This document contains notes from a logic lecture given by Professor Roy Shaff. It discusses basic logical concepts like propositions, arguments, premises, conclusions, validity, soundness, deduction, and induction. It provides examples of identifying premises and conclusions in arguments. It also discusses the difference between valid and invalid arguments, and between sound and unsound arguments. Key terms are defined and different types of arguments are explained.

1. LOGICProf Roy ShaffChapter 1 – Basic Logical Concepts

2. Consider these

3. Consider these

4. Consider these

5. Consider these

6. Consider these

7. Consider these

8. Consider these

9. Lecture Methodology NoteYou must bring your textbook to every classYou must bring your textbook to every classYou must bring your textbook to every classYou must bring your textbook to every class

10. Lecture MethodologyWe will explore terms and chapter ideas (in future classes this will follow previous assigned readings and homework)We will explore application of these ideas in a variety of ways in order to help you understand what they mean in context Ask Questions!We will review at the end of class. Hints for possible quizzes and answers for homework may be given.

11. Key Terms for Ch 1 - COPYLogicProposition Argument PremiseStatement Conclusion ProbabilityValidity Induction NecessitySoundness Deduction Simple propositionCompound proposition Disjunctive propositionHypothetical propositionInference Enthymemes

12. What Logic IsLogic is the study and principals used to distinguish correct from incorrect reasoning

13. Why Study Logic?You can fool some of the people all of the time, and all of the people some of the time, but you cannot fool all of the people all of the time. Abraham LincolnA King can stand people fighting, but he can't last long if people start thinking. Will Rogers

14. Why Study Logic?To sharpen the mind in a world saturated by streams of propaganda and advertisingTo know when a pitchman is conning you, when some "expert" or pundit is propounding a dubious philosophyTo develop an appreciation for tenable arguments and a respect for good reasoningTo become more adept at solving problems, whether they're encountered in business, science, politics, or the law

15. Why Study Logic?1. "No other digital video recorder retailer can beat Sam Kung's prices." If the above statement is true, which one of the following must also be true? a. Only Sam Kung has low prices for digital video recorders. b. Sam Kung's digital video recorders are the least expensive of all video recorders. c. The best buys in digital video recorders are at Sam Kung's. d. Sam Kung's digital video recorders are priced at least as low as other digital recorders sold at other retail shops.

16. Why Study Logic?2. "Now you can save up to 50% and more on many famous brand items at PayLess." For this claim to be true, which one of the following must also be true? What are the minimum conditions necessary for this claim to be true? a. At least one famous brand item must be more than 50 percent off. b. At least some of the famous brand items must be 50 percent off, and a few must be more than 50 percent off. c. At least half the store's items must be 50 percent off and a few famous brand items must be more than 50 percent off. d. At least half of the famous items must be more than 50 percent off.

17. Why Study Logic?3. "Only Chrysler offers 11.9% financing on new cars." Even if this statement is true, which one of the following could be true? a. Some of Chrysler's more expensive cars could have a higher financing rate. b. Another carmaker could have a lower financing rate. c. Many other carmakers could have a lower financing rate. d. a, b, and c.

18. What Logic IsLogic is the study and principals used to distinguish correct from incorrect reasoning

19. PropositionsArguments are built with the building blocks of PropositionsA Statement is a near synonym for Proposition. These statements will be used interchangeably. A Proposition asserts that something is the case. Every Proposition is either true or false.

20. PropositionsPropositions may be either Simple or CompoundPropositions may be Conjunctive (more than one assertion)Propositions may be Disjunctive (statements of non assertion) (ex – traffic court may or may not be…)Propositions may be Hypothetical (or conditional) (ex – if…then)

21. ArgumentAn Argument is a set of two or more Propositions related to each other in such a way that all but one of them (the Premise) are supposed to provide support for the remaining one (the Conclusion). The transition or movement from Premise to Conclusion, the logical connection between them, is the Inference upon which the Argument relies.

22. NOTE:Classroom Approach to ArgumentMany kinds of Arguments will be explored in classThose who attack of defend an Argument are concerned with establishing the truth or the falsehood of ConclusionsOur classroom approach will typically look at the Form of an Argument – is it the kind to Warrant a ConclusionOur approach will also look at the Quality of an Argument – does it yield a Warranted Conclusion

23. Premise IndicatorsGenerally synonymous in function to: “Since” “Because” List on Pg. 13 of your text

24. Conclusion IndicatorsGenerally synonymous in function to: “Therefore” “So” List on Pg. 12 of your text

25. Identify Premise(s) and ConclusionExample (from your textbook): A well-regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed. US Constitution, Amendment 2

26. Identify Premise(s) and ConclusionExample: A well-regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed. US Constitution, Amendment 2 Premise: A well-regulated militia is necessary for the security of a free state.Conclusion: The right of the people to keep and bear arms shall not be infringed.

27. Identify Premise(s) and ConclusionExample: What stops many people from photocopying a book and giving it to a pal is not integrity but logistics; it’s easier and inexpensive to buy your friend a paperback copy. NY Times Mag, Randy Cohen

28. Identify Premise(s) and ConclusionExample: What stops many people from photocopying a book and giving it to a pal is not integrity but logistics; it’s easier and inexpensive to buy your friend a paperback copy. NY Times Mag, Randy CohenPremises: (1) It’s easier (than photocopying) to buy your friend a paperback copy of a book. (2) It’s inexpensive to buy and give it.Conclusion: What stops many people from photocopying a book and giving it to a pal is not integrity, but logistics.

29. Identify Premise(s) and ConclusionExample: Thomas Aquinas argued that human intelligence is a gift from God and therefore “to apply human intelligence to understand the world is not an affront to God, but pleasing to him.” - Recounted by Charles Murray in Human Accomplishment

30. Identify Premise(s) and ConclusionExample: Thomas Aquinas argued that human intelligence is a gift from God and therefore “to apply human intelligence to understand the world is not an affront to God, but pleasing to him.” - Recounted by Charles Murray in Human AccomplishmentPremise: Human intelligence is a gift from God.Conclusion: To apply human intelligence to understand the world is not an affront to God, but is pleasing to him.

31. Group Exercises#4. Premise: Sir Edmund Hilary dedicated his life to helping build schools and hospitals for the Sherpas who helped him to climb Mount Everest.Conclusion: He is, for that reason, a hero.

32. Group Exercises#5. Premises: (1) Standardized tests have a disparate racial impact, as illustrated by the difference in the average scores of different ethnic groups. (2) Ethnic differences arise on all kinds of tests, at all levels.Conclusion: If a racial is evidence of discrimination, then all tests discriminate.

33. Group Exercises#6. Premise: Everybody thinks himself so abundantly provided with good sense, that even those most difficult to please in all other matters do not commonly desire more of it than they already possess.Conclusion: Good sense is of all things in the world the most equally distributed.

34. Group Exercises#7. Premise: Any words new to the United States are either stupid or foreign.Conclusion: There is no such things as the American language; there’s just bad English.

35. Group Exercises#8. Premise: In New York State alone taxpayers spent more than $200 million in a failed death penalty experiment, with no one executed.Conclusion: The death penalty is too costly.Premise: [There has been] an epidemic of exonerations of death row inmates upon postconviction investigation, including ten New York inmates freed in the last 18 months from long sentences being served for murders or rapes they did not commit.Conclusion: Capital punishment is unfair in its application, in addition to being too costly.

36. Group Exercises#9. Premise: Houses are built to live in, not to look on.Conclusion: Use is to be preferred before [i.e. above] uniformity.

37. Group Exercises#10. Premises: (1) A boycott, although not violent, can cause economic harm to many: (2)The greater the impact of a boycott, the more impressive is the statement it makes. (3) The economic consequences of a boycott are likely to be felt by innocent bystanders who are caused loss of income by it.Conclusion: The boycott weapon ought to be used sparingly, if at all.

38. Group Exercises#11. Premises: (1) In the early part of the 20th century forced population shifts were not uncommon. (2) In that period multicultural empires crumbled and nationalism drove the formation of new, ethnically homogenous countries.Conclusion: Ethnic cleansing was viewed not so long ago as a legitimate tool of foreign policy.

39. Group Exercises#12. Premises: (1) If a jury is sufficiently unhappy with the government’s case or the government’s conduct, it can simply refuse to convict. (2) This possibility puts powerful pressure on the state to behave properly.Conclusion: A jury is one of the most important protections of a democracy.

40. Group Exercises#13. Premises: (1) Orangutans spend more than 95 percent of their time in the trees, which, along with vines and termites, provide more than 99 percent of their food. (2) Their only habitat is formed by the tropical rain forests of Borneo and Sumatra.Conclusion: Without forests, orangutans cannot survive.

41. Group Exercises#14. Premise: If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence.Conclusion: God cannot change his mind about his intervention.Premise: God cannot change his mind about his intervention.Conclusion: If God is omniscient he is not omnipotent.Premise: If God is omniscient hi is not omnipotent.Conclusion: Omniscient and omnipotence are mutually incompatible.

42. Group Exercises#15. Premises: (1) Reason never comes to the aid of spiritual things. (2) More frequently than not, reason struggles against the divine Word, treating all that comes from God with contempt.Conclusion: Reason is the greatest enemy that faith has.

43. Context-ing Argument Some Argument will occur without “Premise or Conclusion Indicators” An Atheist agued “Half of the American population believes that the universe is 6000 years old. They are wrong about this. Declaring them so is not “irreligious intolerance.” It is intellectual honesty.

44. Non-Declarative Premise(s)Rhetorical Question (weak argument method – under suspect)NY Times critic argues against Presidential Spouse coins “I am irked by the new set of coins being issued. While some First Ladies have influenced our country, should we bestow this honor on people who are unelected, whose only credential is having a prominent spouse?”

45. Unstated Proposition(s)An Argument can be obscure because one (or more) of the Propositions is assumed to be understood. These are Enthymemes. [en-thuh-meems]Example: “If the proponent of the death penalty is incorrect in his belief that the death penalty deters homicide, then he is responsible for the execution of murderers who should not be executed.”Unstated Premise – “Homicide-deterrence is the only argument for the death penalty.”

46. Arguments and ExplanationsSome apparent Arguments are explanationsOne textbook example (pg. 19) …Lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt, and where thieves do not break through nor steal: For where your treasure is, there will your heart be also. Matt 6:20-21

47. Exercises (pgs. 21-26)Some of the following contain explanations, some contain arguments, some may be interpreted as both/or either. Explain….and demonstrate Premise and Conclusion or state Explanation as appropriate.

48. Deductive ArgumentArgument from many Propositions to specific Conclusion

49. Inductive ArgumentArgument from one Propositions to one or more specific Conclusion(s) – implications and applications. Logic..Because this is true then….This is a weaker form of Argument than Deductive Argument

50. Validity and TruthSuccessful Arguments are Valid in Logic. This is an assessment of the connectivity an entire Argument. The Conclusion follows with logical necessity from the Premise.

51. Validity and TruthTruth and falsity are attributes of individual Propositions.Argument can be invalid or true propositions.A Conclusion can be true with false propositionsValidity is about the connection between the parts of an the Argument as a whole.

52. Sound ArgumentWhen an Argument is Valid and all of its Premises are true, we call it Sound. Only a Sound Argument can establish the truth of its Conclusion

53. Examples Some valid arguments contain only true propositions-true premises and a true conclusion: All mammals have lungs. All whales are mammals. Therefore, all whales have lungs.

54. Examples Some valid arguments contain only false propositions-false premises and a false conclusion: All four legged creatures have wings, All spiders have four legs. Therefore all spiders have wings,

55. Examples Some invalid arguments contain only true propositions-all their premises are true, and their conclusions are true as well: If I owned all the gold in Fort Knox, then I would be wealthy. I do not own all the gold in Fort Knox. Therefore I am not wealthy.

56. Examples Some invalid arguments contain only true premises and have a false conclusion. This is illustrated by an argument exactly like the previous one (III) in form, changes only enough to make the conclusion false. If Bill Gates owned all the gold in Fort Knox, then Bill Gates would be wealthy. Bill Gates does not own all the gold in Fort Knox. Therefore Bill Gates is not wealthy.

57. Examples Some valid arguments have false premises and a true conclusion: All fishes are mammals. All whales are fishes. Therefore all whales are mammals.

58. Examples Some invalid arguments also have false premises and a true conclusion: All mammals have wings. All whales have wings. Therefore all whales are mammals.

59. Examples Some invalid arguments, of course, contain all false propositions-false premises and a false conclusion: All mammals have wings. All whales have wings. Therefore all mammals are whales.

60. ExercisesSee Handout