CHAPTER 8- INDUCTION

1. CHAPTER 8- INDUCTION • Induction: goes beyond what premises guarantee • Allows us to reason from what is known, usually bits and pieces, to what is true of those bits and pieces. • Reasoning from premises to find what makes premises true. Premises are generalizations. • Comes in several patterns and forms • These forms are strong or weak, cogent or not

2. ENUMERATIVE INDUCTION • 1ST form • Reasoning from premises about individual members of a group to conclusions about the group as a whole. • Form: X per cent of the observed members of group A have property P. Therefore, X percent of all members of group A probably have property P • Does not always have to do with percentages

3. TERMS OF E. INDUCTION • Target group: • The group as a whole. What we aim to draw a conclusion about. • Sample: • The observed members of the group • E.g. Every Gizmo computer I’ve bought in the last two years has had a faulty Windows program. Therefore, all Gizmo computers probably have faulty Windows programs. • Relevant Property: “faulty Windows program.” • Occurs in the predicate of the sentence

4. CRITERIA FOR GOOD/STRONG ENUMERATIVE INDUCTIONS • 1. Sample must be sufficiently large • 2. Sample must be representative • Sample Size: What is large enough? Avoiding Hasty generalization. One instance will not do! • The larger the better! • Rule of thumb: The more homogeneous a target group is in traits relevant to the property in question, the smaller the sample can be; the less homogeneous, the larger the sample should be. • Traits: how diverse is the target group? Are members of the target group all very similar?

5. REPRESENTATIVENESS • Sample must resemble the target group in all the ways that matter. If not, biased. • Two principles to help us here. • 1. The sample must have all the same relevant characteristics (share essential properties, attributes) • 2.Sample must have these characteristics in the same proportions that the target group has. • Sample must reflect the make-up of the target group

6. OPINION POLLS AS INDUCTIONS • Surveying a population or group to arrive at generalizations about anything, often political preferences • Should be strong, cogent, use a large enough sample, be representative and generate accurate data. • Problem of data generation: sometimes data is processed inaccurately, poorly phrased questions are asked or interviews are botched. • Accurate samples for large populations are surprisingly small: 1000-1500

7. OPINION POLLS continued • Other criterion: • Sample should be selected randomly: randomness helps sample be representative. • Non-random selection is usually biased because the researcher uses pre-conceived ideas about what characteristics are representative. • Sample should not be self-selected: respondents should not be allowed to choose to be part of the sample • Many opinion polls done by CTV, CNN, TSN are done this way: They admit to being non-scientific

8. OPINION POLLS continued • Two other criterion/requirements • 1. Margin of error • 2. Confidence level • Margin of error: An error due to inadequate sample. Results are only approximations. • e.g. Candidate X will receive 62 % of the popular vote plus or minus 3 • Margin of error expressed as plus or minus (+) • Range of possible support: from 59-65%

9. OPINION POLLS continued • 2. Confidence level: The probability that the sample will accurately represent the target group within the margin of error. • 95% confidence level still leaves 5% chance that results are not accurate! • Relationships among sample size, margin of error and confidence. • Larger the sample, small the margin of error; but increase over 1,500 to 10,000 does not substantially decrease margin of error. • The lower the confidence level, the smaller the sample size needs to be. • The larger the margin of error, the higher the confidence level

10. EXERCISES • 8.1: 1, 4, 5, 12 • 8.3: 1, • 8.4: 1 • 8.5: 1

11. ANALOGICAL INDUCTION • Arguments by analogy • Analogies are comparisons and can be metaphors or similes, in science, literature and in philosophy, etc. • Basic thrust of the reasoning: two or more things are similar in some or several respect(s), hence they must be similar in a further or additional respect. • Form/Pattern: • Thing A has properties Pi, Pii, Piii, plus Piv • Thing B has properties P1-Piii • Therefore, thing B has property Piv

12. STRENGTH OF A. INDUCTIONS • How do we sort out good arguments from faulty analogies? Use knowledge of fallacy first! • Four items of criteria • 1. Relevant similarities • 2. Relevant dissimilarities • 3. The number of instances compared • 4. Diversity among cases

13. CRITERIA cont. • 1. Relevant similarities • Related to the number of similarities given. • Irrelevant factors, beware! Non-essential attributes • Adding more relevant similarities is like adding more relevant premises! • 2. Relevant dissimilarities • The more the number of relevant dissimilarities between things being compared, the weaker the argument. • A critical tool

14. CRITERIA, cont. • 3. Number of instances being compared. • Increasing items or things being compared. • Increases likelihood that conclusion follows • 4. Diversity among cases. • The more diverse the things being compared, the better or stronger the argument • Ex. 8.6 First few

15. CAUSAL ARGUMENTS • Causal arguments are attempts to give support to a causal claim. • Such arguments can be made using enumerative induction or analogy or inference to the best explanation. • We are concerned with the methods to test for cause developed by John Stuart Mill • Each of these methods, when employed, gives us reason to think that some factor is a cause of some effect

16. TEST FOR CAUSES • Method of Agreement • Essence: Some factor is common to all cases and then we can surmise that it is causal. All cases agree on this factor • Schema: • Case 1: factors a, b, c -------------- E • Case 2: a, c, d ----------------------- E • Case 3: b, c, d ----------------------- E • Case 4: c, d -------------------------- E • C is a probable cause of E • Example: Illness at Elmo’s Bar

17. METHOD OF DIFFERENCE • Essence: removing one factor and not getting the effect • Schema: • Case 1: a,b,c -------------- E • Case 2: a, b---------------- ~E Hence, c is causal • Joint Method of Agreement and Difference • Putting both together • Elmo’s bar again: We discover either wine or tacos made patrons ill • Schematic: • Case 1: a, b, c ----------- E • Case 2: a, b, d ----------- E • Case 3: b, c -------------- ~E • Case 4: b, d ------------- ~E • Conclude: a is a likely cause

18. CORRELATION • Often called concomitant variations • Very familiar in medical science because it has to do with levels or amounts • i.e. you observe the more you practice logic exercises the better you become at logic. You conclude that there is some correlation between the two and that practicing is a causal factor • In medicine, a dose-response relationship

19. CORRELATION, cont. • Careful: correlations can be inverse. You raise some level or dose and then the effect is lowered. i.e. I increase my exercise and my cholesterol level goes down. • Coincidental correlations: often larger scales. • i.e. increase in p.c. sales and increase in cases of aids in Africa.

20. SCHEMA FOR CORRELATION • Case 1: a, b, c ------------ E (control) • Case 2: a+, b, c ----------- E+ • A is causal • The inverse: • Case 1: a, b, c ------------ E (control) • Case 2: a+ (or a-), b, c ----------- E- (or E+) • Put together: • Case 1: a, b, c --------------- E • Case 2: a, b, c+ -------------- E+ • Case 3: a, b, c- --------------- E- • Hence c is correlated to E and causal • Exercise: 8.8 First few

21. CAUSAL CONFUSIONS • Relevant factors: factors that are possibly causal. • Method of Agreement: mere presence of factor! • i.e: Case one: coke, scotch ------------ drunk • Case two: coke, rum --------------- drunk • Case three: coke, gin -------------- drunk • Therefore, coke causes drunkenness

22. MULTIPLE FACTORS/COINCIDENCE • The sheer number of factors can be overwhelming. We need to consider all possible explanations. Avoid False Dilemma! • Coincidence: • Factors can coincide and many do but mere coinciding does not mean cause. • i.e. More people buying mp3 players coincides with higher intakes of water. • Easy to confuse cause or correlation with coincidence. • Careful: we require reasons for suspecting causal connections

23. POST HOC, ERGO PROPTER HOC • “AFTER THIS, THEREFORE BECAUSE OF IT.” • Event X occurs before event Y. Hence, X caused Y. • Another fallacy. • Superstition fallacy! • All causes seem to temporally precede effects but merely being earlier in time does not in any way guarantee cause. • i.e. Before I won the lottery, I rubbed my lucky rabbit’s foot. My rabbit’s foot caused me to win!

24. CONFUSING CAUSE AND EFFECT • So often we switch the two. • Be on look out for when someone switches them. • Claim: Listening to Mozart improves your spatial reasoning. Or, do people with already good spatial reasoning listen to Mozart! • Ask: could the effect really be the cause and the cause the effect?

25. NECESSARY AND SUFFICIENT CONDITIONS • Both relate not so much to causes but to how for every effect, there are any number of conditions that are required to bring it about. • Necessary condition: • One without which the event will not occur. It is needed • Usually many necessary conditions or clusters that cause some event • Sufficient condition: • One that guarantees even occurs • i.e. if p then q; • P is a sufficient condition but not a necessary one!

26. NECESSARY AND SUFFICIENT CONDITIONS, cont. • Necessary conditions: when we are interested in preventing or eliminating state of affairs we often focus on these. • Only need to eliminate one and the whole Effect will be eliminated. • Identifying all or most relevant and then eliminating one. • Sufficient conditions: Used when we want to bring about a state of affairs. • i.e. medications: taking drug x will lower your cholesterol. It is sufficient. It alone will do it. • Ex. 8.10