NB: As a result of criticism and advances, the second edition of PM (1927) replaces ✱9 with a new ✱8 (Appendix A). This new section eliminates the first edition's distinction between real and apparent variables, and it eliminates "the primitive idea 'assertion of a propositional function'.p. xiii of 1927 appearing in the 1962 paperback edition to ✱56. To add to the complexity of the treatment, ✱8 introduces the notion of substituting a "matrix", and the Sheffer stroke: Matrix: In contemporary usage, PMs matrix is (at least for propositional functions), a truth table, i.e., all truth-values of a propositional or predicate function. Sheffer stroke: Is the contemporary logical NAND (NOT-AND), i.e., "incompatibility", meaning: "Given two propositions p and q, then ' p | q ' means "proposition p is incompatible with proposition q", i.e., if both propositions p and q evaluate as true, then and only then p | q evaluates as false." After section ✱8 the Sheffer stroke sees no usage.
NB: As a result of criticism and advances the second edition of PM (1927) replaces ✱9 with a new ✱8 (Appendix A). This new section eliminates the first edition's distinction between real and apparent variables, and it eliminates "the primitive idea 'assertion of a propositional function'.p. xiii of 1927 appearing in the 1962 paperback edition to ✱56. To add to the complexity of the treatment, ✱8 introduces the notion of substituting a "matrix", and the Sheffer stroke: Matrix: In contemporary usage, PMs matrix is (at least for propositional functions), a truth table, i.e., all truth-values of a propositional or predicate function. Sheffer stroke: Is the contemporary logical NAND (NOT-AND), i.e., "incompatibility", meaning: "Given two propositions p and q, then ' p | q ' means "proposition p is incompatible with proposition q", i.e., if both propositions p and q evaluate as true, then and only then p | q evaluates as false." After section ✱8 the Sheffer stroke sees no usage.