The Theory of Implication [1905–06]

Among the papers in the present volume, this was the first to be written. Dealing largely with propositional logic, it was sent on 23 July 1905 to Frank Morley, a mathematician at Johns Hopkins University who was the editor of the American Journal of Mathematics as well as a friend of Whitehead from their undergraduate days at Trinity. It was published there in April 1906. No doubt Russell submitted it to this journal because Morley had earlier shown himself sympathetic to mathematical logic by printing Whitehead’s article “On Cardinal Numbers” (1902), for which Russell had written a section. The first two paragraphs of the present paper were reprinted in Principia Mathematica as the introduction to “The Theory of Deduction” (Whitehead and Russell 1910 , 90).