{"id":3210,"date":"2023-06-17T08:24:18","date_gmt":"2023-06-17T12:24:18","guid":{"rendered":"https:\/\/josmfs.net\/?p=3210"},"modified":"2024-05-26T14:30:14","modified_gmt":"2024-05-26T18:30:14","slug":"peirces-law","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/06\/17\/peirces-law\/","title":{"rendered":"Peirce\u2019s Law"},"content":{"rendered":"

\"\"The June 2023 Carnival of Mathematics # 216<\/a><\/em> at Eddie\u2019s Math and Calculator Blog has the rather arresting item concerning Peirce\u2019s Law from the American logician Charles Sanders Peirce (1839 \u2013 1914).<\/p>\n

\u201cPeirce’s\u00a0Law:\u00a0 Jon Awbrey of the Inquiry Into Inquiry blog<\/strong><\/p>\n

This article explains Pierce’s Law and provides the proof of the law.\u00a0 The proof is provided in two ways:\u00a0 by reason and graphically.\u00a0 Simply put, for propositions P and Q, the law states:<\/p>\n

P must be true if there exists Q such that the statement \u201cif P then Q\u201d is true.\u00a0 In symbols:<\/p>\n

(( P \u21d2 Q) \u21d2 P) \u21d2 P<\/p>\n

The law is an interesting tongue twister to say the least.\u201d<\/p>\n

Perhaps another way of saying it is \u201cif the implication P \u21d2 Q implies that P is true, then P must be true.\u201d\u00a0 Still, it sounds weird.<\/p>\n

See Peirce\u2019s Law<\/a><\/p>\n

(Update 6\/20\/2023)\u00a0 Appendix: Valid Argument<\/strong> <\/p>\n

I thought it might be beneficial to expand on the explanation of my approach to proving Peirce\u2019s Law by giving excerpts from Copi\u2019s Introduction to Logic<\/em> (14th<\/sup> ed. 2014) concerning the meaning of a valid argument, which really is what Peirce\u2019s Law is an example of.<\/p>\n

See Valid Argument<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

The June 2023 Carnival of Mathematics # 216 at Eddie\u2019s Math and Calculator Blog has the rather arresting item concerning Peirce\u2019s Law from the American logician Charles Sanders Peirce (1839 \u2013 1914). \u201cPeirce’s\u00a0Law:\u00a0 Jon Awbrey of the Inquiry Into Inquiry blog This article explains Pierce’s Law and provides the proof of the law.\u00a0 The proof […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[174,256,265],"class_list":["post-3210","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-logic","tag-truth-tables","tag-valid-argument"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=3210"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3210\/revisions"}],"predecessor-version":[{"id":3216,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3210\/revisions\/3216"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}