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To first part:Monadology - part A.


41. Whence it follows that God is absolutely perfect; for perfection is nothing but amount of positive reality, in the strict sense, leaving out of account the limits or bounds in things which are limited. And where there are no bounds, that is to say in God, perfection is absolutely infinite. (Theod. 22, Pref. [E. 469 a; G. vi. 27].)

Here we have this Scholastic perfection I spoke of. I do not understand much of (41), and one my puzzlements with perfections, alluded to in the last remark, is that I find absent toothaches (and many other evils) much more perfect that present toothaches. Voltaire was similarly puzzled, and based his novel "Candide" on it, which lampoons Leibniz in the shape of Dr. Pangloss ["Dr. Allwords"], who tries to defend a Leibnizian notion that we all live in the most perfect of all possible worlds in the face of much trouble, pain and misery, that in the end also mean the death of Pangloss.

42. It follows also that created beings derive their perfections from the influence of God, but that their imperfections come from their own nature, which is incapable of being without limits. For it is in this that they differ from God. An instance of this original imperfection of created beings may be seen in the natural inertia of bodies. (Theod. 20, 27-30, 153, 167, 377 sqq.)

Why this would follow as a matter of logic escapes me, but it is quite obvious to me why "created beings" would want to believe that their good qualities are reflections of the good qualities of their powerful and benevolent maker: it is nice to attribute divine qualities to oneself, especially if one has no pleasant self-image to start with, and nice to portray oneself as made in the image of the maker of all.

The argument that human "imperfections come from their own nature" is a version of the argument that really and truly evil either does not exist, or else does exist because God, in his great goodness, saw that its existence made the world a better place than its non-existence.

In my eyes, such arguments, well-intended though they may be, seem to be merely ways not to face unpleasant facts, or to make them seem more pleasant than they are: "OK - six million Jews were gassed in Auschwitz, but this happened only because God in his goodness saw that it was better that it happened than that it did not happen."

There simply is a very fundamental logical problem for everybody who wishes to maintain that the world was created by an all-powerful benevolent God and the palpable fact that very much happens in the world that is quite evil, both according to the followers of such a God, in terms of the teachings they attribute to this God, and to others, who have other Gods or no Gods.

Also, while I have no problems with someone who claims that there is evil and misery in the world, and he does not really understand why this must be so, I do have problems with someone who claims that there is no evil and no misery in the world, and that I could see the same if my brain or moral character were better: I think it is far more probable such a person is a liar and a hypocrite than that such a person has true insight. And Voltaire reasoned likewise, although I am personally willing to believe that Leibniz was neither a liar nor a hypocrite, and sincerely meant well - and Leibniz clearly was an extra-ordinary man.

43. It is farther true that in God there is not only the source of existences but also that of essences, in so far as they are real, that is to say, the source of what is real in the possible. For the understanding of God is the region of eternal truths or of the ideas on which they depend, and without Him there would be nothing real in the possibilities of things, and not only would there be nothing in existence, but nothing would even be possible. (Theod. 20.)

Behind this point lies some rather complicated modal logic we need not consider (since it probably was not completely clear to Leibniz, to start with). The point to notice is that "the source of what is real i[s] the possible", for this contains an important insight of Leibniz, that may be stated without any reference to divinities:

What is real is not merely what happens to exist (or have existed), but includes what is possible and what may and might have been with what happens to exist, for to exist is to exclude certain things as impossible, namely what cannot be consistently combined with it, and to include certain things as possible, namely what can be consistently combined with it. And these possible combinations, whether realised or not, are as much part of reality as those combinations that are real, and the possibilities that inhere in things are fundamental to our understanding of what may arise from what is.

It should be noted that this is an important insight (whatever its ultimate status), for human beings normally reason in terms of both possibilities and realities, and not merely in terms of the latter: nearly all one's acts and choices are based on one's beliefs about presently unrealised possibilities included in what one believes to be real, that one desires to see realised or to remain unrealised.

44. For if there is a reality in essences or possibilities, or rather in eternal truths, this reality must needs be founded in something existing and actual, and consequently in the existence of the necessary Being, in whom essence involves existence, or in whom to be possible is to be actual. (Theod. 184-189, 335.)

One may, of course, agree with this, but with the understanding that the "necessary Being" is Nature rather than God. But if one does so, the remark under the last point remains standing: in any case there really are unrealised possibilities and realised possibilities in reality, and the former are as real and important as the latter.

45. Thus God alone (or the necessary Being) has this prerogative that He must necessarily exist, if He is possible. And as nothing can interfere with the possibility of that which involves no limits, no negation and consequently no contradiction, this [His possibility] is sufficient of itself to make known the existence of God a priori. We have thus proved it, through the reality of eternal truths. But a little while ago we proved it also a posteriori, since there exist contingent beings, which can have their final or sufficient reason only in the necessary Being, which has the reason of its existence in itself.

This again consists of arguments for God's existence I mostly commented on before. The first statement is a version of what Leibniz thought of as his own argument for God's existence, roughly on the following line: God is by definition such that He must exist if He may exist; God may exist, ergo God must exist.

Apart from modal unclarities, there is no reason to accept such a definition of God, and reason not to, for such a definition that declares something real simply because it may be real seems - "it exists because it may exist!" - confuses what is real and what may be thought about what may be real.

Also, in general, the step from 'I can think of it' to 'so it exists' seems to validate at best the existence of a thought but not the existence of what the thought is about, and seems to confuse the former and the latter. (And those who - with Anselm and Descartes - like this type of argument for God should spend some thought on a unicorn that I came across in my thoughts, that claimed all and only unicorns exist because they are thought about. This unicorn I was thinking about also had a mate, who claimed that female unicorns exist because they are not thought about.)

46. We must not, however, imagine, as some do, that eternal truths, being dependent on God, are arbitrary and depend on His will, as Descartes, and afterwards M. Poiret, appear to have held. That is true only of contingent truths, of which the principle is fitness [convenance] or choice of the best, whereas necessary truths depend solely on His understanding and are its inner object. (Theod. 180-184, 185, 335, 351, 380.)

This addresses another problem that was already discussed by the Greeks and Romans. As far as Leibniz is concerned, God's power extends over contingent truths, but He cannot do what is logically impossible. The Greeks and Romans discussed the problem in a form like: If your God is all-powerful, why can He not make 2 equal to 3 or create a married spinster? It seems Leibniz held that God must think by logical principles, and that Leibniz held God always chooses to create the best possible.

47. Thus God alone is the primary unity or original simple substance, of which all created or derivative Monads are products and have their birth, so to speak, through continual fulgurations of the Divinity from moment to moment, limited by the receptivity of the created being, of whose essence it is to have limits. (Theod. 382-391, 398, 395.)

Of course, something similar may be said about Nature, or the Big Bang, especially if the reader knows that a "fulguration", according to the Shorter Oxford English Dictionary, is "The action of lightening or flashing like lightning."

48. In God there is Power, which is the source of all, also Knowledge, whose content is the variety of the ideas, and finally Will, which makes changes or products according to the principle of the best. (Theod. 7, 149, 150.) These characteristics correspond to what in the created Monads forms the ground or basis, to the faculty of Perception and to the faculty of Appetition. But in God these attributes are absolutely infinite or perfect; and in the created Monads or the Entelechies (or perfectihabiae, as Hermolaus Barbarus translated the word) there are only imitations of these attributes, according to the degree of perfection of the Monad. (Theod. 87.)

So, according to Leibniz, all of reality consists of physical bodies that are kept together and coordinated in their acts by some Monad, which is always a perceiving entity, and a desiring entity in the case of men, animals and the Supreme Monad, who made all.

It should be noticed that two of Leibniz's reasons to introduce Monads are to account for the unity, coherence, properties and acts of things, and to account for perception and desire, which Leibniz believed could not be explained in physical terms (see (17) and the remarks under it).

49. A created thing is said to act outwardly in so far as it has perfection, and to suffer [or be passive, patir] in relation to another, in so far as it is imperfect. Thus activity [action] is attributed to a Monad, in so far as it has distinct perceptions, and passivity [passion] in so far as its perceptions are confused. (Theod. 32, 66, 386.)

Here we have two applications of the concept of perfection: the less perfect something is, the more it depends on other things, and the less perfect something is, the less it can understand. Also, everything acts or is acted upon, and the less perfect a thing is, the more it is acted upon (while God alone only acts and is not acted upon).

50. And one created thing is more perfect than another, in this, that there is found in the more perfect that which serves to explain a priori what takes place in the less perfect, and it is on this account that the former is said to act upon the latter.

This extends the previous point, and may be taken as Leibniz's metaphysical explanation of knowledge: The more complicated, more perfect monads may understand the less perfect monads in a way similar to God's knowing all there is to know, only not with the same degree of perfection or accuracy. (There is a real problem here, which is this: How can an infinitesimally small part of the known universe, such as a man or a group of men, come to really know the (nearly) infinitally great universe they are part of?)

51. But in simple substances the influence of one Monad upon another is only ideal, and it can have its effect only through the mediation of God, in so far as in the ideas of God any Monad rightly claims that God, in regulating the others from the beginning of things, should have regard to it. For since one created Monad cannot have any physical influence upon the inner being of another, it is only by this means that the one can be dependent upon the other. (Theod. 9, 54, 65, 66, 201. Abrege, Object. 3.)

Here the underlying point is Leibniz's earlier statement that Monads have no windows. As far as I can see, what Leibniz meant was that Monads, being mental or ideal entities, have no intercourse with the physical world, nor indeed with each other, except through special intervention of the Supreme Monad that created all.

52. Accordingly, among created things, activities and passivities are mutual. For God, comparing two simple substances, finds in each reasons which oblige Him to adapt the other to it, and consequently what is active in certain respects is passive from another point of view; active in so far as what we distinctly know in it serves to explain [rendre raison de] what takes place in another, and passive in so far as the explanation [raison] of what takes place in it is to be found in that which is distinctly known in another. (Theod. 66.)

Apart from Leibniz's own ideas about how to explain perceptions and feelings, this seems related to the Scholastic notion that only God is a pure act and purely ideal, and all other things consist of various mixtures of the divine and of coarse physical matter.

53. Now, as in the Ideas of God there is an infinite number of possible universes, and as only one of them can be actual, there must be a sufficient reason for the choice of God, which leads Him to decide upon one rather than another. (Theod. 8, 10, 44, 173, 196 sqq., 225, 414-416.)

Here we arrive at another of Leibniz's philosophical innovations: The notion of a possible world - indeed, as he says, of infinities of possible worlds. Apart from God, one quite easy interpretation of such possible worlds is as arising from all those things one may do, of which one does only a small fraction, but could have done some different fraction.

One problem that is not addressed here is why God was satisfied with just one real possible world: Why was it not better for God to create myriads of equally real possible worlds? (Indeed, such a conception - to the effect that what may happen does happen, if not in this world then in another equally real possible world - is at the basis of one of the interpretations of Quantum Mechanics, due to Everett, that often is called 'the Many Worlds interpretation', for this reason.)

54. And this reason can be found only in the fitness [convenance], or in the degrees of perfection, that these worlds possess, since each possible thing has the right to aspire to existence in proportion to the amount of perfection it contains in germ. (Theod. 74, 167, 350, 201, 130, 352, 345 sqq., 354.)

This reiterates what was said before, in (48), that God, who is benevolent and all-powerful, though He also cannot do the logically impossible, always chooses to make real what is best. In view of the fact that much of what is real is quite painful to many, this is bound to lead to problems. For example, agreeing for the moment with Leibniz that God, in his goodness, saw that the holocaust upon the Jews was necessary, then why, in his goodness, was it also necessary to make what happened in Auschwitz so painful?

Put otherwise, on a less forbidding historical level: Accepting that all human beings must die seems easy, whatever the reasons or causes - but if there is an all-powerful benevolent God, then why must some quite harmless or rather good human beings die such miserable, cruel and painful deaths by some incurable disease?

The reader should note what my problem is: Supposing God saw correctly that the sum of good in the world is greater if this baby dies, why, if it had to die, did it have to die so awfully, for example from spina biffida - which the Good Lord might have prevented by supplying its mother with a little folic acid during her pregnancy?

And my problem is especially with the arrogance of priestly divine mouthpieces: How can they know what they claim to know? And if they cannot know what they claim to know, what right do they have to claim to know or believe or propound such statements that these babies or those Jews had to die so cruelly and miserably for the good of the world? (The reader may care to know that I am a philosophical unbeliever who occasionally listens to religious programs on the BBC, largely to remain amazed about what religious people dare to claim and seek to impose on others. And the religious reader should consider that by his or her own religious lights his or her all-powerful benevolent God has arranged a world in which all the many millions of believers in other faiths are deluded, immoral, and hellward bound, normally, and millions are and have been killed by religious conflicts.)

55. Thus the actual existence of the best that wisdom makes known to God is due to this, that His goodness makes Him choose it, and His power makes Him produce it. (Theod. 8, 78, 80, 84, 119, 204, 206, 208. Abrege, Object. 1 and 8.)

Now let us for a moment do away with God, His goodness, His wisdom, His power, and His choices. Suppose there is only a natural world, that somehow came into being, nobody really knows how or why, in which people are born and must die. There is then, apart from other wild hypotheses, nothing to fear after death, and also no rewards after death; and there is no Almighty Father in the sky to look up to, to damn, or to pray to.

Indeed, one of my own problems about such an Almighty Father in the sky is that He, if He exists, has left behind such questionable evidence of his existence and properties, that even great geniuses like Leibniz cannot understand Him, and certainly cannot convince most other people that they did if they did understand Him.

For somebody like me, indeed, this is a fundamental argument for atheism: It seems most of the best human minds have tried to frame some proof that there is a God, but none of these proofs is valid, while the different concepts of God different people reach are different and often contradictory. So if there is a God, He (She, It) is beyond human understanding, and what is beyond human understanding is beyond human dogmatising, postulating, preaching or teaching: Of what one cannot understand, one can only speak nonsense.


Incidentally: There are some proofs of God that are logically valid - but they all have two shortcomings. First, they depend on premisses that often are not credible or seem arbitrary. Second, what these valid proofs prove, from assumptions that are not clearly true, that may be propositions like "there is a first cause", do not at all prove that any god as conceived in any theology or religion exists.


56. Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.)

Here we return from God to more mundane things, at least as conceived by Leibniz: Each Monad is (as) a perpetual living mirror of the universe. It should be noticed that the analogy or metaphor of the mirror for perception and thought has been often used, but Leibniz meant it in a rather wider sense than is normal: He believed each Monad somehow mirrors all other Monads, and thus the whole universe, although this mirroring will be quite confused or indistinct, especially if the Monad's position in the schema of things is low (and therefore the Monad cannot properly think). Also, insofar as physical mirrors reflect rather than project their environments - see under (11) - Leibniz term 'mirror' is metaphorical and at least a little misleading.

It should also be remarked that Leibniz believed that each Monad is infinite, even if infinitely small, so it may represent all, presumably rather like any small segment of the real numbers is equinumerous to all real numbers (and thus each non-empty interval of real numbers may be taken as containing a segment that copies all the real numbers).

57. And as the same town, looked at from various sides, appears quite different and becomes as it were numerous in aspects [perspectivement]; even so, as a result of the infinite number of simple substances, it is as if there were so many different universes, which, nevertheless are nothing but aspects [perspectives] of a single universe, according to the special point of view of each Monad. (Theod. 147.)

This perspectivism (as it is sometimes called) arises here from Leibniz's idealism, as an explanation of how appearance and reality (as construed in Leibniz's metaphysics) can come to be and differ so much. And the explanation (or helpful analogy) is that one and the same reality may have a quite different appearance for different things.

Another way to make the same or a similar point is simply to think of the different ideas and values and different points of view different people have about - what we will assume is - the one world they all live in. Each human being carries his or her own version and appreciation of the universe around, and none of these versions or appreciations is directly accessible to any other human being: they all can share their ideas and values only by representing these by signs, symbols and gestures that can be experienced and interpreted by all, or some.

We shall come to consider the Leibnizian hypothesis of the Pre-Established Harmony below, but may here point out that in common sense reality a hypothesis like it is accepted, namely to the effect that

(1) all human beings have similar experiences in similar circumstances (and thus each human being may know what any other would or does feel when (mal-)treated in many ways);
(2) the experience of no human being is directly accessible to any other human being;
(3) all human beings, if sane, can communicate some of their ideas and feelings to other human beings, thereby making their private experience indirectly accessible to others, and
(4) all human beings live in one and the same world, of which they each have their own version and appreciation.

These are rather fundamental metaphysical assumptions, however commonsensical they seem, as is shown by Leibniz' need to appeal to God's Pre-Established Harmony of different humans individual ideas to account for it within his idealist philosophy.

58. And by this means there is obtained as great variety as possible, along with the greatest possible order; that is to say, it is the way to get as much perfection as possible. (Theod. 120, 124, 241 sqq., 214, 243, 275.)

Precisely how this relates to the previous point is not clear to me, but it is obvious that here we have another application of the concept of perfection.

For readers unfamiliar with philosophy, it should perhaps be added, in fairness to Leibniz, that such arguments involving perfections are quite common in Aristotle and the Scholastic philosophers, and that the idea of perfection expressed something like the following assumption: each and every thing has an end, which is to be that thing, and to become whatever that thing's end is. Thus the end of an acorn is to be an acorn and become an oak, and similarly for all other things: they are, change and develop according to their ends.

And for readers unfamiliar with physics, it should then be added that, while it seems entirely natural for human beings to speak of themselves and other living things as acting for ends, there are no human ends in physics, at least outside brains (i.e. unreal situations that are imagined by physical things - such as oaks and rocks - that serve as the end the things who incorporate them try to bring about). (This is one of the problems addressed under (17), that may be summarised as: So far there is no reduction of the mental to the physical, and if the brain is the organ that makes us think and feel, than so far it is not known how the brain does this.)

59. Besides, no hypothesis but this (which I venture to call proved) fittingly exalts the greatness of God; and this Monsieur Bayle recognized when, in his Dictionary (article Rorarius), he raised objections to it, in which indeed he was inclined to think that I was attributing too much to God - more than it is possible to attribute. But he was unable to give any reason which could show the impossibility of this universal harmony, according to which every substance exactly expresses all others through the relations it has with them.

We are talking of the Pre-Established Harmony, which Leibniz started talking about in (57), without mentioning the name. I did in my comment to (57). One reason for Leibniz to introduce his hypothesis was to explain how Monads could communicate in an orderly way and reflect (on) the same reality: Because God has arranged it to be so once and forever that all Monads mirror all things in their own, possibly confused and indistinct, ways. This hypothesis was also directed against the so-called Occasionalists, who held that God continuously interferes in the world, and against people who maintained there is no real world. I have given my own version under (57), in the form of four widely accepted hypotheses, that may all be false.

60. Further, in what I have just said there may be seen the reasons a priori why things could not be otherwise than they are. For God in regulating the whole has had regard to each part, and in particular to each Monad, whose nature being to represent, nothing can confine it to the representing of only one part of things; though it is true that this representation is merely confused as regards the variety of particular things [le detail] in the whole universe, and can be distinct only as regards a small part of things, namely, those which are either nearest or greatest in relation to each of the Monads; otherwise each Monad would be a deity. It is not as regards their object, but as regards the different ways in which they have knowledge of their object, that the Monads are limited. In a confused way they all strive after [vont a] the infinite, the whole; but they are limited and differentiated through the degrees of their distinct perceptions.

I suppose "the reasons a priori why things could not be otherwise than they are" is Leibniz's contention that God is a necessary being on whom all beings fully depend, and who always chooses the best possible.

Another thing to notice is that the nature of each Monad is to represent, i.e. to assign meanings, which is one of the problematic things we found under (17).

And I suppose "the infinite" all Monads strive after in their own ways is God.

61. And compounds are in this respect analogous with [symbolisent avec] simple substances. For all is a plenum (and thus all matter is connected together) and in the plenum every motion has an effect upon distant bodies in proportion to their distance, so that each body not only is affected by those which are in contact with it and in some way feels the effect of everything that happens to them, but also is mediately affected by bodies adjoining those with which it itself is in immediate contact. Wherefore it follows that this inter-communication of things extends to any distance, however great. And consequently every body feels the effect of all that takes place in the universe, so that he who sees all might read in each what is happening everywhere, and even what has happened or shall happen, observing in the present that which is far off as well in time as in place: sympnoia panta, as Hippocrates said. But a soul can read in itself only that which is there represented distinctly; it cannot all at once unroll everything that is enfolded in it, for its complexity is infinite.

It is a common assumption that things have effects upon distant bodies in proportion to their distance, in general in the sense that the greater the distance, then - ceteris paribus - the smaller the effect. Another common assumption is that effects take time to move through space from one thing to another. Taken together these assumptions entail problems for the notion that every Monad mirrors all of the universe, even if every Monad is infinite, since it may take a long time for effects of things that did happen to propagate through space and arrive at each and every Monad.

A problem I have with Leibniz's last claim is why an infinite Monad could not represent to itself its own infinity - after all, it is the mark of the infinite to have proper subsets as large as itself.

62. Thus, although each created Monad represents the whole universe, it represents more distinctly the body which specially pertains to it, and of which it is the entelechy; and as this body expresses the whole universe through the connexion of all matter in the plenum, the soul also represents the whole universe in representing this body, which belongs to it in a special way. (Theod. 400.)

Leibniz mounted his assumption of Pre-Established Harmony to account, among other things, for the relation between the soul and the body. A problem I have with the present point is how a Monad knows what is "the body which specially pertains to it" i.e. of which it is the Monad. For if the Monad is mental, and the body is not, why couldn't a Monad's body be at a completely other place than the Monad itself? And if this couldn't happen, what is the link between a Monad and "the body which specially pertains to it"? (That a Monad thinks something like 'I feel my body and I am so and so' seems not sufficient, since some insane people have thought they are Napoleon. Also, insanity in this context is not a sufficient counter-argument, since it is at least logically possible that most souls are mistaken about their real status - as indeed all followers of all major religions must hold is true about all the followers of all other major religions than their own.)

63. The body belonging to a Monad (which is its entelechy or its soul) constitutes along with the entelechy what may be called a living being, and along with the soul what is called an animal. Now this body of living being or of an animal is always organic; for, as every Monad is, in its own way, a mirror of the universe, and as the universe is ruled according to a perfect order, there must also be order in that which represents it, i.e. in the perceptions of the soul, and consequently there must be order in the body, through which the universe is represented in the soul. (Theod. 403.)

If this answers my questions under the last point, the answer is in the end: the universe is represented in the soul "through" the body. But this hardly answers my questions.

64. Thus the organic body of each living being is a kind of divine machine or natural automaton, which infinitely surpasses all artificial automata. For a machine made by the skill of man is not a machine in each of its parts. For instance, the tooth of a brass wheel has parts or fragments which for us are not artificial products, and which do not have the special characteristics of the machine, for they give no indication of the use for which the wheel was intended. But the machines of nature, namely, living bodies, are still machines in their smallest parts ad infinitum. It is this that constitutes the difference between nature and art, that is to say, between the divine art and ours. (Theod. 134, 146, 194, 403.)

Here we have the interesting notion of a "divine machine or natural automaton, which infinitely surpasses all artificial automata". There is a discussion of the import of his point in the appendix on a logic of parts. (It seems that Leibniz here, if not already much earlier, has revised his concept of 'part', without saying so, and, so far as I can see, without being aware of his revision.)

For Leibniz, this is evidently related to minds being purposive (end directed), while in modern terms Leibniz might be taken as claiming (by implication) that if human beings are algorithmic automata, they are not finite machines, such as computers are, but - at least - infinite machines. And it should be added that the notion of an infinite algorithmic machine is not at all an incoherent notion, mathematically speaking, and that there is a good introduction to both subjects in Marvin Minsky's "Finite and infinite machines".

65. And the Author of nature has been able to employ this divine and infinitely wonderful power of art, because each portion of matter is not only infinitely divisible, as the ancients observed, but is also actually subdivided without end, each part into further parts, of which each has some motion of its own; otherwise it would be impossible for each portion of matter to express the whole universe. (Theod. Prelim., Disc. de la Conform. 70, and 195.)

Precisely what Leibniz may have had in mind here is unclear to me, but there is a suggestion that Leibniz conceived of an infinity like the real numbers, including infinitely divisible intervals, and not merely like the natural numbers.

Also, it seems Leibniz here asserts two different concepts of infinity: as what is divisible without end, and as what is produced when such a infinite division has been carried out. (These two concepts are sometimes distinguished as the syncategorematic or mathematical infinite, and as the categorematic or metaphysical infinite. It is interesting that in the context of mathematics Leibniz usually claimed that infinitesimals are merely a 'facon de parler'. See A.W. Moore 'The Infinite'. )

66. Whence it appears that in the smallest particle of matter there is a world of creatures, living beings, animals, entelechies, souls.

In other words, in the downward direction, towards the smaller and smaller, there would be an infinity of things, or perhaps rather infinity upon infinity of things. It seems to me not very plausible that, as one goes towards the smaller and smaller, on each smaller level there is the same kind and degree of complexity as on the higher levels, and likewise the inverse direction, towards the larger and larger, is not very plausible, if one believes the extent of the universe is finite.

Besides, as a child I speculated that the motes in sun-beams might be tiny universes in which there might be creatures like me speculating about the motes in sun-beams, and rejected it because of the infinite regress it entailed. In the end the reason was Ockhamistic: not to make more assumptions than is necessary to explain what one seeks to explain.

67. Each portion of matter may be conceived as like a garden full of plants and like a pond full of fishes. But each branch of every plant, each member of every animal, each drop of its liquid parts is also some such garden or pond.

This mirrors the idea of individual things being like a microcosms in the (macro)cosmos, where the microcosms mirrors or represents the macrocosms, and has at least in part the same laws and relations, besides being made from the same kinds of things (apart from size). This is a nice idea, but as my remarks to the previous points indicate, I don't think it is safely generalised from a few size-levels to all size-levels. Besides, things that represent normally are not of the same kind as what they represent (in that a thought is not normally the fact it represents nor a map the territory it is about nor a picture of flesh made of flesh).

One of the things that did influence Leibniz here is the discovery by Leeuwenhoeck of the microscope, and thereby the discovery of many kinds of small animals in drops of water, and flagellating entities in drops of sperm, that were until their discovery quite unsuspected.

68. And though the earth and the air which are between the plants of the garden, or the water which is between the fish of the pond, be neither plant nor fish; yet they also contain plants and fishes, but mostly so minute as to be imperceptible to us.

As pointed out in the previous remark, that this is so was in Leibniz's time a recent discovery.

69. Thus there is nothing fallow, nothing sterile, nothing dead in the universe, no chaos, no confusion save in appearance, somewhat as it might appear to be in a pond at a distance, in which one would see a confused movement and, as it were, a swarming of fish in the pond, without separately distinguishing the fish themselves. (Theod. Pref. [E. 475 b; 477 b; G. vi. 40, 44].)

That nothing is dead in the universe follows from the hypothesis that all things are what they are through a Monad that makes them the things they are, which is a perceiving and striving entity. The rest of what is said is a figurative restatement of earlier points.

70. Hence it appears that each living body has a dominant entelechy, which in an animal is the soul; but the members of this living body are full of other living beings, plants, animals, each of which has also its dominant entelechy or soul.

Indeed, and so on 'ad infinitum' as in Swift's poem:

'So, naturalists observe, a flea
Hath smaller fleas that on him prey
And these have smaller fleas to bite 'em
And so proceed ad infinitum"

As my remarks under (66) and (67) indicate, like Swift I am somewhat sceptical about this, 'ad infinitum'.

71. But it must not be imagined, as has been done by some who have misunderstood my thought, that each soul has a quantity or portion of matter belonging exclusively to itself or attached to it for ever, and that it consequently owns other inferior living beings, which are devoted for ever to its service. For all bodies are in a perpetual flux like rivers, and parts are entering into them and passing out of them continually.

This attempts to answer some of the problems I indicated under (62). Leibniz rejects that "each soul has a quantity or portion of matter belonging exclusively to itself or attached to it for ever", because "all bodies are in perpetual flux" (which is a notion he supported for independent reasons also). But this does not solve my problems: Should one suppose that each body somehow contains its - indivisible, infinitely small - dominating Monad that is its soul, like a volume may contain a much smaller particle, though the particle may be moving about in the volume? Again note that the basic problem is how what is supposed to be mental and non-physical is connected to the non-mental physical thing it displays the mentality of. And the problem with the notion that the body contains its soul like it contains a very small volume, is that it speaks of a soul as if it is a body.

72. Thus the soul changes its body only by degrees, little by little, so that it is never all at once deprived of all its organs; and there is often metamorphosis in animals, but never metempsychosis or transmigration of souls; nor are there souls entirely separate [from bodies] nor unembodied spirits [genies sans corps]. God alone is completely without body. (Theod. 90, 124.)

Of course, metamorphosis - as relates caterpillars to butterflies - is a pretty stunning event however one accounts for it, and indeed metamorphosis always involves the change of one thing into another, which does happen in time and gradually. But this does not settle at all that there could not be metempsychosis.

And indeed this would follow from theses like Leibniz states, viz. that no soul is ever entirely separate of a body (however it is attached to it) except God, who has no body at all.

But I have seen no argument from which either would follow, whereas there is a problem with God, thus conceived: How is it possible that God is wholly without body, if all other souls are never separate of the body they are the soul of? This is logically somewhat of a problem, if one disregards theology, especially since Leibniz's argument for the thesis that souls are never separate from the bodies they are the souls of seems to have been that souls are like relations or forms, and relations and forms cannot exist without bodies to relate or be the form of. If so, what exempts God from this? (The appendix on a simple logic of parts may shed some light on this, for it shows that one may do without God while maintaining a rather Leibnizian system of assumptions.)

73. It also follows from this that there never is absolute birth [generation] nor complete death, in the strict sense, consisting in the separation of the soul from the body. What we call births [generations] are developments and growths, while what we call deaths are envelopments and diminutions.

Suppose so. Then what do souls do after their bodies stopped being alive and were committed to the earth and the worms, or the flames of an incinerary? Put otherwise: what is the point of being the soul of a living entity on earth, if, after a very short time animating that body, after the body's death the soul keeps thinking and experiencing as before (being a Monad)? And why is life not a waste of time between two infinities? (I suppose Leibniz would have replied: 'Because God imposed a moral task on his creatures', which seems somewhat unfair on all those creatures that are to dumb to understand it - such as caterpillars eaten alive by the larvae of wasps, because God in his great goodness has arranged it that way - while it seems that human beings anyway are free to frame and strive for their own ends, which indeed is what makes them (im)moral and purposive.)

74. Philosophers have been much perplexed about the origin of forms, entelechies, or souls; but nowadays it has become known, through careful studies of plants, insects, and animals, that the organic bodies of nature are never products of chaos or putrefaction, but always come from seeds, in which there was undoubtedly some preformation; and it is held that not only the organic body was already there before conception, but also a soul in this body, and, in short, the animal itself; and that by means of conception this animal has merely been prepared for the great transformation involved in its becoming an animal of another kind. Something like this is indeed seen apart from birth [generation], as when worms become flies and caterpillars become butterflies. (Theod. 86, 89. Pref. [E. 475 b; G. vi. 40 sqq.]; 90, 187, 188, 403, 86, 397.)

Here Leibniz very probably was thinking of a debate that occurred in his time: that between the ovarists, who claimed that all life starts from an egg i.e. a seed, and their opponents. At present, it is widely believed that the scientific explanation for growth and form somehow involves DNA. (But this explanation so far is very incomplete and partial, and does not address problems of consciousness.)

75. The animals, of which some are raised by means of conception to the rank of larger animals, may be called spermatic, but those among them which are not so raised but remain in their own kind (that is, the majority) are born, multiply, and are destroyed like the large animals, and it is only a few chosen ones [elus] that pass to a greater theatre.

It seems Leibniz thought of conception in terms of metamorphosis - which, the reader should remember, literally means "change of form". If so, he should have held that the sperm and egg from which arises a human being are themselves not human beings, but beings capable of becoming so.

76. But this is only half of the truth, and accordingly I hold that if an animal never comes into being by natural means [naturellement], no more does it come to an end by natural means; and that not only will there be no birth [generation], but also no complete destruction or death in the strict sense. And these reasonings, made a posteriori and drawn from experience are in perfect agreement with my principles deduced a priori, as above. (Theod. 90.)

This repeats (72) and (73), and I suppose the "if" should be read as "since": all animals are created by God, who miraculously joined their souls to their bodies, to which they will be joined everlastingly after. This answers none of my questions under (72) and (73).

77. Thus it may be said that not only the soul (mirror of an indestructible universe) is indestructible, but also the animal itself, though its mechanism [machine] may often perish in part and take off or put on an organic slough [des depouilles organiques].

The Shorter Oxford English Dictionary tells us that

Slough (...) [ME (..) perhaps related to LG sluwe, slu, husk, peel, shell.] 1. The outer or scarf skin periodically cast or shed by a snake, adder etc.; also generally, the skin of a serpent, eel, etc. b. The skin of a caterpillar, locust, etc. cast in the course of transformation, as from the nymphal to the imago stage 1681. c. fig. A feature , quality, etc. which is thrown off 1583. 2. A skin, caul, or membrane, enclosing the body or some part of it ME. b. An enclosing or covering layer, coat, or sheath of some kind 1610. c. dial. The outer skin of certain fruits; a husk 1660. 3. Path A layer or mass of dead tissue or flesh formed on the surface of a wound, sore or inflammation (...)

This seems to give a fair indication of what Leibniz had in mind. Thus, he seems to have believed that

(1) Each and every real thing whatsoever has a form and a substance.
(2) The form of each and every real thing is mental, in that it perceives and acts for ends, and the substance is material, in that it does not perceive and does not act for ends, but is capable of being acted upon.
(3) God joined form and substance originally and everlastingly, and is Himself the only form without substance to be the form of.
(4) If they are the form and substance of what we call animate nature, the substances are transformed, which manifests itself as birth, metamorphosis, and death.
(5) If they are the form and substance of what we call inanimate nature, the substances are not transformed, but may combine with other substances to form composite substances.

As I noted before, this does pose a number of questions about God's purpose for this sort of creation, for example, what is the end of being alive, since this takes such a small part of the creatures' infinitely long existence. And as also noted before, God's own status is logically precarious, in that His utter substancelessness makes Him differ from everything else. Indeed, as far as the above restatement of Leibnizian theses is concerned, one might rewrite (3) substituting "Nature" for "God", and do totally without forms without any substance. But this surely was not Leibniz's intent, as we shall see (although it may have been Spinoza's).

78. These principles have given me a way of explaining naturally the union or rather the mutual agreement [conformite] of the soul and the organic body. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe. (Pref. [E. 475 a; G. vi. 39]; Theod. 340, 352, 353, 358.)

This restates earlier points, it may be helpful to bring out the logic of the argument:

(1) The soul perceives the universe and moves the body through its appetites.
(2) The body is moved by the soul in conformity to its perceptions and appetites.
(3) All souls of all bodies perceive the same universe in the same ways, apart from their capacities for perception and reasoning, which may be large.

And this should be compared to my remarks under (77).

79. Souls act according to the laws of final causes through appetitions, ends, and means. Bodies act according to the laws of efficient causes or motions. And the two realms, that of efficient causes and that of final causes, are in harmony with one another.

Here we come to another fundamental difference between souls and bodies: A soul acts towards ends, that have no embodied reality in themselves, but which it does conceive as an idea of something desired; a material body acts only through being effected by some other existing material body or by effecting some other existing material body.

This opposition of acting for future ends or being acted upon by prior bodies is as old as Aristotle, and conforms quite well to how things appear to human beings. It also is another fundamental distinction between the mental and the physical, which I have remarked upon under (17).

80. Descartes recognized that souls cannot impart any force to bodies, because there is always the same quantity of force in matter. Nevertheless he was of opinion that the soul could change the direction of bodies. But that is because in his time it was not known that there is a law of nature which affirms also the conservation of the same total direction in matter. Had Descartes noticed this he would have come upon my system of pre-established harmony. (Pref. [E. 477 a; G. vi. 44]; Theod. 22, 59, 60, 61, 63, 66, 345, 346 sqq., 354, 355.)

Here we are to a considerable extent concerned with physics as it was being developed in Leibniz's time, when people first hit upon principles of least action, extremal principles, and principles of conservation. A considerable part of the reason such principles could be stated and discovered was due to Leibniz himself, for such principles are normally stated in terms of the maxima or minima of differentials, and Leibniz was one of the discoverers of the differential and integral calculus.

One such principle is that, in the physical world, the total amount of force is conserved (remains always the same), which has dire consequences for non-physical souls, as Descartes noted, for it follows that they have no available means of effecting the physical world.

In this situation, one might conclude that, therefore, it is quite unlikely there are any non-physical souls, or, if there are, they are as ephemeral and ineffective as shadows. One problem with that conclusion is that it leaves many experienced facts unexplained; another problem with it is that it goes against religion as Leibniz knew it and appreciated it.

Hence Leibniz's alternative resolution of the problem of the relation of body and soul: although there is no physical interaction between the two (all physical interactions are between bodies), the soul does, after its capacities, truly represent its body and the world, for God has made souls and bodies in that way - so that each body has a soul joined to it that perceives the world the body is in, and does so, after its capacities, truly and adequately (if it is not disturbed by emotions).

81. According to this system bodies act as if (to suppose the impossible) there were no souls, and souls act as if there were no bodies, and both act as if each influenced the other.

The last statement is the Pre-Established Harmony, and Leibniz's reason to write "as if" at this place is as explained under (80): it is physically impossible body and soul influence each other, at least in any physical way. And as I explained under (58), there is a set of quite ordinary assumptions most people accept, briefly to the effect that all human beings feel and think similarly in similar circumstances, that is quite close to Leibniz's Pre-Established Harmony (but without being tied up in the same way with dualism).

82. As regards minds [esprits] or rational souls, though I find that what I have just been saying is true of all living beings and animals (namely that animals and souls come into being when the world begins and no more come to an end that the world does), yet there is this peculiarity in rational animals, that their spermatic animalcules, so long as they are only spermatic, have merely ordinary or sensuous [sensitive] souls; but when those which are chosen [elus], so to speak, attain to human nature through an actual conception, their sensuous souls are raised to the rank of reason and to the prerogative of minds [esprits]. (Theod. 91, 397.)

Note that the levels of being, so to speak, Leibniz presupposed: a piece of rock perceives and has appetites (for being a rock) but neither feels nor thinks nor reasons; a plant perceives, has appetites, and feels, but neither thinks nor reasons; an animal perceives, has appetites, feels and thinks, but does not reason; a human being perceives, has appetites, feels, thinks and reasons. It may be added that, in terms of my remarks under (29)-(32), 'thinks and reasons' is to be read as 'deduces and abduces': only human beings attempt to explain their experiences in terms of assumptions of things not given in experience. (And here lies a reason for Leibniz's rationalism.)

One way of reading (82) is as a contribution to the recent debate about abortion: On Leibniz's principles, before a certain point - conception, for him - the parts from which a future human being might be built are not future human beings but merely animals: only those sperms and those eggs that succeed in combining animate a human being, and what is added to mere animality is the capacity of reasoning. (Those who argue in favour of medical abortion may be taken to claim that this point occurs somewhere after conception and before birth, and that a medically correct abortion occurs before this point.)

83. Among other differences which exist between ordinary souls and minds [esprits], some of which differences I have already noted, there is also this: that souls in general are living mirrors or images of the universe of created things, but that minds are also images of the Deity or Author of nature Himself, capable of knowing the system of the universe, and to some extent of imitating it through architectonic ensamples [echantillons], each mind being like a small divinity in its own sphere. (Theod. 147.)

Thus animals are not capable of reflecting (appropriately or at all) upon the splendours of the Deity, but human beings are, and therefore they have the faculty of reason. Apart from the splendours of the Deity, we have seen abduction - alternatively definable as: the capacity to think creatively, of new explanations or solutions - is what enables human beings to think rationally and understand and explain their experiences.

Furthermore, the Deity is known, for Leibniz, at least in part as a set of necessary principles according to which one must think and feel, and according to which God Himself thinks and feels, only much better than human beings could. The reason to insert "and feels", also for God Himself, is that Leibniz believed that God is bound to realise the best possible world, like human beings are bound to try to do what they think is best, if they do anything at all. (Leibniz does not seem have considered wilful perversion, neither on God's part - 'let's create a devil, to liven things up!' - nor on the part of human beings - 'I know like p more than not-p, but I try to get not-p just for the hell of it.' Yet this seems possible if one has a free will, as Leibniz believed one has.)

84. It is this that enables spirits [or minds- esprits] to enter into a kind of fellowship with God, and brings it about that in relation to them He is not only what an inventor is to his machine (which is the relation of God to other created things), but also what a prince is to his subjects, and, indeed, what a father is to his children.

Most of this is conventional Protestant theology Leibniz subscribed to and sought to defend by philosophy, but it is interesting to note that the "fellowship" between God and men is based on a sharing of the capacity of reasoning.

85. Whence it is easy to conclude that the totality [assemblage] of all spirits [esprits] must compose the City of God, that is to say, the most perfect State that is possible, under the most perfect of Monarchs. (Theod. 146; Abrege, Object. 2.)

The notion of "the City of God" is an old one, and St. Augustine wrote a large book of that title, explaining a similar conception.

Personally, I believe it is unwise to believe in real things that are perfect: it seems much more sensible to assume that everything that is real is limited, capable of becoming worse or better on many standards, and usually is neither the worst possible nor the best possible in any sense. The reason I believe it is unwise to believe in real things that are perfect is that it is all too easy to support fanaticism: if you really believe you know the Lord's intentions, it turns out to be quite natural for human beings to set up an inquisition to torture others into believing as you do. (Also, on a personal note others may also have experienced: I have seen perfection several times in my life. Epiphanic perfection in my case always took the shape of a young woman, and I always was mistaken; knew I was mistaken while I was mistaken; and could not believe I was mistaken as long as I was in love.)

86. This City of God, this truly universal monarchy, is a moral world in the natural world, and is the most exalted and most divine among the works of God; and it is in it that the glory of God really consists, for He would have no glory were not His greatness and His goodness known and admired by spirits [esprits]. It is also in relation to this divine City that God specially has goodness, while His wisdom and His power are manifested everywhere. (Theod. 146; Abrege, Object. 2.)

More Protestant theology. One problem I have is why God needs creatures to have glory: why could he not bask in the same sort of self-satisfaction he had according to the Old Testament after a step of creation. (The Book of Genesis, in the King James translation, has it that "God saw the light, that it was good", and similarly for "the dry land", the grass, trees and herbs; the day and the night, the whales and winged fowl, and the cattle. Only after creating males and females, at the end of the first chapter of Genesis, "God saw every thing that he had made, and, behold, it was very good". I conclude the dear Lord did glorify in his work before he created any rational creatures.)

Also, wholly apart from Protestant theology, the Society of Human Beings is a moral world in the natural world, maintained and designed by moral people if not by a moral God.

To my mind it is a moral and intellectual mistake to try to base a moral system on a system of metaphysical theology: human being need to make moral agreements, if they want to avoid making the lives of others and themselves more painful than is necessary, and they may do so simply on the basis of agreements about the properties of human beings, and without any dubitable appeal to entities other human beings might not at all believe in.

The belief that 'if God would not exist, everything would be permitted' is a belief of a person who does not seem to wish to take personal responsibility, and instead prefers to follow authorities, and indeed that authority who is supposed to have most power. (Cp. 'If the boss has not forbidden it I can do it.')

87. As we have shown above that there is a perfect harmony between the two realms in nature, one of efficient, and the other of final causes, we should here notice also another harmony between the physical realm of nature and the moral realm of grace, that is to say, between God, considered as Architect of the mechanism [machine] of the universe and God considered as Monarch of the divine City of spirits [esprits]. (Theod. 62, 74, 118, 248, 112, 130, 247.)

Even so, the problem remains why there should be both souls and bodies: why could God in his wisdom not create a world in which all souls are material, or all bodies mental? It is true that this is where the problem starts: How to account for the apparent fundamental differences between human experiences and the physical facts they experience?

But it is also true that what Leibniz ends with is the same given distinction writ large and denied all resolution: Leibniz started with the dualism of the mental and the physical commented upon under (17), and also ended with it - except that in the interim he convinced himself that it was the necessary outcome of God's will.

88. A result of this harmony is that things lead to grace by the very ways of nature, and that this globe, for instance, must be destroyed and renewed by natural means at the very time when the government of spirits requires it, for the punishment of some and the reward of others. (Theod. 18 sqq., 110, 244, 245, 340.)

This I take to be more theology, and skip, except for the remark that I find it quite unsatisfactory that the Lord and Maker of everything, supposing Him to exist, has made it so extra-ordinarily difficult to find any conclusive evidence for His existence and intentions, that is understandable and evident to any ordinarily gifted man or woman, in the same way as any ordinarily gifted man or woman can understand as evident the truths of arithmetic.

Why are the Divine Commandments not as clear and self-evident as is 2+2=4 to every thinking human being, who, on Leibniz's reasoning, contains a spark of the divine that can come to understand universal truths? Surely, an all-powerful benevolent and moral God would think it more important that his creatures behave well towards one another than that they can keep proper account of their profits in slave-dealing?

89. It may also be said that God as Architect satisfies in all respects God as Lawgiver, and thus that sins must bear their penalty with them, through the order of nature, and even in virtue of the mechanical structure of things; and similarly that noble actions will attain their rewards by ways which, on the bodily side, are mechanical, although this cannot and ought not always to happen immediately.

See my remarks to the previous point. I do not have Leibniz's faith, and among many other reasons, one important reason is the problem of evil: I cannot understand how it is possible that there would be an omnipotent benevolent God who created a world in which there is manifestly so much undeserved pain and suffering. Also, I find the basic argument for the existence of God incoherent: if something that exists requires an existing maker to exist, so does a maker, since He (She, It) exists. So that is an infinite regress I prefer not to start. It follows that if something that exists requires an existing maker to exist, there is no existing maker.

90. Finally, under this perfect government no good action would be unrewarded and no bad one unpunished, and all should issue in the well-being of the good, that is to say, of those who are not malcontents in this great state, but who trust in Providence, after having done their duty, and who love and imitate, as is meet, the Author of all good, finding pleasure in the contemplation of His perfections, as is the way of genuine 'pure love,' which takes pleasure in the happiness of the beloved. This it is which leads wise and virtuous people to devote their energies to everything which appears in harmony with the presumptive or antecedent will of God, and yet makes them content with what God actually brings to pass by His secret, consequent and positive [decisive] will, recognizing that if we could sufficiently understand the order of the universe, we should find that it exceeds all the desires of the wisest men, and that it is impossible to make it better than it is, not only as a whole and in general but also for ourselves in particular, if we are attached, as we ought to be, to the Author of all, not only as to the architect and efficient cause of our being, but as to our master and to the final cause, which ought to be the whole aim of our will, and which can alone make our happiness. (Theod. 134, 278. Pref. [E. 469; G. vi. 27, 28].)

This certainly seems to have been what Leibniz sincerely believed. The only thing I want to remark upon is the phrase 'that it is impossible to make it better than it is' - it being the world such as it is - which seems to be rather fatalistic. But then perhaps optimists like Leibniz should be fatalists, on the ground that eventually things will work out as desired 'Alles sal reg kom', in Afrikaans).


To first part: Monadology - part A
To the index: Sections and subjects of the Monadology
To the appendix:
A simple logic of parts

Copyright remarks:

Colofon: This text was written in 1998, and was once corrected in November 2003, and a second time in September 2006. In either case the corrections were small, and mostly stylistical or typographical.  

Maarten Maartensz       
last update: Sep 11 2006