Argument, Logic,
& Logical
Fallacies
• Based on 2 statements with a 3rd that follows the first
two.
• One major premise
• One minor premise
• Conclusion
• Premise: statement used as evidence for a conclusion
• Conclusion: statement that is supported by at least one
premise
• Arguments can be good or bad.
What is an Argument?
1) Fido is my dog. major premise
2) Fido is a mother. minor premise
3) Therefore, Fido is my mother. conclusion
HUH??????
Both premise 1 & 2 are true, so why is the conclusion
ridiculous?
Bad Argument
1) If Gandhi was a sadist, then he would have hurt people.
2) It is not the case that Gandhi hurt people.
3) Therefore, it is not the case that Gandhi was a sadist.
THAT’S BETTER!
Premises 1 & 2 are true, so the conclusion is true. Why
does this one work?
Good Argument
• The difference between the two earlier arguments is that
one includes an informal fallacy.
• Aristotle cataloged many illogical patterns of reasoning,
informal fallacies, in his book Fallacies of the Sophists.
• These help us detect bad argumentation.
• Sometimes there are exceptions, so these are only rough
guidelines rather than absolute rules.
Informal Fallacies
(Logical Fallacies)
• An attack on a person’s character instead of the content of
the person’s argument.
• “Heidegger was a poor philosopher since he was a member
of the Nazi party.”
• “Bob is an alcoholic, so don’t take his advice too seriously.
• “Jones would argue for gun control; he’s a democrat!”
Argument against the
Person (ad hominem)
• This is concluding that something is true just because you
can’t prove it is false.
• “God must exist, since no one can show that he does not.”
• “How do you know you’re not a witch if you do not know
what a witch is?”
• McCarthy: “I do not have much information on this except
the general statement of the agency that there is nothing in
the files to disprove his Communist connection.”
Argument from Ignorance
• This is appealing to a person’s unfortunate circumstances
in order to get someone to accept a conclusion.
• “You need to give me an ‘A’ in this course, or I will lose my
scholarship if you don’t.”
• “I beg you to find Mrs. Bobbit not guilty of mutilating her
husband because her home life was so traumatic!”
• “Yes, I murdered my parents, but take pity on me because
now I’m an orphan.”
Appeal to Pity
• This means going along with the crowd in support of a
conclusion.
• “All the other guys carry guns to school.”
• “Aw mom, everybody else’s mom is letting them go.”
Appeal to the Masses
(bandwagon effect)
• This is when a person appeals to a popular figure who is
not an authority in that area.
• “Einstein believed in God, so God must exist.”
• “Bill Gates dropped out of college and became a billionaire,
so I can too.”
• “Bart Simpson likes Butterfingers, so they must be good.”
Appeal to Authority
• This is when a person draws a conclusion that does not
follow from the evidence.
• “My business failed last year, so Obama is bad president.”
• “My shoe string broke; I guess that means I have to buy a
new car.”
Irrelevant Conclusion
(non sequitur)
• A slippery slope argument is not always a fallacy.
• This is an argument that says adopting one policy or
taking one action will lead to a series of other policies or
actions also being taken without showing a causal
connection.
• This is a form of non sequitur.
• “If we legalize marijuana, the next thing you know we'll
legalize heroin, LSD, and crack cocaine.”
Slippery Slope
• This is when a person infers a casual connection based on
mere correlation. Or more simply, the argument assumes
one event caused another just because one happened
before the other.
• “The number of stroke victims in hospitals is directly
proportional to the number of tar bubbles on the road; thus,
tar bubbles cause strokes.”
• “Successful people wear expensive clothing; therefore, the
best way to become a success is to have expensive clothes.”
False Cause
• This is implicitly using your conclusion as a premise.
• “God must exist since the Bible says that God exists, and
the Bible is true because God wrote it.”
• “It is impossible to talk without using words, since words
are necessary for talking.”
Circular Reasoning
(begging the question)
• This is an argument based on two definitions of one
word.
• “Good steaks are rare these days, so you shouldn’t order
yours well done.”
• Jones is a poor man, and he loses whenever he plays poker;
therefore, Jones is a poor loser.”
• “You don’t find cars like yours in these parts, so don’t let
your car out of your sight.”
Equivocation
• This is when a person assumes that the whole must have
the properties of its parts.
• “Each part of this machine is light; therefore, the whole
machine is light.”
• “A bus uses more gas than a car; therefore, all busses
combined use more gas than all cars combined.”
Composition
• This is the opposite of Composition—assuming that the
parts of a whole must have the properties of the whole.
• “This corporation is important, hence each worker in this
corporation is important.”
• “Students study Math & English; therefore, each student
studies Math & English.”
Division
• This argument introduces an irrelevant or secondary
subject, thereby diverting attention from the main subject.
Basically, its something that takes attention away from
the real issue or point.
• “Side impact airbags in cars do not really increase safety,
and, besides, most cars with side impact airbags are
Japanese imports.”
• “The curfew law is the city council’s attempt to usurp
parental authority.”
Red Herring
• This is an argument that distorts an opposing view so that it is
easy to refute.
• Imagine a fight in which one of the combatants sets up a man
of straw, attacks it, then proclaims victory. All the while, the
real opponent stands by untouched.
• “Vote against gun control, since gun control advocates believe that
no one should own any type of fire arm.”
• “If we liberalize the laws on beer, then any society with
unrestricted access to intoxicants loses its work ethic and goes
only for immediate gratification.”
• “Our society should be taxed less because it’s unjust for a society
to neglect the poor.”
Straw Man
• This is the fallacy of making a sweeping statement and
expecting it to be true of every specific case.
• "Women are on average not as strong as men and less able
to carry a gun. Therefore women can't pull their weight in a
military unit."
Sweeping Generalization
(stereotyping)
PROPOSITIONAL LOGIC
Sentential Logic
• Assists in constructing arguments which fit valid
argument forms.
1) If Gandhi was a sadist, then he would have hurt people.
2) It is not the case that Gandhi hurt people.
3) Therefore, it is not the case that Gandhi was a sadist.
• The logical structure of this argument is this:
1) if P then Q
2) not Q
3) therefore, not P
• Logic is founded on the concept of a proposition.
• You must distinguish between three related concepts:
• Utterance: The most general form of verbal expression.
Utterances include nonsense expressions, such as “ob la di ob la
da,” as well as statements.
• Statement: an utterance which conveys meaning. Statements
include questions, commands, expressions of feelings, and
propositions.
• Proposition: An either true or false statement about the world.
• Every statement in an argument must be a proposition.
Propositions
Simple propositions are only one type of proposition used
in logic.
Complex propositions are a combination of two or more
simple ones.
In constructing complex propositions, logicians use:
 Four basic logical connectives:
 P and Q------------conjunction
 P or Q--------------disjunction
 not P----------------negation
 if P then Q---------conditional
Complex Propositions
FOUR LOGICAL CONNECTIVES
Conjunction, Disjunction, Negation, Conditional
“P and Q”
“Bob is rich and Sam is poor.”
 Simple proposition: P—Bob is rich
 Simple proposition: Q—Sam is poor
Conjunction constructs can be disguised
 P, but Q
 P, although Q
 P; Q
 P, besides Q
 P, however Q
 P, whereas Q
“Sherman and Xavier are computer software pirates”
 Translates to:
 “Sherman is a computer software pirate, and Xavier is a computer
software pirate.”
Conjunction
• “P or Q”
• “Mom pawned her wedding ring or Mom sold her blood.”
• Simple proposition: P—Mom pawned her wedding ring.
• Simple proposition: Q—Mom sold her blood.
• The “P” and “Q” elements are referred to as disjuncts.
• Disjuncts can be switched around like conjunctions.
• Or can be used two ways:
• Inclusively: Mom could have pawned her ring, or she could have
sold her blood, or both.
• Exclusively: “Mary is dead, or Mary is alive.” Mary can’t be both
dead and alive at the same time.
• In logic, “or” is used only inclusively.
Disjunction
• “Not P”
• “It is not the case that Fido just left his territorial mark.”
• Simple proposition: P—Fido just left his territorial mark.
• A sentence with a negative word in it, not, never, or none,
may often (not always) be translated into a negative
proposition.
• Consider—“I knew that Jurgan was not really a Nazi.”
• This is an assertion about my knowledge; it does not translate
into a negation.
Negation
• “If P then Q”
• “If you eat of the forbidden fruit, then you will surely die.”
• Simple proposition: P—you eat of the forbidden fruit.
• antecedent
• Simple proposition: Q—you will surely die.
• consequent
• In conditionals, if the P’s and Q’s are switched around, it
changes the meaning of the sentence.
• Consider—“If you die, then you will have eaten of the forbidden
fruit.”
• These sentences clearly do not mean the same thing.
• Assume that everyone who eats the forbidden fruit subsequently
dies; but not all who die will have eaten of the forbidden fruit.
Conditional
•
•
•
•
•
•
•
•
•
•
If P, it follows that Q
P implies Q
P entails Q
P only if Q
Whenever P, Q
P, therefore Q
P is a sufficient condition for Q
Q follows from P
Q is a necessary condition for P
Q, since P
Disguised Conditionals
• Complex propositions often contain several logical connectives
“nested” within each other.
• “I will not hurt you and your old lady if you simply hand over your
wallet.”
• Negation
• Conjunction
• Conditional
• If P then not (Q and R)
• P = you will simply hand over your wallet
• Q = I will hurt you
• R = I will hurt your old lady
• The benefit is that it is possible to put even very complicated
propositions into standard form.
Nested Logical
Connectives
• Modus Ponens
• premise 1: if P then Q
• premise 2: P
• concl. 3: therefore, Q
1. If the president pushes the button, then a nuclear bomb will go off.
2. He pushed the button.
3. Therefore, a nuclear bomb will go off.
• Fallacious Modus Ponens: fallacy of affirming the consequent
•
•
•
premise 1: if P then Q
premise 2: Q
concl. 3: therefore, P
1. If the president pushes the button, then a nuclear bomb will go off.
2. A nuclear bomb went off.
3. Therefore, the president pushed the button.
Valid Argument Forms
• Modus Tollens
• premise 1: if P then Q
• premise 2: not Q
• concl. 3: therefore, not P
1. If Bob desecrated the Bible, then he would have been struck by
lightening.
2. It is not the case that he was struck by lightning.
3. Therefore, it is not the case that Bob desecrated the Bible.
• Fallacious Modus Tollens: fallacy of denying the antecedent
•
•
•
premise 1: if P then Q
premise 2: not P
concl. 3: therefore, not Q
1. If Bob desecrated the Bible, then he would have been struck by
lightening.
2. It is not the case that Bob desecrated the Bible.
3. Therefore, it is not the case that he was struck by lightning.
Valid Argument Forms
• Disjunctive Syllogism: (two versions)
• premise 1: P or Q
• premise 2: not P
• concl. 3: therefore, Q
premise 1: P or Q
premise 2: not Q
concl. 3: therefore, P
1. Either Smith bites the dust, or Smith bites Jones.
2. It is not the case that Smith bites the dust.
3. Therefore, Smith bites Jones.
• Fallacious Disjunctive Syllogism: fallacy of asserting an alternative
•
•
•
premise 1: P or Q
premise 2: P
concl. 3: therefore, not Q
premise 1: P or Q
premise 2: Q
concl. 3. therefore, not P
1. Either Smith bites the dust, or Smith bites Jones.
2. Smith bites the dust.
3. Therefore, it is not the case that Smith bites Jones.
Valid Argument Forms
• Hypothetical Syllogism
• premise 1: if P then Q
• premise 2: if Q then R
• concl. 3: therefore, if P then R
1. If you bribe the officer, then he will tear up the ticket.
2. If he tears up the ticket, then you won’t pay a fine.
3. Therefore, if you bribe the officer, then you won’t pay a fine.
Valid Argument Forms
• The first step in forming a good argument is that it must be valid.
• However, a good argument must be valid and have all true premises.
• This is called soundness.
• Valid form but not true premises—
1.
2.
3.
•
Either Uncle Bob is a tennis shoe, or Uncle Bob is a golfing shoe.
It is not the case that Uncle Bob is a golfing shoe.
Therefore, Uncle Bob is a tennis shoe.
True premises but no valid form—
1.
2.
3.
If the President was the pilot of Air Force One, then he could fly in the
presidential plane.
The President can fly in the presidential plane.
Therefore, the President is the pilot of Air Force One.
• Two ways that an argument can be unsound:
•
•
It will be invalid
It will have at least one false premise.
Sound & Unsound
Argument
Works Cited & Consulted
Fieser, James. "ELEMENTARY LOGIC." The University of Tennessee at
Martin - Http://www.utm.edu. 9 Sept. 2008. Web. 17 Oct. 2011.
<http://www.utm.edu/staff/jfieser/class/120/logic-chapter.htm>.
"Logical Fallacies and the Art of Debate." California State University,
Northridge. 29 Jan. 2001. Web. 17 Oct. 2011.
<http://www.csun.edu/~dgw61315/fallacies.html>.