Logic

1. Logic HUM 200 Categorical Syllogisms Lectures taken from Copi, I., & Cohen, C. (2009). HUM200: Introduction to logic: 2009 custom edition (13th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

2. Objectives • When you complete this lesson, you will be able to: • Describe a standard-form categorical syllogism • Recognize the terms of the syllogism • Identify the mood and figure of a syllogism • Use the Venn diagram technique for testing syllogisms • List and describe the syllogistic rules and syllogistic fallacies • List the fifteen valid forms of the categorical syllogism

3. Standard-Form Categorical Syllogisms • Syllogism • Any deductive argument in which a conclusion is inferred from two premises • Categorical syllogism • Deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions

4. Standard-Form Categorical Syllogisms, continued • Example • No heroes are cowards. • Some soldiers are cowards. • Therefore some soldiers are not heroes. • Standard-form categorical syllogism • Premises and conclusion are all standard-form categorical propositions • Propositions are arranged in a specific standard order

5. Terms of the Syllogism • To identify the terms by name, look at the conclusion • “Some soldiers are not heroes.” • Major term • Term that occurs as the predicate (heroes) • Minor term • Term that occurs as the subject (soldiers) • Middle term • Never appears in the conclusion (cowards)

6. Terms of the Syllogism, continued • Major premise • Contains the major term (heroes) • “No heroes are cowards” • Minor premise • Contains the minor term (soldiers) • “Some soldiers are cowards” • Order of standard form • The major premise is stated first • The minor premise is stated second • The conclusion is stated last

7. Mood of the Syllogism • Determined by the types of categorical propositions contained in the argument • No heroes are cowards (E proposition) • Some soldiers are cowards (I proposition) • Some soldiers are not heroes (O proposition) • Mood is EIO • 64 possible moods

8. The Figure of the Syllogism • Determined by the position of the middle term • Types • First figure • Middle term is the subject term of the major premise and the predicate term of the minor premise • Second figure • Middle term is the predicate term of both premises • Third figure • Middle term is the subject of both premises • Fourth figure • Middle term is the predicate term of the major premise and the subject of the minor premise

9. M – P S – M ∴ S – P P – M S – M ∴ S – P M – P M – S ∴ S – P P – M M – S ∴ S – P First Figure Second Figure Third Figure Fourth Figure The Figure of the Syllogism, continued

10. The Figure of the Syllogism, continued • Example • No heroes are cowards. • Some soldiers are cowards. • Therefore some soldiers are not heroes. • Middle term (cowards) appears as predicate in both premises (second figure) • The syllogism is EIO-2

11. The Formal Nature of Syllogistic Argument • A valid syllogism is valid by virtue of its form alone • AAA-1 syllogisms are always valid • All M is P. • All S is M. • Therefore all S is P. • Valid regardless of subject matter • All Greeks are humans. • All Athenians are Greeks. • Therefore all Athenians are humans.

12. P S SPM SPM SPM SPM SPM SPM SPM SPM M Venn Diagram Technique for Testing Syllogisms • If S stands for Swede, P for peasant, and M for musician, then • SPM represents all Swedes who are not peasants or musicians • SPM represents all Swedish peasants who are not musicians, etc.

13. P S M P S M Venn Diagram Technique for Testing Syllogisms, continued • “All M is P” • Add “All S is M” • Conclusion“All S is P” confirmed

14. Dogs Cats Cats that are not dogs Dogs that are not cats Mammals Venn Diagram Technique for Testing Syllogisms, continued • Invalid argument • All dogs are mammals. • All cats are mammals. • Therefore all cats are dogs.

15. Egotists Paupers x Artists Venn Diagram Technique for Testing Syllogisms, continued • Diagram the universal premise first if the other premise is particular • All artists are egotists. • Some artists are paupers. • Therefore some paupers are egotists.

16. Venn Diagram Technique for Testing Syllogisms, continued • Example • All great scientists are college graduates. • Some professional athletes are college graduates. • Therefore some professional athletes are great scientists. Greatscientists Professionalathletes x Collegegraduates

17. Venn Diagram Technique for Testing Syllogisms, continued • Label the circles of a three-circle Venn diagram with the syllogism’s three terms • Diagram both premises, starting with the universal premise • Inspect the diagram to see whether the diagram of the premises contains a diagram of the conclusion

18. Syllogistic Rules and Syllogistic Fallacies • Rule 1. Avoid four terms • Syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument • Fallacy of four terms

19. Syllogistic Rules and Syllogistic Fallacies, continued • Rule 2. Distribute the middle term in at least one premise • If the middle term is not distributed in at least one premise, the connection required by the conclusion cannot be made • All Russians were revolutionists. • All anarchists were revolutionists. • Therefore, all anarchists were Russians. • Fallacy of the undistributed middle

20. Syllogistic Rules and Syllogistic Fallacies, continued • Rule 3. Any term distributed in the conclusion must be distributed in the premises • When the conclusion distributes a term that was undistributed in the premises, it says more about that term than the premises did • Fallacy of illicit process • Fallacy of an illicit major • Fallacy of an illicit minor

21. Syllogistic Rules and Syllogistic Fallacies, continued • Rule 4. Avoid two negative premises • Two premises asserting exclusion cannot provide the linkage that the conclusion asserts • Fallacy of exclusive premises

22. Syllogistic Rules and Syllogistic Fallacies, continued • Rule 5. If either premise is negative, the conclusion must be negative • Class inclusion can only be stated by affirmative propositions • Fallacy of drawing an affirmative conclusion from a negative premise

23. Syllogistic Rules and Syllogistic Fallacies, continued • Rule 6. From two universal premises no particular conclusion may be drawn • Universal propositions have no existential import • Particular propositions have existential import • Cannot draw a conclusion with existential import from premises that do not have existential import • Existential fallacy

24. Exposition of the 15 Valid Forms of the Categorical Syllogism • Mood (64 possible) • Figure (4 possible) • Logical form ( 64 x 4 = 256) • Out of 256 forms, only 15 are valid • Valid forms have names that contain the vowels of the mood • EAE-1 is Celarent • EAE-2 is Cesare

25. The 15 Valid Forms of the Categorical Syllogism • Valid form in the First Figure • AAA-1 Barbara • EAE-1 Celarent • AII-1 Darii • EIO-1 Ferio

26. The 15 Valid Forms of the Categorical Syllogism, continued • Valid forms in the Second Figure • AEE-2 Camestres • EAE-2 Cesare • AOO-2 Baroko • EIO-2 Festino

27. The 15 Valid Forms of the Categorical Syllogism, continued • Valid forms in the Third Figure • AII-3 Datisi • IAI-3 Disamis • EIO-3 Ferison • OAO-3 Bokardo

28. The 15 Valid Forms of the Categorical Syllogism, continued • Valid forms in the Fourth Figure • AEE-4 Camenes • IAI-4 Dimaris • EIO-4 Fresison

29. Summary • Standard-form categorical syllogism • Syllogism terms • Mood and figure • Venn diagram technique for testing syllogisms • Syllogistic rules and syllogistic fallacies • Valid forms of the categorical syllogism