WORKING WITH SYLLOGISMS

The traditional syllogism comes down to us from Aristotle and was the standard for formal logic down to this century. To work with syllogisms you will need to be able to do two things:

(1) Restate information in the simplest way possible in order to show whether you have--


In doing this keep in mind the impact of the word "only" since it indicates a need to reverse the order of the terms in thinking through the statement.  For instance, "Only fun things are easy" has to be rephrased as "All easy things are fun."  Knowing that something is fun does not mean it is easy, but if we do have something easy it is in the class of things that are fun.


 (2) Organize your statements in standard form so that you have the middle (connecting) term as the first part of the top premise but the second part of the bottom premise, as in this example:
We want to prove that "Some tests are hard" by showing the linkage between the idea that anything long is hard and the idea that some tests are long.

 There are several ways to recognize whether what you have is a valid form (meaning, one in which true premises could not give you a false conclusion).
(1) For an invalid form it is possible to set up a parallel example with different terms so that you definitely have true premises but there is an obviously false conclusion.
(2) For an invalid form you can imagine a counterexample--a story in which the premises stay the same but the conclusion is the opposite, and you supply some explanation for how this is possible.
(3) You can work with Venn diagrams.
(4) You can do what are called Euler circles--diagrams in which again you keep the premises the same but try to show a false conclusion.
(5) You can apply a mechanical list, such as the "BARBARA CELARENT" type of thing from the Middle Ages.
(6) You can run through the following checklist.

  • Rule 1: A syllogism works with only three terms used with exactly the same meaning throughout.
  • Rule 2: Nothing follows from two negative premises.
  • Rule 3: Nothing follows from two particular premises.
  • Rule 4: Any negative premise calls for a negative conclusion.
  • Rule 5: Any particular premise calls for a particular conclusion.
  • Rule 6: The middle term must be distributed (meaning, it is used universally at least once in the premises).
  • Rule 7: There cannot be a universal subject or predicate in a conclusion if the term was not used universally in the premises.