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:
“It is in the nature of allegory, as opposed to symbolism, to beg the question of absolute reality. The allegorist avails himself of a formal correspondence between “ideas” and “things,” both of which he assumes as given; he need not inquire whether either sphere is “real” or whether, in the final analysis, reality consists in their interaction.”
—Charles, Jr. Feidelson, U.S. educator, critic. Symbolism and American Literature, ch. 1, University of Chicago Press (1953)