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Suppose you have a paper topic and you are required to prove a categorical syllogism is valid by means of a Venn diagram. Now suppose that you have no idea how to construct a Venn diagram for a paper. Now what do you do?

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How to handle Venn diagram problems

Suppose you have a paper topic and you are required to prove a categorical syllogism is valid by means of a Venn diagram. Now suppose that you have no idea how to construct a Venn diagram for a paper. Now what do you do?

The following diagram should look familiar. It is the diagram that kept popping up for your first examination. You have three interlocking circles with the numbers 1-7 showing up in each area of the circles. This numbering is standard. Everyone has agreed to put 1 in a particular region, 2 in a particular region, and so on.

  7   6   5   4   3   2   1   M   P   S  

Suppose we have this syllogism:

All P are M

Some M are not S

No S are P

How would we provide a Venn diagram for this syllogism, using this sort of diagram? We would not provide any shading and we would not draw in any X. Instead, we would give the numbers for the regions that are shaded and we would give the numbers for the regions in which the X would appear.

DO THIS

For this syllogism, we would say this: Shade regions 2 and 3. The X appears on the line between regions 6 and 7.

DO NOT DO THIS

We want to shade the part of the P circle that is outside of the M circle and we want to put an x on the line in the M circle outside of the S circle. If you give this explanation in a paper, you will earn 0 points. I don’t accept this. I have seen too many students give this explanation as they blithely shaded the wrong regions and placed an X in the wrong region. They could talk the talk but they could not walk the walk—they could describe how to diagram the circles but they could not actually do it. So, if you give me this explanation, you better accompany it with the actual diagram. But if you have the actual diagram, there is no need for the explanation.

© May 2009

C. Bolton

 
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