Maarten Maartensz

Leibniz wrote the Monadology - in French - in 1714, when he was about 68. It was intended as a sort of summary of his philosophy in the form of theses. What follows is an English translation of the complete Monadology, that dates from 1898, together with my comments, that date from 1998.

Leibniz's text is indented and reproduced completely. It consists of 90 theses, and summarises a set of basic reasons for Leibniz's philosophy. Although it does not at all supply all of Leibniz's assumptions, considerations and arguments, it is a remarkable summary of philosophical principles by one of the best human intellects there have been - and even if it is wholly or mostly mistaken at least it has the great merit of addressing some of the fundamental philosophical problems in a relatively clear way.

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To second part: Monadology - part B
To the appendix: A simple logic of parts
To the index: Sections and subjects of the Monadology
To Leibniz's Preface to the Nouveaux Essays
To Remark on Robert Latta's Translation

 

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The Monadology starts as follows, with a clarification of the unfamiliar term 'Monad':

1. The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts.' (Theod. 10.)

I shall take this as a definition of the term "Monad". There are two related senses of 'simple', namely 'what is primitive' (in the sense of: 'what must be presumed from the beginning') and 'what cannot be defined', rather than as 'what is without parts'. But these senses, although suggested by connotation, seem not to be meant. So I exclude these senses, though I keep in mind the suggestions, which seem to have been conscious on Leibniz's part, since Monads in his schema of things play the role of building blocks of which (and by which) everything is built.

Next, there is an immediate problem, because it is not said in what sense 'parts' is to be taken, and this is not said in - at least - three senses: whether the parts are proper parts or whether something may be a (n improper) part of itself; whether the parts are physical or non-physical or perhaps both; and in any case what sort of logical principles apply to the terms 'parts', 'part', 'is a part of', and the like.

The reason that there is an immediate problem is, first, that the term 'part' may be understood in two ways: as 'part of x or all of x' or as 'part of x but not all of x', where in this last case one may also speak of 'proper part of x', and, second, that while Leibniz spoke of 'parts' he seems to have meant (mostly and in his point (1)) 'proper part'.

Indeed, what Leibniz says in (1) makes sense if 'part' is taken as 'proper part', but does not seem to make much sense in the other sense of 'part', for in the other sense of part every thing is its own part, and so every thing is part of itself, and there just are no things 'without parts', though there seem to be things 'without proper parts', namely the smallest real things there are, such as atoms, or atomic particles.

Of course, the sense of 'part' in which parts are proper or identical to what they are part of is easily defined using only the notions of proper part and identity and is more convenient than mere proper parts for several reasons, one of which is that it is convenient to be able to say that something is a part of itself, though not a proper part of itself. The intended definition is: 'x is a part of y iff x is a proper part of y or x=y'. There is an appendix on a logic of parts, in which I am a little more formal about what Leibniz might have had in mind, that uses this definition, and derives a number of interesting theorems.

Leibniz seems to have thought mainly in terms of spatial and physical analogies when thinking of parts (volumes contained in volumes), and while he offers no explicit logic of parts (or mereology, which means 'logic of parts'), what he will say about monads should be at least consistent with any such logic, one would presume, and therefore what he says can be taken as clues to mereological principles he might have endorsed. Some simple mereological principles he might have endorsed are considered in an appendix. Since this appendix uses a little formal logic, and I have decided not to clutter these remarks with technicalities, I refer the reader to this appendix if interested.

2. And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things.

This seems to involve a tacit premise like 'Everything is either without - proper - parts or a compound of parts without - proper - parts'. In view of the comments under (1) this premise has various possible readings, some of which are considered in the appendix (in which it is argued Leibniz confused 'part' and 'proper part', but that if this confusion is undone something rather close to what he does say can be reconstructed).

3. Now where there are no parts, there can be neither extension nor form [figure] nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things.

I.o.w.: There is no extension, form or divisibility without parts. The idea seems to be that extension is having proper parts; as is divisibility; while form is having relations between proper parts. All of this sounds more or less intuitive, but that is no guarantee of anything, and my main problem here is how composites come to be, since nothing seems supplied that would make such composites stick together and not fall apart. Leibniz also saw that problem, and addresses it somewhat later.

4. No dissolution of these elements need be feared, and there is no conceivable way in which a simple substance can be destroyed by natural means. (Theod. 89.)

Here the reasoning seems to be: only what has proper parts can be taken apart, and only what can be taken apart can dissolve. Also, this seems to involve the tacit premise that nothing exists without a reason, for else one could object that monads might simply disappear or appear from nowhere. (Indeed, Leibniz did believe that nothing exists without a reason.)

5. For the same reason there is no conceivable way in which a simple substance can come into being by natural means, since it cannot be formed by the combination of parts [composition].

Here the reasoning is obviously: only what has proper parts can be put together. One may well ask, though, why it would be impossible for a composite thing to emit simple things. I suppose Leibniz's reply would be: Of course that's possible - provided they were its parts before emission.

6. Thus it may be said that a Monad can only come into being or come to an end all at once; that is to say, it can come into being only by creation and come to an end only by annihilation, while that which is compound comes into being or comes to an end by parts.

But then it seems both creation and annihilation are miraculous, which indeed is probably what is suggested (God being Leibniz's cause of miraculously created things). They are miraculous, because their existence involves something that cannot exist if what was laid down is true.

I would prefer to assume instead, assuming Leibniz's principles about things and parts, that there always have been and will be the same fundamental particles. (This is consistent with modern physics - which is pleasant to remark though hardly a guarantee of truth. But it should give some people some pleasure to know that their bodies contain some of the same atoms as were contained in Aristotle's body, for example - which is highly probable every human being does, if it may be assumed that rain, wind and water have spread some of Aristotle's bodily parts over the globe over the past 2400 years. Indeed, on the same principle every living human beings contains some atoms that were part of each human being that died 2000 or more years ago.)

7. Further, there is no way of explaining how a Monad can be altered in quality or internally changed by any other created thing; since it is impossible to change the place of anything in it or to conceive in it any internal motion which could be produced, directed, increased or diminished therein, although all this is possible in the case of compounds, in which there are changes among the parts. The Monads have no windows, through which anything could come in or go out. Accidents cannot separate themselves from substances nor go about outside of them, as the 'sensible species' of the Scholastics used to do. Thus neither substance nor accident can come into a Monad from outside.

The first statement is based on the premises that only what has proper parts can be changed internally (namely by altering some of those proper parts or their relations), while the reference to 'any other created thing' is meant to suggest that God, who is no created thing, could alter Monads.

That 'Monads have no windows' is in part a statement of Leibniz's idealism, and in part an answer to how perception and thought are possible, as indicated by his denial of the existence of the 'sensible species' of the Scholastics. It also makes sense, apart from idealism, on the basis of what was assumed about Monads, since windows are parts of something they are the windows of, and Monads have no parts.

Let's not consider Leibniz's idealism for the moment (which we will consider below) and consider Monads for a moment. The problem is that a Monad now seems to have become a very simple sort of something indeed, of which it is difficult to see it can do anything at all. (For example, because to do anything something has to have proper parts - or thus it might seem.) This problem will be taken up under the next point (and in more detail in the appendix on a simple logic of parts)

Leibniz's aim with this point was to oppose the Scholastic idea of 'sensible species'. The idea of 'sensible species' was more or less that we see, hear and smell things because something - the sensible species - leaves the things they belonged to and travels through space to our senses, where it arrives and gets identified as a 'sensible species' - say the sight, sound and smell of a shitting sow.

Clearly, if Monads have no windows, and sensible species consist of parts, there is no way a sensible species can enter a Monad.

Without troubling ourselves too much about what the Scholastics might have meant by 'sensible species', we may frame a few assumptions in more modern terms that address the problem the assumption of sensible species was concerned with. Namely:

(1) all things T effect the states and properties of certain other things S in systematic ways, causing specific states and changes in the other things, amounting to, say, S', which are such that
(2) a thing X equipped to sense these states and their properties is capable of concluding that there is or was a thing T with certain states and properties that are conveyed by S'.

Thus, there are hearable, smellable, visible properties of things that - as we say - inform a thing capable of sensing them there is, was or will be something with certain properties that are inferred, among other things, from these hearable, smellable or visible properties. (In case of the 'sensible species' of a cow such an inference might be: 'We might get some milk.')

What the Scholastics called 'sensible species' seems to have been - in the present terms - the systematic effects S' of a thing T on the properties and states of things S. But of course the main problem does not concern these systematic effects S' of T, but how and why a thing may sense these systematic effects and conclude that there is or was or will be a T in state T' from sensing that S was in state S'.

8. Yet the Monads must have some qualities, otherwise they would not even be existing things. And if simple substances did not differ in quality, there would be absolutely no means of perceiving any change in things. For what is in the compound can come only from the simple elements it contains, and the Monads, if they had no qualities, would be indistinguishable from one another, since they do not differ in quantity. Consequently, space being a plenum, each part of space would always receive, in any motion, exactly the equivalent of what it already had, and no one state of things would be discernible from another.

This takes up my initial problem with (7), that Monads seem thus far not to be able to do or be much at all. My problem with (8) is that it follows that qualities are not all dependent on parts or their relations: Apparently a simple thing may have qualities that do not depend on its parts or relations between its parts, since it has no - proper - parts.

Most of the argument of (8) I find difficult to follow. Apparently something on the following lines is meant: Where there are neither distinctions in quality nor in number of things, there are no distinctions of things.

And in any case I believe Leibniz was somewhat confused about parts. My reasons are in the appendix.

9. Indeed, each Monad must be different from every other. For in nature there are never two beings which are perfectly alike and in which it is not possible to find an internal difference, or at least a difference founded upon an intrinsic quality [denomination].

This is merely dogmatic: it seems an argument, but the second sentence merely restates the first, or if it doesn't, the first merely states that is necessary what the second states is a fact. But I do not believe that 'in nature there are never two beings which are perfectly alike'.

First, I believe the same relation may exist here and there, say 'being a father of'. Next, I believe the same quality may exist here and there, say 'is approximately circular'. And third, I see no reason to deny that, to all intents and purposes, one atom of Helium is just like another, apart from its place, and so, as far as its qualities are concerned, atoms are also indistinguishable.

This is in fundamental opposition to Leibniz, but I shall not spend more argumentation on it, and instead simply affirm the opposite in the same dogmatic fashion. The reader may make up his own mind to decide whether he believes all relations, all qualities and all atomic substances are unique particulars.

10. I assume also as admitted that every created being, and consequently the created Monad, is subject to change, and further that this change is continuous in each.

It follows that such changes must be changes in the qualities of the Monad, it seems. Why and in what sense these changes should be 'continuous' is unclear, but part of Leibniz's intentions was to attribute some sort of infinity to Monads (and continuous changes seem to involve infinite divisibility).

11. It follows from what has just been said, that the natural changes of the Monads come from an internal principle, since an external cause can have no influence upon their inner being. (Theod. 396, 400.)

Presumably, because a Monad has no windows. One reasonable image at this point is that of a dewdrop in which the environment is reflected - except that, for Leibniz, the reflection is, in metaphysical reality, a projection of the monad rather than a reflection of the environment, though it seems to be a reflection. (Here lies a theme taken up by Kant, while also the theme of appearance versus reality is involved. In terms of the analogy of the dewdrop, the difference is that, on Leibniz's principles, a dewdrop does not really receive 'sensible species' from external things which it then reflects in its own way, but really projects external things from its own constitution. As we shall learn below, Leibniz believed this projection has been engineered by God in such a fashion that it does represent what really is so.)

12. But, besides the principle of the change, there must be a particular series of changes [un detail de ce qui change], which constitutes, so to speak, the specific nature and variety of the simple substances.

I take it that such a particular series of changes is what identifies a Monad - its essence, individuality or haeccity, to use Scotus' term. It should be noted that, for Leibniz, this is like the pattern of a series rather than like its elements, in a similar sense as it belongs to the essence of a human being to change from baby, to child, to pubescence, adolescence, and senescence, and as it belongs to the essence of a butterfly to have become from a caterpillar. (Similarly, the infinite series <1/2, 1/4, 1/8, ... 1/2^n ...> has the characteristics of having successive terms half the size of preceding terms and of summing to 1.)

13. This particular series of changes should involve a multiplicity in the unit [unite] or in that which is simple. For, as every natural change takes place gradually, something changes and something remains unchanged; and consequently a simple substance must be affected and related in many ways, although it has no parts.

This is rather mysterious, and the best sense I can make of it is through the analogy of the dewdrop's reflections and the premise that one and the same monad may have many qualities. A way to make sense of these qualities is to say that any monad, simply by existing, has many relations to other monads, and some of these relations are its qualities. Also, part of Leibniz's intent is to do justice to the fact (or assumption) that it is the same individual that grows from baby to graybeard, and the same insect that grows from caterpillar into butterfly.

Even so, an important problem for Leibniz crops up here, for it seems as if these qualities are at least like parts of whatever they are the qualities of (and one easily speaks of one's qualities being part of one, though the sense of 'part' is unclarified here, and may be metaphorical), and it also seems more clarity is needed about what qualities are supposed to be. Leibniz answers some of this in the next point (and I take up some of the problems of what Leibniz might have meant in the appendix).

14. The passing condition, which involves and represents a multiplicity in the unit [unite] or in the simple substance, is nothing but what is called Perception, which is to be distinguished from Apperception or Consciousness, as will afterwards appear. In this matter the Cartesian view is extremely defective, for it treats as non-existent those perceptions of which we are not consciously aware. This has also led them to believe that minds [esprits] alone are Monads, and that there are no souls of animals nor other Entelechies. Thus, like the crowd, they have failed to distinguish between a prolonged unconsciousness and absolute death, which has made them fall again into the Scholastic prejudice of souls entirely separate [from bodies], and has even confirmed ill-balanced minds in the opinion that souls are mortal.

Continuing the previous remark, these - let's say - reflecting qualities are at least partially unconscious, and Leibniz was a lot earlier with assuming an unconscious mind than was Freud, who as late as 1935 claimed - fraudulently - to be the discoverer of the unconscious. (There even is a sound recording of this - "I deescovered zee ooncoonscious.")

Leibniz believed, contra Descartes, who argued that animals are mere machines, that animals are animated like human beings are animated, and that what animates a thing is a soul or entelechy, which is an entity that desires and believes and acts purposively, towards ends. Indeed, this is what a Monad is.

Leibniz denied what he called 'the Scholastic prejudice of souls entirely separate [from bodies]', holding that there are no souls without bodies, apparently for the same sort of reason that made Aristotle assume there are no universals and no relations without things: A soul is more like a relation than like a substance, and there are no relations without things to relate.

I myself, who has no religious axe to grind, have sofar seen no reason not to believe that a soul may die as well as a body may die. Indeed, since bodies die, it seems more plausible to presume that these bodies die because their souls die, if their souls are what animated their bodies, than to assume that souls animate bodies and bodies may die but souls may not. (Analogously, if you tear up a piece of paper both it and its form are destroyed, intuitively, rather than that the paper is destroyed while its form is floating about somewhere in a heaven for paper forms.)

In any case, it should be clear by now that Leibniz reasoned more or less as follows - and my terms are chosen in conformity with my results in the appendix, for which reason the terminology I use is not quite the same as that of Leibniz, although its sense seems to be close to what he had in mind:

Physical compound things have simple proper parts (for which reason what is a physical compound can be taken apart); so what has no simple proper parts is not a physical compound. Since all real compound things are composed of simple things without proper parts, there are simple things without proper parts. As things without qualities do not exist, things without simple proper parts have qualities, and as things without changes do not exist either, things without simple proper parts change. Since whatever happens, happens for a reason, their changes are orderly. Since things without simple proper parts have no physical parts to be effected by physical parts, their changes issue from themselves (or their creator, Leibniz would have added). And since things without simple proper parts are not physical, their qualities must be mental, and therefore some kind or quality of experience.

As far as I can see this was the sort of intuitive reasoning in the back of Leibniz's mind - except that he was both a little more confused concerning parts and considerably more ingenuous, as the reader will find out below and in the appendix.

15. The activity of the internal principle which produces change or passage from one perception to another may be called Appetition. It is true that desire [l'appetit] cannot always fully attain to the whole perception at which it aims, but it always obtains some of it and attains to new perceptions.

Note that Leibniz here does introduce an active internal principle of Monads: they all have something like desires, and this is what makes them active and change their qualities. One reason to write out an alternative of Leibniz's way of reasoning at the end of my remarks to (14) is to make clear that he had found an original way to introduce experience.

16. We have in ourselves experience of a multiplicity in simple substance, when we find that the least thought of which we are conscious involves variety in its object. Thus all those who admit that the soul is a simple substance should admit this multiplicity in the Monad; and M. Bayle ought not to have found any difficulty in this, as he has done in his Dictionary, article 'Rorarius.'

Indeed, if we have souls, that are Monads, that are again like focal points in a dewdrop, in which its environment is reflected. (One argument that could be used in support of this is the premise that all relations are mental. F.H. Bradley took this line. This may not make much intuitive sense, but the reader who has been exposed to modern mathematical logic, in which a relation turns out as a set of pairs, ought to know from experience that relations are problematic entities.)

17. Moreover, it must be confessed that perception and that which depends upon it are inexplicable on mechanical grounds, that is to say, by means of figures and motions. And supposing there were a machine, so constructed as to think, feel, and have perception, it might be conceived as increased in size, while keeping the same proportions, so that one might go into it as into a mill. That being so, we should, on examining its interior, find only parts which work one upon another, and never anything by which to explain a perception. Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for. Further, nothing but this (namely, perceptions and their changes) can be found in a simple substance. It is also in this alone that all the internal activities of simple substances can consist. (Theod. Pref. [E. 474; G. vi. 37].)

Here we have an important line of argument to the effect that there is no good mechanical (or materialist) explanation of perception. By "mechanical" Leibniz means, he says, "figures and motions", but he might as well have said "in terms of physics".

Let's first consider Leibniz's argument and then two other arguments to a related effect.

First, Leibniz's argument. It may be restated in the form of two claims. 

(1) In a thinking machine, there are only figures and motions, and figures and motions are not perceptions. 
(2) And we can see this if we imagine such a thinking machine magnified to such a size that we could walk around in it: we would see no perceptions, but only figures and motions.

The second claim might be seen as merely a heuristic restatement of the first. But there is an interesting reply to the second, so we shall consider that reply after considering the first and main argument.

The first claim reduces to the thesis that figures and motions are not perceptions. But why would it be impossible for figures and motions to be perceptions? It may be granted that not all figures and motions are perceptions, but why could there not be some special kind of figures or motions, perhaps standing in some special relation, that are perceptions, when seen or conceived in the proper way? Why could the brain not be such a place?

Leibniz does not say why he thought no figures and motions whatever, in no - physical - relations whatever, could be perceptions, and presumably thought it obvious. But we need an argument, so we turn below to a line of argument he might have agreed to, and may have had in mind, when we consider the next argument for the thesis that there are no mechanical explanations of perception.

To the second claim formulated above one may reply that this involves a mistake: Of course we would not see perceptions if we were to walk around in a thinking machine, but then we should not expect to see them as figures and motions, but, rather, as relations between figures and motions, or, more precisely, relations between relations between qualities of figures and motions. Similarly, if we would be able to walk around between the dots that form a straight line, we would not see a line, but only the dots we walk around between, but this doesn't mean the dots form no straight line: we simply have not chosen the appropriate point of view to see it. And perception may be related to physical elements like straightness is related to physical points: as a kind of - physical - relation between them. (Note that the sense in which straightness is physical is this: for any given velocity, it takes less time to move from a to b along a straight line than along any other line, so straightness thus defined indeed is a quality of motions, and need not be given in direct perception, since it requires measurements of times of travel.)

This reply to the second claim is interesting, and not easy to weigh. The main problem seems to be whether there are any figures and motions that are relations between relations between qualities of figures and motions, and may, in some sense, represent such relations.

In any case, Leibniz's argument is neither conclusive nor complete, so we consider two other arguments that aim at establishing that there is no good explanation of perception in merely physical terms or that there are no physical machines that think.

Second, there is the argument of the difference between the mental and the physical. 

This may be stated as follows - I give one survey of some versions of arguments that attempt to establish that the mental and the physical are fundamentally distinct, and so the one cannot be explained in terms of the other.

Physical elements, like atoms and molecules, have many kinds of physical qualities and relations, such as voltages and velocities, that mental elements, like pains, aches, desires, and feelings do not have, or do not have in the same way and the same sense. Conversely, mental elements, like pains, aches, desires and feelings have many properties, qualities and relations, such as being annoying, interesting or desirable, that physical elements do not have in the same way and the same sense. Besides, mental elements, unlike physical elements, all have a directedness and extra component, physical elements lack: they are the pains, aches, desires, feelings, and beliefs of some person, concerning something, that is not identical with these pains, aches, desires, feelings and beliefs. Furthermore, when we consider the mental elements that are beliefs and desires, we notice that their objects - what the beliefs represent or what the desires are for - may not exist, and sometimes may not possibly exist, in which case we may be said to have an idea - surely also a mental element - of something that does not or cannot possibly exist. That is: certain mental elements are directed towards quite specific things - such as would exist if specific beliefs were true or specific desires were satisfied - that do not exist as physical elements. Yet these quite specific things may have a quite specific mental existence, as ideas, fantasies, or imagined things: one knows what they would look like and how they would behave, but one also knows, for example, that they could not possibly exist physically. (Thus, one's identical twin, if one had one, would look like one.) Moreover, there is a sense of self that every normal person seems to have, that involves many such beliefs and desires that transcend the physical facts, in that these very beliefs and desires posit ideal things, ideals, and fantastic and impossible situations and things, and thus imply that the sense of self transcends the physical facts. Again, one may have many ideas of imaginary situations and things, and of possible things, and of impossible things, and of things and situations one does not know whether they are real, or possible, that have no physical existence, yet exist as ideas. Finally, and in brief: To experience, to desire, to believe, to perceive, to feel are not physical elements or events, and mental events - ideas, feelings, desires, beliefs, sensations - are not physical events - changes of states of atoms or molecules.

Thus it may be argued.

To the last argument, which is a kind of dogmatic conclusion and restatement of the others, the reply is that it is true that it is not known which kinds of changes of which states of which atoms or molecules are experiences, if any, but from the fact it is unknown it does not follow such an explanation is impossible.

And in general it may be remarked that while there is at present no sound reduction of the mental to the physical, nor of the physical to the mental, two problems with insisting both the mental and the physical exist are that it is to assume more than may be necessary, and that it is not clear how the mental and the physical would be related - which is a problem one does not have if one of these is shown to be a form or appearance or aspect of the other.

The other arguments given above in the argument that the physical and the mental are neither identical nor reducible to one or the other may be divided into the following ones:

(1) Not all the properties of mental elements are physical, nor are all the properties of physical elements mental.
(2) Mental elements are directed to, stand for, represent, or mean (the actual terminology one prefers here is far less important than the idea meant) something other than themselves, and physical elements never do.
(3) What mental elements mean may not exist, and may even be impossible. Yet meanings are specific, and may be quite lively fantasies.
(4) The sense of self is of something non-physical, and involves the assumption of ideal and non-physical things.

Compressed thus, and given that one agrees that it is a fact that there is at present no sound explanation of physical facts in terms of mental events, nor of mental events in terms of physical facts, nor a clear proof either explanation in impossible, it may be concluded that none of these arguments are conclusive, and all point to things that must be explained on a materialist or physicalist hypothesis: how mental events may seem to have qualities when experienced that differ from the qualities of physical things; how mental events represents something other than themselves; how it is possible that one may mentally represent specific impossible and non-existent things; and how the sense of self is possible in a merely physical thing.

And this points to two specific fundamental problems: that of meaning or representation, and that of the sense of self. Both enter into the next argument.

Third, a version of Searle's Chinese Room argument. 

Searle's argument was originally directed against arguments to the effect that computers are thinking machines, i.e. they are machines, and they think. It has been widely discussed, and I present here a version that is in some respects clearer than the original.

Suppose one is in a university where there is a computer-terminal from which one can select a sequence of Chinese characters, key it in, and receive, in many cases, the German translation of the sequence, if such there is, or else the message "Can't translate this. Sorry." And suppose the output of the terminal is relayed to three rooms. In the first room, it is received by a computer-program that implements an algorithm that produces a translation into German of the given sequence of Chinese characters if it found any, or else the message it can't translate it. In the second room, it is read by a fluent speaker of Swahili, without any knowledge of either Chinese or German, and no head for languages, who has dictionaries in Chinese and German, and who follows the same algorithm as the computer program does. If he finishes applying the algorithm, he has agreed to key in the result, whatever it is, including possibly the message "Can't translate this. Sorry." (He is a mighty fast worker as regards looking up things according to recipe, or time doesn't matter, but this is by the by.) In the third room, the terminal's output is read by a fluent speaker of Chinese, who also is a fluent speaker of German and English. She thinks of a translation and keys it in as answer, or thinks it is too complicated, nonsense, or not worth the trouble, in which case she gives the agreed message "Can't translate this. Sorry." and this is what she has agreed to do.

Now, apart from the time it takes, and supposing that in either case sufficiently many decent translations are produced, as judged by competent speakers of Chinese and German: What are the differences between what happens in these three rooms?

We have agreed that the Swahili speaker doesn't know Chinese or German, so perfect as the translations that leave his hands may be, he does not know any Chinese or German. (And therefore the qualities of the translation are wholly due to the algorithm he uses.)

And we have agreed the computer-program uses precisely the same algorithm (if perhaps a little faster), so the computer-program, whatever the quality of its translations, does not understand Chinese either: after all, both the Swahili speaker and the computer end up with a result they can't make sense of and do not know the meaning of. But the fluent speaker of Chinese, in the third room, obviously knows Chinese - and so she is the only person that understands the meaning of what is going on, and that, accordingly, is what a computer-program lacks, like the Swahili-speaker.

But now let us take a closer look at the only one who understands the meaning of what is going on: the fluent Chinese speaker in the third room, who knows Chinese. What is so special about her? How does she achieve her result? Either she uses precisely the same algorithm or she doesn't. Suppose for a moment she does. Then what is the difference? That there is somebody who knows that this is the translation of that.

For consider the Swahili-speaker. We may assume that he knows when he is done, when he has finished his algorithmic recipe (that is: when it terminates), and we may assume that he does not know what he has achieved: a translation into German of a Chinese sentence. For all he knows it might be Hungarian, Mexican, or some mysterious output - he only follows a recipe. Also, he might not know what he is translating from (not knowing the differences between Chinese and Japanese, say).

And about the Chinese speaker we assumed that she also knows fluent English, and so is capable of thinking in English that such and such in Chinese means so and so in German. In any case, the difference remains that even if the Chinese speaker achieves her feat, unconsciously of course, in some way we need not spell out, by precisely the same algorithm, then still in her case there is someone at the end who knows that such and such in Chinese means so and so in German - indeed, fundamentally because such and such and so and so mean (almost) the same, whether in fact or fiction - and in the case of the other two rooms all that is going on is systematic matching of meaningless sequences according to recipe.

So in this sense mere algorithmic following of a recipe, such as a computer may do, is not sufficient for understanding. And the understanding the Chinese speaker has, is that she can supply the meaning of the Chinese and of the German sentences, and knows they are the same, or at least sufficiently similar to make the one count as translation of the other. Incidentally, this is also the reason that the Chinese speaker, although she may use the same algorithm as the Swahili speaker and the computer, must after or during its use introduce something extra, that supplies the meaning that the computer and the Swahili-speaker do not arrive at nor supply.

What has not been proved is that this understanding the Chinese speaker has, or for that matter the Chinese speaker herself, cannot possibly be based on an algorithm. What has been proved is that to understand something requires supplying a meaning to a symbolism, and thus to move outside the symbolism and add something to the symbolism, in a systematic way, generally depending on rules and on the symbolism itself. But while meanings may be arrived at by applying some algorithm to some symbolism, the essential point is that meanings must be added to the symbolism, and are not given with it.

But what is added, i.e. such a meaning, is in fact, for the Chinese speaker, a belief or desire or fantasy or memory about something, that may or may not be physically real, which is what the Chinese input and its German translation mean. Furthermore, the fluent Chinese speaker knows she understands Chinese, and, since she is also a fluent German speaker, knows how to translate what she understands into German.

Now this is a cogent refutation of the notion that present-day computers understand or know anything they correctly translate, where the correctness is judged by real people who know the languages involved, if the translation takes place in the specified way - which is a fair summary of how translation programs do work.

But it is not a cogent refutation of a somewhat different set-up, that may be specified as follows.

Suppose there is a computer as before, which has a camera attached to it, that can make and store pictures of things, and also has a sort of reverse camera inside, that displays stored pictures on demand. Thus, the camera plays the role of a sense-organ, and the reverse camera inside plays the role of the mind's eye. In either camera, what gets effected may be supposed to be photo-sensitive cells, but in the first camera the input is light and the output pictures, while the input of the reverse camera is symbols and its output pictures. This suggests that the internal eye may use something analogous to the retina of the eye: the eye's retina is triggered by light and produces a picture, and the internal eye's retina is triggered by symbols and also produces a picture (that was earlier somehow combined with the symbol, when the symbol was learned). And the picture, in either case, may be taken as some state of the retina or its analogue, that may be stored.

If now there is a pairing between symbols and pictures, the computer at least has the basis for supplying meanings (namely stored pictures) that are not implicit in, though paired with symbols, that was missing in the previous set-up. And obviously, if all pairings are by recipe, it seems this involves somehow adding recipes to deal with stored pictures.

18. All simple substances or created Monads might be called Entelechies, for they have in them a certain perfection (echousi to enteles); they have a certain self-sufficiency (autarkeia) which makes them the sources of their internal activities and, so to speak, incorporeal automata. (Theod. 87.)

The term "Entelechy" is originally Greek, and was used by Aristotle. "The Shorter Oxford English Dictionary", gives this (minus some Greek and some phonological information):

"Entelechy. (...) Also entelecheia, entelechia. 1603. [...] 1. In Aristotle's use: The condition in which a potentiality has become an actuality. 2.a. That which gives form or perfection to anything. b. The soul, as opp. to the body. 1603. 3. A monad in the system of Leibnitz."

It seems that "That which gives form (..) to anything." begs the fewest questions, and that, thus understood, Leibniz believed that what gives form to composite things are simple things that form or relate them, because these simple things are moved by - something like - desires for ends, where it has to be noted that, for Leibniz, human beings know these fundamental springs of action and formation from their own experiences as desires for ends, while they know the fundamental springs of action and formation of other things, like magnets, by analogy.

One problem this introduces is that it seems to make everything whatsoever that is composite and real and has some form an - embodiment of an - entelechy, and thus it seems to make the very rocks and their molecules and atoms have desires, feelings and perceptions, that may not be as intricate and refined as those of human beings, but which nevertheless are desires, feelings and perceptions all the same, and mental qualities that keep the physical rock together as a rock, much like our own beliefs about ourselves keep us behaving as the person we are. Leibniz's next point is concerned with this point.

19. If we are to give the name of Soul to everything which has perceptions and desires [appetits] in the general sense which I have explained, then all simple substances or created Monads might be called souls; but as feeling [le sentiment] is something more than a bare perception, I think it right that the general name of Monads or Entelechies should suffice for simple substances which have perception only, and that the name of Souls should be given only to those in which perception is more distinct, and is accompanied by memory.

So Leibniz's solution to the problem that, on his intended sense of "entelechy" everything whatsoever that is real, composite, and with some form, must have a Soul in the sense of perceptions and desires, is in effect that more simple apparently inanimate real things do have a simple form of perception, whereas less simple real things have, next to perception, also feeling or at least remembered perceptions.

This seems to me more a verbal concession to the human feeling that rocks have no feelings than a clearly reasoned argument, for one should like to know, if so, what is the 'more' in feeling that distinguishes it from bare perception, and not merely be told that there is more to feeling than to perception. But Leibniz does have some example in mind of what he means, to which we now turn.

20. For we experience in ourselves a condition in which we remember nothing and have no distinguishable perception; as when we fall into a swoon or when we are overcome with a profound dreamless sleep. In this state the soul does not perceptibly differ from a bare Monad; but as this state is not lasting, and the soul comes out of it, the soul is something more than a bare Monad. (Theod. 64.)

That rocks may have perceptions like human beings is in fact argued by the fact that human beings may be alive while lacking feelings, awareness, consciousness, or conscious perceptions, while they do have unconscious perceptions, since they may be woken up by loud noises or made conscious by smelling salts.

Of course, Leibniz's conclusion only holds if the soul is a Monad to begin with. Apart from that, it should be remarked that similar theses, to the effect that human perceptions are refined forms of a perceiving faculty anything whatsoever that exists has, have been defended by other people, varying from Anaximenes to Fechner and Whitehead. It is sometimes called 'pan-psychism' i.e. everything is animated, and there is a useful article on it in the Encyclopedia of Philosophy, Ed. P. Edwards.

Panpsychism is an attempt to bridge the apparent or real gap between the mental and the physical commented upon under (17). It does this by denying that there is anything real without some mental qualities. Apart from the unplausibility of attributing mental qualities to rocks, water and other things without any spontaneous movement, metabolism, or nervous system, one problem panpsychism leaves unsolved is the reason for the huge differences between mental qualities: what does keep a stone from enjoying Beethoven and mathematical puzzles? Or why can a man not be as unperturbed as a rock seems to be when coming into contact with fire or electricity?

21. And it does not follow that in this state the simple substance is without any perception. That, indeed, cannot be, for the reasons already given; for it cannot perish, and it cannot continue to exist without being affected in some way, and this affection is nothing but its perception. But when there is a great multitude of little perceptions, in which there is nothing distinct, one is stunned; as when one turns continuously round in the same way several times in succession, whence comes a giddiness which may make us swoon, and which keeps us from distinguishing anything. Death can for a time put animals into this condition.

This extends what was said in the former point, and may be seen as a restatement of what was said in (14), namely that human beings not only have a conscious mind but also an unconscious mind. As remarked under (20), one argument that such an unconscious minds perceives unconsciously is that one may be woken from a dreamless sleep by a noise.

22. And as every present state of a simple substance is naturally a consequence of its preceding state, in such a way that its present is big with its future; (Theod. 350.)

This adds in fact another attribute to Monads: their states change and develop orderly and systematically, dependent on their preceding states and their own properties as Monads. And this is why one may predict the future and test one's theories. (However, apart from its attribution to Monads a principle like (22), to the effect that what will happen is a consequence of what has happened, seems to be generally assumed in all explanations.)

23. And as, on waking from stupor, we are conscious of our perceptions, we must have had perceptions immediately before we awoke, although we were not at all conscious of them; for one perception can in a natural way come only from another perception, as a motion can in a natural way come only from a motion. (Theod. 401-403.)

This takes up the theme of a remark of mine under (21), with the implied addition that only mental elements can produce mental elements. Leibniz's insertion of "in a natural way" is to take care of the possibility of the Lord (a mental entity) creating motions by willing them and giving their existence His divine fiat.

One problem I have at this point is why such a Lord would go to the trouble of really creating things that move if all that he requires is the creation of experiences of things that move: why add material entities if these in any case are merely hypothetical entities underlying the experiences of whatever experiences? (This is one version of the problem of philosophical idealism: if all there is are ideas made by the Great Idea, then why and whence would there be any material things corresponding to ideas? A Leibnizian answer to this might run as follows, by the way: On philosophical idealism there also are merely possible ideas that say, for example, how things might have been but are not. Thus the real things in philosophical idealism - which are what philosophical materialists call material - are those possibilities God elected to be real, as contrasted with those possibilities He did not elect to be real.)

Another problem is that 'one perception can (..) come only from another perception, as a motion can (...) come only from a motion' seems false to me. It may be true for motion, and it may also be that an idea can only come from an idea (as Berkeley claimed), but it seems to me that a perception is what arises from the contact of a properly perceiving organ and a physical stimulus for that organ - and that physical stimulus itself is no perception (but photons, air-pressures etc.).

24. It thus appears that if we had in our perceptions nothing marked and, so to speak, striking and highly-flavoured, we should always be in a state of stupor. And this is the state in which the bare Monads are.

Leibniz is still, in effect, concerned with the perceptions of rocks, water, and the like: On his theory such things do perceive, but not consciously, similar to our own unconscious perceiving when we are in dreamless sleep. This should be compared to my remarks under (17): Leibniz would have no trouble admitting a computer perceives, only he would presumably have denied it is or can be conscious.

25. We see also that nature has given heightened perceptions to animals, from the care she has taken to provide them with organs, which collect numerous rays of light, or numerous undulations of the air, in order, by uniting them, to make them have greater effect. Something similar to this takes place in smell, in taste and in touch, and perhaps in a number of other senses, which are unknown to us. And I will explain presently how that which takes place in the soul represents what happens in the bodily organs.

Unlike Descartes, Leibniz believed animals have both perceptions and feelings, and something like consciousness. Of course, one - partial - explanation is that animals have evolved and use their perceptions and feelings like humans do: to guide them through a dangerous environment in which they try to survive by making veridical guesses about what is going on in their environment.

It is noteworthy that Leibniz articulates an account of perception in (25) that is difficult to combine consistently with what he said in (23).

26. Memory provides the soul with a kind of consecutiveness, which resembles [imite] reason, but which is to be distinguished from it. Thus we see that when animals have a perception of something which strikes them and of which they have formerly had a similar perception, they are led, by means of representation in their memory, to expect what was combined with the thing in this previous perception, and they come to have feelings similar to those they had on the former occasion. For instance, when a stick is shown to dogs, they remember the pain it has caused them, and howl and run away. (Theod. Discours de la Conformite, &c., ss. 65.)

Leibniz ended his previous point by saying "I will explain presently how that which takes place in the soul represents what happens in the bodily organs.", but his (26) is not so much an explanation of how the mind represents as it is a statement of what happens when the mind represents. (This is not at all the same: the former would explain it; the latter takes such an explanation for granted.)

That some of the fundamental problems lie here follows from my remarks to (17), and thus (26) is somewhat disappointing: it states well-known facts as if by such statement these facts are explained.

27. And the strength of the mental image which impresses and moves them comes either from the magnitude or the number of the preceding perceptions. For often a strong impression produces all at once the same effect as a long-formed habit, or as many and oft-repeated ordinary perceptions.

This may be taken as a statement of a principle of learning, and is in line with what was said in (22). Note that as a general statement of a principle of learning it is quite clear, and seems to suggest that

(1) every impression and mental image has its own value
(2) every impression and mental image is associated with some other memorised impressions or mental images
(3) the composite value of an impression or mental image is the sum of the values of its associated impressions or images, including its own value.
(4) Values once assigned remain as assigned until changed.

(Thus (1) a child might like to steal a plum because it likes the taste of plums but (2) thinks of the punishment it will receive if it is found out it stole the plum so (3) decides not to steal the plum because the pain of the punishment exceeds the pleasure of the plum.)

28. In so far as the concatenation of their perceptions is due to the principle of memory alone, men act like the lower animals, resembling the empirical physicians, whose methods are those of mere practice without theory. Indeed, in three-fourths of our actions we are nothing but empirics. For instance, when we expect that there will be daylight to-morrow, we do so empirically, because it has always so happened until now. It is only the astronomer who thinks it on rational grounds.

That is to say, the principle of learning hinted at in (27), that may be stated in brief terms as the more familiar "similar events have similar consequences", that requires only a consultation of one's memories to see whether the present event is similar to one has experienced before, to find what consequences the event may or will (probably) have, is shared by men and animals.

Incidentally, the reason the principle of learning under (27) may be stated in brief terms as "similar events have similar consequences" is that - on the stated principle of learning - similarity is judged by attributed value, and it is also assumed values once attributed remain the same.

29. But it is the knowledge of necessary and eternal truths that distinguishes us from the mere animals and gives us Reason and the sciences, raising us to the knowledge of ourselves and of God. And it is this in us that is called the rational soul or mind [esprit].

The difference between men and animals is "the knowledge of necessary and eternal truths". These seem to be added to perceived events in a similar way as meanings are added to symbols. Indeed, if we divide the principles of inference human beings use in three classes:

the deductive, where a conclusion is inferred because the conclusion follows from given premises;

the abductive, where premises are inferred because given conclusions follow from these premises; and

 the inductive, where a premise inferred by abduction is judged more (less) probable because it has been found to deductively entail a conclusion that is (not) true,

then we see that what Leibniz calls Reason and considers typically human is especially our abductive and deductive capacities, that enables us to find, formulate, prove and support truths of fact that go beyond any facts given in experience or memory. (Incidentally, it should be noted that the simple inductions based on 'similar conditions, similar consequences' that animals are also capable of also go beyond the given evidence, but without introducing any principle or assumption not given with the evidence. Abductions introduce such principles.)

Also, it seems quite plausible to assume that this human capacity to use Reason and find science is, at least, very much involved with the typically human capacity for language and the use of symbols.

30. It is also through the knowledge of necessary truths, and through their abstract expression, that we rise to acts of reflexion, which make us think of what is called I, and observe that this or that is within us: and thus, thinking of ourselves, we think of being, of substance, of the simple and the compound, of the immaterial, and of God Himself, conceiving that what is limited in us is in Him without limits. And these acts of reflexion furnish the chief objects of our reasonings. (Theod. Pref. [E. 469; G. vi. 27].)

First, it seems "acts of reflexion" are also required to establish scientific truths, even if these are merely contingent and not necessary.

Second, in either case, when we do know something through the faculty of reason it seems to be of a symbolic nature: what we have achieved in such a case is some inner, conscious representation of some fact, that may itself be necessary or contingent.

Third, Leibniz has not explained what necessary truths are, and not countered the possibility that what seem to be necessary truths are, in fact, merely conventions - statements of rules and relations that are set up by convention and in such a way that there is no counter-example to them, just like it is a conventional but no natural necessity that if we call her a spinster we also call her not married, simply because we have agreed to used the words "spinster" and "married" thus and not otherwise.

And fourth, if my remarks on abduction under (30) make sense, then, in those terms, Leibniz proposed that the concept of self is reached by abduction - assumed as an explanation for given facts, but going beyond the given facts.

31. Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; (Theod. 44, 169.)

This is somewhat compressed and confusing, for it neither defines what a contradiction is, nor does it distinguish between truth and consistency. Since our reasonings are, at least, normally capable of being expressed by language, we may define a contradiction as the conjunction of a statement and its negation. However, the mere absence of contradictions in a piece of prose - which is what makes that piece of prose consistent - does not imply that, therefore, the prose relates the truth, for it may be a non-contradictory fairy-story, or a scientific theory that is not known to be contradictory nor known to be true.

32. And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us. (Theod. 44, 196.)

The principle of sufficient reason has a chequered history, and is also somewhat unclear, especially since Leibniz sometimes confused the stated principle with another one like it, that requires explanations of natural facts in terms of ends rather than causes (and this is how the term "reason" is often used in everyday language: The 'reason' one does such and such is that one believes doing so will bring one's closer to some desired end one has).

Personally, I like to approach the principle of sufficient reason through the concept of abduction, as defined under (29). Using this, we can say that we have no explanation of a statement of fact without an abduction of premises from which that statement of fact follows. This is true, but not quite the same as the principle of sufficient reason, that may be construed as adding to this that every statement of fact in fact has a true explanation, which in one reading implies that there can be no such thing as real chance. I believe there is real chance, and besides and apart from that I believe that some true statement of fact have as a true explanation that they are coincidences (in the sense this term was used by Sadi Carnot, which is that of two things that were hitherto unrelated are coming together).

It should also be remarked that if one speaks in terms of abductions rather than sufficient reasons there is less of a temptation to regard the abductions as necessary: an abduction is a possible explanation, but not at all necessarily the only one or a correct one even if it does deductively entail what it was set up to explain.

33. There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, its reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary. (Theod. 170, 174, 189, 280-282, 367. Abrege, Object. 3.)

This concerns an important distinction of Leibniz. An important problem with it was mentioned under (30): how are necessary truths analysed? Note that the analysis of necessary truths as depending on some convention does provide a reason which is considerably clearer than the sort of reason Leibniz had in mind for his necessary truths: rather than statements of the real essences of things, they would, if conventional, be statements that follow from symbolic conventions, that are always to be followed in a given argument, but not by any natural necessity, but by mere agreement to the convention.

Thus, if one agrees that (i) all proposition are to have the attributes true or false (ii) no proposition has both attributions at the same time, one has the beginning of a proof by conventions that any proposition is true or false - not because that is the nature of things, but because that is how we have set up our conventional agreements to talk sensibly about things.

I am not claiming that this always results in a plausible analysis of what might be meant by "necessary truths" (since making a statement of naturally existing regularity hold by some human convention does not at all explain why the naturally existing regularity does exist) but I do claim that before ascribing necessary truths to matters of fact one should have provided some analysis how facts can be necessarily true as different from statements of these facts, the truth of which may depend on nothing but convention. (For a statement by a logician of this sort of theory, see Quine's "Truth by Convention" in his "Selected Logic Papers". And for a more extensive statement by a mathematician and philosopher see Poincaré's "Science and hypothesis".)

34. It is thus that in Mathematics speculative Theorems and practical Canons are reduced by analysis to Definitions, Axioms and Postulates.

Indeed, but here the same remarks apply, with this addition that it seems most though not all mathematicians are realists about the provably true statements of mathematics: they believe such statements are not merely true by convention, but do represent some real domain, that really is as the mathematical truths about it say it is.

The fundamental reason most mathematicians are realists seems to be that they assume (i) the statements of mathematics are true of something (numbers, figures, sets, curves etc.) (ii) the sense of 'true' in (i) is understood as correspondence: a statement is true in a domain of things if and only if what the statement says is a fact in the domain of things (and false in the domain of things if and only if what the statement says is not a fact in the domain of things).

An intermediate position would allow fantastic domains, whether of Greek gods (in the domain of the legends about the Greek gods it is true Zeus married Hera) or of differential manifolds, continuous groups of transformations, or of real numbers.

35. In short, there are simple ideas, of which no definition can be given; there are also axioms and postulates, in a word, primary principles, which cannot be proved, and indeed have no need of proof; and these are identical propositions, whose opposite involves an express contradiction. (Theod. 36, 37, 44, 45, 49, 52, 121-122, 337, 340-344.)

This is what one would assume when one reads a text like that of Euclid's "Elements", which indeed is set up on the basis of similar assumptions.

One problem I have with this is that it is unexceptional as a description of how one sets up formal arguments in a formal language: Indeed, one must then assume certain terms as primitive; one must assume certain axioms involving these terms; and one must assume certain principles of inference to obtain conclusions form the axioms - but then all of this concerns the linguistic presentation of reasoning, and need not be true nor carried over to the domain the reasoning is about, nor to the ideas about the domain the linguistic presentation expresses.

36. But there must also be a sufficient reason for contingent truths or truths of fact, that is to say, for the sequence or connexion of the things which are dispersed throughout the universe of created beings, in which the analyzing into particular reasons might go on into endless detail, because of the immense variety of things in nature and the infinite division of bodies. There is an infinity of present and past forms and motions which go to make up the efficient cause of my present writing; and there is an infinity of minute tendencies and dispositions of my soul, which go to make its final cause.

That "there must also be a sufficient reason for contingent truths or truths of fact" follows from (32) if (32) is true, in the sense Leibniz intended it. But if the principle is reconstructed along abductive lines, as I did under (32), it seems that while each and every fact may be somehow explained, this does not mean that each and every explanation, even if true, is necessary: it may well be that the true and sufficient reason for a fact is a mere coincidence or chance event.

Next, Leibniz was much impressed with the infinitely small and the infinitely large, and so am I, but it seems to me as if human beings may only hope to explain such things as can be characterised adequately by finitely many attributes, and by much abstraction, schematisation and idealisation of what really goes on.

Hence, it seems to me that while one can grant that in some sense there is infinite (or at least incalculable or unbounded) variety in reality, one important reason human beings may understand such a reality with infinite variety is that these varieties come in finitely many kinds, which are related amongst each other again in finitely many ways. (The deeper theme underlying these remarks is the notion of compactness, which essentially comes down to the notion that an infinite class is compact if each element of it belongs to some finite class of classes.)

37. And as all this detail again involves other prior or more detailed contingent things, each of which still needs a similar analysis to yield its reason, we are no further forward: and the sufficient or final reason must be outside of the sequence or series of particular contingent things, however infinite this series may be.

This is preparatory to a deduction of God's existence, in the next point. The main step is "the sufficient or final reason must be outside of the sequence or series of particular contingent things". Now it may be granted that when we explain something we generally explain it by reference to and in terms of something else, which we often call the cause of what we explained, and it may also be granted that such a cause may be explained again in terms of yet another cause, and so on. But this constitutes no proof or evidence to the effect that there must be some sufficient or final reason outside such a sequence. Instead, it seems more reasonable to say: we can only explain given things by relating them to other things, so ultimate explanations of given things must be by relating them to all other things (which is difficult or impossible for human beings - and not because they cannot conceive it linguistically, but because they cannot imagine such a conception non-linguistically, just as they can easily think of 5 billion people using languaghe, but do not have the time available to count them all, or the mental space to remember or imagine them all distinctly and individually.)

38. Thus the final reason of things must be in a necessary substance, in which the variety of particular changes exists only eminently, as in its source; and this substance we call God. (Theod. 7.)

Why "the final reason of things must be in a necessary substance" escapes me, and why we would call it "God" rather than "Nature" or "all of Nature" or "all there is" also escapes me. (It seems Leibniz concluded a necessary substance by stepping outside the series of causes of causes, as criticised under (37), and it seems he called it "God" because he believed such a necessary substance to be ideal rather than material, but I find these reasons not at all conclusive or plausible.)

And in any case, it seems there simply are no ultimate explanations available to human beings (if we disregard the claims of followers of revealed religions, who are much more probably mentally disturbed than divinely enlightened), in either sense: not in terms of divine plans or desires, and not in terms of the totality of Nature, for either - if real - is too comprehensive to be fully comprehended by human beings. (The reader who believes he or she has an all-comprehensive mind of course also knows that there are about 3.3 * 10^22 molecules in one cubic centimetre of water, and has tracked all their possible paths and relations.)

39. Now as this substance is a sufficient reason of all this variety of particulars, which are also connected together throughout; there is only one God, and this God is sufficient.

It is easier to understand why there would be one Nature than why there would be one God, especially if Nature is physical, and a God non-physical. For there can be only one totality of all things, but, if there is any maker of all things, there also may be many makers of all things, and makers of makers of things, and so on. (Too few people who believe God is the maker of all things consider the question that, if so, who made God, and why, if they answer "He himself or He existed always", the same could not be said with much more plausibility of Nature, which believers and non-believers both postulate as what has to be somehow explained, in outline if not in detail.)

40. We may also hold that this supreme substance, which is unique, universal and necessary, nothing outside of it being independent of it,- this substance, which is a pure sequence of possible being, must be illimitable and must contain as much reality as is possible.

Again, this sort of argument seems much more applicable to the totality of Nature than to a divinity. This holds especially in view of the last part, that the supreme substance "must contain as much reality as is possible". Leibniz's reason to include this was his sympathy with Scholastic arguments for God's existence, that attribute perfection to God, and derive from that attribute that God must be perfectly comprehensive and thus contain all there is, and that God must exist, on the rather puzzling ground that it is more perfect to exist than not to exist (as if a world with Hitler or Stalin is more perfect than what would be otherwise the same world but without Hitler or Stalin, e.g. because some benevolent creature smothered them while they were babies, or took care they were aborted before birth.)

To second part: Monadology - part B
To the appendix: A simple logic of parts
To the index: Sections and subjects of the Monadology
To Leibniz's Preface to the Nouveaux Essays
To Remark on Robert Latta's Translation

Continued: Monadology - part B

Maarten Maartensz       
last update: Sep 11 2006