IN A NUTSHELL : WHAT IS A VENN DIAGRAM?

Transcription

1 For anyone who tries to Google anything today (August 4, 2014), you may notice that, according to Google, today is the 180 th birthday of the logician John Venn. Those who have taken a course in logic may be familiar with Venn diagrams. A Venn diagram is a diagram which is often used to provide a kind of intuitive understanding of categorical arguments. Much of the time Venn diagrams are used in the simple analysis of categorical syllogisms. Logic is of course the study of arguments. An argument is a group of statements in which at least one or more of those statements (called premises ) are used in such a way as to support a statement called a conclusion. A statement is a sentence which is either true or false. A syllogism is a category of deductive arguments, all of which consist of two premises and one conclusion. (Syllogism is derived from the Greek word syllogismos which means conclusion or inference.) Here is an example of a syllogism (BTW: formally known as Modus Ponens or the mode that puts ): A categorical syllogism is a category of all syllogisms in which all three statements are categorical propositions. A proposition is essentially the informational content of a statement. A categorical proposition is a category of statement which relates two classes or categories to each other: Here is an example of a categorical statement: Here is another example of a categorical statement: Both statements directly above involve the relation of two categories, that of philosophers and that of people. Here is an example of a categorical syllogism : Page 1 of 5

2 In a Venn diagram a category is represented by a circle. Inside the circle are all those things that belong in a particular category. Outside the circle are all those things which do NOT belong in the particular category. Here is an example of a category. Call this category people. The black X s represent people who are philosophers and the red X s represent all other people who are not philosophers. Here is an example of a Venn circle containing the members of the category people. Notice that both Socrates and General Douglas MacArthur are both included in the category called people. Now I m going to draw another circle to represent the category philosophers. Page 2 of 5

3 Notice that Socrates (the black X with an underline) is part of the group Philosophers. General Douglas MacArthur (the red X with an underline) is not a philosopher and therefore outside the group. Finally I ll draw a circle around a category I will call mortals. Notice that the category mortals also includes all of the category people. Both Socrates and General Douglas MacArthur are included in the category mortals. So when we combine all the Venn circles we come up with this: Page 3 of 5

4 Here are the various areas of a relatively simple Venn diagram for a categorical syllogism. All this is just the tip of the iceberg. Venn diagrams are a relatively easy way of evaluating whether a conclusion of an argument is a good one, without doing all the math and calculating. Venn diagrams can also be done for more complex arguments than syllogisms (remember a syllogism essentially has 3 statements; two premises and a conclusion). Theoretically there is no limit to the number of statements that can be included in a Venn diagram. On the next page is a Venn diagram encompassing 6 categories: Page 4 of 5

5 Source: Wikipedia, public domain (accessed 8/4/14) So here is a Venn diagram of an argument in the category of categorical syllogisms, in a nutshell of the category coconut shells. (I m not very good at drawing almonds, peanuts, acorns etc.) Page 5 of 5