3. Inductive Reasoning
Induction reasons from evidence about
some members of a class in order to form a
conclusion about all members of a class.
A conclusion derived through inductive
reasoning is called a hypothesis and is
always less certain than the evidence itself.
In other words, the conclusion is probable.
4. Inductive Reasoning
Induction can be done through the
following:
Sensory Observation
Enumeration
Analogical Reasoning
Pattern Recognition
Causal Reasoning
Statistical Reasoning
5. Sensory Observation
In 1903, French Chemist, Francois
Benedictus accidently dropped a flask.
When it did not shatter, he observed the
chemical that coated the inside of the flask.
From this observation, Benedictus
developed a fabricated glass plastic to
reduce injuries in car accidents.
6. Enumeration
If I want to know how many cashews are in
a can of Planter’s cashews, I could buy 3
cans and count them. Then I would
generalize that all Planter’s cashews cans
contained XX amount of cashews.
7. Analogical Reasoning
This is where a comparison is made that
while some components are similar it
should be concluded that the two parts are
the same.
Lawyers use analogical reasoning when
citing case law. Case law establishes a
precedent. The lawyer draws a parallel
between one small aspect of a prior case
and its settlement with the case at hand.
8. Pattern Recognition
Doctors, psychologists, chemists, biologists
and sociologists, to name a few, rely on
pattern recognition for their discipline.
When you go to a doctor, the doctor looks
for a pattern of symptoms to make a
diagnosis.
9. Causal and Statistical Reasoning
Causation argues that the causes of one
event generalize or apply to the causes of
another event
Our world often depends on numerical
measurements to make decisions in the
face of uncertainty. Statisticians use
quantitative abilities, statistical knowledge,
and communication skills to work on many
challenging problems.
10. Inductive Reasoning
Inductive reasoning is used when
examining all data would be an impossible
task. In this case, induction uses statistical
samplings (a form of enumeration) and
extrapolations.
11. Five Basic Rules for Evaluating
Inductive Arguments.
1. Greater sample size yields greater probability.
2. A sampling must be representative in order to
lead to reliable results.
3. One counter example can refute an inductive
arguments.
4. Sufficient statistical evidence is necessary to
verify an inductive argument.
5. Examine the results of polls, the polling agency,
and the polling questions for bias.
12. Inductive Example
Evidence: The Krispy Kreme doughnut store in
Torrance has been a phenomenal success.
Evidence: The Krispy Kreme doughnut shop in Van
Nuys is doing a booming business.
Evidence: The Krispy Kreme shop that recently
opened in Fremont has been a big hit.
Conclusion: If my family opens a Krispy Kreme
shop in Daly City, it is sure to be a success.
13. You Try…
“Now let’s see—one
sashweight, one butcher’s
cleaver, on galvanized-iron
tub, fifty feet of half-inch
rope, one gunny sack, one
electric torch, one pickaxe,
one shovel, twenty pounds
of quicklime, a box of
cigars, and a beach chair.”
Drawing by Chas. Addams
The New Yorker Magazine
From the Critical Eye by
Sally Taylor, 1990
15. Deductive Syllogism
Syllogism: An argument arranged in three
parts
1. Major Premise: General Principle
2. Minor Premise: Specific Instance
3. Conclusion: Follows Logically
Standard, everyday language is arranged into
verbal equations
16. Syllogisms
Major Premise: All men are mortal (general
principle)
Minor Premise: Socrates is man (specific
instance)
Conclusion: Socrates is mortal (follows
logically from the major)
Valid Argument: The conclusion follows logically
from the major and minor premise.
17. Practice with Syllogisms
Major Premise: Stealing is a criminal act.
Minor Premise: Shoplifting is stealing.
Conclusion: Therefore?
Shoplifting is a criminal act.
Notice: A claim of definition
is a form of syllogism.
18. Valid and Invalid Syllogisms
Major Premise: When Gabriele drinks
coffee she always gets a headache.
Minor Premise: Gabriele has a headache.
(Fact?)
Conclusion: Therefore?
Gabriele drank coffee.
Valid or Invalid?
True?
19. Valid versus True
Valid: the conclusion follows logically from the
major and minor premise.
Keep in mind—While we use the term “valid” in
everyday speech, it has a very specific meaning in
logic.
True: Corresponds to reality, believable, provable.
Sound: both valid and true.
20. What Do You Think?
Major Premise: Drug dealers wear
electronic pagers.
Minor Premise: Doctors wear electronic
pagers.
Conclusion: Therefore?
Therefore Doctors are drug dealers.
Valid or Invalid? True? Sound?
Logical Fallacy: Guilt by association.
21. Complete the Syllogism
All Italians are volatile.
Jesse is Italian.
Therefore:
Jesse is volatile
Valid?
True?
Sound?
This syllogism is based on a hasty generalization.
Therefore, it is not sound.
22. Complete the Syllogism
All kids who wear Abercrombie and Fitch to
school will be accepted by the popular group.
Adrienne wears Abercrombie and Fitch to school.
Therefore?
She will be accepted by the school’s popular group.
Valid?
True?
Sound?
23. Enthymeme
An argument in which the major premise is left unstated
(often a conclusion supported by a single premise).
She must be a good student since she is on the Dean’s List.
Conclusion Minor Premise
She must be a good student since she is on the Dean’s List.
Major Premise?
All good students are on the Dean’s List.
24. Examples of Enthymemes
I take my VW Jetta to
Heinrich for repairs.
He’s German.
It’s no wonder Linda
Ng scored so high on
the math section of the
SAT. She’s Asian.
If you don’t vote, then
you can hardly criticize
the government.
You are all good
students because you
have your homework
done on time.
Recreate the Syllogism
25. Answers to Enthymemes
(Missing major premises)
All Germans are good car mechanics
All Asians are good at math.
Only voters can criticize the government.
All good students finish their homework on
time.
26. Final Thing to Note
The conclusion of an inductive argument
can become the major premise of a
deductive syllogism.
