Formal Notation
The transposition rule may be expressed as a sequent:
where is a metalogical symbol meaning that is a syntactic consequence of in some logical system;
or as a rule of inference:
where the rule is that wherever an instance of "" appears on a line of a proof, it can be replaced with "";
or as the statement of a truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:
where and are propositions expressed in some formal system.
Read more about this topic: Transposition (logic)
Famous quotes containing the word formal:
“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)