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

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

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

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?

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

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

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

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%

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

EXERCISES 8.1: 1, 4, 5, 12 8.3: 1, 8.4: 1 8.5: 1

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

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

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

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

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

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

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

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

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.

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

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

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

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!

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?

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!

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