BBI 3420 / 3436

1. BBI 3420 / 3436 ARGUMENTS: Deduction and Induction

2. Overview • Examining deductive and inductive arguments. • Telling the difference between the two. • Different kinds of each argument form. • Types of fallacies

3. Types of arguments • Deductive arguments • An argument in which it is impossible for a conclusion to be false if its premises are true. • Inductive arguments • An argument in which it is improbable for the conclusion to be false if its premises are true.

4. Deductive Reasoning • Starts with a general rule (a premise) which we know to be true. Then, from that rule, we make a true conclusion about something specific.

5. Deductive Reasoning • The process of reasoning from known facts to conclusions. When you reason deductively, you can say “therefore” with certainty. If your facts were firm to begin with, then your conclusions will also be firm. • The conclusion claims to follow necessarily from the premises. • Example: • Socrates is a man. All men are mortal. Therefore, Socrates is mortal.

6. A deductive argument • is one in which it is impossible for the premises to be true but the conclusion false. • It is supposed to be a definitive proof of the truth of the claim (conclusion). • Premise  All men are mortal. • Premise  Socrates was a man. • Conclusion  Socrates was mortal. • If the premises are true (and they are), then it simply isn't possible for the conclusion to be false. • If you have a deductive argument and you accept the truth of the premises, then you must also accept the truth of the conclusion.

7. Deductive Reasoning Is… • Deductive reasoning is when you start from things you assume to be true, and draw conclusions that must be true if your assumptions are true. For Example All dogs have a tail. Benji is a dog. Therefore Benji has a tail.

8. True Premise True Premise True Conclusion A deductive argument

9. Deductive Reasoning • Example: • Smith owns only blue pants and brown pants. Smith is wearing a pair of pants today. So, Smith is wearing either blue or brown pants today.

11. Who is known for using Deductive Reasoning?

12. Sherlock Holmes • Sherlock Holmes would use deductive reasoning to help solve crimes. Example: Sherlock Holmes could help solve a mystery by making inferences. If Holmes saw a pack of cigarettes by a victim (the victim did not smoke), Holmes can make the assumption that the killer is a smoker. Andrew Ault

13. However… • Deductive reasoning may not be the most accurate way of solving a problem, cause we all know that assumptions can be wrong.

14. Other faults of deductive reasoning All Graduates of M.I.T. are Engineers George is not from M.I.T. Therefore George is not an Engineer Everybody from Texas is a cowboy Scott is from Texas Scott is a cowboy

15. What professions do you think commonly use Deductive Reasoning?

16. Doctors Journalists And many more... Lawyers Detectives

17. Why? • These professions tend to ask a lot of questions to try to solve problems or to prove a point. • Often they would have to make assumptions to solve problems. • They would use rules and widely accepted beliefs to prove their argument. An attorney states that his client is innocent because the crime victim was hit by a car. Since his client does not have a license. He can deduce that his client is innocent.

18. Deductive Reasoning

19. Deductive Reasoning From vague To specific

20. Inductive Argument • The process of going from observations to conclusions. • This type of conclusion is sometimes called an inference. • Conclusion claims to follow probably from the premises. • Example: • Socrates was Greek. Most Greeks ate fish. Therefore, Socrates probably ate fish.

21. Inductive Reasoning • Observing that something is true many times, then concluding that it will be true in all instances • Using the data to make a prediction

22. Inductive Reasoning

23. Inductive Reasoning From specific To vague

24. An inductive argument • is one in which the premises are supposed to support the conclusion. • If the premises are true, it is unlikely that the conclusion is false. • The conclusion probably follows from the premises. • Premise  Socrates was Greek. • Premise  Most Greeks eat fish. • Conclusion  Socrates ate fish. • Even if both premises are true, it is still possible for the conclusion to be false (maybe Socrates was allergic to fish). • Words which tend to mark an argument as inductive include probably, likely, possibly and reasonably.

25. A inductive argument True Premise True Premise Probably True Conclusion

26. Inductive Reasoning • Example: • January has been cold here in Siberia. Today is January 14, so it is going to be another cold day in Siberia.

28. Premise: Everything made of copper conducts electricity. Premise: This wire is made of copper. Conclusion: This wire will conduct electricity. Deductive Argument

29. Weaknesses in Inductive Reasoning There are two possible weaknesses in inductive generalizations. 1) the sample may not be representative of the population it is drawn from. Is the sample representative? 2) The sample may be too small, and thus there is a second question we should ask: Is the sample large enough? If the sample is unrepresentative or too small then the premises will be inadequate to support the conclusion.

30. Weaknesses in Inductive Reasoning Sampling: Examples • Just one observation of the effect of cold metal on a human tongue is enough for most kids to form a good generalization. • Similarly, we need not observe the case history of every smoker who has ever lived in order to conclude that smoking is a health hazard. • On the other hand, someone who concludes that “all the good ones are taken” on the basis of two bad dates might sensibly be advised to keep looking.

31. Inductive argument • The local branch of Wachovia Bank was robbed yesterday. Jenny needed money to pay off her gambling debts. She just bought a gun two days ago, and I saw her hanging around the local Wachovia Bank yesterday morning. Today the bookie’s goons stopped looking for Jenny. So Jenny robbed Wachovia Bank yesterday.

32. Premise: All turtles have shells. Premise: The animal I have captured is a turtle. Conclusion: I conclude that the animal in my bag has a shell. Deductive Argument

33. Deductive Argument Sherlock Holmes and Watson were on a camping trip. They had gone to bed and were lying there looking up at the sky. Holmes said, “Watson, look up. What do you see?” “I see thousand of stars.” “And what does that mean to you?” “I guess it means we will have another nice day tomorrow. What does it mean to you, Holmes?” “To me, it means someone has stolen our tent.” • Deductive reasoning drives you to a conclusion based on known facts.

34. Premise: Tonya is seen walking from her car to her home with a set of golf clubs. Premise: Tonya’s husband Jeff loves golf and tomorrow is his birthday. Conclusion: Tonya has bought the set of golf clubs for Jeff. Inductive argument • Inductive reasoning depends on human observation. • Tonya, after all, may be borrowing the golf clubs. Or she may have taken up golf herself! • You wouldn’t know unless you observed carefully, and even then, you would have to describe your conclusion as “probable” but not firm.

35. The cut-off date for swim camp registration is June 15. After that date, applicants go on a wait list - no exceptions allowed. You have missed the cut-off to date to register by two days. You won’t be registered and your name will go on the waiting list. Deductive argument

36. How do we tell inductive from deductive? • The distinction between inductive and deductive arguments is based on the strength of an argument’s inferential claim. • An inferential claim is based on a certain reasoning process – it is the relationship between the premises and conclusion of an argument. • But the strength of a claim is hardly ever stated outright, so we have to evaluate it. • Three criteria for measuring an argument’s strength: • 1) The occurrence of special indicator words. • 2) The actual strength of the inferential link between the premises and conclusion. • 3) The form of argumentation used by the person making the argument. • Certain indicator words lean more towards inductive and some lean towards deductive. But they’re not always accurate. Pay attention to the context of the argument. • Example: The word “probably” tends to be used in inductive arguments, and words like “therefore” and “necessarily” tend to lean towards deductive arguments.

37. The Indicator Word Test Nadia is a B.A (English) student.Most B.A. (English) students own laptops.So, probablyNadia owns a laptop. The indicator word test asks whether there are any indicator words that provide clues whether a deductive or inductive argument is being offered. Common deduction indicator words include words or phrases like necessarily, logically, it must be the casethat, and this proves that. Common induction indicator words include words or phrases like probably, likely, it is plausible tosuppose that, it is reasonable to think that, and it's agood bet that. In the example above, the word probablyshows that the argument is inductive.

38. The Strict Necessity Test No Texans are architects.No architects are Democrats.So, no Texans are Democrats. The strict necessity test asks whether the conclusion follows from the premises with strict logical necessity. If it does, then the argument is deductive. In this example, the conclusion does follow from the premises with strict logical necessity. Although the premises are both false, the conclusion does follow logically from the premises, because if the premises were true, then the conclusion would be true as well.

39. Forms of deductive arguments • Argument based on mathematics • The conclusion depends on a mathematical or geometric measurement. • Has to be deductive since it follows necessarily --- meaning there’s no room for it “probably” being right. • Example: 1+1 = 2 • There’s no room for a different answer by reevaluating the argument. 1 + 1 will always equal 2. If you have 1+1, then it’ll always equal 2. • Argument from definition • The conclusion is claimed to depend on the definition of a word or phrase used either in a premise or in the conclusion. • They follow necessarily because the argument depends completely on the definition of the word being used. • Example: John is a kleptomaniac, so it follows forth that he steals things. • The argument is deductive since the definition of the word leads the argument to one conclusion alone.

40. More deductive forms • Categorical syllogisms • A 3-line argument. Made up of exactly two premises and one conclusion. Begin with the words “all”, “some”, and “no”. • Example: • All oaks are trees* • All trees are plants • All oaks are plants . • Hypothetical Syllogisms • Syllogisms (two premises and one conclusion) that have a conditional statement for one (or both) of its premises. • Example: • If it rains, we will not have a picnic. • If we don't have a picnic, we won't need a picnic basket. • Therefore, if it rains, we won't need a picnic basket. • If you have A, then you have B. • If you have B, then you have C. • Therefore, if you have A, then you have C. • . Hypotheticals work like chains…one leads to the next and ties them all together

41. Inductive argument forms • Prediction • An argument that works based off our knowledge of the past in order to make a claim about the future. • Example: • There tends to be a lot of rain in the Midwest, so it will probably rain there tomorrow. • Claims about the future can’t be known with any certainty, so they can’t be absolutely true, even though they can be justified. That makes them inductive. • Argument from analogy • Depends on the existence of an analogy (or similarity) between two separate things. • Example: • My Honda gets good gas mileage. • So it follows that John’s Honda also gets good gas mileage. • The truth of an argument like this is based on chance, so and that chance makes it an inductive argument.

42. More inductive argument forms • Generalization • An argument that is applied to a whole group based on knowledge gained from a small sample of people. • Example: • Five out of ten people in Ellis Hall said they support abortion. So I can say that half of Athens supports abortion. • Statistical data is not always accurate, so the truth of this form of argument can not be made certain. It remains only probable. • Argument from authority • An argument that concludes something is true because an expert said it is. • Example: • Centrum vitamins work because Dr. Jones did a study that proved it. • This type of argument is only true with probability since studies can be wrong or mistaken.

43. Even more inductive argument forms • Argument based on signs • Conclusion based on knowledge gained from a sign about what the sign claims to mean. • Example: • A sign on the side of the road says “School Zone” so I can assume that a school is somewhere up ahead. • The sign could have been moved from somewhere else, or it could simply be wrong, so it can’t be true with absolute certainty. • Causal inference • Argument that proceeds from knowledge of a cause to a claim about its effect, or vice versa, that knowledge of an effect can provide information about its cause. • Example: • I left a soda in the freezer last night, so I can assume that it is frozen.

44. Is the argument below deductive or inductive? All bats are mammals. All mammals are warm-blooded. So, all bats are warm-blooded. Deductive. If the premises are true, the conclusion, logically, must also be true.

45. Tess: Are there any good Italian restaurants in town?Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagne col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes. Is this argument deductive or inductive? How can you tell? Inductive. The argument is an inductive generalization, which is a common pattern of inductive reasoning. Also, the conclusion does not follow with strict necessity from the premises.

46. I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough. Is this argument deductive or inductive? How can you tell? Deductive. This argument is an argument based on mathematics, which is a common pattern of deductive reasoning. Plus, the conclusion follows necessarily from the premises.

47. Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts, and he broke out in a severe rash.Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then. Is the father's argument deductive or inductive? How can you tell?

48. Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts, and he broke out in a severe rash.Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then. Inductive. The father's argument is a causal argument, which is a common pattern of inductive reasoning. Also, the conclusion does not follow necessarily from the premises. (Billy might have developed an allergic reaction to walnuts since last spring.)

49. John is an agnostic. It necessarily follows that he doesn't believe in God. Is this argument deductive or inductive? How can you tell? Deductive. This argument is an argument by definition, which is a common pattern of deductive inference. Also, the phrase "it necessarily follows that" is a deduction indicator phrase. Also, the conclusion follows from the premises.

50. Larry: Do you think Representative Miller will be re-elected?Norman: I doubt it. Miller's district has become more conservative in recent years. Miller is a liberal Democrat, and 63% of the registered voters in his district are now Republicans. Is this argument deductive or inductive? How can you tell? Inductive. This argument is both a statistical argument and a predictive argument, which are two common patterns of inductive reasoning. Also, the conclusion does not follow necessarily from the premises.