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Logic Primer

Definitions and Examples of Logical Fallacies
by

Georganna Ulary

on 4 September 2013

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Transcript of Logic Primer

Logical Fallacies
Begging the Question or
"Circular Reasoning"
You assume the conclusion you are trying to prove; circular reasoning
"We know God exists because we can see the perfect order of His Creation, an order which demonstrates supernatural intelligence in its design."

"The Bible states that God exists and the Bible is the Word of God. Therefore, God exists."

“I have a right to say what I want, therefore you shouldn’t try to silence me.”

"Women have a right to choose whether to have an abortion or not, therefore abortion should be allowed.”

“The unborn has a right to life, therefore abortion is immoral”.
False Dilemma: Either/Or
You create a false dichotomy, limiting a complex issue to only two options
Sometimes there really are only two options, but in arguable issues, it is not often the case.
"Either we rebuild the World Trade Center or the terrorists win."

"We must raise taxes, or the country will go bankrupt."
False Analogies
Comparing two things or issues that do not share much in common at all.
"People are like dogs. They respond best to clear discipline."

"A school is not so different from a business. It needs a clear competitive strategy that will lead to profitable growth."

"Education is like cake; a small amount tastes sweet, but eat too much & your teeth will rot out. Likewise, more than two years of education is bad for a student."
Hasty Generalization
Example of faulty induction, when you assume something is the case based on superficial evidence.
"Some Muslims are terrorists; therefore, Islam is a dangerous religion."
Non Sequitur: all formal fallacies are special cases of non sequitur
"It does not follow." Trying to tie together two unrelated ideas.
Very common in advertisement (especially sex-appeal ads).
"If you buy this car, your family will be safer."

"The government spent $1 million studying North American forests. The government is obviously wasteful with our tax dollars."
False Cause
Assuming a causal relationship that is not warranted.
"Since Lebron James moved to Miami, my car won't start. It's all his fault!"
"There wasn't all this unemployment when Pres. Obama was elected. Everyone must have lost their job because he came into office."
Slippery Slope
Assuming that moving in one direction will necessarily lead to an extreme on that side.
"If we have universal health care, this country will soon become just like Stalinist Russia."
"If Arizona keeps their new immigration law, the whole country will become just like Nazi Germany."
Red Herring
Strawman Fallacy
Ad hominem
A misleading piece of evidence that doesn't relate to the argument at hand. The piece of evidence might be valid, but it doesn't relate in the current context.
"The level of mercury in seafood may be unsafe, but what will fishers do to support their families?"
This is when you create a misleading depiction of the other side's argument in order to knock it down.
"People who don't support the proposed state minimum wage increase hate the poor."
"Environmentalists think that human beings are a plague on the planet."
When you make a personal attack rather than actually debating the claims being made.
i.) Abusive: attacking the person's character
ii.) Circumstantial: person's circumstances are noted
iii.) Person doesn't Practice what is Preached
Appeal to Emotion
arousing irrelevant emotions in order to get others to accept a conclusion s/he otherwise would not accept
"The position in the accounting department should be given to Frank Thompson. Frank has six hungry children to feed, and his wife desperately needs an operation to save her eyesight.
Appeal to Force
"During the past 2 months, every time I sit in my green chair, the Yankees lose.
Thus, if the Yankees want to win again, I can't sit in my green chair.
Equivocation
"Some triangles are obtuse.
Whatever is obtuse is ignorant.
Therefore, some triangles are ignorant."

"I put my money in the bank.
A bank is a side of a river.
Hence, I put my money in the side of a river.
Amphiboly
Using a term with one meaning for part of the argument and then shifting
to another meaning for the rest of the argument.
Ambiguous statement due to
faulty grammar.
"Professor Johnson said that he will give a lecture about heart failure in the biology lecture hall . It must be the case that a number of heart failures have occurred there recently."
Division
Composition
attributing characteristics of the whole to the parts
"The jigsaw puzzle, when assembled, is rectangular in shape.
Therefore, each piece is rectangular in shape."
Attributing characteristics of the parts to the whole
"Zola likes anchoviews. She also likes raspberry ice cream.
Therefore, it is certainly the case that Zola would like raspberry ice cream topped with anchovies."
Using threats or intimidation to convince someone of something.
"Surely you welcome the opportunity to join our protective organization. Think of all the money you will lose from broken windows, overturned trucks, and damaged merchandise in the event of your not joining."
Appeal to the Crowd
Accepting the truth of a position on the basis that many people believe it.
Gay marriages are just immoral.
70% of Americans think so.
Appeal to Ignorance
Affirming a truth on the basis of a lack of evidence to the contrary
"People have been trying for centuries to provide conclusive evidence for the claims of astrology, and no one has ever succeeded.
Therefore, we must conclude that astrology is a lot of nonsense."

"Bigfoot must exist because no one has been able to prove that he doesn't."

"There is no proof that the parapsychology experiments were fraudulent, so I'm sure they weren't."
Accident
Applying a general rule to a specific situation in which it doesn't apply.
"Whoever thrusts a knife into another person should be arrested.
Surgeons do precisely this when operating. Therefore, surgeons should be arrested."
Converse Accident
Creating a general rule on the basis of an atypical instance
"After only one year, the alternator went out in my uncle's new Chevy.
My aunt's Oldsmobile developed a transmission problem after six months.
The obvious conclusion is that everything that GM makes is just a pile of junk."
Fallacies of Ambiguity
Fallacies of Omission:
Complex Question
Conjoining 2 otherwise unrelated points into a single proposition.
"You should support home education and the
God-given right of parents to raise their children according to their own beliefs."
"Do you support freedom and the right to bear arms?"
Component Fallacies:
Fallacies of Relevance:
Appeal to Authority
Errors that result because arguer leaves out
necessary material in an argument or misdirects
others from missing information
Errors in inductive & deductive reasoning
Appeal to evidence or examples that are
not relevant to the argument at hand
Appealing to a person who is not an expert in the field;
experts in the field disagree; the authority was joking, drunk, etc.
"Noted psychologist Dr. Fraser Crane recommends that you that buy the EZ-Rest Hot Tub."
"85% of consumers purchase PC computers rather than Macs;
all those people can't be wrong."
Genetic Fallacy
When you claim that an idea,
product, or person must be
untrustworthy because of its racial,
geographic, or ethnic origin.
"That car can't possibly be any good!
It was made in Japan!"

"Why should I listen to her argument? She is
from California, and we all know those people are flakes."

"Ha! I'm not reading that book. It was published in Tennessee,
and we know all Tennessee folk are hillbillies and rednecks!"
i.) "You may argue that God doesn't exist, but
you are just following a fad."

ii.)"We should discount what Senator Jones
says about taxation because he won't be
hurt by the increase."

"We should disregard Bush's energy policy because
he is being funded by the oil industry."

iii.) "You say I shouldn't drink, but you haven't
been sober for more than a year."
Appeal to Tradition/Custom
Asserting that a premise must be true
because people have always believed it or done it.
Formal Fallacies
Informal Fallacies
A fallacy is an error in reasoning
Occur when an invalid argument is confused with a valid one:
mistakes in the "formal" structure of the argument
Denying the Antecedent
Affirming the Consequent
(P1) If Inez studies she will pass the exam.
(P2) Inez did not study.
(C) She will not pass the exam.
(P1) If it snowed then Joe read Plato.
(P2) Joe read Plato.
(C) It snowed.
LOGIC PRIMER
Argument = set of statements one of which, the conclusion (C),is supposed to be supported by the other statements (P).It is an attempt to prove something true by providing reasons.
2 Types of Arguments:
Deductive Arguments
Inductive Arguments
Examples:
(P) If it rained last night then the pavement is wet.
(P) It rained last night.
(C) Therefore, the pavement is wet.
(P) I can doubt the existence of the body.
(P) I cannot doubt the existence of the mind.
(C) Thus, the mind is not the same thing as the body.
Arguments in which the conclusion
necessarily follows from the premises.
(P) It is immoral to kill persons.
(P) Capital punishment is the killing of persons.
(C) Therefore, capital punishment is immoral.
(P) All Quakers are pacifists.
(P) Jane is a Quaker.
(C) So, Jane is a pacifist.
NOTE: in a well constructed argument, the P give good reasons for believing the C is true.
Arguments in which the conclusion
probably follows from the premises
Example:
(P) All men are mortal.
(P) Socrates is a man.
(C) Therefore, Socrates is mortal.
Example:
(P) All birds have feathers.
(P) Chickens are birds.
(C) Thus, chickens have feathers.
A deductive argument is valid in which it is impossible for theP to be true & the C to be false.

NOTE: validity is determined solely by the "form" of the argument; the "content" is irrelevant.

Invalid arguments = those in which the truth of the conclusion fails to logically follow from the premises -- the assumed truth of the premises do not guarantee the truth of the conclusion.
Validity
Valid Forms
Modus Ponens
Modus Tollens
"affirming the antecedent"
"denying the consequence"
(P) If P then Q.
(P) P.
(C) Therefore Q.
(P) If P then Q.
(P) Not Q
(C) Therefore not P.
Examples:
(P) 75% of Marist students are from the Eastern U.S.
(P) Johnny is a Marist Student.
(C) Therefore, Johnny is probably from the eastern U.S.
Soundness
A sound deductive argument is one that
is valid and that has true premises.
NOTE: soundness is determined by the
"content" of the argument.
Invalid Forms
Denying the Antecedent
Affirming the Consequent
(P) If Joe is a bachelor, then Joe is male.
(P) Joe is not a bachelor.
(C) Therefore, Joe is not male.
(P)If it rained last night, then the streets are wet.
(P) The streets are wet.
(C) Therefore, it rained last night.
(P) If P then Q.
(P) Not P.
(C) Therefore not Q
(P) If P then Q.
(P) Q.
(C) Therefore P.
Enumerative Induction
Analogical Induction
making generalization on the basis of some sample
making a claim that 2 things are similar on the basis of some other similarity
Strength/Weakness
A "strong" inductive argument is one
in which the C most probably follows
from the truth of P.

A "weak inductive argument is one in
which the C probably doesn't follow
from the P.
Cogency
A cogent inductive argument is a strong
inductive argument that has true premises.
i.) how complete & reliable is the evidence (e.g., how big is the sample size, what is the source of the evidence)?
ii.) is the sample set representative?
iii.) how similar are the two objects being compared?
Evaluating Inductive Arguments:
Errors occur with ambiguous words or phrases, the meanings of which
shift & change in the course of the argument
God exists.
Because the Bible says God exists.
Because the Bible is the inspired word of God
why should I believe
that?
why should I believe anything
the Bible says?
Example
"If we allow the gov't to infringe upon our right to privacy on the Internet, it will then feel free to infringe upon our privacy on the telephone.
After that, FBI agents will be reading our mail. Then they will place cameras in our houses.
We must not let any gov't agency interfere with our Internet communications, or privacy will completely vanish in the United States."
"If it ain't broke, don't fix it."
The Maki people of the South are known to be invading our towns! They are corrupting our children and taking our jobs!! Vote for me and I will eradicate this menace!
"My roommate said her philosophy class was hard, and the one I'm in is hard too. All philosophy classes must be hard."
(P) If Spot is a dog, then Spot is a mammal.
(P) Spot is a dog.
(C) Therefore, Spot is a mammal.
(P)If it rained last night, then the streets are wet.
(P) The streets are not wet.
(C) Therefore it didn't rain last night.
"Last night I shot an elephant in my pajamas.
What he was doing in my pajamas I will never know."
conclusion indicator words:
therefore, so, hence, thus, consequently
premise indicator words:
since, because, for, given that
(P) If Ronald Regan was a U.S. president, then he was famous.
(P) Ronald Reagna was famous.
(C) Therefore, Ronald Reagan was a U.S. president.
Example of Valid Unsound Argument:
(P) If President George Washington was a horse, then he had five legs.
(P) President George Washington was a horse.
(C) Therefore, President George Washington had five legs.
Logic = the study of methods for evaluating arguments & reasoning; the study of correct inference.
Note: a cogent argument does not absolutely guarantee the conclusion, but it does give us good reasons for believing the conclusion.
Abductive: inference to the best explanation
doesn't try to directly prove the truth of a theory -- rather it tries to show that the theory is superior to all its competitors & that it is therefore the one most likely to be true.
1. There is a collection of data that needs an explanation.
2. A theory is proposed that offers an explanation of the data.
3. This theory offers the best explanation of all known alternatives.
4. Therefore, until a better explanation is proposed, it is rational to believe this theory.
Philosophy is not simply the sharing of personal opinions. It is the attempt to find reasons for accepting, rejecting, or modifying our own opinions/beliefs & those of others.
Goal of philosophy = to have beliefs that are true, i.e., we want beliefs that will provide us with the best possible understanding of ourselves & of our world so that we can live our lives effectively.
way/method to arrive at this understanding is through constructing & analyzing arguments for and against various alternatives.
the philosophy which has the best arguments in its support is the one that deserves to be embraced.
Criteria for Evaluating Philosophical Claims, Theories, Arguments:
1. Conceptual Clarity: how well/clearly are the terms defined?
2. Logical Consistency: does it avoid logical inconsistencies & self-referential inconsistency?
3. Rational Coherence: how well to the various parts "hang together"?
4. Comprehensiveness: does it make sense of wide range of phenomena?
5. Compatibility: is it compatible w/ well-established facts/theories?
Conclusion indicator words:
thus, therefore, so, hence, consequently
Premise indicator words:
since, because, for, given that
Conditional/hypothetical Statements
contains 2 simpler statements connected with the words "if-then":
antecedent = first part of conditional
consequent = second part of conditional
EG: "if is raining, then the ground is wet",
"if you study, then you will get good grades"
"if Jones is pregnant, then Jones is a female."
A conditional statement claims that the truth of the antecedent is a "sufficient condition" for the truth of the consequent.
to say that A is a sufficient condition for B means that if A is true, then B is true.
sometimes the conditions that would make the antecedent true would cause conditions that would make the consequent true (as in 1st two examples); however Jones being pregnant does not cause Jones to be female.
A conditional statement also claims that the consequent is a necessary condition for the antecedent to be true.
to say that A is a necessary condition for B means that for B to be true, A must be true.
E.g., being a female is a necessary condition for being pregant; however, being a female is not a sufficient condition for being pregnant.
Types of Deductive Arguments:
1. Arguments based on mathematics
2. Arguments from definition
3. Categorical syllogisms (ea. statement begins w/ one of the works: "all," "no," or "some.")
4. Hypothetical syllogisms (one or both of its premises contain a conditional)
5. Disjunctive syllogisms (one of the statements contains a disjunctive, "either... or...")
A syllogism = an argument consisting
of exactly 2 premises and 1 conclusion
All lasers are optical devices.
Some lasers are surgical devices.
Therefore, some optical devices are surgical instuments.
If quartz scratches glass, then quartz is harder than glass.
Quartz scratches glass.
Therefore, quartz is harder than glass.
Either breach of contract is a crime or it is not punishable by the state.
Breach of contract is not a crime.
Therefore, it is not punishable by the state.
Types of Inductive Arguments:
1. Predictions
2. Arguments from analogy
3. Inductive generalization
4. Arguments from authority
5. Arguments based on signs
6. Causal inferences
(P) All emeralds previously found have been green.
(C) Therefore, the next emerald to be found will be green.
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