On the Improvement of the Understanding

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On the Improvement of the Understanding (Treatise on the Emendation of the Intellect) (1677)
by Benedictus de Spinoza, translated by R. H. M. Elwes
115194On the Improvement of the Understanding (Treatise on the Emendation of the Intellect)R. H. M. ElwesBenedictus de Spinoza



First part of method:

Second part of method:

Conditions of definition

Notice to the Reader


(This notice to the reader was written by the editors of the Opera Postuma in 1677. Taken from Curley, Note [3], at end)

This Treatise on the Emendation of the Intellect etc., which we give you here, kind reader, in its unfinished [that is, defective] state, was written by the author many years ago now. He always intended to finish it. But hindered by other occupations, and finally snatched away by death, he was unable to bring it to the desired conclusion. But since it contains many excellent and useful things, which - we have no doubt - will be of great benefit to anyone sincerely seeking the truth, we did not wish to deprive you of them. And so that you would be aware of, and find less difficult to excuse, the many things that are still obscure, rough, and unpolished, we wished to warn you of them. Farewell.

[1] (1) After experience had taught me that all the usual surroundings of social life are vain and futile; seeing that none of the objects of my fears contained in themselves anything either good or bad, except in so far as the mind is affected by them, I finally resolved to inquire whether there might be some real good having power to communicate itself, which would affect the mind singly, to the exclusion of all else: whether, in fact, there might be anything of which the discovery and attainment would enable me to enjoy continuous, supreme, and unending happiness.

[2] (1) I say "I finally resolved," for at first sight it seemed unwise willingly to lose hold on what was sure for the sake of something then uncertain. (2) I could see the benefits which are acquired through fame and riches, and that I should be obliged to abandon the quest of such objects, if I seriously devoted myself to the search for something different and new. (3) I perceived that if true happiness chanced to be placed in the former I should necessarily miss it; while if, on the other hand, it were not so placed, and I gave them my whole attention, I should equally fail.

[3] (1) I therefore debated whether it would not be possible to arrive at the new principle, or at any rate at a certainty concerning its existence, without changing the conduct and usual plan of my life; with this end in view I made many efforts, in vain. (2) For the ordinary surroundings of life which are esteemed by men (as their actions testify) to be the highest good, may be classed under the three heads - Riches, Fame, and the Pleasures of Sense: with these three the mind is so absorbed that it has little power to reflect on any different good.

[4] (1) By sensual pleasure the mind is enthralled to the extent of quiescence, as if the supreme good were actually attained, so that it is quite incapable of thinking of any other object; when such pleasure has been gratified it is followed by extreme melancholy, whereby the mind, though not enthralled, is disturbed and dulled. (2) The pursuit of honors and riches is likewise very absorbing, especially if such objects be sought simply for their own sake, [a] inasmuch as they are then supposed to constitute the highest good.

[5] (1) In the case of fame the mind is still more absorbed, for fame is conceived as always good for its own sake, and as the ultimate end to which all actions are directed. (2) Further, the attainment of riches and fame is not followed as in the case of sensual pleasures by repentance, but, the more we acquire, the greater is our delight, and, consequently, the more are we incited to increase both the one and the other; on the other hand, if our hopes happen to be frustrated we are plunged into the deepest sadness. (3) Fame has the further drawback that it compels its votaries to order their lives according to the opinions of their fellow-men, shunning what they usually shun, and seeking what they usually seek.

[6] (1) When I saw that all these ordinary objects of desire would be obstacles in the way of a search for something different and new - nay, that they were so opposed thereto, that either they or it would have to be abandoned, I was forced to inquire which would prove the most useful to me: for, as I say, I seemed to be willingly losing hold on a sure good for the sake of something uncertain. (6:2) However, after I had reflected on the matter, I came in the first place to the conclusion that by abandoning the ordinary objects of pursuit, and betaking myself to a new quest, I should be leaving a good, uncertain by reason of its own nature, as may be gathered from what has been said, for the sake of a good not uncertain in its nature (for I sought for a fixed good), but only in the possibility of its attainment.

[7] (1) Further reflection convinced me that if I could really get to the root of the matter I should be leaving certain evils for a certain good. (2) I thus perceived that I was in a state of great peril, and I compelled myself to seek with all my strength for a remedy, however uncertain it might be; as a sick man struggling with a deadly disease, when he sees that death will surely be upon him unless a remedy be found, is compelled to seek a remedy with all his strength, inasmuch as his whole hope lies therein. (7:3) All the objects pursued by the multitude not only bring no remedy that tends to preserve our being, but even act as hindrances, causing the death not seldom of those who possess them, [b] and always of those who are possessed by them.

[8] (1) There are many examples of men who have suffered persecution even to death for the sake of their riches, and of men who in pursuit of wealth have exposed themselves to so many dangers, that they have paid away their life as a penalty for their folly. (2) Examples are no less numerous of men, who have endured the utmost wretchedness for the sake of gaining or preserving their reputation. (3) Lastly, are innumerable cases of men, who have hastened their death through over-indulgence in sensual pleasure.

[9] (1) All these evils seem to have arisen from the fact, that happiness or unhappiness is made wholly dependent on the quality of the object which we love. (2) When a thing is not loved, no quarrels will arise concerning it - no sadness be felt if it hatred, in short no disturbances of the mind. (3) All these arise from the love of what is perishable, such as the objects already mentioned.

[10] (1) But love towards a thing eternal and infinite feeds the mind wholly with joy, and is itself unmingled with any sadness, wherefore it is greatly to be desired and sought for with all our strength. (2) Yet it was not at random that I used the words, "If I could go to the root of the matter," for, though what I have urged was perfectly clear to my mind, I could not forthwith lay aside all love of riches, sensual enjoyment, and fame.

[11] (1) One thing was evident, namely, that while my mind was employed with these thoughts it turned away from its former objects of desire, and seriously considered the search for a new principle; this state of things was a great comfort to me, for I perceived that the evils were not such as to resist all remedies. (11:2) Although these intervals were at first rare, and of very short duration, yet afterwards, as the true good became more and more discernible to me, they became more frequent and more lasting; especially after I had recognized that the acquisition of wealth, sensual pleasure, or fame, is only a hindrance, so long as they are sought as ends not as means; if they be sought as means, they will be under restraint, and, far from being hindrances, will further not a little the end for which they are sought, as I will show in due time.

[12] (1) I will here only briefly state what I mean by true good, and also what is the nature of the highest good. (2) In order that this may be rightly understood, we must bear in mind that the terms good and evil are only applied relatively, so that the same thing may be called both good and bad according to the relations in view, in the same way as it may be called perfect or imperfect. (3) Nothing regarded in its own nature can be called perfect or imperfect; especially when we are aware that all things which come to pass, come to pass according to the eternal order and fixed laws of nature.

[13] (1) However, human weakness cannot attain to this order in its own thoughts, but meanwhile man conceives a human character much more stable than his own, and sees that there is no reason why he should not himself acquire such a character. (2) Thus he is led to seek for means which will bring him to this pitch of perfection, and calls everything which will serve as such means a true good. (13:3) The chief good is that he should arrive, together with other individuals if possible, at the possession of the aforesaid character. (4) What that character is we shall show in due time, namely, that it is the knowledge of the union existing being the mind and the whole of nature. [c]

[14] (1) This, then, is the end for which I strive, to attain to such a character myself, and to endeavor that many should attain to it with me. (2) In other words, it is part of my happiness to lend a helping hand, that many others may understand even as I do, so that their understanding and desire may entirely agree with my own. (3) In order to bring this about, it is necessary to understand as much of nature as will enable us to attain to the aforesaid character, and also to form a social order such as is most conducive to the attainment of this character by the greatest number with the least difficulty and danger.

[15] (1) We must seek the assistance of Moral Philosophy [d] and the Theory of Education; further, as health is no insignificant means for attaining our end, we must also include the whole science of Medicine, and, as many difficult things are by contrivance rendered easy, and we can in this way gain much time and convenience, the science of Mechanics must in no way be despised.

[16] (1) But before all things, a means must be devised for improving the understanding and purifying it, as far as may be at the outset, so that it may apprehend things without error, and in the best possible way. (2) Thus it is apparent to everyone that I wish to direct all science to one end [e] and aim, so that we may attain to the supreme human perfection which we have named; and, therefore, whatsoever in the sciences does not serve to promote our object will have to be rejected as useless. (3) To sum up the matter in a word, all our actions and thoughts must be directed to this one end.

[17] (1) Yet, as it is necessary that while we are endeavoring to attain our purpose, and bring the understanding into the right path we should carry on our life, we are compelled first of all to lay down certain rules of life as provisionally good, to wit the following:-

  1. (2) To speak in a manner intelligible to the multitude, and to comply with every general custom that does not hinder the attainment of our purpose. (3) For we can gain from the multitude no small advantages, provided that we strive to accommodate ourselves to its understanding as far as possible: moreover, we shall in this way gain a friendly audience for the reception of the truth.
  2. (17:4) To indulge ourselves with pleasures only in so far as they are necessary for preserving health.
  3. (5) Lastly, to endeavor to obtain only sufficient money or other commodities to enable us to preserve our life and health, and to follow such general customs as are consistent with our purpose.

[18] (1) Having laid down these preliminary rules, I will betake myself to the first and most important task, namely, the amendment of the understanding, and the rendering it capable of understanding things in the manner necessary for attaining our end. (2) In order to bring this about, the natural order demands that I should here recapitulate all the modes of perception, which I have hitherto employed for affirming or denying anything with certainty, so that I may choose the best, and at the same time begin to know my own powers and the nature which I wish to perfect.

[19] (1) Reflection shows that all modes of perception or knowledge may be reduced to four:-

  1. (2) Perception arising from hearsay or from some sign which everyone may name as he please.
  2. (3) Perception arising from mere experience - that is, form experience not yet classified by the intellect, and only so called because the given event has happened to take place, and we have no contradictory fact to set against it, so that it therefore remains unassailed in our minds.
  3. (19:4) Perception arising when the essence of one thing is inferred from another thing, but not adequately; this comes when [f] from some effect we gather its cause, or when it is inferred from some general proposition that some property is always present.
  4. (5) Lastly, there is the perception arising when a thing is perceived solely through its essence, or through the knowledge of its proximate cause.

[20] (1) All these kinds of perception I will illustrate by examples. (2) By hearsay I know the day of my birth, my parentage, and other matters about which I have never felt any doubt. (3) By mere experience I know that I shall die, for this I can affirm from having seen that others like myself have died, though all did not live for the same period, or die by the same disease. (4) I know by mere experience that oil has the property of feeding fire, and water of extinguishing it. (5) In the same way I know that a dog is a barking animal, man a rational animal, and in fact nearly all the practical knowledge of life.

[21] (1) We deduce one thing from another as follows: when we clearly perceive that we feel a certain body and no other, we thence clearly infer that the mind is united [g] to the body, and that their union is the cause of the given sensation; but we cannot thence absolutely understand [h] the nature of the sensation and the union. (2) Or, after I have become acquainted with the nature of vision, and know that it has the property of making one and the same thing appear smaller when far off than when near, I can infer that the sun is larger than it appears, and can draw other conclusions of the same kind.

[22] (1) Lastly, a thing may be perceived solely through its essence; when, from the fact of knowing something, I know what it is to know that thing, or when, from knowing the essence of the mind, I know that it is united to the body. (2) By the same kind of knowledge we know that two and three make five, or that two lines each parallel to a third, are parallel to one another, &c. (3) The things which I have been able to know by this kind of knowledge are as yet very few.

[23] (1) In order that the whole matter may be put in a clearer light, I will make use of a single illustration as follows. (2) Three numbers are given - it is required to find a fourth, which shall be to the third as the second is to the first. (23:3) Tradesmen will at once tell us that they know what is required to find the fourth number, for they have not yet forgotten the rule which was given to them arbitrarily without proof by their masters; others construct a universal axiom from their experience with simple numbers, where the fourth number is self-evident, as in the case of 2, 4, 3, 6; here it is evident that if the second number be multiplied by the third, and the product divided by the first, the quotient is 6; when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional.

[24] (1) Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid's proposition, but intuitively, without going through any process.

[25] (1) In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end.

  1. (2) To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general.
  2. To collect in this way the differences, the agreements, and the oppositions of things.
  3. To learn thus exactly how far they can or cannot be modified.
  4. To compare this result with the nature and power of man. (4) We shall thus discern the highest degree of perfection to which man is capable of attaining.

[26] (1) We shall then be in a position to see which mode of perception we ought to choose. (2) As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. (3) We may, therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. (4) For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it half way.

[27] (1) The second mode of perception [i] cannot be said to give us the idea of the proportion of which we are in search. (2) Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. (3) Wherefore this mode also must be rejected.

[28] (1) Of the third mode of perception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we aim at.

[29] (1) The fourth mode alone apprehends the adequate essence of a thing without danger of error. (2) This mode, therefore, must be the one which we chiefly employ. (3) How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously unknown? (4) I will proceed to explain.

[30] (1) Now that we know what kind of knowledge is necessary for us, we must indicate the way and the method whereby we may gain the said knowledge concerning the things needful to be known. (2) In order to accomplish this, we must first take care not to commit ourselves to a search, going back to infinity - that is, in order to discover the best method of finding truth, there is no need of another method to discover such method; nor of a third method for discovering the second, and so on to infinity. (3) By such proceedings, we should never arrive at the knowledge of the truth, or, indeed, at any knowledge at all. (30:4) The matter stands on the same footing as the making of material tools, which might be argued about in a similar way. (5) For, in order to work iron, a hammer is needed, and the hammer cannot be forthcoming unless it has been made; but, in order to make it, there was need of another hammer and other tools, and so on to infinity. (6) We might thus vainly endeavor to prove that men have no power of working iron.

[31] (1) But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at making, complicated mechanisms which they now possess. (31:2) So, in like manner, the intellect, by its native strength, [k], makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, [l], and from these operations again fresh instruments, or the power of pushing its investigations further, and thus gradually proceeds till it reaches the summit of wisdom.

[32] (1) That this is the path pursued by the understanding may be readily seen, when we understand the nature of the method for finding out the truth, and of the natural instruments so necessary complex instruments, and for the progress of investigation. I thus proceed with my demonstration.

[33] (1) A true idea, [m], (for we possess a true idea) is something different from its correlate (ideatum); thus a circle is different from the idea of a circle. (2) The idea of a circle is not something having a circumference and a center, as a circle has; nor is the idea of a body that body itself. (3) Now, as it is something different from its correlate, it is capable of being understood through itself; in other words, the idea, in so far as its actual essence (essentia formalis) is concerned, may be the subject of another subjective essence (essentia objectiva). [33note1] (4) And, again, this second subjective essence will, regarded in itself, be something real, capable of being understood; and so on, indefinitely.

[34] (1) For instance, the man Peter is something real; the true idea of Peter is the reality of Peter represented subjectively, and is in itself something real, and quite distinct from the actual Peter. (2) Now, as this true idea of Peter is in itself something real, and has its own individual existence, it will also be capable of being understood - that is, of being the subject of another idea, which will contain by representation (objective) all that the idea of Peter contains actually (formaliter). (3) And, again, this idea of the idea of Peter has its own individuality, which may become the subject of yet another idea; and so on, indefinitely. (4) This everyone may make trial of for himself, by reflecting that he knows what Peter is, and also knows that he knows, and further knows that he knows that he knows, &c. (34:5) Hence it is plain that, in order to understand the actual Peter, it is not necessary first to understand the idea of Peter, and still less the idea of the idea of Peter. (6) This is the same as saying that, in order to know, there is no need to know that we know, much less to know that we know that we know. (7) This is no more necessary than to know the nature of a circle before knowing the nature of a triangle. [n]. (8) But, with these ideas, the contrary is the case: for, in order to know that I know, I must first know.

[35] (1) Hence it is clear that certainty is nothing else than the subjective essence of a thing: in other words, the mode in which we perceive an actual reality is certainty. (2) Further, it is also evident that, for the certitude of truth, no further sign is necessary beyond the possession of a true idea: for, as I have shown, it is not necessary to know that we know that we know. (3) Hence, again, it is clear that no one can know the nature of the highest certainty, unless he possesses an adequate idea, or the subjective essence of a thing: certainty is identical with such subjective essence.

[36] (1) Thus, as the truth needs no sign - it being to possess the subjective essence of things, or, in other words, the ideas of them, in order that all doubts may be removed - it follows that the true method does not consist in seeking for the signs of truth after the acquisition of the idea, but that the true method teaches us the order in which we should seek for truth itself, [o] or the subjective essences of things, or ideas, for all these expressions are synonymous.

[37] (1) Again, method must necessarily be concerned with reasoning or understanding - I mean, method is not identical with reasoning in the search for causes, still less is it the comprehension of the causes of things: it is the discernment of a true idea, by distinguishing it from other perceptions, and by investigating its nature, in order that we may so train our mind that it may, by a given standard, comprehend whatsoever is intelligible, by laying down certain rules as aids, and by avoiding useless mental exertion.

[38] (1) Whence we may gather that method is nothing else than reflective knowledge, or the idea of an idea; and that as there can be no idea of an idea - unless an idea exists previously, - there can be no method without a pre-existent idea. (2) Therefore, that will be a good method which shows us how the mind should be directed, according to the standard of the given true idea.

(38:3) Again, seeing that the ratio existing between two ideas the same as the ratio between the actual realities corresponding to those ideas, it follows that the reflective knowledge which has for its object the most perfect being is more excellent than reflective knowledge concerning other objects - in other words, that method will be most perfect which affords the standard of the given idea of the most perfect being whereby we may direct our mind.

[39] (1) We thus easily understand how, in proportion as it acquires new ideas, the mind simultaneously acquires fresh instruments for pursuing its inquiries further. (2) For we may gather from what has been said, that a true idea must necessarily first of all exist in us as a natural instrument; and that when this idea is apprehended by the mind, it enables us to understand the difference existing between itself and all other perceptions. (3) In this, one part of the method consists.

(39:4) Now it is clear that the mind apprehends itself better in proportion as it understands a greater number of natural objects; it follows, therefore, that this portion of the method will be more perfect in proportion as the mind attains to the comprehension of a greater number of objects, and that it will be absolutely perfect when the mind gains a knowledge of the absolutely perfect being, or becomes conscious thereof.

[40] (1) Again, the more things the mind knows, the better does it understand its own strength and the order of nature; by increased self-knowledge, it can direct itself more easily, and lay down rules for its own guidance; and, by increased knowledge of nature, it can more easily avoid what is useless. (2) And this is the sum total of method, as we have already stated.

[41] (1) We may add that the idea in the world of thought is in the same case as its correlate in the world of reality. (2) If, therefore, there be anything in nature which is without connection with any other thing, and if we assign to it a subjective essence, which would in every way correspond to the objective reality, the subjective essence would have no connection, [p] with any other ideas - in other words, we could not draw any conclusions with regard to it. (41:3) On the other hand, those things which are connected with others - as all things that exist in nature - will be understood by the mind, and their subjective essences will maintain the same mutual relations as their objective realities - that is to say, we shall infer from these ideas other ideas, which will in turn be connected with others, and thus our instruments for proceeding with our investigation will increase. (4) This is what we were endeavoring to prove.

[42] (1) Further, from what has just been said - namely, that an idea must, in all respects, correspond to its correlate in the world of reality, - it is evident that, in order to reproduce in every respect the faithful image of nature, our mind must deduce all its ideas from the idea which represents the origin and source of the whole of nature, so that it may itself become the source of other ideas.

[43] (1) It may, perhaps, provoke astonishment that, after having said that the good method is that which teaches us to direct our mind according to the standard of the given true idea, we should prove our point by reasoning, which would seem to indicate that it is not self-evident. (2) We may, therefore, be questioned as to the validity of our reasoning. (3) If our reasoning be sound, we must take as a starting-point a true idea. (4) Now, to be certain that our starting-point is really a true idea, we need proof. (5) This first course of reasoning must be supported by a second, the second by a third, and so on to infinity.

[44] (1) To this I make answer that, if by some happy chance anyone had adopted this method in his investigations of nature - that is, if he had acquired new ideas in the proper order, according to the standard of the original true idea, he would never have doubted [q] of the truth of his knowledge, inasmuch as truth, as we have shown, makes itself manifest, and all things would flow, as it were, spontaneously towards him. (44:2) But as this never, or rarely, happens, I have been forced so to arrange my proceedings, that we may acquire by reflection and forethought what we cannot acquire by chance, and that it may at the same time appear that, for proving the truth, and for valid reasoning, we need no other means than the truth and valid reasoning themselves: for by valid reasoning I have established valid reasoning, and, in like measure, I seek still to establish it.

[45] (1) Moreover, this is the order of thinking adopted by men in their inward meditations. (2) The reasons for its rare employment in investigations of nature are to be found in current misconceptions, whereof we shall examine the causes hereafter in our philosophy. (3) Moreover, it demands, as we shall show, a keen and accurate discernment. (4) Lastly, it is hindered by the conditions of human life, which are, as we have already pointed out, extremely changeable. (5) There are also other obstacles, which we will not here inquire into.

[46] (1) If anyone asks why I have not at the starting-point set forth all the truths of nature in their due order, inasmuch as truth is self-evident, I reply by warning him not to reject as false any paradoxes he may find here, but to take the trouble to reflect on the chain of reasoning by which they are supported; he will then be no longer in doubt that we have attained to the truth. (2) This is why I have as above.

[47] (1) If there yet remains some sceptic, who doubts of our primary truth, and of all deductions we make, taking such truth as our standard, he must either be arguing in bad faith, or we must confess that there are men in complete mental blindness either innate or due to misconceptions - that is, to some external influence. (2) Such persons are not conscious of themselves. (3) If they affirm or doubt anything, they know not that they affirm or doubt: they say that they know nothing, and they say that they are ignorant of the very fact of their knowing nothing. (4) Even this they do not affirm absolutely, they are afraid of confessing that they exist, so long as they know nothing; in fact, they ought to remain dumb, for fear of haply supposing which should smack of truth.

[48] (1) Lastly, with such persons, one should not speak of sciences: for, in what relates to life and conduct, they are compelled by necessity to suppose that they exist, and seek their own advantage, and often affirm and deny, even with an oath. (2) If they deny, grant, or gainsay, they know not that they deny, grant, or gainsay, so that they ought to be regarded as automata, utterly devoid of intelligence.

[49] (1) Let us now return to our proposition. (2) Up to the present, we have, first, defined the end to which we desire to direct all our thoughts; secondly, we have determined the mode of perception best adapted to aid us in attaining our perfection; thirdly, we have discovered the way which our mind should take, in order to make a good beginning - namely, that it should use every true idea as a standard in pursuing its inquiries according to fixed rules. (49:3) Now, in order that it may thus proceed, our method must furnish us, first, with a means of distinguishing a true idea from all other perceptions, and enabling the mind to avoid the latter; secondly, with rules for perceiving unknown things according to the standard of the true idea; thirdly, with an order which enables us to avoid useless labor. (49:4) When we became acquainted with this method, we saw that, fourthly, it would be perfect when we had attained to the idea of the absolutely perfect Being. (5) This is an observation which should be made at the outset, in order that we may arrive at the knowledge of such a being more quickly.

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.

[33note1]  (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.

Notes by Volunteer

[Note 1]  Used, in part, with kind permission from: http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/

[Note 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."

[Note 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.

[Note 4]  Sentence Numbers, shown thus (1), have been added by volunteer.

[Note 5]  Spinoza's endnotes are shown thus [a]. The letter is taken from Curley, see Note [3].

[Note 6]  Search strings are enclosed in square brackets; include brackets.

[Note 7]  HTML versions of "On the Improvement of the Understanding" are published in the Books On-Line Web Pages; http://www.cs.cmu.edu/books.html and they include: http://www.physics.wisc.edu/~shalizi/Spinoza/TIE/ http://www.erols.com/jyselman/teielwes.htm