Logic Slides 2 Kinds of Arguments

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Logic Slides 2Kinds of Arguments

• PHIL 211
• Cosmos to Citizen
• Dr. Mike Miller
• Mount St. Marys College

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There are really only two types of arguments
Good and Bad But before you can assess if an
argument is good or bad, you must first
understand the two different kinds of good
arguments Deductive and Non-Deductive
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A Deductive argument is one whose premise, if
true, provides conclusive evidence for the truth
of the conclusion.
This means that if we accept the truth of the
premises of a properly formed deductive argument
(sometimes this requires a little imagination),
it is impossible for us to say the conclusion is
false without admitting we are acting
illogically.
Consider the following deductive argument All
cats are mammals. All mammals are animals.
Therefore, all cats are animals. The argument is
set-up in such a way that if we believe the
premises (and that shouldnt be too hard because
they are certainly true), then the conclusion
must also be true. This argument is classified
as a good deductive argument.
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Aristotle said that a person who refuses to
accept the conclusion of a good deductive
argument as true (the type of argument where the
premises really do support the conclusion and the
premises are true), then that person is no better
than a vegetable (that is, alive - but not
thinking)! Aristotle went on to say that it is
impossible to have a rational conversation with
this kind of person.
Dont be fooled, however, into thinking that
every deductive argument is good. There are
plenty of bad deductive arguments out there.
Consider the following
All animals are fish All fish are
mammals Therefore, all animals are mammals.
Although this argument is bad (because the
premises are false) the premises actually would
support the conclusion if they were true. They
are not true, but if they were true they would
provide conclusive evidence for the truth of the
conclusion. Therefore, this argument is
deductive even though it is also a bad argument.
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• We will study 7 different forms of deductive
  arguments later in this presentation (6 of which
  are discussed in detail in Weston, Chapter 6)
• Categorical Syllogism (CS)
• Modus Ponens (MP)
• Modus Tollens (MT)
• Hypothetical Syllogism (HS)
• Disjunctive Syllogism (DS)
• Dilemma
• Reduction ad Absurdum
• These different kinds of deductive arguments are
  called forms because it is the structure of the
  argument (how the premises and conclusion are
  written) and not the content of the premises or
  conclusion that make the argument deductive.

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Now, lets turn our attention to non-deductive
arguments.
A Non-Deductive argument is one whose premises,
if true, provide reliable, although not
conclusive, evidence for the truth of the
conclusion.
This means that in every non-deductive argument
if we admit that the premises are true (again
this often takes an act of imagination) then the
most we can say about the conclusion is that is
likely to be true. Conclusions of non-deductive
arguments are never absolutely certain, even if
they may be almost certain.
Non-deductive arguments usually appeal to some
notion of similarity between what has happened or
been observed in the past and what will happen in
the future.
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Consider the following non-deductive argument
Since the Mount softball team has won their last
19 games this season (all against highly ranked
opponents) and State U has lost 14 straight, it
is likely that the Mount will win their game
against State U tomorrow.
If the premises are true, the conclusion is very
likely true. (If I were a betting man I would
certainly place a bet.) However, since it is
always possible that a highly favored team may
lose a game they are expected to win the
conclusion of this argument does not follow with
absolute certainty (even if the premises are
true). Therefore, the argument is non-deductive.

Please note that non-deductive arguments are not
necessarily worse than deductive arguments
because their conclusions are never certain.
They are just different. Both deductive and
non-deductive arguments are useful and have their
advantages.
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Is the following argument deductive or
non-deductive?
If you dont eat lunch you will collapse like a
car without fuel.
This argument is non-deductive because the
conclusion does not necessarily follow even if
the premise was true. Many people skip lunch and
they dont collapse.
The following is also a non-deductive argument
Since no rational person believes in Santa Claus,
no rational person should believe in Jesus either.
The argument is non-deductive because even if the
premise was true the conclusion does not
necessarily follow. That is, the premise does
not exclude the possibility of a rational person
believing in Jesus because no rational adult
believes in Santa. (If you are interested, the
argument is bad because the difference between
believing in Jesus and believing in Santa is
greater than any possible similarity.)
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There are two different types of non-deductive
arguments

• Inductive
• Generalizations
• Analogies
• Arguments from Authorities

• Arguments about causes
• Agency (who did it?)
• Motivation (why it was done?)
• The Cause of action or event

The next 17 slides will focus upon these
non-deductive arguments (all of which are
discussed in detail in Weston, Chapters 25). We
will first discuss 3 different types of inductive
arguments (generalizations, analogies, and
arguments from authority), and then make some
general comments concerning arguments about
causes.
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Generalization
We generalize every day, arguing that what has
happened before is likely to happen again. For
example,
You are generalizing if you make a conclusion
about a group (the population) from a claim about
some part of it (the sample).
As we increase our experience our generalizations
typically get better because we have more
examples from which to generalize (that is, we
have a bigger sample).
Generalizations can be very good arguments.
Surveys are common examples of generalizations.
Some surveys are outstanding. Others are very
bad. The difference often depends upon the
similarity between the sample and the population.
If generalizations are made with faulty logic,
they commit the fallacy of hasty generalization.
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• Imagine that you wanted to conduct a survey about
  what people in Emmitsburg like to eat for dinner.
  To be a good generalization the survey must
  abide by the following rules
• Rule 8 Give more than one example
• Generally, the larger the population, the more
  samples are needed. If your survey makes a
  conclusion about what 2,000 people like to eat
  for dinner, you cannot simply ask 6 people and
  draw a conclusion.
• Rule 9 Use Representative examples
• Make sure that your samples actually represent
  the population. Even if you ask 200 women (which
  could certainly be a large enough sample), they
  are not representative of all the people in
  Emmitsburg.
• Rule 10 Background information is crucial
• The generalization made must not be misleading or
  bias. Unfortunately many surveys are. It takes
  a lot of work to make a good survey. Be careful
  that a generalization doesnt mislead you.
• Rule 11 Consider Counterexamples
• Ask questions to help you determine if the
  conclusion needs to be revised, limited, or given
  up entirely.

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Are These Good Generalizations?
Your sociology professor asks you to conduct a
survey about attitudes of students on campus
about sex before marriage. So, you ask 28 of
your friends if they think sex before marriage is
a great idea or not. 20 say No and 8 say
Yes. Is this a good survey?
Should the auto plant accept the batch of nuts
and bolts from its supplier? The inspector
chooses 10 pairs from the 20,000 items, inspects
them under a micro-scope, finds that all are
acceptable, and passes the lot. Was that a
right thing to do?
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Be careful not to believe something just because
you hear it many times from many different
sources. That is, be wary when somebody says, I
know a person who . . . Urban legends
(sometimes known as the person who fallacy) are
everywhere, and almost always false. For
example, have you heard the following . . .
Dear Friend. Please forward this message because
Bill Gates is testing a new email tracking system
and will send anyone who forwards this message to
10 other friends to Disney World for free. This
is not a hoax. It happened to a friend of mine.
Kentucky Fried Chicken changed its name to KFC
because they were being sued for liable because
their chicken is actually horsemeat.
A warning to all parents Dont let your
children eat the candy know as Pop-Rocks.
Years ago Mikey (from those old Life cereal
commercials) died because he ate Pop-Rocks and
then drank a Coke.
Not sure if what you heard is an urban legend?
Check out http//urbanlegends.about.com
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Reasoning by Analogy
When you Reason by Analogy you argue from a
similarity between two cases.
Generally, an argument by analogy tries to argue
that since two things (an item or an event) are
similar in many ways, the second thing discussed
must also have a certain characteristic that the
first one has.
A argument involving an analogy typically sound
like this Since objects A and B have properties
a, b, c, . . . n and object A has property x, we
can infer that object B also has property x.
The Mayor did not give the citys firefighters a
raise last year when they asked for one.
Therefore, the Mayor should not give the citys
sanitation workers a raise this year.
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• Note that analogies are not always expressed as
  formal arguments, but simply sketches of
  arguments. Since many things in analogies are
  left unstated, you must often
• Infer the conclusion.
• Come up with the similarities and/or the
  differences between the things being compared.
• Determine what general principle is being
  applied to both sides of the analogy. This
  principle is the glue which the person giving
  the analogy uses to unite both sides.
• For an analogy to be good
• All the premises must be true.
• Rule 12 The Analogy requires a relevantly
  similar example. If there are more significant
  differences than similarities between the two
  sides, the analogy is a bad one.

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Is the following a good analogy?
Blaming soldiers for war is like blaming firemen
for fires.
What is the unstated conclusion? What are the
similarities? What are the differences? Whats
the general principle at work here? (That is,
what is the glue that unites the two examples
in the analogy?) Is it a good analogy?
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You wouldnt buy a kitten at a pet store to give
to your dog. Why, then, do you consider it
acceptable to buy white rats for your boa
constrictor?
What is the unstated conclusion? What are the
similarities? What are the differences? Whats
the general principle at work here? (That is,
what is the glue that unites the two examples
in the analogy?) Is it a good analogy?
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Arguments from Authority
No one is an expert on everything. Sometimes we
must rely on the expertise of other people,
organizations or referenced works to tell us what
we need to know. Heres a typical argument from
Authority
Dr. Renpher, a two time winner of the Noble Prize
for biology, says that the corpus luteum secretes
progesterone. Therefore, the corpus luteum does
secrete progesterone.
However, as you know, you should not trust
everything that everyone says.
Little Johnny, the six-year-old kid down the
street, says the Japanese economy will recover in
three months only if their banking system no
longer leverages pre-tax buyouts on foreign debt.
Maybe he is right, but do you think it reasonable
for a six-year-old be an expert of foreign
monetary policy? I would trust what a
six-year-old has to say about dinosaurs or Dr.
Seuss books, but not technical and abstract
material unless (by some unusual circumstance)
there was some reason to think he actually is an
expert.
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A good argument from authority must follow
these rules
Rule 13 Sources should be cited A detailed claim
is more likely to be believed if a reference is
given. If you are unsure if the fact is true,
you can look it up yourself. Unnamed sources are
generally not to be trusted. Rule 14 Seek
informed sources Sources must be qualified about
the fact being discussed. You should question
the veracity of claims made by someone if you
have no evidence to think that they are experts
in that field. Also, beware of anyone making
claims to know what cannot be known (such as what
Princess Diana was thinking just before her car
crashed in Paris). Rule 15 Seek impartial
sources Those that have something to gain or lose
in a dispute are generally not the best sources
of information. Impartial sources of information
are usually the best. Rule 16 Cross check
sources When experts disagree, look for other
authorities to back-up the claim.
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Would you accept the following arguments? Why or
why not?
Your mother You can get AIDS by touching someone
with AIDS. Friend My uncle in San Francisco
says that President Carter failed second
grade. 55 year-old salesman I think this car is
the coolest car on the planet! Everyone in the
dorm is going to love it. The Lancet Journal
(April 4, 2003) Women who use oral
contraceptives have a 60 greater chance for
cervical cancer than those who do not.
Is your Mom an authority about medicine? What
have you learned about AIDS? Is she right?
I wouldnt accept this claim, unless I knew your
uncle was a presidential historian.
The salesman is probably biased because he wants
to make a sale. And is it likely that he knows
what a college student would love?
The Lancet is a respectable journal with peer
reviewed articles. I would believe it.
Dont forget your own authority. Your experience
counts too.
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There is a difference between attacking what a
person says and the character of the person
speaking. The two are not the same. Since you
cant assume that bad people always give bad
arguments, the following rule applies Rule 17
Personal attacks do not disqualify a source That
is, when considering the quality of an argument
or a claim, the personal quality of the person
speaking makes no difference! Consider the
following
Johns argument to put a stop light at 5th and
Main Street cant be right because John is a real
jerk! Just yesterday he hit an old lady!
Dont make this mistake (called an ad hominem
fallacy). Johns argument might be a good one,
even if John really is a jerk. You must consider
Johns argument and Johns character separately.
Note Good people do not necessarily make good
arguments either. However, character does matter
in a court of law, as when a witness has been
convicted of a felony. Why is this an exception
to the general rule?
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Arguments about Causes
Arguments about cause and effect are very common.
In these arguments you are looking for the
correlation between two events or kinds of
events. For example . . .
The facts Spot barked. Sean woke up. Is it
fair to say that Spots barking woke Sean up?
Effective arguments about causes Rule 18
Explain how cause leads to effect Good arguments
not only show the correlation between events A
and B, they explain why A caused B. Obviously,
the cause must precede the effect and take place
close to the effect in space and time. Rule 19
Propose the most likely cause The most likely
causes are ones that fit with well-established
beliefs. The best arguments are those where it
is impossible for the cause to happen and the
effect not happen, given normal conditions.
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Be certain not to forget the following rules when
making arguments about causes. If someone breaks
any one of the following rules they are making a
mistake in reasoning called a false cause
fallacy Rule 20 Correlated events are not
necessarily related
I won the lottery because I wore my lucky socks.
Really? Putting on the socks may have happened
before you won the lottery, but how did the socks
cause you to win?
Rule 21 Correlated events may have a common cause
Cleo is irritable because she cant sleep
properly.
Well, maybe Cleo is irritable and unable to sleep
because she drinks 6 cups of espresso every day.
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Rule 22 Either of two correlated events may
cause the other
Sitting close to the TV will give you bad
eyesight.
Whoever made this brief argument has probably
reversed the cause and the effect. I think it
more likely that having bad eyesight leads one to
sit too close to the TV.
Rule 23 Causes may be complex
If people really want the help those who are
starving in the world today, they should try to
eat less themselves. Then there would be more
left over for everyone else.
Well, less consumption of food would help
alleviate world hunger, but it certainly couldnt
end it alone. The problem with global poverty is
simply too complex to be solved by one solution.
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We are now near the end of our discussion about
non-deductive arguments (arguments by example,
arguments by analogy, arguments from authority,
and arguments about causes). In each of the
argument types the premises, if true, provided
reliable, although not conclusive, evidence for
the truth of the conclusion. No one can be
absolutely sure that non-deductive arguments
provide a certain truth because the content of
the arguments does not allow such confidence.
(The content of an argument is what the argument
is about, whether it be a neighbors barking dog,
the outlook for the Japanese economy, or the
safety of 20,000 bolts.) Think about it, how can
anyone be certain that things that have not yet
happened will happen, or that things that are
related in some ways are actually related in
additional ways? And, how can we be sure that
even an unbiased expert might not make a mistake?
Or for that matter, can we be confident that
what appears to cause something to happen
actually did so if we didnt clearly see it
with our own eyes?
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The content of non-deductive arguments simply
cant give us absolutely certain truth. But this
does not mean that non-deductive arguments are
not any good. In fact, we use non-deductive
arguments all the time (we would be hard pressed
to make it through the day without doing so).
And even though the conclusions of non-deductive
arguments are never certain, some non-deductive
arguments provide conclusions that are very,
very, very likely to be true. For instance,
would anyone doubt this inductive argument?
The sun has risen for over 15 billions years.
Therefore, the sun will rise tomorrow.
I trust you remember that deductive arguments are
different. For in their case the premises, if
true, provide conclusive evidence for the truth
of the conclusion. This means that if the
content of non-deductive arguments makes them
what they are, then deductive arguments are made
by their form.
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Deductive Arguments
The form of a deductive argument is its
structure, without regard to its content. As a
matter of fact, you can recognize deductive
arguments by stripping them of all their
content. To do this, you ignore what the
argument is about, and look how it is
structured. For example, take a look at the
following three arguments.
All Zobots are Quizars All Quizars are
Venmores Therefore, all Zobots are Venmores
All Pick-ups are trucks All trucks are motor
vehicles Therefore, all pick-ups are motor
vehicles
All Dogs are Mammals All Mammals are
Animals Therefore, all Dogs are Animals
All three arguments have the same form, even
though they are about different things. Do you
recognize this form? All A are B All B are
C Therefore, all A are C
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The type of deductive argument we just looked at
is called a Categorical Syllogism (CS). The CS
form has two premises and one conclusion, each of
which include the qualifiers some, no and/or
all. For instance, the following are all
examples of Categorical Syllogisms
Some dogs are mean. No mean things are
loved. Therefore, all dogs are not loved.
All cars are blue. Some things in the Smithsonian
Museum are blue. Therefore, some cars are in the
Smithsonian Museum.
No Gigowitz is Reggotin. All Reggotin things are
Peffin. Therefore, some Gigowitz are Peffin.
Some US presidents have been born in Nevada. Some
US presidents have the middle name of
Herbert Therefore, some Presidents born in
Nevada have the middle name of Herbert.
As it turns out, all of the arguments above are
bad (either the premises do not actually
support the conclusion, or at least one premise
is false), but even then all of the arguments
above are categorical syllogisms. Do you
understand why?
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Since the form and not the content of all
deductive arguments makes the arguments
deductive, logicians often use symbols to make
the form of deductive arguments more clear. That
is, using symbols help focus on the form and not
the content. In deductive arguments letters often
take the place of words (any letter will do, as
long as a unique letter takes the place of one
term every time it is used in the argument). For
example All Apples are Fruit All
Alaskans are named Fred All A are F All Fruits
are Delicious All Freds are
Dead All F are D Therefore, all Apples are
Delicious So, all Alaskans are
Dead Thus, all A are D When you are trying to
recognize the type of deductive argument pay
attention to the form, and not the content. So,
each of the three arguments above has the CS
form. In other deductive arguments letters can
also take the place of sentences. For example,
If you hit a grand slam, then we will win the
game becomes if H, then W (or if S, then G
or if P, then Q the letters dont matter if
you are consistent).
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It is important to understand that valid does not
mean true. That is, an argument may be valid but
its conclusion false. For example, the following
categorical syllogism is valid that is, if the
premises were true then the conclusion must be
true as well but the arguments premises are
obviously false. Thus, we should not accept the
conclusion is true because of the argument
All cats are brown. All brown things are
amphibian. Therefore, all cats are amphibian.
We will next discuss 6 different forms of
deductive arguments in the following slides.
Please note that the following 6 forms discussed
in this set of slides (unlike the categorical
syllogism just discussed) are always valid
meaning that if the premises are true the
conclusion must be true too!
Now, once again, the following 6 deductive forms
are always valid. That does not mean, however,
that you should always consider their conclusions
true. It just means that if the premises are
true, then the conclusion also has to be true.
This is an important point. For if you give a
valid deductive argument and can prove your
premises to be true, then the person to whom you
are giving your argument must accept your
conclusion as true! Now that is power!
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A deductive argument that is easy to recognize is
called Modus Ponens (Latin for method of
putting). It has the following form If P then
Q. P. Therefore, Q (where P and Q stand for
any proposition). Here are two modus ponens (MP)
The mayor said that if it rains the town picnic
will be cancelled. It is raining. Therefore,
the picnic is cancelled.
If Ohio State football is on television, then
Grandpa is watching the game at home. Ohio State
is on television, so we can find Grandpa at home.
Can you write each in its symbolic form?
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Modus Tollens (meaning the method of taking) is
somewhat similar to MP. However, MT has the
following form If P, then Q. Not-Q. Then
not-P Dont be confused by not-Q or not-P.
It just means the logical opposite of whatever Q
and P stand for. For example Q I can ride a
bike not-Q I cannot ride a bike I like Brad
Pitt I hate Brad Pitt I dont enjoy
rollercoasters. I love rollercoasters (Do
you understand why not-Q has a positive
sound to it here?) Here are two examples of
MT If Biff wins the election, then he will throw
a party at his house tonight. There is no party
at Biffs house tonight. He must not have won
the election. If it is raining, then the street
will be wet. The street is dry. So, it must not
be raining.
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A Hypothetical Syllogism (HS) has the following
form If P, then Q If Q, then R Therefore, if P,
then R For instance, Hypothetical
syllogisms can have any number of premises, as
long as each has the form if P, then Q. For
instance If P, then Q. If Q, then R. If R,
then S. If S, then T. If T, then U. Therefore,
if P, then U.
If Gabby wins the lottery, she will want to pay
back her debts. If she wants to pay back her
debts, she will give me the 1,000 she owes me.
So, if Gabby wins the lottery, Ill get my 1,000
back.
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The Disjunctive Syllogism (DS) has the following
form P or Q Not-P Therefore, Q
Here are a couple of examples
Either he is alive or dead. Hes not
alive. Therefore, hes dead.
Either Jesus is a madman, or he is God. Jesus is
not a madman. Therefore, Jesus is God
Either the British must come by land or by
sea. They did not come by sea. Therefore, they
must come by land.
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Dilemma are also deductive arguments.
Traditionally, dilemmas involve choices between
two bad consequences. In logic, the consequences
can both be bad, good or indifferent. Dilemma
have the following form P or Q If P, then R. If
Q, then S. Therefore, R or S.
Either I stay up and read philosophy, or I go to
sleep. If I read philosophy, Ill learn something
useful. If I go to sleep, Ill feel better in the
morning. Therefore, either Ill learn something
useful or Ill feel better in the morning.
This argument doesnt tell you what to do (other
arguments are needed to help you there), but it
does make clear the consequences of your choices.
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The last deductive argument we will examine is
called Reductio ad Absurdum (or, a reduction to
the absurd). Those that use this argument form
well prove their point by showing that the exact
opposite of what they want to prove leads to a
contradiction (or an absurd conclusion).
Imagine my brother thinks that Im harming my 4
year-old daughter by not letting her watch movies
like Star Wars and Harry Potter. He thinks kids
should be aware that life is often dangerous and
hard, and if you keep them too protected they
will grow up unprepared for the reality of life.
I want to prove him wrong. I would start my
argument by assuming that I should let my
daughter watch Star Wars because it will toughen
her up. If true, I probably should let her
watch Rocky and Jaws as well. Maybe I should sit
her down to watch The Godfather while Im at it.
And if I really wanted to prepare my daughter for
life, I should not feed her for a day, or make
her walk home from preschool once in a while.
But these things would be absurd. So, I wont
let her watch movies like Star Wars.
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Be assured, deductive and non-deductive arguments
are often more complex than the ones we have
looked at. However, once you recognize how the
arguments work, you should be able to recognize
them no matter how complex they might be. Keep
your eyes and ears open and you will find
examples of the arguments we just examined all
over the place. Keep a special lookout for
examples of these arguments in our class
readings. In this set of slides we discussed
several mistakes in reasoning (called fallacies).
In the 3rd set of slides we will discuss a
number of other common fallacies.
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• Please contact me with any questions about the
  information in these slides or the related
  assigned reading
• Weston, Chapters II VI
• Logic Handout, p. 4-5