|E2: PROP. 32. 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 (E2P7C), therefore (E1A6) they are all true. Q.E.D.
|Referenced in: E2P33,- E2P34,- E2P36,- E2P43N,- E4P1,- E5P17
|E2: PROP. 33. 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 (E2P32); external to God it cannot be or be conceived (E1P15). Therefore there is nothing positive in ideas which causes them to be called false. Q.E.D.
|Referenced in: E2P35,- E2P43N,- E4P1
|E2: PROP. 34. 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 (E2P11C), that the idea is adequate and perfect in God, in so far as he constitutes the essence of our mind; consequently (E2P32), we say that such an idea is true. Q.E.D.
|Referenced in: E2P41,- E2P43,- E2P43N
|E2: PROP. 35. 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 (E2P33); 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.
|Referenced in: E2P41,- E2P43N,- E2P49CN,- E4P1
| E2: PROP. 35, Note.
--In the note to E2P17CN I explained
how error consists in the
of knowledge, but in order to throw more light on the subject I
will give an example. For instance, men are mistaken in thinking
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 [and] 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.
|Referenced in: E2P43N,- E2P49CN,- E3DOE27,- E4P1N,- E5P5
|E2: PROP. 36. Inadequate and confused ideas follow by the same necessity, as adequate or clear and distinct ideas.
|Proof.--All ideas are in God (E1P15), and in so far as they are referred to God are true (E2P32) and (E2P7C) adequate; therefore there are no ideas confused or inadequate, except in respect to a particular mind (cf. E2P24 and E2P28); therefore all ideas, whether adequate or inadequate, follow by the same necessity (E2P6) [E2P6C]. Q.E.D.
|E2: PROP. 37. That which is common to all (cf. E2P13L2), 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 (E2D2) 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.
|Referenced in: E2P44C2
|E2: PROP. 38. 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 (E2P7C), 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 (E2P16, E2P25, E2P27) involve in part the nature of the human body and the nature of external bodies; that is (E2P12, E2P13), 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 (E2P11C) 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.
|Referenced in: E2P38C,- E2P44C2,- E2P46,- E5P4,- E5P7
|E2: PROP. 38, Corollary.--Hence it follows that there are certain ideas or notions common to all men.
|For (by E2P13L2) all bodies agree in certain respects, which (by the foregoing Prop. E2P38) must be adequately or clearly and distinctly perceived by all.
|Referenced in: E2P40N2,- E3P3
|E2: PROP. 39. 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 (E2P7C), 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 (E2P16), and therefore (E2P7C) 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 (E2P13), in so far as he constitutes the nature of the human mind; therefore (E2P11C) this idea is also adequate in the human mind. Q.E.D.
|Referenced in: E2P40N2
|E2: PROP. 39, Corollary.--Hence it follows that the mind is fitted to perceive adequately more things, in proportion as its body has more in common with other bodies.
|Referenced in: E2P40N2
|E2: PROP 40. 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 (E2P11C), 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.
|Referenced in: E2P40N2,- E4P26,- E4P52,- E5P4CN,- E5P31
| E2: PROP. 40, Note 1.
--I have thus set forth the cause of those notions, which are common to
all men, and which form the basis of, our ratiocination.
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 E2P17CN) within itself at the same time; if this number be exceeded, the images will begin to be confused; if this number of images, 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 E2P17C and E2P18) 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, etc. 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, etc. 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, etc.) 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.
|Referenced in: E3P1,- E3P55C1N,- E3P56
| E2: PROP. 40, Note 2.
--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 (E2P29C); 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 (E2P18N). 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 (E2P38C, E2P39, E2P39C, and E2P40); this I call reason and knowledge of the second kind.
[(4.)] 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.
|Referenced in: E2P41,- E2P42,- E2P47N,- E3P1,- E3P56,- E3P58,- E4P26,- E4P27,- E5P7,- E5P10,- E5P12,- E5P25,- E5P28,- E5P31.- E5P36CN