Ultimate, indivisible unit, used by the neo-Platonists to signify the One; for instance, in the letters of the Christian Platonist Synesius, God is described as the Monad of Monads
Monad (from the Greek monas, monados), in the sense of ultimate, indivisible unit, appears very early in the history of Greek philosophy. In the ancient accounts of the doctrines of Pythagoras, it occurs as the name of the unity from which, as from a principle (arche), all number and multiplicity are derived. In the Platonic "Dialogues" it is used in the plural (monades) as a synonym for the Ideas. In Aristotle's "Metaphysics" it occurs as the principle (arche) of number, itself being devoid of quantity, indivisible and unchangeable. The word monad is used by the neo-Platonists to signify the One; for instance, in the letters of the Christian Platonist Synesius, God is described as the Monad of Monads. It occurs both in ancient and medieval philosophy as a synonym for atom, and is a favorite term with such writers as Giordano Bruno, who speak in a rather indefinite manner of the minima, or minutely small substances which constitute all reality. In general, it may be affirmed that while the term atom, not only in its physical, but also in its metaphysical meaning, implies merely corporeal, or material attributes, the monad, as a rule, implies something incorporeal, spiritual, or, at least, vital. The term monad is, however, generally understood in reference to the philosophy of Leibniz, in which the doctrine of monadism occupies a position of paramount importance. In order to understand his doctrine (see System of Leibniz) on this point, it is necessary to recall that he was actuated by a twofold motive in his attempt to define substance. He wished, in accordance with his general irenic plan, to reconcile the doctrine of the atomists with the scholastic theory of matter and form, and besides he wished to avoid on the one hand the extreme mechanism of Descartes, who taught that all matter is inert, and on the other the monism of Spinoza, who taught that there is but one substance, God. All this he hoped to accomplish by means of his doctrine of monads. Descartes had defined substance in terms of independent existence, and Spinoza was merely inferring what was implicitly contained in Descartes's definition when he concluded that therefore there is only one substance, the supremely independent Being, who is God. Leibniz prefers to define substance in terms of independent action, and thus escapes Descartes's doctrine that matter is by nature inert. At the same time, since the sources of independent action may be manifold, he escapes Spinoza's pantheistic monism. The atomists had maintained the existence of a multiplicity of minute substances, but had invariably drifted into a materialistic denial of the existence of spirits and spiritual forces. The scholastics had rejected this materialistic consequence of atomism and, by so doing, had seemed to put themselves in opposition to the current of modern scientific thought. Leibniz thinks he sees a way to reconcile the atomists with the scholastics. He teaches that all substances are composed of minute particles which, in every case, in the lowest minerals as well as in the highest spiritual beings, are partly material and partly immaterial. Thus, he imagines, the sharp contrast between atomistic materialism and scholastic spiritualism disappears in presence of the doctrine that all differences are merely differences of degree.
The monads are, therefore, simple, unextended substances, if by substance we understand a center of force. They cannot begin or end except by creation or annihilation. They are capable of internal activity, but cannot be influenced in a physical manner by anything outside themselves. In this sense they are independent. Moreover, each monad is unique; that is, there are no two monads alike. At the same time the monads must have qualities; "otherwise", says Leibniz (Monadol., n. 8), "they would not even be entities". There must, therefore, be in each monad the power of representation, by which it reflects all other monads in such a manner that an all-seeing eye could, by looking into one monad, observe the whole universe mirrored therein. This power of representation is different in different monads. In the lowest kind of substances it is unconscious—Leibniz finds fault with the Cartesians because they overlooked the existence of unconscious perception. In the highest kind it is fully conscious. We may, in fact, distinguish in every monad a zone of obscure representation and a zone of clear representation. In the monad of the grain of dust, for example, the zone of clear representation is very restricted, the monad manifesting no higher activity than that of attraction and repulsion. In the monad of the human soul the region of clear representation is at its maximum, this kind of monad, the "queen monad", being characterized by the power of intellectual thought. Between these two extremes range all the monads, mineral, vegetable, and animal, each being differentiated from the monad below it by possessing a larger area of clear representation, and each being separated from the monad above it by having a larger area of obscure representation. There is then in every created monad a material element, the region of obscure representation, and an immaterial element, the area of clear representation. Everything in the created world is partly material and partly immaterial, and there are no abrupt differences among things, but only differences in the extent of the immaterial as compared with the material. Minerals shade off insensibly (in the case of crystals) into living things, plant life into animal life, and animal sensation into human thought. "All created monads may be called souls. But, as feeling is sometimes more than simple perception, I am willing that the general name monads, or entelechies, shall suffice for those simple substances which have perception only, and that the term souls shall be confined to those in which perceptions are distinct, and accompanied by memory" (Monadol., n. 19). "We ascribe action to the monad in so far as it has distinct perceptions, and passivity, in so far as its perceptions are confused" (ibid., n. 49). If this is the only kind of activity that the monad possesses, how are we to account for the order and harmony everywhere in the universe? Leibniz answers by introducing the principle of Pre-established Harmony. There is no real action or reaction. No monad can influence another physically. At the beginning, however, God so prearranged the evolution of the activity of the myriads of monads that according as the body evolves its own activity, the soul evolves its activity in such a way as to correspond to the evolution of the activity of the body. "Bodies act as if there were no souls, and souls act as if there were no bodies; and yet both act as if one influenced the other" (Ibid., n. 81). This preestablished harmony makes the world to be a cosmos, not a chaos. The principle extends, however, beyond the physical universe, and applies in a special manner to rational souls, or spirits. In the realm of spirits there is a subordination of souls to the beneficent rule of Divine Providence, and from this subordination results the "system of souls", which constitutes the City of God. There is, therefore, a moral world within the natural world. In the former God is ruler and legislator, in the latter He is merely architect. "God as architect satisfies God as legislator" (ibid., n. 89), because even in the natural world no good deed goes without its recompense, and no evil deed escapes its punishment. Order among monads is thus ultimately moral.
Since Leibniz' time the term monad has been used by various philosophers to designate indivisible centers of force, but as a general rule these units are not understood to possess the power of representation or of the Leibnizian monad. Exception should, however, be made in the case of Renouvier, who, in his "Nouvelle monadologie," teaches that the monad has not only internal activity but also the power of perception.