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Diagrams & Complex Reasoning
1 Basic Diagramming
1. In preparation for evaluating reasoning, it can be helpful to put the reasons and
target into standard form or a diagram, or both.
Standard form is the more basic of the two. Standard form lists each proposition
that is a premise or explainer on a separate line, then draws a horizontal line (with an "E"
or "J" to denote causal explanation or justification of belief), and finally, on a line by itself,
gives the proposition that is the conclusion or explainee. In this way, it is clear which
propositions are reasons and which is the target, and it is also clear what the individual
propositions are.
Diagramming illustrates the structure of the reasoning with arrows and other
symbols. This is particularly useful when analyzing long or complicated passages. A
diagram is accompanied by a numbered list of propositions. This facilitates diagramming
because only the number of each proposition is used in the diagram, which means that
there is more room to illustrate the structure.
2. Consider the following passage. The initial analysis has already been completed,
as per the instructions in Classifying & Analyzing Reasoning. In brief, the target is
underlined, each reason is bracketed, and both target and reasons are numbered. These
numbers are then used in the standard form.
The headmaster of a school is speaking to proud students and their parents. 1
McKinley is an excellent high-school. (It owes its excellence to) 2 [its dedicated
teachers], 3 [good leadership], 4 [modern facilities], and 5 [the support of parents.]
(1) McKinley is …
(2), (3), (4), (5) McKinley has …
In standard form, the explanation would be written as follows:
2. McKinley has dedicated teachers.
3. McKinley has good leadership.
4. McKinley has modern facilities.
5. McKinley has the support of parents.
E -------------------------------------------1. McKinley is an excellent high school.
This is all there is to standard form: a list of the reasons, a horizontal line, and the
target. Let's turn to diagramming.
3. Notice that standard form just lists the reason-propositions above the line
without telling us anything about how they work together (if they do). The equivalent
diagram is to draw an arrow with a split tail going from the numbers for the reasonpropositions to the target.
The diagram for the McKinley passage (here together with a list of the propositions
– notice that there is no horizontal line) is as follows:
2
1.
2.
3.
4.
5.
McKinley is an excellent high-school.
McKinley has dedicated teachers.
McKinley has good leadership.
McKinley has modern facilities.
McKinley has the support of parents.
As in standard form, we write a "J" (for "justifies believing") or (as in this case) "E"
(for "causally explains") next to the arrow in the diagram. This diagram can be read as "2
and/or 3 and/or 4 and/or 5 is supposed to explain 1.", or for short, "All or some of 2, 3, 4
and 5 is supposed to explain 1.".
One reason for starting with this example (about McKinley school) is that there is
no structure to the reasoning; there is simply a pile of reasons. This example involves
multiple reasons without any clues as to whether they form a single explanation or are
each a sufficient explanation of the school's excellence. This is very typical, since many
people do not give much thought to the structure of their arguments and explanations,
but simply provide a variety of different reasons (hopefully) justifying or explaining the
target. Here is another example of such reasoning:
(It's obvious why) 1 doctors are among society's most respected members. 2
[Doctors are paid well.] 3 [They are also known for their hard work] and 4 [they
help people in times of extreme need.]
This passage is best diagrammed as . . .
1.
2.
3.
4.
Doctors are among society's most respected members.
Doctors are paid well.
Doctors are also known for their hard work.
Doctors help people in times of extreme need.
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This diagram can be read as "2 and/or 3 and/or 4 is supposed to explain 1.", or for
short, "All or some of 2, 3 and 4 is supposed to explain 1.". Again, the speaker seems to be
throwing out a number of different considerations, without really knowing what
relationship, if any, the premises have to one another.
Here is a final example of a speaker who is simply throwing out reasons without
making clear whether they are individually sufficient or must be combined:
1 [Ireland has spectacular scenery] and 2 [mild weather throughout the summer.]
What's more, 3 [the dollar is strong against the euro right now.] (So), 4 Americans
should consider Ireland for their summer vacation.
Here the speaker presents three reasons which justify considering Ireland as a
place to spend one's summer holidays. It is not clear whether the reasons in this argument
are to be understood as together justifying the conclusion or whether we have three
independent arguments. You thus would diagram using a split-tailed arrow, just as in the
previous two examples.
In all of these three examples, the split-tailed arrow is the best we can do in terms
of diagramming the structure of the reasoning. The split tail represents the idea that you
do not know how many inferences or explanations there are, or what the structure of the
inference or explanation is. It is possible that any one of the reasons, or any subset of the
reasons, might be sufficient to justify or explain the target.
4. The split-tailed arrow is the basic arrow; you should always start by thinking of
the split-tailed arrow.
However, if the passage gives you more information or you can see how the reasonpropositions work together, you should advance beyond the split-tailed arrow.
One kind of structure is that a single reason in an inference or explanation can be
presented in multiple propositions. Consider the following passage:
I just heard that Jack got a dog, called Jim. (Since) 1 [Jim is a dog] and 2 [a dog
has a tail,] (I bet,) 3 Jim has a tail.
Even as you are reading the passage, you might see that the two premises work together
to express a single line of support for the conclusion, based on Jim's being a dog. The
appearance in both premises of the idea of 'being a dog' is a clue to the fact that they go
together to express a single line of support. If there is a single argument being expressed
in multiple premises, you can use the plus-sign ("+") instead of the split-tailed arrow. The
complete diagram, with its list of propositions, is as follows:
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1. Jim is a dog.
2. A dog has a tail.
3. Jim has a tail.
This diagram can be read as "(1) together with (2) provides a single line of support
intended to justify belief of (3).". Note that an arrow can point from a symbol which
groups together numbers (in this case, the plus-sign between (1) and (2)) but it must
always point at a (single) number.
4. Speakers might also add words or phrases which indicate that multiple separate
reasons must be added together. Consider the following argument, with its analysis
already completed:
1 [The new iPhone 3G allows you to access the internet using your phone.] When
you add the 2 [extensive coverage of AT&T,] 3 it's the obvious choice.
(2) = "The iPhone uses AT&T, which provides extensive coverage."
(3) "it" = The iPhone 3G
This passage contains multiple reasons (like the three split-tailed examples above
but unlike the 'Jim has a tail' example). In other words, the fact that the phone can access
the internet and the fact that AT&T has extensive coverage are separate considerations
and don't naturally fit together to express one reason. So perhaps the speaker intends that
each of these reasons, by itself, is enough to convince us to buy an iPhone 3G. But notice
the words "when you add"; these indicate that the speaker is not giving two arguments
but only one, and that the two reasons must be combined if the conclusion is to be
accepted. Although these are not two parts of a single line of reasoning (as in the example
about Jim), we diagram with a plus-sign between the numbers standing for the premises.
This is because the speaker has made it clear that if either reason is false, she thinks the
argument fails, just like when multiple propositions express a single reason. This
argument is diagrammed as follows:
1. The new iPhone 3G allows you to access the internet
using your phone.
2. The iPhone uses AT&T, which provides extensive coverage.
3. The new iPhone 3G is the obvious choice.
This diagram can be read as "(1) together with (2) is supposed to justify (3).".
Here is a version of the McKinley high school example, this time as an argument,
and with words which indicate that the support from the premises must be combined:
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A headmaster is speaking to prospective students and their parents: Many
reasons combine to make 1 McKinley an excellent high-school. It has 2 [dedicated
teachers,] 3 [good leadership,] 4 [modern facilities,] and 5 [the support of local
parents.]
(1) McKinley is …
(2), (3), (4), (5) McKinley has …
There are four lines of support in this set of propositions, and the speaker uses the
phrase "many reasons combine" to make clear that (he thinks) the conclusion follows
because the school has many beneficial factors. Diagram as follows:
1.
2.
3.
4.
5.
McKinley is an excellent high-school.
McKinley has dedicated teachers.
McKinley has good leadership.
McKinley has modern facilities.
McKinley has the support of local parents.
5. We have now seen examples of unstructured reasoning (or, a pile of reasons),
which is diagrammed with a split-tailed arrow, and of joined reasons (expressing a single
line of reasoning) and combined reasons, both of which are diagrammed with a plus-sign
and regular arrow.
A single passage can involve more than one of these types. Consider the following
argument, which involves two sets of joined premises, but no indication of whether the
two sets are separate arguments, or should also be combined:
1 [A lot of fruit is sweet,] and 2 [tomatoes are sweet.] What's more, 3 [apples are
fruit] and 4 [tomatoes are about the same size as apples.] (So), 5 tomatoes are fruit.
When we diagram, use plus-sign to make clear that there are two premises in each
set, but then use the split arrow to indicate the uncertainty about whether the two sets are
separate arguments or should be combined. The words "What's more" suggest that the
speaker is starting a new line of thought, but "what's more" doesn't make it obvious
whether the two sets should be combined, or are two separate arguments for the same
conclusion. (As mentioned already, people are often very sloppy in how they present
reasons and so you often have to use your judgment when thinking about whether you
can say anything about the structure of the reasons.)
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With the following key, the argument would be diagrammed as follows:
1.
2.
3.
4.
5.
A lot of fruit is sweet.
Tomatoes are sweet.
Apples are fruit.
Tomatoes are about the same size as apples.
Tomatoes are fruit.
The first plus sign indicates that (1) and (2) form a joined line of support. The same
is true of (3) and (4). Between the two pairs, however, we use the split arrow, to indicate
that either one might be sufficient to convince us of the conclusion.
6. Note that a single passage can contain multiple inferences or explanations, and
these can be for different targets or for a single target. Consider the following passage:
1 Downloading music from peer-to-peer services should be prosecuted vigorously.
2 [If it is not, young people will not appreciate the creative talent of musicians.]
Alternately, 3 [record companies will go out of business.] When it comes right
down to it, 4 [it's simply a form of theft.]
(2), (3) "If downloading is not prosecuted vigorously, . . ."
(4) Downloading music from peer-to-peer services …
(1) is the conclusion. The main clue as to the relation of (2), (3), and (4) to (1) is the
word "Alternately" prior to (3) and then the words "And when it comes right down to it",
prior to (4). Each of these suggests not only that there are separate lines of support, but
that the speaker thinks each of them is sufficient to justify the conclusion. There are, thus,
three arguments, all for the same conclusion. In diagram form, these would be presented
separately, each with (1) as the conclusion. In the first, (2) is the premise. In the second,
(3) is the premise. In the third, (4) is the premise. Diagram in either of these ways:
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or
When trying to decide how many inferences/explanations there are, a
key question to ask yourself is: Do I think that the speaker thinks that the reasons
(together – either because joined or added) are needed to justify/explain the target, or
does the speaker think that each one (or subsets of them, but not all of them) are
sufficient? If the former, your diagram will use the plus-sign and have a single arrow. If
the latter, your diagram will have multiple arrows from the reason(s) to the target. And if
you can't tell, use the split-tailed arrow.
7. Separate explanations and arguments for the same target proposition can
appear in a single passage. For example:
Jones:
Smith:
Jones:
Smith:
Jones:
1 The reservoir is at a low level.
It is? How do you know?
2 [I just walked by there this morning.]
Huh. I wonder why.
It's because of 3 [several releases to protect the downstream ecology.]
(2) I = Jones; there = the reservoir
(3) There have been …
Again, one option is that you could simply diagram the argument and the
explanation separately, as follows:
1. The reservoir is at a low level.
2. Jones walked by the reservoir this morning.
and
1. The reservoir is at a low level.
2. There have been several releases
to protect the downstream ecology.
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But since they refer to the same target proposition you could also put them in the
same diagram, as follows:
1. The reservoir is at a low level.
2. Jones walked by the reservoir this morning.
3. There have been several releases
to protect the downstream ecology.
2 Summary — Basic Diagramming
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Exercises
(i) Analyze the passage. (Classifying will be done in step (v).)
(ii) Give a list of propositions.
(iii) Diagram the reasoning. (There is no need to make a new list of propositions; use the
numbers from the analysis.) (If editing in Drive, create a diagram using 'Insert >
Drawing'.)
(iv) Explain your diagram in writing.
(v) Use "J" or "E" in your diagram in order to to classify the reasoning as either Justifying
Belief or Causally Explaining. Explain your classification as necessary.
Sample: 1 [Chicago is north of Columbus], and 2 [it is north of Miami]. And, of course, 3
[Miami is north of Memphis]. (Therefore), 4 Chicago is north of Memphis.
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1.
2.
3.
4.
Chicago is north of Columbus.
Columbus is north of Miami.
Miami is north of Memphis.
Chicago is north of Memphis.
I put all three reasons together (joined reasons) because the three pieces of
geographical information are related to another by the repetition of cities –
Chicago appears in 1 and 2 and Miami appears in 2 and 3.
1. A proposal at a business: Since outsourcing jobs to foreign countries is often more
cost-effective than doing them in-house, we [Acme Incorporated] should look into
finding foreign companies to take care of our customer service.
2.
A terrible realization: Chips Ahoy cookies aren't healthy food, and neither are
Oreo cookies. So, I guess Girl Scout Cookies aren't healthy!
3.
Smith is talking to Jill: I can't go to yoga today. I am too busy at work. And even if
I weren't, I pulled a muscle last time and I need to rest it.
4.
Child to Dad: There are lots of reasons we should get a dog, Dad. They're good
company, promote exercise, and can protect the house during the day when we're at work.
5.
Part of a conversation at Championship Records: How can we explain the
remarkable fact that people still remember Wheatus's song "Teenage Dirtbag" ten years
after it was a hit? In a word: catchiness.
6.
A detective inspects a burgled premises. There are no marks on any of the doors
or windows. Therefore, the burglar must have had a key to the premises.
7. A university president speaks: Hingson's report from 2005 found that 1700 (U.S.)
students died from alcohol-related injuries and 600,000 more were non-fatally
injured. Hingson's report is reliable. It follows that many college students these days
drink too much.
8. At a school board meeting: Since creationism can be discussed effectively as a
scientific model, and since evolutionism is fundamentally a religious philosophy
rather than a science, it is unsound educational practice for evolution to be taught and
promoted in the public schools to the exclusion or detriment of special creation.
(Kitcher (1982) p. 177, citing Morris.)
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9.
On the side of a carton of orange juice: Oranges are high in vitamin C. Fruit that's
high in vitamin C helps fight colds. So, oranges help fight colds.
10.
Bill is trying to get Henry to quit: You should give them up. Cigarettes are bad for
your health. And they make you smell, too.
11.
Smith: Is that the new Android phone?
Jones: Yes. I got it because it has great battery life and cool apps. And it
automatically knows not to ring when I'm in a meeting.
12.
At a lecture on women's suffrage in the US: Women were not citizens in
nineteenth century USA. because a citizen is someone who is eligible, under the
constitution of the nation, to participate in some form of judgment or deliberation, and at
the time, women were not eligible to vote or serve on juries.
Answers to 2, 6, 8
2. A terrible realization: 1 [Chips Ahoy cookies aren't healthy food,] and 2 [neither are
Oreo cookies]. (So,) 3 I guess Girl Scout Cookies aren't healthy!
1. Chips Ahoy cookies aren’t healthy food.
2. Oreo Cookies aren’t healthy.
3. Girl Scout Cookies aren’t healthy.
Joined reasons. When people argue from instances of a type (in this case, Chips Ahoy and
Oreos as different kinds of cookie) they argue (implicitly) not only on the grounds that,
because there are two kinds of unhealthy cookie, a third kind is likely to be unhealthy, but
also
that
these
two
are
representative
of
all/most
cookies.
('Added support' would be acceptable
Definitely not unstructured, since we are dealing with instances of a type. Arguing from
instances is a natural and familiar way of arguing.)
6. A detective inspects a burgled premises. 1 [There are no marks on any of the doors]
2 [or windows.] (Therefore,) 3 the burglar must have had a key to the premises.
1. There are no marks on any of the doors.
2. There are no marks on the windows.
3. The burglar had a key to the premises.
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2 = There are no marks on the windows
I tend to leap to 'joined', as I'm thinking that the speaker is arguing that the doors and
windows are the only ways to get into the building, and so the speaker has eliminated all
of the possible options, except using a key.
8.
At a school board meeting: (Since) 1 [creationism can be discussed effectively as a
scientific model,] and (since) 2 [evolutionism is fundamentally a religious
philosophy rather than a science,] 3 it is unsound educational practice for
evolution to be taught and promoted in the public schools to the exclusion or
detriment of special creation. (Kitcher (1982) p. 177, citing Morris.)
1. Creationism can be discussed effectively as a scientific model.
2. Evolutionism is fundamentally a religious philosophy rather than a science.
3. It is unsound educational practice for evolution to be taught and promoted in the
public schools to the exclusion or detriment of special creation.
Joined reasons. Since the conclusion concerns the relative educational status of two
things, the speaker intends (1) and (2) to be joined in a single line of argument.
3 Reasoning With A Conjunction In The Target Proposition
1. The word "and" is often used to conjoin propositions. The chapter on basic
analysis advises that when an "and" appears in the reasons (and is being used to conjoin
two propositions) you should split the long proposition into two separate propositions.
What about when the target proposition (the conclusion or the explainee) is a
conjunction? Consider the following passage:
At the pet store: Labs aren't known as good guard dogs, but they do make great
pets for young children. The reason is because they are gentle and friendly dogs.
When analyzing we divide each sentence into two. The first is divided into "Labradors are
not known as guard dogs." and "Labradors make great pets for young children.". The
second is divided into "Labs are gentle." and "Labs are friendly.". How should we diagram
this? If the conclusion were a premise, we would simply divide it into its component
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propositions and write each of them down. Following this practice with the conclusion
would give us something like this:
or perhaps
(There is a plus-sign between (1) and (2) because the words "The reason is …" in the
original passage suggest that the support from the two reasons is being combined.) But
neither of these make any sense. In the first one, a comma is not one of the symbols we
use in diagramming. The second runs into the problem that an arrow must point at a
number (not a plus-sign). They both violate the rule that explanations and inferences only
have one target.
We cannot simply pick one — either (3) or (4) — and discard the other because the
speaker is not trying to explain (3) or (4), but both (3) and (4). We must therefore break
the passage into two independent explanations, as follows:
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Since the reasons are the same in both, we could combine the two diagrams above
into one, with two arrows from the reasons, one to each of the conclusions, and each
labeled as an explanation, as follows:
Conjunctions can be expressed in a variety of ways and so sometimes the two
conclusions which follow from the same set of premises might not be presented using
"and". It is also possible that they might be presented in different sentences entirely. An
arguer might use some variant, for example by drawing one conclusion and then saying
"It also follows from these considerations that … ." and go on to state another conclusion.
4 Compound Reasoning
1. Inferences or explanations can be made by arguing first for one target
proposition (which we will call an interim target) and then using that proposition as a
reason to infer or explain another target. These are compound or extended inferences or
explanations. An inference or explanation is compound when one or more propositions
functions as the target in one part of the reasoning and as a premise in another.
2. Consider the following example:
Honey is produced by bees, which live naturally. As a result, honey is natural.
Natural things are good for you. So, honey is good for you.
This is a compound inference. In this inference, the speaker initially argues for (3)
"Honey is natural.", and then adds (4) "Natural things are good for you." in order to
conclude (5) "Honey is good for you." In this inference, (3) is both a conclusion and a
premise. It is the conclusion following from (1) and (2) together, and it is a premise which,
along with (4), supports (5). Using the procedure in Classifying & Analyzing Reasoning,
we would both underline and bracket (3), as follows:
1 [Honey is produced by bees], 2 [which live naturally]. (As a result,) 3 [honey is
natural.] 4 [Natural things are good for you.] (So), 5 honey is good for you.
(2) "which" = "bees"
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Notice that proposition 3 is both bracketed and underlined. It is underlined
because it is the target of 1 and 2, and it is bracketed because it is a reason, along with
4, for 5.
Here is a list of propositions and a diagram for this inference:
1. Honey is produced by bees.
2. Bees live naturally.
3. Honey is natural.
4. Natural things are good for you.
5. Honey is good for you.
Keep the ultimate conclusion at the end and write the reason which most
immediately justify it above it. The reasons which justify line (3) are written above it.
There are two sub-inferences: the first involves (1) and (2) justifying (3); the second
involves (3) and (4) justifying (5). (3) is common to both, as the conclusion in the first and
a premise in the second.
3. Consider the following inference:
Prenatal genetic testing, even for fatal diseases, should be outlawed. This is
because such testing will surely lead people to start testing for non-essential
qualities, such as intelligence and height. The reason for this is that people cannot
help but try to get an advantage over one another. This comes from our
evolutionary background and the scarcity of mates.
Each sentence is a single proposition. Assigning numbers to the propositions, we get:
1 Prenatal genetic testing, even for fatal diseases, should be outlawed. (This is
because) 2 [such testing will surely lead people to start testing for non-essential
qualities, such as intelligence and height.] (The reason for this is that) 3 [people
today cannot help but try to get an advantage over one another.] This comes from
4 [the competition for mates in our evolutionary past.]
(2) "such" = "pre-natal genetic"
(4) There has been …
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Here is a list of the propositions and a diagram. (Notice that the word "surely" has been
removed from proposition 2 — it's not part of the proposition; and don't let anyone tell
you how good their reasoning is; that's up to you to decide!):
4.
3.
2.
There has been competition for mates in our evolutionary past.
People today cannot help but try to get an advantage over one another.
Prenatal genetic testing, even for fatal diseases, will lead people to start testing
for non-essential qualities, such as intelligence and height.
1. Prenatal genetic testing, even for fatal diseases, should be outlawed.
(1) is the ultimate target conclusion, and is supported by (2). This is one of the subinferences. (2), in turn, is supported by (3). This is another sub-inference. Last, (3) is
supported by (4). So in this kind of compound inference, the premise for the main
conclusion is itself the conclusion of another sub-inference, and the premise in that
inference is the conclusion of a third sub-inference, and the premise in that inference is
the conclusion of a fourth sub-inference, and so on.
4. You might notice that the passages are generally getting longer. Consider the
inference in the following passage:
1 Smith would make an excellent choice as our candidate. 2 [He is a superior
speaker,] as is clear from the fact that 3 [his performance at the debate last week
was great] and 4 [he has performed well any time he has appeared on the Sunday
political shows.] 5 [He is also a great fund-raiser] — 6 [he has raised over a million
dollars in the week since the Pennsylvania primary.] 7 [He also uniquely appeals
to a broad cross-section of the population.] 8 [He has polled well across all major
demographics (except Hispanics and those in the upper fifth of income).]
(2), (3), (4), (5), (6), (7), (8) He/His = Smith/Smith's
It's long, but it shouldn't frighten you. This structure of the reasoning is fairly
straightforward. The phrase "As is clear from the fact that" functions as a premise
indicator. There are no conclusion flag words. (1) — the claim that Smith is the better
candidate — is the main conclusion. (2), (5), and (7) — that he is a superior speaker, an
excellent fund-raiser, and appeals to a broad cross-section of society — are intended to
convince us of (1), and each is a separate line of inference and it is not clear whether all
three are needed to convince us of the conclusion. (3) and (4) are supposed to justify (2),
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and might each do so independently. (6) is supposed to justify (5). (8) justifies (7).
Diagram as follows:
Exercises
(i) Analyze the passage. (Classifying will be done in step (v). Re-writing will be done in
step (ii).)
(ii) Give a list of propositions. Each item should be a free-standing proposition.
(iii) Diagram the reasoning using the numbers from the list. (If editing in Drive, create a
diagram using 'Insert > Drawing'.)
(iv) Explain your diagram in writing.
(v) Use "J" or "E" in your diagram in order to to classify the reasoning as either Justifying
Belief or Causally Explaining. Explain your classification as necessary.
Sample: Smith notices that Jones doesn't eat potatoes: 1 [Potatoes are vegetables], and 2
[vegetables are good for you]. (So), 3 [potatoes are good for you]. 4 [They're also
cheap]. (So), 5 you should be sure to include them in your diet.
1.
2.
3.
4.
5.
Potatoes are vegetables
Vegetables are good for you.
Potatoes are good for you.
Potatoes are cheap
You should include them in your diet.
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(iv) I put 1 and 2 together (joined reasons) because they're both about vegetables – 1 is
specifically about potatoes as a vegetable and 2 is about vegetables generally. I put 3 and
4 together (added reasons) because of "also" and because the speaker doesn't assert the
target until after 4.
1. Jones says: House-builders work awfully hard. Their workday is longer than 8 hours;
the job involves heavy lifting; there's the possibility of accidents; they also have to
contend with the weather.
2.
Jack and Henry are at the park with Jim the Great Dane: Jim will go after
anything interesting he gets a whiff of. It looks like he's smelling something right now. So,
he'll go running after it. We don't want to lose him. So, hold on to the leash tightly.
3.
In a letter to the editor: The oil leak in the Gulf happened because of Deepwater
Horizon's poor workmanship and its lax safety standards. Since those who are responsible
should pay for the resulting costs, Deepwater Horizon should pay for the costs
4.
An employee is discussing the future of a colleague: Most bosses fire employees
who don't show up on time without a good reason. Cindy never shows up on time. She has
no excuse — she lives only two minutes from her place of employment. So, the boss should
fire her.
5.
Jack is worried about the impact of antidepressants: When people are happy, they
don't strive as much as when they are not. This follows from the fact that slightly less
happy people are more successful than those who are completely content with life.
Antidepressants make people feel happy when they otherwise might not. As a result,
antidepressants should be used only in extreme situations.
6.
A political pundit speaks: Gas prices are rising sharply due to a shortage in refining
capacity. So, the oil companies should increase refining capacity, and the government
should be active on the world political stage.
7.
A member of the jury speaks: The old woman's testimony is questionable, since
she was 60 feet away and it was nighttime. And the man's testimony is dodgy, too — how
could he have heard the fight with the train rolling by? Those are the only witnesses to the
crime. So, we don't know for certain that the accused is guilty. (Based on 12 Angry Men)
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8.
Apes and chimps are not completely human. And so, research done with them in
order to gain insights into the human condition is flawed. Flawed research is not worth
funding. So, psychological research on apes and chimps is not worth funding. Another
reason not to fund such research is that apes and chimps are sentient beings, and so it's
not right to do research on them that wouldn't be done on humans.
9.
Socrates is speaking at his trial: My accuser says I believe in spiritual matters but
that I don't believe in gods. Now, who could believe in spiritual matters without believing
in spirits? So, I believe in spirits.
Spirits are the offspring of gods and since no one can believe in the offspring
and not believe in the parents, then, of course, I must believe in gods.
So, it's clear that contradicts himself, and so, that he doesn't know what he's
talking about. (Based on Plato's Socrates' Defense)
Answers To Selected Exercises
4. 1 [Most employers fire employees who don't show up on time without a good reason.]
(2) [Cindy never shows up on time.] (3) [She [= Cindy] has no excuse] — (4) [she
[= Cindy] lives only two minutes from her place of employment]. So, (5) she
[Cindy] should be fired by her employer.
1.
2.
3.
4.
5.
Most employers fire employees who don't show up on time without a good reason.
Cindy never shows up on time.
Cindy has no excuse.
Cindy lives only two minutes from her place of employment.
Cindy should be fired by her employer.
1, 2, and 3 are joined: 1 is a general principle about what happens to people who are noshows without excuses and 2 and 3 state that Cindy falls into both of these categories.
6.
1 [When people are happy, they don't strive as much as when they are not.] 2 This
follows from the fact that [slightly less happy people are more successful than those
who are completely content with life.] 3 [Antidepressants make people feel happy
20
when they otherwise might not.] (As a result,) 4 antidepressants should be used
only in extreme situations.
1. When people are happy, they don't strive as much as when they are not.
2. Slightly less happy people are more successful than those who are completely content
with life.
3. Antidepressants make people feel happy when they otherwise might not.
4. Antidepressants should be used only in extreme situations.
1 and 3 are joined – the connection between them is happiness: less happy people are
more successful and antidepressants make people happier
9. 1 [My accuser says I [Socrates] believe in spiritual matters] but 2 [not in gods.] Now,
3 [who could believe in spiritual matters without believing in spirits?] (So,) 4 [I
believe in spirits.] 5 [Spirits are the offspring of gods] and (since) 6 [no one can
believe in the offspring and not believe in the parents,] then, of course, 7 [I must
believe in gods.] (So,) it's clear that 8 [he [the accuser] contradicts himself,] and
(so,) that 9 he [the accuser] doesn't know what he's talking about. (Based on Plato's
Socrates' Defense)
3 is a rhetorical question — the answer is 'No one (can believe in spiritual matters …)'
1.
2.
3.
4.
5.
6.
7.
8.
9.
The accuser says Socrates believes in spiritual matters
Socrates' accuser says he doesn't believe in gods.
No one can believe in spiritual matters and not believe in spirits.
Socrates believe in spirits.
Spirits are the offspring of gods.
No one can believe in the offspring and not believe in the parents.
Socrates believes in gods.
The accuser contradicts himself.
The accuser doesn't know what he's talking about.
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1 and 3 are joined by being about 'spiritual matters' and combine to reach 4. 4, 5, and 6
are joined by being about how spirits are the offspring of gods and so if you believe in
one you believe in the other. This leads to 7, that Socrates believes in gods. 7 and 2 have
to go together because they are contradictories – the accuser says that Socrates both
believes and doesn't believe in gods – which proves 8 – that he has contradicted himself.
5 Diagramming Dialogue
1. So far in this chapter, we have focused on diagramming the reasons which justify
or explain a target proposition. But inferences and explanations sometimes aren't
immediately successful and are subject to objection. The objection(s) can then be
supported with reasons or can be countered by reasons.
2. When the original speaker (person A) has put forward a reason which is
supposed to justify or explain a target, the second speaker (person B) can raise two types
of objection against the inference or explanation. He can object that (i) one or more of the
propositions expressing the reason(s) is false or that (ii) the reason, even if true, does not
justify or explain the target.
Imagine that speaker A presents the following inference to B:
1 [Bill Gates does not own lots of gold.] 2 [If Bill Gates owns lots of gold, Bill Gates
is rich.] (So,) 3 Bill Gates is not rich.
B might now respond with an objection of either type. Various words or phrases
will tell you which kind of objection he is making.
To indicate an objection to a reason, B might respond by saying "Your premise is
false.". There are other phrases, not from the study of logic or argumentation which can
be used to indicate criticism of a premise, such as "You have your facts wrong." and
"Actually, no.". (There is a risk of ambiguity with phrases which challenge the truth of a
proposition, as these could be used as a challenge to either the target or to the premise.
The word "facts" in "You have your facts wrong.", or "evidence" or "data" might more
strongly suggest the premise.)
22
To indicate an objection to the reasoning (the strength of the connection between
the reasons and the target), he might use the language of argumentation and logic.
Phrases such "That inference is weak." or "That's not a valid argument." indicate
dissatisfaction with the inference using language from logic. Less formal ways of stating
that an inference is weak include "That doesn't follow.", "That won't explain what
happened.", "That's not much to go on." or (especially for practical reason, where the
speaker is trying to convince the audience to do something) "You'll need more than that
to convince me.".
Unfortunately, some of the vocabulary of logic used to flag an objection has entered
into everyday English and lost its precision. So you have to be careful in interpreting the
words the objector uses to introduce his objection.
"Not valid", for example, has come to be applied to propositions as well as to the
reasoning, and so can be ambiguous. At present, in fact, "(not) valid" is applied to
standpoints as much as if not more than to the inference. Another problem with "valid" is
that is that it is often used just to mean "worth considering" or "having some weight",
whereas valid reasoning is a guarantee of a conclusion's truth, assuming the premises are
true.
Like "valid", "fallacious" is also now applied to propositions as well as to reasoning.
For example, "Rosetta [Tharpe] is often seen as a country singer, but that's a fallacy." (PBS
American Masters, Godmother of Rock'n'Roll.) An argument is perhaps implicit, as
though the speaker were saying "Whatever reasons people have for thinking Tharpe was
a country singer are insufficient.", but those reasons haven't been presented.
A logic student hearing "not necessarily" would think that a purportedly valid
inference is being criticized. However, "not necessarily" is sometimes used to mean "The
target is not necessarily true." even in the absence of reasons from A. B might use it to be
polite, indicating with "not necessarily" that A's target is true in some or many cases
before pointing out the exceptions. For example:
A: A mother would never hurt her children.
B: That's not necessarily true.
As a result, someone who says "not necessarily" in the context of an argument might be
commenting on either the reasoning or a specific proposition. For example:
A: A mother would never hurt her children. After all, they're her own flesh and blood.
B: That's not necessarily true.
The upshot of these remarks is this: in this book you are learning the precise
meaning of various terms (such as "valid", "fallacious" and "(not) necessarily)") in the
context of reasoning, but many everyday speakers use these terms loosely and so you
cannot rely on them unthinkingly when you see them in everyday discourse.
A speaker will sometimes make it clear that he is objecting to the reasoning rather
than a reason by noting that the reason is true. Consider the following exchange:
A: Warren Buffett lives in a fairly regular house in Omaha, Nebraska. He isn't rich.
B: That's true, but he could still be rich.
23
Here, B concedes the truth of the reason but expresses non-agreement with the target.
This means that he is criticizing the reasoning – the reasons (even though they are true)
are not sufficient to justify belief of the target.
Some indicator phrases are designed to work like this, admitting the reason but
doubting the inference and so the target: "Even so, …", "And yet …", "Yeah, but …", and
verbs and adverbs indicating concession, such as "I concede … but …", "I grant … but …",
"Admittedly … but …". Here is another example:
A: Large lectures are an efficient use of faculty. We should increase the number we
offer and do away with some low-enrollment courses.
B: Efficiency is important, of course, and large lectures might be OK for some
courses, but pedagogical concerns are more important …
B grants the premise, that large lectures are efficient, but thinks there are other
considerations, which A has omitted. He thus is objecting to A's reasoning.
Here is another example, in which B accepts the premise, rejects the target, and so,
must think that the reasoning is weak:
A: 1 [Warren Buffett can't be very rich]. 2 [He lives in Omaha, Nebraska.]
B: Even so, I think 3 [he is].
(1) "can't be" = "is not"
(2), (3) "he" = Warren Buffett
The "can't" in proposition (1) suggests that (1) is a conclusion, with (2) as the supporting
premise. In B's reply, "even so" grants the truth of the premise and "I think he is."
expresses non-agreement with the target (and indeed, expresses a counter-position). As
a result, B must think A's inference is weak, even though no objection to it is articulated
or no flag word specific to objecting to the reasoning is used.
4. To diagram the mere fact that speaker B objects, we can use the dashed arrow
pointing at the arrow representing the reasoning (on the left) or at the number standing
for the reason (on the right).
The arrow diagrams the objection flag word or phrase, or the fact that speaker B
objects.
The objection itself (that is, the proposition) is given a number and can be added
to the diagram.
In the case of Bill Gates not owning a lot of gold, the audience might say something
like "But there are other ways he could be rich besides owning lots of gold, such as owning
lots of gems.". This is an objection to the strength of the reasoning, not a criticism of the
24
reason, and so we are using the diagram on the right. The objection itself is added (as
number (4)) to the diagram:
Notice three things: (i) the arrow has a dashed shaft – this tells us that it is an
objection; (ii) the objection-arrow points upwards – this is because the arrows
representing objections go in the opposite direction from the arrow involved in the
inference or explanation that is being objected to, which in this case is the downward
arrow from "1 + 2" to 3; (iii) the objection-arrow points at the initial arrow – the objection
is not to the truth of either reason but to the reasoning (the connection between reasons
and target).
5. For an example of an objection to the truth of a reason (a premise or explainer),
we turn to Monty Python's celebrated "Argument Clinic" sketch. At one point, Michael
Palin's character is trying to convince John Cleese's character that he has paid him some
money so that Cleese will argue with him. The dialogue proceeds as follows:
Palin: 1 [If you are arguing, I paid.] 2 [You are arguing.] (So), 3 I paid.
Cleese: 4 [I could be arguing in my spare time.]
With his objection (4) Cleese challenges the truth of the first premise. It could be
false, he says, that arguing indicates that he was paid, since he could be arguing without
having been paid. He is not challenging the reasoning, the connection between the
premises and the conclusion; if premises (1) and (2) were true, the conclusion would also
be true.
To represent the objection in a diagram, draw a dashed arrow, again pointing in
the opposite direction to the original arrow, but this time pointing at the premise whose
truth is being doubted:
6. The objector might give reasons in support of the objection, whether the
objection is an objection against a reason or against the reasoning. In the example just
above, Cleese might support his objection to Palin's reason (that he could be arguing in
his spare time) by saying (5) "I really like arguing a lot.". This would be added to the
diagram as follows:
25
Notice two things: the arrow between 5 and 4 is a solid arrow and it points upward.
It is a solid arrow because 5 is supporting 4 and we diagram support with a solid arrow.
It points upward because 4 points upward (against 1) and 5 helps 4.
Support for an objection to the reasoning would look similar, except that the
objection-arrow would go against the initial arrow rather than against the number
standing for the reason.
7. Here are two points to note when diagramming any objection (whether an
objection to a reason or an objection to the reasoning). You do not need to label arrows
representing an objection with an "J" or an "E", because objections are all argumentative.
This is true even when A gives an explanation: if B lodges an objection to the explanation,
A and B are now arguing about the quality of the explanation. Consider the following
dialogue:
Jack: Did you hear that the game is cancelled?
Jill: I did. Do you know why it is cancelled?
Jack: It's because of the heavy rain we had yesterday.
Jill: I doubt that—the new drainage system should be able to handle the rain.
Jack: Maybe it is malfunctioning …
When she speaks for the second time, Jill doubts that the explanation offered is
correct. Jack seems to concede Jill's criticism because he attempts to improve his
explanation.
Second — and this one is most important — you might be tempted to include the
words or phrases that the speakers use to describe their disagreements as propositions
and to include them in the diagram. This is a mistake. The diagram will show what kind
of objection is being made and the diagram will show that there is disagreement. Thus,
do not include anything like "I disagree.", "I don't that that follows." or "The conclusion
does not follow from your reasons".
Here is an example:
Jack: 1 I was late to work this morning because 2 [the traffic was terrible].
26
Jill: But 3 [you left so early]! I don't buy your explanation.".
The diagram for is passage is below. Jill does not disagree that the traffic was bad;
she only questions whether the bad traffic is a good explanation for Jack's lateness.
Diagram as follows:
Notice that the sentence "I don't buy your explanation." is not given a number and
it is not included in the diagram. This is because these words merely make explicit the
idea that Jill thinks Jack's explanation is insufficient, and the diagram shows this, by
including (3) as an objection against the solid arrow.
8. Once an objection has been made, the proposition(s) expressing the objection
can become the subject of further argument.
A rebuttal is an objection to an objection, and it is with rebuttals that the reason
for having arrows of two types (solid and dashed) and in two directions (upward and
downward) become useful. If speaker A objections to B's objection, the arrow will be
dashed and point downward. In the following diagram, the arrow from (5) indicates that
(5) is a reason for thinking that (4)'s challenge to the truth of (1) is not successful.
In response to the rebuttal (5), an re-rebuttal might be given, either against the
truth of 5 or against the 5's power to block 4 as an objection to 1. As an objection to the
truth of 5, we would diagram as follows:
9. In sum:
A solid arrow means "is a reason for accepting"
A dashed arrow means "is a reason for not accepting" and has two
specific forms depending on what it points at: if it points at a number
representing a proposition (whether premise or target), it means "is
a reason for not accepting as true"; if at an arrow, it means "is a
reason for not accepting as sufficient".
The direction (upward or downward) of each arrow depends upon its
role in the overall diagram.
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6 Analyzing Long Passages
1. With the inclusion of objections and rebuttals, the passages are beginning to get
longer and more complex. Let's pause to make two important points. These two points
are so important that they get their own section.
The first is something that has been said already, but which bears repeating.
Speakers presenting complex inferences or explanations often include phrases which tell
the audience what the impact of a new proposition is. For example, a speaker might say
"that (premise) is false, because of …." or "that (target) is not explained by (4) and (5),
because of (6).". There is no need to include these remarks about the impact of the
objection as propositions in the diagram. The positioning of the arrows in the diagram
will show what work the new proposition is doing. In the complex diagram above, you can
see that (4) challenges the truth of (2) and that (7 + 8) rebuts (9)'s objection to the truth
of (3).
Similarly, objectors will often comment on the quality of the reasoning they are
responding to, by saying such things as "That's obviously wrong." or "The reasoning is
unsound." or "Your belief is baseless." or "That's a bunch of B.S." or lots of other things.
Again, there is no need to include these remarks about the quality of the
reasons/reasoning/target as propositions in the diagram. The diagram will show these
comments.
2. Second, objections (and support for and rebuttals to them) often appear in
passages delivered by a single speaker. In such cases, you should expect to see a (brief)
summary of an initial inference or explanation, and then, in full propositions, the
objection(s). The summary of the initial reasoning is often flagged with a phrase
attributing the inference to some person(s) such as "the editorial in today's newspaper
argues …" or "my opponents argue …" or "Dr. Cornmire explains that …". The difficulty
here is that the speaker will (often) not present the inference or explanation being
criticized one proposition at a time. It is your job, in such cases, to extract the information
you need, put it into propositional form, and reconstruct the original inference or
explanation.
One way of telling when the summary has ended is to pay attention for the moment
when the speaker switches to her own objection(s). Common phrases introducing
objections are "however" and "but", and comments on the original inference such "they
are wrong", "they have forgotten" and other forms of criticism, which also provide a segue
to the speaker's own contribution. Such a phrase might also indicate whether the upcoming objection will challenge the truth of a premise or the strength of the reasoning.
For example, "they have their facts wrong" indicates that the objection will be an objection
to the truth of a premise.
Exercises
(i) Analyze the passage. (Classifying will be done in step (v). Re-writing will be done in
step (ii).)
(ii) Give a list of propositions. Each item should be a free-standing proposition.
(iii) Diagram the reasoning using the numbers from the list. (If editing in Drive, create a
diagram using 'Insert > Drawing'.)
(iv) Explain your diagram in writing.
28
(v) Use "J" or "E" in your diagram in order to to classify the reasoning as either Justifying
Belief or Causally Explaining. Explain your classification as necessary.
Sample: 1 The estate tax should be abolished once and for all (because) 2 [it is immoral]
— 3 [it is a second tax on income that already has been taxed.] The fact that 4 [the budget
deficit is so great] and 5 [could be reduced by a return of the tax] is irrelevant — 6 [if the
money is ill-gotten, it should not be used for any purpose, reducing the deficit or
otherwise.]
1.
2.
3.
4.
5.
6.
The estate tax should be abolished once and for all.
The estate tax is immoral.
The estate tax is a second tax on income that already has been taxed.
The budget deficit is very great.
The budget deficit could be reduced by a return of the [estate] tax.
If money is ill-gotten, it should not be used for any purpose.
In this diagram, the target is 1 and 2 is a reason for 1 and 3 is a reason for 2. This is
all in the first sentence of the passage. The passage then mentions two reasons (4
and 5 – I think these are joined reasons because they are both about how the tax
could be used to reduce the deficit) which suggest that 2 isn't sufficient reason for
1 – this is why I have an arrow (dashed because it's an objection and pointing up
because it is contrary to the downward arrow between 1 and 2) pointing at the
arrow between 2 and 1. The passage claims that these objections are irrelevant, that
is, that even if 4 and 5 are true, they don't break the connection between 2 and 1.
So, I have put 6 as a dashed arrow pointing down against the objection-arrow from
(4 + 5). The reasoning context is Justifying Belief throughout.
1. Jill is talking to Henry about Jim, the Great Dane: Jack says that Jim scratches
himself because he has fleas. But maybe he has dry skin, instead.
2.
At the market. Jones says: You know, granola bars aren't actually healthy. Just
check the ingredients: lots of processed sugars.
Smith: Yeah but they say "all natural" on the packet.
3.
Republicans argue that Guantanamo must remain open because moving prisoners
from Guantanamo to mainland U.S.A. puts American citizens at risk. But this is absurd.
The prisons they would be held in are super-max facilities that are completely secure.
29
Indeed, the shoe-bomber and one of the 9/11 plotters are already securely incarcerated in
U.S. prisons.
4. On a blog: Those who argue that Shellie Ross is an unfit mother for "tweeting"
during her son's drowning simply have their facts wrong. She did not tweet any
information until she was in the hospital after her son was receiving medical attention.
5.
A letter to the editor of ESPN magazine: The Associated Press has named Serena
Williams as its 'Female Athlete of the Year' for 2009, on the basis of her win at Wimbledon
and her #1 ranking. The AP's decision is a mistake, however. At the US Open, Williams
lost her temper and physically threatened a line-judge who had called a foot-foul against
her. We should not be promoting this kind of behavior.
Answers To 2, 4
2. At the market. Jones says: You know, 1 [granola bars aren't actually healthy.] 2 [Just
check the ingredients: lots of processed sugars.]
Smith: Yeah but 3 [they say "all natural" on the packet.]
1. Granola bars aren't healthy.
2. According to the ingredients, granola bars contain lots of processed sugars.
3. It says "all natural" on granola bars.
Saying they're full of sugars is a reason for thinking that granola bars aren't healthy; so, I
have an arrow from 2 to 1. The fact that they are 'all natural' is an objection. I have
diagrammed it as an objection to the connection between 2 and 1: Smith doesn't challenge
the fact that they are full of sugar, but she seems to think that they might still be healthy
because they are 'all natural'.
4.
On a blog: Those who argue that 1 Shellie Ross is an unfit mother 2 [for "tweeting"
during her son's drowning] simply have their facts wrong. (3) [She did not tweet
any information until she was in the hospital after her son was receiving medical
attention.]
1. Shellie Ross is an unfit mother.
2. Ross was "tweeting" during her son's drowning.
3. Ross did not tweet any information until she was in the hospital after her son was
receiving medical attention.
30
The passage starts by quickly reviewing the reason that some people think Ross is an
unfit mother (because she was tweeting) – so 2 is a reason for 1. But then there is an
objection directly against (2) – she was not tweeting during the drowning but only later.
7 Analyzing Very Long Passages
1. Long passages can be difficult to analyze because (typically) they involve many
propositions, with multiple reasons, and they involve objections and rebuttals. This
section suggests that you add a step of looking for the large-scale structure of the passage
before attempting to isolate the individual propositions.
2. Consider this editorial on getting Iraq to pay some of the cost of the U.S.'s
operations. (http://blogs.usatoday.com/oped/2008/05/our-view-on-war.html)
As always, you should begin by trying to isolate the target (conclusion) of the piece.
To do this, read the whole piece, paying particular attention to the headline (and the subheadlines, if any) and the start and end of the articles. Do not rely on the headline and
sub-headlines. Often they merely serve to set the scene or the topic of the piece. The
beginning and end of the piece are typically more reliable, but are inferior to reading the
whole thing.
Our specific example poses a bit of trouble, because of some variation. The
conclusion of this argument seems to be …
1. Iraq should bear more of the cost of U.S. operations in Iraq.
… but note that this is not exactly the conclusion suggested by the sub-headline,
which makes reference only to security, whereas the article mentions other types of
operation. The last line of the article seems to do a better job of capturing the article's
main thesis.
3. Having isolated a (working) conclusion, your next step would normally be to
look for the premises. But it would be potentially confusing to approach an article of this
length by numbering the propositions one by one from the beginning and assuming that
the structure will reveal itself straightforwardly. There are too many propositions to keep
in mind at once.
Rather, you should attempt to summarize the main lines of reasoning in the
article. (One way to do this is to pretend that you are giving a very brief summary of the
article to another person.) Try to find the propositions around which the reasons for and
against cluster. (If necessary, make up a summary proposition for each one, as interim
conclusions.)
Let's demonstrate these practices with our working article. Reading through the
article, the main reasons (for Iraq taking on more of the cost) are
the U.S. is struggling economically
the war costs a lot, and
31
Iraq has money to spare.
We note that there are a reasons given for each of these, and some objections to
the idea that Iraq could pay, as well as some objections that don't seem to be attacking
any of these three reasons and so are objections to the inference between these three and
the target.
These three can be considered as interim conclusions, which then go together to
justify the conclusion. We can sketch the macro-structure of the argument as follows:
1. Iraq should bear more of the cost
of U.S. operations in Iraq.
2. The war costs a lot.
3. The U.S. is struggling economically.
4. Iraq has money to spare.
We know there will be reasons for each of the main three ideas, and that there will be
objections to the idea that Iraq can pay and to the inference from the three main ideas.
These are diagrammed for now with arrows but not proposition numbers. At this stage,
we are only trying to get a broad sense of what the reasons for the target are and we can
leave out a lot of details, such as the detailed reasons for each of the three or the
propositions describing precisely what costs Iraq could cover.
4. Now we can move to the second stage and give a list of all of the propositions
and try to relate them to the basic structure above. In support of (2), the propositions
concerning cost to the US are:
5.
6.
7.
8.
9.
The U.S. has spent more than $500B since 2003.
The U.S. is paying $10B/month for fighting, reconstruction and training.
The U.S. needs another $1B for rebuilding.
The U.S. spends $90M/month to pay for other groups.
The U.S. spends $153M/month to pay for fuel.
The propositions concerning Iraqi ability to pay (4) are:
10. Iraq has the world's fourth largest oil reserve.
11. Iraq has made a $70B profit from oil.
32
(We might also include "Iraq subsidizes gasoline for its citizens." if the implication
is that some of that subsidy could be transferred to the US forces. But it's not clear that
this is in fact what is implied. A proposition that a subsidy is deserved will, however, be
added, below.)
The propositions concerning US's struggling economy (3) are:
12. The U.S. is running huge deficits.
13. U.S. consumers are suffering at the pump.
14. The U.S. is teetering on the brink of a recession.
We add (14) here because, although it is introduced later as a response to some
objections, it does not seem to respond to them particularly. So, we include it as part of
the early thread on the state of the US economy.
There are also two other considerations which seem to be unrelated to the three
main points identified so far. The proposition …
15. There are bills pending in Congress to make Iraq pay more.
16. U.S. forces deserve the same subsidy on gas as Iraqi citizens get.
(15) seems to be added as an appeal to authority and/or popularity. The main
inference is presumably sufficient to justify the conclusion, and these are thrown onto the
pile.
There are also propositions which serve as objections. We will return to these once
we have the positive reasoning mapped out in detail.
5. Now that we have a list of the propositions which support the three main points
(and so support the overall target) we must figure out how the propositions in each group
are related to each other and to the interim conclusion. No specific inter-relation seems
to be indicated in the inference, and so we can simply represent them as a pile of reasons
using split-tailed arrows. Using the numbered propositions above, the diagram at this
stage (and without the objection arrows) looks like this:
33
Let us now consider the reasons against:
17.
18.
19.
20.
21.
22.
Iraq's economy is shaky.
Contributing more might risk Iraq's agreements with IMF.
Contributing more might risk Iraq's debt forgiveness efforts.
The U.S. wants to retain efficiency.
The U.S. wants to retain control.
Iraq's oil revenue is a small fraction of what's needed.
(17) and (22) are related to the idea that Iraq has the resources to contribute more
funds, but they do not challenge either (10) or (11) specifically. So they challenge the move
from (10) and (11) to (3). (18) through (21) do not challenge the truth of any of the
premises; they present new information entirely and so are construed as (individually)
challenging the main inference.
The diagram now looks like this:
6. The detailed diagram is now complete.
As you can see from reading this analysis, long passages, and especially editorials,
can be very messy and difficult. In a number of places above, it was hard to say exactly
how to incorporate some part of the article into the analysis. Don't panic. This is
typical.Analyze the piece as best you can. It is likely that the article actually is unclear. It
is a sign that you have done a good job if you have generated various questions about the
structure of the reasoning in the course of your analysis. As a critical reasoner you will
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very often end up with questions since you are spending more time and effort on what is
said than the speaker!
8 Evaluating The Various Reasoning Complex Structures*
1. With a little care, the Basic Evaluation questions — 'Are the propositions
expressing the reasons true?' and 'Do they justify or explain the target?' — can be applied
to any of the reasoning structures you have seen, including those with objections.
2. For any inference or explanation whose structure is diagrammed with a single
regular arrow, such as just one premise or joined premises or combined support, ask the
basic questions.
3. For any inference or explanation whose structure is diagrammed with a splittailed arrow (a pile of reasons) you must remember that it is possible that a subset of the
reasons is sufficient. It is possible that the inference or explanation will still be good even
if objections undermine one or more (but not all) of the reasons.
4. Conclusion Conjunction structures (section 2) are evaluated by evaluating each
inference or explanation separately.
5. Compound structures (section 3) are evaluated by evaluating each stage of the
reasoning in turn, each of which must do its job. This means that if any of them are
rejected, the whole must be rejected. Consider the following example (the numbers in the
diagram follow the numbers in the standard form):
1. Honey is a fruit.
2. Some fruits are sweet.
3. Honey is sweet.
4. Sweet things are good for you.
5. Honey is good for you.
The diagram can be read as: (1) and (2) together justifies belief of (3), which, together
with (4), justifies belief of (5). In evaluating this inference, we must examine both the
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support given by (1) and (2) to (3) and by (3) and (4) to (5). You can see that the reasoning
in the first sub-inference is weak: (2) says that some fruit is sweet and the first premise
does not give us any reason to think that honey is one such fruit. The reasoning in the subinference involving (3), (4) and (5) is strong. But since (3) is being used as a premise in
the inference for (5), the inference as a whole gives us no good reason for accepting (5),
which is the main conclusion. For soundness, the reasoning in the inference must be
strong throughout.
6. Passages involving objections (and support for and rebuttals to them) are
evaluated in the same manner as compound structures, except that sub-structures are
sometimes working against one another. Take a simple case in the abstract, which shows
a challenge to the strength of the connection between the premise and the target:
The initial inference/explanation will considered good if (1) and (2) are true and
the connection between (1 + 2) and (3) is tight, and some fault is found with (4)'s
challenge — either (4) is false or it does follow from the truth of (4) that the original
connection is weak. When rebuttals to objections are added you must continue the
process. For example, if a rebuttal (5) is added, challenging the truth of (4), as follows,
… you must check this specific piece of reasoning, that is, you must ask whether (5)
is true and whether it would follow from the truth of (4) that (5) is not true. (And note
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that if (5) is effective in showing that (4) is not true, it has thereby helped you in the
evaluation of (4)'s impact on the original reasoning.)
The messiest type of structure to evaluate is a pile of reasons (using the split-tailed
arrow) both for and against, as in the following diagram:
In this case, you must examine each reason and the work it does in justifying or
explaining or objecting, and decide whether the target proposition is justified or explained
despite whatever weight there is to the objections.
Exercises
Editorials (and opinion-editorials) provide us with a good opportunity to practice our
skills of argument analysis because they are frequently very messy. Like any argument
they state a claim and offer some reason(s) for believing it, but the structure of the
argument is often complex — editorials are often multiple reasons arguments, and they
often consider objections to the opinion and provide rebuttals. (Finally, the connection
between premises and conclusion is often unclear, which makes them difficult to
evaluate.)
Here is an editorial adapted from the New York Times. Read it and follow the instructions
below.
Harsh Treatment for Youthful Offenders
The Texas Youth Commission's new leadership is proposing a rule change so it can
make more frequent use of pepper spray against unruly detainees.
Juvenile justice experts, the federal courts and the Justice Department have all
condemned excessive use of pepper spray. Pepper spray is a caustic substance that
produces burning and respiratory distress and can also cause nerve damage.
In addition to being inhumane, the policy is counterproductive. It undermines
institutional discipline, further angering and alienating young detainees.
The agency claims that the new policy is necessary to help understaffed institutions
maintain control.
It also insists that the spray will be judiciously used.
In a lawsuit filed earlier this year, however, Texas child welfare advocates charged
that the system was using pepper spray excessively, including on mentally ill detainees
who were supposed to be exempted. Among the cases cited in court documents was that
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of a mentally ill 15-year-old who was said to have been sprayed three times while
attempting to harm himself.
There's also no need to increase use of pepper spray. In Los Angeles County, Calif.,
the agency instead reformed its disciplinary practices. According to a recent analysis by
the Washington-based Center for Children’s Law and Policy, the county achieved its
improvements by retraining its staff, improving mental health services, and embracing
less violent systems of crisis management. Texas can to follow the same course.
The Article As A Whole
1. What is the overall claim of the article? Is it to support some position? Or to reject
some position?
2. Explain how you know what the overall claim is.
It is often necessary to read the entire piece in order to identify the conclusion, and
indeed, sometimes it is necessary to perform the other steps first. Obvious things to pay
attention to are the title or headline to the piece (though sometimes the title will simply
state the topic, rather than the target), and the opening or closing sentences/paragraphs,
or flag words, or the overall structure of the argument.
Many articles start out by attacking other claims and inference, and only later on is the
writer's own position evident.
Isolate The Parts Of The Article
3.
Write a paragraph summarizing the parts. To do this, it might help think of what
you would include if you were summarizing the article for a friend:
"I read this interesting article in the paper today.
It argued that <target>. First is gave a reason(s) in favor: <main reason1>, <main
reason2> ...
Then, in support of <main reason1> there was the idea that <supporting reason1> ...
Then, <main reason1> was also objected to, by <objection1>.
Finally there was also <objection1> ... undermining the support for the target."
Try to write this as a blow-by-blow account of the article, tracking its twists and turns.
If an article is well-written, each paragraph will be a point and each point will get its own
paragraph; however, articles do not always follow this rule, and so you will sometimes
have to divide up a single paragraph into multiple points.
TWO Diagrams - Big-Picture & Fine-Grained
4.
Diagram 1 – Big-Picture: Give a basic diagram based on step 3. (See the text for an
example.)
Explain your diagram in writing.
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5.
Diagram 2 – Fine-Grained: Copy the diagram from step 4 and flesh it out with the
details. Work on one chunk at a time.
Explain your diagram in writing.
In your explanations, include (at a minimum) an explanation of the structure of each part
of the diagram: why there is a split-tailed arrow/separate arrows/plus-sign; why the
arrow is solid/dashed; why the arrow points in the direction it does).
Because the structure in editorials is often sloppy, you might also discuss alternate
possibilities.
If you left out any propositions/point from the article, explain why.
9 Summary — Complex Diagramming
Types of Objection
Objection to one of the premises, i.e. that a premise is false or dubious.
Objection to the reasoning; i.e. that even if the reason(s) are true, the conclusion
is not justified by them, or that the explainee might not occur.
Diagramming Objections, Support for Objections, and Rebuttals
A regular arrow means "justifies what it points at" or "is a reason for believing"
A dashed arrow means "challenges what it points at" or "is a reason for not
believing" (A dashed arrow pointing at the target means "is a reason for believing
<the proposition> is false")
The direction of each arrow depends upon its role in the overall diagram.
Hints for Passages Including Objections, & Long Passages
If the passage is argumentative, look for a very quick summary, perhaps just one
sentence, of the inference or explanation being responded to.
There is no need to include in the diagram remarks about what the impact of
objections (and rebuttals) is.
For very long passages, look for the large-scale structure of the passage before
attempting to isolate the individual propositions.
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