Lecture Supplement on Leibniz’ Discourse and Monadology

     Copyright © 2012 Bruce W. Hauptli

     Click here to go directly to Monadology section.

1. Discourse On Metaphysics [post., composed in 1686, first published in 1846]:

In their introduction to their translation of the work, Daniel Garber and Roger Ariew note that:

in February 1686, Leibniz wrote a letter to Landgrave Ernst von Haessen-Reifels, saying: "being somewhere having nothing to do for a few days, I have lately composed a short discourse on metaphysics...."  The "short discourse" was not published or even circulated in Leibniz's lifetime, to the best of our knowledge; at best Leibniz seems to have circulated summaries of its sections to...Antoine Arnauld, sparking a celebrated exchange of views....But the work that resulted from these few days of leisure is generally regarded as one of the most important statements of Leibniz's mature thought, a summary of his metaphysical system as it appeared to him in that very productive decade.1 
The manuscript and copies had no title, and the Discourse has become known by its name from the allusion to it in the above citation.

     Bertrand Russell echoes the above praise in his A Critical Exposition of the Philosophy of Leibniz, saying that the Discourse threw a flood of light on Leibniz' philosophical theories for him.2  In their "Introduction" to their translation of the work, Peter Lucas and Leslie Grint maintain that:

there is no major element in the Discourse which cannot be found singly in earlier writings, except for the one idea of expression or representation—that each substance expresses God and the universe from a point of view.  This is Leibniz's alternative picture to the picture which was then and still is common of a universe consisting of objects and animate beings which have their separate individual existences but act and are acted on in a mechanical or quasi-mechanical system.  This new picture or metaphor of the universe as a system of representation provided the impulse which enabled Leibniz to synthesise his attitude to life, his religion and his various separate philosophical principles into the metaphysical system which is contained in the Discourse.3 
They also note that:
one of the political purposes for which Leibniz hoped to use the metaphysics of the Discourse was as the basis of a universal rational theology which would make possible the re-union of the churches.4 
According to them, the text may be divided into six sections:5  1. God (sections 1-7)

2. Created Substances (sections 8-16)

3. Force and final causes (sections 17-22)

4. The human understanding (sections 23-29)

5. The human will (sections 30-31)

6. Piety and religion (sections 32-37).6 

I will be following their division, and paying particular attention to the sections which I have "stared" below. 

(A). On God (sections 1-7):

1. On divine perfection, and that God does everything in the most desirable way. 
-God is an absolutely perfect being, and "...possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking...." 

*2. Against those who claim that there is no goodness in God's works, or that the rules of goodness and beauty are arbitrary:

-"...all acts of will presuppose a reason for willing and...this reason is naturally prior to the act of will." 
--Here we have a clear indication of Leibniz' rationalism: acts of willing presuppose reasons (which are prior to the will), and, thus, everything which happens has a reason why it happensWe also need to pause and contrast what differences this betokens in contrast to Spinoza’s theory! 
*3. Against those who believe that God might have made things better:
-"...to act with less perfection than one could have is to act imperfectly." 

-"...[we have] only an inadequate knowledge ...[of] the general harmony of the universe and of the hidden reasons for God's conduct." 

4. That the love of God requires our complete satisfaction and acquiescence with respect to what he has done without our being quietists as a result.

*5. What the rules of perfection of divine conduct consist in, and that the simplicity of the ways is in balance with the richness of the effects:

-"...God does nothing for the best that can harm those who love him.  But to know in detail the reasons that could have moved him to choose this order of the universe—to allow sins, to dispense his saving grace in a certain way—surpasses the power of a finite mind, especially when it has not yet attained the enjoyment of the vision of God." 

-"...the most perfect of all beings, those that occupy the least volume, that is, those that least interfere with one another, are minds, whose perfections consist in their virtues.  That is why we mustn't doubt that the happiness of minds is the principal aim of God and that he puts this into practice to the extent that the general harmony permits it." 

--Note that minds not having "volume" is one and the same as lacking "extension"--and for him all substances must be non-extended (otherwise they would be divisible, and not substances).  The special role for minds, which is hinted at here, does not translate, in his thought, to the only substances being minds--that would lead to idealism, and that is not yet on the horizon of the thought of the period. 

*6. God does nothing which is not orderly and it is not even possible to imagine events that are not regular:
-"...what passes for extraordinary [events] is extraordinary only with respect to some particular order established among creatures; for everything is in conformity with respect to the universal order." 
--That is, if there were "miracles," they would be violations of the "universal order," and Leibniz' thoroughgoing rationalism will not allow for this. 
-"...God has chosen the most perfect world, that is, the one which is at the same time the simplest in hypotheses and the richest in phenomena...."7 
--In his "Perfection and Happiness in the Best Possible World," David Blumenfeld discusses different possible meanings of "perfection" here, and maintains that: "throughout his career, but especially in his maturity, [Leibniz] insists on the unsurpassable richness of things; in the Discourse, for example, he says that the world is "the richest in phenomena"; in the Principles of Nature and Grace he declares that it has "the greatest variety together with the greatest order"; and in the Monadology he asserts flatly that it has "the greatest variety possible."  All of this indicates that God is not required to trade-off variety in his selection of the best possible world."8  Blumenfeld further asserts that "in light of all of this, we must attribute to Leibniz a more radical position than the ones we have considered.  Ultimately, he thinks the best world contains the most diverse phenomena and the simplest laws of nature; indeed, he believes that the greatest number and variety of things is unobtainable apart from such laws.  I shall dub this doctrine "the harmony of variety and simplicity."9 

7. That miracles conform to the general order, even though they may be contrary to the subordinate maxims; and about what God wills or permits by a general or particular volition:

-"...God does everything following his most general will, which is in conformity with the most perfect order he has chosen, but we can also say that he has particular volitions which are exceptions to these aforementioned subordinate maxims.  For the most general of God's laws, the one that rules the whole course of the universe, is without exception." 
(B) On Created Substances (sections 8-16):
*8. To distinguish the actions of God from those of creatures, we explain the notion of an individual [created] substance:
-"...all true predication has some basis in the nature of things and...when a proposition is not an identity, that is, when the predicate is not explicitly contained in the subject, it must be contained in it virtually....Thus the subject term must always contain the predicate term, so that one who understands perfectly the notion of the subject would also know that the predicate belongs to it." 

--That is, truths about created substances (true subject-predicate statements) all have the form of identities (either explicit or implicit). 

--"...God, seeing Alexander's individual notion or haecceity,10 sees in it at the same time the basis and reason for all the predicates which can be said truly of him...he even knows a priori (and not by experience) whether he died a natural death or whether he was poisoned....from all time in Alexander's soul there are vestiges of everything that has happened to him and marks of everything that will happen to him and even traces of everything that happens in the universe, even though God alone could recognize them all." 

*9. That each singular substance expresses the whole universe in its own way, and that all its events, together with all their circumstances and the whole sequence of external things, are included in its notion:
-"...it is not true that two substances can resemble each other completely and differ only in number...." 
--This is his Principle of the Identity of Indiscernibles.

-"It also follows that a substance can begin only by creation and end only by annihilation; that a substance is not divisible into two; that one substance cannot be constructed from two; and that thus the number of substances does not naturally increase or decrease, though they are often transformed. 

Moreover, every substance is like a complete world and like a mirror of God or of the whole universe, which each one expresses in its own way, somewhat as the same city is variously represented depending upon the different positions from which it is viewed." 

*10. That the belief in substantial forms11 has some basis, but that these forms do not change anything in the phenomena and must not be used to explain particular effects:

-While this notion is much decried "today," and while it is not useful in physics, it is necessary in metaphysics. 

-See the Appendix below for a further discussion of the traditional "doctrine of substantial forms." 

11. That the thoughts of the theologians and philosophers who are called scholastics are not entirely to be disdained. 

12. That the notions involved in extension contain something imaginary and cannot constitute the substance of body. 

*13. Since the individual notion of each person includes once and for all everything that will ever happen to him, one sees in it the a priori proofs of the truth of each event, or why one happened rather than another.  But these truths, however certain, are nevertheless contingent, being based on the free will of god or of his creatures, whose choice always has its reasons, which incline without necessitating:

-"...it seems that this would eliminate the difference between contingent and necessary truths, that there would be no place for human freedom, and an absolute fatalism would rule all our actions as well as all the other events of the world.  To this I reply that we must distinguish between what is certain and what is necessary.  Everyone grants that future contingents are certain, since God foresees them, but we don't concede that they are necessary on that account.  But (someone will say) if a conclusion can be deduced infallibly from a definition or notion, it is necessary.  And it is true that we are maintaining that everything that must happen to a person is already contained virtually in his nature or notion, just as the properties of a circle are contained in its definition; thus the difficulty still remains.  To address it firmly, I assert that connections or following...is of two kinds.  The one whose contrary implies a contradiction is absolutely necessary; this deduction occurs in the eternal truths, for example, the truths of geometry.  The other is necessary only ex hypostesi and, so to speak, accidentally, but it is contingent in itself, since its contrary does not imply a contradiction.  And this connection is based not purely on ideas and God's simple understanding, but on his free decrees and on the sequence of the universe." 
--"...I say that whatever happens in conformity with these predeterminations...is certain but not necessary, and if one were to do the contrary, he would not be doing something impossible in itself, even though it would be impossible [ex hypostesi] for this to happen." 

--"...nothing is necessary whose contrary is possible." 

-Leibniz sent the section headings of the Discourse to Antoine Arnauld through an intermediary (Count Ernst von Hessen-Rheinfels).   Arnauld was a French theologian, philosopher, and skeptic who was well-known for his criticisms of Descartes, his co-authorship of La logique, ou l'art de penser [1662], and his correspondence with many figures of the day.  Arnauld replied to Leibniz' initial letter with a critique of this section which contended that it implies a rigid determinism which would not be accepted by the Catholic Church, and the ensuing correspondence is long enough to constitute a book-length work.12  Arnauld's claim that the Catholic Church would not accept Leibniz' point of view here should be viewed within the context of Arnauld's Jansenism—on January 1, 1656 he was stripped of his doctorate in theology from the Sorbonne for his refusal to recant the Jansenist doctrines, and his work at Port-Royal (he was a good friend of Blaise Pascal).  The correspondence is frequently appealed to by those studying Leibniz, as he there makes clear(er) some of his most basic ideas and distinctions.  The following passages from Leibniz in this correspondence are, I believe, important and illuminating:
--...always in every affirmative proposition...the concept of the predicate is comprised...in that of the subject.  Either the predicate is in the subject or else I do not know what truth is.13 
---Note that for Descartes, truth seems to be a matter of correspondence between an idea and that which the idea represents; while, for Spinoza, truth appears to be a matter of coherence (of propositions with each other). 

--..."there must always be some foundation for the connection of the terms of a proposition, and this is found in their concepts."  This is my fundamental principle, which I think all philosophers ought to agree to, and one of whose corollaries is that commonly accepted axiom: that noting happens without a reason which can be given why the thing turned out so rather than otherwise.  This reason, however, often produces its effects without necessitation.14 

--It is therefore much more reasonable and more worthy of God to suppose that he has created the machinery of the world in such a fashion from the very start, that without doing violence at every moment to the two great laws of nature, that of force and that of direction, but rather by following them exactly (except in the case of miracles) it so comes about that the internal springs of bodies are ready to act of themselves, as they should, at the very moment with the soul has a conforming desire or thought.  The soul, in turn, has had this desire or thought only conformably to preceding states of the body and thus the union of the soul with the machinery of the body and with the parts which compose it, and the action of the one upon the other consists only in this concomitance, which betokens the wonderful wisdom of the Creator much more than any other hypothesis.  It cannot be denied that this at least is possible, and that God is a sufficiently great workman to be able to carry it out; therefore, it can easily be decided that this hypothesis is the most probable, being the simplest and most intelligible and at once avoiding all difficulties...15 

*14. God produces various substances according to the different views he has of the universe, and through God's intervention the proper nature of each substance brings it about that what happens to one corresponds with what happens to all the others, without their acting upon one another directly:
-"...God...turns on all sides and in all ways the general system of phenomena which he finds it good to produce in order to manifest his glory, and he views all the faces of the world in all ways possible, since there is no relation that escapes his omniscience." 

-"...perceptions or expressions of all substances mutually correspond in such a way that each one, carefully following certain reasons or laws it has observed, coincides with others doing the same...." 

-"And God alone (from whom all individuals emanate continually and who sees the universe not only as they see it but also entirely differently from all of them) is the cause of this correspondence of their phenomena and makes that which is particular to one of them public to all of them...." 

-"...nothing can happen to us except thoughts and perceptions, and all our future thoughts and perceptions are merely consequences, though contingent, of our preceding thoughts and perceptions, in such a way that, if I were capable of considering distinctly everything that happens or appears to me at this time, I could see in it everything that will ever happen or appear to me." 

15. The action of one finite substance on another consists only in the increase of degree of its expression together with the diminution of the expression of the other, insofar as God requires them to accommodate themselves to one another. 

16. God's extraordinary concourse is included in that which our essence expresses, for this expression extends to everything.  But this concourse surpasses the powers of our nature or of our distinct expression, which is finite and follows certain maxims. 

(C) On Force and Final Causes (sections 17-22):

I will not be lecturing on this section of the Discourse. In their "Introduction," Lucas and Gint maintain that this section discusses the notion of force and:

contains an argument with the Cartesians which may be found obscure and is expressed in words which had plainly not yet become a stable terminology.... 

There is a law of conservation in dynamics to which Leibniz wishes to allude as an example of a metaphysically grounded law of nature, in order to support his argument that natural philosophy [that is science] requires in scholastic terms, substantial forms, or in his own later terms, monads.  The doctrine of the Cartesians is that `quality of motion' is conserved, defined in Leibniz' terms as `speed multiplied by size', or in modern terms as velocity multiplied by mass, namely momentum.  `Quality of motion' is taken by the Cartesians to be equivalent to `motive force', in modern terms energy; it is this equivalence that Leibniz wishes to refute. 

Leibniz's thesis is that `force' (energy) is conserved, and is not identical with `quality of motion' (momentum).  He establishes this from the example of falling bodies.  He assumes with the Cartesians that in the case of bodies being lifted, equal `forces' will be required for equal products of `weight' and `height'; or in modern terms for equal work done....16 

17. An example of a subordinate maxim or law of nature, in which it is shown, against the Cartesians and many others, that God always conserves the same force but not the same quantity of motion. 

18. The distinction between force and quantity of motion is important, among other reasons, for judging that one must have recourse to metaphysical considerations distinct from extension in order to explain the phenomena of bodies. 

19. The unity of final causes in physics:

-"...God always intends the best and most perfect." 
20. A noteworthy passage by Socrates in Plato against philosophers who are overly materialistic. 

21. If mechanical rules depend only on geometry without metaphysics, the phenomena would be entirely different. 

22. Reconciliation of two ways of explaining things, by final causes and by efficient causes, in order to satisfy both those who explain nature mechanically and those who have recourse to incorporeal natures. 

(D) On the Human Understanding (sections 23-29):
*23. To return to immaterial substances, we explain how God acts on the understanding of minds and whether we always have the idea of that about which we think:
-"...God exists necessarily, if he is possible.  It is indeed the prerogative of divine nature, one that surpasses all others, that divine nature needs only its possibility or essence in order actually to exist, and it is precisely this that is called ens a se." 

*24. What is clear or obscure, distinct or confused, adequate or intuitive or suppositive knowledge; nominal, real, causal, and essential definition:

-"...we sometimes know something clearly, without being in any doubt whether a poem or a picture is done well or badly....But when I can explain the marks which I have, the knowledge is called distinct." 

-"...distinct knowledge has degrees....But when everything that enters into a distinct definition or distinct knowledge is known distinctly, down to primitive notions, I call this knowledge adequate.  And when my mind understands all the primitive ingredients of a notion at once and distinctly, it has intuitive knowledge of it; this is extremely rare, since the greater part of human knowledge is only confused or suppositive." 

-"It is also good to distinguish nominal and real definitions.  I call a definition nominal when one can still doubt whether the notion defined is possible...." 

-"...there are...great differences between the kinds of real definitions.  For when possibility is proved only by experience, as in the definition of quicksilver,16a whose possibility we know because we know that there actually is such a body which is an extremely heavy but rather volatile fluid, the definition is merely real and nothing more; but when the proof of the possibility is a priori, the definition is both real and causal, as when it contains the possible generation of the thing.  And when the definition pushes the analysis back to the primitive notions, without assuming anything requiring an a priori proof of its possibility, it is perfect or essential." 

25. In what case our knowledge is joined to the contemplation of the idea. 

26. That we have all ideas in us; and of Plato's doctrine of Reminiscence. 

27. How our soul can be compared to empty tablets and how our notions come from the senses. 

*28. God alone is the immediate object of our perceptions, which exist outside of us, and he alone is our light:

-"Now, in rigorous metaphysical truth, there is no external cause acting on us except God alone, and he alone communicates himself to us immediately in virtue of our continual dependence.  From this it follows that there is no other external object that touches our soul and immediately excites our perception." 

29. Yet we think immediately through our own ideas and not through those of God. 

(E) On The Human Will (sections 30-31):
*30. How God inclines our soul without necessitating it; that we must not ask why Judas sins but only why Judas the sinner is admitted to existence in preference to some other possible persons.  On original imperfection before sin, and the degrees of grace:
-"But someone else will say, why is it that this man will assuredly commit this sin?  The reply is easy: otherwise he would not be this man.   For God sees from all time that there will be a certain Judas whose notion or idea (which God has) contains this free and future action.   Therefore only this question remains, why does such a Judas, the traitor, who is merely possible in God's idea, actually exist?  But no reply to this question is to be expected on earth, except that, in general, one must say that God foresaw, it must be that this sin is paid back with interest in the universe, that God will derive a greater good from it, and that it will be found that, in sum, the sequence of things in which the existence of that sinner is included is the most perfect among all possible sequences." 

-"Yet one sees clearly that God is not the cause of evil. For not only did original sin take possession of the soul after the innocence of men had been lost, but even before this, there was an original imperfection or limitation connatural to all creatures, which makes them libel to sin or capable of error....the root of evil is in nothingness, that is to say, in the privation or limitation of creatures, which God graciously remedies by the degree of perfection it pleases him to give." 

31. On the motives of election, on faith foreseen, on middle knowledge, on the absolute decree and that it all reduces to the reason why God has chosen for existence such a possible person whose notion includes just such a sequence of graces and free acts; this puts an end to all difficulties at once:
-"...with respect to this single question, why it pleased God to choose him from among so many other possible persons, one would have to be very unreasonable not to be content with the general reasons we have given...." 
(F) On Piety and Religion (sections 32-37):
*32. The utility of these principles in the matters of piety and religion:  
-The Principle of Perfection when combined with "...the principle that the notion of a substance contains all its events with all their circumstances, far from harming, serve to confirm religion, to dispel enormous difficulties, to enflame souls with a divine love, and to elevate minds to the knowledge of incorporeal substances, much more than hypotheses we have seen until now.
--Cf., Lady Marsham's (Damais Cudworth) June 3, 1704 letter to Leibniz.  She maintains that: "...the advantages proposed from this hypothesis are very desirable.  But it appears not yet to me that this is more than a hypothesis; for as God's ways are not limited by our conceptions.  The unintelligibleness or inconceivableness by us of any body but one, does not methinks, much induce a belief of that, being the way which God has chosen to make use of."17  She rightly inquires why we should accept such "hypotheses" as true, however desirable they may be.  In this and other letters to him, she raises a number of central criticisms of Leibniz' theories. 

--Here it is profitable to consider the contemporary epistemological orientation which recommends that we employ the principle of "inference to the best explanation," and how it manifests itself in Leibniz' thought (and, of how it should be the principle of "inference to the best available explanation"). 

33. Explanation of the union of soul and body, a matter which has been considered as inexplicable or miraculous, and on the origin of confused perceptions:
-"...the very idea or essence of the soul carries with it the fact that all its appearances and perceptions must arise spontaneously from its own nature and precisely in such a way that they correspond more particularly and more perfectly to what happens in the body assigned to it, because the soul expresses the state of the universe in some way and for some time, according to the relation other bodies have to its own body.  This also allows us to know how our body belongs to us, without, however, being attached to our essence." 

34. On the differences between minds and other substances, souls or substantial forms, and that the immortality required includes memory:

-Bodies "...express the whole universe, although more imperfectly than minds do.  But the principal difference is that they do not know what they are nor what they do, and consequently, since they do not reflect on themselves, they cannot discover necessary and universal truths.  It is also because they lack reflection about themselves that they have no moral qualities.  As a result, though they may pass through a thousand transformations, like those we see when a caterpillar changes into a butterfly, yet from the moral or practical point of view, the result is as if they had perished...." 

35. The excellence of minds and that God considers them preferable to other creatures.  That minds express God rather than the world, but that the other substances express the world rather than God:

-"...there is no reason to doubt that the substances which express the universe with the knowledge of what they are doing and which are capable of knowing great truths about God and the universe, express it incomparably better than do those natures, which are either brutish and incapable of knowing truths or completely destitute of sensation and knowledge." 

-"Since God himself is the greatest and wisest of all minds, it is easy for him to judge that the beings with whom he can, so to speak, enter into conversation, and even into society—by communicating to them his views and will in a particular matter and in such a way that they can know and love their benefactor—must be infinitely nearer to him than all other things, which can only pass for the instructions of minds." 

36. God is the monarch of the most perfect republic, composed of all minds, and the happiness of this City of God is his principal purpose. 

37. Jesus Christ has revealed to men the mystery and admirable laws of the kingdom of heaven and the greatness of the supreme happiness that God prepares for those who love him. 

(end)

2. The Principles of Philosophy, or The Monadology [post, 1714]:

The former title is probably the one Leibniz intended, but the work is generally known by the latter title, which it received from an 18th century editor.  I think the work may be broken down into the following parts:

(A) 1-9 Simple substances

(B) 10-18 Change

(C) 19-48 Souls, Eternal Truths, and God

(D) 49-60 Created things [Creatures] and their regulation

(E) 61-81 Composites.

(F) 82-90 Morality

I will be paying particular attention to the "stared" sections. 

(A) 1-9: Simple Substances:

*1. The monad is nothing else than a simple substance. 

*2. There must be simple substances because there are composites; for a composite is nothing else than a collection or aggregatum of simple substances. 

-Note the "oddity" of this beginning point.  Since he is a rationalist, one could assume that he wouldn't want to offer such an a posteriori rationale!   Contrast his "beginning point" with Descartes' and Spinoza's. 

*3. Now, where there are no constituent parts there is possible neither extension, nor form, nor divisibility.  These monads are the true Atoms of nature, and, in fact, the Elements of things. 

-Here, we are back on the rationalist track, the claim is a deductive consequence of the first proposition above. 

4. There is no way conceivable by which a simple substance can perish through natural means. 

5. Nor can monads come into being through natural means. 

6. The existence of monads can begin or end only all at once.  Composites, however, begin or end gradually. 

*7. There is also no way of explaining how a monad can be altered or changed in its inner being by any other created thing, since there is no possibility of transposition within it, nor can we conceive of any internal movement which can be produced, directed, increased, or diminished there within the substance, such as can take place in the case of composites where a change can occur among the parts.  Monads have no windows! 

8. Nonetheless, monads must have some qualities, otherwise they would not even be existences.  They must differ in qualities otherwise they would all be alike. 

*9. Principle of the Identity of Indiscernibles.

(B) 10-18: Change:

*10. "I also take it for granted that every created being, and consequently the created monad, is subject to change, and even that this change is continual in each thing." 
-Note the "assumption" here!  We have a "new" topic here.  Is this "given" a priori or a posteriori?  Note again the difference between his "beginning points" and those of Descartes and Spinoza. 

-In his "Rorarius," Pierre Bayle maintains that: "it is clearly conceivable that a simple being will always act uniformly if not hindered by some external cause.  If it were composed of several parts, like a machine, it would act diversely because the particular activity of each piece might change the course of that of the others at any moment.  But in a unified substance, where can you find the cause of the change of its operation?"18 

*11. The natural changes of the monad come from an internal principle, because an external cause can have no influence upon its inner being. 
-Here, again, we are "on the rationalist track!" Deductive consequences of what was said above. 

*12. "...there must be a diversity in that which changes, which produces...the specification and variety of simple substances." 

*13. Since every natural change takes place by degrees, there must something which changes and something which remains unchanged, and consequently there must be in the simple substance a plurality of conditions and relations, even though it has no parts. 

*14. The changes are called perceptions.  They are to be distinguished from apperceptions, or consciousness. 

*15. Appetition is the internal principle of change. 

16. We all experience a multitude within the simple substance which is ourselves. 

*17. Perception is inexplicable by mechanical causes.  Imagine a machine large enough to go inside—we would never see anything resembling perception.  "Furthermore, this is all one can find in the simple substance—that is, perceptions and their changes." 

(C) 19-48: Souls, Eternal Truths, and God:
*19. The general name of monad or entelechy will be used for simple substances which have only perception, while he reserves the term "soul" for those whose perception is more distinct and is accompanied by memory

*20-29. The distinctions between simple substances and souls is marked out by the sorts of characteristics which the Monads in question have.  The simplest substances will have limited perceptions and lack memory altogether.  Some souls will have memory at times and lack it at other times (for example, dreams).  Each monad's present is big with its future. 

*29. "But the knowledge of eternal and necessary truths is what distinguishes us from mere animals and gives us reason and the sciences, by raising us to a knowledge of ourselves and of God"—we are rational souls

30. Reflective acts—knowledge of necessary truths. 

*31-32. The basis of our reasoning—the principles of contradiction and sufficient reason:

*33. Truths of reason:                     Truths of fact:

necessary,                             contingent,

opposites are impossible.      opposites are possible

*34-35. Axioms and postulates: "...primitive principles, which cannot be proved and which no need of proof....the identical propositions19 whose opposites involve an explicit contradiction." 

*Sections 36-39: a posteriori proof of the deity's existence:

36. There must be a sufficient reason for contingent truths of fact. 

37. This sufficient or ultimate reason must be outside the sequence or series of this multiplicity of contingencies." 

38. "...that is why the ultimate reason for things must be in a necessary substance in which the detail of the diversity of changes is only eminent, as in its source.  This is what we call God." 

39. "Since this substance is a sufficient reason for all this diversity, which is utterly interconnected, there is only one God, and this God is sufficient

-Again, note the difference here between Leibniz and Spinoza—the latter "proves" what the former asserts!   Cf., sections 44-45 below! 

*Sections 40-45: a priori proof of the deity:

40. God is unlimited. 

41. Thus it follows that God is absolutely perfect. 

42. "...created things derive their perfections from God's influence, but...they derive their imperfections from their own nature, which is incapable of being without limits." 

-Cf., his Theodicy!20 

*43. In God is found not only the source of existences, but also that of essences. "...God's understanding is the realm of eternal truths or that of the ideas upon which they depend; without him there would be nothing real in possibilities, and not only would nothing exist, but also nothing would be possible." 

-In combination with the following passage, this passage is important, and it is far too easy to overlook what it says.  For Leibniz, and the other Rationalists, there can be nothing (actual, or possible, real or essential) outside substance or their deity. 

44. "For if there is reality in essences or possibles, or indeed, in eternal truths, this reality must be grounded in something existent and actual, and, consequently, it must be grounded in the existence of the necessary being, in whom essence involves existence, that is, in whom possible being is sufficient for actual being." 

45. "Thus God alone...has this privilege, that he must exist if he is possible...." 

-Here we have the a priori proof which is different from the a posteriori proof given in 36-39!  [N.B.: proper emphasis can have this version of the ontological proof deal only with perfection and limitation and can give it the "uniqueness proof" which Spinoza supplies {by appealing to the principle of the identity of indiscernibles}]. 

-Note, however, that there is a significant difference in this version of the ontological argument: it maintains that if possible, then the deity is necessary.  This raises the question, which, to his credit, he tries to answer: "is the deity a possible thing?"  Impossible things, here, would be things whose essence involve contradictions (round squares, married bachelors, etc.).  Leibniz argues that "...nothing can prevent the possibility of what is without limits, without negation, and consequently without contradiction, this by itself is sufficient for us to know the existence of God a priori."  

--In his "The Ontological Argument," William Rowe questions whether the deity is a "possible thing:" "...the positive integer than which none larger is possible is an impossible object.  Perhaps this is also true of the being than which none greater is possible.  That is, perhaps no matter how great a being may be, it is possible for there to be a being greater than it.  If this were so, then.   Like the integer than which none larger is possible...God would not be a possible object.  The mere fact that there are degrees of greatness, however, does not entitle us to conclude that...God is like the integer than which none larger is possible.  There are, for example, degrees in the size of angles—one angle is larger than another—but it is not true that no matter how large an angle is it is possible for there to be an angle greater than it."  The question is, then, is God like the integer or like the angle. 21 
*46. Necessary (or eternal) truths depend upon his understanding, and are not (as Descartes thought) arbitrary. Contingent truths depend on his will (and on the principle of fitness, or the choice of the best. Cf., sections 53-55. 

48. God: power, knowledge and will. 

(D) 49-60: Created Things [Creatures] and Their Regulation:
49. Created things [Creatures] act outwardly insofar as they have perfection, and are acted upon by another insofar as they are imperfect. 

*50. One created thing is more perfect than another when we find in the first that which gives an a priori reason for what occurs in the second. 

*51. In the case of simple substances the influence which one monad has upon another is only "ideal."  There really is a primal regulation

**53-55. There are an infinity of possible universes in the ideas of the deity, and only one of them can exist, thus there must be a sufficient reason for the choice of God which determines him to select one rather than another—this is his principle of perfection/best

-*55. God's wisdom permits him to know the best; his goodness causes him to choose it; and his power enables him to create it. 
56. Each monad "mirrors the world." 

58. The greatest variety and order is, thus, achieved. 

59. Universal Harmony! 

60. Monads are limited not in the object they would represent, but in their capacity to represent. 

(E) 61-81: Composites and Their Regulation:

Composites are apparent collections of monads.  Since monads don't actually interact, however, these collections are merely "ideal" or "phenomenal" [apparent]—it might seem that such "collections" would be merely arbitrary groupings, but Leibniz does not think so.  Indeed, we find that each collection has a "dominant" monad—if you note that each monad is related (although "ideationally" rather than "causally" to the others,22 then this notion of dominance will make some sense.  Thus the general in an army on its way to battle knows the big picture and the general movement of the army (as well as the reasons for such movements), while the humble private may not know much of what is going on in the larger battle field. 

61. Composites fill a continuum. 

*62. Composites reflect the whole universe though they reflect one spot in the universe more fully. 

*64. Bodies are composites of an infinitude of monads. 

*70. Every living body has a dominating entelechy, which in animals is the soul.  The parts of this living body are full of other living beings, plants and animals, which in turn have each one its entelechy or dominating soul." 

76. No generation or decay of monads. 

*78. These principles furnish the means of explaining on natural grounds the union, or rather the conformity between the soul and the organic body.  The soul follows its own laws and the body likewise follows its own laws.  They are fitted to each other in virtue of the preestablished harmony between all substances, since they are all representations of one and the same universe. 

79. Souls act in accord with the laws of final causes. Bodies act in accord with the laws of efficient causes. 

(F) 82-90: Morality:
*82. Souls. 

*83. Souls mirror the deity. 

*84. Souls are capable of entering into a social relationship with god

*85. The totality of spirits compose a city of god

86. City of god is a moral world within a natural world. 

87. There is a harmony of these two worlds. 

*90. There will be no good action unrewarded and no evil action unpunished; everything must turn out for the well-being of the good. 

(end)

3. Appendix on the Traditional Conception of Substantial Forms:

As noted above in a footnote above, in his "Forma," William Frankena offers the following definition of "substantial forms:"

...that constitutive element of a substance which is the principle or source of its activity and which determines it to a definite species, or class, and differentiates it from any other substance.23 
In his "Introduction," Paul Janet maintains that:
when Descartes, in the first half of the seventeenth century, said that there are only two kinds of things or substances in nature, namely, extended substances and thinking substances, or bodies and spirits; that, in bodies, everything is reducible to extension with its modifications of form, divisibility, rest and motion, while in the soul everything is reducible to thinking with its various modes of pleasure, pain, affirmation, reasoning, will, etc...; when he in fact reduced all nature to a vast mechanism, outside of which there is nothing but the soul which manifests to itself its existence and its independence through the consciousness of its thinking, he brought about the most important revolution in modern philosophy.  To understand its significance however an account must be given of the philosophical standpoint of the time. 
  In all the schools at that time the dominant theory was that of the Peripatetics [Scholastic Aristotelians], altered by time and misunderstood, the theory of substantial forms.  It posited in each kind of substance a special entity which constituted the reality and the specific difference of that substance independently of the relation of its parts.  For example, according to a Peripatetic of the time, "fire differs from water not only through the position of its parts but through an entity which belongs to it quite distinct from the materials.  When a body changes its condition, there is no change in the parts, but one form is supplanted by another."24  Thus, when water becomes ice, the Peripatetics claimed that a new form substituted itself in place of the preceding form to constitute a new body.  Not only did they admit primary or basal entities, or substantial forms to explain the differences in substances, but for small changes also, and for all the sensible qualities they had what they called accidental forms: thus hardness, heat, light were beings quite different from the bodies in which they were found. 
  To avoid the difficulties inherent in this theory, the Schoolmen were led to adopt infinite divisions among the substantial forms.  In this way the Jesuits of Colmbre admitted three kinds of these forms: first, the being which does not receive its existence from a superior being and is not received into the inferior subject,—this being is God; second, the forces which receive their being from elsewhere without being themselves received into matter,—these are the forms which are entirely free from any corporeal concretion; third, the forms which depend in every respect, which obtain their being from a superior cause and are received into a subject, —these are the accidents and the substantial forms which determine matter. 

Other Schoolmen adopted divisions still more minute and distinguished six classes of substantial forms, as follows: first, the forms of primary matter or of the elements; second those of inferior compounds, like stones; third, those of higher compounds, like drugs; fourth those of living beings, like plants; fifth, those of sensible beings, like animals; sixth above all the rest, the reasoning (rationalis) substantial form which is like the others in so far as it is the form of a body but which does not derive from the body its special function of thinking. 

Some have thought, perhaps, that Moliere, Nichole, Malbranche and all those who in the seventeenth century ridiculed the substantial forms, calumniated the Peripatetic Schoolmen and gratuitously imputed absurdities to them.  But they should read the following explanation, given by Toletus, of the production of fire: "The substantial form of fire," says Toletus "is an active principle by which fire with heat for an instrument produces fire."  Is not this explanation even more absurd than the virtus dormitiva?  The author goes on to raise an objection, that fire does not always come from fire.   To explain this he proceeds, "I reply that there is the greatest difference between the accidental and the substantial forms.  The accidental forms have not only a repugnance but a definite repugnance, as between white and black, while between substantial forms there is a certain repugnance but it is not definite, because the substantial form repels equally all things.  Therefore it follows that white which is an accidental form results only from white and not from black, while fire can result from all the substantial forms capable of producing it in air, in water or in any other thing." 
  The theory of substantial or accidental forms did more than to lead to nonsense like the above; it introduced errors which stood in the way of any clear investigation of real causes.  For example, since some bodies fell toward the earth while others rose in the air, it was said that gravity was the substantial form of the former and lightness of the latter.  Thus heavy and light bodies were distinguished as two classes of bodies having properties essentially different, and they where kept from the inquiry whether these apparently different phenomena did not have an identical cause and could not be explained by the same law.  It was thus, again, that seeing water rise in an empty tube, instead of inquiring under what more general fact this phenomena could be subserved, they imagined a virtue, an occult quality, a hatred on the part of the vacuum, and this not only concealed the ignorance under a word void of sense but it made science impossible because a metaphor was taken for an explanation. 
  So great had become the abuse of the substantial forms, the occult qualities, the sympathetic virtues, etc., that it was a true deliverance when Gassendi on the one hand and Descartes on the other founded a new physics on the principle that there is noting in the body which is not contained in the mere conception of bodies, namely extension.  According to these new philosophers, all the phenomena of bodies are only modifications of extension and should be explained by the properties inherent in extension, namely, form, position, and motion.  Upon this principle nothing happens in bodies of which the understanding is not able to form a clear and distinct idea.  Modern physics seems to have partially confirmed this theory, when it explains sound and light by movements (vibrations, undulations, oscillations, etc.), either of air or of ether. 
  It has often been said that the march of modern science has been in the opposite direction from the Cartesian philosophy, in that the latter conceives of matter as a dead and inert substance while the former represents it as animated by forces, activities and energies of every kind.  This it seems to me is to confuse two wholly different points of view, that is the physical and the metaphysical points of view.  The fact seems to be that from the physical point of view, science has rather followed the line of Descartes, reducing the number of occult qualities and as far as possible explaining all the phenomena in terms of motion.  In this way all the problems tend to become problems of mechanics; change of position, change of form, change of motion—these are the principles to which our physicists and our chemists have recourse whenever they can. 
  ....For the physicist and for the chemist, forces are only words representing unknown causes.  For the metaphysician they are real activities.  It is metaphysics, therefore, and not physics which is rising above mechanicalism.  It is in metaphysics that mechanicalism has found, not its contradiction, but its completion through the doctrine of dynamics.  It is this latter direction that philosophy has taken since Descartes and in this the prime mover was Leibniz.25  

Back to point in Supplement which referred to Appendix

Notes:

1 Daniel Garber and Roger Ariew, introductory comment to their translation in Discourse on Metaphysics and Other Essays, trans. and eds. Daniel Garber and Roger Ariew (Indianapolis: Hackett, 1991), p. 1.  See footnote 12 below for more information on the Leibniz-Arnauld correspondence.  Back

2 Cf., Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz [1900, 1937] (Cambridge: Cambridge U.P., 1990), pp. xiii-xiv.   Back

3 Peter Lucas and Leslie Grint, "Introduction" to their translation of Leibniz' Discourse on Metaphysics (Manchester: Manchester U.P., 1953), pp. xiii-xxix, p. xiv.  Back

4 IbidBack

5 This division is, largely, seconded by Richard Woolhouse and Richard Francks, in their "Summary of the Text," which precedes their translation of the Discourse, in G.W. Leibniz: Philosophical Texts, trans. Richard Francks and R.S. Woolhouse (Oxford: Oxford U.P., 1998), p. 53.   Back

6 Ibid.  Back

7 Emphasis added to text twice.  Back

8 David Blumenfeld, "Perfection and Happiness in the Best Possible World," in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (Cambridge: Cambridge U.P., 1995), pp. 382-410, p. 386.  Back

9 Ibid., p. 389.  Back

10 The translators' note indicates that the term (coined by John Duns Scotus [~1270--1308] means "individual essence"--a thing's "thisness" (as contrasted with its "suchness").  It would be that which makes this particular philosophy professor me (my "thisness") rather than what makes me, generically, a philosophy professor (a member of such a class--my "suchness").  Back

11 In his "Forma," William Frankena offers the following definition here: "...that constitutive element of a substance which is the principle or source of its activity and which determines it to a definite species, or class, and differentiates it from any other substance" [contained in Dictionary of Philosophy (Fifteenth Edition), ed. Dagobert Runes (N.Y.: Philosophical Library, 1960, p. 111].   Back

12 Cf., Antoine Arnauld, "Letter to Count Ernest von Hessen-Rheinfels," March 13, 1686, in "Correspondence Relating to the Metaphysics," trans. George Montgomery, in Leibniz: Basic Writings (LaSalle: Open Court, 1968), pp. 67-248, p. 74.  Back

13 Leibniz, "Correspondence Relating to the Metaphysics," in Leibniz: Basic Writings, ibid., p. 132.  Back

14 Ibid.  Back

15 Ibid., pp. 187-188.  Back

16 Peter Lucas and Leslie Grint, "Introduction," op. cit., pp. xxiii-xxiv.  Back

16a That is, mercury.  Back 

17 Damaris Cudworth [Lady Marsham], "Selections from her Correspondence with Leibniz," [3, June 1704] in Women Philosophers of the Early Modern Period, ed. Margaret Atherton (Indianapolis: Hackett, 1994), pp. 81-85, p. 83.  Back

18 Pierre Bayle, "Rorarius," in his Historical and Critical Dictionary [1697], trans. and ed. Richard H. Popkin (Indianapolis: Hackett, 1991), p. 239.  Back

19 That is, logical truths where the subject and predicate are readily seen to be "identical"—for example: "Squares have four sides," or "Simple substances have no parts."  Back

20  Among other places, Leibniz' Theodicy [1710] may be found in The Philosophy of the 16th and 17th Centuries, ed. Richard H. Popkin, op. cit., pp. 333-339.  Back

21 William Rowe, "The Ontological Argument," in Reason and Responsibility [seventh edition], ed. Joel Feinberg (Belmont: Wadsworth, 1985), pp. 8-17, p. 12.  Back

22 That is, the "connections" between the monads are not causal ones, but rather deal with the inter-relatedness of the truths which they "mirror."  That is, they are connected ideationally.  The connections between individual monads are like the connections between the various characters in the Sherlock Holmes corpus--Arthur Conan Doyle did not have to use the same detective over and over (Agatha Christie, for example, does not), nor did he have to assign him consistent characteristics from book to book.  But having so conceptualized the character, there is a connection between the Sherlock of the first and the Sherlock of the last novels.  Of course, there is no causal connection, instead the connection is in the ideas and the will of the author!  Back

23 William Frankena, "Forma," in the Dictionary of Philosophy (Fifteenth Edition), ed. Dagobert Runes (N.Y.: Philosophical Library, 1960), p. 111.  Back

24 Janet cites L.P. Lagrange as follows: Les Principes de la Philosophie contre les Nouveaux Philosophes.--See Bouillier's Historie de la Philosophie Cartesienne, Vol. I. Chap. 26."  Back

25 Paul Janet, "Introduction," to Leibniz: Discourse on Metaphysics, Correspondence With Arnauld, and Monadology, trans. George Montgomery (LaSalle: Open Court, 1968), pp. vii-xxiii, p. vii-x.  Back

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