Chapter 9 Lecture Notes
An Introduction to
Inductive Arguments
Chapter 9
Induction is the basis for our commonsense beliefs about
the world.
In the most general sense, inductive reasoning, is that in
which we extrapolate from experiences to what we have
not yet experiences.
In this chapter we are going to focus on: inductive
generalizations, statistical syllogisms, and common
errors or fallacies that are associated with inductive
reasoning in general.
Chapter 9
Many logic texts define inductive arguments in contrast with
deductive arguments. We aren’t going to do that. For
us, inductive arguments have the following
characteristics:
1.
2.
3.
4.
The premises and the conclusion are all empirical propositions.
The conclusion is not deductively entailed by the premises.
The reasoning used to infer the conclusion from the premises is based on
the underlying assumption that the regularities described in the premises
will persist.
The inference is either that unexamined cases will resemble examined
ones or that evidence makes an explanatory hypothesis probable.
See page 255 for a full explanation.
Chapter 9
This means that inductive and deductive are contrary
predicates, not contradictory predicates. We will also
see that there are arguments that are neither inductive
nor deductive and so we will have to have another
category for those in future chapters.
For inductive arguments, it is always some possibility that
the conclusion will turn out to be false even though the
premises are true. (256)
Following David Hume, this is the problem of induction.
Chapter 9
Inductive Generalizations (IG)
In an IG, the premises describe a number of observed
objects or events as having some particular feature.
From this observed set of objects or events a conclusion
asserts a claim about all (or most) of the objects and
events of the same type have the feature in question.
1. 85% of polled students at Notre Dame think the football team is great.
So, probably:
1. 85% of all Notre Dame students think the the football team is great.
The word probably indicates that there is an extrapolation
from the polled (observed) group the the entire group.
Chapter 9
Phrases like: probably, in all likelihood, and most likely are
often used in inductive arguments.
Inductive arguments and inductive reasoning is used in
contexts of prediction. Reasoning from the past to the
future. Cases where we reason from the present to the
past (as in archeology) is called retrodiction. We might
make a claim about which dinosaurs went extinct first
based on current fossil records. This would be an
inductive, retrodictive argument.
Induction require a belief in the regularities in the world.
Chapter 9
Some important points about the many types of IGs.
We need to take into account:
(1) Sample size relative to the size of the target population.
(2) Samples need to be random
Random for samples is defined as: every member of the
population having an equal chance of being chosen for
the sample. If this is the case, then the sample is
random.
Chapter 9
Problems of Sampling:
Size issues: more samples of a population does not
necessarily make an IG stronger. What one needs for
the sample is for it to be representative.
Representativeness will work as a substitute condition
for randomness. Sometimes it is more reliable than
random depending on the point of the sample.
What one needs for a sample sixe depends on the
variability of the population. (260)
Chapter 9
Often it is useful (in medical trials and the like) to move to
what is called stratified sampling.
A stratified sampling occurs when a sample is selected in
such a way that significant characteristics within the
population are (approximately) proportionately
represented within it.
The Gallup polling group uses stratified sampling to predict
political outcomes with fewer members in the sample
population being polled. When done properly, it can be
quite useful for predicting outcomes. (263)
Chapter 9
Guidelines for Evaluating Inductive Generalizations
1. Try to determine what the sample is and what the population is. If it is not stated what
the population is, make an inference as to what population is intended, relying on the
context for cues.
2. Note the size of the sample. If the sample is lower than 50, then, unless the
population is extremely uniform or itself very small, the argument is weak.
3. Reflect on the variability of the population with regard to the trait or property, x, that
the argument is about. If the population is not known to be reasonably uniform with
regard to x, the sample should be large enough to reflect the variety in the population.
4. Reflect on how the sample has been selected. Is there any likely source of bias in the
selection process? If so, the argument is inductively weak.
5. For most purposes, samples based on volunteers, college students, or persons of a
single gender, race, or social class are not representative.
6. Taking the previous considerations into account, try to evaluate the
representativeness of the sample. If you can give good reasons to believe that it is
representative of the population, the argument is inductively strong. Otherwise, it is
weak.
Chapter 9
Statistical Syllogism (SS)
In SS argument we reason from characteristics that are
generally present (or absent) within a certain reference
lass to a characteristic likely present (or absent) in a
member of the reference class. Typically the premise of
a SS is derived from the conclusion of some IG or other.
1. 95% of Notre Dame students are football fans.
2. Gordon is a Notre Dame student
So, probably,
3. Gordon is a Notre Dame football fan.
SS arguments can work in the other direction with low %s.
Chapter 9
Language Problems in the Context of Induction:
Pseudoprecision: these are claims that appear to be
precise because of the use of numbers, but cannot be
precise because of the impossibility of obtaining
knowledge to the level of exactness described. Typically
there is a problem with an operational definition when
this occurs.
Examples of pseudoprecision are experation dates on food,
calorie content on foods and many studies relating to
increases in usage and the like. (see page 270-2)
Chapter 9
Questionable Operational Definitions
Sometimes an operational definition used in science or the
like is used in a manner that is illicit. So when a term or
phrase that is vague or imprecise is used (like:
unfocused hyperactivity) and a precise measurement is
applied (like 40% reduction), then we have an instance
of a term that has been operationalized.
The claim or number is misleading because there is no
precision, but only pseudoprecision (272).
Chapter 9
Common Errors in Inductive Reasoning
The Biased Sample: this occurs with cases of over- or
under- emphasized characteristics being sampled. Or it
could occur because the sample isn’t random or the
question in a poll is presented in such a way to
guarantee the outcome desired by the poll taker.
A hasty generalization occurs when the sample is
hopelessly inadequate based on the size of the sample.
Chapter 9
Anecdotal arguments describe premises from one
person’s experiences and try to base a conclusion.
Typically the problem with these anacdotal arguments is
that they don’t satisfy the G condition from our ARG
conditions. There is no good grounds to accept a robust
conclusion.
Anecdotal arguments are a form of hasty generalization
and are thus fallacies. See pages 277-8 for a fuller
example of an anecdotal argument.
Chapter 9
The Fallacy of Composition and Division
These two fallacies deal with inferences that occur between
the part and the whole or members of a group and the
group itself.
Fallacy of Composition: a conclusion about a whole or
group is reached based on premises about its parts or
members.
Fallacy of Division: a conclusion about a part or member is
reached based on premises about the whole or group.
Chapter 9
Examples of the fallacies of composition and division.
Composition: Each apartment is small. So the whole
apartment building is small.
We can see that the building could be quite large.
Division: The Florida Marlins baseball team is 16 years
old. So, each Florida Marlins baseball player is 16 years
old.
We know that the professional baseball players are not all
16 years old. These are mistakes in reasoning.
Chapter 9
Terms to review:
Anecdotal argument
Fallacy of composition
Hasty inductive generalization
Inductive generalization
Operationalized
Random sample
Retrodiction
Statistical syllogism
Biased sample
Fallacy of division
Inductive argument
Inductive reasoning
Pseudoprecision
Representativeness
Sample/Stratified sample
Target population