LEIBNIZ ON TRUTH

A. Truth (falsity) is a property of propositions or statements.

    1. Forms of proposition - affirmative/negative, universal/particular, subject-predicate/relational/existential

    2. Elements of propositions - terms, notions, concepts; subjects and predicates


B. The truth of a (subject-predicate, affirmative) proposition consists in the connection between its subject 
      and its predicate; more specifically, it consists in the containment of the (concept of the) predicate by the 
      (concept of the) subject.

    1. This is the 'concept-containment theory of truth'.

    2. It contrasts with the 'correspondence (or Aristotelian) theory', according to which the truth of a proposition 
      consists of its agreement or correspondence with the fact expressed by the proposition.

    3. For every truth there is a reason for its being true.


C. Truths are either necessary or contingent.

    1. A necessary truth cannot possibly not be true.

        a. Its reason for being true is the Principle of Identity or Noncontradiction: its denial is a contradiction - a 
          proposition that 'contradicts itself'.

        b. Its truth can be 'demonstrated with geometrical rigor', hence can be known a priori.

        c. It either is, or it can be reduced to, an explicit identity proposition: a=a, or: if P then P.

            To reduce a proposition is to analyse its terms or notions, using definitions.

    2. A contingent proposition is one whose falsehood is possible.

        a. Its reason for being true is the Principle of Sufficient Reason, which amounts to God's having freely 
          chosen to create something which makes it true.

        b. Its truth cannot be demonstrated, but can only be known (by human beings) by experience, or a posteriori.

        c. It is somehow equivalent to an identity proposition, but it cannot be reduced thereto, at least not through 
          any finite number of steps, hence not by human beings, though God can so reduce it and so know its truth 
          a priori.