Leibniz#


Texts#

  • Ariew, Roger & Daniel Garber (transls). (1991). G. W. Leibniz: Discourse on Metaphysics and Other Essays. 9th Ed. Hackett: Hackett Classics.

  • Ariew, Roger & Daniel Garber (transls). (1989). G. W. Leibniz: Philosophical Essays. Hackett: Hackett Classics.

  • Duchesneau, François. (2016). The Leibniz-Stahl Controversy. Yale University Press: The Yale Leibniz Series.

  • Duchesneau, François. (1993). Leibniz et la méthode de la science. Presses universitaires de France.

  • Garber, Daniel. (2011). Leibniz: Body, Substance, Monad. Oxford University Press.

  • [ h ] Grosholz, Emily.

  • Mates, Benson. (1989). The Philosophy of Leibniz: Metaphysics and Language. Oxford University Press.

  • Meli, Domenico Bertolini. (1997). Equivalence and Priority: Newton versus Leibniz. Oxford Clarendon Press.

  • Parkinson, G. H. R. (ed). (1992). De Summa Rerum: Metaphysical Papers, 1675-1676. Yale University Press: The Yale Leibniz Series.

  • Parkinson, G. H. R. (ed,transl). (1966). Logical Papers: A Selection. Oxford University Press.

  • Perkins, Franklin. (2007). Leibniz and China: A Commerce of Light. Cambridge University Press.

  • Remnant, Peter & Jonathan Bennett (eds). (1996). Leibniz: New Essays on Human Understanding. Cambridge University Press: Cambridge Texts in the History of Philosophy.

  • [ h ] Rutherford, Donald. (1998). Leibniz and the Rational Order of Nature. Cambridge University Press.

  • [ h ] Rutherford, Donald. The Logic of Leibniz.


Terms#

  • [SEP][W] Leibniz, Gottfried Wilhelm (1646-1716)

    • [SEP] Leibniz’ Ethics

    • [SEP] Leibniz’ Exoteric Philosophy

    • [SEP] Leibniz’ Influence on 19th Century Logic

    • [SEP] Leibniz’ Influence on Kant

    • [SEP] Leibniz’ Modal Metaphysics

    • [SEP] Leibniz on Causation

    • [SEP] Leibniz on the Problem of Evil

    • [SEP] Leibniz’ Philosophy of Mind

    • [SEP] Leibniz’ Philosophy of Physics

  • [SEP] Identity of Indiscernibles (Leibiz’ Law)

  • [SEP] Infinity

  • [SEP] Principle of Sufficient Reason

  • [W] Clarke, Samuel (1675-1729)

  • [W] Alphabet of Human Thought

  • [W] Calculus Ratiocinator

  • [W] Characteristica Universalis

  • [W] De Arte Combinatoria

  • [W] Golden Rule

  • [W] In Esse

  • [W] Indiscernibility of Identicals

  • [W] Leibniz-Clarke Correspondence

  • [W] Lingua Generalis

  • [W] Mathesis Universalis

  • [W] Monad

  • [W] Pre Established Harmony

  • [W] Principle of Economy

  • [W] (PII) Identity of Indiscernibles (Leibiz’ Law)

  • [W] (PB) Principle of the Best

  • [W] (PC) Principle of Contradiction

  • [W] Principle of Parsimony (Occam’s Razor)

  • [W] (PSR) Principle of Sufficient Reason

  • [W] Vis Viva

  • [W] Vis Viva Equation


Discourse on Metaphysics#

  1. On divine perfection, and that God does everything in the most desirable way.

    • The most widely accepted and meaningful notion we have of God is expressed well enough in these words, that God is an absolutely perfect being; yet the consequences of these words are not sufficiently considered.

    • And, to penetrate more deeply into this matter, it is appropriate to remark that there are several entirely different perfections in nature, that God possesses all of them together, and that each of them belongs to him in the highest degree.

    • We must also know what a perfection is.

    • A fairly sure test for being a perfection is that forms or natures that are not capable of a highest degree are not perfections, as for example, the nature of number or figure.

    • For the greatest of all numbers (or even the number of all numbers), as well as the greatest of all figures, imply a contradiction, but the greatest knowledge and omnipotence do not involve any impossibility.

    • Consequently, power and knowledge are perfections, and, insofar as they belong to God, they do not have limits.

    • Whence it follows that God, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking, and that, with respect to ourselves, we can say that the more enlightened and informed we are about God’s works, the more we will be disposed to find them excellent and in complete conformity with what we might have desired.

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

    • Thus I am far removed from the opinion of those who maintain that there are no rules of goodness and perfection in the nature of things or in the ideas God has of them and who say that the works of God are good solely for the formal reason that God has made them.

    • For, if this were so, God, knowing that he is their author, would not have had to consider them afterwards and find them good, as is testified by the Sacred Scriptures–which seem to have used such anthropomorphic expressions only to make us understand that the excellence of God’s works can be recognized by considering them in themselves, even when we do not reflect on this empty external denomination which relates them to their cause.

    • This is all the more true, since it is by considering his works that we can discover the creator.

    • His works must therefore carry his mark in themselves.

    • I confess that the contrary opinion seems to me extremely dangerous and very near to the opinion of the recent innovators who hold that the beauty of the universe and the goodness we attribute to the works of God are but the chimeras of those who conceive of God in terms of themselves.

    • Thus, in saying that things are not good by virtue of any rule of goodness but solely by virtue of the will of God, it seems to me that we unknowingly destroy all of God’s love and all his glory.

    • For why praise him for what he has done if he would be equally praiseworthy in doing the exact contrary?

    • Where will his justice and wisdom reside if there remains only a certain despotic power, if will holds the place of reason, and if, according to the definition of tyrants, justice consists in whatever pleases the most powerful?

    • Besides, it seems that all acts of will presuppose a reason for willing and that this reason is naturally prior to the act of will.

    • That is why I also find completely strange the expression of some other philosophers who say that the eternal truths of metaphysics and geometry and consequently also the rules of goodness, justice, and perfection are merely the effects of the will of God; instead, it seems to me, they are only the consequences of his understanding, which, assuredly, does not depend on his will, any more than does his essence.

  3. Against those who believe that God might have made things better.

    • Nor can I approve of the opinion of some moderns who maintain boldly that what God has made is not of the highest perfection and that he could have done much better.

    • For it seems to me that the consequences of this opinion are wholly contrary to the glory of God: As a lesser evil is relatively good, so a lesser good is relatively evil.

    • And to act with less perfection than one could have is to act imperfectly.

    • To show that an architect could have done better is to find fault with this work.

    • This opinion is also contrary to the Sacred Scripture, which assures us of the goodness of God’s works.

    • For, if their view were sufficient, then since the series of imperfections descends to infinity, God’s works would always have been good in comparison with those less perfect, no matter how he created them, but something is hardly praiseworthy if it can be praised only in this way.

    • I also believe that a great many passages from Sacred Scripture and the holy fathers will be found favoring my opinion, but scarcely any will be found favoring the opinion of these moderns, an opinion which is, in my judgment, unknown to all antiquity and which is based only on the inadequate knowledge we have of the general harmony of the universe and of the hidden reasons for God’s conduct.

    • This enables us to judge audaciously that many things could have been rendered better.

    • Besides, these moderns insist on certain dubious subtleties, for they imagine that nothing is so perfect that there is not something more perfect–this is an error.

    • They also believe that in this way they are able to safeguard God’s freedom, as though it were not freedom of the highest sort to act in perfection following sovereign reason.

    • For to believe that God does something without having any reason for his will–overlooking the fact that his seems impossible–is an opinion that conforms little to his glory.

    • Let us assume, for example, that God chooses between A and B and that he takes A without having any reason to prefer it to B.

    • I say that this action of God is at the very least not praiseworthy; for all praise must be based on some reason, and by hypothesis there is none here.

    • Instead I hold that God does nothing for which he does not deserve to be glorified.

  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.

    • The general knowledge of this great truth, that God acts always in the most perfect and desirable way possible, is, in my judgment, the foundation of the love that we owe God in all things, since he who loves seeks his satisfaction in the happiness or perfection of the object loved and in his actions.

    • To will the same and dislike the same is true friendship.

    • And I believe that it is difficult to love God well when we are not disposed to will what God wills, when we might have the power to change it.

    • In fact, those who are not satisfied with what God does seem to me like dissatisfied subjects whose attitudes are not much different from those of rebels.

    • I hold, therefore, that, according to these principles, in order to act in accordance with the love of God, it is not sufficient to force ourselves to be patient; rather, we must truly be satisfied with everything that has come to us according to his will.

    • I mean this acquiescence with respect to the past.

    • As for the future, we must not be quietists and stand ridiculously with arms folded, awaiting that which God will do, according to the sophism that the ancients called logon aergon, the lazy reason.

    • But we must act in accordance with what we presume to be the will of God, insofar as we can judge it, trying with all our might to contribute to the general good and especially to the embellishment and perfection of that which affects us or that which is near us, that which is, so to speak, in our grasp.

    • For although the outcome might perhaps demonstrate that God did not wish our good will to have effect at present, it does not follow that he did not wish us to act as we have.

    • On the contrary, since he is the best of all masters, he never demands more than the right intention, and it is for him to know the proper hour and place for letting the good designs succeed.

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

    • Therefore, it is sufficient to have the confidence that God does everything for the best and that nothing 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.

    • However, we can make some general remarks concerning the course of providence in the governance of things.

    • We can therefore say that one who acts perfectly is similar to an excellent geometer who can find the best constructions for a problem; or to a good architect who makes use of his location and the funds set aside for a building in the most advantageous manner, allowing nothing improper or lacking in the beauty of which it is capable, or to a good householder, who makes use of his holdings in such a way that there remains nothing uncultivated and sterile; or to a skilled machinist who produces his work in the least difficult way possible; or to a learned author who includes the greatest number of thruths in the smallest possible volume.

    • Now, 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 general harmony permits is.

    • We shall say more about this below.

  6. God does nothing which is not orderly and it is not even possible to imagine events that are not regular.

    • The volitions or acts of God are commonly divided into ordinary or extraordinary.

    • But it is good to consider that God does nothing which is not orderly.

    • Thus, what passes for extraordinary is extraordinary only with some particular order established among creatures; for everything is in conformity with respect to the universal order.

    • This is true to such an extent that not only does nothing completely irregular occur in the world, but we would not even be able to imagine such a thing.

    • Thus, let us assume, for example, that someone jots down a number of points at random on a piece of paper, as do those who practice the ridiculous art of geomancy.

    • I maintain that it is possible to find a geometric line whose notion is constant and uniform, following a certain rule, such that this line passes through all the points in the same order in which the hand jotted them down.

    • And if someone traced a continuous line which is sometimes straight, sometimes circular, and sometimes of another nature, it is possible to find a notion, or rule, or equation common to all the points of this line, in virtue of which these very changes must occur.

    • For example, there is no face whose contours are not part of a geometric line and cannot be traced in one stroke by a certain regular movement.

    • But, when a rule is extremely complex, what is in conformity with it passes for irregular.

    • Thus, one can say, in whatever manner God might have created the world, it would always have been regular and in accordance with a certain general order.

    • But 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, as might be a line in geometry whose construction is easy and whose properties and effects are extremely remarkable and widespread.

    • I use these comparisons to sketch an imperfect likeness of divine wisdom and to point out something that can at least elevate our minds to conceive in some way what cannot be sufficiently expressed.

    • But I do not claim to explain in this way the great mystery upon which the entire universe depends.

  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.

    • Now, since nothing can happen which is not in the order, one can say that miracles are as much within the order as are natural operations, operations which are called natural because they are in conformity with certain subordinate maxims that we call the nature of things.

    • For one can say that this nature is only God’s custom, with which he can dispense for any stronger reason than the one which moved him to make use of these maxims.

    • As for the general or particular volitions, depending on how the matter is understood, we can say that 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.

    • We can also say that God wills everything that is an object of his particular volition.

    • But we must make a distinction with respect to the objects of his general volition, such as the actions of other creatures, particularly the actions of those that are reasonable, actions with which God wishes to concur.

    • For, if the action is good in itself, we can say that God wills it and sometimes commands it, even when it does not take place.

    • But if the action is evil in itself and becomes good only by accident, because the course of things (particularly punishment and atonement) corrects its evilness and repays the evil with interest in such a way that in the end there is more perfection in the whole sequence than if the evil had not occurred, then we must say that God permits this but does not will it, even though he concurs with it because of the laws of nature he has established and because he knows how to draw a greater good from it.

  8. To distinguish the actions of God from those of creatures we explain the notion of an individual substance.

  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.

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

  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.

[7]

Everything occurs according to the general order. Miracles occur. Therefore, miracles are a part of the general order.

  • the general, most perfect order

    • natural operations according to the laws of nature, subordinate maxims, God’s custom

    • miracles are particular volitions of God which are exceptions to the laws of nature

  • general volition, in accordance with the general, most perfect order

    • objects of God’s general volition

  • particular volition

    • objects of God’s particular volition are willed by God

  • permittance

  1. On divine perfection, and that God does everything in the most desirable way.

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

  3. Against those who believe that God might have made things better.

  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 the perfection of divine conduct consist in, and that the simplicity of the ways is in balance with the richness of the effects.

  6. God does nothing which is not orderly and it is not even possible to imagine events that are not regular.

  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.

  8. To distinguish the actions of God from those of creatures we explain the notion of an individual substance.

  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.

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

  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 his creatures, whose choice always has its reasons, which incline without necessitating.

  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.

  15. The action of one finite substance on another only 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 accomodate 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 subordinate maxims.

  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.

13

  • necessity vs certainty

2

  • God is good

  • the rules of goodness,beauty,perfection are not arbitrary, but rational

  • Suppose the works of God were good because God determined them; then God, knowing that he is the author of his works, would not have had to consider whether his works were good after making them as it is testified. Rather, there is an independent criterion of goodness that does not depend on whether God determined one thing or another.

  • We proceed from the goodness of God’s works to the goodness of God; not the other way around.

  • critique of Spinoza

    • wisdom is just will

    • justice is just power

  • for Leibniz, will presupposes a reason for will

  • critique of Descartes

    • reason is just an effect of God’s will

  • for Leibniz, God’s will is an effect of reason; God’s essence and understanding do not follow from God’s will, but are independent of it and prior to it

1

  • God is an absolutely perfect being

    • possesses greatest/infinite/supreme/unlimited

      • omnibenevolence: goodness

      • omniscience: knowledge/wisdom

      • omnipotence: power

  • there are several entirely different perfections in nature; God possesses all of them together; each of them belongs to him in the highest degree

  • perfection

    • has a highest degree

    • not perfections: greatest number, greatest figure

    • perfections: greatest knowledge, greatest omnipotence, greatest power

  • because perfections belong to God in the highest degree, they are unlimited

  • God acts perfectly, in both metaphysical and moral sense

  • the more we understand God’s work, the more we find them excellent and desirable


Why is human freedom problematic for Leibniz?

(absolutely, logically) necessity

  • not up to god’s will

  • true in all possible worlds

  • the contrary is a logical contradiction

  • explicit containment: the predicate is contained in the subject explicitly

certainty (“metaphysically, hypothetically necessary”)

  • up to god’s will, because it is actualized in the actual world (conditioned on god’s creation of this world)

  • true in some possible worlds, true in the actual world

  • the contrary is not a logical contradiction

  • implicit containment: the predicate is contained in the subject implicitly

truths of reason (necessary truths)

  • explicit containment

  • reducible to primary truths in finite number of steps

truths of (contingent truths)

  • implicit containment

  • reducible to primary truths in infinite number of steps

material bodies cannot be substances because they do not have enough unity and activity

  • material bodies are composites, they decompose

  • substance needs absolute unity

  • material bodies are passive, not the source of action/activity

  • only soullike things can be substances

  • bodies are well-grounded phenomena

physical universe is ideal, depends on metaphysical entities

malebranche’s occasionalism

deus ex machina

preestablished harmony

  • there is no real interaction between substances, but occasionalism is not a good solution

  • a substance cannot receive anything, any causal force, from outside, but from within itself (spontaneous)

  • each monad contains the entire universe

substance perceives in body

physical bodies are in causal interaction, in perception

at any given time, set of perceptions

appetite/volition moves set of perceptions at some time to another set of perctions at the next time, caused from within

no intersubstantial causation, only intrasubstantial causation

p0 causes p1 causes p2 etc.

determinism from within substance, not from without


Principle of Predicate in Subject

  • The predicate is always included in the subject

necessarily true proposition

  • a triangle has three sides

logical necessity, the contrary is a logical contradiction

attempts at solving the problem of human freedom

  • necessity vs certainty

    • logically necessary

possible worlds semantics

Principle of Contradiction, logical laws

  • no possible world can contain anything that is contradictory

  • A is A in all possible worlds

necessity, related to the event itself

certainty, related to knowledge of the event

unconditional truth

  • no logical possibility of the contrary

  • explicit containment

conditional/hypothetical truth

  • the contrary is logically possible

  • implicit containment

pre established harmony

  • there are no intersubstantial causations

  • intra substantial causation: the causal force is in the subject

  • there is perfect harmony between two substances across time

  • we are caused by our own previous states

just Spinoza’s idea of freedom

certainty is just strong inclination without necessitation


monad

substance

  • simples, without parts

  • do enter into composites

  • atoms, elements

  • no extension, because they are not divisible (a line can be divided)

  • do not come to be and dissolve

  • no external cause

simple monads have perceptions (perception)

souls are monads with perception and memory (apperception)

god

  • understanding -> possibilities

  • will -> existence

freedom, will informed by reason

arbitrariness is not praiseworthy; there must be a norm/standard by which things are judged praiseworthy

PB depends on PSR; god’s choices must have sufficient reason

god

  • omniscient

  • omnipotent

  • omnibenevolent

  • optimization problem? principle of economy simplicity or rules (min laws), richnes of effects (max effects)

inhabitants/members (substances)

a world, events in the world (state of substances)

laws

how do we account for evil, then?

everything is pre determined (subjects’ predicates)

complete concept, complete notion

everything in the universe is related, informs everything else

if you know one substance well enough, you know the history of the universe

not one of causality, but one of pre established harmony

nothing happens after some time t if the thing that happened at time t didn’t happen

explicit (a priori, logical, necessary) vs implicit (a posteriori, empirical, contingent?) containment of predicates in subjects

necessary truths vs contingent truths

for descartes, god is not constrained; for leibniz, god is constrained by logical truths

logical necessity (contrary is a logical contradiction) vs metaphysical necessity (contrary is not a logical contradiction)

god is the author of the laws of thought that god must subscribe to

  • a more democratic conception of god, vs monarchical conception

spinoza’s god cannot change anything but thought god was the free-est being

every truth is subject to PSR, whether logically necessary or just metaphysically necessary

necessary truths are true in all possible worlds

contingent truths are true in some possible worlds (the actual world)

anything that is true in all possible worlds is a logical/necessary truth

Cartesian Duality

Spinoza denies mind-body dualism

Substance Pluralism

Idealism

Monads

Descartes, Spinoza are systematic, clear, single magnum opus

developmental account of Leibniz’ philosophy

Spinoza

  • argued against transcendental notion of God

  • pantheist, immanent, by necessity

metaphysics

  • God is a substance

  • God entertains an infinite number of possibile worlds

  • God chooses one world to actualize, the best of all possible worlds

  • infinite number of substances

  • each monad is windowless, a closed system, “a world apart”

  • but the monads seem to be in perfect harmony

Leibniz also rejects intersubstantial causation

substances are metaphysical entities for Leibniz, not physical

  • body is not a substance, only mind is a substance

  • since they are metaphysical, they do not occupy any space; are not in space

  • bodies as physical are grounded in these metaphysical entities

  • each person is a system of monads

arch monad, the soul: the soul is the monad of the brain

  • the arm has a monad, the hand has a monad, the pinky finger has a monad, etc.

there is a hierarchy without causation

  • higher order monads include the explanation of what happens with the lower order monads

physical entities don’t contain monads, they are grounded in monads

works

  • Discourse on Metaphysics

  • Correspondence with Arnauld

  • Primary Truths

  • New System

  • Monadology

Principle of Contradiction (PC)

  • two propositions P and not P cannot be true at the same time

  • consistency is the primary condition of truth

  • two propositions contradicting each other cannot be true at the same time

Principle of Sufficient Reason (PSR)

  • nothing comes about without a reason; everything has a sufficient reason for it to be the case

  • every (positive) truth has a siufficient explanation as to why that is the case and not otherwise

Principle of the Best (PB)

  • God always opts for the best alternative

  • this world is the best of all possible worlds

Predicate-in-Subject (PIS)

  • in every true positive/affirmative proposition S is P the predicate P is contained in the subject S

  • every true proposition is necessarily true

Identity of Indiscernibles (PII)

  • S1+predicate, S2+predicate, then they are one and the same thing

  • for two substances to be different, their predicates must differ

  • two substances are the same wrt to their predicates then they are one and the same

perfection

  • only if has an ultimate degree; only if it’s maximizable

Plato’s Euthyphro, the nature or ultimate source of goodness

  • P is good bc God commands it

  • God commands it bc P is good

first, arbitrariness of mind norms

second, norms independent of god

for Leibniz, there is no arbitrary will

  • not arbitrary, based on reason, has a sufficient explanation


Prompt: Why is human freedom a problem for Leibniz? How does he try to address this problem and argue that humans are in fact free?#