How to Diagram Arguments in Logic;
Premise and Conclusion Indicators
Abstract: Analyzing the structure of
arguments is clarified by representing the logical relations of premises
and conclusion in diagram form. Ordinary language argument examples are
explained and diagrammed.
Arguments in
logic are composed of premises offered as reasons in support of a
conclusion. They are not defined as quarrels or disputes.
The use of the term “argument” in logic is in
accordance with this precising definition; the term is not used
in logic to refer to bickering or contentious disagreements.
Formal arguments are evaluated by their logical structure; informal
arguments are studied and evaluated as parts of ordinary language
and interpersonal discourse.
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 for the truth of some other statement.
Generally speaking, these reasons are presented as verbal reports.
The reasons might not always be initially presented in declarative
sentences, but in context must have their meaning preserved by
translation or paraphrase into a
statement or proposition.
A verbal expression in sentence form which is either true or
false (but not both) — i.e., a sentence with a truth
value.
How to Identify the Presence of an Argument
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.
Example:
[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 reasons” are omitted in the text for
stylistic reasons — leaving the structure of the argument
to be inferred from the meanings of the statements used and
less obvious transitional phrases which might indicate reasons or
conclusions.
The author uses argument indicators signifying
the presence of an argument.
Example:
[1] Since the solution turns litmus paper red,
[2] I conclude it is acidic, [3] inasmuch
as acidic substances react with litmus to form a
red color.
In this argument, “since” is being used as a
premise indicator and “conclude” is used as a
conclusion indicator, and “inasmuch as” is another
premise indicator.
Ask yourself “What is the author trying to prove
in this passage?” In order to determine whether or
not an argument is present in a passage, it sometimes helps to pose
this question. If an answer is directly forthcoming, then the passage
is most likely an argument.
Despite that, the presence of an argument cannot be always known
with certainty; often the purpose of the passage can only be
contextually surmised. Establishing the intention of a speaker
or writer is sometimes the only determining factor of whether or not
an argument is present.
A charitable, and insofar as
possible, an impartial conventional interpretation of the context,
content, and purpose of the passage should be sought.
What if indicators are not present in a passage?
The identification of arguments without argument indicators present
is achieved by recognizing from the meanings of the sentences themselves
when evidence or reasons are being provided in support of a concluding
statement.
For example, evaluate this passage:
“[1] The types of sentences you use are quite varied. [2] I've
noticed that your recent essays are quite sophisticated. [3] You have
been learning much more about sentence structure.”
Note that if we ask upon reading this passage, “What is being
proved?,” then the answer in statement [3] suggests itself as
resulting naturally from the first two sentences.
That is, statements [1] and [2] are direct observational evidence
giving reasons for the main point (or that which is intended to be
proved): namely, the inference to [3] “You have been learning much
more about sentence structure.”
So, in the context of a simple argumentative passage, if statements are
given as suppositions, observations, or facts without evidence or logical
support, those statements are premises. If a statement is given logical
or evidential support from another statement or statements, that
statement is a conclusion (or subconclusion if the argument is complex).
How to Analyze Simple Arguments
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 a following argument — just as a daughter in one
family can become a mother in another family.
For example, consider this “chained argument”:
“[1] Because of our preoccupation with the present moment
and the latest discovery, [2] we do not read the great books
of the past. [2] Because we do not do this sort of reading, and
[3] do not think it is important, [4] we do not bother about trying
to learn to read difficult books. [5] As a result, we do not learn
to read well at all.” [1]
Diagramming the argument illustrates the internal logical structure
more clearly than the written description: “Statement [1] provides
evidence for [2], and [2] together with [3] gives evidence for [4],
and as a result of [4], statement [5] follows with some degree of
probability.”
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.[2] Considering both
cases, the conclusion is often the first or the last
sentence in a passage.[3]
Example argument:
[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 [1] which
is 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 highlighted below under separate headings.
Example Argument:
[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 can be inferred by attending to
the
premise and conclusion indicators even
though the content of the argument might not be understood.
Working with Premise Indicators:
Premise indicators are terms which
often indicate and precede the presence of reasons. Frequently used premise
indicators include the following terms:
for
since
as
because [* when the term means “for the
reason that” but not when it means “from
the cause of”]
in as much as
follows from
after all
in light of the fact
assuming
seeing that
granted that; given that
in view of
as shown by; as indicated by
deduced from
inferred from; concluded from
due to the fact that
for the reason [* often mistaken for a conclusion
indicator]
Examples of their use in arguments:
“[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 could have also
have been set up as follows:
[2a] Reading the point of intersection of a
graph depends on the accuracy with which the lines are drawn.
[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.
So under this interpretation, [2a] together with [2b] is evidence for [1].
A simpler argument with a premise indicator:
[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.
Try the following examples for yourself:
“[1] [I]t seems hard to prove that the composition
of music and words was ever a simultaneous process. [2] Even
Wagner sometimes wrote his ‘dramas’ years before
they were set to music; [3] and, no doubt, many lyrics were
composed to fit ready melodies.” [4]
Although there are no indicators for the first two statements
in this passage, the second two statements are an example which
supports or gives evidence for the first more general statement.
Therefore, the first statement is the conclusion of the argument.
This is a weak inductive argument: the conclusion is supported
by only one example.
“[1] [A]ny kind of reading I think better than leaving a
blank still a blank, [2] because the mind must receive a degree
of enlargement and [3] obtain a little strength by a slight
exertion of its thinking powers.”[5]
The premise indicator “because” indicates the first
premise. Note that the “and [3]” before the last clause
in this passage connects clauses of equal standing; so [3] is tacitly
translated to the independent clause:
“[3] [the mind must] obtain a little strength by a slight
exertion of its thinking powers.”
The conjunction “and” connects statements of
equal status, so the statement following it is also a premise —
that leaves the first statement as the conclusion of this argument.
Argument reconstruction of this kind is often done for clearer
understanding of the reasoning for purposes of evaluation.
(This argument is inductive since the conclusion does not follow
with certainty.)
Working with Conclusion Indicators:
Conclusion indicators are
words which often indicate the statement which logically follows
from the reasons given. Common conclusion indicators include the
following:
thus
therefore
consequently
hence
so
it follows that
proves that; demonstrates that; shows that
indicates that
accordingly [* an indicator often missed]
implies that; entails that; follows that
this means
we may infer; it can be inferred that
suggests that
results in
in conclusion
for this reason; for that reason [* often mistaken for premise indicators]
Examples of their use in arguments:
[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 reasoning.
[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.
Try the following examples for yourself:
“[1] We humans appear to be meaning-seeking creatures who
have had the misfortune of being thrown into a world devoid of
meaning. [2] One of our major tasks is to invent a meaning sturdy
enough to support a life and [3] to perform the tricky maneuver
of denying our personal authorship of this meaning. [4] Thus we
conclude instead that it [our meaning of life] was ‘out
there’ waiting for
us.” [6]
The only indicator in the argument is the conclusion indicator
“Thus” in statement [4]. The first two sentences
are divided here into three statements which provide the reasons
for concluding statement [4].
(It would have been acceptable also to interpret the sentence
beginning with [2] as one statement. If this whole argument were
related to other arguments, the choice of how to divide up the
statements would be made by translations which best match the
related ideas.)
The central idea of the passage is that since [the author thinks]
life has no intrinsic meaning, to live well we must invent a meaning
for our lives and then believe this imposed meaning is genuinely real.
”[1] The fact is that circulating in the blood of
the organism, a carcinogenic compound undergoes chemical
changes. [2] This is, for instance, the case in the
liver, which is literally crammed with enzymes capable of
inducing all sorts of modifications. [3] So it may well be
that cancer is induced not by the original substances
but by the products of their metabolism once inside the
organism.” [7]
The only indicator is the conclusion indicator “So” in
statement [3]. The first two statements describe a possible instance
of the final generalization [3].
Notice that statement [3] could have been interpreted as two
statements:
“[3] So it may well be that cancer is induced not by
the original substances but [4] [it may well be that cancer
is induced] by the products of their metabolism once inside
the organism.”
However, in this case, it seems clearer to keep [3] and [4] as
one statement since [3] and [4] express one complete thought.
Either interpretation is possible; the simpler one is taken here.
Working with Equal Status Indicators:
Indicators of Equal Status of Premises or
Conclusions: 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. Indicators of clauses of equal status also
include certain adverbial clauses, “conditional, concessive, and
contrastive terms,” informing of some type of expectation or
opposition between clauses:
or (the inclusive “or”,
i.e. “either or or both”)
and
in addition
although
despite; in spite of
besides
though
but
yet
however
moreover
nevertheless
not only … but also
(and also the semicolon “;”)
If one of the clauses has already been identified as a premise
or a conclusion of an argument, then its coordinating clause is
probably the same type of statement. Check the following examples.
The equal status indicator “and”:
[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.
Comment: Notice that statements [2] and [3] work together
as a reason, so both together provide evidence for [1].
Having separate arrows for [2] and [3] leading to conclusion [3] would
represent a misunderstanding of the argument.
The equal status indicator “not only …
but also.”
[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.
Comment: Notice that sentence [3] could have been divided into two
statements as follows:
“ … [3] it depends on the indices of refraction
of the lens material and [4] [it depends on] the surrounding
medium.”
(Again, how sentences should be divided into different statement depends,
to a large degree, on how the argument under analysis is related to any
other contextual statements and arguments.)
Try the following examples for yourself:
“[1] Mystery is delightful, but [2] unscientific,
[3] since it depends upon ignorance.” [8]
We could simply consider [1] and [2] as one statement, but
the argument seems be clearer to consider [2] as elliptically
expressing the statement “[2] [Mystery is] unscientific.”
The premise indicator “since” identifies the only
premise.
“[1] Many of those children whose conduct has been
most narrowly watched, become the weakest men, [2] because
their instructors only instil certain notions into their minds,
that have no other foundation than their authority; [3] and if
they be loved or respected, the mind is cramped in its exertions
and wavering in its advances.” [9]
The premise indicator “because” indicates the first
premise connected by the equal status connector “and”
which identifies the second premise. By elimination, then first
independent clause is the conclusion.
“[1] For there is altogether one fitness (or harmony).
[2] And as the universe is made up out of all bodies to
be such a body as it is, [3] so out of all existing causes
necessity (destiny) is made up to be such a cause as it
is.” [10]
The argument is clearly marked with indicators:
For {1} and {2}, so {3}.
The premise indicator “for” connects another clause
of equal standing, with the conclusion marked by the conclusion
indicator “so.”
How to Analyze Complex Arguments
When analyzing complex arguments, it can be helpful to reconstruct
the argument by identifying the main conclusion first, and then by working
backwards, locate the premises by any premise indicators present.
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:
as because thus
The argument is complex:
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. (It is also the
last sentence in the paragraph.)
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.
The only statements not yet examined are [1] and [6].
After a bit of thought, the structure of the first statement [1] considered
together with statement [5] should suggest itself as a common argument form:
[1] If students were environmentally
Aware,
[then] they would Object to
the endangering of any species of animal.
[5] No student Objected
[to the endangering of the Greenwood white squirrel].
which can be abbreviated as follows:
[1] If A then
O
[5] Not O
The negation of the consequent clause O
by the second premise leads us to expect the conclusion “Not
A”.
Aha! “Not A” is the same
thing as the conclusion [6] we identified in step 1:
“[6] Thus, Lander students are not environmentally
Aware,”
(Later in the course we will see that this often used argument structure is
termed modus tollens.)
So the diagram of this internal sub-argument then is as follows:
[1] If A then O
[5] Not O
[6] Not A
(Note that “Not A” is the same statement as [6].)
Hence the whole argument can now be pieced together as the following
complex argument:
Caution: In same contexts, the use of indicator words such as
those listed above do not typically indicate the presence of an argument.
For instance, “because” and “so” are used as indicator
words in explanations; “since” and “as” are used in
other contexts than argumentative contexts also.
Consider this passage:
“The explanation as to why productivity has slumped since
2004 is a simple one. That year coincided with the creation of
Facebook”[11]
The passage here is probably intended to amuse rather than explain
why productivity has slumped. The explanation also has cogency as an
argument, as well. In cases like this, the import of the passage can
only be determined from its context. (Notice that “since”
in the above argument is used as a preposition, not as a conjunctive
adverb used as a premise indicator.)
So, the presence of argument indicators is not a sure sign an argument
is present. Here are two examples of passages where it's doubtful that
the writer intended to offer an argument:
Literary
Implication: For example, in following book
review, two prose images drawn from the work of the poet
Stevie Smith illustrate a literary insight.
In the passage excerpted below, the emphasized phrase “The
implication … is” does not function as an
argumentative conclusion indicator. Instead, the prose images are
intended to suggest a meaning beyond the literal interpretation of
the events pictured:
“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
in both cases is that art is not safe, and that this is why
it's needed.” [emphasis mine] [12]
From a logical point of view, literary implication is a type of imaginative
generalization meant to enlighten rather than provide evidence or demonstrate.
So it's important to realize that the presence of terms in the argument
indicator lists is not a sure sign the passage is an argument — these
words are also used in other contexts. The use of these terms are determined
within the contexts in which they appear.
By way of example, consider this passage from the Hindu texts of the
Upanishads:
“He asked: ‘Who are the
Âdityas?’
Yâgñavalkys replied: ‘The
twelve months of the year, and they are Âdityas, because they
move along (yanti) taking up everything [i.e., the lives of
persons, and the fruits of their work] (âdadânâh).
Because they move along, taking up everything, therefore they are
called Âdityas.’”[13]
Evaluated superficially, this passage could be analyzed as a
circular argument
Also termed “begging the question” or
“petitio principii,” the
argumentative fallacy of assuming in a premise the same statement
which was to be proved. Formally the argument is valid, but is
considered by some logicians fallacious when deceptive.
— but in context, the purpose of the passage is merely to define
and explain the meaning of the word “Âdityas.”
Links to Diagramming Online Quizzes with
Suggested Solutions
Test your understanding with any of the sections for diagramming on the
following quizzes, tests, or exercises:
“There is however a method for extracting
arguments and setting out their structure. This is how it goes.
First go through the text circling the inference indicators
“thus” “therefore” etc. Next identify the
main conclusion of the argument and underline it. Then look
for the reasons given to support that conclusion and place them
in angle (brackets). Now iterate the following procedure for as
long as possible. Take a (reason) and look for reasons given to
support it. If you find any, then underline the (reason) which is
now also a conclusion. When the process terminates the (reasons)
that are not underlined are the premisses to the argument, the
(reasons) underlined are intermediate conclusions.”
Peter Mott, review of The Logic of Real Arguments,
by Alec Fisher, The Philosophical Quarterly 39 no. 156
(July, 1989), 370-373.
Notes: Diagramming Arguments
1. Mortimer J. Adler, How to Read a Book (New York: Simon and Schuster: 1940), 89. ↩
2. Some English textbooks describe argumentative paragraph structure
as deductive (proceeding from general to specific statements
or inductive (proceeding from specific to general statements).
For example, educator and rhetorician Fred Newton Scott writes:
“There are two orders of progress in thought, one proceeding
from the statement of a general principle to particular applications
of the principle (deductive reasoning), the other proceeding from
the statement of particular facts to a general conclusion from those
facts (inductive reasoning). In deductive reasoning, the general
principle (stated usually at the beginning) is applied in the
particulars; in inductive reasoning the general principle (stated
usually at the end) if inferred from the particulars, as a conclusion.
In a deductive paragraph, as would be expected, the sentences
applying the principle to the particular case in hand, usually follow
the topic-statement, which announces the principle. In an inductive
paragraph the sentences stating the particular facts usually precede
the topic-statement, which gives the general conclusion.”
[emphases deleted]
Fred Newton Scott, Paragraph-Writing (Boston: Allyn and
Bacon, 1909), 62-63.
Since this distinction between induction and
deduction proves faulty for many arguments, deductive argument
are now described as those that provide total support for their conclusion
(i.e.,a they logically entail the conclusion); whereas, an inductive
argument give partial support for their conclusion (i.e., they
provide only some evidence for the conclusion.)↩
3. Most paragraphs have a three-part structure: introduction (often a
topic sentence), body (often supporting sentences), and conclusion (often
a summary statement). In argumentative writing, the conclusion of an
argument is often the topic sentence or main idea of a paragraph.
Consequently, the first sentence or last sentence of many argumentative
paragraphs contain the conclusion.↩
4. René Wellek and Austin Warren, Theory of Literature
(New York: Harcourt, Brace: 1956), 127.↩
10. Marcus Aurelius, Meditations, trans George Long
(New York: Sterling: 2006), 69.↩
11. Nikko Schaff, “Letters: Let the Inventors Speak,”
The Economist 460 no. 8820 (January 26, 2013),
16.↩
12. Matthew Bevis, “What Most I Love I Bite,” in the
“Review of The Collected Poems and Drawings of Stevie
Smith,” London Review of Books 38
No. 15 (28 July 2016), 19.↩
13. Brihadâranyaka-Upanishad
in The Upanishads, Pt. II, trans. F. Max Müller in
The Sacred Books of the East, Vol. XV, ed. F. Max Müller
(Oxford: Clarendon Press, 1900), 141.↩
Jean Goodwin, “Wigmore's
Chart Method,” Informal Logic 20 no. 3 (January, 2000),
223-243. doi:
10.22329/il.v20i3.2278 Tree diagram method for complex argument
representation and inference strength assessment for legal analysis.
Mara Harrell, Creating Argument Diagrams, Carnegie
Mellon University. Tutorial on identification of indicators, rewriting
statements, providing missing premises, and reconstruction of arguments.
(28 pp.)
Dale Jacquette, “Enhancing
the Diagramming Method in Logic,” Argument:
Biannual Philosophical Journal 1 no. 2 (February, 2011),
327-360. Also here.
An extension of the Beardsley diagramming method for disjunctive and
conditional inferences as well as other logical structures.
Michael Malone, “On Discounts and Argument Identification,”
Teaching Philosophy 33 no. 1 (March, 2010), 1-15.
doi: 10.5840/teachphil20103311
Discount indicators such as “but”, “however”, and
“although” are distinguished from argument indicators, but help
in argument identification.
Jacques Moeschler, “Argumentation and Connectives,” in
Interdisciplinary Studies in Pragmatics, Culture and Society,
eds. Alessandro Capone and Jacob L. Mey (Cham: Springer, 2016), 653-676.
John Lawrence and Chris Reed, “Argument
Mining: A Survey,” Computational Linguistics
45 no. 4 (September, 2019), 765-818. doi: 10.1162/coli_a_00364
Review of recent advances and future challenges for extraction of
reasoning in natural language.
Frans H. van Eemeren, Peter Houtlosser, and Francisca Snoeck Henkemans,
Argumentative Indicators in Discourse (Dordercht: Springer, 2007).
Sophisticated study of indicators for arguments, dialectical exchanges, and
critical discussion. doi:
10.1007/978-1-4020-6244-5
Wikipedia contributors, “Argument Map,
Wikipedia. History, applications, standards, and references
for argument maps used in informal logic.
(Free) Online Tutorials with Diagramming
Carnegie Mellon University, Argument
Diagramming v1.5 (Open + Free). Free online course on
argument diagramming using built-in iLogos argument
mapping software by Carnegie Mellon's Open Learning Initiative.
(With or registration and two weeks to completion).
Harvard University, Thinker/Analytix: How We Argue. Free online course
on critical thinking with argument mapping with Mindmup
free diagramming software, videos, and practice exercises. (Requires registration
and 3-5 hrs. to complete).
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