|E2: PROP. 41. 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 E2P40N2) assigned all those ideas, which are inadequate and confused; therefore this kind of knowledge is the only source of falsity (E2P35). Furthermore, we assigned to the second and third kinds of knowledge those ideas which are adequate; therefore these kinds are necessarily true (E2P34). Q.E.D.
|Referenced in: E2P44,- E2P44C2,- E4P27,- E4P35,- E4P62
|E2: PROP. 42. 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 (E2P40N2), he must know the true and the false by the second or third kind of knowledge.
|E2: PROP. 43. 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 (E2P11C). 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 E2P20, 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 E2P11C), 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 (E2P34), 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.
|Referenced in: E2P43N,- E2P49CN,- E3P58,- E4P27,- E4P52,- E4P56,- E4P62,- E5P27
| E2: PROP. 43, Note.
--I explained in the note E2P21N what is
meant by the idea of an
idea; but we may remark that the foregoing proposition
E2P43 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
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
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 true ideas 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 E2P35, the former is related to the latter as being is to not-being. The causes of falsity I have set forth very clearly in E2P19 and [to] E2P35 with the note E2P35N. 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 (E2P11C); therefore, the clear and distinct ideas of the mind are as necessarily true as the ideas of God.
|Referenced in: E2P49CN,- E4P27,- E4P62
|E2: PROP. 44. 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 (E2P41), namely (E1A6), as they are in themselves--that is (E1P29), not as contingent, but as necessary. Q.E.D.
|Referenced in: E2P44C2
|E2: PROP. 44, Corollary 1.--Hence it follows, that it is only through our imagination that we consider things, whether in respect to the future or the past, as contingent.
| E2: PROP. 44 Corollary 1,
--How this way of looking at things arises, I will briefly explain. We
have shown above (E2P17 and Coroll.
E2P17C) that the
regards things as present to itself, even though they be not in existence,
until some causes arise which exclude their existence and presence.
Further (E2P18), 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 to-day he again sees Peter in the morning. It is evident, from E2P18, 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.
|Referenced in: E2P49CN,- E3P17N,- E3P18,- E3P18N1,- E4P62N
|E2: PROP. 44, Corollary 2.--It is in the nature of reason to 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 (E2P44). Reason perceives this necessity of things (E2P41) truly--that is (E1A6), as it is in itself. But (E1P16) 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 (E2P38), which answer to things common to all, and which (E2P37) 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.
|Referenced in: E4P62,- E5P29
|E2: PROP. 45. 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 [E2P8C]. Now particular things cannot be conceived without God (E1P15); but, inasmuch as (E2P6) 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 (E1A4) the conception of the attribute of those ideas--that is (E1D6), the eternal and infinite essence of God. Q.E.D.
|Referenced in: E2P46,- E2P47,- E5P20N,- E5P29N
|E2: PROP. 45, 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 (E1P16). 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. E1P24C).
|Referenced in: E5P29N
|E2: PROP. 46. 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. E2P45), 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 (E2P38) this knowledge will be adequate. Q.E.D.
|Referenced in: E2P47,- E5P18,- E5P31
|E2: PROP. 47. The human mind has an adequate knowledge of the eternal and infinite essence of God.
|Proof.--The human mind has ideas (E2P22), from which (E2P23) it perceives itself and its own body (E2P19) and external bodies (E2P16C1 and E2P17) as actually existing; therefore (E2P45, E2P46) it has an adequate knowledge of the eternal and infinite essence of God. Q.E.D.
|Referenced in: E4P36,- E4P36N,- E4P37,- E5P18
| E2: PROP. 47, Note.
--Hence we see, that the
essence and the eternity of
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
know, and we may form that
third kind of knowledge
of which we spoke in
the note E2P40N2, and of the excellence and
use of which we shall have
occasion to speak in Part 5 (E5).
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.
|Referenced in: E2P49CN,- E4P36,- E5P10,- E5P20N,- E5P36CN