{"id":111,"date":"2015-01-31T02:47:27","date_gmt":"2015-01-31T02:47:27","guid":{"rendered":"http:\/\/aristotle2digital.blogwyrm.com\/?p=111"},"modified":"2015-01-31T02:47:27","modified_gmt":"2015-01-31T02:47:27","slug":"it-isnt-elementary","status":"publish","type":"post","link":"https:\/\/aristotle2digital.blogwyrm.com\/?p=111","title":{"rendered":"It Isn’t Elementary"},"content":{"rendered":"

I suppose that this post grew out of a recent opportunity I had to re-watch the M*A*S*H television series<\/a>. One particular episode, entitled The Light That Failed<\/a><\/em>, finds the army surgeons and nurses of the 4077th<\/sup> unit suffering a brutal Korean winter and desperately low on supplies.\u00a0 The supply truck soon arrives bearing a cargo more suited for a military unit in the Guam or the Philippines and not mainland Asia.\u00a0 As the troops are left wondering what they can do with mosquito netting, ice cream churns, and swim fins when the temperature is hovering around freezing, someone notices that one of the doctors, B J Hunnicutt, has received a very rare object \u2013 a book.<\/p>\n

And this is not just any book, but a murder mystery by the famed writer Abigail Potterfield called the Rooster Crowed at Midnight<\/em>.\u00a0 Either out of the goodness of his heart or out of a desire to end the constant nagging (probably both), B J decides to tear portions of the book out so that it can circulate throughout the camp.\u00a0 As the old saying goes, no good deed goes unpunished, and soon he discovers that the last page of the book, in which all is revealed, is missing.\u00a0 And thus begins the great debate as to who committed the murders, how they did it, and why.<\/p>\n

The team comes up with many answers, all of which are first widely embraced as the solution and then scuttled when someone gives a counterexample that pokes a hole in the theory.\u00a0 They eventually place a long distance phone call to the author herself, now residing in Australia, to get the answer.\u00a0 But even this authoritative voice doesn’t quell the skepticism.\u00a0 Shortly after they ring off, Col. Potter, the commanding officer, points out that Abigail Porterfield\u2019s own solution can\u2019t be true.\u00a0 The episode closes with the delivery of the much-needed supplies, and some comic hijinks, but with no satisfactory explanation as to who the culprit was.<\/p>\n

I was in middle school when I first saw that episode and it left a lasting impression on me.\u00a0 For many years I carried misconceptions about mystery stories and I wondered why anyone would ever read them. \u00a0In particular, I held a very skewed idea about deductive reasoning and what can and cannot be determined from the evidence.\u00a0 With the perspective of years (really decades) I am both happy and disappointed to say that I was not alone in my poor understanding of what logic and reason are capable of achieving.<\/p>\n

Let\u2019s talk about deductive logic first.\u00a0 The basic idea behind deductive logic is that the conclusion is infallible if the premises are true.\u00a0 It is a strong approach to logic, since it argues from first principles that apply to a broad class or set of objects and, from those, narrows down a conclusion about a specific object.\u00a0 In a pictorial sense, deductive logic can be thought of in terms of Venn diagrams.\u00a0 If we want to conclude something about an object we simply need to know into what categories or classes this object falls and we will be able to exactly conclude something about it by noting where all of the various categories to which it belongs intersect.<\/p>\n

Deductive reasoning is, unfortunately, also limited by the fact that we are not born with nor does anyone have the universe\u2019s user manual that spells out in detail what attributes each object has and into what categories they may be grouped. \u00a0So, the standard objections that are raised in deductive logic fall squarely on disagreements about the truth of one or more premises.<\/p>\n

For example, the syllogism<\/p>\n

\n