G.W. Leibniz: Philosophy Leading up to Monads

24 May

Leibniz’s Law of Contradiction consists of propositions and predicates and what kinds of propositions do not follow suit with which. Kinds of propositions are things like analytic to synthetic propositions and the phenomena of necessity and contingency.


Analytic Propositions

Propositions that say something about logic, arithmetic or geometry are analytic. Logic, arithmetic and geometry involve analyzing some sort of mathematic phrase or term that is analyzed. Therefore it is analytic.

Synthetic Propositions

Propositions that concern existential or metaphysical ideas of philosophy are synthetic mostly because those ideas are mostly of opinion so they are deemed synthetic unless otherwise observed. God is not considered by Leibniz to be a synthetic proposition. God is the only existential metaphysical idea that is not synthetic.

God is only considered synthetic if it is also considered analytic. God is either considered synthetically analytic or God falls in neither category of propositions.

Law of Contradiction

Because of the contradiction that may occur in a premise and proposition, this law states that no conclusion will follow suit in a contradictory statement.
This law can only have one possible conclusion. The conclusion from a contradictory statement, the conclusion is either that there is truth   or that the proposition is false.

Finally, under this if there is a contradiction in an analytic proposition, no possible conclusion will follow suit.


Leibniz never really explains it fully as an entity but in a way that there are 3 kinds of necessity: metaphysical necessity, hypothetical necessity and moral necessity. Analytic proposition must always have metaphysical necessity. Metaphysical and moral propositions apply to the law of contradictions where contradictions take place in the premises and propositions. Analytic propositions in themselves are necessary. Necessity in propositions are ultimate and undefinable.


Synthetic propositions are usually ones that state existential or metaphysical properties. Synthetic propositions are always contingent. Contingent in this case normally means dependent on other things for existence. Synthetic propositions are different from necessary propositions in that necessary propositions are independent in their existence and other things depend on the necessary things. Synthetic propositions are contingent because of how opinions about existence and other metaphysics are usually dependent on other things. While things that are analytic in things like mathematics are necessary because they are independent and other things usually depend on them.

Considering judgments (a different form of opinions), they are necessary in that they have moral necessity and they are synthetic in that they involve existentialism or other metaphysics.

Contingency is relating more to the Law of Sufficient Reason just as necessity relates more to the Law of Contradiction.


Contingency basically is talking about anything with severe generality. If your argument of reason is very vague, it is within the use of contingency. Generality relates to being contingent because if you are general in something, it is dependent upon other ideas to fully explain something. Contingency also involves time or smaller parts of time. The use of time is contingent because it is dependent on other things to explain why the time of something matters to the overall argument of reason. Necessity would never involve any sense of time. God and simply the idea of a higher superior deity is not contingent according to Leibniz. Necessity would involve God and all ideas concerning superior deities. God being an eternal truth involves no idea of time because of the fact that no eternal truth has a sense of time. God falls in the eternal truth category so necessity keeps the idea of God while contingency does not because of how an eternal truth is independent in itself.

On another subject concerning contingency, a  notion of species involves a whole certain group of beings that is usually very large. Notions of species either are or can be an eternal truth. If the notion of species is an eternal truth, they are necessary and contingency has no part in it. Notion of species also involves no time.

Another notion called the notion of an individual or sub ratione possibilitatus refers to only 1 existence and involves much time. This notion also involves fact about that individual that cannot be solid because of the many individuals there are. Because of the vaguness that is a part of sub ratione possibilitatus, the notion of the individual is itself contingent.

Contingency has dependence on other ideas and things and has ambiguity and vagueness in it. Because of the dependence and vagueness of contingency, existence itself cannot be a part of it. Existence of 1 or many is a part of necessity only. One might ask what part existence has in contingency if existence in its pure form belongs to necessity. The essence or main idea of existence (kind of like the form of existence by Plato) does not need to be referred to by a tangible form. The essence or main idea of existence is dependent on tangible things to actually verify a concept of existence, therefore the essence/main idea of existence belongs to contingency. The essence of existence here is described as assertion. Essence discussed in another manner of the word can be discussed as essence of existence belonging to necessity.

Law of Sufficient Reason

There are 2 kinds of existents that are bounded within this law.

  1. Possible Existents- An existent (cause) that is itself possible in any way are only desires and appetites (sometimes of the flesh).
  2. Actual Existents- An existent (cause) that is itself actual in any way are only desires for good. The idea of good here can be rooted all the way back to Plato’s form of the good.

There is reason that people try to use to carry out daily tasks. In the things that people do every day, there are two existents and by existents I mean causes that drive the choices of people. Starting with the Actual Existents, the desire for good does drive people to decide certain things. You see this fact in many philosopher’s ideas. For example, Plato’s line at the top just under dialectic, shows the Form of the Good. The good includes assisting others, having greater knowledge and serving the higher deity. The actual existents enforce the decisions of the better people of the society. The actual existents shows necessity

Possible existents is something different because it reflects items of contingency. Desires and appetites lead people to do something that may feel better to them than doing things toward good (actual existents). Doing things to advocate your desires and appetites lead nowhere towards a God within necessity. The actions in the possible existent lead to synthetic propositions and contingency. Because of the causes the possible existents have shown to cause, Leibniz directs the best option in reason to be sufficient reason in the actual existent.

Leibniz’s biggest known philosophy was Monadism. The concept of substance and activity are concepts of his that lead up to monads.


Lets first understand what a subject and predicate is in logic and reason. A subject is pretty much a premise of an argument. It is the main thing discussed in a sentence of logic. A predicate is the denial or confirmation in a sentence of logic of the subject
Lets define substance:

1) Recognizes of only the subject of logic and not the predicate(s).
2) Consists of many predicates.
3) Goes through constant change

To shortly sum this up, it is the changing form of a subject. In substance alone, time is a contradiction.


This is the metaphysical necessity of substance. This is how substance exists metaphysically in things discussed. This is a phenomenon that is the biggest quality of substance. This is where substance shows itself. Without this, substance would be contingent. Leibniz introduces this idea and does not thoroughly explain it until a whole new phenomena is introduced. Activity is necessary. It is especially necessary for substance to be necessary.


This is an essence that constitutes substance. Force in this case creates activity in substance. This is the biggest principle of activity. This must change and pass in and out in activity. Virtue comes in and out of substance through force

Activity with force is not causation. However, activity with force is an attribute corresponding to the relation of causality. Force is causal to activity. Activity is causal to the appearance of substance.

This is the introduction of Leibniz’s ideas posted because they directly play into monadism.
Leibniz’s Monadism will be explained later. The  concepts of substance, activity and force are the elements of Monadism.

Laws of Continuity

There are 3 laws and the 1st law has 2 laws inside it. Continuity means simply that what is discussed never ceases to continue.

1) Spatio- Temporal Continuity
This breaks down into 2 continuities
– Continuity of Space
– Continuity of Time

2) Continuity of Cases
This applies mainly for laws of nature and reason/logic. If the difference between 2 cases continue to decrease without limit, the result itself will also decrease in difference without limit. For example. if a marsupial mouse and a normal mammal mouse are very different, evolution becomes divergent and the 2 cases without limit become more and more the same, the result will be the same mouse even though they are of different genus.

3) Continuity of Actual Existents/Forms
If 2 substances differ finitely, there is a continuous series of intermediate substances, each differing infinitesimally from the next one in the series (Russel, 1900). The substances that differ and create the intermediate series are actual existents. By Leibniz, ever spot in a series is filled with all certainty. Each spot in a series is not filled twice either.
Continuity is never always equal to actual existents.

Possibility versus Compossibility

If there is a series of existents, the series is possible if none of the existents in the series contradict each other.


If there is a series of existents and 2 of the existents belong to the same possible world, the existents are compossible. Another way to explain this is that if 2 existents coexist in the same possible world, they are compossible.

Being compossible can be confused with when 2 existents fall into the same possible world/category. If this occurs, the 2 existents are contradictory  not compossible. Things cannot coexist if they contradict each other.
There are an infinite number of possible worlds whether or not compossibility exists within them. All worlds respond to each other in one way or another with the existents within them.


There are 3 types of necessity concerning the possible worlds and the compossibility within them.

1) Metaphysical or Geometrical Necessity
-This basically covers the parts of necessity that have been proven past hypotheses. Metaphysics and mathematics that are known to be true are in this category of necessity. The opposite of this necessity is self contradictory.

2) Hypothetical Necessity
– In some ways, hypotheses can have contingency, but some have necessity and those that do are what this discusses. Those existents that are valid concepts that have not been accepted to be metaphysical or mathematical are hypothetically necessary.

3) Moral Necessity
– There is only necessity in morals because morals are only from the good. The good existents are chosen by God and His angels according to Leibniz.

Leibniz’s philosophy of matter/monads should be the next post on Leibniz.
If you did not understand some terminology like the word existents or contingency there are 3 previous posts on Leibniz. Go there to understand all the interwoven concepts within these higher understood concepts.

This is still leading up to the theory of monads as these concepts lay foundation for it. This is one of 2 parts of Leibniz’s Philosophy of Matter.

before the Theory of Dynamics and other concepts can be explained, there are 5 different definitions of matter and body.
1) Materia Prima- this is matter that is known to exist because of extension. Extension is then known as repetition. The translation is primary matter. It is purely passive as defined by Leibniz.
2) Materia Secundus- this is matter given by force. It translates to secondary matter.
3) Primary matter as an element of every monad.
4) Secondary matter described as an aggregate of monads. When secondary matter is described as so, it can also be described as mass. Mass as defined by chemistry is what has matter and takes up space.
5) The organic body of a monad.

Secondary matter and secondary matter as an aggregate of monads is what makes up mass and body. Body is something that is a part of explanations throughout the philosophy of matter.
Corporeal substance is created with the organic body of a monad and a dominant monad.

The aforementioned material may not mean much now, but they are only defined to assist in explanation of later principles.

The Law of Dynamics

As explained by Leibniz, dynamics shows that the essence of matter is not extension (remember that extention is repetition). Also, the total quantity of matter in the universe is not constant, but the quantity of matter in a given direction is constant.


As explained in previous posts, force is a key phenomenon in activity itself and activity is the main principle of substance. In relation to dynamics, force is an ultimate entity that is and remains constant. Force is proportional to the quantity of another phenomenon in energy. Different kinds of force will be explained later.

Where is Dynamics derived?

2) Dynamics is derived from the nature of the extended. Materia prima is the matter that is extended under dynamics.
3) Dynamics is derived from the fact that materia prima is supplemented by force.

Materia Prima

As stated above, dynamics is derived by the fact that force is its supplement. Force is primary matter’s supplement through resistance.
There are 2 types of resistance that materia prima acts upon through force.
1) Impenetrability- other forces or beings cannot penetrate it if the materia prima has sufficient resistance.
2) Inertia- The materia prima resists motion that it endures.

Materia prima has 2 properties:
1) The property of bodies, matter and mass in virtue of which they are in places.
2)  The property of virtue in which they resist any effort to make them change places.

The above 2 properties relate to the 2 kinds of resistance. The first property relates to impenetrability because  of how the bodies, matter and mass attempt to remain in the same places. The second property relates to inertia because of how the materia prima bodies attempt to resist motion in between places.

The materia prima also shows in dynamics to have 2 kinds of power.
Power- according to dynamics, power involves force and energy all inside activity
1) Passive power- power that constitutes matter/mass therefore contains resistance.
2) Active power- power that constitutes form.

The idea of power in dynamics contains passive force. In all power, force is involved so passive force is also involved.

Passive Force

there are 2 kinds of passive force in dynamics.

1) Primitive Passive Force- this kind of passive force always involves ressitance. Primitive force itself resists materia prima.
2) Derivative Passive Force- this kind of passive force resists materia secundis.

to clarify inertia.

Law of Inertia

The fact that a body will not engage in motion when a force acts upon it. The body or mass will remain stationary when the force acts on it and is one of the resistances involved in force.

There are 3 theories of dynamics that surfaced in Leibniz’s time that Leibniz refuted because these 3 principles  contradict his idea of the law of dynamics and through this, he explains what dynamics really is. Leibniz is kind of difficult in how he explains his ideas.

The Doctrine of Hard Extended Atoms

By Leibniz, all atoms are extended/repeated and elastic. This doctrine of these atoms state that even though the atoms are elastic and extended/repeated, they are also hard. Leibniz refutes this because it is not possible for the atoms to be hard while at the same time being elastic and extended/repeated.

The Doctrine of the Plenum

This is a doctrine basically explaining about the possible existence of a vacuum in Leibniz’s dynamics of atoms.
This is getting a little bit into physics and that is not what my aim really is but I think that the doctrine of the plenum does well to explain the philosophy of matter by Leibniz. If you do not know what a vacuum is, it is not the device that sucks up dirt to clean your house. A vacuum in physics is a spot in space/time where there are no atoms or particles of any kind. If a person was in a vacuum, you would suffocate because there is no air in vacuums.
The argument is whether or not a vacuum in space is possible under dynamics of atoms. Leibniz refuted the possible existence of any vacuum because he says that when God made the universe, he took every opportunity there was to create atoms and life to occupy every area within the universe. Leibniz is basically saying that there is no real reason to determine the proportion of filled space to vacuums in the universe so he concludes in this doctrine that an existence of a vacuum anywhere in the universe of atoms is not possible.
Plenum has a clear definition by Leibniz. Plenum is where all matter is connected together. Everything that has atoms is a plenum.

The Doctrine of Unextended Centers of Force

The topic of this doctrine that Leibniz refutes is force actions of atoms upon other atoms. The presupposition is that whether or not atoms act upon each other far away from us. Leibniz concludes that because atoms never act upon each other through force near us, they cannot possibly do so far away. The issue here is merely if or not atoms can act upon each other anyway. It is first determined whether or not they can do so and then it is determined to what lengths they do those force implied actions. Leibniz’s verdict on this is that atoms cannot act forcibly upon each other anyway so the lengths that they do so does not matter in this case.

There are 2 kinds of force that act upon the atoms in this universe.

1) Primitive Force- First of all, this force corresponds to the soul and the substance of atoms. This force consists in every body always. At the beginning of this post when I laid out the 5 definitions of matter, I also included that corporeal substance is the organic body of matter and a dominant monad. This kind of force exists primarily in corporeal substances.

2) Derivative Force- This kind of force is more simple. This force is the result only of conflict between bodies with each other.
Derivative force is also defined as (called impetus) a tendency (called conatus) to some determinate motion by which the primitive force is modified. This shows that both kinds of force are always connected to each other in some way.

This next category is not really a force in its own but it is something that is important to force itself in activity of
atoms. Vis Viva is the sum of the derivative forces throughout the universe’s constance. Vis Viva being a sum of forces is really important to the substance and activity of the atoms in dynamics because this sum is always equal to kinetic energy.

Before the idea of a point can be explained, 2 kinds of beings must be introduced:
1)Simple- Entities consisting of one part and consists of no other parts.
2)Compound- Entities consisting of many parts. Each part of this is a simple entity.

Extension- Regardless of the changes something may go through inside time and space, the extension/repetition of the thing never changes. The time and space the entity extends itself in does not belong to the entity but the extension that is created will always exist and belong to the entity that was extended.
Extension is a plurality because of the ownerships and properties that are involved in the act of extension.

There are 3 points in space and time that Leibniz categorizes things in space and time.

1)Metaphysical Point- first characterized as atoms of matter, Leibniz re-explained metaphysical points as atoms of substance because substance gets more basic than matter. Monads are defined within these points.

2) Physical Point- this is clearly defined as the compressed corporeal substance. If you do not know what corporeal substance is, go to the beginning of this post.

3) Mathematical Point- these points coincide with mathematical relations of space and time and matter.

Monad-an existing substance that is a member of the actual and is of the best possible world. It is of the actual best possible world.

Monads have a few properties that explain nature of monads and how they unite.

Perception- at any moment, each monad/substance perceives all other monad/substance in different degrees of clarity. Every monad is omniscient but confused because of the varying degrees of clarity that monads perceive other substances. Monads perceive other monads on a basis of similarity to themselves.

Representation- or showing. This is the inverse of perception. B perceives A as A is represented in B.
In monads, sometimes a monad represents what they are perceiving.

How do monads differ

Appetition- this causes changes in perceptions of monads (or representation) leading towards appetites of good or evil. This causes more differences and diffusion between similar monads.

Monadic Phenomenon- phenomenon occurs in a monad when something appears to a monad so that it is represented in its perceptions.

  • Well Founded Monadic Phenomenon- a well founded phenomenon is when the thing that appears to the monad has well rooted perception.
  • Mere Phenomenon- if something appears to a monad and has little root in its perception showing  little to no adequate monadic basis, it is mere phenomenon.

Phenomena are just perceptions are just like any other perception that could appear to a monad. Phenomena are just more complex and are able to be distinguished between those that are mere and well founded.

In previous posts where materia secundis was explained, aggregates are those that correlate with that kind of matter. An aggregate is a unity of 2 monads there are 2 unproven possible kinds of aggregation but a for sure kind of aggregation will be explained later.

Monadic Aggregation

Monads do not usually easily unite. The below are 2 possible forms of aggregation.

1) Mere Aggregate- not being a real aggregate, it is confused for a simple collection of similar monads. The monads have similar perceptions of one another showing that it may be a real aggregate. It is classified as a mere aggregate because all the monads within the ‘aggregate’ have similar perceptions, representations and appetitions.

2) Real Unities- Unity of the monads is questioned in the first place because of the lack of similarity in form, perception, representation etc. between the monads. It is classified as a real unity because it is possible that the monads could be an aggregate because similarity is sometimes seen internally and sometimes externally.

*None of the above aggregates are real mutual possible aggregates. These are merely possible aggregates without having another component explained later.

Well Founded Phenomena Aspects

Excluding mere phenomena, well founded phenomena have 2 aspects that correlate them to monads.

  • Subjective- perceiving the monad as a phenomenon unit
  • Objective- seeing similarity of monads in phenomena

Phenomena are aspects that are used to help unite monadic aggregates. That is the big reason why phenomena matters to aggregation.

Ways for Monadic/Aggregate Unity

  • Externally (Merely)- This is not really unity in an aggregate, but monads try to unite as an aggregate through perception. When a monad tries to unite with an external monad, you only have fake unity because you see similarities in perception, representation and appetition, but that is not the way that aggregates are made so unity externally creates only mere aggregates.
  • Internally (Real)- Monads are united by general similarity of mutual perceptions of different monads, so outright similarity is not seen here, but in this case there is a larger chance for a bond between monads.

Monadic Perceptions

1)Simple Delusion- for example, a hallucination

2) Disjointed Aggregate- like a herd of livestock or a mere or a real unity/aggregate

3) Unified Aggregate- like a stone or a real unity without a dominant monad

4) Structural Aggregate- like a plant or animal or a real unity with a dominant monad

Substantial Link between Monads and the Dominant Monad

Dominant Monad is a monad amongst many other monads that has the best perception with the highest degree of clarity above all the other monads. This high monad has the highest good and has the highest amount of  strength and knowledge. A Substantial Link is created when the dominant monad observes all other monads within an aggregate below it.

This diagram does not put one point above others but the dominant monad would be B towards the furthest right because of how all other axioms are leading toward it. The substantial link is made because B perceives all the other monads.

Vinculum Substantiale

As explained in one of the previous posts about Leibniz, a simple substance is one that has no parts. And a compound substance is one that has many parts and each part is of a simple substance. In the beginning of this post I explained why the mere aggregate and the real unity aggregate are not REALLY  true aggregates, because a real aggregate is one that unites well enough that after it is united in the aggregate, it is no longer perceived as 2 monads/substances, but it is perceived as 1. Vinculum Substantiale is where an aggregate is that much of a true aggregate that it is perceived as a quasi-individual. Correlating this to monadic perceptions, aggregates without V.S. are disjunctive aggregates because of how they are not united into quasi individuals. The V.S. aggregate is the monadic perception of unified aggregate or even a structured aggregate because of how they are unified to the utmost extent.

How do monadic aggregates get from disjointed aggregates to unified aggregates with V.S.?

You get unified aggregates with V.S. with dominant monads and substantial links between the D.M and the other monads. Because of the high degree of clarity that the D.M. perceives the other monads, the monads and the D.M. are able to have a unified or even a structured aggregate with vinculum substantiale.


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