[96] In order to be free from this fault, the following rules should be observed in definition:--
I. (1) If the thing in question be created, the definition must (as we have said) comprehend the proximate cause. (2) For instance, a circle should, according to this rule, be defined as follows: the figure described by any line whereof one end is fixed and the other free. (3) This definition clearly comprehends the proximate cause.
II. (4) A conception or definition of a thing should be such that all the properties of that thing, in so far as it is considered by itself, and not in conjunction with other things, can be deduced from it, as may be seen in the definition given of a circle: for from that it clearly follows that all straight lines drawn from the center to the circumference are equal. (5) That this is a necessary characteristic of a definition is so clear to anyone, who reflects on the matter, that there is no need to spend time in proving it, or in showing that, owing to this second condition, every definition should be affirmative. (6) I speak of intellectual affirmation, giving little thought to verbal affirmations which, owing to the poverty of language, must sometimes, perhaps, be expressed negatively, though the idea contained is affirmative.
[97] The rules for the definition of an uncreated thing are as follows:--
I. The exclusion of all idea of cause--that is, the thing must not need explanation by Anything outside itself.
II. When the definition of the thing has been given, there must be no room for doubt as to whether the thing exists or not.
III. It must contain, as far as the mind is concerned, no substantives which could be put into an adjectival form; in other words, the object defined must not be explained through abstractions.
IV. Lastly, though this is not absolutely necessary, it should be possible to deduce from the definition all the properties of the thing defined.
All these rules become obvious to anyone giving strict attention to the matter.
[98] (1) I have also stated that the best basis for drawing a conclusion is a particular affirmative essence. (2) The more specialized the idea is, the more it is distinct, and therefore clear. (3) Wherefore a knowledge of particular things should be sought for as diligently as possible.
[99] (1) As regards the order of our perceptions, and the manner in which they should be arranged and united, it is necessary that, as soon as is possible and rational, we should inquire whether there be any being (and, if so, what being), that is the cause of all things, so that its essence, represented in thought, may be the cause of all our ideas, and then our mind will to the utmost possible extent reflect nature. (2) For it will possess, subjectively, nature's essence, order, and union. (3) Thus we can see that it is before all things necessary for us to deduce all our ideas from physical things--that is, from real entities, proceeding, as far as may be, according to the series of causes, from one real entity to another real entity, never passing to universals and abstractions, either for the purpose of deducing some real entity from them, or deducing them from some real entity. (4) Either of these processes interrupts the true progress of the understanding.
[100] (1) But it must be observed that, by the series of causes and real entities, I do not here mean the series of particular and mutable things, but only the series of fixed and eternal things. (2) It would be impossible for human infirmity to follow up the series of particular mutable things, both on account their multitude, surpassing all calculation, and on account of the infinitely diverse circumstances surrounding one and the same thing, any one of which may be the cause of its existence or non-existence. (3) Indeed, their existence has no connection with their essence, or (as we have said already) is not an eternal truth.
[101] (1) Neither is there any need that we should understand their series, for the essences of particular mutable things are not to be gathered from their series or order of existence, which would furnish us with nothing beyond their extrinsic denominations, their relations, or, at most, their circumstances, all of which are very different from their inmost essence. (101:2) This inmost essence must be sought solely from fixed and eternal things, and from the laws, inscribed (so to speak) in those things as in their true codes, according to which all particular things take place and are arranged; nay, these mutable particular things depend so intimately and essentially (so to phrase it) upon the fixed things, that they cannot either be conceived without them.
[102] (1) But, though this be so, there seems to be no small difficulty in arriving at the knowledge of these particular things, for to conceive them all at once would far surpass the powers of the human understanding. (2) The arrangement whereby one thing is understood, before another, as we have stated, should not be sought from their series of existence, nor from eternal things. (3) For the latter are all by nature simultaneous. (4) Other aids are therefore needed besides those employed for understanding eternal things and their laws. (5) However, this is not the place to recount such aids, nor is there any need to do so, until we have acquired a sufficient knowledge of eternal things and their infallible laws, and until the nature of our senses has become plain to us.
[103] (1) Before betaking ourselves to seek knowledge of particular things, it will be seasonable to speak of such aids, as all tend to teach us the mode of employing our senses, and to make certain experiments under fixed rules and arrangements which may suffice to determine the object of our inquiry, so that we may therefrom infer what laws of eternal things it has been produced under, and may gain an insight into its inmost nature, as I will duly show. (2) Here, to return to my purpose, I will only endeavor to set forth what seems necessary for enabling us to attain to knowledge of eternal things, and to define them under the conditions laid down above.
[104] (1) With this end, we must bear in mind what has already been stated, namely, that when the mind devotes itself to any thought, so as to examine it, and to deduce therefrom in due order all the legitimate conclusions possible, any falsehood which may lurk in the thought will be detected; but if the thought be true, the mind will readily proceed without interruption to deduce truths from it. (104:2) This, I say, is necessary for our purpose, for our thoughts may be brought to a close by the absence of a foundation.
[105] (1) If, therefore, we wish to investigate the first thing of all, it will be necessary to supply some foundation which may direct our thoughts thither. (2) Further, since method is reflective knowledge, the foundation which must direct our thoughts can be nothing else than the knowledge of that which constitutes the reality of truth, and the knowledge of the understanding, its properties, and powers. (3) When this has been acquired we shall possess a foundation wherefrom we can deduce our thoughts, and a path whereby the intellect, according to its capacity, may attain the knowledge of eternal things, allowance being made for the extent of the intellectual powers.
[106] (1) If, as I stated in the first part, it belongs to the nature of thought to form true ideas, we must here inquire what is meant by the faculties and power of the understanding. (2) The chief part of our method is to understand as well as possible the powers of the intellect, and its nature; we are, therefore, compelled (by the considerations advanced in the second part of the method) necessarily to draw these conclusions from the definition itself of thought and understanding.
[107] (1) But, so far as we have not got any rules for finding definitions, and, as we cannot set forth such rules without a previous knowledge of nature, that is without a definition of the understanding and its power, it follows either that the definition of the understanding must be clear in itself, or that we can understand nothing. (2) Nevertheless this definition is not absolutely clear in itself; however, since its properties, like all things that we possess through the understanding, cannot be known clearly and distinctly, unless its nature be known previously, understanding makes itself manifest, if we pay attention to its properties, which we know clearly and distinctly. (3) Let us, then, enumerate here the properties of the understanding, let us examine them, and begin by discussing the instruments for research which we find innate in us. See [31]
[108] (1) The properties of the understanding which I have chiefly remarked, and which I clearly understand, are the following:--
I. (2) It involves certainty--in other words, it knows that a thing exists in reality as it is reflected subjectively.
II. (108:3) That it perceives certain things, or forms some ideas absolutely, some ideas from others. (4) Thus it forms the idea of quantity absolutely, without reference to any other thoughts; but ideas of motion it only forms after taking into consideration the idea of quantity.
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.
[x] (1) Afterwards, when we come to speak of fiction that is concerned with essences, it will be evident that fiction never creates or furnishes the mind with anything new; only such things as are already in the brain or imagination are recalled to the memory, when the attention is directed to them confusedly and all at once. (2) For instance, we have remembrance of spoken words and of a tree; when the mind directs itself to them confusedly, it forms the notion of a tree speaking. (3) The same may be said of existence, especially when it is conceived quite generally as an entity; it is then readily applied to all things together in the memory. (4) This is specially worthy of remark.
[y] We must understand as much in the case of hypotheses put forward to explain certain movements accompanying celestial phenomena; but from these, when applied to the celestial motions, we any draw conclusions as to the nature of the heavens, whereas this last may be quite different, especially as many other causes are conceivable which would account for such motions.
[z] (1) It often happens that a man recalls to mind this word soul, and forms at the same time some corporeal image: as the two representations are simultaneous, he easily thinks that he imagines and feigns a corporeal soul: thus confusing the name with the thing itself. (2) I here beg that my readers will not be in a hurry to refute this proposition; they will, I hope, have no mind to do so, if they pay close attention to the examples given and to what follows.
[61a] (1) Though I seem to deduce this from experience, some may deny its cogency because I have given no formal proof. (2) I therefore append the following for those who may desire it. (3) As there can be nothing in nature contrary to nature's laws, since all things come to pass by fixed laws, so that each thing must irrefragably produce its own proper effect, it follows that the soul, as soon as it possesses the true conception of a thing, proceeds to reproduce in thought that thing's effects. (4) See below, where I speak of the false idea.
[64b] (1) Observe that fiction regarded in itself, only differs from dreams in that in the latter we do not perceive the external causes which we perceive through the senses while awake. (2) It has hence been inferred that representations occurring in sleep have no connection with objects external to us. (3) We shall presently see that error is the dreaming of a waking man: if it reaches a certain pitch it becomes delirium.
[76z] These are not attributes of God displaying His essence, as I will show in my philosophy.
[76a] (1) This has been shown already. (2) For if such a being did not exist it would never be produced; therefore the mind would be able to understand more than nature could furnish; and this has been shown above to be false.
[78a] (1) That is, it is known that the senses sometimes deceive us. (2) But it is only known confusedly, for it is not known how they deceive us.
[83d] (1) If the duration be indefinite, the recollection is imperfect; this everyone seems to have learnt from nature. (2) For we often ask, to strengthen our belief in something we hear of, when and where it happened; though ideas themselves have their own duration in the mind, yet, as we are wont to determine duration by the aid of some measure of motion which, again, takes place by aid of imagination, we preserve no memory connected with pure intellect.
[91e] The chief rule of this part is, as appears from the first part, to review all the ideas coming to us through pure intellect, so as to distinguish them from such as we imagine: the distinction will be shown through the properties of each, namely, of the imagination and of the understanding.
[92f] Observe that it is thereby manifest that we cannot understand anything of nature without at the same time increasing our knowledge of the first cause, or God.
End of "On the Improvement of the Understanding."
Notes by Volunteer.
1. Used, in part, with kind permission from: http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/
2. The text is that of the translation of the Tractatus de Intellectus Emendatione by R. H. M. Elwes, as printed by Dover Publications (NY):1955), ISBN 0-486-20250-X. This text is "an unabridged and unaltered republication of the Bohn Library edition originally published by George Bell and Sons in 1883."
3. Paragraph Numbers, shown thus [1], are from Edwin Curley's translation in his "The Collected Works of Spinoza", Volume 1, 1985, Princeton University Press; ISBN 0-691-07222-1.
4. Sentence Numbers, shown thus (1), have been added by volunteer.
5. Spinoza's endnotes are shown thus [a]. The letter is taken from Curley, see Note 3.
6. Search strings are enclosed in square brackets; include brackets.
7. HTML versions of "On the Improvement of the Understanding" are published in the Books On-Line Web Pages;ttp://www.cs.cmu.edu/books.html and they include:http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/http://www.erols.com/jyselman/teielwes.htm