Template:Featured/2009-06-11

Featured Nicod's reduction of Principia Mathematica is the largely successful attempt of French philosopher Jean Nicod to reduce the number of those indefinable concepts of Principia Mathematica which make up propositional logic. Principia Mathematica uses two indefinable logical connectives and six axioms (or axiom schema), one of which is a detachment rule, Modus Ponens. Nicod's system, on the other hand, uses only one logical connective, the Sheffer stroke discovered by Henry Sheffer, and two axioms. Again, one of these axioms is a detachment rule, a slightly generalised version of Modus Ponens. The only other axiom, called the Prop for proposition, is a clever combination of an identity statement, a syllogism and a permutation. These axioms are enough to derive the Principia axioms from them.