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- 1. Logic <br /> HUM 200<br /> Categorical Syllogisms<br />1<br />
- 2. Objectives<br />2<br />When you complete this lesson, you will be able to:<br />Describe a standard-form categorical syllogism<br />Recognize the terms of the syllogism<br />Identify the mood and figure of a syllogism<br />Use the Venn diagram technique for testing syllogisms<br />List and describe the syllogistic rules and syllogistic fallacies<br />List the fifteen valid forms of the categorical syllogism<br />
- 3. Standard-Form Categorical Syllogisms <br />3<br />Syllogism<br />Any deductive argument in which a conclusion is inferred from two premises<br />Categorical syllogism<br />Deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the constituent propositions <br />
- 4. Standard-Form Categorical Syllogisms, continued <br />4<br />Example<br />No heroes are cowards.<br />Some soldiers are cowards.<br />Therefore some soldiers are not heroes. <br />Standard-form categorical syllogism<br />Premises and conclusion are all standard-form categorical propositions <br />Propositions are arranged in a specific standard order <br />
- 5. Terms of the Syllogism <br />5<br />To identify the terms by name, look at the conclusion <br />“Some soldiers are not heroes.”<br />Major term<br />Term that occurs as the predicate (heroes)<br />Minor term<br />Term that occurs as the subject (soldiers)<br />Middle term<br />Never appears in the conclusion (cowards)<br />
- 6. Terms of the Syllogism, continued <br />6<br />Major premise<br />Contains the major term (heroes)<br />“No heroes are cowards” <br />Minor premise<br />Contains the minor term (soldiers)<br />“Some soldiers are cowards” <br />Order of standard form<br />The major premise is stated first<br />The minor premise is stated second<br />The conclusion is stated last<br />
- 7. Mood of the Syllogism <br />7<br />Determined by the types of categorical propositions contained in the argument <br />No heroes are cowards (E proposition)<br />Some soldiers are cowards (I proposition)<br />Some soldiers are not heroes (O proposition)<br />Mood is EIO<br />64 possible moods<br />
- 8. The Figure of the Syllogism <br />8<br />Determined by the position of the middle term <br />Types<br />First figure<br />Middle term is the subject term of the major premise and the predicate term of the minor premise <br />Second figure<br />Middle term is the predicate term of both premises <br />Third figure<br />Middle term is the subject of both premises <br />Fourth figure<br />Middle term is the predicate term of the major premise and the subject of the minor premise <br />
- 9. The Figure of the Syllogism, continued <br />9<br />M – P<br />S – M <br />∴ S – P<br />P – M<br />S – M <br />∴ S – P<br />M – P<br />M – S <br />∴ S – P<br />P – M<br />M – S <br />∴ S – P<br />First Figure<br />Second Figure<br />Third Figure<br />Fourth Figure<br />
- 10. The Figure of the Syllogism, continued <br />10<br />Example<br />No heroes are cowards.<br />Some soldiers are cowards.<br />Therefore some soldiers are not heroes.<br />Middle term (cowards) appears as predicate in both premises (second figure)<br />The syllogism is EIO-2<br />
- 11. The Formal Nature of Syllogistic Argument <br />11<br />A valid syllogism is valid by virtue of its form alone <br />AAA-1 syllogisms are always valid<br />All M is P.<br />All S is M.<br />Therefore all S is P. <br />Valid regardless of subject matter<br />All Greeks are humans.<br />All Athenians are Greeks.<br />Therefore all Athenians are humans. <br />
- 12. Exercises<br />12<br />No nuclear-powered submarines are commercial vessels, so no warships are commercial<br />vessels, since all nuclear-powered submarines are warships.<br />Solution<br />Step 1. The conclusion is “No warships are commercial vessels”.<br />Step 2. “Commercial vessels” is the predicate term of this conclusion, and is therefore the<br />major terms of the syllogism.<br />Step 3. The major premise, the premise that contains this term, is “No nuclear-powered<br />submarines are commercial vessels”.<br />Step 4. The remaining premise, “All nuclear-powered submarines are warships”, is indeed<br />the major premise, since it does contain the subject term of the conclusion, “warships”.<br />Step 5. In standard form this syllogism is written thus:<br />No nuclear-powered submarines are commercial vessels.<br />All nuclear-powered submarines are warships.<br />Therefore no warships are commercial vessels.<br />Step 6. The three propositions in this syllogism are, in order, E, A and E. The middle term<br />“nuclear-powered submarines,” is the subject term of both premises, so the syllogism<br />is in the third figure. The mood and figure of the syllogism therefore are<br />EAE-3.<br />
- 13. Exercises - Answer<br />13<br />Some objects of worship are fir trees. <br />All fir trees are evergreens.<br />Therefore some evergreens are objects of worship. IAI-4.<br />
- 14. Exercises - Answer<br />14<br />Some artificial satellites are not American inventions.<br />All artificial satellites are important scientific achievements.<br />Therefore some important scientific achievements are not American inventions.<br />OAO-3.<br />
- 15. Group Exercises - Answer<br />15<br />#4<br />All certified public accounts are people of good business sense.<br />No television stars are certified public accountants.<br />Therefore no television stars are people of good business sense.<br />AEE-1.<br />
- 16. Group Exercises - Answers <br />16<br />#6<br />No delicate mechanisms are suitable toys for children.<br />All CD players are delicate mechanisms.<br />Therefore no CD players are suitable toys for children.<br />EAE-1.<br />
- 17. Group Exercises - Answers <br />17<br />#7<br />Some juvenile delinquents are products of broken homes.<br />All juvenile delinquents are maladjusted individuals.<br />Therefore some maladjusted individuals are products of broken homes.<br />IAI-3.<br />
- 18. 18<br />P<br />S<br />SPM<br />SPM<br />SPM<br />SPM<br />SPM<br />SPM<br />SPM<br />SPM<br />M<br />Venn Diagram Technique for Testing Syllogisms <br />If S stands for Swede, P for peasant, and M for musician, then <br />SPM represents all Swedes who are not peasants or musicians<br />SPM represents all Swedish peasants who are not musicians, etc. <br />
- 19. 19<br />P<br />S<br />M<br />P<br />S<br />M<br />Venn Diagram Technique for Testing Syllogisms, continued <br />“All M is P”<br />Add “All S is M”<br />Conclusion“All S is P” confirmed<br />
- 20. Venn Diagram Technique for Testing Syllogisms, continued <br />20<br />Invalid argument<br />All dogs are mammals.<br />All cats are mammals.<br />Therefore all cats are dogs. <br />Dogs<br />Cats<br />Cats that are not dogs<br />Dogs that are not cats<br />Mammals<br />
- 21. Exercises pg. 232-233<br />21<br />#1<br />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.<br />One possible refuting analogy is this: <br />All bipeds are astronauts, <br />All astronauts are humans <br />Therefore all humans are bipeds.<br />
- 22. Group Exercises pg. 232-233<br />22<br />Do numbers 3, 4, 5 and 7<br />
- 23. 23<br />Diagram the universal premise first if the other premise is particular<br />All artists are egotists.<br />Some artists are paupers.<br />Therefore some paupers are egotists. <br />Egotists<br />Paupers<br />x<br />Artists<br />Venn Diagram Technique for Testing Syllogisms, continued <br />
- 24. Venn Diagram Technique for Testing Syllogisms, continued <br />24<br />Example<br />All great scientists are college graduates.<br />Some professional athletes are college graduates. <br />Therefore some professional athletes are great scientists. <br />Greatscientists<br />Professionalathletes<br />x<br />Collegegraduates<br />
- 25. Venn Diagram Technique for Testing Syllogisms, continued <br />25<br />Label the circles of a three-circle Venn diagram with the syllogism’s three terms <br />Diagram both premises, starting with the universal premise<br />Inspect the diagram to see whether the diagram of the premises contains a diagram of the conclusion <br />
- 26. Group Exercises<br />26<br />Do 2,3,4 and 6<br />
- 27. Group Exercises #2<br />27<br />
- 28. Group Exercises #3<br />28<br />
- 29. Group Exercises #4<br />29<br />
- 30. Group Exercises #6<br />30<br />
- 31. Syllogistic Rules and Syllogistic Fallacies <br />31<br />Rule 1. Avoid four terms<br />Syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument <br />Fallacy of four terms<br />Power tends to corrupt <br />Knowledge is power <br />Knowledge tends to corrupt <br />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. <br />
- 32. Syllogistic Rules and Syllogistic Fallacies, continued <br />32<br />Rule 2. Distribute the middle term in at least one premise<br />If the middle term is not distributed in at least one premise, the connection required by the conclusion cannot be made <br />Fallacy of the undistributed middle<br />All sharks are fish <br />All salmon are fish <br />All salmon are sharks <br />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. <br />
- 33. Syllogistic Rules and Syllogistic Fallacies, continued <br />33<br />Rule 3. Any term distributed in the conclusion must be distributed in the premises<br />When the conclusion distributes a term that was undistributed in the premises, it says more about that term than the premises did <br />Fallacy of illicit process<br />All tigers are mammals <br />All mammals are animals <br />All animals are tigers<br />Worth Diagramming<br />
- 34. Syllogistic Rules and Syllogistic Fallacies, continued <br />34<br />Rule 4. Avoid two negative premises<br />Two premises asserting exclusion cannot provide the linkage that the conclusion asserts<br />Fallacy of exclusive premises <br />No fish are mammals <br />Some dogs are not fish <br />Some dogs are not mammals<br />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. <br />
- 35. Syllogistic Rules and Syllogistic Fallacies, continued <br />35<br />Rule 5. If either premise is negative, the conclusion must be negative<br />Class inclusion can only be stated by affirmative propositions <br />Fallacy of drawing an affirmative conclusion from a negative premise<br />All crows are birds <br />Some wolves are not crows <br />Some wolves are birds <br />
- 36. Syllogistic Rules and Syllogistic Fallacies, continued <br />36<br />Rule 6. From two universal premises no particular conclusion may be drawn<br />Universal propositions have no existential import<br />Particular propositions have existential import <br />Cannot draw a conclusion with existential import from premises that do not have existential import<br />Existential fallacy<br />All mammals are animals <br />All tigers are mammals <br />Some tigers are animals <br />
- 37. Exposition of the 15 Valid Forms of the Categorical Syllogism <br />37<br />Mood (64 possible)<br />Figure (4 possible)<br />Logical form ( 64 x 4 = 256)<br />Out of 256 forms, only 15 are valid<br />Valid forms have names that contain the vowels of the mood<br />EAE-1 is Celarent<br />EAE-2 is Cesare<br />
- 38. The 15 Valid Forms of the Categorical Syllogism <br />38<br />Valid form in the First Figure<br />AAA-1Barbara<br />EAE-1Celarent<br />AII-1Darii<br />EIO-1Ferio<br />
- 39. The 15 Valid Forms of the Categorical Syllogism, continued <br />39<br />Valid forms in the Second Figure<br />AEE-2Camestres<br />EAE-2Cesare<br />AOO-2Baroko<br />EIO-2Festino<br />
- 40. The 15 Valid Forms of the Categorical Syllogism, continued <br />40<br />Valid forms in the Third Figure<br />AII-3Datisi<br />IAI-3Disamis<br />EIO-3Ferison<br />OAO-3Bokardo<br />
- 41. The 15 Valid Forms of the Categorical Syllogism, continued <br />41<br />Valid forms in the Fourth Figure<br />AEE-4Camenes<br />IAI-4Dimaris<br />EIO-4Fresison<br />
- 42. Exercises pg 253<br />42<br />
- 43. Exercises pg 253<br />43<br />
- 44. Summary <br />44<br />Standard-form categorical syllogism<br />Syllogism terms<br />Mood and figure<br />Venn diagram technique for testing syllogisms<br />Syllogistic rules and syllogistic fallacies<br />Valid forms of the categorical syllogism<br />

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