Traditional Logic and Conclusion

. One good method to test quickly syllogisms is the Venn Diagram technique. This class assumes you are already familiar with diagramming categorical propositions. You might wish to review these now: Venn Diagrams. | | A. A syllogism is a two premiss argument having three terms, each of which is used twice in the argument. | | B. Each term ( major, minor, and middle terms) can be represented by a circle. | | C. Since a syllogism is valid if and only if the premisses entail the conclusion, diagramming the premisses will reveal the logical geography of the conclusion in a valid syllogism. If the syllogism is invalid, then diagramming the premisses is insufficient to show the conclusion must follow. | | D. Since we have three classes, we expect to have three overlapping circles. |

1. The area in the denoted circle represents where members of the class would be, and the area outside the circle represents all other individuals (the complementary class). The various area of the diagram are noted above. | | | 2. Shading represents the knowledge that no individual exists in that area. Empty space represents the fact that no information is known about that area. | | | 3. An "X" represents "at least one (individual)" and so corresponds with the word "some." |

| | | | | II. Some typical examples of syllogisms are shown here by their mood and figure. | A. EAE-1 |
1. The syllogism has an E statement for its major premiss, an Astatement for its minor premiss, and an E statement for its conclusion. By convention the conclusion is labeled with S (the minor term) being the subject and P (the major term) being the predicate. The position of the middle term is the "left-hand wing." | | | 2. The form written out isNo M is P.All S is MNo S is P. | | | 3. Note, in the diagram below, how the area in common between S and P has been completely shaded out indicating that "No S is P." The conclusion has been reached from diagramming only the