PROP. 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. vii. Coroll.), therefore (I. Ax. vi.) they are all true. Q.E.D.
PROP. XXXIII. 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.
PROP. 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. Coroll.), 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.
PROP. 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.
PROP. 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. Coroll.) 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.
PROP. 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.
PROP. 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. Coroll.), 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. Coroll.) 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.
Corollary—Hence it follows that there are certain ideas or 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.
PROP. 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. Coroll.), 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. Coroll.) 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. Coroll.) this idea is also adequate in the human mind. Q.E.D.
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.
PROP. 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. Coroll.), 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 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 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. Coroll., and xviii.) that the human mind
