What Russell thought best in Leibniz's theory of monads is his two kinds of space, one subjective, in the perceptions of each monad, and one objective, consisting of the assemblage of points of view of the various monads. This is still useful in relating perception to physics(plviii)
Every soul is a world apart, independent of everything else except God(pl43)
By Leibniz's invention of monads as real units the continuum was rendered discrete(pl71)
There must be as many monads as possible, and that there must, therefore, be an infinity of substances other than one-self(pl73)
Leibniz often attempted to deny that monads have anything corresponding to position in space(pl87)
In order to preserve their mutual independence, it is only necessary to regard the attraction or repulsion as due to the perception of one monad by the other(pl91)
It is in virtue of this common quality of materia prima that a collection of monads is extended(pl103)
Entelechies or forms, denote, when accurately used, not the whole monad, but its activity, or that in it which is analogous to a soul, as opposed to its materia prima, which is passive, and is matter also in the Aristotelian sense, opposed to form(pl104)
Space consists of an assemblage of relations of distance; the terms of such relations, taken simply as terms, are mathematical points. They are thus mere modalities, being a mere aspect or quality of the actual terms, which are metaphysical points or monads(pl105)
The monad alone is a substance, body is substances, not a substance(pl108)
Aggregates, not having unity, are nothing but phenomena, for except the component monads, the rest is added by perception alone, by the very fact of their being perceived at one time(pl115)
Each separate monad is real apart from the perception of it, but a collection, as such, acquires only a precarious and derived reality from simultaneous perception(pl116)
Monads, though they are not extended, have a certain kind of situation, i.e. an Ordered relation of coexistence to other things(pl125)
As the body consists of monads, the obvious question arises: Where is the body? None of his devices, in short, give Leibniz any escape from an objective space, prior to the phenomenal and subjective space in each monad's perceptions; and this ought to have been obvious to him, from the fact that there are not as many spaces as monads, but one space, and even one only for all possible worlds. The confusions into which Leibniz falls are the penalty for taking extension as prior to space, and they reveal a fundamental objection to all monadisms. For Spinoza, we may say, had shown that the actual world could not be explained by means of one substance; Leibniz showed that it could not be explained by means of many substances. It became necessary, therefore, to base metaphysics on some notion other than that of substance- a task not yet accomplished(pl126)
Leibniz states that if monads were not different, motion in a plenum would make no difference, for each place could receive only the equivalent of what it had before- again an argument involving a place which is not merely in the perceptions of monads(pl129)
Volition is confined to self-conscious monads(pl133)
Monads differ in the clearness of their perceptions, and those which have clearer perceptions are more active. That monad which is myself is dominant in the body, since, in relation to the other monads, it is active while they are passive(pl140)
There are three great classes in the hierarchy of monads, not sharply distinguished, but merging into each other. These are bare monads, souls and spirits. Bare monads, which are also called forms or entelechies, have the minimum of perception and desire; they have something analogous to souls, but nothing that could strictly be called a soul. Souls are distinguished from the first class by memory, feeling, and attention. Animals have souls, but men have spirits or rational souls(pl141)
Monads other than spirits have no memory of self and thus are merely incessant, i.e. they remain numerically identical without knowing it(pl141)
God takes notice of the superior monad in regulating others(pl142)
Changes in inferior monads exist mainly for the sake of the correlated changes in spirits(pl143)
It is by prime matter that monads are distinguished from God, and rendered limited and finite(pl144)
When one monad is said to be impeded by another, this is to be understood of the representation of that other in itself(pl145)
Monads are subject to passions, and are thus not pure forces(pl145)
The point of view is a part of confused perception, and therefore of prime matter; and the difference of points of view is the source of impenetrability(pl146)
Passivity causes a resistance to a new perception in the monad, resulting in confusion(pl146)
If there were only spirits, they would be without the required connection, without the order of times and places(pl147)
An inorganic body has no such single dominant monad, but is a mere aggregate. But every monad belongs to some organic body, either as dominant or as subordinate monad(pl148)
The dominant monad dominates in the sense that it represents more clearly what the other monads represent very confusedly(pl148)
The Body consists merely of those inferior monads whose points of view, at any given time, are so near that of the dominant monad that they perceive everything less clearly than it does(pl149)
The sum of constituent elements of prime matter gives an extended passive mass, while the sum of the entelechies gives a substantial form animating the mass. Leibniz was extremely anxious to persuade Catholics that they might, without heresy, believe in his doctrine of monads, thus the concession of a diplomatist rather than the creed of a philosopher. The problem of the Real Presence occupied Leibniz from the time when he was in the service of the Archbishop of Mainz, and formed one of his grounds for denying that the essence of matter is extension(pl152)
As every monad is eternal, the monad which is myself must have previously existed. Leibniz holds that it formed one of the monads composing the body either of father or mother. Before conception, he thinks, it was either a mere sensitive monad, or had at any rate only an elementary reason. If monads can naturally become rational, there seems no reason why they should not naturally cease to be so(pl154)
The reality underlying the phenomenon of motion is change of point of view. The monad which changes its point of view has absolute motion, while another which perceives this change has only a relative change of situation(pl155)