Philosophy
6: Logic in Practice
Los Angeles Pierce College
Department of History, Philosophy, & Sociology
Lecture Notes
Lecture
Notes for "Chapter 10: Deriving Generalizations / Forming Hypotheses"
Generalizing & Describing
Generalizations can be
used to justify a conclusion when those justifications are well founded.
"knowledge would
hardly be possible unless we made connections, saw similarities between things,
and reached broad conclusions about them."
Abstraction as a Mode of Generalization
Individuals may have
unique characteristics, but we can find common characteristics amongst them.
And "sees
similarities in the differences that allow a generalization to be
made."
Stereotyping
Stereotyping happens when
"each member of the group is treated as typical and assumed to possess all
the group's features."
Avoiding Stereotyping
We are engaged in
inductive generalizations, so remember, we are in the land of probabilities
only
"Each person should
be treated as an individual even though he or she will probably exhibit some
characteristics of the group."
Fair Generalizations
To have a fair
generalization is to have one that attains an appropriate level of probability
A fair generalization
attains an appropriate level of probability when it is well founded
Good Generalizations
"The main problem in
generalizing, therefore, is figuring out how to achieve reliability."
"in building a
generalization into our argument we must be sure it is based on a fair
sample."
"This means one of
sufficient size and randomness to make the generalization" reasonable or
well-founded.
"It must also be
properly stratified."
Size
"the number of cases
we examine should be large enough to represent the whole."
Judgment here is needed as
the subject matter will determine the acceptable size of the sample
A "way to determine
whether the sample is sufficiently large is to see what the generalization is
about."
Singular E.G.
In some cases, we need a
singular sample
"From the fact that
we burn our hand in fire, we can conclude that fire burns."
Small E.G. Hardness of diamonds
Large E.G. Hardness of wood
Sufficient Size
"The moral of the
story is that if we want to generalize in our argument we need a large enough
sample on which to base it"
Problems
"we may not always
know the subject well enough to determine in advance whether a large or small
sample is needed."
Hands-On Method
"In this method we
increase the sample size until the results begin to repeat
themselves."
"Then we can stop,
knowing we have examined enough cases."
"A hands-on
experiment ... is the most reliable method of determining whether our
generalization is based on an adequate sample size."
Randomness
Here we can thwart biased
generalizations
"we must make sure
that the sample studied represents the whole and does not bias our
conclusion."
"Unless our sample is
random, our generalization will be distorted rather than fair."
The Bias Danger
"we tend to perceive
and remember what we are seeking, and to ignore counter instances."
Stratification
"Here we want to
include all strata or classes that could have an important effect on our
generalization."
"Every relevant group
must be taken into account."
Reliability
With those three steps
completed, our generalization becomes more reliable
Steps to Fair Generalization
Size
Randomness
Stratification
Steps to Fair Generalization / Step One / Size
1) "Check for
adequate size in terms of the nature of the subject matter."
"In an experimental
situation, take repeated samples until the results begin to repeat themselves."
Steps to Fair Generalization / Step Two / Randomness
2) "Be sure the
generalization is random and free from bias in the sampling, so that each of
the relevant elements has an equal chance of being chosen."
Steps to Fair Generalization / Step Three / Stratification
3) "Make certain the
sample is stratified, which means that all relevant categories are included and
none is excluded that would significantly affect the generalization."
Hypotheses in Arguments
"A hypothesis can be
defined as an explanatory principle accounting for known facts."
"In hypothetical
thinking we want to know why something is true, and we reason backward to find
some explanation for the facts, one that makes sense of them."
"We use our
imagination to find some reason why things are the way they are."
Resonance w/ Analogical Arguments
Just as we go from the
known to the unknown in analogical arguments, by employing an
hypothesis, we go from known facts to an unknown explanation.
"the facts are known
but the explanation for the facts is missing."
(See what I did there?)
Evaluating Hypotheses
"How ... do we
separate the genuine hypothesis from the fictional one?"
"What separates a
reliable hypothesis from an unreliable one or, more precisely, what features
must a sound hypothesis possess?"
Developing an Adequate Hypothesis
"We must pay
attention to these five rules in order to develop sound hypotheses."
1) Consistency
2) Plausibility
3) Comprehensiveness
4) Simplicity
5) Predictability
Measuring the Adequacy of Hypotheses / Consistency
"Consistency with
other hypotheses we accept."
"A new hypothesis
should be congruent with the bulk of hypotheses that we believe to be
true."
"It should fit in
with the body of explanations that from our outlook on life."
Consistency and Our Expectations
"We should therefore
demand consistency in any hypothesis we read about, and we should not except
anyone to accept our novel hypothesis if it means that person must radically
revise his or her beliefs."
Really?
Measuring the Adequacy of Hypotheses / Plausibility
"any new hypothesis
must be plausible according to common sense and traditional ideas."
"Every event can be
explained in any number of ways, so to determine which hypothesis should be
accepted we must screen out the very unlikely ones."
"we want to begin our
inquiry with the most credible explanation and end up endorsing the hypothesis
that is the most plausible."
Measuring the Adequacy of Hypotheses / Comprehensiveness
"Any hypothesis that
we present should be the most complete explanation we can find."
"Many hypotheses will
provide a partial answer to the question we are investigating, but we want the
most encompassing one that will not leave important parts
unexplained."
Measuring the Adequacy of Hypotheses / Simplicity
Ockham's Razor / Principle of Parsimony
"It states that
'entities should not be multiplied beyond what is required,' that is, as simple
explanation is preferable to a complicated one."
Measuring the Adequacy of Hypotheses / Predictability
"given the conditions
described in our hypothesis, we can expect certain results to
follow."
"if nothing can be
predicted on the basis of our hypothesis, this counts against its soundness,
and we should hesitate to use it in our argument."