5.2 Venn Diagrams
- Categorical syllogisms have three terms.
- So, Venn diagrams for categorical syllogisms will require three circles.
- The Venn diagrams for categorical syllogisms will be based upon the same strategy as used for categorical propositions.
- So, review the Venn diagrams for the four categorical propositions.
- Here is a sample categorical syllogism:
- No P are M.
- All S are M.
No S are P.
- To start representing this argument on a diagram, we would draw three circles as represented on the following slide.
- Next, the premises should be represented on the diagram.
- If there is a particular premise and a universal premise, diagram the universal premise first.
- Since both premises are universal in this example, either can be diagrammed first.
- So, we will start with the first premise, "No P are M".
- In order to diagram "No P are M", concentrate only on circles P and M.
- The areas where P and M overlap should be shaded, just as they were with two circled diagrams.
- Try to do this on your own, before looking at the diagram on the next slide.
- Now, the next premise must be diagrammed on the Venn diagram.
- So, "All S are M" must be put on the diagram.
- Concentrate only on the S and M circles.
- Just as with two circle diagrams, the regions that are S and NOT M must be shaded.
- Try to do this on your own before viewing the next slide.
- NEVER draw the conclusion on the diagram.
- LOOK for the conclusion on the diagram once you have drawn the premises.
- If the conclusion is represented by drawing the premises, the argument is valid.
- If the conclusion is not represented by drawing the premises, the argument is invalid.
- Look for "No S are P" on the diagram.
- Since regions 3 and 6 are shaded on the Venn diagram, and regions 3 and 6 represent "No S are P", the argument is valid.
- Were regions 3 and 6 not both shaded, the argument would have been invalid.