Fallacies
A defective inference is said to be ‘fallacious.’
A fallacy is a common pattern of defective reasoning.
Fallacies come in two general categories: formal and
informal.
[see With Good Reason: An Introduction to Informal
Fallacies (5th Edition, 1994), by S. Morris Engel.
and
http://gncurtis.home.texas.net/index.html]
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Formal Fallacies
A formal fallacy is one that is defective purely as a result
of the form the argument takes, and one that is easily
confused with a valid form.
E.g. If Clinton passes that law, he’ll be doing the right
thing.
Clinton didn’t pass that law.
 Therefore, Clinton didn’t do the right thing.
This form of reasoning is fallacious no matter what the
argument is about, and it’s easily confused with modus
ponens or tollens.
If p then q.
Not-p
 Therefore, not-q.
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Informal Fallacies
An informal fallacy is defective in part because of its
content.
These are the ones that we will focus on. They are the
more interesting and the more common ones.
There are lots of interesting inter-relations among these
fallacies, but we won’t discuss those in any detail.
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Three Kinds of Fallacy
We’ll look at three kinds of fallacy:

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Fallcies of clarity

Fallacies of relevance

Fallacies of vacuity
Fallacies of Clarity
Reasoning can go wrong because of problems with the
language being used.
If a term is vague, then the argument in which it is being
used may be fallacious.
We’ll consider three fallacies of clarity:
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
The sorites argument;

The slippery slope argument; and

The fallacy of equivocation.
The Sorites Argument
These kinds of argument are also called: fat man, bald
man, and heap arguments.
A sorites argument is one that depends on vague terms,
and the vagueness leads to many borderline cases.
This in turn seems to lead to an absurd conclusion.
Suppose I have a full head of hair. I can then argue as
follows:
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The Sorites Argument
Someone who has lost one hair is not bald.
One cannot become bald by losing one hair.
If someone who has lost one hair is not bald, and one
cannot become bald by losing one hair, then someone
who has lost two hairs is not bald.
If someone who has lost two hairs is not bald, and one
cannot become bald by losing one hair, then someone
who has lost three hairs is not bald.
…
If someone who has lost 49,999 hairs is not bald, and
one cannot become bald by losing one hair, then
someone who has lost 50,000 hairs is not bald.
But, of course, someone who has lost 50,000 hairs is
bald! Where has the argument gone wrong?
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Slippery Slope
Slippery slope arguments (also called arguments of the
beard or fallacies of the beard) is closely related to
sorites arguments and also exploit vagueness and
borderline cases.
Here the idea is to argue that because there is no clear
differences between cases, there is no real difference
between them.
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Slippery Slope
Slippery slope arguments seem to go wrong because
they rely on a principle of this kind:
If case 1 is not significantly different from case 2, and
case 2 is not significantly different from case 3, then case
1 is not significantly different from case 3.
This is clearly mistaken — slippery slope arguments
demonstrate that! — but it’s not easy to say exactly why.
Still, unlike sorites arguments, slippery slope arguments
are sometimes used to convince people of particular
claims, so they are not merely of theoretical interest.
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Varieties
Conceptual slippery slopes: There is little difference
between things at the end of a conceptual continuum.
Fairness slippery slopes: It is unfair to treat small
differences differently.
Causal slippery slopes (also called domino arguments
and parades of horrors): Once a particular event occurs,
then other similar ones will follow and this will lead to a
disaster.
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Conceptual
The law recently passed by the county court explicitly
forbids any “motorized vehicles with wheels” in the park.
Cars are the intended target, of course, but the law is too
vague to exclude cars alone. Motor bikes are not
substantiallly different in design and purpose from cars,
so they are excluded; but if motor bikes are excluded, so
are electric bicycles; and if electric bicycles are excluded,
then so are electric scooters; and if electric scooters are
exlcuded then so are electric wheelchairs. And if electric
wheelchairs are excluded, then the law discriminates
against some handicapped people who pay taxes but will
not get the benefit of the use of this park.
Aside: Success of slippery slopes.
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Fairness
Assisted suicide is morally acceptable because it stops
irremediable pain in people who are terminally ill. On
these grounds, euthanasia should also be permitted since
it is nothing more than an active form of assisted suicide.
If someone is chronically ill, they too are suffering
irremediable pain, so euthanasia in these cases is also
morally acceptable. Since irremediable pain can be
psychological as well as physical, euthanasia for
psychologist distress is also permissible. Finally, since
people suffering irremediable pain are not always the
best judge of what is best for them, involuntary
euthanasia (called “termination of the patient without
explicit request” in the Netherlands) of people suffering
irremediable psychological distress is also morally
acceptable.
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Parade of Horrors
If today you can take a thing like evolution and make it a
crime to teach it in the public schools, tomorrow you can
make it a crime to teach it in the private schools, and
next year you can make it a crime to teach it in the
church. At the next session you can ban books and the
newspapers. Ignorance and fanaticism are ever busy,
indeed feeding, always feeding and gloating for more.
Today it’s the public school teachers, tomorrow the
private. The next day the preachers and the lecturers,
the magazines, the books, the newspapers. After awhile,
your honor, it is the setting of man against man, creed
against creed, until the flying banners and beating drums
are marching backwards to the glorious ages of the
sixteenth century when bigots lighted faggots to burn
the man who dared to bring any intelligence, and
enlightenment, and culture to the human mind.
(Clarence Darrow, cited in Stephen Jay Gould's Hen's Teeth and Horse's
Toes, p. 278.)
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Ambiguity
There is more than one way to think about ambiguity.
For the purposes of investigating fallacies, it is best to
say that a word or phrase is ambiguous when it is
misleading or potentially misleading.
Ambiguity is the basis of a the fallacy of equivocation
where an argument that appears valid or sound only
does so because there is ambiguity in the premises.
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Equivocation
What the lawyer said:
President Clinton should have been impeached only if he
had sexual relations with Monica Lewinsky. He did not
have sexual relations with Lewinsky. Therefore, he
should not have been impeached.
What Clinton meant:
President Clinton should have been impeached only if he
had sexual intercourse with Monica Lewinsky. He did not
have sexual intercourse with Lewinsky. Therefore, he
should not have been impeached.
What the Congress heard:
President Clinton should have been impeached only if he
had sexual contact of any kind with Monica Lewinsky. He
did not have sexual contact of any kind with Lewinsky.
Therefore, he should not have been impeached.
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Fallacies of Relevance
It is a conversational rule that when we offer a reason
for a view, it is a relevant reason.
When someone says something that is irrelevant that is
designed to distract the audience rather than convince
them, they are committing a fallacy of relevance (also
called ignoratio elenchi — “ignorance of refutation”).
We’ll consider two fallacies of clarity:
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
Ad hominem arguments; and

Appeals to authority.
Ad Hominem
Ad hominem is Latin for “against the man.”
This is an argument form in which one attacks the person
rather than the view she is defending.
They are typically (and fallaciously) used to move from
features of the arguer to a claim about the truth of the
argument’s conclusion or its validity.
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Aside: Moral Authority
Ad hominems can be used reasonably — if not always
fairly — when they are used to suggest that the arguer
doesn’t have the moral authority to make the argument.
E.g. One often hears people saying things like: “What
right does a divorced politician have to preach to us
about family values!”
Stricly speaking, of course, he has every right. His own
behavior is strictly irrelevant to the goodness or badness
of his arguments. Still, we tend to have the moral —
note: not logical view — that he who casts the first stone
should be without sin.
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Ad Hominem
Milo:
So what does my opponent have to offer to reduce
the mounting death toll on our nation’s highways?
Opus: Ummm… ‘55 saves lives’!
Milo:
I see. Apparently my opponent would support
saving an additional 45,000 lives per year by
reducing the speed limit to 40mph.
Opus: Gee, 40 is kinda’ slow….
Milo:
Apparently my opponent would send 45,000
innocent civilians to fiery deaths just so he can get
to his manicurist five minutes early.
Opus: I don’t even have a manicurist!
Milo:
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He probably doesn’t. Most mass-murderers don’t.
Hitler didn’t.
Tu Quoque
One kind of ad hominem turns a criticism back onto the
critic. This kind of argument is called tu quoque (Latin for
“you, also” or “you’re another”; also “Oh, yeah?”
“Yeah!”):
Q: Now, the United States government says that you are
still funding military training camps here in Afghanistan
for militant, Islamic fighters and that you're a sponsor of
international terrorism... Are these accusations true?...
Osama Bin Laden: …At the time that they condemn any
Muslim who calls for his right, they receive the highest
top official of the Irish Republican Army at the White
House as a political leader, while woe, all woe is the
Muslims if they cry out for their rights. Wherever we
look, we find the US as the leader of terrorism and crime
in the world…
(From an interview with Osama Bin Laden by Peter Arnett)
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Genetic Fallacy
Ad hominems can be thought of as a particular kind of
genetic fallacy.
This is the fallacy of criticizing the source of an argument
rather than its content.
For example, one might deny the value
of someone’s idea because it came to
him in a dream. Kekulé’s idea about the
structure of benzene came to him
in a dream, but it was a good idea.
Qu i ck Ti me ™a nd a TIFF (Unc om pres se d) de co mp re ss or are n ee de d to s ee th is pi ctu re .
In ad hominems the source is the person themselves.
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Ad Hominem
Aside: There is a different kind of ad hominem argument
which is not fallacious (and indeed is extremely
effective).
In this argument you argue from premises that Jones
himself believes that Jones ought to believe something
else (or that he shouldn’t believe something he does
believe).
This is ad hominem because it is directed at the person’s
beliefs (not at irrelevant facts about them).
Smith to Jones: “I’m not a vegetarian myself, but you are
because you believe it is wrong to use animals for our
own purposes. If that’s true, then you shouldn’t be
wearing those (very attractive) leather shoes.”
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Appeals to Authority
We often cite authorities to back up our views.
This is often perfectly reasonable. Authorities, properly
understood, are those people best placed to make a
judgement about their area of expertise
Often, however, the “authorities” cited are either not
experts in the field they are commenting on, or not
experts at all.
To decide whether an appeal to authority is fallacious or
not, one has to decide whether the authority is an
appropriate one.
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Appeals to Authority
“Mars Rocks and Magnetotactic Bacteria: Life on Mars?”
E. Imre Friedmann, a biologist at NASA's Ames Research
Center in Moffett Field, Calif., said an electron
microscope examination of [the Mars rock] ALH84001
had produced evidence of magnetite crystals formed in
chains.
Friedmann said that on Earth the bacteria that make
magnetite forms the material in chains and that these
chains are surrounded by a membrane. Under the
electron microscope, fossilized images of both the chains
and the membrane can be seen, he said.
“We see chains that could have been formed only
biologically,” said Friedmann. “There is no way you could
come up with a non-biological explanation.”
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Appeals to Authority
“In Vitro Fertilization and Single Women”
E. Imre Friedmann, a biologist at NASA’s Ames Research
Center in Moffett Field, Calif., said that God intended for
children to be born as a result of natural processes and
to be raised by a mother and a father.
“There is no way you could come up with a non-natural
method of reproduction that God would approve of”
Friedman said.
[Note: this example is made up!]
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Related Fallacies
Appeal to popular opinion (the bandwagon fallacy;
argumentum ad populam; or appeal to tradition when the
view has been long shared)
“See America's favorite upright vacuum cleaner at your
Hoover dealer. Like millions of women, you'll like the
basic Hoover and its honest value.”
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Related Fallacies
The appeal to ignorance offers the absence of evidence
for some claim as evidence in favor of its negation:
There is no evidence that air quality is deteriorating in
LA. Therefore, air quality is not deteriorating in LA.
This is a from of argument whose success depends on
background. If a substantial investigation into air quality
in LA has been done, and no evidence of deterioration
has been found, then this is indeed evidence that the air
is not worsening.
But the mere absence of evidence for a claim is not of
itself evidence for the negation of that claim.
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Related Fallacies
An appeal to pity or emotion tries to provide support for
a conclusion based on emotional considerations rather
than considerations of good reasons:
My parents are crazy; I had a job as a hand model, but I
burnt my hands; my girlfriend saw me naked after I had
been swimming and there was shrinkage; therefore I
deserve this apartment more than the person who got
here first.
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Fallacies of Vacuity
Finally, we’ll look at fallacies of vacuity.
We’ll consider three:



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Circular reasoning;
Begging the question; and
Self-sealers.
Circular Reasoning
Fodor’s argument that p
My argument for p is based on three premises:
1. q
2. r
and
3. p
From these, the claim that p deductively follows. Some people
may find the third premise controversial, but it is clear that if
we replaced that premise by any other reasonable premise, the
argument would go through just as well.
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Circular Reasoning
Any argument in which the conclusion — or something
equivalent to the conclusion — is used as a premise.
Notice that circular arguments are valid! They have this
form:
p
p
If p happens to be true, the argument is sound!
So circular arguments and their ilk are exceptions to the
claim that sound arguments are good arguments.
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Begging the Question
A closely related form of reasoning is called begging the
question (or petitio principii).
Aside: A linguistic note.
A premise or argument (or person) begs the question
when it relies on a premise that is not supported by any
reason that is independent of the conclusion; and such a
reason is needed.
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Begging the Question
“To cast abortion as a solely private moral question,...is
to lose touch with common sense: How human beings
treat one another is practically the definition of a public
moral matter. Of course, there are many private aspects
of human relations, but the question whether one human
being should be allowed fatally to harm another is not
one of them. Abortion is an inescapably public
matter.”
(Helen M. Alvaré, The Abortion Controversy, Greenhaven, 1995, p. 23.)
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Begging the Question
Abortion is characterized as fatally harming a human
being.
And: “[h]ow human beings treat one another is
practically the definition of a public moral matter.”
So the conclusion that abortion is a matter of public
morality depends, like the first premise, on the claim that
the fetus is a person.
Since that is a controversial matter, an independent
justification for the premise is required but not given.
The premise (and argument) therefore begs the
question.
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Begging the Question
Note again that arguments that beg the question are
valid: if the premises are true, then the conclusion must
be. E.g.:
God wrote the Bible.
 God exists.
Arguments that beg the question are therefore special
cases of defective arguments.
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Self-Sealers
A self-sealer is a position that cannot be refuted. It is
said to be empty of vacuous.
Since self-sealers are, by definition, unresponsive to any
evidence, they are not based on rational procedures and
ought to be rejected.
Ideologies, prejudices, and clinical delusions tend to be
self-sealers.
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