The June 2023 Carnival of Mathematics # 216 at Eddie’s Math and Calculator Blog has the rather arresting item concerning Peirce’s Law from the American logician Charles Sanders Peirce (1839 – 1914).
“Peirce’s Law: Jon Awbrey of the Inquiry Into Inquiry blog
This article explains Pierce’s Law and provides the proof of the law. The proof is provided in two ways: by reason and graphically. Simply put, for propositions P and Q, the law states:
P must be true if there exists Q such that the statement “if P then Q” is true. In symbols:
(( P ⇒ Q) ⇒ P) ⇒ P
The law is an interesting tongue twister to say the least.”
Perhaps another way of saying it is “if the implication P ⇒ Q implies that P is true, then P must be true.” Still, it sounds weird.
See Peirce’s Law
(Update 6/20/2023) Appendix: Valid Argument Continue reading