reduced to symbols. Its sole record is the occurrence of '⊦. q ' [in other words, the symbols on the left disappear or can be erased]" (PM 1962:9). The use of dots Definitions: These use the "=" sign with "Df" at the right end. Summary of preceding statements: brief discussion of the primitive ideas "~ p" and "p ∨ q" and "⊦" prefixed to a proposition. Primitive propositions: the axioms or postulates. This was significantly modified in the second edition. Propositional functions: The notion of "proposition" was significantly modified in the second edition, including the introduction of "atomic" propositions linked by logical signs to form "molecular" propositions, and the use of substitution of molecular propositions into atomic or molecular propositions to create new expressions. The range of values and total variation Ambiguous assertion and the real variable: This and the next two sections were modified or abandoned in the second edition. In particular, the distinction between the concepts defined in sections 15. Definition and the real variable and 16 Propositions connecting real and apparent variables was abandoned in the second edition. Formal implication and formal equivalence Identity Classes and relations Various descriptive functions of relations Plural descriptive functions Unit classes Primitive ideas Cf. PM 1962:90–94, for the first edition: (1) Elementary propositions. (2) Elementary propositions of functions. (3) Assertion: introduces the notions of "truth" and "falsity". (4) Assertion of a propositional function. (5) Negation: "If p is any proposition, the proposition "not-p", or "p is false," will be represented by "~p" ". (6) Disjunction: "If p and q are any propositions, the proposition "p or q, i.e., "either p is true or q is true," where the alternatives are to be not mutually exclusive, will be represented by "p ∨ q" ". (cf. section B) Primitive propositions The first edition (see discussion relative to the second edition, below) begins with a definition of the sign "⊃"✸1.01. p ⊃ q .=. ~ p ∨ q. Df.✸1.1. Anything implied by a true elementary proposition is true. Pp modus ponens (✸1.11 was abandoned in the second edition.)✸1.2. ⊦: p ∨ p .⊃. p. Pp principle of tautology✸1.3. ⊦: q .⊃. p ∨ q. Pp principle of addition✸1.4. ⊦: p ∨ q .⊃. q ∨ p. Pp principle of permutation✸1.5. ⊦: p ∨ ( q ∨ r ) .⊃. q ∨ ( p ∨ r ). Pp associative principle✸1.6. ⊦:. q ⊃ r .⊃: