**Description: **Axiom *Transp*.
Axiom A3 of [Margaris] p. 49. One of the 3
axioms of
propositional calculus. It swaps or "transposes" the order of
the
consequents when negation is removed. An informal example is that the
statement "if there are no clouds in the sky, it is not raining"
implies
the statement "if it is raining, there are clouds in the sky."
This axiom
is called *Transp* or "the principle of transposition" in
*Principia
Mathematica* (Theorem *2.17 of [WhiteheadRussell] p. 103). We will also
use the term "contraposition" for this principle, although the
reader is
advised that in the field of philosophical logic,
"contraposition" has a
different technical meaning. (Contributed by NM, 30-Sep-1992.) Use its
alias con4 112 instead. (New usage is
discouraged.) |