|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 781, peirce 1664, or notnot2 718.
This axiom swaps or "transposes" the order of the consequents
negation is removed. An informal example is that the statement "if
are no clouds in the sky, it is not raining" implies the statement
is raining, there are clouds in the sky." This axiom is called
or "the principle of transposition" in Principia
*2.17 of [WhiteheadRussell] p.
103). We will also use the term
"contraposition" for this principle, although the reader is
in the field of philosophical logic, "contraposition" has a
technical meaning. (Contributed by NM, 5-Aug-1993.)
(New usage is discouraged.)