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Created by Jennifer Leslie Torgerson, MA

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School of Athens


Gottfried Wilhelm von Leibniz

1646 – 1716 CE





Baird and Kaufmann.  Philosophical Classics:  From Plato to Nietzsche, 2nd Edition. (Upper Saddle River, NJ:  Prentice Hall, 1997 [1994]).


Frederick Copleston,  A History of Philosophy:  Book Two.  (New York, NY:  Doubleday, 1985 [1944]). 


__________,  A History of Western Philosophy:  Hobbes to Hume, 2nd Edition.  (San Diego, CA:  Harcourt Brace, 1980 [1952]).


Nicholas Jolley, Editor.  The Cambridge Companion to Leibniz.  (Cambridge, UK: Cambridge University Press, 1995 [1996]).


Daniel Kolak.  The Mayfield Anthology of Western Philosophy.  (Mountain View, CA:  Mayfield Publishing, 1998).


G. W. Leibniz.  Discourse on Metaphysics, Correspondence with Arnauld and Monadology. (LaSalle, IL:  Open Court Classics, 1995 [1902]).


Louis P. Pojman.  Classics of Philosophy.  (New York, NY:  Oxford University Press, 1998).


T. V. Smith and Marjorie Grene.  Philosophers Speak for Themselves:  From Descartes to Locke.  (Chicago, IL: University of Chicago Press, 1967 [1940]).


P. F. Strawson. Individuals: An Essay in Descriptive Metaphysics. (New York, NY: Routledge, 1959).



The principle works of Leibniz


Discourse on Metaphysics (1686)

The New System of Nature and the Interaction of Substances (1695)

The Principles of Nature and of Grace (1695)

Monadology (1714)


And there remains a great deal of yet unpublished manuscripts.



(1) Leibniz contends that there is an infinity of substances, created and maintained by the existence of God, contrary Spinoza’s view that there is only one substance, the Absolute.

(2) The world, and these substances of which it is composed, are the best of all possible.

(3) Each substance is simple and without parts, and for this reason he called them monads. Monad means unity or unit, and Leibniz argued in Monadology that only units can be substances. “What is truly not one being is not truly one being.” (Letter to Arnauld, 30 April 1687)

(4) Strictly speaking no created substance can act on another. The monads “have no windows, by which anything can come in or go out.” (Monadology, part 7)

(5) The pre-established harmony established by God makes it possible to infer from any state of one substance, to a corresponding state of any other substance.

(6) Leibniz held that every proposition is in the subject-predicate form. We are in effect saying that the concept of the predicate is contained in the subject (when a priori and analytic).

(7) Leibniz insists the human will is free.

(8) Leibniz’s law: if one thing is identical to another, then anything that is true of the one thing is true of the other.

(9) The principle of sufficient reason is: that for every fact (or reason) there is a reason why it is so and not otherwise. This reason takes the form of an a priori proof, founded in the nature of the subject and predicate terms used in stating the fact. Monadology, #32

(10) Truths of fact / truths of reason: Truths of fact are contingent and truths of reason are necessary. Truths of fact are statements that are not necessarily true since they may be denied without contradiction, they just might be true of something about something in this world, or might be true of something in a particular possible world. Statements that are only true about some objects in the universe and not true of all objects in the universe.

Truths of reason are not true by definition. They are true everywhere, in every possible world, and to the externally real world they do apply descriptively. No power, not even God’s can change these truths. An example is the law of noncontradiction, etc.    Monadology, #33                                                                                                                               

Preestablished harmony: This solution, to the mind-body problem, was proposed by the German philosopher, Leibniz and is also called parallelism (or parallel functioning). Leibniz wrote Monadology and Discourse on Metaphysics (to name only 2). Mind and body do not interact. God has established a harmony between mind and body. Mental states and bodily states correspond at every moment due to this preestablished harmony. For example, if two clocks seem to be keeping perfect time, there are three ways this could arise: (1) through mutual influence; (2) through constant adjustments by the mechanic who cares for them; and (3) through their own inbuilt individual exactitude. Leibniz thought that the clocks, which represent the mind and matter universe, were built so perfectly that they will always keep perfect time. Leibniz was a rationalist and an idealist.

Monadology, #80: Descartes saw that souls cannot at all impart force to bodies, because there is always the same quantity of force in matter. Yet he thought that the soul could change the direction of bodies. This was, however, because at that time the law of nature, which affirms also the conservation of the same total direction in the motion of matter, was not known. If he had known the law, he would have fallen upon my system of Pre-established Harmony.

"The 3 primary rules of thought":

(a) The Law of Non-Contradiction: Nothing can both be and not be at the same time and in the same respect. Remember Parmenides' phrasing of the law of non-contradiction?

("What is and cannot not be; and what is not and cannot be."). Monadology, #31

(b) The Law of the Excluded Middle: Something either is or it is not. (The middle position is excluded, namely the impossibility of something both being and not being simultaneously.)

(c) The Law of Identity: Something is what it is.

God alone is without body.

There is no transmigration of soul. Monadology, #72

Not only is there no generation, but also there is no entire destruction or absolute death. Monadology, #76

For he is not only the Architect and the efficient cause of our being, but he is also our Lord and the Final Cause, who ought to be the whole goal of our will, and who alone, can make our happiness. Monadology, #90

Simple ideas cannot be defined.

Primary principles (axioms and postulates) need no demonstration, or cannot be proven, and indeed require no proof. (Monadology, #35)


[For a great discussion of Leibniz, and Monads, see "Monads" in P. F. Strawson, Individuals: An Essay in Descriptive Metaphysics, (New York, NY: Routledge, 1959), pages 117 - 134.]


There must be a higher reason for why substance exists, or an ultimate reason for things.

There is but one God, and this God is sufficient. (Monadology, #38 and #39)

MONADS ~ simples unities

Monads are simple unities, or substances which have no parts. (Monadology, #1)

Monadology, #2: There must be simple substances because there are composites; for a composite is nothing else than a collection or aggregatum of simple substance.

Monadology, #3: Now, where there are no constitute 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.

 They are infinite in number, and each is a mirror of the universe. Monads are said to have no windows, which means that they do not cause anything outside of themselves, and they only can affect internal activities.  Each monad is an unity of activity.  Monads are immaterial and imperishable. (Monadology, #4, #5, and #6)

 Monads are created, and sustained by God.  Monads are unities of perceptions and appetites.  All monads are INCORPOREAL.  All monads are said to have soul. (Monadology, #19) But Leibniz reserves the label soul monad for a certain kind of living being. There are several types of monads:


 also called entelechies (perfections) or automatons

living things such as, plants*

has perceptions (sensations such as touch, smell, etc.)


living things such as, animals

has perceptions and memories (of past experiences of internal activities)


human beings

has perceptions, memories, and rationality (the ability to think)



has perceptions, memories, rationality- but is perfect in every way.  God is the creator of the universe.  He is Necessary Being that maintains all other monads.  Only God is without body and only God knows the location of all monads (He has a window so to speak).

* Plants may be seen as simple monad, rather than soul monad. (Monadology, #19)

Consider the Venus Fly Trap.  Does it have perception?  If so, could it in some way have more than mere perception? Does it remember how to catch its prey or is it just an automatic response?  Animals are different from plants in that they have locomotion, and share many of the same sensations (such as sight) with humans (souls with rationality).  Living things all have soul, but does this include plants? Leibniz answers....

Monadology, #66: Whence we see that there is a world of created things, of living beings, of animals, of entelechies, of souls, in the minutest particle of matter.

Monadology, #67: Every portion of matter may be conceived as like a garden full of plants, and like a pond full of fish. But every branch of a plant, every member of an animal, and every drop of the fluids within it, is also such a garden or such a pond.

Monadology, #68: And although the ground and the air which lies between the plants of the garden, and the water which is between the fish in the pond, are not themselves plant or fish, yet they nevertheless contain these, usually so small, however, as to be imperceptible to us.

Monadology, #70: It is evident, then, that every living body has a dominating entelechy, which in animals is the soul. The parts, however, of this living body are full of other living beings, plants, and animals, which, in turn, have each one its own entelechy or dominating soul.

Monadology, #71: This does not mean, as some who have misunderstood my thought have imagined, that each soul has a quantity or portion of matter appropriated to it or attached to itself for ever, and that it consequently owns other inferior living beings destined to serve it always; because all bodies are in a state of flux like rivers, and the parts are continually entering in and passing out.

Monadology, #72: The soul, therefore, changes its body only gradually and by degrees, so that it is never deprived all at once of its organs. There is frequently a metamorphosis in animals, but never metempsychosis or a transmigration of souls. Neither are there souls wholly separate from bodies, nor bodiless spirits. God alone is without body.

Monadology, #8: Monads must needs have some qualities, otherwise they would not even be existents. And if simple substances did not differ at all in their qualities, there would be no means of perceiving any change in things.

Monadology, #9: (Principle of the Identity of Indiscernibles) Each Monad, indeed, must be different from every other. For there are never in nature two beings which are exactly alike, and in which it is not possilbe to find a difference either internal or based on an intrinsic property.

Monadology, #10: (Principle of Change) I assume it as admitted that every created being, and consequently the created Monad, is subject to change, and indeed that this change in continuous in each. (italics added)

A complete view of monad cannot be known until all the work of Leibniz is published.

 Remember that everything that is real, or actual must be composed of monad (simple or soul). To be actual it must be a true (not an imagined) unity.

Rocks (diamonds, marble, etc.) are not unities, nor are artifacts (tables, chairs, houses)-- these are well-founded phenomena.

NOTE also the different types of entities (in a letter to De Volder):


Composed of fractions, and when we try to find the parts of such fractions, we confuse these with actual entities and enter the labyrinth of the continuum.


Monads (actual composite entities are composed of simple unities).


Material substance  (passive) must have an immaterial substance which accounts for its active force. Bodily substance does not have existence. Organic bodies are a collection of primary matter used like a machine by a soul monad.  

He also wrote in a letter  to De Volder:

"Therefore, I distinguish (1) the primitive entelechy or soul, (2)  primary matter, i.e., primitive passive power, (3)  monads completed from these two, (4) mass, i.e., second matter [...] in which innumerable subordinate monads come together, (5)  the animal, i.e., corporeal substance which a dominating monad makes into a machine."

Note the dependence on phenomenology in Leibniz.  Material substance (corporeal) is dependent upon being perceived by an immaterial substance (monad or the incorporeal).  The phenomena is not what is actual or real.

Monadology, #63: The body belonging to a Monad, which is its entelechy or soul, constitutes together with the entelechy what may be called a living being, and with a sould what is called an animal. Now this body of a living being or of an animal is always organic, because every Monad is a mirror of the universe according to its own fashion, and, since the universe is regulated with perfect order, there must needs be order also in the representation of the soul and consequently in the body through with the universe is represented in the soul.

Monadology, #64: Therefore, every organic body of a living being is a kind of divine machine, or natural automaton, infinitely surpassing all artificial automatons. Because a machine constructed by man's skill is not a machine in each of its parts; for instance, the teeth of a brass wheel have parts or bits which to us are not artificial products and contain nothing in themselves to show the use to which the wheel was designed in the machine. The machines of nature, however, that is to say, living bodies, are still machines in their smallest parts ad infinitum. Such in the difference between nature and art, that is to say, between the Divine art and ours.

Leibniz and his argument for the possibility of the existence of God

Since no one before him had established that God was not only perfect, but that a perfect being was possible, he set out to construct an argument which was based on such a premise.

(1)  A perfection is a simple positive property.

(2)  Hence, there can be no demonstration that there is a formal inconsistency in asserting that various collections of them are instantiated by the same being.

(3)  But if there is no such demonstration, then it is possible that something has them all.

(4)  Hence a perfect being is possible.

This argument was constructed using the a priori conjectural method,  or (an early form of) the hypothetico-deductive method.  He also made contributions to the formal theory of probability, which he considered essential for an account of our knowledge of contingent truths.  But Leibniz is often criticized for elimination of contingent truth possibility.  

The principle of sufficient reason says that for everything that is the case, there is a reason for being the case, and not otherwise, and God knows all the reasons, even prior to their being actual (or complete).  Hence it seems that not only truths of reason would be necessary, but so too would truths of fact, in that they would too have a sufficient reason for their being the case, and not otherwise.  Hence nothing could truly be contingent, or random (free and undetermined).

Monadology, #40: We may hold that the supreme substance, which is unique, universal, and necessary with nothing independent outside of it, which is further a pure sequence of possible being, must be incapable of limitation and must contain as much reality as possible.

Monadology, #41: Whence it follows that God is absolutely perfect, perfection being understood as the magnitude of positive reality in the strict sence, when the limitations or the bounds of those things which have them are removed. There where there are no limits, that is to say, in God, perfection is absolutely infinite.

Monadology, #42: It follows from that created things derive their perfections through the influence of God, but their imperfections come from their own natures, which cannot exist without limits. It is in this latter that they are distinguished from God.


Since all other created monads have limits (in that they are not infinitely perfect, and they are not conceived alone but only through God's creation of them, etc.) they are not like the ultimate monad (God). Leibniz avoids the problem Descartes' had with his (Descartes') definition of substance (at least according to Spinoza). Descartes and Spinoza defined substance as that which is conceived through itself. Descartes understood (in On Substance) that the logical implication of this was that only God was truly substance, but he called mind and body substance anyway. Spinoza arrived at his pantheistic view of reality by following that definition of substance to its logical conclusion while also explaining how thinking mode corresponds to bodily mode. But Leibniz does not agree with Spinoza that God is self-caused. Leibniz also believes in and wants to account for a Creation in his theory of reality. Hence, Leibniz used a different definition of substance. He called substance monad, or simple unity. In this way, Leibniz can maintain, without contradiction that mind is substance as well as God. All created monad must be conceived through something else (namely God's creating them), and God is that which is conceived through itself. For Leibniz, God is uncaused cause, necessary being, the Creator of the universe and all other monad. God is perfect, omnipotent, omnibenevolent, omniscient, and omnipresent.

Sufficient reason dictates that there must be a reason for why something is way it is and not otherwise. This makes it necessary to admit that there is a necessary substance, and that all substances are not merely possible. God is necessary substance.

Monadology, #45: Therefore God alone (or the Necessary Being) has this prerogative that if he be possible he must necessary exist, and, as nothing is able to prevent the possibility of that which involves no bounds, no negation, and consequently, no contradition, this alone is sufficient to establish a priori his existence. We have, therefore, proved his existence through the reality of eternal truths. But a little while ago we also proved it a posteriori, because contingent beings exist, which can have their ultimate and sufficient reason only in the necessary being which in turn, has the reason for existence in itself.

Monadology, #46: Yet we must not think that the eternal truths being dependent upon God are therefore arbitrary and depend upon his will, as Descartes seems to have held, and after him Monsieur Poiret. This is the case only with contingent truths which depend upon fitness or the choice of the greatest good; necessary truths on the other hand depend solely upon his understanding and are the inner objects or it.

Monadology, #47: God alone is the ultimate unity or the original simple substance, of which all created or derivinal simple substances, or which all created or derivative Monads are the products, and arise, so to speak, through the continual outflashings of the divinity from moment to moment, limited by the receptivity of the creature to whom limitation is an essential.

God is both a sufficient and necessary condition for the existence of the universe ( or the creation of all other monad).

Necessary condition: this is a necessary condition for that if and only if that cannot be without this. Oxygen is a necesary condition for fire. Oxygen is a necessary condition for fire if and only if fire cannot be without oxygen. Fire cannot be without oxygen. Without the presence of oxygen, fire will not occur. Oxygen is not a sufficient condition for the presence of fire, or there would be fire everywhere oxygen was present.

Sufficient Condition: this is a sufficient condition for that if and only if this alone is enough to guarantee that. 5 nickels are a sufficient for having twenty-five cents, if and only if having 5 nickels alone will guarantee that I have twenty-five cents. It is not necessary that I have five nickels to have twenty-five cents, merely sufficient.