2. Objectives 2 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 3 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 4 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 5 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 6 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 7 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 8 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. The Figure of the Syllogism, continued 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
10. The Figure of the Syllogism, continued 10 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 11 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. Exercises 12 No nuclear-powered submarines are commercial vessels, so no warships are commercial vessels, since all nuclear-powered submarines are warships. Solution Step 1. The conclusion is “No warships are commercial vessels”. Step 2. “Commercial vessels” is the predicate term of this conclusion, and is therefore the major terms of the syllogism. Step 3. The major premise, the premise that contains this term, is “No nuclear-powered submarines are commercial vessels”. Step 4. The remaining premise, “All nuclear-powered submarines are warships”, is indeed the major premise, since it does contain the subject term of the conclusion, “warships”. Step 5. In standard form this syllogism is written thus: No nuclear-powered submarines are commercial vessels. All nuclear-powered submarines are warships. Therefore no warships are commercial vessels. Step 6. The three propositions in this syllogism are, in order, E, A and E. The middle term “nuclear-powered submarines,” is the subject term of both premises, so the syllogism is in the third figure. The mood and figure of the syllogism therefore are EAE-3.
13. Exercises - Answer 13 Some objects of worship are fir trees. All fir trees are evergreens. Therefore some evergreens are objects of worship. IAI-4.
14. Exercises - Answer 14 Some artificial satellites are not American inventions. All artificial satellites are important scientific achievements. Therefore some important scientific achievements are not American inventions. OAO-3.
15. Group Exercises - Answer 15 #4 All certified public accounts are people of good business sense. No television stars are certified public accountants. Therefore no television stars are people of good business sense. AEE-1.
16. Group Exercises - Answers 16 #6 No delicate mechanisms are suitable toys for children. All CD players are delicate mechanisms. Therefore no CD players are suitable toys for children. EAE-1.
17. Group Exercises - Answers 17 #7 Some juvenile delinquents are products of broken homes. All juvenile delinquents are maladjusted individuals. Therefore some maladjusted individuals are products of broken homes. IAI-3.
18. 18 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.
19. 19 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
20. Venn Diagram Technique for Testing Syllogisms, continued 20 Invalid argument All dogs are mammals. All cats are mammals. Therefore all cats are dogs. Dogs Cats Cats that are not dogs Dogs that are not cats Mammals
21. Exercises pg. 232-233 21 #1 All business executives are active opponents of increased corporation taxes, for all active opponents of increased corporation taxes are members of the chamber of commerce, and all members of the chamber of commerce are business executives. One possible refuting analogy is this: All bipeds are astronauts, All astronauts are humans Therefore all humans are bipeds.
23. 23 Diagram the universal premise first if the other premise is particular All artists are egotists. Some artists are paupers. Therefore some paupers are egotists. Egotists Paupers x Artists Venn Diagram Technique for Testing Syllogisms, continued
24. Venn Diagram Technique for Testing Syllogisms, continued 24 Example All great scientists are college graduates. Some professional athletes are college graduates. Therefore some professional athletes are great scientists. Greatscientists Professionalathletes x Collegegraduates
25. Venn Diagram Technique for Testing Syllogisms, continued 25 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
31. Syllogistic Rules and Syllogistic Fallacies 31 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 Power tends to corrupt Knowledge is power Knowledge tends to corrupt Justification: This syllogism appears to have only three terms, but there are really four since one of them, the middle term “power” is used in different senses in the two premises. To reveal the argument’s invalidity we need only note that the word “power” in the first premise means “ the possession of control or command over people,” whereas the word “power” in the second premise means “the ability to control things.
32. Syllogistic Rules and Syllogistic Fallacies, continued 32 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 Fallacy of the undistributed middle All sharks are fish All salmon are fish All salmon are sharks Justification: The middle term is what connects the major and the minor term. If the middle term is never distributed, then the major and minor terms might be related to different parts of the M class, thus giving no common ground to relate S and P.
33. Syllogistic Rules and Syllogistic Fallacies, continued 33 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 All tigers are mammals All mammals are animals All animals are tigers Worth Diagramming
34. Syllogistic Rules and Syllogistic Fallacies, continued 34 Rule 4. Avoid two negative premises Two premises asserting exclusion cannot provide the linkage that the conclusion asserts Fallacy of exclusive premises No fish are mammals Some dogs are not fish Some dogs are not mammals If the premises are both negative, then the relationship between S and P is denied. The conclusion cannot, therefore, say anything in a positive fashion. That information goes beyond what is contained in the premises.
35. Syllogistic Rules and Syllogistic Fallacies, continued 35 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 All crows are birds Some wolves are not crows Some wolves are birds
36. Syllogistic Rules and Syllogistic Fallacies, continued 36 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 All mammals are animals All tigers are mammals Some tigers are animals
37. Exposition of the 15 Valid Forms of the Categorical Syllogism 37 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
38. The 15 Valid Forms of the Categorical Syllogism 38 Valid form in the First Figure AAA-1Barbara EAE-1Celarent AII-1Darii EIO-1Ferio
39. The 15 Valid Forms of the Categorical Syllogism, continued 39 Valid forms in the Second Figure AEE-2Camestres EAE-2Cesare AOO-2Baroko EIO-2Festino
40. The 15 Valid Forms of the Categorical Syllogism, continued 40 Valid forms in the Third Figure AII-3Datisi IAI-3Disamis EIO-3Ferison OAO-3Bokardo
41. The 15 Valid Forms of the Categorical Syllogism, continued 41 Valid forms in the Fourth Figure AEE-4Camenes IAI-4Dimaris EIO-4Fresison
44. Summary 44 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
