed  through  
different attributes. Thus, whether we conceive nature under the  
attribute of  extension, or under the attribute of thought, or  
under any other attribute, we shall find the  same order, or one  
and the same chain of causes--that is, the same things following  
in  either case.
  
I said that God is the cause of an idea--for instance, of the  
idea of a circle,--in so far as he  is a thinking thing; and of a  
circle, in so far as he is an extended thing, simply because the   
actual being of the idea of a circle can only be perceived as a  
proximate cause through  another mode of thinking, and that again  
through another, and so on to infinity; so that, so  long as we  
consider things as modes of thinking, we must explain the order  
of the whole of  nature, or the whole chain of causes, through  
the attribute of thought only. And, in so far  as we consider  
things as modes of extension, we must explain the order of the  
whole of  nature through the attributes of extension only; and so  
on, in the case of the other  attributes. Wherefore of things as  
they are in themselves God is really the cause, inasmuch  as he  
consists of infinite attributes. I cannot for the present  
explain my meaning more  clearly.
  
VIII. The ideas of particular things, or of modes, that do not  
exist, must be comprehended  in the infinite idea of God, in the  
same way as the formal essences of particular things or  modes  
are contained in the attributes of God.
  
>>>>>Proof--This proposition is evident from the last; it is  
understood more clearly from  the preceding note.
  
<<<< exist, except in so far as they  are comprehended in the  
attributes of God, their representations in thought or ideas do  
not  exist, except in so far as the infinite idea of God exists;  
and when the particular things are  said to exist, not only in so  
far as they are involved in the attributes of God, but also in so  
far as they are said to continue, their ideas will also involve  
existence, through which they  are said to continue.
  
*****Note--If anyone desires an example to throw more light on  
this question, I shall, I  fear, not be able to give him any,  
which adequately explains the thing of which I here  speak,  
inasmuch as it is unique; however, I will endeavour to  
illustrate it as far as possible.  The nature of a circle is  
such that if any number of straight lines intersect within it,  
the  rectangles formed by their segments will be equal to one  
another; thus, infinite equal  rectangles are contained in a  
circle. Yet none of these rectangles can be said to exist,   
except in so far as the circle exists; nor can the idea of any of  
these rectangles be said to  exist, except in so far as they are  
comprehended in the idea of the circle. Let us grant that,   
from this infinite number of rectangles, two only exist. The  
ideas of these two not only  exist, in so far as they are  
contained in the idea of the circle, but also as they involve the  
existence of those rectangles; wherefore they are distinguished  
from the remaining ideas of  the remaining rectangles.
  
IX. The idea of an individual thing actually existing is caused  
by God, not in so far as he  is infinite, but in so far as he is  
considered as affected by another idea of a thing actually   
existing, of which he is the cause, in so far as he is affected  
by a third idea, and so on to  infinity.
  
>>>>>Proof--The idea of an individual thing actually existing is  
an individual mode of  thinking, and is distinct from other modes  
(by the Cor. and Note to Prop. viii. of this part);  thus (by  
Prop. vi. of this part) it is caused by God, in so far only as he  
is a thinking thing.  But not (by Prop. xxviii. of Part i.) in  
so far as he is a thing thinking absolutely, only in so  far as  
he is considered as affected by another mode of thinking; and he  
is the cause of this  latter, as being affected by a third, and  
so on to infinity. Now, the order and connection  of ideas is  
(by Prop. vii. of this book) the same as the order and connection  
of causes.  Therefore of a given individual idea another  
individual idea, or God, in so far as he is  considered as  
modified by that idea, is the cause; and of this second idea God  
is the  cause, in so far as he is affected by another idea, and  
so on to infinity. Q.E.D.
  
<<<<object  
of any idea, the  knowledge thereof is in God, in so far only as  
he has the idea of the object.
  
>>>>>Proof--Whatsoever takes place in the object of any idea, its  
idea is in God (by  Prop. iii. of this part), not in so far as he  
is infinite, but in so far as he is considered as  affected by  
another idea of an individual thing (by the last Prop.); but (by  
Prop. vii. of  this part) the order and connection of ideas is  
the same as the order and connection of  things. The knowledge,  
therefore, of that which takes place in any individual object  
will  be in God, in so far only as he has the idea of that  
object. Q.E.D.
  
X. The being of substance does not appertain to the essence of  
man--in other words,  substance does not constitute the actual  
being (forma) of man.
  
>>>>>Proof--The being of substance involves necessary existence  
(Part i., Prop. vii.).  If, therefore, the being of substance  
appertains to the essence of man, substance being  granted, man  
would necessarily be granted also (II. Def. ii.), and,  
consequently, man would  necessarily exist, which is absurd (II.
Ax. i.). Therefore &c. Q.E.D.
  
*****Note--This proposition may also be proved from I.v., in  
which it is shown that there  cannot be two substances of the  
same nature; for as there may be many men, the being of   
substance is not that which constitutes the actual being of man.  
Again, the proposition is  evident from the other properties of  
substance--namely, that substance is in its nature  infinite,  
immutable, indivisible, &c., as anyone may see for himself.
  
<<<< constituted by certain  modifications of the attributes of God.  
For (by the last Prop.) the being of substance does  not belong  
to the essence of man. That essence therefore (by I. xv.) is  
something which is  in God, and which without God can neither be  
nor be conceived, whether it be a  modification (I. xxv. Cor.),  
or a mode which expresses God's nature in a certain  conditioned  
manner.
  
*****Note--Everyone must surely admit, that nothing can be or be  
conceived without  God. All men agree that God is the one and  
only cause of all things, both of their essence  and of their  
existence; that is, God is not only the cause of things in  
respect to their being  made (secundum fieri), but also in  
respect to their being (secundum esse).
  
At the same time many assert, that that, without which a thing  
cannot be nor be conceived,  belongs to the essence of that  
thing; wherefore they believe that either the nature of God   
appertains to the essence of created things, or else that created  
things can be or be  conceived without God; or else, as is more  
probably the case, they hold inconsistent  doctrines. I think  
the cause for such confusion is mainly, that they do not keep to  
the  proper order of philosophic thinking. The nature of God,  
which should be reflected on  first, inasmuch as it is prior both  
in the order of knowledge and the order of nature, they  have  
taken to be last in the order of knowledge, and have put into the  
first place what they  call the objects of sensation; hence,  
while they are considering natural phenomena, they  give no  
attention at all to the divine nature, and, when afterwards they  
apply their mind to  the study of the divine nature, they are  
quite unable to bear in mind the first hypotheses,  with which  
they have overlaid the knowledge of natural phenomena, inasmuch  
as such  hypotheses are no help towards understanding the divine  
nature. So that it is hardly to be  wondered at, that these  
persons contradict themselves freely.
  
However, I pass over this point. My intention her was only to  
give a reason for not saying,  that that, without which a thing  
cannot be or be conceived, belongs to the essence of that  thing:  
individual things cannot be or be conceived without God, yet God  
does not  appertain to their essence. I said that "I considered  
as belonging to the essence of a thing  that, which being given,  
the thing is necessarily given also, and which being removed, the   
thing is necessarily removed also; or that without which the  
thing, and which itself without  the thing can neither be nor be  
conceived."  (II. Def. ii.)  
  
XI. The first element, which constitutes the actual being of the  
human mind, is the idea of  some particular thing actually  
existing.
  
>>>>>Proof--The essence of man (by the Cor. of the last Prop.) is  
constituted by certain  modes of the attributes of God, namely  
(by II. Ax. ii.), by the modes of thinking, of all  which (by II.
Ax. iii.) the idea is prior in nature, and, when the idea is  
given, the other  modes (namely, those of which the idea is prior  
in nature) must be in the same individual  (by the same Axiom).  
Therefore an idea is the first element constituting the human  
mind.  But not the idea of a non-existent thing, for then (II.
viii. Cor.) the idea itself cannot be  said to exist; it must  
therefore be the idea of something actually existing. But not of  
an  infinite thing. For an infinite thing (I. xxi., xxii.), must  
always necessarily exist; this would  (by II. Ax. i.) involve an  
absurdity. Therefore the first element, which constitutes the   
actual being of the human mind, is the idea of something actually  
existing. Q.E.D.
  
<<<<mind is part of  
the infinite intellect of  God; thus when we say, that the human  
mind perceives this or that, we make the assertion,  that God has  
this or that idea, not in so far as he is infinite, but in so far  
as he is displayed  through the nature of the human mind, or in  
so far as he constitutes the essence of the  human mind; and when  
we say that God has this or that idea, not only in so far as he   
constitutes the essence of the human mind, but also in so far as  
he, simultaneously with the  human mind, has the further idea of  
another thing, we assert that the human mind  perceives a thing  
in part or inadequately.
  
*****Note--Here, I doubt not, readers will come to a stand, and  
will call to mind many  things which will cause them to hesitate;  
I therefore beg them to accompany me slowly,  step by step, and  
not to pronounce on my statements, till they have read to the  
end.
  
XII. Whatsoever comes to pass in the object of the idea, which  
constitutes the human  mind, must be perceived by the human mind,  
or there will necessarily be an idea in the  human mind of the  
said occurrence. That is, if the object of the idea constituting  
the  human mind be a body, nothing can take place in that body  
without being perceived by  the mind.
  
>>>>>Proof--Whatsoever comes to pass in the object of any idea,  
the knowledge  thereof is necessarily in God (II. ix. Cor.), in  
so far as he is considered as affected by  the idea of the said  
object, that is (II. xi.), in so far as he constitutes the mind  
of anything.  Therefore, whatsoever takes place in the object  
constituting the idea of the human mind,  the knowledge thereof  
is necessarily in God, in so far as he constitutes the essence of  
the  human mind; that is (by II. xi. Cor.) the knowledge of the  
said thing will necessarily be  in the mind, in other words the  
mind perceives it.
  
*****Note--This proposition is also evident, and is more clearly  
to be understood from  II. vii., which see.
  
XIII. The object of the idea constituting the human mind is the  
body, in other words a  certain mode of extension which actually  
exists, and nothing else.
  
>>>>>Proof--If indeed the body were not the object of the human  
mind, the ideas of the  modifications of the body would not be in  
God (II. ix. Cor.) in virtue of his constituting  our mind, but  
in virtue of his constituting the mind of something else; that is  
(II. xi. Cor.)  the ideas of the modifications of the body would  
not be in our mind: now (by II. Ax. iv.)  we do possess the idea  
of the modifications of the body. Therefore the object of the   
idea constituting the human mind is the body, and the body as it  
actually exists (II. xi.).  Further, if there were any other  
object of the idea constituting the mind besides body,  then, as  
nothing can exist from which some effect does not follow (I.
xxxvi.) there would  necessarily have to be in our mind an idea,  
which would be the effect of that other object  (II. xi.); but  
(I. Ax. v.) there is no such idea. Wherefore the object of our  
mind is the body  as it exists, and nothing else. Q.E.D.
  
*****Note--We thus comprehend, not only that the human mind is  
united to the body,  but also the nature of the union between  
mind and body. However, no one will be able  to grasp this  
adequately or distinctly, unless he first has adequate knowledge  
of the nature  of our body. The propositions we have advanced  
hitherto have been entirely general,  applying not more to men  
than to other individual things, all of which, though in  
different  degrees, are animated (animata). For of everything  
there is necessarily an idea in God, of  which God is the cause,  
in the same way as there is an idea of the human body; thus   
whatever we have asserted of the idea of the human body must  
necessarily also be asserted  of the idea of everything else.  
Still, on the other hand, we cannot deny that ideas, like   
objects, differ one from the other, one being more excellent than  
another and containing  more reality, just as the object of one  
idea is more excellent than the object of another idea,  and  
contains more reality.
  
Wherefore, in order to determine, wherein the human mind differs  
from other things, and  wherein it surpasses them, it is  
necessary for us to know the nature of its object, that is,  of  
the human body. What this nature is, I am not able here to  
explain, nor is it necessary  for the proof of what I advance,  
that I should do so. I will only say generally, that in   
proportion as any given body is more fitted than others for doing  
many actions or receiving  many impressions at once, so also is  
the mind, of which it is the object, more fitted than  others for  
forming many simultaneous perceptions; and the more the actions  
of the body  depend on itself alone, and the fewer other bodies  
concur with it in action, the more fitted  is the mind of which  
it is the object for distinct comprehension. We may thus  
recognize  the superiority of one mind over others, and may  
further see the cause, why we have only a  very confused  
knowledge of our body, and also many kindred questions, which I  
will, in  the following propositions, deduce from what has been  
advanced. Wherefore I have  thought it worth while to explain  
and prove more strictly my present statements. In order  to do  
so, I must premise a few propositions concerning the nature of  
bodies.
  
---Axiom I. All bodies are either in motion or at rest.
  
---Axiom II. Every body is moved sometimes more slowly,  
sometimes more quickly.
  
Lemma I. Bodies are distinguished from one another in respect of  
motion and rest,  quickness and slowness, and not in respect of  
substance.
  
>>>>>Proof--The first part of this proposition is, I take it,  
self-evident. That bodies are  not distinguished in respect of  
substance, is plain both from I. v. and I. viii. It is brought   
out still more clearly from I. xv., Note.
  
Lemma II. All bodies agree in certain respects.
  
>>>>>Proof--All bodies agree in the fact, that they involve the  
conception of one and the  same attribute (II., Def. i.).  
Further, in the fact that they may be moved less or more   
quickly, and may be absolutely in motion or at rest.
  
Lemma III. A body in motion or at rest must be determined to  
motion or rest by another  body, which other body has been  
determined to motion or rest by a third body, and that  third  
again by a fourth, and so on to infinity.
  
>>>>>Proof--Bodies are individual things (II., Def. i.), which  
(Lemma i.) are distinguished  one from the other in respect to  
motion and rest; thus (I. xxviii.) each must necessarily be   
determined to motion or rest by another individual thing, namely  
(II. vi.) by another body,  which other body is also (Ax. i.) in  
motion or at rest. And this body again can only have  been set  
in motion or caused to rest by being determined by a third body  
to motion or rest.  This third body again by a fourth, and so on  
to infinity. Q.E.D.
  
<<<< motion, until it is  determined to a state of rest by some other  
body; and a body at rest remains so, until it is  determined to a  
state of motion by some other body. This is indeed self-evident.  
For  when I suppose, for instance, that a given body, A, is at  
rest, and do not take into  consideration other bodies in motion,  
I cannot affirm anything concerning the body A,  except that it  
is at rest. If it afterwards comes to pass that A is in motion,  
this cannot have  resulted from its having been at rest, for no  
other consequence could have been involved  than its remaining at  
rest. If, on the other hand, A be given in motion, we shall, so  
long as  we only consider A, be unable to affirm anything  
concerning it, except that it is in motion.  If A is  
subsequently found to be at rest, this rest cannot be the result  
of A's previous  motion, for such motion can only have led to  
continued motion; the state of rest therefore  must have resulted  
from something, which was not in A, namely, from an external  
cause  determining A to a state of rest.
  
-----Axiom I--All modes, wherein one body is affected by another  
body, follow  simultaneously from the nature of the body  
affected and the body affecting; so that one  and the same body  
may be moved in different modes, according to the difference in  
the  nature of the bodies moving it; on the other hand, different  
bodies may be moved in  different modes by one and the same body.
  
-----Axiom II--When a body in motion impinges on another body at  
rest, which it is  unable to move, it recoils, in order to  
continue its motion, and the angle made by the line  of motion in  
the recoil and the plane of the body at rest, whereon the moving  
body has  impinged, will be equal to the angle formed by the line  
of motion of incidence and the  same plane.
  
So far we have been speaking only of the most simple bodies,  
which are only distinguished  one from the other by motion and  
rest, quickness and slowness. We now pass on to  compound  
bodies.
  
Definition--When any given bodies of the same or different  
magnitude are compelled by  other bodies to remain in contact, or  
if they be moved at the same or different rates of  speed, so  
that their mutual movements should preserve among themselves a  
certain fixed  relation, we say that such bodies are 'in union,'  
and that together they compose one body  or individual, which is  
distinguished from other bodies by the fact of this union.
  
-----Axiom III--In proportion as the parts of an individual, or  
a compound body, are in  contact over a greater or less  
superficies, they will with greater or less difficulty admit of   
being moved from their position; consequently the individual  
will, with greater or less  difficulty, be brought to assume  
another form. Those bodies, whose parts are in contact  over  
large superficies, are called 'hard;' those, whose parts are in  
contact over small  superficies, are called 'soft;' those, whose  
parts are in motion among one another, are  called 'fluid.'  
  
Lemma IV. If from a body or individual, compounded of several  
bodies, certain bodies be  separated, and if, at the same time,  
an equal number of other bodies of the same nature  take their  
place, the individual will preserve its nature as before, without  
any change in its  actuality (forma).
  
>>>>>Proof--Bodies (Lemma i.) are not distinguished in respect of  
substance: that which  constitutes the actuality (formam) of an  
individual consists (by the last Def.) in a union of  bodies; but  
this union, although there is a continual change of bodies, will  
(by our  hypothesis) be maintained; the individual, therefore,  
will retain its nature as before, both in  respect of substance  
and in respect of mode. Q.E.D.
  
Lemma V. If the parts composing an individual become greater or  
less, but in such  proportion, that they all preserve the same  
mutual relations of motion and rest, the  individual will still  
preserve its original nature, and its actuality will not be  
changed.
  
>>>>>Proof--The same as for the last Lemma.
  
Lemma VI. If certain bodies composing an individual be compelled  
to change the motion,  which they have in one direction, for  
motion in another direction, but in such a manner,  that they be  
able to continue their motions and their mutual communication in  
the same  relations as before, the individual will retain its own  
nature without any change of its  actuality.
  
>>>>>Proof--This proposition is self-evident, for the individual  
is supposed to retain all  that, which, in its definition, we  
spoke of as its actual being.
  
Lemma VII. Furthermore, the individual thus composed preserves  
its nature, whether it  be, as a whole, in motion or at rest,  
whether it be moved in this or that direction; so long  as each  
part retains its motion, and preserves its communication with  
other parts as  before.
  
>>>>>Proof--This proposition is evident from the definition of an  
individual prefixed to  Lemma iv.
  
*****Note--We thus see, how a composite individual may be  
affected in many different  ways, and preserve its nature  
notwithstanding. Thus far we have conceived an individual  as  
composed of bodies only distinguished one from the other in  
respect of motion and  rest, speed and slowness; that is, of  
bodies of the most simple character. If, however, we  now  
conceive another individual composed of several individuals of  
diverse natures, we  shall find that the number of ways in which  
it can be affected, without losing its nature, will  be greatly  
multiplied. Each of its parts would consist of several bodies,  
and therefore (by  Lemma vi.) each part would admit, without  
change to its nature, of quicker or slower  motion, and would  
consequently be able to transmit its motions more quickly or more  
slowly to the remaining parts. If we further conceive a third  
kind of individuals composed  of individuals of this second kind,  
we shall find that they may be affected in a still greater   
number of ways without changing their actuality. We may easily  
proceed thus to infinity,  and conceive the whole of nature as  
one individual, whose parts, that is, all bodies, vary in   
infinite ways, without any change in the individual as a whole.  
I should feel bound to  explain and demonstrate this point at  
more length, if I were writing a special treatise on  body. But  
I have already said that such is not my object; I have only  
touched on the  question, because it enables me to prove easily  
that which I have in view.
  
POSTULATES I. The human body is composed of a number of  
individual parts, of diverse nature, each  one of which is in  
itself extremely complex.
  
II. Of the individual parts composing the human body some are  
fluid, some soft, some  hard.
  
III. The individual parts composing the human body, and  
consequently the human body  itself, are affected in a variety of  
ways by external bodies.
  
IV. The human body stands in need for its preservation of a  
number of other bodies, by  which it is continually, so to speak,  
regenerated.
  
V. When the fluid part of the human body is determined by an  
external body to impinge  often on another soft part, it changes  
the surface of the latter, and, as it were, leaves the   
impression thereupon of the external body which impels it.
  
VI. The human body can move external bodies, and arrange them in  
a variety of ways.
  
PROPOSITIONS XIV. The human mind is capable of perceiving a  
great number of things, and is so in   proportion as its body is  
capable of receiving a great number of impressions.
  
>>>>>Proof--The human body (by Post. iii. and vi.) is affected in  
very many ways by  external bodies, and is capable in very many  
ways of affecting external bodies. But (II.xii.)  the human mind  
must perceive all that takes place in the human body; the human  
mind is,  therefore, capable of perceiving a great number of  
things, and is so in proportion, &c.  Q.E.D.
  
XV. The idea, which constitutes the actual being of the human  
mind, is not simple, but  compounded of a great number of ideas.
  
>>>>>Proof--The idea constituting the actual being of the human  
mind is the idea of the  body (II. xiii.), which (Post. i.) is  
composed of a great number of complex individual  parts. But  
there is necessarily in God the idea of each individual part  
whereof the body is  composed (II. viii. Cor.); therefore (II.
vii.), the idea of the human body is composed of  each of these  
numerous ideas of its component parts. Q.E.D.
  
XVI. The idea of every mode, in which the human body is  
affected by external bodies,  must involve the nature of the  
human body, and also the nature of the external body.
  
>>>>>Proof--All the modes, in which any given body is affected,  
follow from the nature  of the body affected, and also from the  
nature of the affecting body (by Ax. i., after the  Cor. of Lemma  
iii.), wherefore their idea is also necessarily (by I, Ax. iv.)  
involves the  nature of both bodies; therefore, the idea of every  
mode, in which the human body is  affected by external bodies,  
involves the nature of the human body and of the external  body.  
Q.E.D.
  
<<<<mind  
perceives the nature of a  variety of bodies, together with the  
nature of its own.
  
<<<< we have of external bodies,  indicate rather the constitution of  
our own body than the nature of external bodies. I have  amply  
illustrated this in the Appendix to Part I.
  
XVII. If the human body is affected in a manner which involves  
the nature of any external  body, the human mind will regard the  
said external body as actually existing, or as present  to  
itself, until the human body be affected in such a way, as to  
exclude the existence or the  presence of the said external body.
  
>>>>>Proof--This proposition is self-evident, for so long as the  
human body continues to  be thus affected, so long will the human  
mind (II. xii.) regard this modification of the body  --that is  
(by the last Prop.), it will have the idea of the mode as  
actually existing, and this  idea involves the nature of the  
external body; therefore the mind (by II. xvi., Cor. i.) will   
regard the external body as actually existing, until it is  
affected, &c. Q.E.D.
  
<<<<mind is able to regard as present external  
bodies, by which the  human body has once been affected, even  
though they be no longer in existence or present.
  
>>>>>Proof--When external bodies determine the fluid parts of the  
human body, so that  they often impinge on the softer parts, they  
change the surface of the last named (Post. v);  hence (Ax. ii.,  
after the Cor. of Lemma iii.) they are refracted therefrom in a  
different  manner from that which they followed before such  
change; and, further, when afterwards  they impinge on the new  
surfaces by their own spontaneous movement, they will be   
refracted in the same manner, as though they had been impelled  
towards those surfaces by  external bodies; consequently, they  
will, while they continue to be thus refracted, affect the  human  
body in the same manner, whereof the mind (II. xii.) will again  
take cognizance  --that is (II. xvii.), the mind will again  
regard the external body as present, and will do so,  as often as  
the fluid parts of the human body impinge on the aforesaid  
surfaces by their  own spontaneous motion. Wherefore, although  
the external bodies, by which the human  body has once been  
affected, be no longer in existence, the mind will nevertheless  
regard  them as present, as often as this action of the body is  
repeated. Q.E.D.
  
*****Note--We thus see how it comes about, as is often the case,  
that we regard as  present many things which are not. It is  
possible that the same result may be brought about  by other  
causes; but I think it suffices for me here to have indicated one  
possible  explanation, just as well as if I had pointed out the  
true cause. Indeed, I do not think I  am very far from the  
truth, for all my assumptions are based on postulates, which  
rest,  almost without exception, on experience, that cannot be  
controverted by those who have  shown, as we have, that the human  
body, as we feel it, exists (Cor. after II. xiii.).  Furthermore  
(II. vii. Cor., II. xvi. Cor. ii.), we clearly understand what is  
the difference  between the idea, say, of Peter, which  
constitutes the essence of Peter's mind, and the  idea of the  
said Peter, which is in another man, say, Paul. The former  
directly answers to  the essence of Peter's own body, and only   
implies existence so long as Peter exists; the  latter indicates  
rather the disposition of Paul's body than the nature of Peter,  
and,  therefore, while this disposition of Paul's body lasts,  
Paul's mind will regard Peter as  present to itself, even though  
he no longer exists. Further, to retain the usual phraseology,   
the modifications of the human body, of which the ideas represent  
external bodies as  present to us, we will call the images of  
things, though they do not recall the figure of  things. When  
the mind regards bodies in this fashion, we say that it imagines.  
I will here  draw attention to the fact, in order to indicate  
where error lies, that the imaginations of the  mind, looked at  
in themselves, do not contain error. The mind does not err in  
the mere act  of imagining, but only in so far as it is regarded  
as being without the idea, which excludes  the existence of such  
things as it imagines to be present to it. If the mind, while  
imagining  non-existent things as present to it, is at the same  
time conscious that they do not really  exist, this power of  
imagination must be set down to the efficacy of its nature, and  
not to a  fault, especially if this faculty of imagination depend  
solely on its own nature--that is (I. Def. vii.), if this  
faculty of imagination be free.
  
XVIII. If the human body has once been affected by two or more  
bodies at the same  time, when the mind afterwards imagines any  
of them, it will straightway remember the  others also.
  
>>>>>Proof--The mind (II. xvii. Cor.) imagines any given body,  
because the human body  is affected and disposed by the  
impressions from an external body, in the same manner as  it is  
affected when certain of its parts are acted on by the said  
external body; but (by our  hypothesis) the body was then so  
disposed, that the mind imagined two bodies at once;  therefore,  
it will also in the second case imagine two bodies at once, and  
the mind, when  it imagines one, will straightway remember the  
other. Q.E.D.
  
*****Note--We now clearly see what 'Memory' is. It is simply a  
certain association of  ideas involving the nature of things  
outside the human body, which association arises in the  mind  
according to the order and association of the modifications  
(affectiones) of the  human body. I say, first, it is an  
association of those ideas only, which involve the nature  of  
things outside the human body: not of ideas which answer to the  
nature of the said  things: ideas of the modifications of the  
human body are, strictly speaking (II. xvi.), those  which  
involve the nature both of the human body and of external bodies.  
I say, secondly,  that this association arises according to the  
order and association of the modifications of  the human body, in  
order to distinguish it from that association of ideas, which  
arises from  the order of the intellect, whereby the mind  
perceives things through their primary causes,  and which is in  
all men the same. And hence we can further clearly understand,  
why the  mind from the thought of one thing, should straightway  
arrive at the thought of another  thing, which has no similarity  
with the first; for instance, from the thought of the word   
'pomum' (an apple), a Roman would straightway arrive at the  
thought of the fruit apple,  which has no similitude with the  
articulate sound in question, nor anything in common  with it,  
except that the body of the man has often been affected by these  
two things; that  is, that the man has often heard the word  
'pomum,' while he was looking at the fruit;  similarly every man  
will go on from one thought to another, according as his habit  
has  ordered the images of things in his body. For a soldier,  
for instance, when he sees the  tracks of a horse in sand, will  
at once pass from the thought of a horse to the thought of a   
horseman, and thence to the thought of war, &c.; while a  
countryman will proceed from  the thought of a horse to the  
thought of a plough, a field, &c. Thus every man will follow   
this or that train of thought, according as he has been in the  
habit of conjoining and  associating the mental images of things  
in this or that manner.
  
XIX. The human mind has no knowledge of the body, and does not  
know it to exist, save  through the ideas of the modifications  
whereby the body is affected.
  
>>>>>Proof--The human mind is the very idea or knowledge of the  
human body (II. xiii.),  which (II. ix.) is in God, in so far as  
he is regarded as affected by another idea of a  particular thing  
actually existing: or, inasmuch as (Post. iv.) the human body  
stands in  need of very many bodies whereby it is, as it were,  
continually regenerated; and the order  and connection of ideas  
is the same as the order and connection of causes (II. vii.);  
this  idea will therefore be in God, in so far as he is regarded  
as affected by the ideas of very  many particular things. Thus  
God has the idea of the human body, or knows the human  body, in  
so far as he is affected by very many other ideas, and not in so  
far as he  constitutes the nature of the human mind; that is (by  
II. xi. Cor.), the human mind does not  know the human body. But  
the ideas of the modifications of body are in God, in so far as   
he constitutes the nature of the human mind, or the human mind  
perceives those  modifications (II. xii.), and consequently (II.
xvi.) the human body itself, and as actually  existing; therefore  
the mind perceives thus far only the human body. Q.E.D.
  
XX. The idea or knowledge of the human mind is also in God,  
following in God in the  same manner, and being referred to God  
in the same manner, as the idea or knowledge of  the human body.
  
>>>>>Proof--Thought is an attribute of God (II. i.); therefore  
(II. iii.) there must  necessarily be in God the idea both of  
thought itself and of all its modifications,  consequently also  
of the human mind (II. xi.). Further, this idea or knowledge of  
the mind  does not follow from God, in so far as he is infinite,  
but in so far as he is affected by  another idea of an individual  
thing (II. ix.). But (II. vii.) the order and connection of  
ideas  is the same as the order and connection of causes;  
therefore this idea or knowledge of the  mind is in God and is  
referred to God, in the same manner as the idea or knowledge of  
the  body. Q.E.D.
  
XXI. This idea of the mind is united to the mind in the same way  
as the mind is united to  the body.
  
>>>>>Proof--That the mind is united to the body we have shown  
from the fact, that the  body is the object of the mind (II. xii.
and xiii.); and so for the same reason the idea of the  mind must  
be united with its object, that is, with the mind in the same  
manner as the mind  is united to the body. Q.E.D.
  
*****Note--This proposition is comprehended much more clearly  
from what we have said  in the note to II. vii. We there showed  
that the idea of body and body, that is, mind and  body (II.
xiii.), are one and the same individual conceived now under the  
attribute of  thought, now under the attribute of extension;  
wherefore the idea of the mind and the mind  itself are one and  
the same thing, which is conceived under one and the same  
attribute,  namely, thought. The idea of the mind, I repeat, and  
the mind itself are in God by the  same necessity and follow from  
him from the same power of thinking. Strictly speaking,  the  
idea of the mind, that is, the idea of an idea, is nothing but  
the distinctive quality  (forma) of the idea in so far as it is  
conceived as a mode of thought without reference to  the object;  
if a man knows anything, he, by that very fact, knows that he  
knows it, and at  the same time knows that he knows that he knows  
it, and so on to infinity. But I will treat  of this hereafter.
  
XXII. The human mind perceives not only the modifications of the  
body, but also the ideas  of such modifications.
  
>>>>>Proof--The ideas of the ideas of modifications follow in God  
in the same manner,  and are referred to God in the same manner,  
as the ideas of the said modifications. This is  proved in the  
same way as II. xx. But the ideas of the modifications of the  
body are in the  human mind (II. xii.), that is, in God, in so  
far as he constitutes the essence of the human  mind; therefore  
the ideas of these ideas will be in God, in so far as he has the  
knowledge  or idea of the human mind, that is (II. xxi.), they  
will be in the human mind itself, which  therefore perceives not  
only the modifications of the body, but also the ideas of such   
modifications. Q.E.D.
  
XXIII. The mind does not know itself, except in so far as it  
perceives the ideas of the  modifications of the body.
  
>>>>>Proof--The idea or knowledge of the mind (II. xx.) follows  
in God in the same  manner, and is referred to God in the same  
manner, as the idea or knowledge of the  body. But since (II.
xix.) the human mind does not know the human body itself, that is  
(II. xi. Cor.), since the knowledge of the human body is not  
referred to God, in so far as  he constitutes the nature of the  
human mind; therefore, neither is the knowledge of the  mind  
referred to God, in so far as he constitutes the essence of the  
human mind; therefore  (by the same Cor. II. xi.), the human mind  
thus far has no knowledge of itself. Further the  ideas of the  
modifications, whereby the body is affected, involve the nature  
of the human  body itself (II. xvi.), that is (II. xiii.), they  
agree with the nature of the mind; wherefore the  knowledge of  
these ideas necessarily involves knowledge of the mind; but (by  
the last  Prop.) the knowledge of these ideas is in the human  
mind itself; wherefore the human mind  thus far only has  
knowledge of itself. Q.E.D.
  
XXIV. The human mind does not involve an adequate knowledge of  
the parts composing  the human body.
  
>>>>>Proof--The parts composing the human body do not belong to  
the essence of that  body, except in so far as they communicate  
their motions to one another in a certain fixed  relation (Def.
after Lemma iii.), not in so far as they can be regarded as  
individuals without  relation to the human body. The parts of  
the human body are highly complex individuals  (Post. i.), whose  
parts (Lemma iv.) can be separated from the human body without in  
any  way destroying the nature and distinctive quality of the  
latter, and they can communicate  their motions (Ax. i., after  
Lemma iii.) to other bodies in another relation; therefore (II.
iii.)  the idea or knowledge of each part will be in God,  
inasmuch (II. ix.) as he is regarded as  affected by another idea  
of a particular thing, which particular thing is prior in the  
order of  nature to the aforesaid part (II. vii.). We may affirm  
the same thing of each part of each  individual composing the  
human body; therefore, the knowledge of each part composing  the  
human body is in God, in so far as he is affected by very many  
ideas of things, and not  in so far as he has the idea of the  
human body only, in other words, the idea which  constitutes the  
nature of the human mind (II. xiii.); therefore (II. xi. Cor.),  
the human mind  does not involve an adequate knowledge of the  
human body. Q.E.D.
  
XXV. The idea of each modification of the human body does not  
involve an adequate  knowledge of the external body.
  
>>>>>Proof--We have shown that the idea of a modification of the  
human body involves  the nature of an external body, in so far as  
that external body conditions the human body in  a given manner.  
But, in so far as the external body is an individual, which has  
no reference  to the human body, the knowledge or idea thereof is  
in God (II. ix.), in so far as God is  regarded as affected by  
the idea of a further thing, which (II. vii.) is naturally prior  
to the  said external body. Wherefore an adequate knowledge of  
the external body is not in God,  in so far as he has the idea of  
the modification of the human body; in other words, the idea  of  
the modification of the human body does not involve an adequate  
knowledge of the  external body. Q.E.D.
  
XXVI. The human mind does not perceive any external body as  
actually existing, except  through the ideas of the modifications  
of its own body.
  
>>>>>Proof--If the human body is in no way affected by a given  
external body, then  (II. vii.) neither is the idea of the human  
body, in other words, the human mind, affected in  any way by the  
idea of the existence of the said external body, nor does it in  
any manner  perceive its existence. But, in so far as the human  
body is affected in any way by a given  external body, thus far  
(II. xvi. and Cor.) it perceives that external body. Q.E.D.
  
<<<<mind imagines an external  
body, it has not an  adequate knowledge thereof.
  
>>>>>Proof--When the human mind regards external bodies through  
the ideas of the  modifications of its own body, we say that it  
imagines (see II. xvii. note); now the mind  can only imagine  
external bodies as actually existing. Therefore (by II. xxv.),  
in so far as  the mind imagines external bodies, it has not an  
adequate knowledge of them. Q.E.D.
  
XXVII. The idea of each modification of the human body does not  
involve an adequate  knowledge of the human body itself.
  
>>>>>Proof--Every idea of a modification of the human body  
involves the nature of the  human body, in so far as the human  
body is regarded as affected in a given manner (II. xvi.). But  
inasmuch as the human body is an individual which may be affected  
in many  other ways, the idea of the said modification, &c.  
Q.E.D.
  
XXVIII. The ideas of the modifications of the human body, in so  
far as they have  reference only to the human mind, are not clear  
and distinct, but confused.
  
>>>>>Proof--The ideas of the modifications of the human body  
involve the nature both of  the human body and of external bodies  
(II. xvi.); they must involve the nature not only of  the human  
body but also of its parts; for the modifications are modes  
(Post. iii.), whereby  the parts of the human body, and,  
consequently, the human body as a whole are affected.  But (by  
II. xxiv., xxv.) the adequate knowledge of external bodies, as  
also of the parts  composing the human body, is not in God, in  
so far as he is regarded as affected by the  human mind, but in  
so far as he is regarded as affected by other ideas. These ideas  
of  modifications, in so far as they are referred to the human  
mind alone, are as consequences  without premisses, in other  
words, confused ideas. Q.E.D.
  
*****Note--The idea which constitutes the nature of the human  
mind is, in the same  manner, proved not to be, when considered  
in itself and alone, clear and distinct; as also  is the case  
with the idea of the human mind, and the ideas of the ideas of  
the modifications  of the human body, in so far as they are  
referred to the mind only, as everyone may easily  see.
  
XXIX. The idea of the idea of each modification of the human  
body does not involve an  adequate knowledge of the human mind.
  
>>>>>Proof--The idea of a modification of the human body (II.
xxvii.) does not involve  an adequate knowledge of the said body,  
in other words, does not adequately express its  nature; that is  
(II. xiii.) it does not agree with the nature of the mind  
adequately; therefore  (I. Ax. vi.) the idea of this idea does  
not adequately express the nature of the human mind,  or does not  
involve an adequate knowledge thereof.
  
<<<<mind, when it  
perceives things after the  common order of nature, has not an  
adequate but only a confused and fragmentary  knowledge of  
itself, of its own body, and of external bodies. For the mind  
does not know  itself, except in so far as it perceives the ideas  
of the modifications of body (II. xxiii.). It  only perceives  
its own body (II. xix.) through the ideas of the modifications of  
body (II. xxiii.). It only perceives its own body (II. xix.)  
through the ideas of the modifications, and  only perceives  
external bodies through the same means; thus, in so far as it has  
such ideas  of modification, it has not an adequate knowledge of  
itself (II. xxix.), nor of its own body  (II. xxvii.), nor of  
external bodies (II. xxv.), but only a fragmentary and confused   
knowledge thereof (II. xxviii. and note). Q.E.D.
  
*****Note--I say expressly, that the mind has not an adequate but  
only a confused  knowledge of itself, its own body, and of  
external bodies, whenever it perceives things  after the common  
order of nature; that is, whenever it is determined from without,  
namely,  by the fortuitous play of circumstance, to regard this  
or that; not at such times as it is  determined from within, that  
is, by the fact of regarding several things at once, to   
understand their points of agreement, difference, and contrast.  
Whenever it is determined  in anywise from within, it regards  
things clearly and distinctly, as I will show below.
  
XXX. We can only have a very inadequate knowledge of the duration  
of our body.
  
>>>>>Proof--The duration of our body does not depend on its  
essence (II. Ax. i.), nor  on the absolute nature of God (I.
xxi.). But (I. xxviii.) it is conditioned to exist and operate   
by causes, which in their turn are conditioned to exist and  
operate in a fixed and definite  relation by other causes, these  
last again being conditioned by others, and so on to infinity.  
The duration of our body therefore depends on the common order of  
nature, or the  constitution of things. Now, however a thing may  
be constituted, the adequate knowledge  of that thing is in God,  
in so far as he has the ideas of all things, and not in so far as  
he has  the idea of the human body only (II. ix. Cor.).  
Wherefore the knowledge of the duration  of our body is in God  
very inadequate, in so far as he is only regarded as constituting  
the  nature of the human mind; that is (II. xi. Cor.), this  
knowledge is very inadequate to our  mind. Q.E.D.
  
XXXI. We can only have a very inadequate knowledge of the  
duration of particular things  external to ourselves.
  
>>>>>Proof--Every particular thing, like the human body, must be  
conditioned by another  particular thing to exist and operate in  
a fixed and definite relation; this other particular  thing must  
likewise be conditioned by a third, and so on to infinity (I.
xxviii.). As we have  shown in the foregoing proposition, from  
this common property of particular things, we  have only a very  
inadequate knowledge of the duration of our body; we must draw a   
similar conclusion with regard to the duration of particular  
things, namely, that we can only  have a very inadequate  
knowledge of the duration thereof. Q.E.D.
  
<<<< contingent and perishable.  For we can have no adequate idea of  
their duration (by the last Prop.), and this is what we  must  
understand by the contingency and perishableness of things (I.
xxxiii., Note i.). For  (I. xxix.), except in this sense,  
nothing is contingent.
  
XXXII. All ideas, in so far as they are referred to God, are  
true.
  
>>>>>Proof--All ideas which are in God agree in every respect  
with their objects (II. ii. Cor.), therefore (I. Ax. vi.) they  
are all true. Q.E.D.
  
XXXII. There is nothing positive in ideas, which causes them to  
be called false.
  
>>>>>Proof--If this be denied, conceive, if possible, a positive  
mode of thinking, which  should constitute the distinctive  
quality of falsehood. Such a mode of thinking cannot be  in God  
(II. xxxii.); external to God it cannot be or be conceived (I.
xv.). Therefore there  is nothing positive in ideas which causes  
them to be called false. Q.E.D.
  
XXXIV. Every idea, which in us is absolute or adequate and  
perfect, is true.
  
>>>>>Proof--When we say that an idea in us is adequate and  
perfect, we say, in other  words (II. xi. Cor.), that the idea is  
adequate and perfect in God, in so far as he constitutes  the  
essence of our mind; consequently (II. xxxii.), we say that such  
an idea is true. Q.E.D.
  
XXXV. Falsity consists in the privation of knowledge, which  
inadequate, fragmentary, or  confused ideas involve.
  
>>>>>Proof--There is nothing positive in ideas, which causes them  
to be called false (II. xxxiii.); but falsity cannot consist in  
simple privation (for minds, not bodies, are said to err  and to  
be mistaken), neither can it consist in absolute ignorance, for  
ignorance and error  are not identical; wherefore it consists in  
the privation of knowledge, which inadequate,  fragmentary, or  
confused ideas involve. Q.E.D.
  
*****Note--In the note to II. xvii. I explained how error  
consists in the privation of  knowledge, but in order to throw  
more light on the subject I will give an example. For  instance,  
men are mistaken in thinking themselves free; their opinion is  
made up of  consciousness of their own actions, and ignorance of  
the causes by which they are  conditioned. Their idea of  
freedom, therefore, is simply their ignorance of any cause for   
their actions. As for their saying that human actions depend on  
the will, this is a mere  phrase without any idea to correspond  
thereto. What the will is, and how it moves the  body, they none  
of them know; those who boast of such knowledge, and feign  
dwellings  and habitations for the soul, are wont to provoke  
either laughter or disgust. So, again,  when we look at the sun,  
we imagine that it is distant from us about two hundred feet;   
this error does not lie solely in this fancy, but in the fact  
that, while we thus imagine, we  do not know the sun's true  
distance or the cause of the fancy. For although we afterwards   
learn, that the sun is distant from us more than six hundred of  
the earth's diameters, we  none the less shall fancy it to be  
near; for we do not imagine the sun as near us, because  we are  
ignorant of its true distance, but because the modification of  
our body involves the  essence of the sun, in so far as our said  
body is affected thereby.
  
XXXVI. Inadequate and confused ideas follow by the same  
necessity, as adequate or  clear and distinct ideas.
  
>>>>>Proof--All ideas are in God (I. xv.), and in so far as they  
are referred to God are  true (II. xxxii.) and (II. vii. Cor.)  
adequate; therefore there are no ideas confused or  inadequate,  
except in respect to a particular mind (cf. II. xxiv. and  
xxviii.); therefore all  ideas, whether adequate or inadequate,  
follow by the same necessity (II. vi.). Q.E.D.
  
XXXVII. That which is common to all (cf. Lemma II, above), and  
which is equally in a  part and in the whole, does not constitute  
the essence of any particular thing.
  
>>>>>Proof--If this be denied, conceive, if possible, that it  
constitutes the essence of some  particular thing; for instance,  
the essence of B. Then (II. Def. ii.) it cannot without B   
either exist or be conceived; but this is against our hypothesis.  
Therefore it does not  appertain to B's essence, nor does it  
constitute the essence of any particular thing. Q.E.D.
  
XXXVIII. Those things, which are common to all, and which are  
equally in a part and in  the whole, cannot be conceived except  
adequately.
  
>>>>>Proof--Let A be something, which is common to all bodies,  
and which is equally  present in the part of any given body and  
in the whole. I say A cannot be conceived except  adequately.  
For the idea thereof in God will necessarily be adequate (II.
vii. Cor.), both in  so far as God has the idea of the human  
body, and also in so far as he has the idea of the  modifications  
of the human body, which (II. xvi., xxv., xxvii.) involve in part  
the nature of  the human body and the nature of external bodies;  
that is (II. xii., xiii.), the idea in God will  necessarily be  
adequate, both in so far as he constitutes the human mind, and in  
so far as  he has the ideas, which are in the human mind.  
Therefore the mind (II. xi. Cor.)  necessarily perceives A  
adequately, and has this adequate perception, both in so far as  
it  perceives itself, and in so far as it perceives its own or  
any external body, nor can A be  conceived in any other manner.  
Q.E.D.
  
<<<< notions common to all  men; for (by Lemma ii.) all bodies agree  
in certain respects, which (by the foregoing Prop.)  must be  
adequately or clearly and distinctly perceived by all.
  
XXXIX. That, which is common to and a property of the human body  
and such other  bodies as are wont to affect the human body, and  
which is present equally in each part of  either, or in the  
whole, will be represented by an adequate idea in the mind.
  
>>>>>Proof--If A be that, which is common to and a property of  
the human body and  external bodies, and equally present in the  
human body and in the said external bodies, in  each part of each  
external body and in the whole, there will be an adequate idea of  
A in  God (II. vii. Cor.), both in so far as he has the idea of  
the human body, and in so far as he  has the ideas of the given  
external bodies. Let it now be granted, that the human body is   
affected by an external body through that, which it has in common  
therewith, namely, A;  the idea of this modification will involve  
the property A (II. xvi.), and therefore (II. vii. Cor.) the  
idea of this modification, in so far as it involves the property  
A, will be adequate  in God, in so far as God is affected by the  
idea of the human body; that is (II. xiii.), in so  far as he  
constitutes the nature of the human mind; therefore (II. xi.
Cor.) this idea is also  adequate in the human mind. Q.E.D.
  
<<<<mind is fitted to  
perceive adequately more  things, in proportion as its body has  
more in common with other bodies.
  
XL. Whatsoever ideas in the mind follow from ideas which are  
therein adequate, are also  themselves adequate.
  
>>>>>Proof--This proposition is self-evident. For when we say  
that an idea in the human  mind follows from ideas which are  
therein adequate, we say, in other words (II. xi. Cor.),  that an  
idea is in the divine intellect, whereof God is the cause, not in  
so far as he is  infinite, nor in so far as he is affected by the  
ideas of very many particular things, but only  in so far as he  
constitutes the essence of the human mind.
  
*****Note I--I have thus set forth the cause of those notions,  
which are common to all  men, and which form the basis of our  
ratiocinations. But there are other causes of certain  axioms or  
notions, which it would be to the purpose to set forth by this  
method of ours; for  it would thus appear what notions are more  
useful than others, and what notions have  scarcely any use at  
all. Furthermore, we should see what notions are common to all  
men,  and what notions are only clear and distinct to those who  
are unshackled by prejudice, and  we should detect those which  
are ill-founded. Again we should discern whence the notions   
called "secondary" derived their origin, and consequently the  
axioms on which they are  founded, and other points of interest  
connected with these questions. But I have decided  to pass over  
the subject here, partly because I have set it aside for another  
treatise, partly  because I am afraid of wearying the reader by  
too great prolixity. Nevertheless, in order  not to omit  
anything necessary to be known, I will briefly set down the  
causes, whence are  derived the terms styled "transcendental,"  
such as Being, Thing, Something. These terms  arose from the  
fact, that the human body, being limited, is only capable of  
distinctly  forming a certain number of images (what an image is  
I explained in the II. xvii. note)  within itself at the same  
time; if this number be exceeded, the images will begin to be   
confused; if this number of images, of which the body is capable  
of forming distinctly  within itself, be largely exceeded, all  
will become entirely confused one with another. This  being so,  
it is evident (from II. Prop. xvii. Cor., and xviii.) that the  
human mind can  distinctly imagine as many things simultaneously,  
as its body can form images  simultaneously. When the images  
become quite confused in the body, the mind also  imagines all  
bodies confusedly without any distinction, and will comprehend  
them, as it  were, under one attribute, namely, under the  
attribute of Being, Thing, &c. The same  conclusion can be drawn  
from the fact that images are not always equally vivid, and from   
other analogous causes, which there is no need to explain here;  
for the purpose which we  have in view it is sufficient for us to  
consider one only. All may be reduced to this, that  these terms  
represent ideas in the highest degree confused. From similar  
causes arise those  notions, which we call "general," such as  
man, horse, dog, &c. They arise, to wit, from  the fact that so  
many images, for instance, of men, are formed simultaneously in  
the  human mind, that the powers of imagination break down, not  
indeed utterly, but to the  extent of the mind losing count of  
small differences between individuals (e.g. colour, size,  &c.)  
and their definite number, and only distinctly imagining that, in  
which all the  individuals, in so far as the body is affected by  
them, agree; for that is the point, in which  each of the said  
individuals chiefly affected the body; this the mind expresses by  
the name  man, and this it predicates of an infinite number of  
particular individuals. For, as we have  said, it is unable to  
imagine the definite number of individuals. We must, however,  
bear in  mind, that these general notions are not formed by all  
men in the same way, but vary in  each individual according as  
the point varies, whereby the body has been most often  affected  
and which the mind most easily imagines or remembers. For  
instance, those who  have most often regarded with admiration the  
stature of man, will by the name of man  understand an animal of  
erect stature; those who have been accustomed to regard some   
other attribute, will form a different general image of man, for  
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 II--From 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.
  
>>>>>Proof--To 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.
  
>>>>>Proof--This 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.
  
>>>>>Proof--A 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.
  
*****Note--I 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  
thinking--namely, 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  
questions--namely, 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 question--as to how a  
man can be sure that he has ideas that agree with  their objects,  
I have just pointed out, with abundant clearness, that his  
knowledge arises  from the simple fact, that he has an idea which  
corresponds with its object--in other words,  that truth is its  
own standard. We may add that our mind, in so far as it  
perceives things  truly, is part of the infinite intellect of God  
(II. xi. Cor.); therefore, the clear and distinct  ideas of the  
mind are as necessarily true as the ideas of God.
  
XLIV. It is not in the nature of reason to regard things as  
contingent, but as necessary.
  
>>>>>Proof--It is in the nature of reason to perceive things  
truly (II. xli.), namely (I. Ax. vi.), as they are in  
themselves--that is (I. xxix.), not as contingent, but as  
necessary.  Q.E.D.
  
<<<< imagination that we  consider things, whether in respect to the  
future or the past, as contingent.
  
*****Note--How this way of looking at things arises, I will  
briefly explain. We have  shown above (II. xvii. and Cor.) that  
the mind always regards things as present to itself,  even though  
they be not in existence, until some causes arise which exclude  
their existence  and presence. Further (II. xviii.), we showed  
that, if the human body has once been  affected by two external  
bodies simultaneously, the mind, when it afterwards imagines one   
of the said external bodies, will straightway remember the  
other--that is, it will regard both  as present to itself, unless  
there arise causes which exclude their existence and presence.  
Further, no one doubts that we imagine time, from the fact that  
we imagine bodies to be  moved some more slowly than others, some  
more quickly, some at equal speed. Thus,  let us suppose that a  
child yesterday saw Peter for the first time in the morning, Paul  
at  noon, and Simon in the evening; then, that today he again  
sees Peter in the morning. It is  evident, from II. Prop.
xviii., that, as soon as he sees the morning light, he will  
imagine that  the sun will traverse the same parts of the sky, as  
it did when he saw it on the preceding  day; in other words, he  
will imagine a complete day, and, together with his imagination  
of  the morning, he will imagine Peter; with noon, he will  
imagine Paul; and with evening, he  will imagine Simon--that is,  
he will imagine the existence of Paul and Simon in relation to a   
future time; on the other hand, if he sees Simon in the evening,  
he will refer Peter and Paul  to a past time, by imagining them  
simultaneously with the imagination of a past time. If it   
should at any time happen, that on some other evening the child  
should see James instead  of Simon, he will, on the following  
morning, associate with his imagination of evening  sometimes  
Simon, sometimes James, not both together: for the child is  
supposed to have  seen, at evening, one or other of them, not  
both together. His imagination will therefore  waver; and, with  
the imagination of future evenings, he will associate first one,  
then the  other--that is, he will imagine them in the future,  
neither of them as certain, but both as  contingent. This  
wavering of the imagination will be the same, if the imagination  
be  concerned with things which we thus contemplate, standing in  
relation to time past or time  present: consequently, we may  
imagine things as contingent, whether they be referred to  time  
present, past, or future.
  
<<<<perceive  
things under a certain form of  eternity (sub quadam aeternitatis  
specie).
  
>>>>>Proof--It is in the nature of reason to regard things, not  
as contingent, but as  necessary (II. xliv.). Reason perceives  
this necessity of things (II. xli.) truly--that is (I. Ax. vi.),  
as it is in itself. But (I. xvi.) this necessity of things is  
the very necessity of the eternal  nature of God; therefore, it  
is in the nature of reason to regard things under this form of   
eternity. We may add that the bases of reason are the notions  
(II. xxxviii.), which answer  to things common to all, and which  
(II. xxxvii.) do not answer to the essence of any  particular  
thing: which must therefore be conceived without any relation to  
time, under a  certain form of eternity.
  
XLV. Every idea of every body, or of every particular thing  
actually existing, necessarily  involves the eternal and infinite  
essence of God.
  
>>>>>Proof--The idea of a particular thing actually existing  
necessarily involves both the  existence and the essence of the  
said thing (II. viii.). Now particular things cannot be   
conceived without God (I. xv.); but, inasmuch as (II. vi.) they  
have God for their cause,  in so far as he is regarded under the  
attribute of which the things in question are modes,  their ideas  
must necessarily involve (I. Ax. iv.) the conception of the  
attributes of those  ideas--that is (I. vi.), the eternal and  
infinite essence of God. Q.E.D.
  
*****Note--By existence I do not here mean duration--that is,  
existence in so far as it is  conceived abstractedly, and as a  
certain form of quantity. I am speaking of the very nature  of  
existence, which is assigned to particular things, because they  
follow in infinite numbers  and in infinite ways from the eternal  
necessity of God's nature (I. xvi.). I am speaking, I  repeat,  
of the very existence of particular things, in so far as they are  
in God. For although  each particular thing be conditioned by  
another particular thing to exist in a given way, yet  the force  
whereby each particular thing perseveres in existing follows from  
the eternal  necessity of God's nature (cf. I. xxiv. Cor.).
  
XLVI. The knowledge of the eternal and infinite essence of God  
which every idea  involves is adequate and perfect.
  
>>>>>Proof--The proof of the last proposition is universal; and  
whether a thing be  considered as a part or a whole, the idea  
thereof, whether of the whole or of a part (by  the last Prop.),  
will involve God's eternal and infinite essence. Wherefore,  
that, which  gives knowledge of the eternal and infinite essence  
of God, is common to all, and is equally  in the part and in the  
whole; therefore (II. xxxviii.) this knowledge will be adequate.  
Q.E.D.
  
XLVII. The human mind has an adequate knowledge of the eternal  
and infinite essence of  God.
  
>>>>>Proof--The human mind has ideas (II. xxii.), from which (II.
xxiii.) it perceives  itself and its own body (II. xix.) and  
external bodies (II. xvi. Cor. i. and II. xvii.) as actually   
existing; therefore (II. xlv. and xlvi.) it has an adequate  
knowledge of the eternal and  infinite essence of God. Q.E.D.
  
*****Note--Hence we see, that the infinite essence and the  
eternity of God are known to  all. Now as all things are in God,  
and are conceived through God, we can from this  knowledge infer  
many things, which we may adequately know, and we may form that  
third  kind of knowledge of which we spoke in the note to II.
xl., and of the excellence and use of  which we shall have  
occasion to speak in Part V. Men have not so clear a knowledge  
of  God as they have of general notions, because they are unable  
to imagine God as they do  bodies, and also because they have  
associated the name God with images of things that  they are in  
the habit of seeing, as indeed they can hardly avoid doing,  
being, as they are,  men, and continually affected by external  
bodies. Many errors, in truth, can be traced to  this head,  
namely, that we do not apply names to things rightly. For  
instance, when a man  says that the lines drawn from the centre  
of a circle to its circumference are not equal, he  then, at all  
events, assuredly attaches a meaning to the word circle different  
from that  assigned by mathematicians. So again, when men make  
mistakes in calculation, they have  one set of figures in their  
mind, and another on the paper. If we could see into their  
minds,  they do not make a mistake; they seem to do so, because  
we think, that they have the same  numbers in their mind as they  
have on the paper. If this were not so, we should not  believe  
them to be in error, any more than I thought that a man was in  
error, whom I lately  heard exclaiming that his entrance hall had  
flown into a neighbour's hen, for his meaning  seemed to me  
sufficiently clear. Very many controversies have arisen from the  
fact, that  men do not rightly explain their meaning, or do not  
rightly interpret the meaning of others.  For, as a matter of  
fact, as they flatly contradict themselves, they assume now one  
side,  now another, of the argument, so as to oppose the  
opinions, which they consider mistaken  and absurd in their  
opponents.
  
XLVIII. In the mind there is no absolute or free will; but the  
mind is determined to wish  this or that by a cause, which has  
also been determined by another cause, and this last by  another  
cause, and so on to infinity.
  
>>>>>Proof--The mind is a fixed and definite mode of thought (II.
xi.), therefore it cannot  be the free cause of its actions (I.
xvii. Cor. ii.); in other words, it cannot have an absolute   
faculty of positive or negative volition; but (by I. xxviii.) it  
must be determined by a cause,  which has also been determined by  
another cause, and this last by another, &c. Q.E.D.
  
*****Note--In the same way it is proved, that there is in the  
mind no absolute faculty of  understanding, desiring, loving, &c.  
Whence it follows, that these and similar faculties are  either  
entirely fictitious, or are merely abstract and general terms,  
such as we are  accustomed to put together from particular  
things. Thus the intellect and the will stand in  the same  
relation to this or that idea, or this or that volition, as  
"lapidity" to this or that  stone, or as "man" to Peter and  
Paul. The cause which leads men to consider themselves  free has  
been set forth in the Appendix to Part I. But, before I proceed  
further, I would  here remark that, by the will to affirm and  
decide, I mean the faculty, not the desire. I  mean, I repeat,  
the faculty, whereby the mind affirms or denies what is true or  
false, not  the desire, wherewith the mind wishes for or turns  
away from any given thing. After we  have proved, that these  
faculties of ours are general notions, which cannot be  
distinguished  from the particular instances on which they are  
based, we must inquire whether volitions  themselves are anything  
besides the ideas of things. We must inquire, I say, whether  
there  is in the mind any affirmation or negation beyond that,  
which the idea, in so far as it is an  idea, involves. On which  
subject see the following proposition, and II. Def. iii., lest  
the  idea of pictures should suggest itself. For by ideas I do  
not mean images such as are  formed at the back of the eye, or in  
the midst of the brain, but the conceptions of thought.
  
XLIX. There is in the mind no volition or affirmation and  
negation, save that which an  idea, inasmuch as it is an idea,  
involves.
  
>>>>>Proof--There is in the mind no absolute faculty of positive  
or negative volition, but  only particular volitions, namely,  
this or that affirmation, and this or that negation. Now let  us  
conceive a particular volition, namely, the mode of thinking  
whereby the mind affirms,  that the three interior angles of a  
triangle are equal to two right angles. This affirmation   
involves the conception or idea of a triangle, that is, without  
the idea of a triangle it cannot  be conceived. It is the same  
thing to say, that the concept A must involve the concept B,  as  
it is to say, that A cannot be conceived without B. Further,  
this affirmation cannot be  made (II. Ax. iii.) without the idea  
of a triangle. Therefore, this affirmation can neither be  nor  
be conceived, without the idea of a triangle. Again, this idea  
of a triangle must involve  this same affirmation, namely, that  
its three interior angles are equal to two right angles.  
Wherefore, and vice versa, this idea of a triangle can neither be  
nor be conceived without  this affirmation, therefore, this  
affirmation belongs to the essence of the idea of a triangle,   
and is nothing besides. What we have said of this volition  
(inasmuch as we have selected  it at random) may be said of any  
other volition, namely, that it is nothing but an idea.  Q.E.D.
  
<<<<understanding are one and the same.
  
>>>>>Proof--Will and understanding are nothing beyond the  
individual volitions and ideas  (II. xlviii. and note). But a  
particular volition and a particular idea are one and the same   
(by the foregoing Prop.); therefore, will and understanding are  
one and the same. Q.E.D.
  
*****Note--We have thus removed the cause which is commonly  
assigned for error. For  we have shown above, that falsity  
consists solely in the privation of knowledge involved in  ideas  
which are fragmentary and confused. Wherefore, a false idea,  
inasmuch as it is false,  does not involve certainty. When we  
say, then, that a man acquiesces in what is false, and  that he  
has no doubts on the subject, we do not say that he is certain,  
but only that he does  not doubt, or that he acquiesces in what  
is false, inasmuch as there are no reasons, which  should cause  
his imagination to waver (see II. xliv. note). Thus, although  
the man be  assumed to acquiesce in what is false, we shall never  
say that he is certain. For by certainty  we mean something  
positive (II. xliii. and note), not merely the absence of doubt.
  
However, in order that the foregoing proposition may be fully  
explained, I will draw  attention to a few additional points, and  
I will furthermore answer the objections which  may be advanced  
against our doctrine. Lastly, in order to remove every scruple,  
I have  thought it worth while to point out some of the  
advantages, which follow therefrom. I say  "some," for they will  
be better appreciated from what we shall set forth in the fifth  
part.
  
I begin, then, with the first point, and warn my readers to make  
an accurate distinction  between an idea, or conception of the  
mind, and the images of things which we imagine.  It is further  
necessary that they should distinguish between idea and words,  
whereby we  signify things. These three--namely, images, words,  
and ideas--are by many persons either  entirely confused  
together, or not distinguished with sufficient accuracy or care,  
and hence  people are generally in ignorance, how absolutely  
necessary is a knowledge of this doctrine  of the will, both for  
philosophic purposes and for the wise ordering of life. Those  
who  think that ideas consist in images which are formed in us by  
contact with external bodies,  persuade themselves that the ideas  
of those things, whereof we can form no mental picture,  are not  
ideas, but only figments, which we invent by the free decree of  
our will; they thus  regard ideas as though they were inanimate  
pictures on a panel, and, filled with this  misconception, do not  
see that an idea, inasmuch as it is an idea, involves an  
affirmation or  negation. Again, those who confuse words with  
ideas, or with the affirmation which an  idea involves, think  
that they can wish something contrary to what they feel, affirm,  
or  deny. This misconception will easily be laid aside by one,  
who reflects on the nature of  knowledge, and seeing that it in  
no wise involves the conception of extension, will therefore   
clearly understand, that an idea (being a mode of thinking) does  
not consist in the image of  anything, nor in words. The essence  
of words and images is put together by bodily  motions, which in  
no wise involve the conception of thought.
  
These few words on this subject will suffice: I will therefore  
pass on to consider the  objections, which may be raised against  
our doctrine. Of these, the first is advanced by  those, who  
think that the will has a wider scope than the understanding, and  
that therefore  it is different therefrom. The reason for their  
holding the belief, that the will has wider  scope than the  
understanding, is that they assert, that they have no need of an  
increase in  their faculty of assent, that is of affirmation or  
negation, in order to assent to an infinity of  things which we  
do not perceive, but that they have need of an increase in their  
faculty of  understanding. The will is thus distinguished from  
the intellect, the latter being finite and  the former infinite.  
Secondly, it may be objected that experience seems to teach us   
especially clearly, that we are able to suspend our judgment  
before assenting to things  which we perceive; this is confirmed  
by the fact that no one is said to be deceived, in so  far as he  
perceives anything, but only in so far as he assents or  
dissents.
  
For instance, he who feigns a winged horse, does not therefore  
admit that a winged horse  exists; that is, he is not deceived,  
unless he admits in addition that a winged horse does  exist.  
Nothing therefore seems to be taught more clearly by experience,  
than that the will  or faculty of assent is free and different  
from the faculty of understanding. Thirdly, it may  be objected  
that one affirmation does not apparently contain more reality  
than another; in  other words, that we do not seem to need for  
affirming, that what is true is true, any  greater power than for  
affirming, that what is false is true. We have, however, seen  
that  one idea has more reality or perfection than another, for  
as objects are some more  excellent than others, so also are the  
ideas of them some more excellent than others; this  also seems  
to point to a difference between the understanding and the will.  
Fourthly, it  may be objected, if man does not act from free  
will, what will happen if the incentives to  action are equally  
balanced, as in the case of Buridan's ass? Will he perish of  
hunger and  thirst? If I say that he would not, he would then  
determine his own action, and would  consequently possess the  
faculty of going and doing whatever he liked. Other objections   
might also be raised, but, as I am not bound to put in evidence  
everything that anyone may  dream, I will only set myself to the  
task of refuting those I have mentioned, and that as  briefly as  
possible.
  
To the first objection I answer, that I admit that the will has a  
wider scope than the  understanding, if by the understanding be  
meant only clear and distinct ideas; but I deny  that the will  
has a wider scope than the perceptions, and the faculty of  
forming  conceptions; nor do I see why the faculty of volition  
should be called infinite, any more  than the faculty of feeling:  
for, as we are able by the same faculty of volition to affirm an   
infinite number of things (one after the other, for we cannot  
affirm an infinite number  simultaneously), so also can we, by  
the same faculty of feeling, feel or perceive (in  succession) an  
infinite number of bodies. If it be said that there is an  
infinite number of  things which we cannot perceive, I answer,  
that we cannot attain to such things by any  thinking, nor,  
consequently, by any faculty of volition. But, it may still be  
urged, if God  wished to bring it about that we should perceive  
them, he would be obliged to endow us  with a greater faculty of  
perception, but not a greater faculty of volition than we have   
already. This is the same as to say that, if God wished to bring  
it about that we should  understand an infinite number of other  
entities, it would be necessary for him to give us a  greater  
understanding, but not a more universal idea of entity than that  
which we have  already, in order to grasp such infinite entities.  
We have shown that will is a universal  entity or idea, whereby  
we explain all particular volitions--in other words, that which  
is  common to all such volitions.
  
As, then, our opponents maintain that this idea, common or  
universal to all volitions, is a  faculty, it is little to be  
wondered at that they assert, that such a faculty extends itself  
into  the infinite, beyond the limits of the understanding: for  
what is universal is predicated alike  of one, of many, and of an  
infinite number of individuals.
  
To the second objection I reply by denying, that we have a free  
power of suspending  our judgment: for, when we say that anyone  
suspends his judgment, we merely mean that  he sees, that he does  
not perceive the matter in question adequately. Suspension of   
judgment is, therefore, strictly speaking, a perception, and not  
free will. In order to  illustrate the point, let us suppose a  
boy imagining a horse, and perceive nothing else.  Inasmuch as  
this imagination involves the existence of the horse (II. xvii.
Cor.), and the boy  does not perceive anything which would  
exclude the existence of the horse, he will  necessarily regard  
the horse as present: he will not be able to doubt of its  
existence,  although he be not certain thereof. We have daily  
experience of such a state of things in  dreams; and I do not  
suppose that there is anyone, who would maintain that, while he  
is  dreaming, he has the free power of suspending his judgment  
concerning the things in his  dream, and bringing it about that  
he should not dream those things, which he dreams that  he sees;  
yet it happens, notwithstanding, that even in dreams we suspend  
our judgment,  namely, when we dream that we are dreaming.
  
Further, I grant that no one can be deceived, so far as actual  
perception extends--that is, I  grant that the mind's  
imaginations, regarded in themselves, do not involve error (II.
xvii. note); but I deny, that a man does not, in the act of  
perception, make any affirmation. For  what is the perception of  
a winged horse, save affirming that a horse has wings? If the   
mind could perceive nothing else but the winged horse, it would  
regard the same as present  to itself: it would have no reasons  
for doubting its existence, nor any faculty of dissent,  unless  
the imagination of a winged horse be joined to an idea which  
precludes the  existence of the said horse, or unless the mind  
perceives that the idea which it possess of a  winged horse is  
inadequate, in which case it will either necessarily deny the  
existence of  such a horse, or will necessarily be in doubt on  
the subject.
  
I think that I have anticipated my answer to the third objection,  
namely, that the will is  something universal which is predicated  
of all ideas, and that it only signifies that which is  common to  
all ideas, namely, an affirmation, whose adequate essence must,  
therefore, in  so far as it is thus conceived in the abstract, be  
in every idea, and be, in this respect alone,  the same in all,  
not in so far as it is considered as constituting the idea's  
essence: for, in  this respect, particular affirmations differ  
one from the other, as much as do ideas. For  instance, the  
affirmation which involves the idea of a circle, differs from  
that which  involves the idea of a triangle, as much as the idea  
of a circle differs from the idea of a  triangle.
  
Further, I absolutely deny, that we are in need of an equal power  
of thinking, to affirm  that that which is true is true, and to  
affirm that that which is false is true. These two   
affirmations, if we regard the mind, are in the same relation to  
one another as being and  not-being; for there is nothing  
positive in ideas, which constitutes the actual reality of   
falsehood (II. xxxv. note, and xlvii. note).
  
We must therefore conclude, that we are easily deceived, when we  
confuse universals with  singulars, and the entities of reason  
and abstractions with realities. As for the fourth  objection, I  
am quite ready to admit, that a man placed in the equilibrium  
described  (namely, as perceiving nothing but hunger and thirst,  
a certain food and a certain drink,  each equally distant from  
him) would die of hunger and thirst. If I am asked, whether such  
an one should not rather be considered an ass than a man; I  
answer, that I do not know,  neither do I know how a man should  
be considered, who hangs himself, or how we should  consider  
children, fools, madmen, &c.
  
It remains to point out the advantages of a knowledge of this  
doctrine as bearing on  conduct, and this may be easily gathered  
from what has been said. The doctrine is good,  
  
1. Inasmuch as it teaches us to act solely according to the  
decree of God, and to be  partakers in the Divine nature, and so  
much the more, as we perform more perfect actions  and more and  
more understand God. Such a doctrine not only completely  
tranquilizes our  spirit, but also shows us where our highest  
happiness or blessedness is, namely, solely in  the knowledge of  
God, whereby we are led to act only as love and piety shall bid  
us. We  may thus clearly understand, how far astray from a true  
estimate of virtue are those who  expect to be decorated by God  
with high rewards for their virtue, and their best actions,  as  
for having endured the direst slavery; as if virtue and the  
service of God were not in  itself happiness and perfect freedom.
  
2. Inasmuch as it teaches us, how we ought to conduct ourselves  
with respect to the gifts  of fortune, or matters which are not  
in our power, and do not follow from our nature. For  it shows  
us, that we should await and endure fortune's smiles or frowns  
with an equal  mind, seeing that all things follow from the  
eternal decree of God by the same necessity,  as it follows from  
the essence of a triangle, that the three angles are equal to two  
right  angles.
  
3. This doctrine raises social life, inasmuch as it teaches us to  
hate no man, neither to  despise, to deride, to envy, or to be  
angry with any. Further, as it tells us that each should  be  
content with his own, and helpful to his neighbour, not from any  
womanish pity,  favour, or superstition, but solely by the  
guidance of reason, according as the time and  occasion demand,  
as I will show in Part III.
  
4. Lastly, this doctrine confers no small advantage on the  
commonwealth; for it teaches  how citizens should be governed and  
led, not so as to become slaves, but so that they may  freely do  
whatsoever things are best.
  
I have thus fulfilled the promise made at the beginning of this  
note, and I thus bring the  second part of my treatise to a  
close. I think I have therein explained the nature and   
properties of the human mind at sufficient length, and,  
considering the difficulty of the  subject, with sufficient  
clearness. I have laid a foundation, whereon may be raised many   
excellent conclusions of the highest utility and most necessary  
to be known, as will, in  what follows, be partly made plain.

          The End

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