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## 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.

1. #### “Argument” Defined

Arguments in logic are composed of premises offered as reasons in support of a conclusion. They are not defined as quarrels or disputes.

1. 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.

2. 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.

2. #### How to Identify the Presence of an Argument

1. There are three main ways of judging the presence of an argument:

1. 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.

2. 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.

3. 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.

2. 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).

3. #### 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.

1. 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.”

2. The number of arguments in a passage is conventionally established by the number of conclusions in that passage.

3. 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.

1. 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.

2. 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.
3. 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.

4. #### 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

in view of

as shown by; as indicated by

given that

inferred from; concluded from; deduced from

due to the fact that

for the reason [* often mistaken for a conclusion indicator]

1. Examples of their use in arguments:

1. “[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].

2. 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.

2. Try the following examples for yourself:

1. “[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.

2. “[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.)
5. #### 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

indicates that

accordingly [* an indicator often missed]

implies that; entails that; follows that

this means

we may infer

suggests that

results in

demonstrates that

for this reason; for that reason [* often mistaken for premise indicators]

1. Examples of their use in arguments:

1. [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.

2. [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.

3. [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.

2. Try the following examples for yourself:

1. “[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.

2. ”[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.

6. #### 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

although

despite; in spite of

besides

though

but

yet

however

moreover

nevertheless

not only … but also

(and also the semicolon “;”)

1. 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.

2. The equal status indicatorand”:

[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.

3. 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.)

4. Try the following examples for yourself:

1. “[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.

2. “[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.

3. “[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.”

7. #### 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.

1. 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:

1. 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.)

2. 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.

3. 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].)

4. Hence the whole argument can now be pieced together as the following complex argument:

2. 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:

1. 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.

2. 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?’

avalkys 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 — but in context, the purpose of the passage is merely to define and explain the meaning of the word “Âdityas.”

Test your understanding with any of the sections for diagramming on the following quizzes, tests, or exercises:

Quiz: Diagramming Simple Arguments
Problem Set 1 PDF
Problem Set 2 PDF
Problem Set 3 PDF
Test: Structure of Arguments Part I

“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.

5. Mary Wollstonecraft, Vindication of the Rights of Woman (1792 London: T. Fisher Unwin, 1891), 273.

6. Irvin D. Yalom, The Gift of Therapy (New York: Harper Perennial, 2009), 133.

7. Maxim D. Frank-Kamenetskii, Unraveling DNA trans. Lev Liapin (New York: VCH Publishers, 1993), 175.

8. Bertrand Russell, The Analysis of Mind (London: 1921 George Allen & Unwin, 1961), 40.

9. Wollstonecraft, Vindication, 175.

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.

#### Readings: Diagramming Arguments

Carnegie Mellon University, iLogos: Argument Diagram Software and User Guide Free software cross-platform. Also, a list with links to other argument diagramming tools.

Martin Davies, Ashley Barnett, and Tim van Gelder, “Using Computer-Aided Argument Mapping to Teach Reasoning,” in Studies in Critical Thinking, ed. J. Anthony Blair (Windsor, ON: Open Monograph Press, 2019), 131-176. Chapter outlining how to use argument mapping software in logic classes. doi: 10.22329/wsia.08.2019

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).

Joe Lau, “Argument Mapping ” Module A10 on the Critical Thinking Web at the University of Hong Kong. (No registration and an hour to complete).

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