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III. (108:5) Those ideas which the understanding forms absolutely express infinity; determinate ideas are derived from other ideas. (6) Thus in the idea of quantity, perceived by means of a cause, the quantity is determined, as when a body is perceived to be formed by the motion of a plane, a plane by the motion of a line, or, again, a line by the motion of a point. (7) All these are perceptions which do not serve towards understanding quantity, but only towards determining it. (108:8) This is proved by the fact that we conceive them as formed as it were by motion, yet this motion is not perceived unless the quantity be perceived also; we can even prolong the motion to form an infinite line, which we certainly could not do unless we had an idea of infinite quantity.
IV. (9) The understanding forms positive ideas before forming negative ideas.
V. (108:10) It perceives things not so much under the condition of duration as under a certain form of eternity, and in an infinite number; or rather in perceiving things it does not consider either their number or duration, whereas, in imagining them, it perceives them in a determinate number, duration, and quantity.
VI. (108:11) The ideas which we form as clear and distinct, seem to follow from the sole necessity of our nature, that they appear to depend absolutely on our sole power; with confused ideas the contrary is the case. (12) They are often formed against our will.
VII. (108:13) The mind can determine in many ways the ideas of things, which the understanding forms from other ideas: thus, for instance, in order to define the plane of an ellipse, it supposes a point adhering to a cord to be moved around two centers, or, again, it conceives an infinity of points, always in the same fixed relation to a given straight line, angle of the vertex of the cone, or in an infinity of other ways.
VIII. (108:14) The more ideas express perfection of any object, the more perfect are they themselves; for we do not admire the architect who has planned a chapel so much as the architect who has planned a splendid temple.
[109] (1) I do not stop to consider the rest of what is referred to thought, such as love, joy, &c. (2) They are nothing to our present purpose, and cannot even be conceived unless the understanding be perceived previously. (3) When perception is removed, all these go with it.
[110] (1) False and fictitious ideas have nothing positive about them (as we have abundantly shown), which causes them to be called false or fictitious; they are only considered as such through the defectiveness of knowledge. (2) Therefore, false and fictitious ideas as such can teach us nothing concerning the essence of thought; this must be sought from the positive properties just enumerated; in other words, we must lay down some common basis from which these properties necessarily follow, so that when this is given, the properties are necessarily given also, and when it is removed, they too vanish with it.
The rest of the treatise is wanting.
Spinoza's Endnotes: Marks as per Curley, see Note 5 above.
[a] (1) This might be explained more at large and more clearly: I mean by distinguishing riches according as they are pursued for their own sake, in or furtherance of fame, or sensual pleasure, or the advancement of science and art. (2) But this subject is reserved to its own place, for it is not here proper to investigate the matter more accurately.
[b] These considerations should be set forth more precisely.
[c] These matters are explained more at length elsewhere.
[d] N.B. I do no more here than enumerate the sciences necessary for our purpose; I lay no stress on their order.
[e] There is for the sciences but one end, to which they should all be directed.
[f] (1) In this case we do not understand anything of the cause from the consideration of it in the effect. (2) This is sufficiently evident from the fact that the cause is only spoken of in very general terms, such as--there exists then something; there exists then some power, &c.; or from the that we only express it in a negative manner--it is not or that, &c. (3) In the second case something is ascribed to the cause because of the effect, as we shall show in an example, but only a property, never an essence.
[g] (1) From this example may be clearly seen what I have just drawn attention to. (2) For through this union we understand nothing beyond the sensation, the effect, to wit, from which we inferred the cause of which we understand nothing.
[h] (1) A conclusion of this sort, though it be certain, is yet not to be relied on without great caution; for unless we are exceedingly careful we shall forthwith fall into error. (2) When things are conceived thus abstractedly, and not through their true essence, they are apt to be confused by the imagination. (3) For that which is in itself one, men imagine to be multiplex. (4) To those things which are conceived abstractedly, apart, and confusedly, terms are applied which are apt to become wrested from their strict meaning, and bestowed on things more familiar; whence it results that these latter are imagined in the same way as the former to which the terms were originally given.
[i] I shall here treat a little more in detail of experience, and shall examine the method adopted by the Empirics, and by recent philosophers.
[k] By native strength, I mean that not bestowed on us by external causes, as I shall afterwards explain in my philosophy.
[l] Here I term them operations: I shall explain their nature in my philosophy.
[m] I shall take care not only to demonstrate what I have just advanced, but also that we have hitherto proceeded rightly, and other things needful to be known.
[33 note1] (1) In modern language, "the idea may become the subject of another presentation." (2) Objectivus generally corresponds to the modern "subjective," formalis to the modern "objective." [Trans.- Note 1]
[n] (1) Observe that we are not here inquiring how the first subjective essence is innate in us. (2) This belongs to an investigation into nature, where all these matters are amply explained, and it is shown that without ideas neither affirmation, nor negation, nor volition are possible.
[o] The nature of mental search is explained in my philosophy.
[p] To be connected with other things is to be produced by them, or to produce them.
[q] In the same way as we have here no doubt of the truth of our knowledge.
[r] See below the note on hypotheses, whereof we have a clear understanding; the fiction consists in saying that such hypotheses exist in heavenly bodies.
[s] (1) As a thing, when once it is understood, manifests itself, we have need only of an example without further proof. (2) In the same way the contrary has only to be presented to our minds to be recognized as false, as will forthwith appear when we come to discuss fiction concerning essences.
[t] Observe, that although many assert that they doubt whether God exists, they have nought but his name in their minds, or else some fiction which they call God: this fiction is not in harmony with God's real nature, as we will duly show.
[u] (1) I shall presently show that no fiction can concern eternal truths. By an eternal truth, I mean that which being positive could never become negative. (2) Thus it is a primary and eternal truth that God exists, but it is not an eternal truth that Adam thinks. (3) That the Chimaera does not exist is an eternal truth, that Adam does not think is not so.
