{"id":32,"date":"2009-02-05T08:46:21","date_gmt":"2009-02-05T13:46:21","guid":{"rendered":"http:\/\/dwaynephillips.net\/workingup\/?p=32"},"modified":"2009-02-05T08:46:21","modified_gmt":"2009-02-05T13:46:21","slug":"proving-anything-from-nothing-implication-part-1","status":"publish","type":"post","link":"https:\/\/dwaynephillips.net\/workingup\/2009\/02\/proving-anything-from-nothing-implication-part-1\/","title":{"rendered":"Proving Anything from Nothing &#8211; Implication Part 1"},"content":{"rendered":"<p>by Dwayne Phillips<\/p>\n<p>This is dangerous &#8211; I am splitting a blog post into two parts. Hang in there with me.<\/p>\n<p>People are not always logical. That bothers logical engineers like me to no end. There is a mathematical and logical method to prove the non-logical behavior of people. That math helps me understand the how and why of the way people behave and how I can behave with them.<\/p>\n<p>Part 1 of this blog post discusses the math and logic. Part 2 of this blog post discusses how people reflect this.<\/p>\n<p>This is all based on something called <strong><em>implication<\/em><\/strong>. Implication basically states that if we accept something that is FALSE, we can prove anything. Yikes.<\/p>\n<p>Below is the truth table for implication: (the symbols &#8220;A =&gt; B&#8221; is read &#8220;A implies B&#8221;)<\/p>\n<blockquote><p>Case &#8230;&#8230; A &#8230;&#8230; B &#8230;&#8230; A =&gt; B<\/p>\n<p>0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 false\u00a0\u00a0\u00a0\u00a0 false\u00a0\u00a0\u00a0\u00a0 true<\/p>\n<p>1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 false\u00a0\u00a0\u00a0\u00a0 true\u00a0\u00a0\u00a0\u00a0\u00a0 true<\/p>\n<p>2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 true\u00a0\u00a0\u00a0\u00a0\u00a0 false\u00a0\u00a0\u00a0\u00a0 false<\/p>\n<p>3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 true\u00a0\u00a0\u00a0\u00a0\u00a0 true\u00a0\u00a0\u00a0\u00a0\u00a0 true<\/p><\/blockquote>\n<p>Start with Case 3 as it is simple. Let A be the statement &#8220;1=1&#8221; which is TRUE. Let B be the statement &#8220;3=3&#8221; which is also TRUE. In math, we can prove that &#8220;1=1&#8221; <em>implies<\/em> &#8220;3=3&#8221;, i.e. A=&gt;B is TRUE. Simply multiply both sides of &#8220;1=1&#8221; by 3 and we have &#8220;3=3&#8221;.<\/p>\n<p>Next to Case 2. Let A be the statement &#8220;1=1&#8221;\u00a0 which is TRUE. Let B be the statement &#8220;2=3&#8221; which is FALSE. In math, we can prove that &#8220;1=1&#8221; <em>does not imply<\/em> &#8220;2=3&#8221;, i,e, A=&gt;B is FALSE.<\/p>\n<p>Next to Case 1. Let A be the statement &#8220;1=2&#8221; which is FALSE. Let B be the statement &#8220;3=3&#8221; which is TRUE. We don&#8217;t have to go to math for any proofs because no matter how often or loudly we proclaim that &#8220;1=2&#8221;, we know that &#8220;3=3&#8221;. Hence, A=&gt;B is TRUE.<\/p>\n<p>Now to crazy Case 0 &#8211; the one that predicts human illogical behavior. Let A be the statement &#8220;1=2&#8221; which is FALSE. Let B be the statement &#8220;2=3&#8221; which is also FALSE. Using math, I can now prove that &#8220;2=3&#8221;, so A=&gt;B is TRUE.<\/p>\n<p>Here is the proof:<\/p>\n<blockquote><p>Statement A says that &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211; 1 = 2<\/p>\n<p>Add 1 to both sides of the above and we have &#8212; 2 = 3<\/p><\/blockquote>\n<p>A simple, one-step proof that &#8220;2=3&#8221;. See, a logical proof that validates illogical human behavior.<\/p>\n<blockquote><p>If I accept something that I know is FALSE, I can prove anything else that I know is FALSE<\/p><\/blockquote>\n<p>Come back for Part 2 in which <strong><em>implication<\/em><\/strong> allows me to prove all sorts of nonsense.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>by Dwayne Phillips This is dangerous &#8211; I am splitting a blog post into two parts. Hang in there with me. People are not always logical. That bothers logical engineers like me to no end. There is a mathematical and logical method to prove the non-logical behavior of people. That math helps me understand the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,13,10,3],"tags":[130,136,133,126],"class_list":["post-32","post","type-post","status-publish","format-standard","hentry","category-judgment","category-logic","category-people","category-technology","tag-judgment","tag-logic","tag-people","tag-technology"],"_links":{"self":[{"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/posts\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/comments?post=32"}],"version-history":[{"count":3,"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":35,"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/posts\/32\/revisions\/35"}],"wp:attachment":[{"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/media?parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/categories?post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dwaynephillips.net\/workingup\/wp-json\/wp\/v2\/tags?post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}