Gottfried Wilhelm Leibniz (1646-1716)

Leibniz on contingency, necessity and freedom[1]

I.

Leibniz held many views on necessity and contingency due to his efforts to reconcile his necessitating position with divine and human freedom. He tried to find a middle way which stayed away from the Scylla of blind determinism and the Charybides of mere caprice and chance.

I will in this paper give a survey of this compatibility doctrine and its problems. There are several issues at stake here; the contingencies of God’s choice of this world, of mankind and his/her actions, of hypothetical truths, of the demonstrability of contingency, the necessity of striving possibilities etc., all related to each other. The most complicated, controversial and basic view seems to be God’s free choice of a possible world among many, so let us see where he starts.

II.

Leibniz maintains that God choose in one act of will this world out of infinitely many others, that they were possible for him to choose since they did not imply any contradictions. They were all, hypothetically, metaphysically and logically possible to actualise (with exception if an evil world implied  eternal damnation of the saved, which would not even be possible for God to take as an alternative).

This choice may be viewed as contingent from the initial choice, but once chosen, it becomes necessary in a hypothetical way. That is what is implied in the formula of the necessity of the consequence (more on that later).

chooses what is best out of his wisdom and freedom, and his preference for perfection (a principle which will be brought up later concerning the string of possibilities).  This means that this world is the best one. Not because God choose it, but because it is the best.

If it was the best one because God chooses it, he would not have chosen it out of his wise choice, but be determined to choose it. The choice among worlds must be out of sufficient, divine and intelligible reasons. “The nature of things, taken without intelligence and without choice, has no sufficiently determining” Leibniz says[2].

We must here distinguish between moral, hypothetical and logical (absolute) necessity. It is not possible to create a world where 2 + 2 = 5, i.e. a logical contradiction, just as it is neither possible for God not to exist. But it is hypothetically possible to create a world different from ours. Since God is Absolute Goodness per se, one could interpret Leibniz as saying that he is bound by moral necessity and therefore chooses necessarily our actual and best world.

God could hypothetically make another choice, but not morally. In Leibniz’ words:

“It is a moral necessity that the wisest is obliged to choose the best”[3] and “This necessity is called moral, because for the wise what is necessary and what is owing are equivalent things; and when it is always followed by its effect, as it indeed is in the perfectly wise, that is, in God, one can say that it is a happy necessity”[4]

Does this lead God to be determined to choose this world? We will discuss this in moment, but let’s first see how Leibniz reasons.

He is aware of this problem, but sees it as confusion by human beings of two divine spheres: God’s will and God’s power:

“But to say that God can only chose what is best and to infer from that what he does not choose is impossible, this I say, is confounding of terms: ‘tis blending power and will,  metaphysical necessity and moral necessity/ . . ./ For what is necessary is so by its essence, since the opposite implies a contradiction. But a contingent, who exists, owes its existence to the principle of what is best, which is a sufficient reason for the existence of things”[5].

To state therefore that God could have done otherwise is to say that God could have willed otherwise, which is plainly false according to Leibniz. For pious if not obvious reasons to Leibniz and his rationalist contemporaries.

But then again, is the moral necessity not deterministic? We could say that it is, but for Leibniz it is the only way to save sufficient reasons for choosing this world and God’s integrity.  But does God really have an alternative? “If it is contingent that this world is actual, it must either be contingent that God chooses whatever is best, or else contingent that this is the best. Which is it that is contingent? / . . ./ “This is the best world” or “God chooses the best” ’, the Leibniz scholar R.M. Adams asked[6].

Leibniz himself seem to oscillate between the two views, privately holding at times that even both were contingent, openly stating only the second as contingent. There are passages in the Theodicy where the first is affirmed, but Leibniz was hesitant about viewing God’s affirmation of the best world as contingent.

III.

The problem of (God’s) freedom and causality can be stated differently as Leibniz himself did in his essay On contingency, writing upon the difference between ‘necessitatis consequentis’ (of the consequent,) and ‘necessitatis consequentiae’ (of the consequence, i.e. hypothetical necessity). The editors of Leibniz’ Philosophical essays edify this somewhat when they state the difference[7]:

Does “if p has greater reason then p is true” entail “if p has greater reason then p”? I.e. does p have to exist?

A formal way to put the difference is:

“If P then Q” can mean either,

P ––  Q  (necessity of the consequence)

Or

If  “P” exists then “Q” must exist (necessity of the consequent, Q)

In On contingency, Leibniz denies that the consequent “If p has greater reason then p” entails the consequence “If p has greater reason then p is true”, with a reference to how geometrical and divine truths are made true. These cannot lead evidence to any contingent proposition. All we may infer is that it is morally necessary for God to choose the best world. It is not possible to demonstrate however that this world is the best. I.e. only the necessity of the consequence holds true. If it exists it has to be the best.

But if the antecedent is absolutely necessary as in “It is absolutely necessary that God chooses the best world” and the whole consequence is “If God chooses a world, then it is necessary that it must be the best one”, when they were taken together as in Leibniz system, they form a necessary absolute truth and a modal logic axiom:

P — Q                                                       (hypothetical consequence)

P                                                               (absolute necessary antecedent)

Q                                                              (a logical conclusion, which Leibniz denies)

Leibniz saw this himself in Profession de foi du philosophe[8]  but reverted to form two separate conceptions of necessity; necessity by absoluteness (God or geometry) and necessity ex alteribus hypothesi (necessary on the hypothesis of something else).  Since the antecedent, God’s absolute Goodness in this case (P), is external to the consequence (Q), this implies only a hypothetical necessity according to Leibniz, but hard to view as true I think. A true antecedent yields a true consequent, if the biconditional is to be true.

IV.

Leibniz himself knew what was going to be said on this in the Theodicy and added therefore objections to his own argument in an appendix[9]:

Whoever cannot fail to choose the best is not free.

God cannot fail to choose the best.

Therefore God is not free

In his answer to this syllogism, he says that “It is true freedom and the most perfect, to be able to make the best use of one’s free will”. To say that God was dependent upon things outside him, ‘in need of external things’, when choosing this world is, Leibniz continues, “only a sophism. He creates them freely: but when he had set before him an end, that of exercising his goodness, his wisdom determined him to choose the means most appropriate for obtaining that end”[10].

He adds that although God’s will is always in force and ‘all other things follow his will’, the evil is always possible in itself. Without this possibility of evil would the world be deterministic.

‘Necessity of good is geometrical/ . . . /metaphysical, absolute, the contingency of things be destroyed and there would be no choice ‘[11], and further that ‘when a wise being, and especially God who has supreme wisdom, chooses what is best,  he is not the less free upon that account; on the contrary, it is the most perfect liberty not to be hindered from acting in the best manner’[12].

This compatibility doctrine is Leibniz’s idea of “rational spontaneity”. Further evidence on this divine freedom: ‘God produces the best not by necessity but because he wills it’, from On freedom and possibility[13] and ‘God’s decisions about contingents are certainly not necessary’[14].

But Leibniz was reluctant to this view since it would lead to infinite regress if God’s will willed to will to will . . . etc., to choose the best world. But what is really a choice for God and mankind? Let’s turn to see to what a choice in Leibnizian terms would be and what a comparison between different possible worlds would be.

V.

Leibniz’ rationalism contained two principles; the Identity Principle which gives the concept of each individual substance its very specific definition and predication, and the Principle of Sufficient reason, which give it, together with God’s choice of this world, rational reasons to exist and act.

From them he concludes that there is a way to reason deductively down to a concept’s primary sufficient reason, as in a logical a priori concept. If not, it is only possible by stating all the infinite reasons and predicates for that concept. In the latter case, the truth is contingent. Since worlds are contingent and only can be fully analysed and compared by stating all characteristics of it, only God can see, ‘in one stroke of the mind’, the end of why just this world is better than another.

“It is clear why no demonstration of any contingent proposition can be found, no matter how far the analysis of concepts is continued”, Leibniz writes[15]. In fact, he states that it is not even possible for God to view the end of the infinite analysis, but he can get the whole picture by viewing the reasons a priori for a certain world.

We humans cannot even pose the question of another beginning in time of this world. ‘For we cannot find in any of the individual things, or even in the entire collection and series of things, a sufficient reason for why they exist’, from the On the ultimate origination of things[16].

But since we cannot know why things are rather than not, we have to rely on experience Leibniz says, while still maintaining sub principium rationis sufficientis  Without such a reason, we would be lost and have no reason at all for contingent truths and that would lead us to irrationalism, blind fatalism and indifference.

Since it is not possible to demonstrate how one could compare the alternatives, and due to this fact of analysis of contingent truths, the choices must be contingent. But this solution may leave contingency as an illusory and empty choice. However, Leibniz is not talking about the epistemological difference between the analysis of contingent and absolute propositions, Adams claims (with N. Rescher) in a defence[17] since not even God can view the end of the infinite analysis of contingent truths. It is a logical distinction between the (in) demonstrability of necessary and contingent truths, Rescher and Adams maintain.

VI.

We turn now to some problems in the contingency of mankind and human acts. A difficult problem is how to view the certainty and necessity in a hypothetical situation, with reference to the whole range of predicates attributed to a subject.

Every property that an individual substance has, except for existence is an essential part of his/her/its nature. “The complete or perfect notion of an individual substance contains all of its predicates, past, present and future”, from Leibniz’ Primary truths[18].

This view has been labelled “super essentialism” and discussed by D. Blumenfield in an essay on its relation to counterparts (in other possible worlds) and freedom.  “One might suppose that super essentialism implies that all truths are necessary and that freedom – which presupposes contingency – is ruled out thereby. But Leibniz claims that this conflates absolute with merely hypothetical necessity”[19], as mentioned before.

What does it mean?  It is clear  if Adam exists he will sin, but it is not hypothetically necessary, since God could have chosen another world in which Adam did otherwise than in this world or did not even exist. What we humans do is to infer from a fact that something exists, that its predicated consequences are necessary.

Yet it is true if the whole biconditional is true, that is, “If Adam exists, then he must sins” (P    Q) is true. But the antecedent “Adam exists” (the “P”) is not necessary. ‘Sinning is a part of Adam’s concept but existence is not”[20]  as we saw before and will discuss again concerning striving for existence.

In order to save himself from determinism, Leibniz rejected in several places logos aeroe, the sloth’s fatalistic syllogism, that says whatever happens happens and one cannot do other than what one does.  For moral advice he said: “Since we know nothing of what is foreseen, we should do our part over the useless question as to whether success is foreseen or not”, in the Dialogue on human freedom[21].

Our best hope when we are at dismay, Leibniz says, is not to sin. “It is only a matter of willing/ . .  . / act according to your duty, which you do know”[22]. Perhaps it is not within our concept to sin. Our sincere and moral volition can lead us straight through the divergent paths of life. Defect is only a matter of privation of goodness (as St Augustine had it), of nothingness (as in Leibniz’ Dialogue of human freedom), of not knowing (as Socrates had it) etc. Just try hard enough.

But one could say that in this world, the fact of its existence and the fact of the events of individual men are one and the same fact, since they both hang together in their conceptions. In the Discourse on metaphysics Leibniz states boldly that “whatever happens in conformity with these predeterminations [advances] 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 hypothesi] for this to happen”[23].

Only with Leibniz’ philosophical diplomacy do we have a genuine choice among limited alternatives.  “It is untrue”, Leibniz writes firmly in the Theodicy, “that the event happens whatever one may do: it will happen because one does what leads thereto; and if the event is written beforehand, the cause that will make it happen is written also”[24].

If we knew the complete concept of an individual subject with all its predicates, we would understand fully why some course of action was taken, freely but necessarily. As Leibniz scholar B. Mates states it:

“For if some man were able to carry out the complete demonstration of which he could prove this connection between the subject, who is Caesar, and the predicate, which is his successful undertaking, he would actually show that the future dictatorship of Caesar is based on his concept or nature and that there is a reason in that concept why he has resolved to cross Rubicon rather that stop there/ . . ./ and why it was reasonable and consequently assured that this should happen”[25].

We must distinguish here between what is certain and what is necessary, Leibniz says. But it may be a distinction without any value one could say, since we really do not have a possibility to weigh alternatives in an infinite analysis of contingent facts. Adams argues in his essay on contingency that the choices of actions must be  “general” in order to preserve some notion of reality without crossing worlds or problems of compossibility:

“Caesar’s alternatives on the bank of Rubicon must be crossing and not crossing, rather than Caesar’s crossing and Caesar’s not crossing. Individual concepts must be kept out of the objects of choice”, Adams maintains[26]. But this concept of generality does not sound like anything Leibniz would like, I believe.

Even though this argument shows a way in which the reality of Caesar’s choice is preserved, it does not provide reasons for its contingency. I myself find this area of Leibniz’s views of freedom hard to accept. It seems just like a number in his system, whatever he does with it. God is supposed to “continually conserve and produce our being in such a way that thoughts come to us spontaneously or freely”[27]

He has also freely decreed that always do what is most perfect and from this decree of freedom it follows with respect to human nature, that also ‘man will always do (although freely) that which appear to be best’[28]. Freedom is furthermore necessary in order to that man be judged and rightly punished, Leibniz writes in the Theodicy.   Leibniz tried hard to preserve a real sense of freedom, but it was hard with his deterministic premises.

VII.

Exigentia existentiae, the striving urge for existence, might be another way to view the problem of contingency. If something exists rather than nothing, its reasons for existence must be intelligible. ‘Perfection, or essence, is an urge for existence’, Leibniz writes in On freedom and possibility[29].

With the Principle of Sufficient reason and the Principle of Perfection, this urge is a way to see why something happens rather than not. ‘And it seems to be common to things that exist, both necessarily and contingently, that they have more reason  for existing than others would, were they put in place’, Leibniz writes in On contingency[30].   God views possible essences in ‘a certain realm of ideas, so to speak, namely, in God himself’, and selects thereafter the ones that have most perfection and possibility.

Essence itself strives for existence, but it can never rise to the level of metaphysical necessity, since then it would be as God and then pantheism threatens. Also, if it was the most absolutely perfect world, even without causing itself, it would be identical to God which is against the Principle of Identity. Leibniz thought that this best actual world must therefore involve some degree of imperfection. It is the best world, but not the must perfect one.

“The one that exists is the one through which the most essence or possibilities brought to existence”, he says in On the ultimate origination of things[31].

Since existent things cannot come out of nothing existing, its existence must come from something metaphysically necessary existing, God or the eternal mathematical laws. Leibniz views geometrical perfection on the same level as God’s choice of a most perfect world on the same level of reason in this short essay.

Just like tiles perfectly laid out on a floor or a completed chess board, the world has as much possible essence filled in every corner as possible, due to “the wonderful way in which metaphysical laws of cause, power and action, have their place in the whole of nature”[32]. But all this lies on the assumption that ‘at some time being is to prevail over nonbeing’, which is not explained.

Everything possible will exist unless hampered. Its reason for being actualised is its degree of perfection and its quantity of existence. D. Blumenfield finds this theory ‘bizarre’ and echoes Leibniz’s own doubts how one should interpret the possible worlds or essences as real in some way, while not reducing them to mere figments:

“If this were so, they could hardly be the metaphysical basis of the origination of things. Leibniz replied that the possibles have a certain kind of reality, since that exist from eternity in the mind of God’, from ‘Leibniz’s theory of striving possibilities”[33].

But how is this striving from possible essence to actual existence through their intrinsic principle of perfection compatible with God’s free choice of the best possible world.  In the theory of urge for existence, God invents possibles and lie back to watch them fight for existence, while in the theory of God’s free choice he actualises one possible world, by one free choice. Blumenfield claims that “/. . . /since the possibles have an intrinsic drive to exist, there cannot also be a room for God’s free selection of this world”[34].

Leibniz’ defenders have maintained that the two accounts are compatible, N. Rescher for instance, in saying that,

“/. . . /it is only because God has chosen to subscribe to the standard of perfection in selecting a possible world for actualisation that possible substances come to have (figurative) “claim” to existence’./. . . /the relationship between “quantity of essence” or “perfection”/. . . /and claim or conatus to existence/. . . [is] a connection mediated by a free act of will on the part of God”[35].

There is also evidence of this interpretation in the Theodicy, where Leibniz writes that the conflict of possibles is ‘only ideal’ and ‘a conflict of reasons in the most perfect understanding’. The struggle is both God’s and the possibles, but this leads also to pantheism I believe.

VIII.

At last let us view Leibniz’ view on how the power of small  unnoticeable perceptions influences us leads to another kind of necessity, though related to the whole concept of individual substances, the monads. Man is “inclined” by the mass of  “petit perceptions” in his soul-monad, so that his/her  choice follows the greatest inclination (by which I understand both passions and reasons, true or apparent”, Leibniz writes in Letter to Coste[36]. And further, “but the good, either true of apparent, in a word the motive – inclines without necessitating, that is, without imposing an absolute necessity”[37].

Like weights on a balance, our (unnoticed) perceptions and inclinations, lead us, supported by our virtues and reasons, to do what is good. ‘The mass of these makes an uneasiness which pushes us without the subject of it seen’[38].  Since we cannot understand through infinite analysis these influences, Leibniz views them as contingent, though with its sufficient reasons. In the Monadology he states:

“But there must also be a sufficient reason in contingent truths, or truths of fact, that is, in the series of things distributed throughout the universe of creatures, where the resolution into particular reasons could proceed into unlimited details/. . . /There is an infinity of past and present shapes and motions that enter into the efficient cause of my present writing, and there is an infinity of small inclinations and dispositions of my soul, present and past, that enter into its final cause”[39].

IX.

Leibniz never seemed to have viewed all the problems with freedom that I have found in the secondary literature. It seems like the doctrines that we find incompatible were, if not easily, at least possible to fit together for him.

 

Notes on Leibniz’ theory of knowledge[40]

INTRODUCTION

I am here going to discuss various aspects on Leibniz’ epistemology. Generally speaking, Leibniz worked out an epistemology that would account for his teleology and metaphysics and therefore it cannot be understood as an independent attempt, but suited to his larger concerns.   All work on his epistemology is reconstructive in a sense, more here than anywhere else.  I will try to give some account of his theories, though very sketchy in details.

INNATENESS

Leibniz’ rationalist epistemology is most well known for his debate with Locke on the nature of innate knowledge, i.e. concepts and principles independent of perception and sensations.  It is in his theory of man’s reflection upon thoughts (with a term he coined ”apperception”) that he grounds the idea of innate knowledge.   In this heuristic process of reflection, man has a direct apprehension of his/her identity, of magnitude, of substance, duration etc.

It is the notion of principles that interest Leibniz, in contrast with Locke’s emphasis on ideas (which they differed upon defining). Locke seemed to want a hard- lined proponent of innate almost empirical ideas and actions in his critique, whereas Leibniz did not seem to have a crude version of innateness. For example, he never held that babies or ignorant people consciously knew the principle of contradiction or of numbers, but that in the process of reflection, innate principles may became accessible to the mind.

In the preface to the New Essays[41], he brought up the innateness of ’inclinations, dispositions, tendencies or natural potentialities and not as actions’. The actions that follow from sensations and thoughts when judged by a human faculty are in this way lead by the innate dispositions of the faculty. Leibniz could not think of a faculty without any guiding directions at all. Therefore he fought Locke’s idea of a tabula rasa.

The difference between necessary and contingent truths is something else that Leibniz held as very important in the discussion of innate truths and principles.  For him,’ I deem all necessary truths to be innate’[42] which they rely on the Great Principle of Identity (or of Contradiction).

Without this principle embedded within us, nothing would be possible to know, distinguish or judge right or wrong. We use these innate unknown principles. ’Everyone uses the rules of deduction by a natural logic without being aware of it’, he wrote.[43]

But he also viewed practical moral truths as instincts which are innate in a special way, and not as necessary truths of reason which are known by a lumen naturale.

In summing up the several views on kinds of knowledge, Robert McRae states in his discussion of innateness, that   Leibniz rendered only metaphysical  and mathematical concepts (though in a special way) as innate and the only worthy principle was the principle of contradiction or identity[44]. Other principles were more of the”vein of marble” type; being there in the beginning but needed an artisan to fully be noticed.

A question remains what the relation between monads and innateness is all about. If all concepts are within the monad’s own complete definition, are not all its truths innate?

Bertrand Russell thought that this was the inevitable conclusion in this early 20th century study, but later Nicholas Rescher defended Leibniz.  Rescher saw two separate domains of the monadological epistemology; that of intention with outwardly monads and that of apperception with inwardly monads.  Only certain ideas and truths that are of the second type may properly be called innate, as logically independent of the first kind[45].

This distinction is drawn be Rescher to show a difference of content rather than a temporal one. Since all ideas are present in the mind, potentially and virtually, we easily think of them as all there from the beginning of time, but this is too simple for someone like Leibniz.

CLEAR, DISTINCT, ADEQUATE AND INTUITIVE KNOWLEDGE

The analysis of knowledge, truth and ideas in his 1684 Meditations on Knowledge, Truth, and Ideas is also central to Leibniz epistemology. He tried there to expand on Descartes’ earlier attempt 1641 in his Meditations, and the Arnauld- Malebranche controversy. The distinctions that Leibniz established were useful in determining what kind of knowledge one has of a represented object by way of rational questioning in Cartesian style, going from the simple definitions to the complicated.

We should ask ourselves: Is the object represented able to be distinguished from other objects? Yes – yields clear knowledge, no – obscure. Is it possible to enumerate its various determinate marks? Yes – yields distinct (and clear) knowledge, no – confused.  Are the separate determinate marks able to identity? Yes – yields adequate (and clear and distinct) knowledge, no – inadequate.

At last, is it possible to hold all definitions of all minute parts of the complex whole of the object in mind at the same time? Yes – yields intuitive (and in fact divine) knowledge, no – blind or symbolic.

Leibniz said that we for the most time view and think of composites of monads in symbolic manner. Concerning man’s possibilities for adequate knowledge, he thought it was only possible within truths of reason, not what concerns truths of facts, which would involve an infinite analysis of details of factual knowledge. In logic and metaphysics however, we can attain adequate knowledge after serious studies

Leibniz’ logical distinction of nominal and real definitions is also valuable here as a way of establishing criteria for truth and possibility. Nominal definitions contain only certain marks that distinguish it from other objects, while real definitions actually established an object as possible.  Definitions were the highest form of human knowledge for Leibniz.

MINUTE RATIONAL PERCEPTIONS

For Leibniz, the whole spectre of knowledge is gradual, since we always perceive the universe in our own way. We go from sensible conception to intellectual apprehension by way of degrees in manifest rationality. Our understanding understands by apprehending an idea, not understanding an idea. Similarity, the senses never understand, only the intellect does. Viewed this way, Kant was right when he argued that Leibniz intellectualised appearances.

In one end of Leibniz’ rationalist epistemological spectre, there are passive monads in obscurity, in the other divine end, active monads with adequate intuitive knowledge. In both ends, Leibniz holds that rational thoughts of various degrees of force are the basic elements, not sensual perceptions. “We can even say that there is all at once a virtually infinite number of [thoughts] contained in our sensations”, he even claimed[46].

We perceive (for Leibniz and Descartes, think) all the time while living, even in our sleep. To explain this, Leibniz came up with a theory of minute insensible perceptions. The ordinary perceptions that a monad has of other monads concern all kinds of monads; material, animal, human, angelic etc.  But minute (petit) perceptions that while perceived remain unnoticed by the monad are only for human and spiritual monads.

Minute perceptions are those small pricklings that helps the monad to rely in an unconscious way on the outside world. “They constitute in that connection that each being has with the rest of the universe”[47].  The world exists only in these small representatives as long as they are perceived by the monad, thereby giving the monad’s perceptions a heightened goal. “The task of perception entails pulverizing the world, but also one a spiritualising its dust”, as G. Deleuze put it[48].

Even while asleep, they keep us conscious enough to be able to alert if needed. We are never aware of these small perceptions, just like we do not sense or understand the pressure of air upon our bodies. To refute some one of Locke’s thinking Leibniz let his protagonist Theophilus say: “There would have been nothing wrong with objecting to you simply that thought need not stop just because one is not aware of it”[49].

The common example of the sea shore where the sounds of each wave are lost in the total roar by all waves is used by Leibniz. But all large totalities of perceptions need not be noticed and can be minute even though they are great. For instance, the sound of a water mill that I am very accustomed to, or a deadening effect by something too powerful to notice.

We humans may also have confused perceptions of monadic aggregates, which may be fully analysed into distinct wholes. And furthermore, the aggregate’s various parts may be analysed down to its parts and give rise to adequate knowledge (though very seldom and by very few). Minute and confused knowledge is understood in such a way that when a human (or spiritual) monad perceives a whole confusedly, its perceptions are there, however infinitely small.

The inner state of the monad is furthermore very important since it is there that the activity of monads and their notions of past, present and future characteristics and attributes are present.  Since the entire world is perceived though dimly by the monad, its ability for various changes is immense, but the orderliness and continuity of the monadological changes are holding the multi various chaos back.  Optimal variety and optimal order must mutually reign.

Between each change of state in the monad there are always infinite minute steps. ’The division of the continuous must not be taken as of sand dividing into grains, but as that of a sheet of paper or of a tunic infolds, in such a way that an infinite number of folds can be produced, some smaller than other, but without the body ever dissolving into points or minima’[50].  For Leibniz, Nature makes no leap, ’we always pass from small to great and from great to small through what is intermediate between them, in degrees as in parts’[51].

PERSPECTIVAL KNOWLEDGE

The monads can perform two functions; perceive the world from a certain perspective and change its perceptions by appetition. ’I hold perception to be the representation of plurality in the simple and appetite to be the striving from one perception to another. But these two things occur in all monads, for otherwise a monad would have no relation to the rest of the world’[52].

If we start with his general ideas of knowledge we find a kind of  ”open system”, like a cybernetic flow, where the center is the individual substance, the windowless monad. From that centre, the world is perceived and expressed continuously from a certain point of view, a perspective.  These inner perceptions in the monad are all there is, Leibniz claims, or all we need to take into account. For the rest of the world, its materiality is irrelevant of the question of the systematic perspectives of innumerable monads.  In the monads, all we can find are perceptions and their changes, their appetites[53]. This does not make the world idealist, but bases these perceptions on a metaphysical level of expressive monadological properties.

The doctrine of expression and expressive monads is central to Leibniz and one of its most fascinating features. He held in fact that intellectual knowledge, animal sensations and natural perception all are different species of the genus expression[54]. To go from expression to perception however, Leibniz stated that the perceiving creatures must be aware of its role. An animal may express the whole universe, but not be aware of it. Behind expression, there must be a spiritual monad, human or divine.  Then by way of expression, a chaotic manifold may be represented in the manner of signs, characters etc., so that we may perceive them properly.

The monad expresses the certain ”closer” parts of the other monads better and other ones,  more ”further away”, more dimly. At all times, the single monad expresses the whole universe of monads, but almost all in a very confused and obscure way. To every instant of every other monad there corresponds a response, an expression, by another monad.

The term ”expression” must not be understood in a substantive way like perception of something, but more in a formal and mathematical. In a relation between two things, “one thing expresses another, / . . . /when there is a constant and regulated relation between what can be said of the one and of the other”[55]. This relationship does not have to mutual. One thing A may express B better than B expresses A. A perspective is not a shared world, but a certain angle of a shared world that is impossible to share totally with another monad.

The facts of the world of monads are only truths of facts, not reasons. Only God can perceive the last fundaments of these facts in his contingent choice of this contingent world. We ourselves perceive all of this and are thus omniscient but in a confused way. Now, if all monads perceive the same things, that is, express the same world, how they differ, Rescher asks[56]. He comes up with two criteria;

1) Monads differ in point of view

2) In their clearness of perception

In the Monadology Leibniz states how the monads interact and how every body is affected by everything that happens in the universe. Only by what is ”closer”, ”greatest with respect to each monad” or has a particularity affected by it” is a certain corner of the universe expressed more vividly.

Like a special block in a city is more known than others, a monad perceives a certain subdivision of the world more clearly.  The same block may be represented, or expressed, by several monads, all of them differently. Leibniz gave examples of mathematical, geometrical or verbal entities which could be expressed in different ways.

“Thus one must allow that each soul represents the universe to itself according to its point of view, and through a relation which is peculiar to it; but a perfect harmony always subsists therein”[57]. Here it is very clear how Leibniz used his theory of predestined harmony in epistemological and coordinate matters, rather than in a moral and fatalistic sense).

PERCEPTIVE KNOWLEDGE

When the soul is aware of its own perceptions, a transformation is occurring that Leibniz named ”apperception”.  “Thus it is well to make the distinction between perception which is the internal state of the monad representing internal things, and apperception which is consciousness, or the reflexive knowledge of this internal state”[58].

Leibniz did not mean however that all consciousness is apperceptive, but self- consciousness.  Reflection upon what goes on in the mind is decisive in apperception, not just being conscious.

 

 

[1] Both course papers for prof W. Waxman at The Graduate Faculty, New School for Social Research, New York, 1993

[2] Theodicy, § 350.

[3] Op. cit., § 367.

[4] Op. cit., appendix, obj. II.

[5] Letters to Clarke, V, 9.

[6] Adams ‘Theories of contingency’, ed. M. Hooker  Leibniz: Critical and interpretative essays, (Minneapolis , Univ of Minnesota Press, , 1982), p. 254 -255.

[7]  Philosophical essays, (Indianapolis : Hackett, 1989), note 57, p. 30)

[8] An early draft to Theodicy from 1673.

[9] Theodicy, Objection VIII.

[10]  Ibid.

[11] Ibid.

[12] Letters to Clarke, V, 7.

[13] Philosophical essays, p. 20.

[14] Leibniz quoted in Adams  1982, p. 266.

[15] Op cit, . 258.

[16] Philosophical essays, p. 149.

[17] Adams 1982, p. 260.

[18] Philosophical Essays, p. 32.

[19] Blumenfield in Hooker ed. 1982, p. 103.

[20] Blumenfield, op. cit., p. 104,

[21] Philosophical essays, p. 113.

[22] ‘Discourse’, §30.

[23] Discourse on metaphysics, § 13.

[24] Preface, Theodicy,  (La Salle, Open Court, 1985), p. 57.

[25] The philosophy of Leibniz, (Oxford UP) p. 112.

[26] Adams 1982, p. 264.

[27] Discourse on metaphysics, § 30.

[28] Op cit, § 13.

[29] Philosophical essays, p. 20.

[30] Op. cit., p. 28.

[31] Op cit, p. 150.

[32] Op cit, p. 152.

[33] Blumenfield in Leibniz: Metaphysics and philosophy of science, ed. R.S. Woolhouse (Oxford UP, 1981), p, 79.

[34] Op. cit., p. 80.

[35] Rescher quoted in op cit, p. 80.

[36] Philosophical essays, p. 194.

[37] Letters to Clarke, V, 8.

[38] Quoted in Adams 1982, p. 265.

[39] Monadology, § 36.

[40] Course paper for prof. W. Waxman at The Graduate Faculty, New School for Social Research, New York, 1993.

[41] In Philosophical essays, (Indianapolis : Hackett, 1989). Written 1704 and published 1765.

[42] Op. cit., book 1, ch. 2, §16.

[43] Op. cit., §3.

[44]  McRae, Leibniz: Perception,  Apperception, Thought (Toronto, University of Toronto Press, 1976), p. 125.

[45] Rescher, Leibniz, (London : University Press of America/Eurospan, 2nd ed 1976), p. 122.

[46] Quoted in McRae, p. 127. But I will here limit the theory of minute perceptions without complicating the matter of Leibniz’ ”intellectual perceptions” as distinct from sensual notions.

[47] New Essays, preface.

[48] Deleuze, The Fold:Leibniz and the baroque  (Minneapolis : Univ. of Minnesota Press, 1993) p. 87.

[49] New Essays, book 2, ch.2, §11.

[50] Leibniz’ opuscules et  fragments, ed. Couturat, (Hanover, Hildesheim Olms 1961), p. 614- 5.

[51] In the preface to his New Essays,

[52] Philosophical papers and Letters, ed. Loemker, (Dordrecht : Reidel, 1976, 2n ed.), p. 662-3.

[53] Monadology, § 17.  Original from 1714.

[54] In his Letter to Arnauld 1687.

[55] Leibniz in Loemker edition, p. 339.

[56] Rescher, op cit, p 71.

[57] Theodicy, § 357. Original 1710.

[58] Principles of nature and grace, sec. 4. Original 1714.