Syllogisms*

1. Syllogisms* • A syllogism is an argument with exactly two premises. • A standard form categorical syllogism is a syllogism entirely of standard-form categorical propositions, presented as follows: major premise first, minor premise second, conclusion last. Example: Some politicians are women. No wealthy men are women. So, some wealthy men are not politicians.

2. Valid ? Some politicians are women. No wealthy men are women. So, some wealthy men are not politicians.

3. Standard Form Categorical Syllogism Middle Term(in both premises) P M Some politicians are women. No wealthy men are women. Some wealthy men are not politicians. Major Premise M S Minor Premise S P Minor Term(subject of conclusion) Major Term(predicate of conclusion)

4. Forms of the Syllogism The form of a standard form categorical syllogism is completely specified by its mood and figure. Examples: AAA-1 EIO - 4 mood figure

5. Mood of Syllogism • The mood of a syllogism is specified by listing the form of each proposition as it appears in that syllogism. Example: I Some politicians are women. No wealthy men are women. So, some men are not politicians. E O Mood: I E O -

6. Figure of the Syllogism The figure of a syllogism is determined by the relative placement of the middle term in the premises, as shown below: M P P MM P P M S M S MM S M S 1 2 3 4

7. 1 2 3 4

8. Go Figure !

9. The Form of Our Syllogism M I Some politicians are women. No wealthy men are women. So, some men are not politicians. M E O I E O - 2

10. Forms of the Syllogism • 256 Possible Forms • Fifteen Valid from Hypothetical Viewpoint • Nine more are valid, provided existential assumptions are made. • See page 51 Barker, for a list.

11. Test for Validity by Form Some politicians are women. No wealthy men are women. So, some wealthy men are not politicians. I E O - 2 Not listed. Invalid.

12. A Second Test of Validity by Form M No working poor are wealthy bankers. Some wealthy bankers are Republicans.Some Republicans are not working poor. E I O M Valid ? Valid E I O - 4

13. A Third Test of Validity by Form M All Republicans are wealthy women.No working poor are wealthy women. No working poor are Republicans. A O O M Valid ? A O O - 2 Listed Valid

14. Why Are Some Forms Valid, Others Invalid ? Valid forms have no counterexamples Invalid forms admit counterexamples. .

15. First Argument: Some politicians are women. No men are women. So, some men are not politicians. Counterexample: Some mammals are women. No baby humans are women. So, some baby humans are not mammals. A Counterexample to Our First Argument:

16. Can you create a plausible* counterexample to this invalid argument ? First Argument: Some women are politicians. No men are women. So, some men are not politicians. Counterexample: ? *One which would convince an intelligent person with no training in logic.

17. A Counterexample to Our Second Argument ? Second Argument: No working poor are wealthy bankers. Some wealthy bankers are Republicans.Some Republicans are not working poor. Counterexample: ? No counterexample possible.

18. A Counterexample to Our Third Argument ? Second Argument: All Republicans are wealthy women.No working poor are wealthy women. So, no working poor are Republicans.. Counterexample: ? No counterexample possible.

19. Venn Diagrams for Testing Syllogisms M 1 2 4 S P 3 5 6 7 8

20. Map Of Our Universe M SMP 1 S SMP SMP 3 P 2 4 SMP SMP SMP SMP SMP 5 6 7 8

21. Venn Diagram Validity Test forSyllogisms Diagram both premises (not the conclusion). Conclusion appears in diagram of the combined premises? No Yes Argument Valid Argument Invalid

22. Venn Diagram Testing IEO-2 Syllogism P M M Some politicians are women. No wealthy men are women. So, some wealthy men are not politicians. M S S P 1 * 2 4 I E O - 2 S P 3 5 6 7 Invalid 8