Formal Versus Informal Logic
Deductive Versus Inductive
Forms of Reasoning
Two basic categories
of human reasoning
• Deduction: reasoning from general premises, which are
known or presumed to be known, to more specific, certain
conclusions.
• Induction: reasoning from specific cases to more general,
but uncertain, conclusions.
• Both deductive and inductive arguments occur frequently
and naturally…both forms of reasoning can be equally
compelling and persuasive, and neither form is preferred
over the other (Hollihan & Baske, 1994).
Deduction Vs. Induction
Deduction:
Induction
• commonly associated •
with “formal logic.”
• involves reasoning
from known premises, •
or premises presumed
to be true, to a certain
conclusion.
• the conclusions
•
reached are certain,
inevitable,
inescapable.
commonly known as
“informal logic,” or
“everyday argument”
involves drawing
uncertain inferences,
based on probabalistic
reasoning.
the conclusions
reached are probable,
reasonable, plausible,
believable.
Deductive Versus
Inductive Reasoning
Deduction
• It is the form or structure
of a deductive argument
that determines its validity
• the fundamental property
of a valid, deductive
argument is that if the
premises are true, then
the conclusion necessarily
follows.
• The conclusion is said to
be “entailed” in, or
contained in, the premises.
– example: use of DNA
testing to establish
paternity
Induction
• By contrast, the form or
structure of an inductive
argument has little to do with
its perceived believability or
credibility, apart from making
the argument seem more
clear or more well-organized.
• The receiver (or a 3rd party)
determines the worth of an
inductive argument
Inductive or deductive reasoning?
• A sample of fifty
motorists who were
stopped by the CHP at a
sobriety checkpoint on a
Saturday at midnight
revealed that one in four
drivers were either
uninsured, intoxicated,
or both. Thus, if you get
involved in an accident
on the freeway there is a
25% chance the other
motorist will be drunk or
uninsured.
• The Law of the Sea
treaty states that any
vessel beyond a 12 mile
limit is in international
waters. The treaty also
states that any vessel in
international waters
cannot be legally stopped
or boarded. Therefore,
when the U.S. Coast
Guard intercepts boats
coming from Cuba or
Haiti more than 12 miles
from the U.S. coast, it is
violating the Law of the
Sea.
Sample Deductive and Inductive Arguments
Example of
Deduction
• major premise: All
tortoises are
vegetarians
• minor premise:
Bessie is a tortoise
• conclusion:
Therefore, Bessie
is a vegetarian
Example of
Induction
• Boss to employee:
“Biff has a tattoo of an
anchor on his arm. He
probably served in the
Navy.”
sample “Venn diagram”
of a deductive argument
vegetarian animals
tortoises
Thus, Bessie
must be a
vegetarian
All tortoises
fall in the
circle of
animals that
are
vegetarians
Bessie falls into the circle
of animals that are
tortoises
Bessie
Other types of
deductive arguments
• Suppose every place in
the world that people
live is represented by
the blue space inside
the rectangle. Suppose
the long pink oval
represents all the
wooden houses in the
world. And, suppose
the green circle
represents Canada.
The most logical
conclusion one can
draw from the figure is:
A. all wooden houses
are found in Canada
B. Everyone lives in a
wooden house
C. Some Canadians live
in wooden houses
D. No one lives in
Canada
Other types of
deductive arguments
• Suppose the following
statements are all true:
– Person L is shorter
than person X
– Person Y is shorter
than person L
– Person M is shorter
than person Y
• What additional piece
of information would
be required to
conclude that “Person
Y is shorter than
Person J”?
A.
B.
C.
D.
E.
Person L is taller than J
Person X is taller than
J
Person J is taller than L
Person J is taller than
M
Person M is taller than
Y
Solution: Answer C
M<Y<L<X
So, if J is taller than L,
Y must be shorter than J
Other types of
deductive arguments
A mother wants to order
one large pizza, with
exactly 5 toppings for her
three picky children. She
can choose from 7
toppings; cheese,
mushrooms, olives, ham,
sausage, onions, and
pineapple.
– Fifi says there has to be
pineapple
– Mona says there cannot
be any olives
– Rex says that if there is
going to be sausage,
then there has to be
ham too.
Which combination of
toppings should she
select if she is to satisfy
all three children’s
combined demands?
A.
B.
C.
D.
pineapple, onions,
cheese, mushrooms,
sausage
cheese, sausage, ham,
olives, pineapple
cheese, mushrooms,
ham, onions, pineapple
sausage, mushrooms,
onions, cheese, and
ham.
the five topping solution
chee
se
mushro
om
oliv
e
ham
sausag
e
Fifi
Mona
Rex
onio
n
pineapp
le
Yes
No
then
ham
if
sausa
ge
Note: the statement “if sausage, then ham” doesn’t
imply “If ham then sausage.” The obverse doesn’t
necessarily follow.
Deduction Versus Induction
---continued
• Deductive
reasoning is either
“valid” or “invalid.” A
deductive argument
can’t be “sort of”
valid.
• Inductive reasoning
enjoys a wide range of
probability; it can be
plausible, possible,
reasonable, credible,
etc.
• the inferences drawn
may be placed on a
continuum ranging from
cogent at one end to
fallacious at the other.
• If the reasoning
employed in an
argument is valid
and the argument’s
premises are true,
then the argument is
said to be sound.
valid reasoning fallacious
+ true premises
= sound
argument
cogent
Deduction Versus Induction
--still more
• Deductive reasoning is
commonly found in the
natural sciences or
“hard” sciences, less so
in everyday arguments
• Occasionally, everyday
arguments do involve
deductive reasoning:
Example: “Two or more
persons are required to
drive in the diamond
lane. You don’t have
two or more persons.
Therefore you may not
drive in the diamond
lane”
• Inductive reasoning is
found in the courtroom,
the boardroom, the
classroom, and
throughout the media
• Most, but not all everyday
arguments are based on
induction
– Examples: The
“reasonable person”
standard in civil law, and
the “beyond a
reasonable doubt”
standard in criminal law