Monad

Monad is an English term meaning "one," "single," or "unit," especially in technical contexts. It comes from the Late Latin stem monad-, derived from the Greek word monos or μονάς (from the word μόνος, which means "one," "single," or "unique").

The term “monad” was used by the Pythagoreans as the name of the beginning number of a series, from which all following numbers derived. In ancient philosophy, Epicurus described "monads" that were the smallest units of matter, much like Democritus's notion of an atom. For many Greek philosophers, including Pythagoras, Parmenides, Xenophanes, Plato, Aristotle, and Plotinus, Monad was a term for God or the first being, the totality of all beings, the source or the One. Gnostics used the term “monad” to refer to the most primal aspect of God. In De monade, numero et figura liber (“On the Monad, Number, and Figure,” 1591) Giordano Bruno described three fundamental types of monads: God, souls, and atoms.

The term "monad," however, is best known as a concept of Gottfried Wilhelm Leibniz. Leibniz, in Monadologia (Monadology, 1714), proposed that the universe is made up of monads, basic individual substances that encompass complete concepts and are immaterial, lacking spatial extension. Each monad is a unique, indestructible, dynamic, soul-like entity whose properties are a function of its perceptions and appetites. Monads have no true causal relation with other monads, but all are perfectly synchronized with each other by God in a pre-established harmony. Based upon the the principle of the "Identity of Indiscernibles" ("if and only if entities have the same properties in common, they are identical"), Leibniz explained the multiplicity of beings by ascribing the individuation of each being to the concept of monad. His concept of monad has a logical aspect as well. Mondad is the subject that all possible predicates are ascribable to.

Philosophy of Leibniz

Monadology as a philosophical system is usually associated with the mature metaphysics of Gottfried Leibniz, outlined in his work, Monadology (1714). His fundamental thesis is that the basic individual substances that make up the universe are monads, immaterial soul-like entities without spatial extension.

Substance as Monads

Around the end of the seventeenth century, Leibniz began to use the word "monad" (meaning “that which is one, has no parts and is therefore indivisible”) to refer to his concept of the fundamental units of existence. His theory was an alternative to the mechanistic theory of atoms that was becoming popular in natural philosophy at the time. While atoms were the smallest unit of extension out of which all larger extended things are built, monads had no spatial extension (Leibniz viewed spatial extension as an illusion). A monad was the reality represented by a complete concept, containing within itself all the predicates of the subject of which it was the concept; these predicates were related by sufficient reasons into a vast single network of explanation. A monad, having all these properties within itself, was self-sufficient and did not need to relate to or be influenced by any other monad.

Instead of cause and effect as the basic agency of change, Leibniz posited a theory of pre-established harmony to explain the apparently inter-related behavior of things. A common analogy is that of two clocks situated on different sides of a room, both keeping accurate time. A person who does not understand clocks might suspect that one was the master clock and is causing the other clock to always follow it. Another person who knows about clocks would explain that the two clocks have no influence on each other, but instead that they share a common cause (the last person who turned them on and synchronized them) and have been independently keeping correct time. When two things are observed to behave in corresponding ways, it is often assumed (without any real evidence) that causation is occurring. According to Leibniz, every monad is like a clock, behaving independently of other monads. Nevertheless, all monads are perfectly synchronized with one another by God, according to His vast conception of the perfect universe.

Leibniz’ theory of pre-established harmony argued that monads do not affect one another, and that each monad expresses the entire universe. Leibniz stated that every monad mirrors the whole of the universe in that it expresses every other monad, but no monad has a window through which it can actually receive or supply causal influences. Since a monad cannot be influenced, there is no way for a monad to be born or destroyed; all monads are thus eternal and immutable.

Leibniz and Descartes

Leibniz posited that human souls were a special kind of monad, termed a dominant, or rational, monad, which included consciousness and the ability to reflect, a capacity which Leibniz termed “apperception.” All other simple monads had two basic qualities, appetite and perception, while some monads also had memory.

Leibniz was one of the first philosophers to examine the importance of the "unconscious" mind. The concept of the human soul as a "mirror" of the whole universe entailed an infinite number and complexity of perceptions. An individual could not apperceive (be conscious of) all these little perceptions, as Leibniz called them, and even conscious perceptions were composites of vast numbers of individual perceptions. Leibniz used the analogy of the roar of waves on the beach; their seemingly singular sound was actually composed of vast numbers of small individual sounds. Leibniz considered that Descartes had made a major error in assuming that the human consciousness could actively perceive everything.

According to Leibniz, everything which is perceived as a unified being must be a single monad. Everything else is a composite of many monads. A coffee cup, for example, is actually composed of an infinite number of monads, all of them are acting together so that it is perceived as a single thing. The human soul, however, and the soul of every other living thing, is a single monad which "controls" a composite body. Leibniz posited substantial form, for living things, as the principle of the unity of certain living composites. In opposition to the empiricists of his time, Leibniz used the term "innate idea" to distinguish an idea which is intrinsic to the mind rather than arriving in some way from outside it. On a metaphysical level, since monads have no "windows," it is inherent that all ideas are innate. An idea in a peron’s monad/soul is just another property of that monad, which occurs according to an entirely internal explanation represented by the complete concept. At the phenomenal level, however, many ideas are represented as arriving through one's senses.

Influence of Leibniz’s Monadism

Leibniz's approach to reality was very influential on eighteenth–century philosophy, suggesting ideas which revived an interest in rational metaphysics and laying the foundation for the idealism of Kant and Hegel. During the twentieth century, Leibniz was appreciateded by Anglo-American analytic philosophers as a gifted logician who made significant contributions to the theory of identity and modal logic. Leibniz has been given less importance in continental European philosophy, although the writings of Heidegger and, much later, Deleuze, demonsrate the continuing fertility of his philosophical ideas.

Other Uses of the term “Monad”

In Monism, the metaphysical and theological view that all is of one essence, this essence is sometimes called the monad.
In Hermetica, a category of popular Late Antique literature purporting to contain secret wisdom, The Cup or Monad is one of the texts making up the Corpus Hermetica.
In ancient philosophy, Epicurus described "monads" that were the smallest units of matter, much like Democritus's notion of an atom. For many others, including Pythagoras, Parmenides, Xenophanes, Plato, Aristotle, and Plotinus, Monad was a term for God or the first being, the totality of all beings, the source or the One.
In Gnosticism, monad refers to the most primal aspect of God.
In early biology, the indivisible life essence, either the cell or nucleus, was called “monad.”
In category theory, a monad is a type of functor.
Monads are type constructors that are used in functional programming languages to capture various notions of sequential computation.
A monadic function or operator may be the same as a unary one, or one somehow having to do with either of the previous kinds of monad. Monadic predicate calculus is a form of logic based on unary operators.
A monad in music is a single note, as opposed to a dyad or trichord.

References
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Bruno, Giordano. 1591. De monade, numero et figura liber (“On the Monad, Number, and Figure”).
Leibniz, Gottfried Wilhelm, and Nicholas Rescher. 1991. G.W. Leibniz's Monadology : an edition for students. Pittsburgh, PA: University of Pittsburgh Press. ISBN 0822936704 ISBN 9780822936701 ISBN 0822954494 ISBN 9780822954491
Savile, Anthony, and Gottfried Wilhelm Leibniz. 2000. Routledge philosophy guidebook to Leibniz and the Monadology. Routledge philosophy guidebooks. London: Routledge. ISBN 041516575X ISBN 9780415165754 ISBN 0415171148 ISBN 9780415171144 ISBN 0415165768 ISBN 9780415165761 ISBN 041517113X ISBN 9780415171137
Singer, Dorothea Waley, and Giordano Bruno. 1968. Giordano Bruno; his life and thought. With annotated translation of his work, On the infinite universe and worlds. New York: Greenwood Press. OCLC: 442921

External links

All links retrieved November 9, 2022.

Monad – The Catholic Encyclopedia
Stanford Encyclopedia of Philosophy entries:

General Philosophy Sources

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