Chapter 4
Reasoning: Drawing Deductively Valid Conclusions
Review of Deductive Reasoning Skills
Category description: The skills presented in this chapter are used to determine if a conclusion is
valid--that it, it must be true if the premises are true. These skills are used in many contexts
including law, medicine, financial projections, and the science.
Skill
a. discriminating
between deductive and
inductive reasoning
b. identifying premises
and conclusions
c. using quantifiers in
reasoning
d. using circle diagrams
to check category
membership
e. solving categorical
syllogisms with verbal
rules
Description
Recognizing the
differences between
reasoning from a rule
to an individual
(deductive) and from
individual
observations to
formulate rules
(inductive)
Being able to
recognize what is
being advocated and
the reasons for it
Understanding the
use of terms like
"every," "some," and
"not"
Combining class
membership
categories to
determine what can
be concluded with
circles that represent
category relationships
There are 7 rules that
can used to determine
if the conclusion
from a categorical
syllogism is valid.
Examples of Use
Inferring attitudes from behaviors (inductive)
and predicting behavior from someone’s
stated attitudes (deductive).
Reading a ballot issue and knowing the
positions that are supported and why they are
being supported
Knowing that "doctors recommend" means
"some doctors recommend."
Some high school students studied Latin. All
students who studied Latin went to college.
Can we conclude that some high school
students went to college? Solve this with
circle diagrams by combining all
combinations of representations of the
premises.
All students need math. Harry is not a
student. Is it valid that Harry does not need
math? Check for middle term (one not in
conclusion) and whether it is distributed in a
premise. Check for negation in the
conclusion and premises and whether the
conclusion is particular. By going though
each rule, you can determine if a conclusion
is valid.
f. understanding the
difference between truth
and validity
Knowing that a
conclusion can be
valid, but false
g. recognizing when
syllogisms are being
used to change attitudes
A particular attitude
is being advocated
when premises are
followed with
evaluative statements
that support a belief
Being able to arrange
objects along a
dimension
Mark adjectives bias
evaluations
h. using linear diagrams
to solve linear
syllogisms
i. watching for marked
adjectives
j. using the principles of
linear orderings as an aid
to clear communication
k. reasoning with "if,
then" statements
l. avoiding the fallacies
of confirming the
consequent and
denying the antecedent
m. examining reasoning
in everyday contexts
for missing quantifiers
It may be valid to believe that welfare
spending should be increased given a set of
premises, but the premises and the
conclusion may be wrong.
For example, "Juveniles commit many
crimes. They need alternatives to crime. So,
fund activities for juveniles.
Kalin arrived before Joe or Roberto, but after
Alex. Who arrived first?
"How dumb is he?" is not a neutral question.
It is easier to
understand linear
oderings when the
first term in the
second premise is the
second term in the
first premise and
when all statements
are positive.
“If, then” statements
express contingency
relationships.
Running burns more calories than walking,
and walking burns more calories than sitting
.
Denying the
antecedent is saying
that the “if” part did
not occur; affirming
the consequent is
saying that the
consequent occurred.
Often statements will
not include terms like
“all,” “some” or
“no,”
Look at example above. Saying that Heather
does not want to graduate does NOT mean
that she will not study. Saying that she will
study does not mean that she wants to
graduate.
If Heather wants to graduate, she will study.
The “if” part is the antecedent, the “then”
part is the consequence.
Saying that children who are abused will
have difficulty in personal relationships does
not mean “all” children who are abused
although that may be want people hear.