Introduction to Logic:
How to Diagram Arguments
Abstract: Analyzing the structure of arguments
is clarified by representing the logical relations in diagram form.
- Arguments in logic are composed of premises being offered as
reasons in support of a conclusion.
- The use of the term "argument" in logic is in accordance with
this precising definition; the term is not being used to refer to
a dispute or a quarrel.
- The presence of an argument in a passage is discovered by
understanding the author's intention of proving a statement by
offering reasons or evidence. Generally speaking, these reasons
are presented as verbal reports although they might not always
be initially presented in declarative sentences.
- There are three main ways of judging the presence of an argument:
- The author or writer explicitly states the reasons,
evidence, justification, rationale, or proof of a statement.
(1) I conclude the dinosaurs probably had to cope
with cancer. These are my reasons: (2) a beautiful bone
found in Colorado filled with agate has a hole in its center, (3)
the outer layer was eroded all the way through, and (4) this
appearance closely matches metastatic bone tumors in humans.
Usually, however, the emphasized phrases, “I conclude”
and “These are my reason” are omitted omitted in the
text for stylistic reasons &mdash leaving the structure of the argument
to be inferred from the meanings of the statements used.
- The author uses argument indicators signifying the presence of an
(1) Since the solution turned red when the indicator
was added, (2) I conclude it is acidic, inasmuch
as acidic substances react with this indicator to form a
In this argument, “since” is being used as a premise
indicator and “I conclude” is used as a conclusion
- In order to determine whether or not an argument is present
in a passage, it sometimes helps to ask the irreverent question,
“What are you trying to prove?” If an answer is directly
forthcoming, then the passage is most likely argumentative.
Despite that, the presence of an argument cannot be always known
with certainty; often the purpose of the passage can only be
contextually surmised. The intention of the speaker or writer is
often a determining factor.
A charitable, and insofar as
possible, a conventional interpretation of the context, content, and
purpose of the passage should be sought.
(1) The types of sentences you use are quite varied. (2) I've noticed
that your essays are quite sophisticated. (3) You have been learning
much more about sentence structure.
Note that if we ask upon reading this passage, “What are you trying
to prove?,” the answer in statement (3) suggests itself.
- In order to analyze simple and complex arguments, we will find it useful
to construct a diagram of the structure of the argument that details the
relations among the various premises and conclusions.
- The conclusion of one argument can become a premise for another argument.
Thus, a statement can be the conclusion of one argument and a premise of
another argument just as a daughter in one family can become a mother in
- The number of arguments in a passage is conventionally established
by the number of conclusions in that passage.
- In analyzing the structure of an argument, whether simple or complex,
the all-important first step is to find the conclusion. Here
are some specific suggestions as to how to find the conclusion.
- The conclusion might be evident from the content and context
of the paragraph structure. The sequence of sentences is often an
indication of the conclusion. Arrangement of sentences from most
general to specific is a common form of paragraph or passage; the
arrangement of sentences from specific to general is a bit less
common. Considering both cases, the conclusion is often the first
and sometimes the last sentence in a passage.
(1) John didn't get much sleep last night. (2) He has dark
circles under his eyes. (3) He looks tired.
The conclusion is the first sentence in the passage. Statements (2)
and (3) are observational evidence for statement (4) which is being
inferred from those observations.
- Nevertheless, the conclusion can occur anywhere in the paragraph,
especially if the passage has not been revised for clarity. Usually,
if a conclusion is not the first or last sentence of an argumentative
paragraph, a conclusion indicator is present, or the last sentence
is presented as an after-thought with a premise indicator. Frequently
used argument indicators are listed below.
(1) Studies from rats indicate that neuropeptide Y in
the brain causes carbohydrate craving, and (2) galanin causes
fat craving. (3) Hence, I conclude that food cravings
are tied to brain chemicals (4) because neuropeptide
Y and galanin are brain chemicals.
- The structure of the argument be inferred by attending to the
following kinds of
premise and conclusion
- Premise indicators are terms which often indicate
the presence of reasons. Frequently used premise indicators
include the following terms:
for the reason
in light of the fact
for the reason [*often mistaken for conclusion indicator]]
(1) The graphical method for solving a system of equations
is an approximation, (2) since reading the point
of intersection depends on the accuracy with which the lines
are drawn and on the ability to interpret the coordinates
of the point.
The term “since” indicates that the second clause
of this passage is a premise, the first clause is left as the
conclusion. In practice, the second clause can be broken down
into two separate premises so that the argument can be set up
(2a) Reading the point of intersection of a graph depends on
the accuracy with which the lines are drawn.
Another Argument with premise indicator:
(2b) Reading the point of intersection also depends upon
the ability to interpret the coordinate of the point.
(1)Thus, the graphical method for solving a system of
equations is an approximation.
(1) Questionable research practices are far more common than
previously believed, (2) after all, the Acadia Institute
found that 44 percent of students and 50 percent of faculty from
universities were aware of cases of plagiarism, falsifying
data, or racial discrimination.
- Conclusion indicators are words which often indicate the
statement which logically follows from the reasons given. Common
conclusion indicators include the following:
Examples of their use in arguments:
it follows that
[*especially note this term]
for this reason [*term often mistaken for premise indicator]
(1) No one has directly observed a chemical bond, (2) so
scientists who try to envision such bonds must rely on experimental
clues and their own imaginations.
(1) Math grades for teens with bipolar disorder usually drop noticeably
about one year before their condition is diagnosed, thus (2)
probably bipolar disorder involves a deterioration of mathematical
(1) Coal seams have been discovered in Antarctica. (2) This
means that the climate there was once warmer than it is now.
(3) Thus, either the geographical location of the continent
has shifted or the whole Earth was once warmer than it is now.
- Equal Status Indicators: Conjunctives (including
some conjunctive adverbs) often indicate equal status of premise or
conclusion in connecting clauses or sentences. Noticing these
conjuncts is especially helpful in argument analysis:
If one of the clauses has already been identified as a premise
or a conclusion then its coordinating clause is of the same type
Indicators of clauses of equal status include:
Example of the Equal Status Indicator “and”:
not only &helip; but also
(and also the semicolon “;”)
(1) Some students absent today are unprepared for this test,
since (2) the law of averages dictates that only 10% of
students are absent due to illness, and (3) more than
10% are absent.
(1) Lenses function by refracting light at their surfaces.
(2) Consequently, not only does their action depends
on the shape of the lens surfaces but also (3) it
depends on the indices of refraction of the lens material and
the surrounding medium.
- When analyzing complex arguments, it can be helpful to reconstruct
the argument by identifying the conclusion first, and then by working
backwards, locate the premises.
- Consider the following argument:
(1) If students were environmentally aware, they would object to
the endangering of any species of animal. (2) The well-known
Greenwood white squirrel has become endangered (3) as it has
disappeared from the Lander Campus (4) because the building of
the library destroyed its native habitat. (5) No Lander students
objected. (6) Thus, Lander students are not environmentally aware.
Note that the following indicators are given in this passage:
The argument is complex.
The premise indicators suggest that (2) is a subconclusion
of (3) since the indicator “as” connects them, and (3),
in turn, is a subconclusion of (4) since the indicator
“because” connects those two statements.
- Statement (6) is the final conclusion since it has the conclusion
indicator “thus” and the import of the paragraph indicates
that this statement is the main point of the argument.
- Intuitively, the structure of the first statement (1) together
with statement (5) is a common argument form:
If students were environmentally Aware,
they would Object to the endangering
of any species of animal.
which can be abbreviated as follows:
No student O
bjected (to the endangering of the Greenwood white squirrel).
If A then O
and the negation of clause O is
logically equivalent to conclusion (6).
(Later in the course we will see that this argument structure is termed
If A then O
(Note that A is the same statement as (6).)
Hence the whole argument can now be pieced together as the following
- In some contexts, the use of indicator words such as those listed
above do not typically indicate the presence of an argument.
- Literary Implication: For example, in following book review, two
example passages drawn from the work of the poet Stevie Smith illustrate
a literary insight into her writing.
In the passage excerpted below, the emphasized phrase “The
implication … is” does not function as an argumentative
conclusion indicator. Instead, these examples are intended to suggest
a meaning beyond the literal interpretation of the events described:
“In The Voyage of the Dawn Treader, the ship's
prow is ‘gilded and shaped like the head of a dragon with
wide open mouth’ so when, a moment later, the children stare
at the picture ‘with open mouths’, they are being
remade in its image … The painted ocean to which Joan is
drawn is ‘like a mighty animal’, a ‘wicked virile
thing’. The implication [emphasis mine] in both
cases is that art is not safe, and that this is why it's needed.”
From a logical point of view, literary implication is a type of literary
generalization meant to enlighten.
[Matthew Bevis, “What Most I Love I Bite,” in the
&ldquopReview of The Collected Poems and Drawings of Stevie
Smith,” London Review of Books 38 No.
15 (28 July 2016), 19.]