最終更新日:2022/12/24
Consider Peirce's law, ((P→Q)→P)→P). If Q is true, then P→Q is also true so the law reads If truth implies P then deduce P
which certainly makes sense. If Q is false, then (P→Q)→P≡(P→⊥)→P≡¬P→P≡¬P→P and ¬P≡¬P→⊥≡¬¬P so the law reads ¬¬P→P, which is intuitionistically false but equivalent to the classical axiom ¬P∨P.
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元となった例文
Consider
Peirce's
law,
((P→Q)→P)→P).
If
Q
is
true,
then
P→Q
is
also
true
so
the
law
reads
"If
truth
implies
P
then
deduce
P"
which
certainly
makes
sense.
If
Q
is
false,
then
(P→Q)→P≡(P→⊥)→P≡¬P→P≡¬P→P
and
¬P≡¬P→⊥≡¬¬P
so
the
law
reads
¬¬P→P,
which
is
intuitionistically
false
but
equivalent
to
the
classical
axiom
¬P∨P.