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
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TERMS OF E. INDUCTION
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Target group:
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The group as a whole. What we aim to draw a conclusion
about.
Sample:
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The observed members of the group
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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?
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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
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OPINION POLLS AS INDUCTIONS
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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
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Other criterion:
Sample should be selected randomly: randomness helps
sample be representative.
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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
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Margin of error: An error due to inadequate
sample. Results are only approximations.
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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
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2. Confidence level: The probability that the sample
will accurately represent the target group within the
margin of error.
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95% confidence level still leaves 5% chance that results
are not accurate!
Relationships among sample size, margin of error and
confidence.
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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
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ANALOGICAL INDUCTION
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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:
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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
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CRITERIA cont.
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1. Relevant similarities
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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
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The more the number of relevant dissimilarities
between things being compared, the weaker the
argument.
A critical tool
CRITERIA, cont.
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3. Number of instances being compared.
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4. Diversity among cases.
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Increasing items or things being compared.
Increases likelihood that conclusion follows
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
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TEST FOR CAUSES
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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:
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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
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Essence: removing one factor and not getting the effect
Schema:
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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:
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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
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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.
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SCHEMA FOR CORRELATION
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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:
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Case 1: a, b, c --------------- E
Case 2: a, b, c+ -------------- E+
Case 3: a, b, c- --------------- EHence 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
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Case two: coke, rum --------------- drunk
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Case three: coke, gin -------------- drunk
 Therefore, coke causes drunkenness
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MULTIPLE FACTORS/COINCIDENCE
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The sheer number of factors can be overwhelming. We
need to consider all possible explanations. Avoid False
Dilemma!
Coincidence:
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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.
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Careful: we require reasons for suspecting causal connections
POST HOC, ERGO PROPTER HOC
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“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?
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NECESSARY AND SUFFICIENT
CONDITIONS
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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:
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One without which the event will not occur. It is needed
Usually many necessary conditions or clusters that cause some
event
Sufficient condition:
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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.
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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