Source:

Textes inédits tome 2
Gaston Grua (ed)
pp 553-555



Date: after 1695?

*** refers to illegible text

Translated from the French



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LEIBNIZ: DOUBLE INFINITY IN PASCAL AND MONAD


[Gr p553]

     The actual infinity in material things, as much as in the increasingly large as in the vanishingly small,1 that is, the actual division of each part of matter to infinity and at the same time the infinite vastness of matter, has been supported by Mr Pascal, and it is evident that those who have contemplated his Pensées, as well as the bishops and doctors who have approved it, have agreed with it. Here is one of the passages which show it: it is at number 22, entitled General knowledge of man:
     'The first thing which presents itself to man when he looks at himself is his body ... to abysses.'2
     This is as far as Mr Pascal goes.3
     What Mr. Pascal says about the double infinity, which surrounds us in the increasingly large and the vanishingly small, when in his Pensées [Gr p554] (n.22) he talks about the general knowledge of man, is only an entrance into my system. What would he not have said with that power of eloquence he possessed if he had gone further, if he had known that all matter is organic everywhere, and that, however small a portion one takes, it contains representatively, by virtue of the actual decreasing to infinity that it encloses, the actual increasing to infinity which is outside it in the universe. That is, each small portion contains, in an infinity of ways, a living mirror expressing the whole infinite universe that exists with it; so that a sufficiently great mind, armed with a sufficiently penetrating view, could see here everything everywhere. But there is much more: it could even read the whole of the past there, and even the whole infinitely infinite future, since each moment contains an infinity of things, each of which envelops an infinity, and since there is an infinity of moments in each hour or other part of time, and an infinity of hours, of years, of centuries and eons in the whole of future eternity. What an infinity of infinities infinitely replicated, what a world, what a universe perceptible in any assignable corpuscle. But all these wonders are surpassed by the envelopment of what is infinitely above all greatnesses in what is infinitely below all smallnesses. That is, our pre-established harmony, which has only recently appeared on the scene, and which yields even more than absolutely universal infinity, concentrated in the more than infinitely small and absolutely singular, by placing, virtually, the whole series of the universe in each real point which makes a Monad or substantial unity, of which I am one. That is, in each substance truly one, unique, primitive subject of life and action, always endowed with perception and with appetition, always containing in what it is the tendency to what it will be,4 to represent everything else which will be.5 The basic almost-nothing, in coming up from nothing to things, since it is the simplest of them, is also as it were the highest almost-everything [Gr p555] in descending from the multitude of things towards nothing; and yet it is the only thing that deserves to be called a being, a substance after God, because a multitude is only a mass of several substances, and not a being, but beings. It is this simple and primitive subject of tendencies and actions, this interior source of its own changes, which is therefore the only way of true imperishable being, since it is indissoluble and without parts, always subsisting and which will never perish, any more than will God and the universe, which it must always represent and in whole.6 And if this Monad is a mind, that is, a soul capable of reflection and knowledge,7 it will be at the same time infinitely less than a God and incomparably more than the rest of the universe of creatures; it senses everything confusedly, unlike God who knows everything distinctly; it knows something distinctly, unlike the whole of matter which knows and senses nothing of the whole. It will be a diminutive divinity and a universe of matter eminently; God in ectype and this universe in prototype, as the intelligible is always anterior to the sensible in the ideas of the primitive intelligence, the source of things; it will imitate God and be imitated by the universe in relation to its distinct thoughts. It will be subject to God in everything, and dominator of all creatures to the extent that it is an imitator of God.





NOTES:

1. Literally 'in the increasing and the diminishing' [en augmentant et en diminuant].
2. The full passage ('General knowledge of man') reads: 'The first thing which presents itself to man when he looks at himself is his body, that is, a certain portion of matter which is his own. But in order to understand what it is, it should be compared with everything there is above it, and everything there is below it, in order to recognize its proper limits.
     Let man therefore contemplate the whole of nature in her full and grand majesty, and turn his vision from the low objects which surround him. Let him gaze on that brilliant light, set like an eternal lamp to illuminate the universe. Let the earth appear to him a point in comparison with the vast circle described by the sun. And let him wonder at the fact that this vast circle is itself but a very fine point in comparison with that described by the stars in their revolution round the firmament. But if our view be arrested there, let our imagination pass beyond. It will sooner exhaust the power of conception than nature that of supplying material for conception. The whole visible world is only an imperceptible atom in the ample bosom of nature. No idea approaches the extent of nature's spaces. We may enlarge our conceptions; we only produce atoms in comparison with the reality of things. It is an infinite sphere, the centre of which is everywhere, the circumference nowhere. In short, it is one of the greatest sensible marks of the almighty power of God that our imagination loses itself in that thought.
     Returning to himself, let man consider what he is in comparison with all existence. Let him regard himself as lost in this remote corner of nature; and from the little cell in which he finds himself lodged, that is, this visible world, let him learn to estimate the true value of the earth, kingdoms, cities, and himself.
     What is a man in the infinite? Who can comprehend it? But to show him another prodigy equally astonishing, let him examine the most delicate things he knows. Let a mite be given him, with its minute body and parts incomparably more minute, limbs with their joints, veins in the limbs, blood in the veins, humours in the blood, drops in the humours, vapours in the drops. Dividing these last things again, let him exhaust his powers and his conceptions, and let the last object at which he can arrive be now that of our discourse. Perhaps he will think that here is the smallest point in nature. I will let him see therein a new abyss. I will paint for him not only the visible universe, but also everything he is capable of conceiving of nature's immensity in the womb of this imperceptible atom. Let him see therein an infinity of worlds, each of which has its firmament, its planets, its earth, in the same proportion as in the visible world; in this earth of animals, and ultimately of mites, in which he will find again all that the first had, finding still in these others the same thing without end and without cessation. Let him lose himself in wonders as amazing in their littleness as the others in their vastness. For who will not be astounded at the fact that our body, which a little while ago was imperceptible in the universe, itself imperceptible in the bosom of the whole, is now a colossus, a world, or rather a whole, in respect of the final smallness which we cannot reach? He who regards himself in this light will be afraid of himself, and observing himself suspended in the mass given him by nature between those two abysses of the Infinite and Nothing, of which he is equally removed, will tremble at the sight of these marvels; and I think that, as his curiosity changes into admiration, he will be more disposed to contemplate them in silence than to examine them with presumption.
     For, in fact, what is man in nature? A nothing in comparison with the infinite, an All in comparison with the nothing, a mean between nothing and everything. Since he is infinitely removed from the two extremes, and his being is no less distant from the nothing from which he was drawn than from the infinite in which he is swallowed up.
     In the order of intelligible things his intelligence holds the same rank as does his body in the expanse of nature, and all it can do is perceive the appearance of the middle of things, in an eternal despair of knowing either their beginning or their end. All things proceed from the nothing, and are led towards the infinite. Who can follow these marvellous processes? The Author of these wonders understands them. None other can do so.
     This state which holds the mean between two extremes is present in all our potencies. Our senses perceive no extreme. Too much sound deafens us; too much light dazzles us; too great a distance or proximity hinders our view. Too great a length and too much brevity obscures a discourse; too much pleasure disagrees with us; too many consonances are displeasing. We feel neither extreme heat nor extreme cold. Excessive qualities are prejudicial to us and not perceptible by the senses. We no longer feel them, instead we suffer them. Extreme youth and extreme old age hinder the mind; too much and too little food disturb its actions; too much and too little education is stultifying. Extreme things are for us, as if they were not, and we are not within their notice. They escape us, or we them.
     This is our true state; this is what encloses our knowledge within certain limits we cannot pass through, incapable of knowing everything and of being ignorant of absolutely everything. We sail upon a vast sphere, always uncertain and drifting between ignorance and knowledge, and if we think we are going further, our object becomes loose and escapes our clutches; it slips away and flees in an eternal flight. Nothing can stop it. This is our natural condition and yet most contrary to our inclination. We burn with desire to go deeper into everything, and to build a tower reaching to the Infinite. But our whole groundwork cracks, and the earth opens to abysses.' Blaise Pascal, Pensées de M. Pascal sur la religion et sur quelques autres sujets (Paris, 1670), XXII, pp169-75.
3. Leibniz wrote and then deleted the following here: 'What he has just said on the subject of the double infinity is only an entrance into my system. What would he not have said with that power of eloquence he possessed if he had gone further, if he had known that all matter is organic, and that the least portion contains, through the actual infinity of its parts in an infinity of ways, a living mirror expressing the whole infinite universe, so that one could read in it (if one had sufficiently keen sight and mind) not only the present stretched out to infinity, but also the past, and the whole infinitely infinite future, since it is infinite in every moment, and there is an infinity of moments in each part of time, and more infinity than one could express in the whole of future eternity. But the pre-established harmony even surpasses all that, and yields this same universal infinity in each basic almost-nothing (which is at the same time the highest almost-everything and yet the only thing which deserves to be called a substance after God). That is, in each real point, which makes a Monad, of which I am one, and ***, and will not perish any more than God and the universe, which it must always represent, being at the same time less than a God and more than a universe of matter: a sort of diminutive God, and a sort of universe eminently, and as it were a prototype with the intelligible worlds being in ectype the sources of the sensible world in the ideas of God.'
4. Here Leibniz wrote and then deleted: 'and consequently always subsistent'.
5. Here Leibniz wrote and then deleted the following: 'True being alone, the only way of true being, always subsisting, and which will not perish any more than God and the universe, which it must always represent and in whole: being at the same time less than a God and more than a material universe; it is aware of everything confusedly, unlike God who knows everything distinctly; it knows something distinctly, unlike the material universe which senses and knows nothing of the whole. A diminutive divinity, a material universe eminently. God in ectype and this universe in prototype, since the intelligible is the source of the sensible, with regard to the primitive intelligence, source of all things.'
6. Here Leibniz wrote and then deleted the following: ' ; being at the same time infinitely less than a God, and incomparably more than a universe of matter; sensing everything confusedly, unlike God who knows everything distinctly; knowing something distinctly, unlike all matter which senses and knows nothing of the whole. A diminutive divinity, a Universe of matter eminently; God in ectype and this same universe in prototype; imitating God and being imitated by the universe in relation to its distinct thoughts, similar to God through the distinct thoughts, similar to matter through the confused ones; the intelligible always being anterior to the sensible in the ideas of the original intelligence source of things.'
7. Here Leibniz wrote and then deleted 'it will imitate God'.


© Lloyd Strickland 2003