WHAT IS AN
ARGUMENT?
An argument is, to quote the Monty Python
sketch, "a connected series of statements to
establish a definite proposition." There are
three stages to an argument: premises,
inference, and conclusion.
Stage one:
Premises
One or more propositions will be are necessary
for the argument to continue. They must be
stated explicitly. They are called the premises
of the argument. They are the evidence (or
reasons) for accepting the argument and its
conclusions.
Premises (or assertions) are often indicated by
phrases such as because, since, obviously and
so on. (Obviously is often viewed with
suspicion, as it can be used to intimidate
others into accepting dubious premises. If
something doesn't seem obvious to you, don't be
afraid to question it. You can always say "Oh,
yes, you're right, it is obvious" when you've
heard the explanation.)
Stage two:
Inference
The premises of the argument are used to obtain
further propositions. This process is known as
inference. In inference, we start with one or
more propositions which have been accepted. We
then derive a new proposition. There are
various forms of valid inference.
The propositions arrived at by inference may
then be used in further inference. Inference is
often denoted by phrases such as implies that
or therefore.
Stage three:
Conclusion
Finally, we arrive at the conclusion of the
argument, another proposition. The conclusion
is often stated as the final stage of
inference. It is affirmed on the basis the
original premises, and the inference from them.
Conclusions are often indicated by phrases such
as therefore, it follows that, we conclude and
so on.
Types of
Argument
There are two traditional types of argument,
deductive and inductive. A deductive argument
provides conclusive proof of its conclusions;
if the premises are true, the conclusion must
also be true. A deductive argument is either
valid or invalid.
A valid argument is defined as one where if the
premises are true, then the conclusion is true.
An inductive argument is one where the premises
provide some evidence for the truth of the
conclusion. Inductive arguments are not valid
or invalid, but we can talk about whether they
are better or worse than other arguments. We
can also discuss how probable their premises
are.
There are forms of argument in ordinary
language which are neither deductive nor
inductive. However, this document concentrates
on deductive arguments, as they are often
viewed as the most rigorous and convincing.
Here is an example of a deductive argument:
Every event has a cause (premise)
The universe has a beginning (premise)
All beginnings involve an event (premise)
This implies that the beginning of the universe
involved an event (inference)
Therefore the universe has a cause (inference
and conclusion)
Note that the conclusion of one argument might
be a premise in another argument. A proposition
can only be called a premise or a conclusion
with respect to a particular argument; the
terms do not make sense in isolation.
RECOGNIZING AN ARGUMENT
Sometimes an argument will not follow the order
described above. For instance, the conclusions
might be stated first, and the premises stated
afterwards in support of the conclusion. This
is perfectly valid, if sometimes a little
confusing.
Arguments are harder to recognize than premises
or conclusions. Many people shower their
writing with assertions without ever producing
anything which one might reasonably describe as
an argument. Some statements look like
arguments, but are not.
For example:
"If evolution is accurate, Darwin must either
have been insane or a genius."
The above is not an argument; it is a
conditional statement. It does not assert the
premises which are necessary to support what
appears to be its conclusion. (Even if we add
the assertions, it still suffers from a number
of other logical flaws.)
Another example:
"Your country supported you; therefore, do your
duty to your country."
The phrase do your duty to your country is
neither true nor false. (Commands can not be
true or false.) Therefore it is not a
proposition, and the sentence is not an
argument.
Causality is important. Suppose we are trying
to argue that there is something wrong with the
engine of a car. Consider two statements of the
form A because B. The first statement:
"My car will not start because there is
something wrong with the engine."
The statement is not an argument for there
being something wrong with the engine; it is an
explanation of why the car will not start. We
are explaining A, using B as the explanation.
We cannot argue from A to B using a statement
of the form A because B.
However, we can argue from B to A using such a
statement.
Consider:
"There must be something wrong with the engine
of my car, because it will not start."
Here we are arguing for A, offering B as
evidence. The statement A because B is then an
argument.
To make the difference clear, note that A
because B is equivalent to B therefore A. The
two statements then become
"There is something wrong with the engine,
therefore my car will not start."
and
"My car will not start, therefore there is
something wrong with the engine."
If we remember that we are supposed to be
arguing that there is something wrong with the
engine, it is clear that only the second
statement is a valid argument.
IMPLICATION IN DETAIL
There is one very important thing to remember:
The fact that a deductive argument is valid
does not imply that its conclusion holds. This
is because of the slightly counter-intuitive
nature of implication, which we must now
consider more carefully.
Obviously a valid argument can consist of true
propositions. However, an argument may be
entirely valid even if it contains only false
propositions.
For example:
All insects have wings (premise)
Woodlice are insects (premise)
Therefore woodlice have wings (conclusion)
Here, the conclusion is not true because the
argument's premises are false. If the
argument's premises were true, however, the
conclusion would be true. The argument is thus
entirely valid.
More subtly, we can reach a true conclusion
from one or more false premises, as in:
All fish live in the sea (premise)
Dolphins are fish (premise)
Therefore dolphins live in the sea (conclusion)
FALLACIES
I recall at first being a bit intimidated at
the Latin in discussions of logic and the names
given to certain logical fallacies. Don't be:
the English translation is, of course,
provided, and the fallacies make common sense
[the whole point]. To delve further into the
structure of logical arguments would require
lengthy discussion of linguistics and
philosophy. It is simpler and probably more
useful to summarize the major pitfalls to be
avoided when constructing an argument. These
pitfalls are known as fallacies.
In everyday English, the term fallacy is used
to refer to mistaken beliefs as well as to the
faulty reasoning that leads to those beliefs.
This is fair enough, but in logic the term is
generally used to refer to a form of
technically incorrect argument, especially if
the argument appears valid or convincing.
So for the purposes of this discussion, we
define a fallacy as a logical argument which
appears to be correct, but which can be seen to
be incorrect when examined more closely. By
studying fallacies we aim to avoid being misled
by them.
Below is a list of some common fallacies, and
also some rhetorical devices often used in
debate. The list is not intended to be
exhaustive.
Argumentum ad baculum
/ Appeal to force
The Appeal to Force is committed when the
arguer resorts to force or the threat of force
in order to try and push the acceptance of a
conclusion. It is often used by politicians,
and can be summarized as "might makes right."
The force threatened need not be a direct
threat from the arguer.
For example:
"... the terrorists said we had to supply the
money or they would harm the
hostages."
ARGUMENTUM AD
HOMINEM
Argumentum ad Hominem is literally "argument
directed at the man." The abusive variety of
Argumentum ad Hominem occurs when, instead of
trying to disprove the truth of an assertion,
the arguer attacks the person or people making
the assertion. This is invalid because the
truth of an assertion does not depend upon the
goodness of those asserting it.
For example:
"Atheism is an evil philosophy. It is practised
by Communists and murderers."
Sometimes in a court of law doubt is cast upon
the testimony of a witness by showing, for
example, that he is a known perjurer. This is a
valid way of reducing the credibility of the
testimony given by the witness, and not
Argumentum ad Hominem; however, it does not
demonstrate that the witness's testimony is
false. To conclude otherwise is to fall victim
of the Argumentum ad Ignorantiam.
The circumstantial form of Argumentum ad
Hominem is committed when a person argues that
his opponent ought to accept the truth of an
assertion because of the opponent's particular
circumstances. For example:
"It is perfectly acceptable to kill animals
for food. How can you argue otherwise when
you're quite happy to wear leather shoes?"
This is an abusive charge of inconsistency,
used as an excuse for dismissing the opponent's
argument.
This fallacy can also be used as a means of
rejecting a conclusion. For example:
"Of course you would argue that pornography is
not a bad thing. You're a man."
This particular form of Argumentum ad Hominem,
when one alleges that one's adversary is
rationalizing a conclusion formed from selfish
interests, is also known as "poisoning the
well."
Argumentum Ad
Ignorantiam
Argumentum ad ignorantiam means "argument from
ignorance." This fallacy occurs whenever it is
argued that something must be true simply
because it has not been proved false. Or,
equivalently, when it is argued that something
must be false because it has not been proved
true. (Note that this is not the same as
assuming that something is false until it has
been proved true, a basic scientific
principle.)
Examples:
"Of course UFOs are real. Nobody can prove
otherwise."
"Of course telepathy and other psychic
phenomena exist. Nobody has shown any proof
that they aren't real."
Note that this fallacy does not apply in a
court of law, where one is generally assumed
innocent until proven guilty. Also, in
scientific investigation if it is known that an
event would produce certain evidence of its
having occurred, the absence of such evidence
can validly be used to infer that the event did
not occur.
For example:
"A flood as described in the Bible would
require an enormous volume of water to be
present on the earth. The earth does not have a
tenth as much water, even if we count that
which is frozen into ice at the poles.
Therefore no such flood occurred."
In science, we can validly assume from lack of
evidence that something has not occurred. We
cannot conclude with certainty that it has not
occurred, however. See also Shifting the Burden
of Proof
Argumentum Ad
Misericordiam / Appeal to Pity
This is the Appeal to Pity, also known as
Special Pleading. The fallacy is committed when
the arguer appeals to pity for the sake of
getting a conclusion accepted. For example:
"I did not murder my mother and father with an
axe. Please don't find me guilty; I'm suffering
enough through being an orphan."
Argumentum Ad
Populum
This is known as Appealing to the Gallery or
Appealing to the People. To commit this fallacy
is to attempt to win acceptance of an assertion
by appealing to a large group of people. This
form of fallacy is often characterized by
emotive language.
For example:
"Chevrolet — The Heartbeat of America"
"The Earth must be flat. Millions of people
know that it is. Are you trying to tell them
that they are all mistaken fools?" (Isabella to
Columbus)
Argumentum Ad
Numerum
This fallacy is closely related to the
argumentum ad populum. It consists of asserting
that the more people who support or believe a
proposition, the more likely it is that that
proposition is correct.
Argumentum
Ad Verecundiam / Appeal to
Authority
The Appeal to Authority uses the admiration of
the famous to try and win support for an
assertion. For example:
"Isaac Newton was a genius, and he believed in
ghosts."
This line of argument is not always completely
bogus; for example, reference to an admitted
authority in a particular field may be relevant
to a discussion of that subject. For example,
we can distinguish quite clearly between:
"Hawking has concluded that black holes give
off radiation."
and
"Penrose has concluded that it is impossible to
build an intelligent computer."
Hawking is a physicist, and so we can
reasonably expect his opinions on black hole
radiation to be informed. Penrose is a
mathematician, so it is questionable whether he
is well-qualified to speak on the subject of
machine intelligence.
The Fallacy Of
Accident
The Fallacy of Accident is committed when a
general rule is applied to a particular case
whose "accidental" circumstances mean that the
rule is inapplicable. It is the error made when
one goes from the general to the specific. For
example:
"Americans generally dislike eating tofu. You
are an American, so you must dislike tofu."
This fallacy is often committed by moralists
and legalists who try to decide every moral and
legal question by mechanically applying general
rules.
Converse Accident /
Hasty Generalization
This fallacy is the reverse of the Fallacy
of Accident. It occurs when one forms a general
rule by examining only a few specific cases
which are not representative of all possible
cases. For example:
"Jim Bakker was an insincere Christian.
Therefore all Christians are
insincere."
Dicto simpliciter / Sweeping generalization
A sweeping generalization occurs when a general
rule is applied to a particular situation in
which the features of that particular situation
render the rule inapplicable. A sweeping
generalization is the opposite of a hasty
generalization.
Non Causa Pro Causa /
Post Hoc Ergo Propter Hoc
These are known as False Cause fallacies.
The fallacy of Non Causa Pro Causa occurs when
one identifies something as the cause of an
event but it has not actually been shown to be
the cause. For example:
"I took an aspirin and took a nap; then my
headache disappeared. So the aspirin cured me
of the headache."
The fallacy of Post Hoc Ergo Propter Hoc occurs
when something is assumed to be the cause of an
event merely because it happened before the
event. For example:
"The Soviet Union collapsed after taking up
atheism. Therefore we must avoid atheism for
the same reasons."
Cum Hoc Ergo Propter
Hoc
This fallacy is similar to Post Hoc Ergo
Propter Hoc. It asserts that because two events
occur together, they must be causally related,
and leaves no room for other factors that may
be the cause(s) of the events.
Petitio Principii /
Begging The Question
This fallacy occurs when the premises are at
least as questionable as the conclusion
reached.
Circulus in
demonstrando
This fallacy occurs when one assumes as a
premise the conclusion which one wishes to
reach. Often, the proposition will be rephrased
so that the fallacy appears to be a valid
argument.
For example:
"Homosexuals must not be allowed to hold
government office. Hence any government
official who is revealed to be a homosexual
will lose his job. Therefore homosexuals will
do anything to hide their secret, and will be
open to blackmail. Therefore homosexuals cannot
be allowed to hold government office."
Note that the argument is entirely circular;
the premise is the same as the conclusion. An
argument like the above has actually been cited
as the reason for the British Secret Services'
official ban on homosexual employees.
Complex Question /
Fallacy Of Interrogation /
Fallacy Of Presupposition
This is the interrogative form of Begging the
Question. One example is the classic loaded
question:
"Have you stopped hitting your dog?"
The question presupposes a definite answer to
another question which has not even been asked.
This trick is often used by lawyers in
cross-examination, when they ask questions
like:
"Where did you hide the money you stole?"
Similarly, politicians often ask loaded
questions such as:
"How long will this UN interference in our
affairs be allowed to continue?"
or
"Does the Mayor plan two more years of ruinous
privatization?"
Another form of this fallacy is to ask for an
explanation of something which is untrue or not
yet established.
EQUIVOCATION / FALLACY
OF FOUR TERMS
Equivocation occurs when a key word is used
with two or more different meanings in the same
argument. For example:
"What could be more affordable than free
software? But to make sure that it remains
free, that users can do what they like with it,
we must place a license on it to make sure that
will always be freely
redistributable."
Amphiboly
Amphiboly occurs when the premises used in an
argument are ambiguous because of careless or
ungrammatical phrasing.
ACCENT
Accent is another form of fallacy through
shifting meaning. In this case, the meaning is
changed by altering which parts of a statement
are emphasized.
For example, consider:
"We should not speak ill of our friends"
and
"We should not speak ill of our
friends"
FALLACIES OF
COMPOSITION
One Fallacy of Composition is to conclude that
a property shared by the parts of something
must apply to the whole. For example:
"The bicycle is made entirely of low mass
components and is therefore very lightweight."
The other Fallacy of Composition is to conclude
that a property of a number of individual items
is shared by a collection of those items. For
example:
"A car uses less gas and causes less pollution
than a bus. Therefore cars are less
environmentally damaging than buses."
FALLACY OF
DIVISION
The fallacy of division is the opposite of the
Fallacy of Composition. Like its opposite, it
exists in two varieties. The first is to assume
that a property of some thing must apply to its
parts. For example:
"You are studying at a rich college. Therefore
you must be rich."
The other is to assume that a property of a
collection of items is shared by each item. For
example:
"Ants can destroy a tree. Therefore this ant
can destroy a tree."
THE SLIPPERY SLOPE
ARGUMENT
This argument states that should one event
occur, so will other harmful events. There is
no proof made that the harmful events are
caused by the first event.
For example:
"If we legalize marijuana, then we would have
to legalize crack and heroin and we'll have a
nation full of drug-addicts on welfare.
Therefore we cannot legalize marijuana."
A is based on B fallacies / ...is a type of...
fallacies / Fallacy of the Undistributed Middle
These fallacies occur when one attempts to
argue that things are in some way similar
without actually specifying in what way they
are similar. Examples:
"Islam is based on faith, Christianity is based
on faith, so isn't Islam a form of
Christianity?"
"Cats are a form of animal based on carbon
chemistry, dogs are a form of animal based on
carbon chemistry, so aren't dogs a form of
cat?"
Affirmation Of The
Consequent
This fallacy is an argument of the form A
implies B, B is true, therefore A is true. To
understand why it is a fallacy, examine the
truth table for implication given
earlier.
DENIAL OF THE ANTECEDENT
This fallacy is an argument of the form A
implies B, A is false, therefore B is false.
The truth table for implication makes it clear
why this is a fallacy. Note that this fallacy
is different from Non Causa Pro Causa. The
latter has the form A implies B, A is false,
therefore B is false, where A does not in fact
imply B at all. Here, the problem is not that
the implication is invalid; rather it is that
the falseness of A does not allow us to deduce
anything about B.
Converting A
Conditional
This fallacy is an argument of the form If A
then B, therefore if B then A.
Argumentum Ad
Antiquitatem
This is the fallacy of asserting that something
is right or good simply because it is old, or
because "that's the way it's always
been."
Argumentum Ad
Novitatem
This is the opposite of the Argumentum ad
Antiquitatem; it is the fallacy of asserting
that something is more correct simply because
it is new or newer than something
else.
Argumentum Ad
Crumenam
The fallacy of believing that money is a
criterion of correctness; that those with more
money are more likely to be right.
Argumentum Ad
Lazarum
The fallacy of assuming that because someone is
poor he or she is sounder or more virtuous than
one who is wealthier. This fallacy is the
opposite of the argumentum ad
crumenam.
Argumentum Ad
Nauseam
This is the incorrect belief that an assertion
is more likely to be true the more often it is
heard. An "argumentum ad nauseam" is one that
employs constant repetition in asserting
something.
BIFURCATION / FALSE
DILEMMA
Also referred to as the "black and white"
fallacy, bifurcation occurs when one presents a
situation as having only two alternatives,
where in fact other alternatives exist or can
exist.
Plurium
Interrogationum / Many Questions
This fallacy occurs when a questioner demands a
simple answer to a complex question or a single
answer to a multipart question.
NON
SEQUITUR
A non-sequitur is an argument where the
conclusion is drawn from premises which are not
logically connected with it.
RED
HERRING
This fallacy is committed when irrelevant
material is introduced to the issue being
discussed, so that everyone's attention is
diverted away from the points being made,
towards a different conclusion.
Reification /
Hypostatization
Reification occurs when an abstract concept is
treated as a concrete thing.
SHIFTING THE BURDEN OF
PROOF
The burden of proof is always on the person
making an assertion or proposition. Shifting
the burden of proof, a special case of
Argumentum ad Ignorantiam, is the fallacy of
putting the burden of proof on the person who
denies or questions the assertion being made.
The source of the fallacy is the assumption
that something is true unless proven otherwise.
STRAW
MAN
The straw man fallacy is to misrepresent
someone else's position so that it can be
attacked more easily, then to knock down that
misrepresented position, then to conclude that
the original position has been demolished. It
is a fallacy because it fails to deal with the
actual arguments that have been made.
THE EXTENDED
ANALOGY
The fallacy of the Extended Analogy often
occurs when some suggested general rule is
being argued over. The fallacy is to assume
that mentioning two different situations, in an
argument about a general rule, constitutes a
claim that those situations are analogous to
each other.
This fallacy is best explained using a real
example from a debate about anti-cryptography
legislation:
Person 1: "I believe it is always wrong to
oppose the law by breaking it."
Person 2: "Such a position is odious: it
implies that you would not have supported
Martin Luther King."
Person 1: "Are you saying that cryptography
legislation is as important as the struggle for
Black liberation? How dare you!"
Tu
Quoque
This is the famous "you too" fallacy. It occurs
when an action is argued to be acceptable
because the other party has performed it. For
instance:
"You're just being randomly abusive."
"So? You've been abusive too."
This is a personal attack, and is therefore a
special case of Argumentum ad
Hominem.
Audiatur Et Altera
Pars
Often, people will argue from assumptions which
they do not bother to state. The principle of
Audiatur et Altera Pars is that all of the
premises of an argument should be stated
explicitly. It is not strictly a fallacy to
fail to state all of one's assumptions;
however, it is often viewed with suspicion.
Appeal To
Tradition
Sometimes we do things for good reasons;
sometimes we do things simply because we have
always done them. Such is the nature of appeal
to tradition. The following argument appeared
in a letter defending the membership policy of
the Century Club, an all-male club established
in New York in 1847, which was under pressure
to admit women in the 1980s. The following was
written by a Presbyterian minister who opposed
the admission of women:
"I am totally opposed to a proposal which would
radically change the nature of the Century ....
A club creates an ethos of its own over the
years, and I would deeply deplore a step that
would inevitably create an entirely different
kind of place.
A club like the Century should be unaffected by
fashionable whims."
Ad Hoc
There is a difference between argument and
explanation. If we're interested in
establishing A, and B is offered as evidence,
the statement A because B is an argument. If
we're trying to establish the truth of B, then
A because B is not an argument, it is an
explanation.
To argue effectively, you
should avoid fallacies, which are mistakes in
reasoning. Following are the most common of
them - the kind most likely to undermine the
persuasiveness of an argument.
ARGUING BY
ASSOCIATION
It is well-known that Senator Beelzebub is a
critic of the Chilean government. We also know
that Latin American Marxists are critics of the
Chilean government. It is clear, therefore,
that Senator Beelzebub is a Marxist.
Here a deductive argument is misused to promote
guilt by association. Only if we assume that
all critics of the Chilean government are
Marxists must we conclude that any one critic
of that government is.
SHIFTING THE MEANING
OF A KEY TERM
Criminals do everything possible to avoid
and obstruct arrest, prosecution, and
conviction. Likewise, liberal lawyers try in
every possible way to obstruct the work of
police. They are the ones responsible for
things like the Miranda rule, which says that
the police can't even interrogate anyone
they've arrested until they tell the person
what his or her rights are, and if they forget
to do so, the case can be thrown out of court.
Obviously, then, liberal lawyers are no better
than criminals themselves.
This argument uses the word "obstructs" in two
different senses. A criminal obstructs the
police by hiding out, resisting arrest, or
refusing to answer questions. Lawyers obstruct
the police only insofar as they demand respect
for the constitutional rights of the suspect,
who - under the United States system of justice
- must be presumed innocent until proven
guilty. Since the writer uses the word
"obstructs" to identify what lawyers and
criminals have in common, the shift in the
meaning of this key term invalidates the
argument.
INDUCTIVE AND
DEDUCTIVE REASONING
Many people distinguish between two basic kinds
of argument: inductive and deductive. Induction
is usually described as moving from the
specific to the general, while deduction begins
with the general and ends with the specific;
arguments based on experience or observation
are best expressed inductively, while arguments
based on laws, rules, or other widely accepted
principles are best expressed deductively.
Consider the following example:
Adham: I've noticed previously that every time
I kick a ball up, it comes back down, so I
guess this next time when I kick it up, it will
come back down, too.
Rizik: That's Newton's Law. Everything that
goes up must come down. And so, if you kick the
ball up, it must come down.
Adham is using inductive reasoning, arguing
from observation, while Rizik is using
deductive reasoning, arguing from the law of
gravity. Rizik's argument is clearly from the
general (the law of gravity) to the specific
(this kick); Adham's argument may be less
obviously from the specific (each individual
instance in which he has observed balls being
kicked up and coming back down) to the general
(the prediction that a similar event will
result in a similar outcome in the future)
because he has stated it in terms only of the
next similar event--the next time he kicks the
ball.
As you can see, the difference between
inductive and deducative reasoning is mostly in
the way the arguments are expressed. Any
inductive argument can also be expressed
deductively, and any deductive argument can
also be expressed inductively.
Even so, it is important to recognize whether
the form of an argument is inductive or
deductive, because each requires different
sorts of support. Adham's inductive argument,
above, is supported by his previous
observations, while Rizik's deductive argument
is supported by his reference to the law of
gravity. Thus, Adham could provide additional
support by detailing those observations,
without any recourse to books or theories of
physics, while Rizik could provide additional
support by discussing Newton's law, even if
Rizik himself had never seen a ball kicked.
The appropriate selection of an inductive or
deductive format for a specific first steps
toward sound argumentation.
