1 God, according to Leibnitz, is actus pitrus, a pure spirit, without body and without extension. All other beings require bodies. His omnipresence is dynamic. Cf. New Essays, Bk. II., chap. 1, § 12, Th., ante, p. 113; Letter to Des Bosses, Oct. 16, 170(5, Gerhardt, Vol. 2, p. 325, Erdmann, p. 440, b. — TR.
160 LEIBNITZ'S CRITIQUE OF LOCKE [BK, IT CHAPTER XVI OF NUMBER § 4. Ph. In numbers ideas are both more precise and more accurately to be distinguished the one from the other than in extension, where you cannot observe or measure each equality and each excess of size as easily as in numbers, because in space we cannot by thought attain a certain definite smallness beyond which we cannot go, like the unit in number.
Th. [That should be understood of the integer. For other wise number in its extent, comprising the fraction, the surd, the transcendent, and all that may be assumed between two inte gers, is proportional to the line, and there is there as little of a minimum as in the continuum. Thus the definition of num ber as a multitude of units is in place only among the integers. The precise distinction of ideas in extension does not consist in. size: for to distinguish size clearly one must have recourse to integers, or to other (measures) known by means of inte gers; thus from continuous quantity it is necessary to recur to discrete quantity, in order to have a distinct knowledge of size. Thus the modifications of extension, when not joined to num bers, cannot be distinguished by figure, taking this term so generally that it means everything which makes two exten sions dissimilar the one to the other.]
§ 5. Ph. By repeating the idea of a unit and joining it to another unit, we make a collective idea, which we call two. And whoever can do that and advance always by adding one more to the last collective idea to which he gives a particular name, can count so long as he has a set of names and sufficient memory to retain them.
Th. [By this means alone one cannot advance very far. For memory would be too heavily loaded if it must retain an entirely new name for each addition of a new unit. That is why a certain order and a certain repetition of these names is necessary by recommencing in accordance with a certain pro gression.]
Ph. The different modes of numbers are capable of no other en. XVH] ON HUMAN UNDERSTANDING 101 difference than that of more or less; [this is why there are simple modes like those of extension.]
Th. [That may be said of time and of the straight line, but not of figures, and still less of numbers, which are not only different in size but further unlike. An even number may be divided into two equal numbers, but not an uneven. Three and six are triangular numbers, four and nine are squares, eight is a cube, etc. And this principle has place in numbers still more than in figures, for two unequal figures may be per fectly similar to each other, but never two numbers. But I am not astonished that you are often deceived thereupon, be cause one does not commonly have a distinct idea of what is similar or dissimilar. You see then, sir, that your idea or your application of simple or mixed modes is greatly in need of correction.]
§ 6. Ph. [You were right in remarking that it is well to give numbers their own names to be retained.] Thus I believe that it would be convenient in computation to say a billion for brevity's sake instead of a million of millions, and instead of a million of millions of millions, or a million of billions, to say a trillion, and thus in order to nonillions, for there is little need of going farther in the use of numbers.
Th. These denominations are good enough. Let a; =10. That posited, a million will be x6, a billion x12, a trillion a18, etc., and a nonillion x54.
CHAPTER XVII OF INFINITY § 1. Ph. One of the most important notions is that of the finite and the infinite, which are regarded as modes of quantity.
Th. [Properly speaking, it is true that there is an infinite number of things, i.e. that there are always more of them than can be assigned. But there is no infinite number, neither line nor other infinite quantity, if these are understood as veritable wholes, as it is easy to prove. The schools have meant or have been obliged to say that, in admitting a syncategorematic in- M 162 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n finite,1 as they call it, and not a categorematic infinite. The true infinite exists, strictly speaking, only in the absolute, which is anterior to all composition, and is not formed by the additions of parts.2] Ph. When we apply our idea of the infinite to the first Being, we do it primarily in respect to his duration and ubi quity, and, more figuratively, to his power, his wisdom, his goodness, and his other -attributes.
Th. [Not more figuratively, but less immediately, because the other attributes make their importance known through relation to those into which enters the consideration of parts.]
§ 2. Ph. I thought it was established that the mind regards the finite and the infinite as modifications of extension 3 and duration.
Th. [I do not find that it has been established that the con sideration of the finite and the infinite takes place wherever there is bulk and magnitude. And the true infinite is not a modification, it is the absolute; on the contrary, when it is modified, it is limited and forms a finite.]
§ 3. Ph. We have believed that since the power of the mind to expand without limit its idea of space by new addi tions is always the same, it is thence that the idea of an infi nite space is derived.
Th. [It is well to add that this is because the same ratio is seen always to hold good. Let us take a straight line and prolong it until it is double the length of the first. Now it is clear that the second line, being perfectly similar to the first, may be itself doubled in order to have a third, which is still similar to the preceding; and the same ratio holding good always, it is never possible to stop the process; thus the line may be prolonged to infinity, so that the consideration of the infinite arises from that of similarity or from the same ratio, and its origin is the same with that of universal and necessary truths. This shows us how what gives completion 1 An incompletely defined infinite, capable of or needing still further defini tion, but infinite only so far as it cannot really be defined, the indefinite- infinite (infinitum-indeftnitum). — TR.
2 Cf. ante, pp. 16, 17; also New Essays, Bk. II., chap. 13, § 21. — TR.
3 Locke has: "expansion," Philos. Works, Vol. 1, p. 331 (Bohn's ed.). — TR.
CH. xvn] ON HUMAN UNDERSTANDING 163 to the conception of this idea is found in ourselves, and can not come from the experience of our senses, just as necessary truths cannot be proved by induction nor by the senses. The idea of the absolute is in us internally, like that of being; these absolutes are nothing else than the attributes of God, and it may be said that they are not less the source of ideas, because God is himself the principle of beings. The idea of the abso lute in relation to space, is only that of the immensity of God, and so of the others. But you deceive yourself in wish ing to imagine an absolute space which is an infinite whole composed of parts; there is none such, it is a notion which implies a contradiction, and these infinite wholes, and their opposed infinitesimals, are used only in the calculations of geometers, just like the imaginary roots of algebra.]
§ 6. Ph. [We conceive furthermore a magnitude without understanding thereby parts outside of parts.] If to the most perfect idea I have of the whitest whiteness, I add another of an equal or less brilliant whiteness (for I cannot add the idea of a whiter than I have, which I suppose the whitest that I actually conceive), it neither increases nor extends my idea in any way; therefore the different ideas of whiteness are called degrees.]
Th. [I do not fully understand the force of this reasoning, for nothing prevents me from receiving the perception of a whiter whiteness than what is actually conceived. The true reason why we are inclined to believe that whiteness cannot be infinitely increased is because it is not an original quality; the senses give us only a confused knowledge of it; and when we have a distinct knowledge of it, we shall see that it arises from the structure, and is limited by that of the organ of vision. But as regards original or distinctly knowable quali ties, we see that there are sometimes means of going to infinity, not only in the case of extension or, if you prefer, diffusion or what the scholastic philosophy calls partes extra partes, as in time and place, but also in the case of intention or degrees, for example, as regards velocity.]
§ 8. Ph. We have no idea of infinite space, and nothing is plainer than the absurdity of an actual idea of an infinite number.
Th. [I am of the same opinion. But this is not because we 104 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n cannot have the idea of the infinite, but because the infinite cannot be a true whole.]
§ 16. Ph. For the same reason we have then no positive idea of an infinite duration or of eternity, any more than of immensity.
Th. [I believe we have a positive idea of both, and this idea is a true one, provided it is not conceived as an infinite whole, but as an absolute or attribute without limits Avhich exists in reference to eternity, in the necessity of the existence of God, without depending upon parts and without the notions being formed by an addition of time. We see furthermore in that way, as I have said already, that the origin of the notion of the infinite comes from the same source as that of necessary truths.]
CHAPTER XVIII OF OTIIEK SIMPLE MODES Ph. There are besides many simple modes formed from simple ideas. Such are (§2) modes of motion, as sliding, rolling; those of sound (§ 3) which are modified by notes and airs, as colors by degrees, not to speak of tastes and smells (§ 6). These always1 have neither measures nor distinct names any more than in the case of the complex modes (§ 7), because use regulates them, and we will speak of them more fully when we come to words.
Th. [The majority of modes are not sufficiently simple and can be reckoned with the complex, for example, to explain what sliding and rolling is besides motion, you must consider sur face-resistance.]
CHAPTER XIX OF THE MODES OF THINKING § 1. Ph. [Let us pass from the modes which come from the senses to those given us by reflection.] Sensation is, so to speak, the actual entrance of ideas into the understanding by 1 Locke: "ordinarily," Philos. Works, Vol. 1, p. 346 (Bohn's ed.).— TR.
en. xix] ON HUMAN UNDERSTANDING 165 means of the senses. When the same idea comes again into the mind, without the action upon our senses, of the external object which at first caused it to spring up, the act of the mind is called remembrance; if the mind tries to recall it, and only after considerable effort finds and brings it to view, it is recollection (recueillement}.1 If the mind looks upon it atten tively for a long time it is contemplation; when the idea floats about in the mind without any attention on the part of the understanding, it is called reverie. When the mind reflects upon ideas, which present themselves, and when it, so to speak, registers them in its memory, it is attention; and when the mind fixes itself upon an idea with much application, considers it on all sides, and will not be turned aside notwithstanding other ideas which come in the way, we call it study or intense- ness of thoiight. Sleep accompanied by no dream is a cessa tion of all these things; and dreaming is having these ideas in the mind while the outer senses are closed, so that they do not receive the impressions of external objects with their usual quickness. It is, I say, having ideas without any sug gestion from any external objects or known occasion, and apart from any choice or determination in any way of the understanding. As for that which we call ecstasy, I leave others to judge whether it is not dreaming with the eyes open. Tli. [It is well to clear up these notions and I will try to aid in the work. I will say then that it is sensation when an external object is perceived; that remembrance consists in the repetition without the reappearance of the object; but when we know we have had it, it is memory. Recollection (recueille ment) is commonly understood in a sense different from yours, viz.: as a state in which we disengage ourselves from things in order to apply ourselves to some meditation. But since there is no word known to me corresponding to your notion, sir, one may apply to it that which you employ. We give attention to objects which we distinguish and prefer to others. Attention continuing in the mind, whether the external object continues or not, and even whether it is found there or not, is 1 Cf. below, where the French "recueillement," here employed as a trans lation of the English "recollection," is shown to have a different meaning and use from that of the English word. As " recueillement " is, however, used as an equivalent for the English word, I have translated it in the second para graph accordingly. — TK.
106 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n consideration; which, tending to knowledge without reference to action, will be contemplation. Attention, whose aim is to learn (i.e. the attainment of knowledge for the sake of keep ing it), is study. To consider in order to form a plan is to meditate; but reverie appears to be nothing else than following certain thoughts for the pleasure one takes therein, with no other end; this is why reverie may lead to madness; we forget ourselves, we forget the die cur hie, we approach dreams and chimeras, we build castles in Spain. We can distinguish dreams from sensations only because they are not united with them, they are like a world apart. Sleep is a cessation of sen sations, and in this way ecstasy is a very deep sleep from which one finds difficulty in being awakened, a condition which arises from some internal passing cause, which is added in order to exclude this profound sleep, arising from some narcotic or from some continuous injury to the functions, as in lethargy. Ecstasy is sometimes accompanied with visions; but there is vision without ecstasy, and vision seems to be nothing but a dream which passes for a sensation just as if it acquainted us with the truth of objects. And when visions are divine, there is actually truth in them, which may be known for instance when they contain particular prophecies which the outcome justifies.]
§ 4. Ph. From the different degrees of intensity * or relaxa tion of the mind, it follows that thought is the act and not the essence of the soul.
Th. [Doubtless thought is an act and cannot be the essence: but it is an essential act, and all substances are of this charac ter. I have shown above that we always have an infinite number of little perceptions, without being conscious of them. We are never without perceptions, but we are necessarily often without apperceptions, viz.: when there are no distinct per ceptions. It is from not having considered this important point that a relaxed philosophy, as little noble as solid, has prevailed with so many excellent minds, and that we have hitherto almost ignored that which is most beautiful in the soul. This is also the reason why so much probability has been found in that error, which teaches that souls are by nature perishable.]
1 Locke has: "intention and remission," Philos. Works (Bolm's ed.), Vol.
CH. xx] ON HUMAN UNDERSTANDING 167 CHAPTER XX OF MODES OF PLEASURE AND PAIN § 1. Ph. As the sensations of the body, like the thoughts of the mind, are either indifferent or followed by pleasure or pain, the ideas of them cannot be described any more than all other simple ideas, nor can the words which serve to designate them be defined.
Th. [I believe that there are no perceptions which are wholly indifferent to us, but it is enough that their effect be not notable in order that they may be thus spoken of, for pleasure and pain appear to consist in a notable aid or impedi ment. I admit that this definition is not at all nominal and that one may give none at all.]
§ 2. Ph. The good is that which is fitted to produce and increase pleasure in us, or to diminish and cut short some pain. Evil is fitted to produce or increase pain in us, or to diminish some pleasure.
Th. [I am also of this opinion. The good is divided into the virtuous, the agreeable, and the useful, but ultimately I believe that it must be either agreeable itself, or serving some thing else which may give us an agreeable feeling, that is to say, the good is agreeable or useful, and virtue itself consists in a pleasure of mind.]
§§ 4, 5. Ph. From pleasure and pain come the passions. We have love for that which can produce pleasure, and the thought of sadness or of pain that a present or absent cause can produce is hatred. But hatred or love which relates to beings capable of happiness or misery is often an uneasiness or delight which we feel to be produced in us by the considera tion of their existence or of the happiness which they enjoy.
Th. [I also gave nearly this definition of love when I explained the principles of justice, in the preface to my "Codex juris gentium diplomaticus," * viz.: that to love is to 1 The Codex juris gentium diplomaticus, 1093, a collection of public acts and treatises, etc. An excerpt from the Preface of this work, entitled De no- tionibus juris et justifies, is given by Erdmann, pp. 118-120; translation, Dun can, Philos. Works of Leibnitz, note 48, pp. 379-382.— TB.
168 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n be inclined to take pleasure in the complete perfection or hap piness of the object loved. And for that reason one neither considers nor asks for any other pleasure proper than that indeed which is found in the good or pleasure of the one who is loved; but in this sense we do not, properly speaking, love what is incapable of pleasure or happiness, and we enjoy things of this nature without loving them for that reason, unless by a prosopopoeia, and as if we imagined that they themselves enjoy their perfection. It is not, then, properly love when one says that he loves a beautiful picture for the pleasure which he takes in feeling its perfections. But it is allowable to extend the sense of terms, and their usage varies. Philoso phers and theologians even distinguish two kinds of love, viz.: the love which they call the love of complacency, which is nothing but the desire or feeling which we have for the one who gives us pleasure, without concerning ourselves whether he receives it; and the love of benevolence, which is the feeling that one has for the one who, by his pleasure or happiness, gives us some. The first makes us have in view our pleasure and the second that of another, but as making or rather consti tuting ours, for if it did not reflect upon us in some way we could not concern ourselves with it since it is impossible, although they affirm it, to be separated from the good proper. And see how it is needful to understand disinterested or non- mercenary love, in order to reach a favorable conception of nobility and not to fall meanwhile into the chimerical one.]
§ 6. Ph. The uneasiness (French inquietude) which a man feels in himself at the absence of anything which if present would give him pleasure is called desire. Uneasiness is the prin cipal, not to say the only stimulus which excites human industry and action for whatever good is proposed to man; if the absence of this good is followed by no displeasure or pain, and he who is deprived of it can be content and at his ease without its pos session, he does not think of desiring, and less still of making any efforts to enjoy it. He feels for this kind of good only a bare velleity,1 the term used to signify the lowest kind of desire, 1 Schaarschmirlt translates the French " velleite " by the German " Willens- neigung," i.e. inclination of will. The term is borrowed from the Scholastic "velleitas," and is here equivalent to imperfect volition (imperfecta rolitio) or that condition of the soul in which the will, though not in a state of iudifferen. xx] ON HUMAN UNDERSTANDING 169 which approaches nearest to that state in which the soul finds itself with regard to anything which is wholly indifferent to it, when the displeasure which the absence of anything causes is so inconsiderable that it is carried only to feeble longings without being compelled to avail itself of the means of obtain ing it. Desire is moreover extinguished or abated by the opinion that the wished for good cannot be obtained in propor tion as the soul's uneasiness is cured or allayed by that con sideration. [For the rest, I have found what I stated to you about uneasiness in this celebrated English author, whose views I often relate to you. I was a little in difficulty as to the definition of the English word uneasiness. But the French translator 1 whose skill in the fulfilment of this task cannot be called in question, remarks at the foot of the page (chap. 20, § 6,) that by this word the English author understands the state of a man not at his ease, the lack of ease and of tran quillity of soul, which in this regard is purely passive, and that it must be translated by the (French) word inquietude, which does not express exactly the same idea, but approaches it very nearly. This caution (he adds) is above all needful with regard to the following chapter, " Of Power," in which the author reasons much upon this kind of uneasiness; for if you should not attach to this word the idea which has just been indicated, it would be impossible exactly to understand the matters treated of in this chapter and which are the most important and delicate in the entire work.]
Th. [The translator is right and the reading of his excellent author shows me that this consideration of uneasiness is a capi tal point, in which this author has particularly shown his pene trating and profound mind. For this reason I gave it some attention, and after having well considered the matter, it al most appears to me that the (French) word inquietude (restless ness}, if it does not express quite the meaning of the author, nevertheless sufficiently agrees with the nature of the thing; and that the (English) word uneasiness, if it indicated a dis pleasure, fretfulness (chagrin), inconvenience, in a word some effective pain, would not suit his meaning. For I should preence, has not as yet sufficient force to pass over into action (volitio). Cf. New Essays, Bk. II., chap. 21, § 5 sq., also § 30, Th. — TR. 1 M. Pierre Coste. — TR.
170 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n fer to say that in the desire in itself there is rather a disposi tion and preparation for pain than pain itself. It is true that this perception sometimes differs from that which is in pain only more or less, but it is the degree which is the essence of pain, for it is a notable perception. The same is also seen in the difference between appetite and hunger, for when the stomach's irritation becomes too strong it is uncomfortable, so that we must also apply here our doctrine of perceptions too small to be perceived, for if that which goes on in us when we have appetite and desire, were great enough, it would cause us pain. Hence the infinitely wise author of our being arranged it for our good, when he so arranged it that we should often be in ignorance and among confused perceptions, in order to act more promptly by instinct, and in order not to be disturbed by too distinct sensations of a multitude of objects, which do not recur immediately and the nature of which could not go on to obtain their ends. How many insects we swallow without noticing them, how many "persons we see who, having a too penetrating odor, are annoying, and how many disgusting ob jects we should see if our vision were penetrating enough. It is also for the sake of this skill that nature has given us the stimuli of desire, like the rudiments or elements of pain, or so to speak, of semi-pains, or (if you wish to speak extravagantly in order to express yourself more forcibly) the little impercep tible pains, in order that we might enjoy the advantage of evil without its inconvenience; for otherwise if this perception were too distinct, we would always be miserable while await ing the good, while this continual victory over these semi- pains which are felt in pursuing our desire and satisfying in some way this appetite, or this longing, gives us a quantity of semi-pleasures, whose continuity and mass (as in the continuity of the impulse of a heavy body which falls and acquires im petuosity) becomes at last a complete and genuine pleasure. And finally, without these semi-pains there would be no pleas ure at all, nor any means of perceiving that something aids and relieves us while there are some obstacles which prevent us from putting ourselves at ease. It is furthermore in this that we recognize the affinity of pleasure and pain which Soc rates in Plato's " Phaedo," * noticed when his feet itched. This 1 Phsedo, GOB. — TR.
en. xxj ON HUMAN UNDERSTANDING 171 consideration of little aids or little releases and imperceptible deliverances from the fixed tendency, whose result at last is a notable pleasure, serves also to give a more distinct knowl edge of the confused idea which we have, and ought to have, of pleasure and of pain; just as the sensation of heat and of light results from a quantity of little motions which express those of objects, as I said above (chap. 9, § 13) and differ from them only in appearance and because we ourselves are not conscious of this analysis: while many to-day believe that our ideas of sense-qualities differ toto genere from notions and from all that goes on in objects, and are something primitive and inexpli cable, and indeed arbitrary, as if God made the soul sensible of whatever seems good to him, instead of what goes on in the body, a view which is far removed from the true analysis of our ideas. But to return to uneasiness, that is to say to the little imperceptible solicitations which keep us always in suspense; these are confused determinations, so that often we do not know what we lack, while in the case of the inclinations and passions we at least know what we ask for, although confused perceptions enter also into their methods of acting, and the