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Assignment ContentFor this assignment, you will identify a current business problem and justify why change is needed.Review Ch. 2, “Two Kinds of Reasoning,” of Critical Thinking (12th ed.).Select a business. This may be one where you or your team members currently work or a fictional business.Discuss a problem that currently exists within the business.Write a minimum 700-word logical structures of arguments essay about the business problem. Include the following:Summarize the issue.Identify the rules of logic that should have been applied to the issue.Create three arguments for change.Explain how the rules of logic helped you determine the five effective arguments for change that you presented.Format your assignment according to APA guidelines.
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Two Kinds of Reasoning 2
Students will learn to . . .
1.Recognize general features of arguments
2.Distinguish between deductive and inductive arguments and evaluate them for
validity, soundness, strength, and weakness
3.Identify unstated premises
4.Identify a balance of considerations argument and an inference to the best
explanation (IBE)
5.Distinguish between ethos, pathos, and logos as means of persuasion
6.Use techniques for understanding and evaluating the structure and content of
arguments
T
ime to look more closely at arguments—the kind that actually show something (unlike the
red herrings and emotional appeals and other fallacies we are going to be talking about later).
ARGUMENTS: GENERAL FEATURES
To repeat, an argument consists of two parts. One part, the premise, is intended to provide a reason
for accepting the second part, the conclusion. This statement is not an argument:
God exists.
It’s just a statement.
Likewise, this is not an argument:
God exists. That’s as plain as the nose on your face.
It’s just a slightly more emphatic statement.
Nor is this an argument:
God exists, and if you don’t believe it, you will go to hell.
It just tries to scare us into believing God exists.
Page 33
Also not an argument:
I think God exists, because I was raised a Baptist.
Yes, it looks a bit like an argument, but it isn’t. It merely explains why I believe in God.
On the other hand, this is an argument:
God exists because something had to cause the universe.
The difference between this and the earlier examples? This example has a premise (“something
had to cause the universe”) and a conclusion (“God exists”).
As we explained in Chapter 1 (see page 8), an argument always has two parts: a premise part and
a conclusion part. The premise part is intended to give a reason for accepting the conclusion part.
This probably seems fairly straightforward, but one or two complications are worth noting.
Conclusions Used as Premises
The same statement can be the conclusion of one argument and a premise in another argument:
Premise: The brakes aren’t working, the engine burns oil, the transmission needs work, and the
car is hard to start.
Conclusion 1: The car has outlived its usefulness.
Conclusion 2: We should get a new car.
In this example, the statement “The car has outlived its usefulness” is the conclusion of one
argument, and it is also a premise in the argument that we should get a new car.
Clearly, if a premise in an argument is uncertain or controversial or has been challenged, you might
want to defend it—that is, argue that it is true. When you do, the premise becomes the conclusion
of a new argument. However, every chain of reasoning must begin somewhere. If we ask a speaker
to defend each premise with a further argument, and each premise in that argument with a further
argument, and so on and so on, we eventually find ourselves being unreasonable, much like fouryear-olds who keep asking “Why?” until they become exasperating. If we ask a speaker why he
thinks the car has outlived its usefulness, he may mention that the car is hard to start. If we ask
him why he thinks the car is hard to start, he probably won’t know what to say.
Unstated Premises and Conclusions
Another complication is that arguments can contain unstated premises. For example:
Premise: You can’t check out books from the library without an ID.
Conclusion: Bill won’t be able to check out any books.
The unstated premise must be that Bill has no ID.
An argument can even have an unstated conclusion. Here is an example: Page 34
Conclusion Indicators
When the words in the following list are used in arguments, they usually indicate that a premise
has just been offered and that a conclusion is about to be presented. (The three dots represent
the claim that is the conclusion.)
Thus . . .
Consequently . . .
Therefore . . .
So . . .
Hence . . .
Accordingly . . .
This shows that . . . This implies that . . .
This suggests that . . .This proves that . . .
Example:
Stacy drives a Porsche. This suggests that either she is rich or her parents are.
The conclusion is
Either she is rich or her parents are.
The premise is
Stacy drives a Porsche.
The political party that best reflects mainstream opinion will win the presidency in 2020 and the
Republican Party best reflects mainstream opinion.
If a person said this, he or she would be implying that the Republican Party will win the presidency
in 2020; that would be the unstated conclusion of the argument.
Unstated premises are common in real life because sometimes they seem too obvious to need
mentioning. The argument “the car is beyond fixing, so we should get rid of it” actually has an
unstated premise to the effect that we should get rid of any car that is beyond fixing; but this may
seem so obvious to us that we don’t bother stating it.
Unstated conclusions also are not uncommon, though they are less common than unstated
premises.
We’ll return to this subject in a moment.
TWO KINDS OF ARGUMENTS
Good arguments come in two varieties: deductive demonstrations and inductive supporting
arguments.
Deductive Arguments
The premise (or premises) of a good deductive argument, if true, proves or demonstrates (these
being the same thing for our purposes) its conclusion. However, there is more to this than meets
the eye, and we must begin with the fundamental concept Page 35 of deductive logic, validity. An
argument is valid if it isn’t possible for the premise (or premises) to be true and the conclusion
false. This may sound complicated, but it really isn’t. An example of a valid argument will help:
Premise Indicators
When the words in the following list are used in arguments, they generally introduce premises.
They often occur just after a conclusion has been given. A premise would replace the three dots
in an actual argument.
Since . . .
For . . .
In view of . . .
This is implied by . . .
Example:
Either Stacy is rich or her parents are, since she drives a Porsche.
The premise is the claim that Stacy drives a Porsche; the conclusion is the claim that either
Stacy is rich or her parents are.
Premises: Jimmy Carter was president immediately before Bill Clinton, and George W. Bush
was president immediately after Bill Clinton.
Conclusion: Jimmy Carter was president before George W. Bush.
As you can see, it’s impossible for these premises to be true and this conclusion to be false. So the
argument is valid.
However, you may have noticed that the premises contain a mistake. Jimmy Carter was not
president immediately before Bill Clinton. George H. W. Bush was president immediately before
Bill Clinton. Nevertheless, even though a premise of the preceding argument is not true, the
argument is still valid, because it isn’t possible for the premises to be true and the conclusion false.
Another way to say this: If the premises were true, the conclusion could not be false—and that’s
what “valid” means.
Now, when the premises of a valid argument are true, there is a word for it. In that case, the
argument is said to be sound. Here is an example of a sound argument:
Premises: Bill Clinton is taller than George W. Bush, and Jimmy Carter is shorter than George
W. Bush.
Conclusion: Therefore, Bill Clinton is taller than Jimmy Carter.
This argument is sound because it is valid and the premises are true. As you can see, if an argument
is sound, then its conclusion has been demonstrated. Page 36
Inductive Arguments
Again, the premise of a good deductive argument, if true, demonstrates that the conclusion is true.
This brings us to the second kind of argument, the inductive argument. The premise of a
good inductive argument doesn’t demonstrate its conclusion; it supports it. For example:
After 2 P.M. the traffic slows to a crawl on the Bay Bridge.
Therefore, it probably does the same thing on the Golden Gate Bridge.
The fact that traffic slows to a crawl after 2 P.M. on the Bay Bridge does not demonstrate or prove
that it does that on the Golden Gate Bridge; it supportsthat conclusion. It makes it somewhat more
likely that traffic on the Golden Gate Bridge slows to a crawl after 2 P.M.
Here is another example of an inductive argument:
Nobody has ever run a mile in less than three minutes.
Therefore, nobody will ever run a mile in less than three minutes.
Like the first argument, the premise supports the conclusion but does not demonstrate or prove it.
If you are thinking that support is a matter of degree and that it can vary from just a little to a whole
lot, you are right. Thus, inductive arguments are better or worse on a scale, depending on how
much support their premises provide for the conclusion. Logicians have a technical word to
describe this situation. The more support the premise of an inductive argument provides for the
conclusion, the stronger the argument; the less support it provides, the weaker the argument.
Put another way, one argument for a conclusion is weaker than another if it fails to raise the
probability of the conclusion by as much. Thus, the first argument given above is weaker than the
following argument:
After 2 P.M. the traffic slows to a crawl on the Bay Bridge, the San Mateo Bridge, the San Rafael
Bridge, and the Dumbarton Bridge.
Therefore, it probably does the same thing on the Golden Gate Bridge.
This argument is stronger than the first argument because its premise makes the conclusion more
likely. The more bridges in a region on which traffic slows at a given time, the more likely it is
that that phenomenon is universal on the bridges in the region.
One more example of an inductive argument:
Alexandra rarely returns texts.
Therefore, she probably rarely returns emails.
Once again, the premise supports but does not demonstrate or prove the conclusion. The
differences between texting and emailing are sufficiently significant that the premise does not offer
a great deal of support for the conclusion, but it does offer some. If Alexandra rarely returned
telephone calls or letters as well as texts, that would make the argument stronger.
In Chapter 11 we will explain the criteria for evaluating inductive arguments. Page 37
BEYOND A REASONABLE DOUBT
In common law, the highest standard of proof is proof “beyond a reasonable doubt.” If you are a
juror in a criminal trial, evidence will be presented to the court—facts that the interested parties
consider relevant to the crime. Additionally, the prosecutor and counsel for the defense will offer
arguments connecting the evidence to (or disconnecting it from) the guilt or innocence of the
defendant. When the jury is asked to return a verdict, the judge will tell the jury that the defendant
must be found not guilty unless the evidence proves guilt beyond a reasonable doubt.
Proof beyond a reasonable doubt actually is a lower standard than deductive demonstration.
Deductive demonstration corresponds more to what, in ordinary English, might be expressed by
the phrase “beyond any possible doubt.” Recall that in logic, a proposition has been demonstrated
when it has been shown to be the conclusion of a sound argument—an argument in which (1) all
premises are true and (2) it is impossible for the premises to be true and for the conclusion to be
false. In this sense, many propositions people describe as having been demonstrated or proved,
such as that smoking causes lung cancer or that the DNA found at a crime scene was the
defendant’s, have not actually been proved in the logician’s sense of the word. So, in real life,
when people say something has been demonstrated, they may well be speaking informally. They
may not mean that something is the conclusion of a sound deductive argument. However, when
we—the authors—say that something has been demonstrated, that is exactly what we mean.
TELLING THE DIFFERENCE BETWEEN DEDUCTIVE
AND INDUCTIVE ARGUMENTS
A useful strategy for telling the difference between deductive and inductive arguments is to
memorize a good example of each kind. Here are good examples of each:
Valid Deductive Argument: Juan lives on the equator. Therefore, Juan lives midway between
the North and South poles.
Relatively Strong Inductive Argument: Juan lives on the equator. Therefore, Juan lives in a
humid climate.
Study the two examples so that you understand the difference between them. In the left example,
if you know the definition of “equator,” you already know it is midway between the poles. The
right example is radically different. The definition of “equator” does not contain the information
that it is humid. So:
If the conclusion of an argument is true by definition given the premise or premises, it is a valid
deductive argument.
Often it is said that a valid deductive argument is valid due to its “form.” Thus, consider this
argument:
If Juan is a fragglemop, then Juan is a snipette. Juan is not a snipette. Therefore, Juan is not a
fragglemop.
What makes this argument valid is its form: Page 38
If P then Q.
Not-Q.
Therefore not-P.
You can see, however, that ultimately what makes the argument valid, and makes its form a valid
form, is the way the words “If . . . then” and “not” work. If you know the way those words work,
then you already know that the conclusion must be true given the two premises.
Another way of telling the difference between a deductive argument and an inductive argument is
this: You generally would not say of a deductive argument that it supports or provides evidence
for its conclusion. It would be odd to say that Juan’s living on the equator is evidence that he lives
midway between the poles, or that it supports that claim. Thus:
If it sounds odd to speak of the argument as providing evidence or support for a contention, that’s
an indication it is a deductive argument.
It would sound very odd to say, “The fact that Fido is a dog is evidence Fido is a mammal.” Fido’s
being a dog isn’t evidence Fido is a mammal: it’s proof. “Fido is a dog; therefore Fido is a
mammal” is a valid deductive argument.
DEDUCTION, INDUCTION, AND UNSTATED PREMISES
Somebody announces, “Rain is on its way.” Somebody else asks how he knows. He says, “There’s
a south wind.” Is the speaker trying to demonstrate rain is coming? Probably not. His thinking,
spelled out, is probably something like this:
Stated premise: The wind is from the south.
Unstated premise: Around here, south winds are usually followed by rain.
Conclusion: There will be rain.
In other words, the speaker was merely trying to show that rain was a good possibility.
Notice, though, that the unstated premise in the argument could have been a universal statement
to the effect that a south wind always is followed by rain at this particular location, in which case
the argument would be deductive:
Stated premise: The wind is from the south.
Unstated premise: Around here, a south wind is always followed by rain.
Conclusion: There will be rain.
Spelled out this way, the speaker’s thinking is deductive: It isn’t possible for the premises to be
true and the conclusion to be false. So one might wonder abstractly what the speaker intended—
an inductive argument that supports the belief that rain is coming, or a deductive demonstration.
There is, perhaps, no way to be certain short of asking the speaker something like, “Are you 100
percent positive?” But experience (“background knowledge”) tells us that wind from a particular
direction is not a surefire indicator of rain. So Page 39 probably the speaker did have in mind
merely the first argument. He wasn’t trying to present a 100 percent certain, knock-down
demonstration that it would rain; he was merely trying to establish there was a good chance of rain.
You can always turn an inductive argument with an unstated premise into a deductively valid
argument by supplying the right universal premise—a statement that something holds without
exception or is true everywhere or in all cases. Is that what the speaker really has in mind, though?
You have to use background knowledge and common sense to answer the question.
For example, you overhear someone saying,
Stacy and Justin are on the brink of divorce. They’re always fighting.
One could turn this into a valid deductive argument by adding to it the universal statement “Every
couple fighting is on the brink of divorce.” But such an unqualified universal statement seems
unlikely. Probably the speaker wasn’t trying to demonstrate that Stacy and Justin are on the brink
of divorce. He or she was merely trying to raise its likelihood. He or she was presenting evidence
that Stacy and Justin are on the brink of divorce.
Often it is clear that the speaker does have a deductive argument in mind and has left some
appropriate premise unstated. You overhear Professor Greene saying to Professor Brown,
“Flunk her! This is the second time you’ve caught her cheating.”
It would be strange to think that Professor Greene is merely trying to make it more likely that
Professor Brown should flunk the student. Indeed, it is hard even to make sense of that suggestion.
Professor Greene’s argument, spelled out, must be this:
Stated premise: This is the second time you’ve caught her cheating.
Unstated premise: Anyone who has been caught cheating two times should be flunked.
Conclusion: She should be flunked.
So context and content often make it clear what unstated premise a speaker has in mind and
whether the argument is deductive or inductive.
Unfortunately, though, this isn’t always the case. We might hear someone say,
The bars are closed; therefore it is later than 2 A.M.
If the unstated premise in the speaker’s mind is something like “In this city, the bars all close at
2 A.M.,” then presumably he or she is thinking deductively and is evidently proffering proof that
it’s after 2. But if the speaker’s unstated premise is something like “Most bars in this city close at
2 A.M.” or “Bars in this city usually close at 2 A.M.,” then we have an inductive argument that
merely supports the conclusion. So which is the unstated premise? We really can’t say without
knowing more about the situation or the speaker. Page 40
Is an Ad Photo an Argument?
The short answer: No. The longer version: Still no. An advertising photograph can “give you a
reason” for buying something only in the sense that it can cause you to think of a reason.
A photo is not an argument.
The bottom line is this. Real-life arguments often leave a premise unstated. One such unstated
premise might make the argument inductive; another might make it deductive. Usually, context or
content make reasonably clear what is intended; other times they may not. When they don’t, the
best practice is to attribute to a speaker an unstated premise that at least is believable, everything
considered. We’ll talk about believability in Chapter 4.
BALANCE OF CONSIDERATIONS
Should I get a dog? Miss class to attend my cousin’s wedding? Get chemo? Much everyday
reasoning requires weighing considerations for and against thinking or doing something. Such
reasoning, called balance of considerations reasoning, often contains both deductive and
inductive elements. Here is an example:
Should assault weapons be banned? On the one hand, doing that would violate the Second
Amendment to the U.S. Constitution. But on the other hand, when guns were outlawed in Australia
the number of accidental gun deaths fell dramatically; that would probably happen here, too. It is
a tough call.
The first consideration mentioned in this passage—that banning assault weapons would violate the
Second Amendment and therefore should not be done—is a deductive argument. The second
consideration mentioned—that banning assault weapons would reduce the number of accidental
gun deaths—is an inductive argument.
Inductive arguments can be compared as to strength and weakness; deductive arguments can be
compared as t …
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