**Description: **Axiom *Transp*.
Axiom A3 of [Margaris] p. 49.
We take this as an additional axiom which transforms intuitionistic logic
to classical logic, but there are others which would have the same effect,
including exmid 1885, peirce 1760, or notnot2 725.
This axiom 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, 5-Aug-1993.)
(New usage is discouraged.) |