LEIBNIZ: CONSEQUENCES OF THE THEORY OF TRUTH
FROM 'DISCOURSE ON METAPHYSICS'

1. Premises

    P01. God always acts in the most perfect (wisest, best) manner.

    P02. In every true (affirmative) proposition, the predicate either is identical with the subject, or it is contained in it, either 
            explicitly or virtually.

2. Immediate Consequences

    C01. The notion of an individual substance (or complete being) contains all the predicates that belong to that substance 
            (or being).

    C02. 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 (a) vestiges of everything that has happened to it, (b) marks of everything that will happen to it, and 
            (c) traces of everything that happens in the universe.

3. Subsequent Metaphysical Consequences = 'Paradoxes'

    C03. The Principle of the Identity of Indiscernibles [PII]
            No two substances can resemble each other completely and so differ solely in number.

    C04. A substance can begin to exist only by creation and end only by annihilation.

    C05. No substance can be divided into two [substances].

    C06. No substance can be constructed out of two [substances].

    C07. The number of substances cannot naturally increase or decrease, though a substance can be transformed.

    C08. Every substance is like a mirror of God or of the whole universe, and each one expresses or represents God 
            and the whole universe in its own way.

    C09. 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.

    C10. The (quasi-)souls of most bodies are not intelligent, i.e., do not know their own actions, but some bodies have 
            intelligent souls.

    C11. Intelligent souls not only do not perish naturally, they preserve the basis [through memory] for the knowledge 
            of what they are.

    C12. The notion of an individual substance contains everything that will ever happen to it; hence every truth about 
            the substance can be proven a priori, and hence known with certainty, from its notion. But some such truths, 
            though certain, are nonetheless contingent; if they were not, there would be no place for human freedom.

    C13. Contingent truths about individual substances are based upon the free will of God or of his creatures.

    C14. All finite substances are created by God; they are also, once created, kept in existence by God, who keeps 
            producing them by a kind of emanation.

    C15. 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.

    C16. The phenomena of a substance maintain a certain order in conformity with the nature of that substance, and so 
            with the phenomena of all the other substances which that substance expresses and which constitute its world.

    C17. 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.

    C18. These substances are not really connected, however. God alone is the cause of the correspondence of their 
            phenomena and of their perceptions.

    C19. Different created substances express God and other created substances to themselves (or perceive them) with 
            different degrees of perfection.

    C20. Although all the things that happen to a created substance are consequences of its nature, and hence happen in 
            accordance with natural laws, God is able sometimes to influence men and other created substances in such a 
            way that miracles occur, i.e., things that are extraordinary and supernatural.  Even so, such miracles are always 
            in conformity with the universal law of the general order, which God himself always observes.