Source:

Manuscript held by G. W. Leibniz Bibliothek, Hanover
Shelfmark LH 1, 20 Bl. 212-213


Date: c. 1696

Note - The italicised text within + ... + is Leibniz's own comments on the quoted material.

Translated from the French



View this translation in PDF format (117k)

Back to home page


Search texts by keyword(s):

(For search strings, just type the words; don't use quotation marks)

LEIBNIZ: DOUBLE INFINITY IN PASCAL AND MONAD


[LH 1, 20, Bl. 212r]

     The actual infinity in material things, both in the increasingly large and 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 yielded to his view. Here is one of the passages which show it, at number 22, entitled General knowledge of man:
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 to understand what it is, it should be compared with everything above it and everything below it, in order to recognize its proper limits. So let him not stick to looking only at the objects that surround him. Let him contemplate the whole of nature in her full and grand majesty. Let him gaze on that brilliant light, set like an eternal lamp to illuminate the universe. Let the earth appear to him like a point in comparison with the vast circle described by the sun (+ with the orbit of this star +). And let him wonder at the fact that this vast circle is itself but a very fine point in comparison with that encompassed by the stars which revolve in the firmament. But if our sight settles on that, let our imagination pass beyond. It will weary of conceiving sooner than nature of furnishing. Everything we see of the world is only an imperceptible stroke in the ample bosom of nature. No idea approaches the extent of her spaces. We may enlarge our conceptions; we produce only atoms in comparison with the reality of things. It is an infinite sphere whose centre is everywhere, the circumference nowhere. In short, it is one of the greatest sensible marks of the omnipotence of God that our imagination loses itself in that thought. Returning (+ now to himself +), let man consider what he is in comparison with what exists. Let him regard himself as lost in this remote part 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 marvel just as astonishing, let him investigate the most delicate things he knows. Let him be offered a mite, in the smallness of its body, of parts incomparably smaller still, of limbs with their joints, of veins in these limbs, of blood in these veins, of humours in this blood, of drops in these humours, of vapours in these 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 extreme of nature's smallness. I want to show him a new abyss therein. I want to 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 the visible world; in this earth of animals, and ultimately of mites, in which he [LH 1, 20, Bl. 212v] will find again that which the first ones have offered; finding still in the others the same thing (+ or analogous things +) without end and without pause, let him lose himself in these wonders as amazing in their smallness as others in their vastness. For who will not wonder at the fact that our body, which was almost imperceptible in the universe, itself imperceptible in the bosom of the whole, is now a colossus, a world, or rather a whole, with regard to the ultimate smallness at which we cannot arrive?
     He who considers himself in this way will be afraid to see himself in the bodily mass nature has given him suspended, as it were, between those two abysses of the infinite and nothingness, from which he is equally distant. He 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, ultimately, what is man in nature? A nothingness in comparison with the infinite, an all in comparison with nothingness, a middle point between nothing and everything. He is infinitely [distant] from the two extremes, and his being is no less distant from the nothingness 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 neither their beginning nor their end. All things proceed from nothingness, and are led towards the infinite. Who can follow these marvellous proceedings? The author of these wonders understands them. No other can do so. This state which occupies the middle ground between two extremes is present in all our powers. Our senses perceive nothing of the extreme. Too much sound deafens us; too much light dazzles us; too great a distance or proximity hinders our view; too much length and too much brevity obscures a discourse; too much pleasure harms us; too many consonances displease us. We feel neither extreme heat nor extreme cold. Excessive qualities are antagonistic to us and cannot be sensed. We no longer feel them, instead we suffer them. Excessive youth and excessive 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 do not exist, and in respect to them we do not. They escape us, or we them. This is our true state; this is what encloses our knowledge within certain limits we cannot pass through (+ here below +), incapable of knowing everything and of being absolutely ignorant of everything. We are in a vast medium, 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. This is our natural condition and yet the most contrary to our inclination. We burn with desire to go deeper into everything, and to build a tower which reaches up to the infinite. But our whole edifice cracks, and the earth opens up to abysses.2

     Up to here is Mr Pascal.3

[LH 1, 20, Bl. 213r]

     What Mr. Pascal says about the double infinity, which surrounds us in the increasingly large and the vanishingly small, when in his Pensées (n.22) he talks about the general knowledge of man, is only an introduction to my system. What wouldn’t he have said with that power of eloquence he possessed if he had gone further, if he had known that all matter is organic throughout, and that, however small a portion one takes, it contains representatively, by virtue of the actual diminution to infinity it contains, the actual increasing to infinity that is in the universe outside it. 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 sufficiently penetrating sight, could see here everything which is 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 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 eclipsed by the envelopment of what is infinitely above all hugeness in what is infinitely below all smallness. 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 the whole sequence of the universe virtually 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 appetition, always containing in what it is the tendency to what it will be,4 to represent everything else which will be.5 The primary almost-nothingness, in rising up from nothing to things, since it is the simplest of them, as it is also the highest almost-everything 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 manner of true imperishable being, since it is indissoluble and without parts, always subsisting [LH 1, 20, Bl. 213v] and which will never perish, any more than God and the universe, which it must always represent and in full.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; sensing everything confusedly, whereas God knows everything distinctly; knowing something distinctly, whereas all matter senses and knows nothing of the whole. It will be a diminutive divinity and a universe of matter eminently; God in ectype and this universe in prototype, the intelligible always being anterior to the sensible in the ideas of the primitive intelligence, the source of things; imitating God and being imitated by the universe in relation to its distinct thoughts. Subject to God in everything, and dominator of creatures to the extent it is an imitator of God.





NOTES:

1. Literally 'in the increasing and the diminishing' [en augmentant et en diminuant].
2. Leibniz’s source for this passage is the so-called Port-Royal edition of Pascal's Pensées, namely Blaise Pascal, Pensées de M. Pascal sur la religion et sur quelques autres sujets (Paris, 1670), XXII, pp169-75. Note that this edition is notorious for its editorial interventions, with the editors simply removing some material and sometimes modifying what remained, including changing the language and even adding sentences not composed by Pascal. Later editions were more faithful to the source material; the passage Leibniz quotes (mostly faithfully) is longer in these later editions and better represents what Pascal wrote.
3. Pascal. | What he has just said about the double infinity is only an introduction to my system. What wouldn't he 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, a living mirror expressing the whole infinite universe in an infinity of ways, so that one could read in it (if one had sufficiently keen sight and mind) not only the present extended to infinity, but also the past, and the whole infinitely infinite future, since it is infinite at each moment and there is an infinity of moments in each part of time, and more infinity than could be expressed in the whole of future eternity. But the pre-established harmony even surpasses all that, and yields this same universal infinity in each primary almost-nothingness (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 which 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. | deleted. Alongside this deleted passage, which was squeezed into all four margins of the page, Leibniz wrote (but did not delete) "What I added in the margin is better written on another page."
4. be, | and consequently always subsistent. | deleted.
5. be. | 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; perceiving everything confusedly, whereas God knows everything distinctly; knowing something distinctly, whereas the material universe 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. | deleted.
6. full | ; being at the same time infinitely less than a God and incomparably more than a universe of matter; sensing everything confusedly, whereas God knows everything distinctly; knowing something distinctly, whereas all matter senses and knows nothing of the whole. A diminutive divinity, a universe of matter eminently; God in ectype and this very universe in prototype; imitating God and being imitated by the universe in relation to its distinct thoughts; similar to God through distinct thoughts, similar to matter through the confused ones; the intelligible always being anterior to the sensible in the ideas of the primitive intelligence, the source of things. | deleted.
7. knowledge, | it will imitate God. | deleted.


© Lloyd Strickland 2019