LEIBNIZ ON INDIVIDUAL SUBSTANCE

A. Development of Leibniz's view: from PT and DM (1686) through NS (1695) to PNG and M (1714).


B. What is an individual substance?  Earlier works

    1. Nominal Definition: An individual substance is (1) a subject to which predicates (properties; 'actions', 'passions', 'events'; 'phenomena'; 
      'expressions', 'representations', 'perceptions'; etc.) are attributed and (2) a being which itself is not attributed to anything else. (DM 8)

        a. Difference between 'subject' vs. 'substance' and 'predicate' and 'property'

        b. Sentences vs. propositions vs. facts; language vs. meaning vs. the world

    2. An individual substance (or complete being) is a being whose complete concept contains all of the predicates that belong to that substance 
      (or being). (PT, DM)

        a. Hence all the things that ever happen to an individual substance, together with all their circumstances and the whole sequence of external 
          things, are included in the notion of that substance. Hence every individual substance contains within itself (1) vestiges of everything that 
          has happened to it, (2) marks of everything that will happen to it, and (3) traces of everything that happens in the universe. (DM)

        b. Hence every individual substance contains in its perfect notion the entire universe. (PT)

        c. Each created substance is like a world apart, independent of all other things except God. Hence all the phenomena of such a substance, 
          i.e., all the things that happen to it, are consequences only of its own being. (DM)

    3. If a being has a concept which contains enough predicates to differentiate it from every other being, then it is an individual substance. (PT, DM)

        a. In nature, there cannot be two individual things that differ in number alone. (PT)

        b. No two substances can resemble each other completely and so differ solely in number. (DM)

    4. An individual substance is a true unity, and hence is perfectly indivisible. (PT, DM, NS)

        a. No substance can be divided into two [substances]. (DM, NS)

        b. No substance can be constructed out of two [substances]. (DM)

              i. A substance can begin to exist only by creation and end only by annihilation. (DM)

             ii. The number of substances cannot naturally increase or decrease. (DM)

        c. An individual substance is not wholly (or not really) material. (NS 139)

              i. Something lacking extension is required for the substance of bodies. (PT)

             ii. A material substance, or body, does not consist merely in extension. Each such substance must also include a substantial form, which is 
               something immaterial, like a soul. (DM, NS)

            iii. Some individual substances are themselves souls, or like souls. (NS)

        d. Individual substances are active, and are sources of activity. (NS 139)


C. Further truths about individual substances: Earlier Works

    1. Each individual substance is like a mirror of God and of the whole universe, and each one expresses, or represents, or perceives God and the 
      whole universe in its own unique way, or from its own unique point of view. (PT, DM, NS)

    2. No created individual substance really acts upon or influences any other, but every such substance appears, or is perceived, to act upon, and 
      to act in accord with, every other. (PT, DM, NS)

        a. The phenomena of a substance maintain a certain order in conformity with the nature of that substance, and hence with the phenomena of all 
          the other substances which that substance expresses and which constitute its world. (DM)

        b. The expressions or perceptions of all substances mutually correspond in the same way they would if they were really connected and causally 
          influenced one another. (DM)

        c. These substances are not really connected, however. God alone is the cause of the correspondence of their phenomena and of their perceptions. 
          (DM)

    3. Different created substances express God and other created substances to themselves (or perceive them) with different degrees of perfection. (DM)


D. Individual substances (monads) in later works

    1. Individual substances are either simple or composite.

        a. A simple substance, or monad, has no parts.

             i. Bodies have parts.

            ii. Hence a monad is not a body.

        b. Composite substances are collections or aggregates of monads.

    2. Monads cannot be destroyed, nor can they be generated, by natural means.

    3. Monads do change, however.

    4. Monads have no windows.

        a. They are entirely self-sufficient and self-contained.

        b. They are autonomous: all their changes are caused by internal principles.

    5. Monads are mirrors, however.

        a. Each monad expresses every other monad and thus the whole universe from its own point of view.

        b. Each monad also expresses God from its own point of view.

    6. Monads have no parts, but they do have numerous properties.

        a. Different monads have different properties.

        b. No two monads are exactly alike, i.e. have all their properties in common.

    7. The properties of modads are perceptions and appetitions.

        a. Perceptions are passing states by means of which monads express or represent other things.

        b. Appetitions are sources of the actions by which different perceptions succeed one another.

    8. Different perceptions have different degrees of distinctness.

        a. The perceptions of bare monads are quite confused.

        b. The perceptions of animal souls are distinct enough to produce sensation and memory.

        c. The perceptions of minds are even more distinct; they produce apperception.

              i. Minds can perform reflective acts, and hence be conscious of themselves.

             ii. Minds can understand abstract notions, and know necessary truths.

            iii. Minds can engage in reasoning and thus are rational.