Logical Reasoning
An Introduction to Logic
And Fallacious Reasoning
Definitions Related to Logic
• Logic - means correct reasoning. A logical text supports
statements with reasons and evidence. A text is illogical
when it does not provide reasons backed by evidence
(facts and examples).
• Coherence - means “to stick together”. Reasoning is
coherent (or has coherence) when ideas stick together
because they are arranged in an order that makes sense
to the reader. The reasons or evidence must have a
connection; they can’t just jump around.
Types of Reasoning
• Deductive Reasoning – A process of reasoning from known
facts to conclusions. Sometimes it can be thought of as
starting from a general statement that is accepted as true to a
specific statement that is “therefore” true.
• Inductive Reasoning – A process of reasoning that moves
from making observations to forming conclusions. It can also
be thought of as starting from specific examples and moving
toward a general statement. This is also called inference.
• Fallacious Reasoning - false thinking or mistakes in logic.
Fallacious reasoning leads to incorrect conclusions.
Deductive Reasoning
• Deductive Reasoning – A process of reasoning from known facts
to conclusions, or from a general statement that is accepted as
true to a specific statement that is “therefore” true.
• Deductive arguments often start with a categorical claim, which is
simply a statement that states a relationship between two
categories or events. Examples of categorical claims:
–
–
–
–
All cats are mammals.
No cats are reptiles
Some cats are long-haired mammals
Some cats are not long-haired mammals
• You may see other words like never, sometimes, always, etc.
Categorical claims are important to be analyzed to determine if
they are true, and to see if they support a conclusion.
• Deductive Reasoning often uses a 3-step argument
called syllogism, introduced by the Greek philosopher
Aristotle.
• This 3-step process was the beginning of modern
formal logic, or logical thinking.
Theory of Syllogism
Argument (Syllogism) –
Example 1
All “x” has the
characteristic of “y”.
A standard baseball game has
9 innings.
This thing is an “x”.
We watched a standard
baseball game.
Therefore, this “x” has the
characteristic of a “y”.
Therefore, that game had 9
innings.
Examples of Deductive Reasoning
• More examples of deductive reasoning
using syllogism:
• How would you change Example 2 to have a more
standard categorical claim?
Argument (Syllogism) –
Example 2
Argument (Syllogism) – Example 3
The last day to register for the
Disney trip is June 15.
All people are mortal.
Joe missed the registration date. Jim Carey is a person.
Therefore, Joe will not be able to Therefore, Jim Carey is mortal.
register for the trip.
Inductive Reasoning
• A process of reasoning that moves from making
observations to conclusions. This is also called
inference.
• Inductive reasoning can also be thought of as theory
building.
• Successful inductive reasoning depends on the quality of
your observations, or evidence.
• If the quality of the observations are not good enough, or
if not enough observations have been made, inductive
reasoning may not be as dependable as deductive
reasoning.
Examples of Inductive Reasoning
• While Example 2 below is not “cohesive”, inductive
reasoning is not useless. It is the basis of scientific
discovery and investigation, when used correctly.
Inductive Reasoning –
Example 1
Inductive Reasoning –
Example 2
Tonya is seen walking from her Every swan that my family and
car to her home with a set of
I have ever seen is white.
golf clubs.
Tonya’s husband Jeff loves
golf and tomorrow is his
birthday.
This swan is also white.
(Inference)Tonya has bought
Jeff a set of golf clubs.
(Inference)All swans are white.
(are they?)
We Need Both Inductive and
Deductive Reasoning
• In scientific discovery and in life, we use both types of
reasoning.
• For example, we can use inductive reasoning to attempt
to make enough observations to come up with a theory
or conclusion.
• Next, we can switch back to deductive reasoning using
our conclusion or theory (which is general).
• Note that sometimes it is not possible to prove
something is always true, so the best we
can have is a theory.
Example of Using Both
Types of Reasoning
Example Using Both Types of Reasoning
A crime scene investigator gathers evidence, including
fingerprints or DNA. (Inductive)
It is known that fingerprints or DNA uniquely identify a
person. (Deductive)
Therefore, we know that the particular person was at
the crime scene. (Conclusion, based on both inductive
and deductive reasoning)
Fallacious Reasoning
• Fallacious Reasoning means false thinking or
mistakes in logic.
• May be based on: mistakes in logic or
incomplete information.
• Fallacious reasoning leads to false conclusions.
• Inductive reasoning is where we sometimes see
examples of fallacious reasoning (black swan).
Examples of Fallacious
Reasoning
Type and Definition
Examples
Hasty Generalization –
Conclusions made from weak or
insufficient evidence
“Your friend said the concert you’re
Stereotyping –
Believing that all members of a
group share a certain
characteristic
“All concerts are unsafe.”
attending would have extra security.
Obviously, this will be the safest
concert your city has ever had.”
More Examples of
Fallacious Reasoning
Type and Definition
Examples
Personal Attack (Name Calling, or
Ad Hominem) – Attacking the
person making the argument,
rather than the argument itself.
“Your parents don’t want you to
False Dilemma (Either/Or) –
The assumption that a problem or
situation has only one possible
cause or resolution when there
may be several.
“If your parents don’t let you go to
the concert, then they don’t trust
you.”
go to the concert. They obviously
don’t know anything about
anything.“
Yet More Examples of
Fallacious Reasoning
Type and Definition
Examples
False Analogy –
Relying only on comparisons
to prove a point rather than
arguing deductively and
inductively
“Education is like cake; a small amount
Appeal to Fear –
Using a claim that is intended
to produce fear instead of
being actual evidence to
support the claim.
“You know, Professor Smith, I really
tastes sweet, but eat too much and your
teeth will rot out. Likewise, more than
two years of education is bad for a
student.”
need to get an A in this class. I'd like to
stop by later to discuss my grade. I'll be
in your building anyways, visiting my
father. He's your dean, by the way."
Logical Arguments
• A logical argument is a group of statements, called
premises, that are claimed to provide support for, or are
reasons to believe, a conclusion.
• Note that these statements or premises can be either
true or false.
• To reach a logical conclusion, all premises or statements
leading up to the conclusion must support it.
• Some premises may be categorical claims, such as
those presented earlier.
Examples of Arguments
• Argument 1:
(Premise) Isaac can fix anything electric.
(Premise) The electric switch in my lamp is
broken.
(Conclusion)Isaac can fix my lamp.
• What type of reasoning is this?
Logic Problems
Argument 2:
• Lars needs a notebook for some of his
classes.
Lars has three notebooks.
Conclusion: Lars is in three classes.
• What type of reasoning is this?
Logic Problems
Argument 3:
• (Premise) I have 5 dogs for pets.
(Premise) Three of them learned to lie down and
roll over.
(Premise)Three of my dogs were Scotties and
two were Collies.
Conclusion: My collies never learned to lie down
and roll over.
• What type of reasoning is this?
Logic Problems – Cont’d
Argument 4:
• (Premise)None of Barry’s sisters can do a
back dive. (This is a categorical claim)
• (Premise) Lisa can do a back dive
Conclusion: Lisa is not Barry’s sister.
• What type of reasoning is this?
Logic Problems, Cont’d
Argument 5:
• Sometimes Joanna rides her bike when
she goes to the store. (Categorical claim)
I saw Joanne riding her bike.
Conclusion: Joanne was going to the store.
• What type of reasoning is this?