diagram argument critical thinking

Diagramming Arguments, Premise and Conclusion Indicators, with Many Examples

Abstract: Analyzing the structure of arguments is clarified by representing the logical relations of premises and conclusion in diagram form. Many ordinary language argument examples are explained and diagrammed.

“Argument” Defined

• How to Identify Arguments

How to Analyze Simple Arguments

• Premise Indicators
• Conclusion Indicators
• Equal Status Indicators

How to Analyze Complex Arguments

• Links to Diagramming Exercises
• Tutorials for Diagramming

Formal arguments are evaluated by their logical structure; informal arguments are studied and evaluated as parts of ordinary language and interpersonal discourse.

Statement or Proposition:

How to identify the presence of an argument.

[1] I conclude the dinosaurs probably had to cope with cancer. These are my reasons : [2] a beautiful lower leg bone was found in Alberta, [3] the end of the fibula was grossly malformed, and [4] this appearance closely matches osteosarcoma in humans.

Since [1] the solution turns litmus paper red, [2] I conclude it is acidic, inasmuch as [3] acidic substances react with litmus to form a red color.

• 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.

“[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.”

“ Because [1] of our preoccupation with the present moment and the latest discovery, [2] we do not read the great books of the past. Because [3a] we do not do this sort of reading, and [3b] do not think it is important, [4] we do not bother about trying to learn to read difficult books. As a result , [5] we do not learn to read well at all.” [1]

Statement [1] provides evidence for [2].

Next, [2] together with [3] ([3a] and [3b] being combined here as one compound statement for simplification) gives evidence for [4].

Finally, as a result of [4], statement [5] concludes with some degree of probability.

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

[1] John didn't get much sleep last night. [2] He has dark circles under his eyes. [3] He looks tired.

[1] Studies from rats indicate that neuropeptide Y in the brain causes carbohydrate craving, and [2] galanin causes fat craving. Hence , [3] 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 fully understood.

[1] The piano teacher should consider an additional study of the pipe organ. [2] As an organist. the teacher would have added income at times when she is not teaching; consequently , and for this reason [3] she would receive added publicity and prestige. Therefore , [4] she would be likely to attract additional students and additional income.

Working with Premise Indicators:

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 ]

[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.

“[3] [the mind must] obtain a little strength by a slight exertion of its thinking powers.”

Working with Conclusion Indicators:

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 (a conclusion follows these phrases; a premise precedes these phrases .)]

“[3a] So it may well be that cancer is induced not by the original substances but [3b] [it may well be that cancer is induced] by the products of their metabolism once inside the organism.”

Working with Equal Status Indicators:

or [ the inclusive “or,” i.e. “ either or or both ”] and as [* when it connects similar clauses; not when it connects a result with a cause ] 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.

Comment : Notice that statements [2] and [3] work together as a reason, so both together provide evidence for [1].

“ … [3] it depends on the indices of refraction of the lens material and [4] [it depends on] the surrounding medium.”

For [1] and [2], so [3].

[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.

as because thus

• 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.)

[1] If students were environmentally A ware, [ then ] they would O bject to the endangering of any species of animal. [5] No student O bjected [to the endangering of the Greenwood white squirrel].

[1] If A then O [5] Not O

“[6] Thus, Lander students are not environmentally A ware,”

[1] If A then O [5] Not O [6] Not A

“The explanation as to why productivity has slumped since 2004 is a simple one. That year coincided with the creation of Facebook ” [11]

“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]

“He asked: ‘Who are the Âdityas?’ Yâ gñ avalkys replied: ‘The twelve months of the year, and they are Âdityas, because they move along (yanti) taking up everything [ i.e. , taking up the lives of persons, and the fruits of their work] (âdadânâ h ). Because they move along, taking up everything, therefore they are called Âdityas.’”[emphasis mine] [13]

Circular Argument:

Links to diagramming online quizzes with suggested solutions, 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 arguments 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. B ri hadâra n yaka-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 without registration and two weeks for 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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Arguments | Language | Fallacies | Propositions | Syllogisms | Ordinary Language | Symbolic

[A10] Argument mapping

Module: Argument analysis

• A01. What is an argument?
• A02. The standard format
• A03. Validity
• A04. Soundness
• A05. Valid patterns
• A06. Validity and relevance
• A07. Hidden Assumptions
• A08. Inductive Reasoning
• A09. Good Arguments
• A11. Analogical Arguments
• A12. More valid patterns
• A13. Arguing with other people

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An (simple) argument is a set of one or more premise with a conclusion. A complex argument is a set of arguments with either overlapping premises or conclusions (or both). Complex arguments are very common because many issues and debates are complicated and involve extended reasoning. To understand complex arguments, we need to analyze the logical structure of the reasoning involved. Drawing a diagram can be very helpful.

§1. Argument maps

An argument map is a diagram that captures the logical structure of a simple or complex argument. In the simplest possible case, we have a single premise supporting a single conclusion. Consider this argument :

Death is inevitable. So life is meaningless.

This can be represented in an argument map as follows:

We can also use numbers to label the premises and conclusion. (1) = Life is meaningless, (2) = Death is inevitable:

Let us now look at another example:

(1) Paris is in France, and (2) France is in Europe. So obviously (3) Paris is in Europe.

Here is the corresponding argument map:

Note that the two premises are connected together before linking to the conclusion. This merging of the links indicate that the two premises are co-premises which work together in a single argument to support the conclusion. In other words, they do not provide independent reasons for accepting the conclusion. Without one of the premises, the other premise would fail to support the conclusion.

This should be contrasted with the following example where the premises are not co-premises. They provide independent reasons for supporting the conclusion:

[1] Smoking is unhealthy, since [2] it can cause cancer. Furthermore, [3] it also increases the chance of heart attacks and strokes.

Instead of writing the premises and the conclusion in full in the argument map, we can label them and write down their numbers instead:

This diagram tells us that [2] and [3] are independent reasons supporting [1]. In other words, without [2], [3] would still support [1], and without [3], [2] would still support [1]. (Although the argument is stronger with both premises.)

Finally, it is also possible to have a single reason giving rise to multiple conclusions :

[1] Gold is a metal. [2] So it conducts electricity. [3] It also conducts heat.

§2. More complicated examples

Now that we know the basics of argument maps, we can combine the templates we learn above to represent more complicated arguments, by following this proceudre:

• Identify the most important or main conclusion(s) of the argument.
• Identify the premises used to support the conclusion(s). These are the premises of the main argument.
• If additional arguments have been given to support any of these premises, identify the premises of these additional arguments as well, and repeat this procedure.
• Label the premises and conclusions using numerals or letters.
• Write down the labels in a tree structure and draw arrows leading from sets of premises to the conclusions they support.

Let us try this out on this argument:

Po cannot come to the party because her scooter is broken. Dipsy also cannot come because he has to pick up his new hat. I did not invite the other teletubbies, so no teletubby will come up to the party.

We now label and refomulate the premises and the conclusions:

• Po cannot come to the party.
• Po's scooter is broken.
• Dipsy cannot come to the party.
• Dipsy has to pick up his new hat.
• I did not invite the other teletubbies.
• [Conclusion] No teletubby will come up to the party.

We can then draw the argument map like this:

This is an example of what we might call a multi-layered complex argument, where an intermediate conclusion is used as a premise in another argument. So [1] and [3] are the intermediate conclusions, which together with [5] lead to the main conclusion [6]. This complex argument is therefore made up of three overlapping simple arguments in total. Of course, in this particular case you can understand the argument perfectly well without using this diagram. But with more complicated arguments, a picture can be an indispensable aid.

Draw argument maps for the following arguments:

§3. More tutorials

If you are interested to learn more about drawing argument maps, you can visit the Australian company Austhink for a set of detailed online tutorials on argument mapping. An earlier version of these tutorials was commissioned by the University of Hong Kong:

• Online argument mapping tutorials

§4. Software for drawing argument maps

• Argunet - Free argument map editor that runs on Java.

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Argument Diagramming

http://oli.cmu.edu/courses/free-open/argument-diagramming-course-details/

Alexandra Drozd, Carnegie Mellon University, Department of Philosophy Maralee Harrell, Carnegie Mellon University, Department of Philosophy

Argument Diagramming course at the Open Learning Initiative, Carnegie Mellon University

The Argument Diagramming course at the Open Learning Initiative at Carnegie Mellon University helps students take charge of their own thinking, and learning, by introducing or reintroducing them to fundamental critical thinking skills that are useful across courses, majors, and areas of life. Argument Diagramming, is a method of argument analysis using diagrammatic representations.

This material exemplifies connected learning principles because this method of analysis and these ways of thinking can be used across domains and interests, with peers and with colleagues, anywhere from the ultimate Frisbee field to the computer lab to the cafeteria. The Argument Diagramming course focuses on crucial 21st century cognitive competencies; for example, the determining the premise and conclusion of an argument is essential to the Cognitive Processes and Strategies of Critical thinking, Analysis and Reasoning/Argumentation.

We have incorporated openly-available digital Argument Diagramming software, iLogos, into the OLI’s online activity platform, which enables us to collect data about every interaction of every student, with our online course. The data collected informs continued development and redevelopment efforts, as the course is improved to further explicate the objectives and concepts about which students may harbor misconceptions or have remaining questions. Since 2009 we have reorganized the course to better support a “Big Picture” view of the material and provide more effective connections to existing student knowledge.

The Argument Diagramming course unifies student interaction with researcher analysis through persistent collaboration, and adapting through research on this data, to student needs and practices.

The OLI course Argument Diagramming, in existence since 2006 and used by participants at multiple institutions nationwide, exemplifies open learning in a number of ways. As indicated by CC-By ND status and availability Open + Free at http://oli.cmu.edu/courses/free-open/argument-diagramming-course-details/ , it is an “open educational resource”. Also relevant is the course’s “data openness”. The anonymized data collected from the OLI course is openly available so that researchers and learning engineers the world over may learn from this data.

Argument Diagramming appeals to a wide variety of learners, with argument examples on subjects from gun control to poor academic performance as well as a wide variety of activities so learners may practice outcomes in many different ways prior to assessment.

Students drive development of the OLI Argument Diagramming course, from graduate students who led its creation to data continually gathered from student participants that shapes further developments of the course. Key features of this course have emerged from student ideas and in response to student data, including platform integration of the iLogos software, presentation of a high-level Big Picture of Argument Diagramming and the expansion of sections on arguments contained within single sentences and words that frequently indicate parts of arguments.

We incorporate digital resources and practices by providing digital images of all argument diagrams used in the course, integrated digital argument diagramming software to complete activities in the course, and freely available Argument Diagramming software for continued use following the completion of the course.

As we continually collect data, we continually have areas that can be improved. We hope to expand the course to specifically address certain “learning contingencies” revealed in a study of F2012 data. In the current version of the course there are certain questions that nearly perfectly predict performance on exam questions. These are cases where we would like to examine performance on all activities related to a certain learning outcomes and create additional activities where students can achieve said outcomes.

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2.01: Analysis, Standardization, and Diagramming

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Thaddeus Robinson

• Muhlenberg College

Analysis, Standardization, and Diagramming

Section 1: introduction.

In this unit, we will focus on argument identification and analysis.  Argument identification involves spotting arguments and distinguishing them from their surroundings.  We briefly discussed argument identification in Chapter 1, and saw that we need to be on the lookout for particular words (e.g. ‘since’, ‘so’, ‘because’, and ‘hence’) that frequently indicate the presence of an argument.  The other skill we will focus on in this unit is argument analysis.  In general, to analyze an argument is to determine its intended structure.

As we’ve seen, the crucial elements or “bones” of any argument are its premises and its conclusion, and we determine an argument’s structure by identifying these elements and figuring out how they fit together.  We are beginning with the skills of identification and analysis in particular because recognizing and accurately determining  argumentative structure are prerequisites for accurate evaluation.  After all, we can’t assess whether an argument is good or bad until we know what the argument is supposed to be!  More precisely, we can’t say whether an argument is sound or not, unless we know what its conclusion is, and what premises have been offered on its behalf.

Before we get started, it is important to make two notes.  First, you are already skilled at argument identification and analysis.  Again, these are prerequisites for evaluation, and you have been evaluating arguments almost your whole life.  However, these skills are largely intuitive.  The goal here, then, is not to develop new skills, but instead to sharpen or enhance existing ones.  To this end, we will slow down and think through the steps involved in identification and analysis.  By sensitizing ourselves to argumentative language in this way, we will make what is mostly implicit in everyday practice, explicit.  More specifically, this will involve giving names to a variety of argumentative moves and situations, identifying a method for seeing behind an author’s words, and learning some techniques for representing arguments.  Proceeding in this way will allow us to see in detail how arguments are expressed and structured, and will ultimately put us in a better position to evaluate and engage with arguments.

The second note has to do with reading.  We will be focusing on arguments in text, and one of the things that we will find is that in all but the simplest cases, argument analysis requires active engagement with the text.  We actively engage with a text when we ask questions of it: what is the author trying to say?   What reasons does the author give for the conclusion?   Why do they believe the premises are true?    We do not always read actively.  When we read a magazine or a novel, we normally sit back and let the author provide us with information or tell us a story.  However, when it comes to argument analysis passive reading will not do.  In most cases, argument analysis will involve actively looking to the text for clues, and using these clues to piece together the author’s intended argument.  Active engagement with a text can be demanding—especially at first, but it is an important skill, and something you will likely find becomes easier with practice.

Section 2: Analyzing Simple Arguments

Let’s start with a simple argument.

Since Banana Republic’s sale items will go fast, I think we should go there first.

The first thing we should notice in this case is the word ‘since’.  This word typically indicates the presence of an argument, and a look back at the context confirms this.  Now that we have an argument, how do we analyze it?  We need to break the argument into its components, i.e. its premises and conclusion.  Because the word ‘since’ is not only an argument indicator, but a premise indicator, we know that what follows it—‘ Banana Republic’s sale items will go fast’—is being used as a premise.  This premise supports the proposition ‘we should go there first’ which is the conclusion.  We have captured all there is to say about this argument’s structure, and so our analysis is complete.

Importantly, what makes this argument simple, as we will use the term, is not that it is short or easy to understand.  Instead, this argument is simple because  it draws only one conclusion.  As we will see later in the chapter, simple arguments can be chained together to form complex arguments.  For now, however, let us take a look at another simple argument.

The coach will likely be fired, given the allegations of unethical recruiting practices and the team’s sub-par performance the last three years.

The term ‘given’ and a quick look at the context tells us that we have an argument on our hands.  ‘Given’ is a premise indicator, and in what immediately follows the author makes two claims.  The author is claiming that there are allegations of unethical recruiting practices and that the team’s performance over the last three years has been sub-par.  The author is offering these two premises as evidence for the proposition that the coach will likely be fired, and so this latter proposition is the conclusion.

This second example is similar to the first; however, we should note two important differences.  First, in this example there are two premises, whereas in Ex. 1 there was only one.  This does not change the fact that like Ex. 1, Ex. 2 is a simple argument.  Again, what makes an argument simple is that it draws only one conclusion, and this means that simple arguments can have many premises.  The second point has to do with order.  In Ex. 1 the premise came first and the conclusion last, whereas in Ex. 2 the order is reversed.  This teaches us an important lesson: premises are not always presented first, nor are conclusions always presented last .  As it turns out, in everyday speech and writing, arguments are presented in many different ways.  Sometimes, in fact, the conclusion is placed between premises (as we will see).

Section 3: Representing Argumentative Structure

The point of analyzing an argument is to uncover its structure, and it will be useful to have a uniform or standard way of representing the bones of an argument.  For simple arguments we will use the following process of representation.  For each distinct part of an argument (each of its premises and its conclusion), we will assign a unique number, assigning the highest number to the conclusion.  We will then stack the propositions in numerical order, and add a conclusion indicator to the conclusion for clarity.  We will call this way of representing an argument, a standardization .

In Ex.1, the argument consists in two propositions: the premise and conclusion, and so in our standardization we will stack the numbers 1) and 2).  We will assign 2) to the conclusion, and then add the conclusion indicator ‘so’ to the argument.  This gives us the following standardization of Ex. 1:

• Banana Republic’s sale items will go fast.
• So, we should go there first.

The argument in Ex. 2, consists of three propositions: two premises and the conclusion.  As a consequence, our standardization will stack the numbers 1, 2, and 3, we will make 3 the conclusion, and add the indicator word ‘so’ to it.  This gives us the following standardization for Ex. 2:

• There have been allegations of unethical recruiting practices.
• The team’s performance over the last three years has been sub-par.
• So , the coach will likely be fired.

Standardizing arguments is a useful way of representing an argument’s structure, but it is not the only way.  A different way of representing the bones of an argument is called diagramming .  Diagramming is a more abstract way of representing arguments that allows us to see an argument’s structure independently of its subject matter.

Just as we would in a standardization, we start a diagram by assigning each part of an argument a number.  We start numbering at one and reserve the highest number for the conclusion.  This is where the similarity ends, however.  First, when diagramming, we let the assigned number stand in for the whole proposition; we do not rewrite the premises and conclusions as we do in standardizations.  Second, when we diagram we will use numbers with circles around them to indicate propositions.  Third, we will not stack the numbers, but work horizontally to capture the relation between the premise and conclusion.  Doing so, requires the use of two additional symbols: the arrow (‘→’) represents the relationship between an argument’s premises and its conclusion.  The arrow points away from the premises, and toward the conclusion the premises purport to establish.  Further we will use the plus (‘+’).  The + represents the idea that an author intends two or more distinct propositions to be taken together as evidence.

The diagram of Ex. 1 looks like this:

Thus, 1 represents the proposition ‘ Banana Republic’s sale items will go fast’, while 2 represents the conclusion that ‘we should go there first’.  Moreover, the arrow points from 1 to 2 because 1 is the evidence that purports to establish 2.

In the case of Ex. 2, the author offers two pieces of evidence on behalf of his conclusion. and this is reflected here by the conjunction of 1 and 2 (which represent the propositions that there are allegations of unethical recruiting practices and that the team’s performance over the last three years has been sub-par).

Diagram of Ex. 2:

It is important to note that standardization and diagramming are distinct ways of representing argumentative structure, and we can use one without the other.  That is, we might standardize an argument without diagramming it, and vice versa (though if you choose to diagram an argument without also standardizing it, you’ll have to find a way connect your numbers to the propositions they represent).  In this unit, however, we will always standardize and diagram examples, and we will use the numbers assigned in the standardization of an argument for the diagram.   Now that we have discussed simple arguments, let’s see how analysis works in more complex cases.

Section 4: Analyzing Complex Arguments

A simple argument draws only one conclusion.  However, simple arguments can be put together to create complex arguments. As we will see, complex arguments draw one or more sub-conclusions on the way to the main conclusion.  Consider the following case:

You should fill your car’s tires with nitrogen instead of plain air for two reasons. First, nitrogen will diffuse through the tire walls much more slowly than plain air, since nitrogen molecules are bigger than molecules of oxygen.  Second, filling your tires with nitrogen keeps water vapor from getting inside your tires.

Uncovering the structure of this argument means isolating all of the parts and determining their relationships.  We will begin by using indicator words as our guide.  On a first pass, we should be struck by the presence of two indicators: ‘two reasons’ and ‘since’.  The author is claiming that there are two reasons for thinking that “You should fill your car’s tires with nitrogen instead of plain air.”  The author has numbered these premises using the term ‘first’ and ‘second’.  Thus, these two propositions are premises that support the conclusion that you should put nitrogen in your tires.  However, there is one other indicator word here—‘since’.  This suggests that there is a second justification present.  Indeed, the fact that “nitrogen molecules are bigger than molecules of oxygen” is given as a reason to believe that “nitrogen will diffuse through the tire walls more slowly than plain air will.”  This means the author’s claim that “nitrogen will diffuse…” is being used as both a premise and a conclusion.   On the one hand, it is a premise because it supports the proposition that you should fill your tires with nitrogen.  On the other, it is a conclusion because it is supported by the proposition that nitrogen molecules are bigger than oxygen molecules.

Our analysis is complete; we have uncovered all the parts of the argument and we know how they are related.  In order to represent this argument’s structure let’s standardize it.  As we learned above, we should assign a number to each relevant proposition reserving the highest number for the conclusion.  Wait.  There are two conclusions in this argument.  Which one should we assign the highest number?  We will reserve the highest number for the ultimate or main conclusion, which in this case is that “You should fill your car’s tires with nitrogen instead of plain air.”  Can we simply assign numbers to the other propositions, and standardize the argument like this:

Standardization for Ex. 3?

• Nitrogen will diffuse through the tire walls much more slowly than plain air.
• Nitrogen molecules are bigger than molecules of oxygen.
• Filling your tires with nitrogen keeps water vapor from getting inside your tires.
• So, you should fill your car’s tires with nitrogen instead of plain air.

No.  While this standardization captures all the relevant propositions, it misses an important part of the argument’s structure.  Although 1-3 all ultimately support the conclusion, they do not do so in the same way.  The proposition that nitrogen molecules are bigger than molecules of air only supports the conclusion because it gives evidence for the proposition that nitrogen will diffuse more slowly than plain air.  In other words, 2 only supports 4 through its support of 1; let’s say that 2 offers only indirect support of 4 whereas 1 and 3)offer direct support , and our representation of the argument needs to reflect this.  This means that we’ll need to supplement our basic standardization process.

First, let’s follow the convention that conclusions always come after their premises, so we’ll want to assign the proposition ‘nitrogen molecules are bigger than molecules of oxygen’ a higher number than the proposition ‘nitrogen will diffuse through the tire walls much more slowly than plain air’.  Second, since the proposition ‘nitrogen will diffuse…’ is a conclusion, we should make it clear by adding an indicator word to our standardization.  Last, when there are multiple inferences in an argument we need to know for sure what premises lead to what conclusion.  To mark this, let us agree that after every conclusion we will note the premises from which the proposition is drawn. Following these additional rules gives us the following standardization:

Standardization for Ex. 3:

• So , nitrogen will diffuse through the tire walls much more slowly than plain air. (from 1)
• So , you should fill your car’s tires with nitrogen instead of plain air. ( from 2 and 3)

What does a diagram of Ex. 3 look like?  We begin our diagrams with the conclusion.  Following the number system we used in the correct standardization of Ex. 3, our main conclusion is 4, so we should start by drawing the number four with a circle around it.  Evidence is offered on behalf of this conclusion, so we should draw an arrow to the left of our circled number pointing to it.  What evidence is offered on behalf of 4?  The propositions numbered 2) and 3) above are the direct evidence for 4), and we should connect these pieces of evidence using a plus since it is clear that the author intends these pieces of evidence to be taken together.  Last, as we’ve seen, the author offers 1) as evidence for 2), so we should draw an arrow to the left of 2) pointing to it, and 1) to the left of that.  This gives us the following diagram:

Diagram for Ex. 3:

The diagram of this argument shows very clearly that this complex argument is built out of two simple arguments.  Working backwards from the main conclusion, there is the simple argument with 2 and 3 as premises and 4 as the conclusion.  In addition, because the author gives a reason for 2, we have another simple argument from 1 to 2.  Let us turn to some exercises.

Exercise Set 3A:

Directions: For each of the following determine whether the passage contains an argument.  If it does not, write “no argument”.  If it does, then standardize and diagram the argument.

It seems likely that this year will be Morita’s first as a professional without a major win on account of continuing problems with her short game.

Your health care provider will not cover this test on the grounds that it is neither medically necessary nor an expense covered by your policy.

Disney was the first studio to release a truly massive film originally set for theaters onto a streaming platform.  To watch their latest version of Mulan, viewers needed to pay close to $30 on top of their  Disney+ subscription.

Judging from the astonishing range of daily life and human endeavor reflected in his poems and plays, we can only infer that Shakespeare was a keen observer.

You are not eligible for an upgrade, since you haven’t signed up for our newsletter, and signing up is necessary for eligibility.

Advisory boards are limited in authority, and consequently in legal responsibility, to those powers granted by the local government.

Exercise Set 3B:

We can be sure that the murder was committed by the judge, given that it had to be either the butler or the judge, and we know it wasn’t the butler since he was passionately in love with the victim.

Since goat’s milk contains smaller fat globules than cow’s milk, it is easier to digest than cow’s milk.  Consequently, goat’s milk may be a viable alternative for children who have a difficulty digesting cow’s milk.

To insert genes into a cell, scientists often prick it with a tiny glass pipette and inject a solution with the new DNA.  The extra liquid and the pipette itself, however, can destroy it.  In place of a pipette, scientists at BYU have developed a silicon lance.  They apply a positive charge to the lance so that the negative charged DNA sticks.  When the device enters a cell, the charge is reversed and the DNA is set free.  In a recent study using this method, 72 percent of nearly 3,000 mouse eggs cells survived. [1]

The proposed ban on high-capacity magazines doesn’t make any sense.  Think about it: a ban on high-capacity magazines wouldn’t necessarily prevent any of these mass killings, since with practice a person can learn to swap out a depleted 7 round magazine in a couple of seconds or less.

Because attention is a limited resource—we can attend to only 110 bits of information per second, or 173 billion bits in an average lifetime—our moment-by-moment choice of attentional targets determines, in a very real sense, the shape of our lives. [2]

The chief reason painting is superior to sculpture is that painting as a medium affords the artist many more possibilities than sculpture does.  After all, how can you sculpt mist or clouds, or the appearance of reflective surfaces? Likewise, in painting the artist can represent impossible objects, and this is not an option for the sculptor who is bound by the laws of space and time.   

Exercise Set 3C:

Make up a complex argument and write it out.  Once you’ve done this, standardize and diagram your argument.

#2: Below is a standardized argument without any content.  Draw the diagram that corresponds to this standardization.

3) So, xxxxxx (from 1 and 2)

4) So, xxxxxx (from 3)

5) So, xxxxxxx (from 4)

Below is an argument diagram.  Create the standardization that corresponds to this diagram (don’t worry about content, just follow the xxxxx pattern from above).

What is a “rhetorical question”?  Give an example.  Can a rhetorical question be part of an argument?

• Adapted from Giller, G. (2014, July 1).  Hold Still.  Scientific American , 311 (1), 19. ↵
• Adapted from Anderson, S. (2009, May 25). In Defense of Distraction. New York . 43 (18), 28-33, 100-101. ↵

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10 Using Computer-Aided Argument Mapping to Teach Reasoning

Martin davies; ashley barnett; and tim van gelder, introduction [1] , [2].

Argument mapping is a way of diagram m ing the l ogical structure of an argument to explicitly and concisely represent reasoning. (See F igure 1, for a n example.) The use of argument mapping in critical thinking instruction has increased dramatically in recent decades. A brief history of argument mapping is provided at the end of this p a per.

P re- and post-test studies have demonstrate d t he pedagogi cal ben e fit of argument mapping using cohorts of university students and i n telligence analysts as subjects, and by comparing argument map ping intervention s with data from comparison groups or benchmarks from other meta-analytic reviews . It has been found that intensive practice mapping argume n ts with the aid of software has a strong positive e f fect on the critical thinking ability of students . Meta-analys i s has shown that high-intensity argument mapping courses improve critical thinking scores by around 0.8 of a standard deviation — more than twice the typical effect size for standard c ritical thinking courses (van Gelder, 2015) . This strongly suggests that argument mapping is a very effective way to teach critical thinking.

The process of making an argument map is beneficial because it encourages students to construct (or reconstruct) their arguments with a level of clarity and rigor that, when divorced from prose, often goes unnoticed. The shortcomings of a badly-constructed map are plain to see. This is not the case with dense blocks of written prose, which can give an impressionisti c sense of rigor to the reader.

Figure 1. A short argument showing the main conventions used in argument mapping. The main conclusion is placed at the top of the map. The reasons for the main conclusion are identified by green shaded areas connected by lines to the main conclusion. The main conclusion in this example has two reasons, 1A and 1B. Inside the green shaded areas white claim boxes are used to display individual premises. Premises are placed in separate premise boxes because each premise needs its own justification. The surrounding green reason envelope effectively groups together linked premises working together to form a reason for the conclusion. Argument maps clearly show which premises of a reason are supported by further reasoning. For example, 1A-a is a premise, which is itself supported by a reason, 2A-a. As claim 1A-a is both a premise in one inference and a conclusion in another it sometimes called an ‘intermediate conclusion’ or lemma. Objections to claims are identified by a red shaded area. In the map above, there is only one objection, 2C-a. NB: When colour cannot be used the labels to the right of the shading helps to designate reasons and objections (i.e., the words ‘supports’, ‘opposes’).

Argument maps can also help students evaluate reasoning because they can easily focus on eva luating each inferential step of an arg u ment. These inferential steps are indicated by the green and red co n necting lines in the example provided. Students using argument ma p ping software can easily see how their evaluation of each step affects the conclusion. For example, i n the argument in figure 1 , suppose the objection in red is strong enough that we can no longer accept claim 1B-a in the reason above it. That would mean that the second reason given for the contention (formed by claims 1B-a and 1B-b ) no longer offers any support for the con clusion . However, the first reason (formed by claims 1A-a and 1A-b ) is unaffected by the objection and may still be strong enough to establish the conclusion. A map makes this very intuitive. It is much harder to see the implications of chan g ing premises using prose alone and without the visual markers pr o vided by mapping software.

One of the main pitfalls when using argument mapping in teaching is that student s may find the level of rigor and clarity encouraged by the tec hnique to be onerous. However, u sing interesting examples that increase the demands of the argument mapping course gradually and incrementally allow s students to have fun exploring how different argument s work . In most argument mapping software students can freely move the parts of an argument around and experiment with d ifferent logical structures. This ability to “play around” with an a r gument allows students , over time, to gain a deep and practiced u n derstanding of the structure of arguments —an important aim of any critical thinking course . Anecdotally, i t also helps with student e n gagement: by manipulating parts of a map using a software, partic i pants more actively engage with critical thinking tasks than they would do otherwise (i.e., if maps were not being used) .

From an instructor’s point of view, adapting a classroom to teach critical thinking using argument mapping requires flexibility, and a willingness to experiment and try out new methodologies and princ i ples. Some of these are covered in this paper. Fortunately , a variety of s oftware and the exercises needed to run an argument mapping course are available for free online. We return to these later.

Computer-aided argument m apping

Computer-aided argument mapping (CAAM) uses software programs specifically designed to allow students to quickly represent reasoning using box and line diagrams. This can, in principle, be done without software (Harrell, 2008) , but the software makes it much easier. Bo x es are used to contain claims and line s are used to show which claims are reasons for other s . The software does no t itself analyze argume n t ative text s , or ch eck the validity of the argument s , but by making argument maps students can, with practic e, get better at argument analysis and evaluation .

In terms of entry-level skills required to use CAAM, little more is needed other than a solid understanding of the target language, basic computer skills, a broad familiarity with the importance of critical thinking, and a willingness to experiment with argument mapping software. In terms of achieving expertise in using CAAM, however, a rigorous approach to text analysis is involved, along with adoption of a number of CAAM methodical principles, and of course, the help of a dedicated and experienced instructor. Lots of argument mapping practice (LAMP) is also recommended (Rider & Thomason, 2008) .

The theoretical basis for argument mapping improving critical thinking skills is based on two principles:

• It takes for granted the well-established notion of dual coding as it is understood in cognitive science. Human information processing is enhanced by the use of a number of sensory modalities. Diagrams and words allow better cognitive processing of complex information than words alone.
• It assumes the not unreasonable point that cognitive processing capacity in humans is limited, and that understanding complex arguments is enhanced by “off-loading” information as visual displays (in other words, it’s easier to remember and understand information if one can draw a diagram).

Argument mapping is similar to other mapping tools such as mind mapping and concept mapping. All attempt to represent complex rel a tionships. However, there are also important differences. Unlike mind mapping, which is concerned with associational relationships between ideas, and concept mapping, which is concerned with relational co n nections between statements and events, argument mapping is princ i pally concerned with inferential or logical relationships between claims (Davies, 2011) . There is a difference between argument ma p ping and various diagrammatic representations in formal logic too. Argument mapping is concerned with representing informal, i.e., “r e al world”, or natural language argumentation. It thus contrasts with the use of diagrammatic techniques such as Venn diagrams as used in formal logic. In an important sense, argument maps should make i n telligible what is going on in arguments as they are (imperfectly) e x pressed in prose.

As noted, a rgument mapping software provides several benefits in the classroom. The software makes building argument maps easy, so teachers can provide their students with many practical exercises to work on. Because the software allows the students to edit their maps freely, they can engage in sel f-directed exploratory learning as they try out different argument structures to see what works best.

Argument maps also show the anatomy of an argument more clea r ly than can be done in prose . By seeing models of well- constructed map s, students can appreciate how all arguments are made up of claims and how some of these work together as co-premises. They can see at a glance how claims belong to separate line s of reasoning, and can see why some claims are necessary for an argument to su c ceed and why some are not.

For example, o ften when students are presented with a range of re a sons for a conclusion in prose , they will focus on counting the mi s takes and erroneously think that the side of the debate that made the most number of outrageous mistakes must be wrong about the co n clusion. But by presenting the argument in the form of a map illu s trate s the point that these bad reasons neither increase or decrease the reliability of a conclusion, and hence are irrel evant to our final eval u ation. Instead, attention needs to be focused on the strongest reasons, not the number. It i s possible that the side of an argument that pr e sented the worst reasons for a given conclusion also provided the most conclusive reason (s ee figure 2).

Argument maps can make discussing complicated arguments in a classroom much easier too. The number of reasons or objections to a contention can be easily “read-off” an argument map (this is difficult to do with a prose equivalent). Example arguments can be displayed on the projector and the teacher can point precisely to the part of the argument that he or she want to discuss. When debating issues in a classroom using argument maps can help externalize and depersona l ize the debate so that the students are no longer arguing with one a n other in a competitive way but are collaborating on mapping an a r gument together in an attempt to construct the best argument for or against the conclusion. This promotes a sense of involvement in a joint scholarly enterprise.

Figure 2. Argument maps clearly distinguish between separate reasons, so it easier to focus on the logical implications of the good reasons and not get distracted by the bad reasons that should just be ignored when it comes to evaluating the conclusion.

An additional benefit is this: Maps also make assessing student’s reasoning skills much easier in assignments, because the teacher can clearly see what his or her students had in mind without the confounding variables to be found in an argumentative essay (Davies, 2009). Also, asking the students to make an argument map prior to writing an argumentative essay can also help ensure that the basic structure of the argument is adequate before they start writing. For a number of reasons, this can assist in the process of essay writing.

Teaching using computer-aided argument mapping

Let us now look at how to teach critical th inking using argument mapping . Some of these point s apply to any informal logic or critical thinking class, but they are particularly relevant to any class intending to use argument mapping as a teaching tool .

The parts of an argument

In teaching students about argument mapping it is helpful to first di s t inguish the following component parts of an argument and to provide examples of each:

• contention/conclusion (a singular claim being argued for);
• reasons (a set of claims working together to support a conclusion or sub-conclusion)
• objections (a claim, or set of claims working together to oppose or undermine a conclusion, another reason, or an inference);
• inference (a logical move or progression from reasons to contention).
• Inference indicator words (a word or phrase that identifies a logical progression from reasons to a contention, such as ‘because’, ‘therefore’ or ‘it can be concluded that’);
• Evidential sources taken as the endpoint of a line of reasoning (arguments must end somewhere, and often this will be a source of information, e.g. a media report, or an expert opinion , that we expect people to accept without the need for additional arg u ment.)

A rgument mapping concerns itself with relationships between claims or propositions. The first main challenge is to discuss with students the nature of claims. Experience in teaching argument mapping has shown us that students find this concept problematic, a nd , if students are unclear about claims, they cannot easily create argument maps.

How can the notion of a claim be taught to students? One might start with definition s such as:

• A claim is a declarative sentence that has a truth value; or
• A claim is an assertion that can be agreed with or disagreed with (or partly agreed with).

O ften , however, students find such definitions difficult to grasp. It is best to start with examples of simple empirical statements using the first definition above . M odel claims can be instructive here , along with a discussion about the states of affairs that can establish if and whether certain sentences can be said to be true or false (or empirica l ly uncertain) :

• The door is shut . (This might be true, false, or empirically u n clear , i.e., when viewed from an angle ) .
• Donald Trump was elected President of the United States . (T his is clearly true, and there are a number of facts that make it so. )
• Sally is at McDonald’s . (T his could be determined by observ a tional evidence and perhaps knowledge of Sally dining habits . )
• Acid turns blue litmus paper red . (T his could be determined by procedures used in the science of Chemistry . )

Students should then be encouraged to find similar claims in published literature. They should practice reading passages from texts, paying attention to whether the claims meet the standard criteria. The criteria are as follows.

Claims should be:

• Singular declarative sentences (i.e., not making more than one point);
• Complete sentences (not fragments);
• Precisely expressed with a potential truth value (not vague or ambiguous);
• Free of inference indicator words.

Once simple empirical claims are successfully used to clarify the notion of the claim, instructors can begin to use examples less reliant on a truth value, i.e., claims more subject to dispute and more likely to engender arguments. The second definition of a claim is apposite here: an assertion which can be agreed with or disagreed with (or partly agreed with). For example:

• In a democracy, the poor have more power than the rich.

This is not a simple empirical claim (there is no discoverable fact of the matter) yet it is a claim with a potential truth value—even if this is not easily ascertained. While not a claim with an empirical basis, the same criteria for claims still apply. Examples like this can lead to many useful departure points for instruction and debate.

Once appraised of the distinction between an empirical claim and a contestable claim, one can introduce the distinction between claims and reasons. This is where inference indicator words become important. For example, it would be a mistake to include the following inference as a single claim in an argument map, because it contains two claims connected by the inference indicator ‘because’.

• In a democracy the poor have more power than the rich, because there are more of them.

i .e., not :

but instead:

It should be mad e clear to students that t here should be no reaso n ing going on inside a claim box. S tudents should watch out for typical inference indicator terms that occur in passages of text such as: so, since, consequently, therefore, as a result/consequence, in view of the fact that, as shown by (see Table 1 , below). These terms are repr e sented as relationships between the claims and their location in the map rather than in the premise boxes themselves. Because in this e x ample becomes an inference indicator (not part of the statement), and any claims in boxes are rendered as complete sentences (not fra g ments). This is important to stress because the argument mapping software doesn’t check what the students put into the claim boxes. Without instructor input, students can create unintelligible maps b e cause they put either multiple claims into each box or ungrammatical or fra g mentary sentences that don’t have a potential truth value .

It is also important to make clear to students that claims are not questions, commands, demands, exhortations, warnings, and so on. Shut the door! (a demand) is not a claim as it is not potentially true or false. Similarly, interrogative forms such as: Is Sally going to McDonald’s? is not a claim. (One cannot ask: Is the question: Is Sally going to McDonald’s? true or false?) By contrast, one can establish the truth of the assertion: Sally is at McDonald’s . Practice should be emphasised in establishing claims in key passages of text, identifying non-claims, and turning non-claims into claims.

It is generally helpful to make sure that claims are singular statements and do not include conjunctions (e.g., and, but, moreover) though there is nothing logically wrong with putting conjunctions into an argument map. Conjunctions are permitted in a single claim box if they expand or elaborate on a singular claim rather than add another. If they add another claim they must be treated differently. For example, take So c rates is a man but he is not famous . This is two separate claims: So c rates is a man AND Socrates is not famous —the first true; the second clearly false, and in an argument map we generally shouldn’t conflate them. These would be represented in separate claim boxes.

It is also important to stress that claims are always complete sentences. They should also be clearly potentially true or false: “ Reshine moisturiser may make you look better ” is not even a potentially clear claim (how would one decide if it is true or false?) whereas the more precise “ Reshine moisturiser will make all your wrinkles disa p pear from your face within 24 hours ” is a claim that is much easier to verify or falsify. Moreover, it seems to beg a reason (e.g., that Reshine moisturiser might have exfoliate properties) and this suggests at least that there might be some science behind this. In the latter case, but not the former, there is—potentially at least—a fact of the matter that can be empirically determined. All claims can be mapped, but those with reasons and evidentiary support will inevitably be seen as much stronger—as they should.

The distinction between (a) simple empirical claims; (b) contestable claims that unclearly expressed; and (c) clearly expressed contestable claims which potentially admit of reasons that could be potentially true or false, is fundamental to argument mapping and time needs to be given to explore the differences.

These points are important to establish early in argument mapping as one of the ways in which students can fail to map arguments properly is either by (a) constructing a map without claims at all; (b) using unclear claims or truth-dubious claims; or (c) putting more than one claim inside a reason, objection or contention box. Any of these can lead to poorly constructed maps. Argument mapping can help students understand why these problems are important, but the software doesn’t assess students’ work for these problems. Some programs however offer online tutorials that cover some of these points. [3] Importantly, students should be given time to play around with the argument mapping software being used, and to practice putting claims into boxes. Simple examples of prose, e.g., from Letters to the Editor, advertising slogans, or extracts from academic texts can be used for this purpose.

Sources of evidence and the provisional endpoints of arguments

Arguments and argument maps need to stop somewhere and where possible it is good practice to finish a line of reasoning with an evidence source that is uncontentious and can be accepted without further debate. Evidential sources come in many forms. For example, a person might accept the claim that he or she has disease x because they trust the expert opinion of their doctor. Evidence sources include assertions, data, common belief, case studies, legal judgements, expert opinion, personal experience, quotes, statistics, and so on. The argument mapping software Rational e™ allows users to represent sources of evidence as unique claim boxes that can be used to clearly mark the current endpoint of a line of reasoning (see Figures 3 and 4 below).

Of course, whether a source of evidence is uncontentious or not is provisional, and this provisional nature make the notion of an endpoint to an argument difficult to teach to students. Teachers need to make the point clear to students that context matters when deciding if a particular source of evidence can be used as an endpoint in an argument. It is probably fine to take the testimony of one’s housemate that there is no milk in the fridge, but it is not acceptable to take for granted the assertion that Donald Trump is a part of a conspiracy of reptilian space aliens trying to take over the planet. It probably helps to reassure students that deciding on an acceptable endpoint to their argument is a very difficult thing to do and they can always revise their argument map at a later point in time if they tied off a line of debate too quickly.

Figure 3. Example of source of evidence used to end a line of reasoning. The argument mapping software Rationale™ has unique icons for different sources.

Once the notion of a claim is clear, the concept of an argument needs to be introduced and applied using CAAM software. The notion of an argument, like the notion of claim, may also need some explanation. An argument qua an unpleasant interpersonal quarrel between individuals, is in such common use that it can be hard for students to see the alternative. The philosophical concept of an argument is typically defined as a connected series of claims intending to establish some concl u sion, or variations on this, e.g., a sequence of claims with an inference i.e., a logical move, to a conclusion/contention . Students should be taught to appreciate that while claims are singular propositions only, arguments are—by definition—claims for which reason(s) are given.

Figure 4. Ideally, a good argument map requires all premises to be either supported by further reasoning or provisional sources of evidence.

Simple, Complex and Multi-Layer Arguments

Early on, the distinction between simple and complex arguments should be made clear. A simple argument is one for which a single reason is given; a complex, or multi-reason argument—as the name suggests—is one with a set of reasons supporting a contention. Here is an example of each:

Simple argument with a single reason

Complex argument with more than one reason

A key pitfall for students is in telling whether an argument has separate reasons working independently (as in this last example) or whether the reasons work together as dependent co-premises. We return to this later.

As students advance their understanding of argument mapping, multi-layer arguments can be introduced. These arguments have primary reasons supported by secondary level reasons.

An example is provided below. Here is should be noted that the contention of one argument can become a premise of another argument (naturally, mapping an argument does not imply one agrees with it):

A multi-layer argument

It takes a great deal of practice for students to accurately reconstruct multi-layer arguments from a passage of raw text. Gratuitous assumptions are often made in authentic prose, premises are left out, and connections between premises are contentions are not clear. The job of the argument mapper is to make all connections between reasons and contentions, and between primary and secondary-level reasons very explicit. There is no substitute for a skilful pedagogy that builds student’s skills from achieving competence in analysing and reconstructing simple and complex arguments, eventually to multi-layer arguments.

Expressed as a single multi-level argument this becomes:

The notion of an objection can be generally explained without difficulty as it mirrors the structure of reasons. Indeed, objections are simply reasons against something, and likewise, come in simple, complex and multi-layer variations.

When discussing objections, it should be made clear to students that objections can be supported by reasons—reasons here provide evidence that suggests an objection is a good one. For example:

Students should be made aware that very often passages of text are ambiguous. Argument mapping has to deal with such ambiguities. Is the following example a singular claim, or a claim for which a reason is given (an argument)? i.e., is it best rendered as a simple conditional claim?

Or should it be rendered as an argument (a contention with a premise offered in support of it)?:

Such examples are often context-dependent; a function of whether the author is trying to convince the reader of something, or whether they are merely asserting something. Class time should be devoted to looking at passages of text, establishing whether they are arguments or mere assertions and translating them into the argument mapping software.

As well as statements that could be arguments, there are also arguments that have implicit inferences that need elucidation. This phenomenon is very common. For example:

• If you want a new car, now is the time and Hindmarsh is the place.

This advertising slogan for a Building Society money-lender is probably best interpreted (charitably) as an argument, not merely a conditional statement. It is trying to convince us of something. Context, and knowledge of the role of money-lenders in society can help interpret it. A moment’s reflection will tell us that the passage is trying to convince us that we should borrow money from Hindmarsh . Unfortunately for students, this contention is not present in the passage but must be gleaned from it. Indeed, the passage also intimates we want a new car! What seems like a simple conditional assertion appears to be a subtle argument with an intermediate conclusion and number of assumed premises. A possible interpretation of the argument is represented using the argument mapping software Rationale™ below.

No argument software can assist on its own with the interpretation of difficult passages of text like this, and an instructor’s role is essential (Note that argument mapping convention requires that implicit or hidden claims, when explicated, are expressed in square brackets […].).

Exposure to many different texts, and teaching sensitivity to argument context, can help. For example, the following advertising slogan:

• The bigger the burger the better the burger, and the burgers are bigger at [Hungry] Jack’s.

conceals an implicit conclusion: So/Therefore the burgers are better at [Hungry] Jack’s. Not including the contention renders the passage as a simple assertion rather than what it really is, namely, an argument with an implied contention—and a non-sequitur at that!

Enthymematic arguments (with suppressed claims) are difficult for students, and are commonplace in reasoning. In this example, these premises work together as co-premises to support the (implied) contention. We shall discuss how to deal with these below.

As well as dealing with enthymematic arguments, mapping is also helpful in clearly identifying and exposing instances of circular reasoning—where question-begging supporting reasons are provided, as the following example indicates:

Inference indicators

Early in class instruction it is important to introduce the idea of an inference indicator. There are two types: (a) reason indicators and (b) conclusion indicators. The difference between them is the role they play in an argument. It should be demonstrated how these words and phrases have different grammatical roles too. Reason indicators such as because point to the reason in a grammatical construction; conclusion indicators (like so and therefore) point to the contention. The role they play in sentence construction can be introduced and it can be shown how they can be transposed.

Students should learn the different kinds of indicators to help determine what a reason is; and what a conclusion is. They should be given practice in translating passages like these into simply box and arrow diagrams, or—if they are confident—into argument maps. A table showing how the indictors work can be helpful here (examples provided here are not exhaustive).

At present, CAAM software has a limited range of inference indic a tors most ly using because or the neutral term supports exclusively (i.e., premise X supports contention Y ; or X because Y ) . S tudents need to be able to translate the many inference indicators used in text into the blunt categories offered by CAAM software. This is one of its drawbacks. F uture develo pments might address this. Given present limitations, it is important that students understand how to interpret ordinary language arguments replete in inference indicators of diffe r ent kinds. Nothing substitutes for class work using passages of text that illuminate the many examples of indicator words in use.

Over-interpretation of inference indicators

When students are sufficiently informed about inference indicators, they can be prone to overuse their relevance and see arguments when they are not there. This is something the instructor needs to be wary of as well. Take, for example, the sentence: Sally said she was hungry before, so that is why you can see her eating a sandwich now . This appears to have an inference connector, “so”, but the “so” functions grammatically to connect an explanation to an observation, not as an inference indicator. The passage is not concluding that you can see Sally eating a sandwich. Similarly, Synonyms are good servants but bad masters , therefore select them with care . This is not proffering a contention; it is best interpreted as a subtle piece of advice. Inference indicator words are thus not always indicating an inference (neither is the indictor word thus in that sentence). There is a difference between their use in inference-making and their use in grammatical construction. Again, lots of text-based practice is needed.

Tiers of Reasons/Objections :

A procedural approach to argument m apping.

We have mentioned that arguments can be represented in terms of tiers of reasons and objections in the form of multi-layered arg u ments . It is very easy for students to become overwhelmed by the di f ficulty of this task. How is this best taught and what are the things to watch out for?

As always, it is best to start with simple examples and then attempt more complex examples. The following example , the kind of thing to be found in a ‘Letter to the Editor’ , provides an instructive case.

• Dogs fetch balls and cats don’t, so you can play with dogs. I mean, who’d disagree with that? It’s obvious isn’t it? You can’t play with cats, of course. They are too stuck up. Dogs clearly make better pets.

It is clearly an argument. How can one map it to clearly display the reasoning? To establish this, it is best to ask students to follow a s e ries of steps. Th is is important as th ere is a strong tendency for st u dents to jump into the task of mapping a passage without clearly thinking through the text, nor establishing the connections between the component parts of an argument.

Here is a suggested step-by-step approach that could be used with students to help them understand arguments . It is a good idea to a sk student s to follow these steps for any argument under consideration :

This step is follow by: 

Eliminating the redundant expressions not germane to the argument, and the questions (non-claims), we get the following: <1>Dogs fetch balls and cats don’t, so <2>you can play with dogs. I mean, who’d disagree with that? It’s obvious isn’t it? <3>You can’t play with cats, of course. They are too stuck up. <4>Dogs clearly make better pets.

The claims are as follows:

• Dogs fetch balls and cats don’t
• You can play with dogs
• You can’t play with cats
• Dogs make better pets

Using the What’s the point? test mentioned above, the conclusion reveals itself to be the last claim <4>. This is placed at the top of the map, but how are the reasons supporting it to be arranged? The temptation might be that there are two independent reasons supporting the contention: You can play with dogs and You can’t play with cats.

But this representation of the argument is missing something. W hat is to be done with claim <1> Dogs fetch balls but cats don’t? A t this point a ttention should be drawn to the inference indicator “so” that seems to draw a conclusion , i.e., it is not merely functioning gra m matically in the sentence . But this “so” is clearly not an inference to claim <4>; it appears to be an inference to an intermediate conclusion that consists of claim <2> and thus should thus be represented in a multi-level argument like this:

On reflection, it can be seen that that the two supporting reasons <2> and <3> are best rendered as a single claim—an intermediate concl u sion (they are both making a point about “playing”) —and the claim about “ fetching ” can be seen as reasoned support for this . This ca p tures the intended use of the connector word “so” linking <1> to <2>. There is thus another rule to consider:

The resulting argument map provides a clear example of serial re a soning that accurately represents the case being made:

In the case of more complex arguments additional principles need to be followed.

The principle of abstraction

A very useful guideline for argument mapping is the principle of a b straction . In many cases, t he higher the claim in a multi-layered a r gument the greater the degree of abstraction; or to put it differently, the lower the claim the more specific it should be. In the above exa m ple, “playing” is more abstract than “ fetching balls ” , and both claims are less abstract than “better pet ”. They provide serial support for each other . Students should be guided in how to apply this principle, as without this, maps can become a jumble of disorganized claims with no clear hierarchical structure. Once again, this requires practice and students should be given a number of exercises where they are required to rank claims in terms of their degree of abstraction. To our series of rules we can add the following :

The principle of level consistency

Complex arguments have both a vertical and a horizontal axis. A r guments can be multi-layered along the vertical axis (as we have just seen) , but premises are present along a horizontal axis as well. I n sofar as many premises can be brought to bear in an argument it is i m portant to stress another principle, the principle of level consistency. W ithin each horizontal level, reasons or objections should be appro x imately of equal weighting in terms of their abstraction or generality. In the following argument t his rule is not adhered to and is cons e quently hard to interpret:

This argument is improved by subordinating lower-level claims to a more general claims at the middle-level, and ensuring level consiste n cy at the lower level, as follows:

We can thus add another guideline :

Missing Premises

Teaching students how to look out for missing premises is complex, but there are strategies that can help. It is difficult because reasoning is often replete in missing premises. Indeed, it is very rare that all premises are made explicit in reasoning. This is due to the implicit reliance of speakers or writers on the background beliefs assumed to be shared in any argumentative exchange. Here is a simple example.

• Art must represent the world if it is to appeal to a broad audience for generations to come . So t hat’s why Blue Poles will not appeal to a broad audience .

In a normal human exchange, this would be a perfectly clear expression of a (rather dated) view about the painting Blue Poles . It is also an argument. We are giving a reason for a conclusion, as indicated by the words “so that’s why”. However, when teaching argument mapping it is an example of an argument with a missing premise; a premise that needs to be exposed, and made clear. What, precisely, is being argued?

In this case, it is easy to see what missing is. It is the assumption that Blue Poles does not represent the world . Exposing this missing premise allows it to be evaluated, confirmed or rejected. In this example, the missing premise can stated quite easily; in simple passages, this is often the case. But for more complex reasoning a series of steps need to be followed to ensure all missing premises are catered for. Fortunately, there is a very simple way to establish missing premises. This is done by applying two rules: the Rabbit Rule and the Holding Hands Rule . These rules are outlined in more detail in online tutorials available with the software Rationale™ .

Assumptions and how to find them using the Rabbit Rule and Holding Hands Rule

The Rabbit Rule is applied (vertically) to the inferential link between conclusion and the premises. This rule states that no conclusion should come out of thin air. (No rabbits out of hats!) The conclusion term(s) have to be present in the terms of the premises of an argument for it to appear in the conclusion. In the argument under consideration we can see that “ Blue Poles ” appears in the conclusion but does not appear in the available premise. We therefore know that Blue Poles must be supplied to the missing premise.

The Holding Hands Rule is applied horizontally between premises to any remaining terms after the Rabbit Rule has been applied (that is, if a term is not already supplied by means of the Rabbit Rule). The remaining terms must “hold hands” with another premise. No term can appear in one premise alone—there is always a companion term “holding hands”. In this example, we can see that “represent the world” appears in the stated premise, so it must be present in the missing premise. As the argument is negating something about Blue Poles , we similarly apply a corresponding negation to the terms of the missing premise.  The argument can be expressed as follows:

We can add the following to our list of procedural rules to establish missing premises:

The following example of a famous deductively valid argument in Philosophy demonstrates how both the Rabbit Rule and the Holding Hands Rule are satisfied. It also demonstrates an example of co-premises in action:It may not have escaped notice that the two claims that support the above contention are jointly necessary for the conclusion to follow. Strictly speaking they are not two independent reasons supporting the conclusion, but are co-premises that jointing support the conclusion. This raises the important issue of co-premises or “linked” premises. This is another crucial methodological principle that students find difficult.

A co-premise is when two or more premises are jointly necessary for the truth of the conclusion. Co-premises are often enthy me matic and s ome times a co-premise is trivial. For example, a person who reasons that they should rent a house because they should find a place to live as quickly as possible , tacitly assumes that renting a house is quickest way of find ing a place to live .

Such assumed claims are often tacit in arguments in both writing and speech , and are often so trivial they do not need to be stated . However, they are an important feature of arguments. Indeed, every argument has at least two of them. In CAAM this is often mentio ned as “The Golden Rule”: every argument has at least two co-premises. In the following example, we have extended the previous argument discussed by the addition of enthymematic co-premises.

While ubiquitous in reason ing, co-premises are not always unco n troversial . Often, co-premises conceal hidden assumptions that are false or misleading. This is why it is good argument mapping practice to expose them. For example, it need not be accepted (without ev i dence— or even intuitively) that pets that you can play with make be t ter pets than those you can’t [play with] (elderly people , the infirm or disabled , for example, like more docile pets). Being able to e x pose hidden assumption clearly for the purpose of critiquing them is a m a jor advantage of argument mapping. Argu ment mapping software makes identification and representation of hidden claims easier by using color conventions and shading; however, this does not help st u dents deciding how to determine how to locate a co -premise in a pa s sage of text. Clear i nstruction and LAMP is needed. Probably the best way to approach co-premises in the classroom is to begin by discus s in g the differences between complex reasoning and linked reasoning.

Co-p remises (Linke d r easoning)

S tudents find the distinction between linked reasoning (dependent premises) and complex reasoning (independent premises ) hard to grasp. It is best taught by showing students a number of simple multi-premise a rguments and asking them to classify examples of complex and linked reasoning . In the following example, it is fairly easy to see that the supporting premises are independent and not necessary for each other .

Plausibly, neither premise could be true; or both could, or one coul d be true and the other false. If either premise was true t he conclusion could sensibly follow in either case. The conclusion could follow even if one of the claims was missing.

In other examples, co-premises are neede d as the claims are not ind e pendent of each other and are examples of linked reasoning . For i n stance :

• We should go to Rome for our holidays. Rome is beautiful. Also, it will enable us to visit your relatives and this is something really need to do.

The passage complete with numbered claims would look like this:

• <1 We should go to Rome for our holidays>. <2 Rome is beautiful.> Also, <3 It will enable us to visit your relatives> , and <4 this is something really need to do>.

How can one teach students w hich premises are linked and which are independent?

To our set of suggested procedural rules discu ssed earlier, we can add another step:

In the example above the claim Rome is beautiful is an independent reason (it does not depend on visiting relatives) and the contention We should go to Rome for our holidays can be supported by it. The contention can follow from Rome being beautiful regardless of the other claims provided. However, the claims about visiting the relatives appear to be linked. The claim: This is something [Visiting your relatives] we really need to do will not alone support the conclusion without including the claim It [Visiting Rome] will enable us to visit your relatives . Note however, this relationship is not symmetrical. Premise <3> can support the contention without premise <4>. However, <4> can’t without <3>. If one premise can’t support a conclusion without another premise, they are said to be “linked”. In convergent (or divergent) reasoning, none of the claims are dependent on any other claim; either one of the claims might support the conclusion alone. By contrast, in linked reasoning, the claims are not independent; they are necessary for each other for the conclusion to follow.

With <2> as an independent premise, and <3> and <4> being linked premises, the map would appear as follows:

A useful feature of argument mapping is the capacity to display linked premises in an intuitive visual way . Like other software, t he software Rationale™ (used here) uses the colo r green for reasons and the colo r red for objections ( the colo r orange is used exclusiv e ly for rebuttals , i.e., objections to objections ) . Co-premises are ind i cated by an umbrella shading that fades to white . This is a subtle visual indic a tion that no argument is ever complete and more premises could p o tentially be added.

O bjections too can be linked as co-premises as the following exte n sion to the argument indicate. We have added a rebuttal against an objection (in orange) to demonstrate their use.

• On the other hand <5 > travelling to Rome is very expensive ,> primarily because <6 > flights are so expensive>. And <7 > we don’t have a lot of money at the moment>. But then again, <there is plenty of money in the children’s bank account we could use>.

We have laid out the complete map of the argument on page 169.

Note here that the claim that Travelling to Rome is expensive could well object to the conclusion alone, but premise could not (without premise ). The premises under consideration must independently support the conclusion to stand as independent reasons. If this is not the case, the premises are said to be linked.

A brief history of argument mapping

Argument mapping can be traced to the work of Richard Whately in his Elements of Logic (1834/1826) but his notation was not widely adopted. In the early twentieth century, John Henry Wigmore mapped legal reasoning using numbers to indicate premises (Wigmore, 1913; Wigmore, 1931) . Monroe Beardsley developed this, and it became standard model of an argument map (Beardsley, 1950) . On this a p proach, premises are numbered, a legend is provided to the claims identified by the numbers, and serial, divergent and convergent re a soning can be clearly represented. An example of each of these forms of reasoning using the standard model is provided below.

This model is still widely used and is advantageous in contexts where students are required to produce argument maps without access to software (e.g., in paper-based logic and reasoning exams under timed conditions).

In 1958, Stephen Toulmin devised another model of an argument map that included the notion of a “warrant” (which licenses the inference from the reasons, which he called “data”, to the claim), “backing” (which provides the authority for the warrant), modal qualifiers (such as “probably”), and “rebuttals” (which mention conditions restricting the inference) (Toulmin, 1958). An example of a Toulmin map is provided below.

In 1973, Stephen L. Thomas refined Beardsley’s approach (Thomas, 1997/1973) . Thomas included in his approach the important notion of “linked” arguments where two or more premises work together to support a conclusion (the distinction between dependent and ind e pendent premises having being described earlier). This innovation made it feasible for arguments to include “hidden” premises. He is also said to have introduced the terms “argument diagram”, “basic” (or “simple”) reasons, i.e., those not supported by other reasons (as distinct from “complex” reasons). He also made the distinction b e tween “intermediate” conclusions (a conclusion reached before a final conclusion) and a “final” conclusion (not used to support another conclusion). Thomas also suggested including objections as reasons against a proposition, and that these too should be included in arg u ment maps.

In 1976 , Michael Scriven proposed a procedure for mapping that could be recommended to students (Scriven, 1976) . This involved a number of steps: ( 1) writing out the statements in an argument; ( 2) clarifying their meaning; ( 3) listing the statements, including any hi d den claims; and ( 4) using numbers for premises along the lines of the Beardsley-Thomas model. In the case of hidden assumptions, Scriven’s notation used an alphabetical letter to distinguish hidden assumptions from explicit reasons. Scriven also emphasized the i m portance of a rebuttal in argument mapping, a notion identified earlier by Thomas.

In the 1990s a number of innovations occurred. Robert Horn helped popularize the notion of an argument map by producing idiosyncratic, large-format argument diagrams on key issues in philosophy such as “Can Computers Think?” (Horn, 1999; Horn, 2003) . These maps did not adopt either the standard model or Toulmin -style notation for mapping arguments, but did use arrows and pictures to make the co n tent clear, making it obvious for the first time that argument maps could be visually interesting as well as informative. These were di s tributed widely and used in class teaching. In addition, computer software programs began to be developed. This was important, as dedicated argument mapping software allowed premises to be co m posed, edited and placed within an argument map, as distinct from a legend alongside the map.

Argument mapping software

Once dedicated computer software was introduced, the standard mo d el of numbered premises became outdated in all contexts outside its use in examinations. Several iterations of mapping software were d e veloped in Australia and the U . S .A. with increasingly greater levels of sophistication. Tim van Gelder developed Rationale™ and bC i sive ™ , the former designed as a basic argument mapping software, the latter designed for business decision-making applications (van Gelder, 2007, 2013) . Both were later purchased by Dutch company Kritisch Denken BV .

A variety of argument mapping packages are now available, inclu d ing Araucaria, Compendium, Logos, Argunet , Theseus, Convince Me, LARGO, Athena, Carneades and SEAS . These range from single-user software such as Rationale™ , Convince Me and Athena ; to small group software such as Digalo , QuestMap , Compendium, Belvedere, and AcademicTalk ; to collaborative online debating tools for arg u mentation such as Debategraph and Collaboratorium . Enhancements to argument mapping software proceed apace. For example, there are moves to introduce a Bayesian network model to Rationale™ to cater for probabilistic reasoning.

Rationale™ or bCisive are perhaps the easiest programs to use for teaching argument mapping, but they require a subscription. E xcellent free alternative s i nclude the Argumen t Visualization mode in the online MindMup : https://www.mindmup.com/tutorials/argument-visualization.html , and the cross-platform desktop package iLogos

http://www.phil.cmu.edu/projects/argument_mapping/

Argument mapping class room examples

There are a number of free argument resources available online.

• The designers of Rationale™ made tutorials to be used with their software. https://www.rationaleonline.com/docs/en/tutorials#tvy5fw
• Simon Cullen, who helped design the MindMup argument visualisation function, has posted some of the activities he uses for teaching philosophical arguments using argument maps. http://www.philmaps.com
• Ashley Barnett, who has written lots of questions for argument mapping courses for students and intelligence analysts has posted his teaching material on http://www.ergoshmergo.com

In this paper we have covered some of the basic concepts and considerations that teachers need to be aware of when using CAAM in the classroom. A set of procedural steps was suggested that is recommended for use with students. Understanding claims and arguments and how they are structured is only the start. Students should also be aware of how to interpret inference indicators, construct and analyse simple, complex and multi-layer arguments, and be able to integrate objections and rebuttals. They should be wary of misusing inference indicators, confusing reasons with evidence for reasons, and misinterpreting independent reasons for co-premises. There is much more we could have discussed. We have not touched on the use of inference objections (in contrast to premise objections). We have not mentioned argument webs or chains of reasoning, nor have we discussed in detail the appropriate ways to integrate evidence into an argument. However, it should be clear from this brief outline how CAAM can assist students in disentangling arguments in everyday prose—replete, as it often is, with non-sequiturs, repetition, irrelevancies, unstated conclusions, and other infelicities.

Beardsley, M. C. (1950). Practical logic. New York: Prentice-Hall.

Davies, M. (2009). Computer-assisted argument mapping: a rationale approach. Higher Education, 58, 799-820. Higher Education, 58(6), 799-820.

Davies, M. (2011). Mind Mapping, Concept Mapping, Argument Mapping: What are the Differences and Do they Matter? Higher Education, 62 (3), 279-301.

Harrell, M. (2008). No Computer program required: Even pencil-and-Paper argument mapping improves critical-thinking skills. Teaching Philosophy, 31 (4), 351-374.

Horn, R. (1999). Can Computers Think? : Macrovu.

Horn, R. E. (2003). Infrastructure for Navigating Interdisciplinary Debates: Critical Decisions for Representing Argumentation. In P. A. Kirschner, S. J. B. Shum, & C. S. Carr (Eds.), Visualizing argumentation: Software tools for collaborative and educational sense-making . New York: Springer-Verlag.

Rider, Y., & Thomason, N. (2008). Cognitive and Pedagogical Benefits of Argument Mapping: L.A.M.P. Guides the Way to Better Thinking. In A. Okada, S. Buckingham Shum, & T. Sherborne (Eds.), Knowledge Cartography: Software Tools and Mapping Techniques (pp. 113-130): Springer.

Scriven, M. (1976). Reasoning . New York: McGraw-Hill.

Thomas, S. N. (1997/1973). Practical reasoning in natural language (4th ed.). Upper Saddle River, NJ: Prentice-Hall.

Toulmin, S. E. (1958). The uses of argument (first ed.). Cambridge, England: Cambridge University Press.

van Gelder, T. (2007). The Rationale for Rationale™. Law, Probability and Risk, 6 , 23-42.

van Gelder, T. (2013). Rationale 2.0.10. Retrieved from http://rationale.austhink.com/download

van Gelder, T. J. (2015). Using argument mapping to improve critical thinking skills. In M. Davies & R. Barnett (Eds.), The Palgrave Handbook of Critical Thinking in Higher Education (pp. 183-192). New York: Palgrave MacMillan.

Whately, R. (1834/1826). Elements of logic: comprising the substance of the article in the Encyclopædia metropolitana: with additions, &c. (5th ed.). London: B. Fellowes.

Wigmore, J. (1913). The Problem of Proof. Illinois Law Review, 8 , 77.

Wigmore, J. (1931). The Science of Judicial Proof as Given by Logic, Psychology and General Experience and Illustrated in Judicial Trials (2 ed. Vol. Little, Brown and Co. ): Boston.

• © Martin Davies, Ashley Barnett, & Tim van Gelder ↵
• The colored versions of the argument maps in this chapter are available only in the open-access Ebook edition of this book at: https://windsor.scholarsportal.info/omp/index.php/wsia/catalog ↵
• https://www.rationaleonline.com/docs/en/tutorials#tvy5fw). ↵

Studies in Critical Thinking Copyright © by Martin Davies; Ashley Barnett; and Tim van Gelder is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Representing the Structure of a Debate

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• Published: 27 October 2022
• Volume 36 , pages 595–610, ( 2022 )

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In this article I aim to use the 1948 Russell-Copleston debate to highlight some recent problems I have experienced teaching argument analysis in my philosophy courses. First, I will use argument diagramming to represent the arguments in the debate while reflecting on the use of this approach use to teach argument analysis skills. Then, I will discuss the tools and methods scholars have proposed to represent debates, rather than just individual arguments. Finally, I will argue that there is not, but needs to be, a good way to represent argumentative debates in a way that neither obscures the essential details of the exchange nor becomes too unwieldy to extract a sense of the overall debate.

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1 Introduction

In 1948, BBC Radio hosted a debate between Bertrand Russell (1872–1970) and Frederick Copleston (1907–1994) (Russell 1986 ). In that year, Russell was a quite well-known philosopher and logician, while Copleston was an English Roman Catholic Jesuit priest, philosopher, and historian of philosophy who had just begun to publish his multi-volume A History of Philosophy (1946-75). The subject of the debate was arguments for the existence of God, with Copleston insisting that there are good arguments for God’s existence, and Russell maintaining not that there are any good arguments against God’s existence, but rather that there are no good arguments for that conclusion.

While I believe this debate is fascinating in its own right—for both its philosophical and historical significance Footnote 1 —I became interested in this debate as a text to analyze with students. It is better, I thought, that the students should read a serious debate between two very intelligent scholars who are responding to each other in real time than for them to read opposing articles separated by time and space. For this purpose, it served very well—the students were fascinated by both the messiness of the back and forth and also the very nuanced points that each man made.

In this article I aim to use this debate to highlight some recent problems I have experienced in teaching philosophy. First, I will begin to visually represent the arguments in the debate while reflecting on its use to teach argument analysis skills. Then, I will discuss the tools and methods scholars have proposed to analyze debates, rather than just individual arguments. Finally, I will argue that there is not, but needs to be, a good way to represent argumentative debates in a way that neither obscures the essential details of the exchange nor becomes too unwieldy to extract a sense of the overall debate.

2 Diagramming the Russell-Copleston Debate

Although there may be several useful accounts of what constitutes a debate, the description I use is dictated by the pedagogical purposes the debate serves in my classes. Thus, I consider the kind of argumentative debate I find useful to be a discussion between interlocutors in which an argument for a specific claim is considered, and reasons for and against the quality of the argument are exchanged. Footnote 2 Ultimately, I want to teach my students two lessons from a debate: (1) modeling a discussion of an argument that emphasizes support for, and objections to, the claims and inferences made in the argument (and not focus on the person making the argument), and (2) practice determining which parts of an argument are being questioned in the discussion, and what can ultimately be learned about the argument from the exchange.

The Russell-Copleston debate is an excellent example of the kind of argumentative debate I like to use. In it, Copleston proposes three different arguments for the existence of God: the argument from contingency, the argument from religious experience, and the moral argument. The two men agree at the outset on a definition of God, and then Copleston lays out his first argument using Leibniz’s principle of sufficient reason. About halfway through the broadcast, Russell and Copleston turn briefly to the second argument, before moving to the third.

The debate that ensues after Copleston introduces each of the three arguments are illuminating in their own ways, but for the purposes of examining the suitability of the debate for teaching argument analysis skills, I want to focus on the first. Particularly interesting is that (a) Russell objects to Copleston’s argument at various points, each highlighting a different premise or inference that troubles him, and (b) his objections, as well as Copleston’s responses, are themselves arguments with rich structures.

I teach argument representation, analysis, and evaluation using argument diagramming (AD) in all my classes. An AD is a visual representation of the content and structure of an argument, using a very basic graphical structure using nodes and edges. Footnote 3 For example, consider Copleston’s argument from contingency, mentioned above:

First of all, I should say, we know that there are at least some beings in the world which do not contain in themselves the reason for their existence. For example, I depend on my parents, and now on the air, and on food, and so on. Now, secondly, the world is simply the real or imagined totality or aggregate of individual objects, none of which contain in themselves alone the reason for their existence. There isn’t any world distinct from the objects which form it, any more than the human race is something apart from the members. Therefore, I should say, since objects or events exist, and since no object of experience contains within itself reason of its existence, this reason, the totality of objects, must have a reason external to itself. That reason must be an existent being. Well, this being is either itself the reason for its own existence, or it is not. If it is, well and good. If it is not, then we must proceed farther. But if we proceed to infinity in that sense, then there’s no explanation of existence at all. So, I should say, in order to explain existence, we must come to a being which contains within itself the reason for its own existence, that is to say, which cannot not exist. (Russell 1986 , 1p.24)

For the AD, I represent the claims as the nodes (text in boxes) and represent the inferential connections between claims as the edges (arrows indicating direction of inference), and all the excess verbiage Footnote 4 is removed (see Fig.  1 ).

Diagram of Copleston’s opening argument

Research over the past few decades shows that learning to diagram arguments improves students’ critical thinking skills (Chounta et al. 2017 ; Harrell 2011 , 2016 ; Twardy 2004 ; van Gelder 2001 ; Gelder 2003 ; van Gelder et al. 2004 ), writing skills (Harrell and Wetzel 2015 ), and collaboration skills (McLaren et al. 2011 ). Additionally, research specifically on computer-supported argument visualization has shown that the use of software programs specifically designed to help students construct argument diagrams can significantly improve students’ critical thinking abilities over the course of a semester-long college-level course (Kirschner, Shum, and Carr, 2003; Twardy 2004 ; van Gelder 2001 , 2003 ). These computer aids include programs that give students just the bare necessities to construct diagrams (iLogos) to programs that offer hints and suggestions to help students’ construction (Rationale).

By tradition and experimentation, the AD community has developed some syntactic and semantic standards for constructing argumentative exchanges between arguers (or a single arguer considering multiple positions). Inferences made between the main claims of an argument are usually represented by black (or sometimes green) arrows pointing from the premise to the (sub-)conclusion, objections to claims are represented by red arrows (with the head of the arrow at the objectionable claim), and replies to objections are represented either by red arrows (as they are objections to objections) or by orange arrows (although, for a different approach, see, e.g. Peldszus and Stede 2013 ). Thus, a debate can in theory be represented in a single diagram.

For example, after Copleston presents his first argument, Russell’s first objection is to the very idea of a necessary being, and it is supported by a robust argument. Footnote 5 Figure  2 shows this argument in isolation.

Diagram of Russell’s first objection to Copleston’s opening argument

To diagram the exchange between the two we would connect statement 11 in Fig.  2 to statement 1 in Fig.  1 with a red arrow, as shown in Fig.  3 . But, of course, this makes the diagram even bigger than the original, and we’ve just barely started.

Diagram of the combination of Copleston’s opening argument and Russell’s first objection

In general, while it is possible (both in theory and in practice with some programs) to construct an argument diagram with dozens or hundreds of boxes, after 25 + boxes, the usefulness of the diagrams to visualize and understand as a cohesive whole seems to deteriorate. If we continue with this way of diagramming arguments, we can see why.

In the debate, Russell and Copleston fail to come to a resolution on the question of whether a necessary being is possible. So, Russell moves to his next objection, which is to question the truth of premise 8, as shown in Fig.  4 . We can integrate these representations by connecting statement 15 to statement 8 with a red arrow, as seem in Fig.  5 .

Diagram of Russell’s second objection to Copleston’s opening argument

Diagram of the combination of Copleston’s opening argument and Russell’s objections

The exchange, however, doesn’t stop there—Copleston offers a detailed reply to Russell’s second objection, as shown in Fig.  6 . Again, we can further add to the overall diagram by connecting statement 18 to statement 15 with a red arrow, as seen in Fig.  7 .

Diagram of Copleston’s reply to Russell’s second objection

Diagram of Copleston’s opening argument, Russell’s objections, and Copleston’s reply to Russell’s second objection

Map 1 of 7 of Horn’s “Can Computers Think?” argument map

Yoshimi-style map of the Russell-Copleston debate

Dung-style representation of a debate in which A1, A2, A3, and A4 are arguments such that, as indicated by the arrows, A2 attacks A1, A3 attacks A2, and A4 attacks A3

Delhomme-style map of the Russell-Copleston debate

At this point, we are only a quarter of the way through the debate; and we can see that keeping track of the debate in a single diagram on just one page or one screen will eventually become impossible. We can of, of course, do what I have done here—representing each argument, objection and reply in a separate diagram. Ultimately, though, this seems unsatisfactory, since it doesn’t really capture the essence of the flow of the debate, physically keeping the objections and replies apart.

I am not the only one with this view. In 2020, Dana Khartabil wrote a dissertation titled, Visualisation Techniques to Facilitate Argument Exploration . One of her main goals was to the explore argument visualization software by users’ experiences. In so doing, she interviewed many scholars in the AD community.

During the interviews, the experts mentioned limitations of the previous ArgVis [argument visualization] tools and the four main limitations are listed below: (L1) “Most of the tools use nodes and arrows, which are brilliant when you have a small number of arguments but when the number increases to 20–30 nodes, the graph becomes very dense, making exploration very tough.” (L2) “The tools which used node-link have become dense and impenetrable. Arguments can not just be made into pretty pictures because we’re also interested in the content.“ (L3) “The tools we have designed are only for small scale arguments; I would like to have tools that handle a large number of arguments.” (L4) “The biggest challenge of presenting the large-scale arguments is that we want to see the whole picture and see the details of what’s going on using the same tool which we miss in most of the current argument tools”. (Khartabil 2020 , p.50–51)

Another of Khartabil’s main goals was to pilot test some alternative computer supported argumentation visualization tools that tried to counter these limitations. Alternatives of this sort are explored in the next section.

3 Mapping Debates

There are debate representation options other than AD; for example, Bob Horn’s maps of the “Can Computers Think?” debate (Horn et al. 1998 ). Just as an argument diagram is a graph that represents statements as nodes and inferences as edges, a Horn-style map is also a graph that, instead, represents whole arguments as the nodes and support, dispute or restatement as the edges to indicate the relationship between arguments in time (see Fig.  6 ).

As indicated on the map, Fig.  6 is just one of seven maps Horn and his team produced to represent the state of the debate about thinking computers in 1998. Each map is a poster approximately four feet by three feet, and they are truly a work of art. The content necessitates the size, as the debate included many, many arguments.

One of Horn’s collaborators, Jeffrey Yoshimi, came to similar conclusion regarding the visualization of debates in “Mapping the Structure of Debate” (2004). Here, he is striving to improve upon Horn’s method to illustrate the importance of looking beyond individual arguments to exchanges in a debate. “Debate level structures are worth studying for the obvious reason that they are pervasive—any time two or more parties trade off arguments, a debate is underway” (Yoshimi 2004 , p.2). In this article, Yoshimi clearly and succinctly expresses a kind of hybrid approach—creating a graph of graphs.

It is important not to confuse argument-level structures with debate-level structures. For example, argument diagrams—a standard tool in introductory critical reasoning courses—employ graph theory similar to that employed here. But whereas argument diagrams relate premises and conclusions within an argument (allowing one to distinguish divergent, convergent, linked, and serial arguments, among others), debate maps relate whole arguments (allowing one to distinguish different forms of thread, debate, and position). Thus, every node on a debate-map can be represented by its own argument map, resulting in a graph of graphs. (Yoshimi 2004 , p.3)

Yoshimi describes what he calls “debate threads,” in which a thread is a series of arguments offered in a debate offered by each participant representing a line of argument/objection/reply/ objection, and so on. In this scheme, the Russell-Copleston debate (at least the part analyzed above), could be represented by the debate-level structure shown in Fig.  7 .

Additionally, if we were to apply the concept of a graph of graphs, then the nodes in Yoshimi’s scheme would contain the entire argument sections from Figs.  1 , 2 , 4 and 6 , while the edges would represent the red arrows I used to represent the objections in Fig.  7 . Ultimately, then, one could see the overall structure of the exchange between debaters and also drill down to the argument-level structure to see the details of the arguments given.

Tools used to visualize debate structure developed by computer scientists and artificial intelligence (AI) research have come and gone over the past two decades (see, e.g., Baker, et al., 2007; Cerutti, et al., 2016; Corbel, et al., 2002). One of the most recent is AIPA (Argument Interface for Participatory Approach), developed by Delhomme et al. ( 2022 ). In their paper introducing AIPA published just this year, Delhomme and his colleagues lamented the fact that these types of tools have not lasted:

Whether involved in, or observing a debate, more often than not, it is hard to follow its progress; positions are unclear and arguments are unstructured often resulting in circular discussions. This is true both for participants in an ongoing debate hoping to reach a consensus as well as for those who, a posteriori, wish to understand what was discussed and how. However, at the current time, there are to our knowledge no tools to support real-time debates by allowing participants to visualize arguments and identifying opposing points of view in order to resolve conflicts. (Delhomme, et al., 2022 , 1, emphasis mine)

Briefly, they want a representational structure that can serve both to track debates in real time, and also allow students to be able to analyze and evaluate debates and their components after the fact. Nearly all these different tools, including AIPA, have been based on Phan Minh Dung’s ( 1995 ) abstract argumentation framework (AAF).

An important goal of computational argumentation in AI research is to find a system which will allow computers to reason – to accept or reject arguments based on the arguments put forward to support or reject them. According to Dung ( 1995 ), an argumentation framework (AF) consists in a set of arguments and an attacking relation. In the original formulation, we can determine the acceptability of an argument by looking at the relationship between the arguments in the set.

In subsequent adoption and extensions of Dung’s work (Bench-Capon 2003 ; Delhomme et al. 2022 ) it has become standard to represent argument frameworks as graphs in which the arguments are the nodes and the attack relations are the edges. The template of an argument framework might look like this:

Delhomme et al. ( 2022 ) develop a model of debate using Dung’s argumentation framework, AIPA, and demonstrate their web-based implementation of AIPA, WebAipa. This model allows for the visualization of the arguments (or, rather the conclusions of the arguments) in the course of a debate, as well as the attack and support relations between the arguments. The Russell-Copleston debate (as far as I have analyzed it above) might look like this:

An important component of the semantics of these various representations is that an argument is acceptable if all of the arguments that attack it are themselves attacked without rebuttal. As Bench-Capon explains, “The key question to ask about such a framework is whether a given argument A, Aε AR , should be accepted. One reasonable view is that an argument should be accepted only if every attack on it is rebutted by an accepted argument” (Bench-Capon 2003 , p.431). This amounts to a rule that the last attacking argument in a debate is the one that should be accepted. This makes sense if this theory is based on Dung’s original formulation of the graphs he envisions, “Here, an argument is an abstract entity whose role is solely determined by its relations to other arguments. No special attention is paid to the internal structure of the arguments” (Dung 1995 , p.326).

This view about what makes an argument acceptable indicates serious problems for applicability of any computer supported argument visualization tool that may be used in the classroom to teach critical thinking skills. First, it is plainly false that an argument should be accepted on the basis of whether it actually is subjected to an objection or counterargument. Arguments should be accepted or rejected based on truth of their premises and the strength of support the provide the conclusion. Of course, we might set that worry aside if we are only considering debates in which objections and replies are given by all participants. Even so, that brings us to the second problem; this view equates “winning” a debate, in terms of essentially being the last one standing, with making the best case for a particular conclusion. In fact, most critical thinking textbooks warn students against this false equivalence.

Lastly, while this theory of argumentation might allow for implementation in AI systems, it falls far too short of the graph of graphs concept proposed by Yoshimi ( 2004 ). For using debate to teach critical thinking, it is crucial for students to interrogate both the internal structure of the of the individual arguments given and the relationship between these arguments in the context of the entire debate. Footnote 6

4 What is Needed

An ideal representation of an argumentative debate would be one that combines a Delhomme-style graph of the debate structure with a standard diagramming graph of the structure of each of the arguments that are represented by the nodes of the debate structure. To my mind, then, this ideal representation would have the following requirements:

Two levels of representation: the debate graph and the argument diagram.

Each would be a graphical representation with nodes and edges.

The debate graph would represent whole arguments as nodes and the support/object/rebut relationships between arguments as edges.

The argument diagram would represent the statements in which an argument consists as nodes and the inferential connections between the statements as edges.

Both the debate-level graph and the argument level graph should allow for a large number of nodes, although the medium in which the graphs are represented (program, slide, paper) should be a consideration.

The edges of the debate-level graph should allow color-coding of either the nodes or the edges, or both (one color for support, another for objection, and possibly a third for rebuttal, etc.) so it would be straightforward to determine the general flow of the debate at a glance.

The edges of the argument-level graph need not be color coded to indicate support/objection/rebuttal relationships, and so, while not necessary, color-coding could be used instead to represent features of the statements (conditional, probabilistic, etc.) and/or the inferences (deductive, inductive, abductive, etc.).

The user should have a way to “expand” the debate-level nodes to see a graphical representation of the internal structure of any argument, and then “collapse” these nodes so as not to perpetually take up valuable representation space.

Requirement (5) above is, I think the critical feature of the debate representation, and in principle should be straightforward to implement. In her dissertation, Khartabil ( 2020 ) develops and user-tests a few versions of the kind of computer supported argument visualization that does this, although she was not using them to represent the two levels of representation I have outlined here. Rather, she was using them to “zoom in on” the structure of different parts of very complex arguments.

As noted above, Khartabil was trying to accommodate the limitations that experts in the argument diagramming community described as drawbacks to traditional argument diagramming tools; in other words, she wanted to be able to represent arguments with hundreds or more boxes while not giving up the information contained in the box and arrow graphs. All of her versions started with representing the overall argument as a sunburst, instead of the traditional tree structure (see Fig.  12 ).

Khartabil’s sunburst representation of an argument. The white spaces contain the statements, the radial lines represent argument structure, and the colors represent support vs. objection

One of the versions then has a “pop-out” feature that displays a part of the argument as a “node-link” layout (see Fig.  13 ).

Khartabil’s sunburst representation of an argument with the accompanying pop-out representation of the details of part of the argument

The kind of ideal debate representation I have in mind would use the “pop-out” feature to connect the debate level graph with the argument-level graphs (see Fig.  14 ).

A mock-up of my own ideal debate representation

Now, if only I could get someone to build it for me

5 Conclusion

In my own teaching, I value the process of students learning argumentation by constructing argument diagrams. My students create diagrams to represent their individual and collaborative understanding of the arguments in the texts we read, as well as to assist in evaluation of the same arguments. My students also create diagrams of their own essays to aid their writing process, as well as create diagrams of each other’s essay drafts to facilitate peer review. Fortunately, there are many options for computer supported argument visualization, and I can choose according to my specific needs for any given class.

Argument diagrams do, however, have substantial limitations, especially when analyzing long texts. They are also quite limited in their ability to accurately and easily represent debates that authors have either with themselves in a single text, or with others across multiple texts. Using debates in my classes to teach argumentation has, therefore, always been quite frustrating; and despite recognizing the benefits that it might have in many classes, I don’t use it as much as I would like. There are, of course, options available for representing debates, but for the reasons outlined above, they do not meet the requirements I have for a successful tool of this sort.

Thus, I have introduced the specifications for the sort of tool which would allow me to use debates to teach argumentation in my classes. There are so many excellent historic and contemporary debates I could use to teach a variety of concepts, from issues in the nature of the mind to argumentative fallacies. It would also be wonderful to be able to have my students engage in their own debates in class or online while also having a visual way to represent and keep track of those debates for both the short and long term. If I have persuaded anyone to take up the task of building such a program, then I would consider myself a very fortunate teacher indeed.

This point is emphasized by the recent the publication of How Philosophers Argue: An Adversarial Collaboration on the Russell–Copleston Debate , by Leal and Marraud ( 2022 ).

The interlocutors of the debate need not actually be separate people; a single author can present a debate with herself by representing two or more different voices. Many dialogues in the history of philosophy are examples of this kind of debate.

There are, of course, many different models for diagramming arguments, and each has its own ontology, syntax and semantics. For example, in the Toulmin model, there are boxes for different kinds of statements (claim, warrant, etc.) and arrows can point to either boxes or other arrows. In my classes, which consist mostly of first- and second-year college students, I use a modified Beardsley-Freeman model as it is very easy to learn the basics. For an overview of the development of argument diagramming, as well as a description of many models, see Reed et al. ( 2007 ).

For my purposes, “excess verbiage” is defined loosely, and is intended as a guide to help students (re-)write complete, independent statements in the boxes of the diagrams. For example, students do not include the premise/conclusion indicator phrases in the boxes; these phrases are instead “represented” as arrows in the diagram. Additionally, I advise my students to eliminate discounts, repetition, assurances, and hedges. As their argument analysis skills become more sophisticated, these guidelines are relaxed, and students can consider the differences between, for example, claims made with hedges and claims made without hedges.

In the modified Beardsley-Freeman model of argument diagramming that I use, all criticisms of claims in an argument are called “objections.” The reason I do this is for simplicity when guiding students through tasks of argument analysis. Early on, students struggle to determine which claims are being targeted for criticism in a debate. While it is important in the long run to distinguish between an objection to the conclusion of an argument and an objection to a premise of an argument, in the early stages of learning I have found that such distinctions merely confuse students.

I am thankful to an anonymous reviewer for pointing out that I have mentioned only three relations between arguments in the Russell-Copleston debate. This, again, is due to my pedagogical focus on argumentation. In all aspects of argument analysis, I have learned to simplify the kind and amount of argumentation theory I teach my students. Recently, Leal and Marraud ( 2022 ) distinguish many more important relations between arguments in a debate, and in so doing, argue for alternatives to diagramming like “regimented paraphrase.” A discussion of the advantages and disadvantages of each approach is important, but outside the scope of this article.

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Harrell, M. Representing the Structure of a Debate. Argumentation 36 , 595–610 (2022). https://doi.org/10.1007/s10503-022-09586-2

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Argument diagramming and critical thinking in introductory philosophy

In a multi-study naturalistic quasi-experiment involving 269 students in a semester-long introductory philosophy course, we investigated the effect of teaching argument diagramming (AD) on students’ scores on argument analysis tasks. An argument diagram is a visual representation of the content and structure of an argument. In each study, all of the students completed pre- and post-tests containing argument analysis tasks. During the semester, the treatment group was taught AD, while the control group was not. Methodological problems with the first study were addressed in the second. The results were that among the different pre-test achievement levels, the scores of low-achieving students who were taught AD increased significantly more than the scores of low-achieving students who were not taught AD, while the scores of the high-achieving students did not differ significantly between the treatment and control groups. The results for intermediate-achieving students were mixed. The implication of these studies is that learning AD significantly improves low- and intermediate-achieving and students’ ability to analyze arguments.

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A Crash Course in Critical Thinking

What you need to know—and read—about one of the essential skills needed today..

Posted April 8, 2024 | Reviewed by Michelle Quirk

• In research for "A More Beautiful Question," I did a deep dive into the current crisis in critical thinking.
• Many people may think of themselves as critical thinkers, but they actually are not.
• Here is a series of questions you can ask yourself to try to ensure that you are thinking critically.

Conspiracy theories. Inability to distinguish facts from falsehoods. Widespread confusion about who and what to believe.

These are some of the hallmarks of the current crisis in critical thinking—which just might be the issue of our times. Because if people aren’t willing or able to think critically as they choose potential leaders, they’re apt to choose bad ones. And if they can’t judge whether the information they’re receiving is sound, they may follow faulty advice while ignoring recommendations that are science-based and solid (and perhaps life-saving).

Moreover, as a society, if we can’t think critically about the many serious challenges we face, it becomes more difficult to agree on what those challenges are—much less solve them.

On a personal level, critical thinking can enable you to make better everyday decisions. It can help you make sense of an increasingly complex and confusing world.

In the new expanded edition of my book A More Beautiful Question ( AMBQ ), I took a deep dive into critical thinking. Here are a few key things I learned.

First off, before you can get better at critical thinking, you should understand what it is. It’s not just about being a skeptic. When thinking critically, we are thoughtfully reasoning, evaluating, and making decisions based on evidence and logic. And—perhaps most important—while doing this, a critical thinker always strives to be open-minded and fair-minded . That’s not easy: It demands that you constantly question your assumptions and biases and that you always remain open to considering opposing views.

In today’s polarized environment, many people think of themselves as critical thinkers simply because they ask skeptical questions—often directed at, say, certain government policies or ideas espoused by those on the “other side” of the political divide. The problem is, they may not be asking these questions with an open mind or a willingness to fairly consider opposing views.

When people do this, they’re engaging in “weak-sense critical thinking”—a term popularized by the late Richard Paul, a co-founder of The Foundation for Critical Thinking . “Weak-sense critical thinking” means applying the tools and practices of critical thinking—questioning, investigating, evaluating—but with the sole purpose of confirming one’s own bias or serving an agenda.

In AMBQ , I lay out a series of questions you can ask yourself to try to ensure that you’re thinking critically. Here are some of the questions to consider:

• Why do I believe what I believe?
• Are my views based on evidence?
• Have I fairly and thoughtfully considered differing viewpoints?
• Am I truly open to changing my mind?

Of course, becoming a better critical thinker is not as simple as just asking yourself a few questions. Critical thinking is a habit of mind that must be developed and strengthened over time. In effect, you must train yourself to think in a manner that is more effortful, aware, grounded, and balanced.

For those interested in giving themselves a crash course in critical thinking—something I did myself, as I was working on my book—I thought it might be helpful to share a list of some of the books that have shaped my own thinking on this subject. As a self-interested author, I naturally would suggest that you start with the new 10th-anniversary edition of A More Beautiful Question , but beyond that, here are the top eight critical-thinking books I’d recommend.

The Demon-Haunted World: Science as a Candle in the Dark , by Carl Sagan

This book simply must top the list, because the late scientist and author Carl Sagan continues to be such a bright shining light in the critical thinking universe. Chapter 12 includes the details on Sagan’s famous “baloney detection kit,” a collection of lessons and tips on how to deal with bogus arguments and logical fallacies.

Clear Thinking: Turning Ordinary Moments Into Extraordinary Results , by Shane Parrish

The creator of the Farnham Street website and host of the “Knowledge Project” podcast explains how to contend with biases and unconscious reactions so you can make better everyday decisions. It contains insights from many of the brilliant thinkers Shane has studied.

Good Thinking: Why Flawed Logic Puts Us All at Risk and How Critical Thinking Can Save the World , by David Robert Grimes

A brilliant, comprehensive 2021 book on critical thinking that, to my mind, hasn’t received nearly enough attention . The scientist Grimes dissects bad thinking, shows why it persists, and offers the tools to defeat it.

Think Again: The Power of Knowing What You Don't Know , by Adam Grant

Intellectual humility—being willing to admit that you might be wrong—is what this book is primarily about. But Adam, the renowned Wharton psychology professor and bestselling author, takes the reader on a mind-opening journey with colorful stories and characters.

Think Like a Detective: A Kid's Guide to Critical Thinking , by David Pakman

The popular YouTuber and podcast host Pakman—normally known for talking politics —has written a terrific primer on critical thinking for children. The illustrated book presents critical thinking as a “superpower” that enables kids to unlock mysteries and dig for truth. (I also recommend Pakman’s second kids’ book called Think Like a Scientist .)

Rationality: What It Is, Why It Seems Scarce, Why It Matters , by Steven Pinker

The Harvard psychology professor Pinker tackles conspiracy theories head-on but also explores concepts involving risk/reward, probability and randomness, and correlation/causation. And if that strikes you as daunting, be assured that Pinker makes it lively and accessible.

How Minds Change: The Surprising Science of Belief, Opinion and Persuasion , by David McRaney

David is a science writer who hosts the popular podcast “You Are Not So Smart” (and his ideas are featured in A More Beautiful Question ). His well-written book looks at ways you can actually get through to people who see the world very differently than you (hint: bludgeoning them with facts definitely won’t work).

A Healthy Democracy's Best Hope: Building the Critical Thinking Habit , by M Neil Browne and Chelsea Kulhanek

Neil Browne, author of the seminal Asking the Right Questions: A Guide to Critical Thinking, has been a pioneer in presenting critical thinking as a question-based approach to making sense of the world around us. His newest book, co-authored with Chelsea Kulhanek, breaks down critical thinking into “11 explosive questions”—including the “priors question” (which challenges us to question assumptions), the “evidence question” (focusing on how to evaluate and weigh evidence), and the “humility question” (which reminds us that a critical thinker must be humble enough to consider the possibility of being wrong).

Warren Berger is a longtime journalist and author of A More Beautiful Question .

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