COMPLEX ARGUMENTS

COMPLEX ARGUMENTS
Well-Crafted Arguments
The first step in analyzing and evaluating an argument is to indicate which statements in a
passage are premises and which is the conclusion of the argument. For simple arguments, we
can distinguish the premises from the conclusion by underlining premises, double underlining
the conclusion, and ignoring any statements that are not part of the argument. (Using
LogicWorks, we made the distinction by dragging premises and conclusions to different boxes.)
Another technique is to construct what is sometimes called a “well-crafted version” of the
argument. This technique has the advantage of working for arguments that are more complex
than those we have considered so far.
In constructing a well-crafted version of an argument, we will always:
a. Write each premise and the conclusion on a separate line, with the conclusion coming
last.
b. Write the word “so” in front of the conclusion. (This will mean that any statement
without “so” in front of it will be understood to be a premise. It will also mean that we
will not need to use any other premise-indicators or conclusion-indicators.)
c. Number each statement in the argument (whether premise or conclusion).
d. Following the conclusion (and on the same line), place in parentheses the numbers of the
statements that are premises for the conclusion.
For an easy example, let’s apply these rules to a simple argumentative passage:
(A) Paloma has a very high fever. No one with a very high fever can take an exam.
Consequently, Paloma cannot take today’s exam.
A well-crafted version of (A) will look like this:
1. Paloma has a very high fever.
2. No one with a very high fever can take an exam.
So, 3. Paloma cannot take today’s exam. (1, 2)
The numbers in parentheses – (1, 2) – following the conclusion mean that statements 1 and 2 are
premises for the conclusion 3.
We have seen many examples of passages that look very different in English but are in fact just
different ways of expressing the very same argument. Constructing a well-crafted version of the
argument – however it might be expressed – will make this clear.

Consider, for example,
(B) Paloma cannot take today’s exam, for she has a very high fever. No one with a very
high fever can take an exam.
Here we must take advantage of the fact that “for” is a premise-indicator. That means that “she
has a very high fever” is a premise. And it also means that “Paloma cannot take today’s exam”
is a conclusion supported by that premise. This leaves just the third statement, “no one with a
very high fever can take an exam,” with an undetermined role. But we can see that both this
statement and the premise we already have are needed to support the conclusion. So, we should
consider it a premise. A well-crafted version of (B), then, is:
1. Paloma has a very high fever.
2. No one with a very high fever can take an exam.
So, 3. Paloma cannot take today’s exam. (1, 2)
And this is just exactly the same argument that was expressed by (A).
Complex Arguments
The argument expressed in (A) and (B) is typical of those we have so far considered in the
course: one or more premises lead directly to a single conclusion. But arguments are often
much more complex. In particular, arguments often contain one or more arguments as parts.
And when they do, one and the same statement may serve as a premise in one part of the overall
argument and as a conclusion in another part.
Consider (A) for example. It is easy to imagine that Paloma’s mother (for example) would not
simply stop with the conclusion that Paloma cannot take today’s exam. More than likely, she
would go on to argue that Paloma’s instructor should allow Paloma to make up for the missed
exam in some way. Her initial argument might be extended:
(C) Paloma has a very high fever. No one with a very high fever can take an exam.
Consequently, Paloma cannot take today’s exam. If Paloma cannot take today’s exam,
then she should be given a make-up. Therefore, Paloma should be given a make-up.
This argument has a new feature that we’ve not considered before. The statement, “Paloma
cannot take today’s exam” is (as it was in A) the conclusion from “Paloma has a very high fever”
and “no one with a very high fever can take an exam.” But now that very same statement is also
being used as a premise in a further argument: “Paloma cannot take today’s exam. If Paloma

cannot take today’s exam, then she should be given a make-up. Therefore, Paloma should be
given a make-up.”
The dual role of “Paloma has a high fever” is shown clearly in a well-crafted version of (C):
1. Paloma has a very high fever.
2. No one with a very high fever can take an exam.
So, 3. Paloma cannot take today’s exam. (1, 2)
4. If Paloma cannot take today’s exam, then she should be given a make-up.
So, 5. Paloma should be given a make-up. (3, 4)
By placing “so” in front of 3 and “(1, 2)” after, we indicate that 3 (“Paloma cannot take today’s
exam”) is a conclusion from 1 and 2. By placing “so” in front of 5 and “(3, 4)” after, we indicate
that 5 is a conclusion from 3 (“Paloma cannot take today’s exam”) and 4. So, we do indicate the
dual role of 3. And we also indicate that 5 (“Paloma should be given a make-up”), rather than 3,
is the final conclusion of the argument.
Constructing a well-crafted version of a complex argument is not always this easy. When the
structure of an argument is not immediately obvious, I would suggest that you go through these
steps:
First, carefully note all premise-indicators and all conclusion-indicators. (One good way to
do so is to circle all premise-indicators and to box all conclusion-indicators.) Don’t guess
about these! “Recognizing Arguments” on the course website (and included as a Study
Guide on LogicWorks) lists many of the most important premise- and conclusion-indicators.
Second, using the premise-indicators and the conclusion-indicators, identify as many
statements as you can as either premises or conclusions.
Third, try to identify the main or final conclusion of the argument. Place yourself in the
arguer’s position. The arguer’s goal is to provide reasons for believing that some conclusion
is true, and this conclusion is the statement that she or he is most interested in having you
believe. So, ask yourself: of all the statements presented in the argument, which one does
the arguer most want to convince me is true?
Fourth, again placing yourself in the arguer’s position, try to identify with his or her line of
reasoning. Read back to yourself your version of the argument. Does it make any sense? If
it doesn’t, then you probably have it wrong. (This applies even to invalid arguments. These

arguments will not “make sense” logically, but you should be able to see how the arguer
mistakenly got to his conclusion.)
Let’s apply these steps to the following passage:
(D) Paloma should be given a make-up. She cannot take today’s exam, for she has a very
high fever and no one with a very high fever can take an exam. And if she cannot take
today’s exam, Paloma should be given a make-up. Therefore, Paloma should be given
a make-up.
First, we note the premise-indicators and the conclusion-indicators.:
Paloma should be given a make-up. She cannot take today’s exam, for she has a very
high fever and no one with a very high fever can take an exam. And if she cannot take
today’s exam, Paloma should be given a make-up. Therefore , Paloma should be given
a make-up.
Second, we note that the premise-indicator “for” most likely means that “she has a very high
fever” and “no one with a very high fever can take an exam” are premises. If so, then “she
cannot take today’s exam” is a conclusion from those premises. The conclusion-indicator
“therefore” clearly indicates that “Paloma should be given a make-up” is a conclusion.
Third, we have found two conclusions in the passage and we need to determine which of them is
the main or final conclusion of the over-all argument. One conclusion is “Paloma cannot take
today’s exam”; the other is “Paloma should be given a make-up.” If I were Paloma’s parent
speaking on her behalf, I would be arguing for a make-up. (That would be my point in trying to
convince the instructor that Paloma can’t take the exam today.) I also note that the passage
begins with the claim, “Paloma should be given a make-up.” That gives me even more
confidence that this is what the arguer is most interested in arguing for.
Given these considerations, this seems to be a well-crafted version of the argument:
1. Paloma has a very high fever.
2. No one with a very high fever can take an exam.
So, 3. Paloma cannot take today’s exam. (1, 2)
4. If Paloma cannot take today’s exam, then she should be given a make-up.
So, 5. Paloma should be given a make-up. (3, 4)
Finally, let’s apply the fourth suggestion: reading the whole argument back to ourselves, does

the arguer’s line of reasoning make sense? In fact, the inference from 1 and 2 to 3 seems valid
(although we haven’t yet seen a method for showing that it is); and the inference from 3 and 4 to
5 is indeed valid, because it has the form modus ponens.
Our analysis of (C) and (D) shows that they, despite how different they at first appear, are in fact
expressions of the very same argument.
Exercise Set 6 will give you more practice in detecting the structure of complex arguments.