批判性思维 Critical Thinking

1. 批判性思维Critical Thinking 第十四讲（Lecture 14） 归纳概括（Inductive Generalization）

2. Deduction, good, but not sufficient • A deductively sound argument is very good, or even perfect in the sense that the truth of the conclusion is guaranteed. However, for many statements, like the premises in a deductive argument, we cannot get the truth of them only by deductive arguments.

3. Truth of the statements cannot be acquired by deduction alone. • “The water is boiling if the temperature is above 100 degrees centigrade.” • “The sun rises in the east every morning.” • “A planet moves not uniformly but in such a way that a line drawn from it to the sun sweeps out equal areas of the ellipse in equal times.”

4. The second planetary law of Johannes Kepler (1571-1630) • Planets [the lines drawn from planets to the sun] sweep out equal areas in equal times.

5. Kinds of inductive arguments • Inductive generalization (arguments by generalization): enumerative induction and statistic induction • Statistic syllogism • Analogy • Hypothetical reasoning

6. Arguments by generalization • 1. Enumerative induction (universal generalization) • 2. Statistic induction (statistic generalization)

7. Inductive arguments • Criteria of evaluating those inductive arguments must be different from those deductive arguments, because inductive arguments are significantly different from deductive arguments. Their evaluation requires different criteria.

8. 1. Enumerative induction/generalization • General form: • S(a1) is P. This NNU girl (#1) is charming. • S(a2) is P. This NNU girl (#2) is charming. • …… • S(an) is P. This NNU girl (#10) is charming. • (Variety 1: No S has been observed to be non-P.) • Therefore, all S’s are P. All NNU girls are charming. • (Variety 2: Therefore, the next S(an+1) will be P.)

9. Some technical terms: • Population: NNU girls (the class of the things surveyed or denoted by the subject term of the conclusion) • Projected property: charming (the property denoted by the predicate term of the conclusion). • Sample: Our 10 cases (some of the population or the set of observations made of the population).

10. S(a1) is P. This NNU girl (#1) is charming. • S(a2) is P. This NNU girl (#2) is charming. • …… • S(an) is P. This NNU girl (#10) is charming. • Therefore, all S’s are P. All NNU girls are charming. Sample Population Projected Property

11. 2. Statistic induction/generalization • N% of observed S’s (i.e., S(a1), ... S(an)) are P. • -------------------------------------------------------------------------------- • Therefore, N% of all S’s are P. • 70% of 10 NNU girls are charming. • --------------------------------------------------------------------------------- • Therefore, 70% of all NNU girls are charming.

12. Net citizen ＃1 disbelieves in “Zhou’s Tiger.” • Net citizen ＃2 disbelieves in “Zhou’s Tiger.” • …… • Net citizen ＃7 disbelieves in “Zhou’s Tiger.” • Net citizen #8 believes in “Zhou’s Tiger.” • …… • Net citizen #10 believes in “Zhou’s Tiger.” • Therefore, 70% of net citizens disbelieve in Zhou’s “Tiger.”

13. Criteria of evaluating arguments by generalization • 1. Representativeness (Variety) of the Sample: The more representative the sample is, the stronger the argument, other things being equal. • For example, if 10 investigated NNU girls are distributed in different schools and different years or grades, the stronger the argument. • If they come only from School of Art/Music or dancing class of the School, then the weaker the argument.

14. Violating this criterion, one will commit the following fallacy. • Fallacy of Biased Sampling. • Example: there is a bag of French beans in front of me. I pick up every French bean on the top of the bag and they are all green. I conclude that all French beans in the bag are green. In this example, I commit the fallacy of biased sampling because the conditions such as temperature in different positions (in the top, middle and bottom) are different and I only pick up the French beans on the top. Thus, my sampling is biased or my sample is not representative.

15. 2. The size of the sample: The greater the sample size is, the stronger the argument. • Violating this criterion, one will commit the fallacy of Hasty Generalization. • Example: I went to a single bar last night and two women approached obviously not for the lasting relationship but just for sex. Therefore, no women at a single bar are looking for serious relationship. This argument commits the fallacy of Hasty Generalization because the arguer jumps to a general conclusion to all the women at single bars from only two women’s example.

16. 3. Relevance of P (the projected property) to the def. of S (a member of the population): the greater the relevance is, the stronger the argument. • For example, the size of the engine is relevant to the gas mileage but the color is not. • All good gas mileage cars in Arnald Mazda are white. Therefore, all good gas mileage cars are white. • This argument is weak because irrelevant. If the projected property is about cylinders, then it is relevant to the population and the argument could be relatively strong.

17. 4. The scope of the conclusion: the greater the scope of the conclusion, the weaker the argument (or the more the conclusion says, the weaker the argument would be). • For example, suppose I see 10 girls in the school of music and they are all beautiful. I conclude that all girls in the school of music are beautiful. If I conclude that all girls in NNU are beautiful, then my second argument is weaker.

18. 3. Statistical Syllogism • 95 % of NNU students live in Jiangsu. • Zhang Ling is a NNU student. • Therefore, she must live in Jiangsu. • The above arguments are deductively invalid (bad) but we think they are good arguments. Thus, we must adopt different criteria of evaluation. • Instead of validity and soundness, we use strong (reliable), weak (unreliable), cogent and uncogent to evaluate inductive arguments.

19. Strong/reliable argument: if the premise/s were true, the conclusion would be most likely to be true. • Weak/unreliable argument: it fails to meet the criterion above.

20. Form of statistical syllogisms • N % of all F’s are G’s (or Most F’s are G’s). • a is an F. • ------------------------------------------------------------------------- • Therefore, a is a G. • Terms: • The reference class (F’s) • The attribute class (G’s) • Projected property • Individuals (a) • Statistical premise (statement)

21. Exercise • Indicate the reference class and the attribute class in the following argument: • Hardly any freshmen had a philosophy course in high school. • Zhang Ling is a freshman. • --------------------------------------------------------------------------------- • Zhang Ling did not have a philosophy course in high school.

22. Standards of evaluation • 1. The closeness to 100 percent of the statistical premise; the closeness to 0 percent of the statistical premise when the conclusion is negative. • 98 % of NNU students live in Jiangsu; • Zhang Ling is a NNU student. • ------------------------------------------------------------------ • Therefore, she must live in Jiangsu.

23. 2. The rule of total evidence: whether all available relevant evidence has been considered in selecting the reference class. • Case A: • 90 % of freshmen at NNU are residents of Jiangsu. • Zhang Ling is a freshman at NNU. • ------------------------------------------------------------------------------ • Therefore, Zhang Ling is a resident of Jiangsu.

24. Case B: • 2 % of all members of the Hubei Students’ Club (HSC) are Jiangsu residents. • Zhang Ling is a member of the HSC. • Therefore, Zhang Ling is not a Jiangsu resident. • Both arguments (case A and case B) are strong but the conclusions are opposite.

25. To avoid this situation, we need the rule of total evidence. • 5 % of all freshmen at NNU who are members of the HSC are Jiangsu residents. • Zhang Ling is a freshman member of the HSC. • Therefore, Zhang Ling is not a Jiangsu resident.

26. The fallacy of incomplete evidence • If the argument violates the second rule (of total evidence), then it commits this fallacy. • Relevant evidence: any evidence that might influence the probability that a has (is) G. • For instance, sex of students may be irrelevant to whether a has province residence.

27. Your bus for work most of time arrives on time. It will arrive on time today (ignoring the evidence that the city streets are covered with ice). This example commits the fallacy of incomplete evidence. • Most of the Macomb Community College students are male. • Shirley is a MCC student. • ----------------------------------------------------------------------- • Therefore, Shirley is male. • However, this argument commits the fallacy of incomplete evidence, because Shirley is seldom assigned to a male in the northern America.

28. Some other fallacies and special forms of statistical syllogism • 1. Arguments from authority (good) • We cannot get all direct evidence for our position (premise or conclusion). So, we need to listen to experts’ advice and opinion to establish our position. • However, sometimes it is good to do so but sometimes not. • Appeal to unqualified authority (bad) • Why should I be moral? Because of the God’s will.

29. Good or bad depends on two conditions: • (i) the authority is a genuine expert on the matter under consideration; • Jogging every day is good for your health because Jenny Goodman says so and she is a famous expert on exercises and health. (good) • Jogging everyday is good for your health because Obama says. (bad) • (ii) there is an agreement among experts in the area of knowledge under consideration.

30. If the argument does not meet anyone of them, it commits the fallacy of appeal to unqualified authority. • In some areas such as politics, morality, religion, there would be no appropriate authority about certain issues. In that case, if one appeal to authority, one commits the fallacy of appeal to unqualified authority.

31. Statistical form of arguments from authority • Most of what authority a has to say on subject matter S is correct. • a says p about S. • ----------------------------------------------------------------------------------- • Therefore, p is correct.

32. 2. Arguments against the person (ad hominem) • The conclusion is false because it is made by a particular person or group. • Two cases of bad arguments against the person:

33. ad hominem-circumstantial (referring to the arguer’s profession, etc.) • The salesman says that this discounted wine is an overlooked gem and a very good selection. But you have to take what he says with a grain of salt. He’s just trying to move slow merchandise.

34. ad hominem-abusive (verbally attacking the person) • You can’t take Jenny Woods’s words seriously, who is a Congressperson, because she used to be a whore (prostitute). She supports women’s right of abortion.

35. Statistical form • Most of what individual a says about a particular subject matter S is false. • a says p about S. • ------------------------------------------------------------------------------------- • Therefore, p is false.

36. 3. Arguments from consensus (ad populem) or Arguments against people • Good ones have the form: • When most people agree on a claim about a subject matter S, the claim is true. • p is a claim about S that most people agree on. • ---------------------------------------------------------------------------------------------- • Therefore, p is true. • Example for good ones:

37. A deductive argument which is not argument from consensus • A movie is legally pornographic if most people consider it pornographic. • Most people consider movie M pornographic. • ------------------------------------------------------------------------------------------------- • Therefore, Movie M is legally pornographic.

38. Example for bad ones: • (appeal to the people)

39. 4. Incorrect form of inductive argument • Deductive form • All F’s are G’s. • a is an F. • Therefore, a is a G. • Inductively incorrect form • Most F’s are G’s. • Most G’s are H’s. • Therefore, most F’s are H’s. • physicists = F’s, men = G’s, non-physicists = H’s.

40. Thank you!