{"id":299,"date":"2023-12-19T15:40:52","date_gmt":"2023-12-19T15:40:52","guid":{"rendered":"https:\/\/renegrothmann.de\/?p=299"},"modified":"2024-03-15T08:11:52","modified_gmt":"2024-03-15T08:11:52","slug":"logical-flaws","status":"publish","type":"post","link":"https:\/\/renegrothmann.de\/?p=299","title":{"rendered":"Logical Flaws"},"content":{"rendered":"\n<p>The following is the Wason Selection Task, as <a href=\"https:\/\/en.wikipedia.org\/wiki\/Wason_selection_task\">cited<\/a> by Wikipedia.<\/p>\n\n\n\n<p>&#8222;You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other. The visible faces of the cards show 3, 8, blue and red. Which card(s) must you turn over in order to test that if a card shows an even number on one face, then its opposite face is blue?&#8220;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"600\" height=\"320\" src=\"https:\/\/renegrothmann.de\/wp-content\/uploads\/2023\/12\/Wason-1.png\" alt=\"\" class=\"wp-image-303\" srcset=\"https:\/\/renegrothmann.de\/wp-content\/uploads\/2023\/12\/Wason-1.png 600w, https:\/\/renegrothmann.de\/wp-content\/uploads\/2023\/12\/Wason-1-300x160.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n<p>The big misunderstanding starts if we incorrectly interpret the question simplified as: &#8222;Which cards have an even number on one side and are blue on the other?&#8220;. The subtle difference between testing a hypothesis and a fact is not something we encounter in everyday life. To answer the simplified question, we have to turn 8 and the <em>blue<\/em> card, because the 3 and the red card cannot be even and blue.<\/p>\n\n\n\n<p>But to test the hypothesis that each card with an even number is blue on the other side, we need to turn the 8 and the <em>red<\/em> card. The reason is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The card with the 3 does not show an even number. Thus it does not matter if the other side is blue or not. Our hypothesis will be true in any case for this card.<\/li>\n\n\n\n<li>The card with the 8 must be blue on the other side for the hypothesis to hold.<\/li>\n\n\n\n<li>The blue card follows our hypothesis, no matter if the other side is even or not. The hypothesis does not claim that only even cards can have a blue back.<\/li>\n\n\n\n<li>The red card follows our hypothesis only if the back side is not even. Thus we need to turn it around to check if it follows the hypothesis.<\/li>\n<\/ul>\n\n\n\n<p>If you are not careful with the wording in the hypothesis, you may think that only even cards can have a blue background. But the hypothesis does not claim this. It states: &#8222;Each even card has a blue back.&#8220;, mathematically &#8222;even implies blue&#8220;, but not the other way around. A blue card can show anything on the other side and will still satisfy this hypothesis.<\/p>\n\n\n\n<p>According to Wikipedia, this problem is correctly solved only by 10%. Wikipedia is also referring works of psychologists who show that the result is much better if the rule is based on everyday experience, such as:  A person below the age of 18 must not drink alcohol. The rule would be age&lt;18 implies no alcohol. Most would now test the age only if the person is drinking alcohol. If the person is not, there is no point in checking the age.<\/p>\n\n\n\n<p>There is a similar logical flaw which I learned from a YouTube video (I believe by Veritasium). You are required to guess the rule of the sequence<\/p>\n\n\n\n<p class=\"has-text-align-center\">7, 13, 19, &#8230;<\/p>\n\n\n\n<p>The sequence of actions is as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>You guess the next number.<\/li>\n\n\n\n<li>You are told if it follows the rule or not.<\/li>\n\n\n\n<li>If it does, you must explain the rule. If your rule is wrong, you lose.<\/li>\n\n\n\n<li>If not, you start over.<\/li>\n<\/ul>\n\n\n\n<p>Most people try to figure out rules for this sequence, like 7+6=13, 13+6=19, 19+6=25, and guess 25. They are told that the number is correct, but their rule is wrong and they lose. They would also lose if they&#8217;d guess the next but one prime number 29.<\/p>\n\n\n\n<p>Because of this, you need to do a more scientific approach and first try to falsify the most obvious rule: The numbers are simply in ascending order. So guess 5 and if this is wrong, try 1001. If this is right, the most &#8222;likely&#8220; rule is the ascending order. If it is wrong, you go for the more detailed rules.<\/p>\n\n\n\n<p>It is like in real life: You assume the most obvious explanation for an observed phenomenon first. Only, if this is proven to be a false explanation, you go for less obvious ones. <\/p>\n\n\n\n<p>Wikipedia <a href=\"https:\/\/en.wikipedia.org\/wiki\/List_of_fallacies\">has<\/a> an exhaustive list of logical fallacies. Some are fun to learn about.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The following is the Wason Selection Task, as cited by Wikipedia. &#8222;You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other. The visible faces of the cards show 3, 8, blue and red. Which card(s) must you turn [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-299","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/renegrothmann.de\/index.php?rest_route=\/wp\/v2\/posts\/299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/renegrothmann.de\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/renegrothmann.de\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/renegrothmann.de\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/renegrothmann.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=299"}],"version-history":[{"count":4,"href":"https:\/\/renegrothmann.de\/index.php?rest_route=\/wp\/v2\/posts\/299\/revisions"}],"predecessor-version":[{"id":345,"href":"https:\/\/renegrothmann.de\/index.php?rest_route=\/wp\/v2\/posts\/299\/revisions\/345"}],"wp:attachment":[{"href":"https:\/\/renegrothmann.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/renegrothmann.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/renegrothmann.de\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}