Description: Modus tollendo ponens
(original exclusive-or version), aka disjunctive
syllogism, one of the five "indemonstrables" in Stoic logic.
The rule
says, "if φ
is not true, and either φ
or ψ (exclusively)
are true, then ψ
must be true." Today the name "modus tollendo
ponens" often refers to a variant, the inclusive-or version as
defined
in mtp-or 1538. See rule 3 on [Lopez-Astorga] p. 12 (note that the
"or"
is the same as mpto2 1534, that is, it is exclusive-or df-xor 1305), rule 3
of [Sanford] p. 39 (where it is not as
clearly stated which kind of "or"
is used but it appears to be in the same sense as mpto2 1534), and rule A5
in [Hitchcock] p. 5 (exclusive-or is
expressly used). (Contributed by
David A. Wheeler, 4-Jul-2016.) (Proof shortened by Wolf Lammen,
11-Nov-2017.) |