Peirce’s Law

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

I thought it might be beneficial to expand on the explanation of my approach to proving Peirce’s Law by giving excerpts from Copi’s Introduction to Logic (14th ed. 2014) concerning the meaning of a valid argument, which really is what Peirce’s Law is an example of.

See Valid Argument