Using Venn Diagrams to Test Validity

1. Using Venn Diagrams to Test Validity

2. What we are doing. • To test the validity of a syllogism, you may use a Venn diagram. • A Venn diagram is three intersecting circles. There are 8 sections created as a result.

3. How to do it. • To test a syllogism using a Venn diagram, we fill in the major and minor premises. • Do NOT fill in the conclusion. • If the syllogism is valid, the conclusion will already be diagrammed. If it isn’t, the syllogism is invalid.

4. S is the minor term. (Remember: S is the subject of the conclusion.) P is the major term (the predicate of the conclusion.) M is the middle term.

5. Take the following syllogism: All Greeks are mortal. (All M are P) All Athenians are Greek. (All S are M) So, all Athenians are mortal. (All S are P) What is its mood and figure? AAA-1

6. Start with the major premise. • (Remember: M is Greeks, P is mortal.) • What would this part look like?

7. Major premise, diagrammed.

8. Now, diagram the minor premise: All Athenians are Greek. • Out of P, S, and M, which letter do we use for the Athenians? • S • Out of P, S, and M, which letter will we use for the Greeks? • M

9. So what will the minor premise look like?

10. Now, overlap the two premises: • S = Athenians • P = mortal • M = Greeks Is the conclusion valid?

11. Yes. All Greeks are mortal. (All M are P) All Athenians are Greek. (All S are M) So, all Athenians are mortal. (All S are P)

12. Try this one: All mathematicians are rational. (All P are M) All philosophers are rational. (All S are M) SO, all philosophers are mathematicians. (All S are P) What will the diagram look like?

13. Volunteer

14. What rule(s) does this syllogism violate? All mathematicians are rational. (All P are M) All philosophers are rational. (All S are M) SO, all philosophers are mathematicians. (All S are P) • D1: fallacy of the undistributed middle. (Whenever we have exactly 3 shaded regions, we have a fallacy of distribution.)

15. Consider the following: All philosophers are logical. (All P are M.) Some physicists are logical. (Some S are M.) So, some philosophers are physicists. (Some S are P.) What is the mood and figure? AII-2

16. What does this one look like?

17. AII-2 is invalid. Whenever a diagram indicates that a term occupies 2 regions, it is invalid.

18. What rule(s) does this one violate? All philosophers are logical. (All P are M.) Some physicists are logical. (Some S are M.) So, some philosophers are physicists. (Some S are P.) • D2 (fallacy of the undistributed middle)

19. Tweaking it a bit. Some physicists are logical. (Some S are M) No philosophers are logical. (No P are M) So, some physicists are not philosophers. (Some S are not P) What is the mood and figure of this argument? IEO-2

20. What does IEO-2 look like?

21. OEO-4 Some P is not M. No M is S. Some S is not P. • Diagram and test for validity. • OEO-4 commits D2, (fallacy of the illicit major).

22. AEE-3 All M is P. No M is S. No S is P. • AEE is invalid. It commits D2 (fallacy of the illicit major, again).

23. OOO-1 Some M is not P. Some S is not M. Some S is not P. This syllogism commits a D1 violation…2 negative premises. This particular violation is called fallacy of exclusive premises.

24. The problem of EAO-4. • No P is M. • All M is S. • Some S is not P. • According to what we’ve learned, EAO-4 doesn’t violate Q1, Q2, D1, or D2. However, there is nothing to positively indicate the conclusion!

25. One more rule! • You cannot have two universal premises and a particular conclusion. This is called the existential fallacy.

26. Limitations on Venn Diagrams • 4- and 5-term diagrams are possible, but…