argument maps improve critical thinking

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Argument maps improve critical thinking

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Argument maps improve critical thinking

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T1 - Argument maps improve critical thinking

AU - Twardy, Charles

M3 - Article

SN - 0145-5788

JO - Teaching Philosophy

JF - Teaching Philosophy

Improving Critical Thinking Through Argument Mapping

Dual-coding, gestalt grouping, and hierarchical organization..

Posted November 9, 2018

As you may have figured out from the focus of my ongoing blog, my book and my previous research, critical thinking (CT) is my specialty area of research. However, perhaps something that I don’t mention enough within this blog is that CT wasn’t the primary focus of my Ph.D. research—rather, it was The Evaluation of Argument Mapping as a Learning Tool ; that is, argument mapping’s effects on a series of educational outcomes, including memory and CT. To clarify, an argument map is a visual representation of a logically structured network of reasoning, in which the argument is made unambiguous and explicit via a ‘box and arrow’ design, in which the boxes represent propositions (i.e. the central claim, reasons, objections, and rebuttals) and the ‘arrows’ among propositions indicate the inferential relationships linking the propositions together (Dwyer, 2011; van Gelder, 2002). As part of my Ph.D., three large-scale experimental studies were conducted with the main results indicating that argument mapping (AM) can significantly facilitate memory performance beyond that of more traditional study methods and that the provision of AM-infused CT training can significantly enhance CT performance (Dwyer, 2011). Given these observed benefits, I think it worthwhile to share a little bit about AM here and the rationale for why it works, especially for those who wish to enhance their own or even others’ CT.

Notably, though other forms of argument diagramming exist, such as concept mapping and mind-mapping , they differ substantially from AM based on the manner in which they are organized and the way in which each ‘proposition’ is presented. The problem with many concept mapping techniques is that they do not present an argument per se. Instead, they present a graphical structure that acts as a representation of a separate text, which might be used to diagram: the links among concepts, decision-making schemes, a set of plans or instructions, or at best, act as an argument overview – which does not represent the argument in full. Thus, because the text of the argument and the diagram may often be separate entities, concept mapping may become more cognitively demanding by adding the necessity of switching attention from text to diagram and vice versa (e.g. Chandler & Sweller, 1991; Pollock, Chandler & Sweller, 2002; Tindall-Ford, Chandler & Sweller, 1997). In addition, if the reader of a concept map is not familiar with the information from the text that the map is derived, then the map itself becomes meaningless. Neither sentences nor any inferential structures to facilitate comprehension are requisite. In this context, concept mapping strategies may not necessarily be useful pedagogical aids that are open to analysis by everyone.

Although AMs have been in existence for almost 200 years (Buckingham-Shum, 2003; see Whately, 1826), their construction was a slow, tedious task completed through pen and paper; and thus, not widely used as a learning tool, despite potential advantages over standard prose as a medium for presenting reasoning. With the advent of various user-friendly AM software programs, the time required to construct an AM has been substantially reduced. Perhaps as a result of the relatively recent advancements in AM software, little research has been conducted to test its effects on learning. However, the little research that has examined AM’s effects on CT has revealed beneficial effects (Alvarez-Ortiz, 2007; Butchart et al., 2009; Dwyer, Hogan & Stewart, 2011; Dwyer, Hogan & Stewart, 2012; van Gelder, 2001; van Gelder, Bissett & Cumming, 2004). The rationale for why AM has a beneficial effect on CT consists of reasoning pertaining to the former’s diagrammatic, dual-coding nature, Gestalt grouping principles and hierarchical organization.

First, unlike standard text, AMs represent arguments through dual modalities (visual-spatial/diagrammatic and verbal/propositional), thus facilitating the latent information processing capacity of individual learners. Dual-coding theory (Paivio, 1971; 1986), Mayer’s (1997) conceptualisation and empirical analysis of multimedia learning, as well as Sweller and colleagues’ research on cognitive load (Sweller, 2010) suggest that learning can be enhanced and cognitive load decreased by the presentation of information in a visual-verbal dual-modality, provided that both visual and verbal forms of representation are adequately integrated (i.e. to avoid attention-switching demands). Given that AM supports dual-coding of information in working memory via integration of text into a diagrammatic representation, cognitive resources previously devoted to translating prose-based arguments into a coherent, organised and integrated representation are ‘freed up’ and can be used to facilitate deeper encoding of arguments within AMs, which in turn facilitates later recall (e.g. Craik & Watkins, 1973), as well as subsequent, higher-order thinking processes, such as CT (Halpern, 2014; Maybery, Bain and Halford, 1986). Furthermore, previous research on using diagrammatic learning tools, like AM, has shown positive effects on learning outcomes (Berkowitz, 1986; Larkin & Simon, 1987; Oliver 2009; Robinson & Kiewra, 1995) and offers advantages over traditional text-based presentation of information because the indexing and structuring of information can potentially support essential computational processes necessary for CT.

Second, AMs utilize Gestalt grouping principles (e.g. similar color-coding and close proximity) that facilitate the organization of information in working memory and long-term memory , which in turn facilitates CT. For example, color can be used in an AM to distinguish evidence for a claim (i.e. green) from evidence against a claim (i.e. red); thus, all reasons are similarly color-coded, as are objections. More generally, a good AM is designed in such a way that if one proposition is evidence for another, the two will be appropriately juxtaposed and the link explained via a relational cue, such as because , but and however (van Gelder, 2001).

With respect to proximity, modern AM allows single propositions or entire branches of the argument to be removed or transferred from one location to another (and edited in the process) in order to facilitate reconstruction. The manner in which propositions and chains of reasoning can be manipulated within an AM may encourage deeper analysis and evaluation of the argument, as well as further refinements of its inferential structure. Similar propositions can be grouped together, which eases their assimilation and removes the need to switch attention as in text-based information (e.g. from one paragraph, or even one page, to another and back and forth). Such grouping also makes the search for specific, relevant information more efficient, which in turn supports perceptual inferences.

Finally, the third potential reason for why AM has a beneficial effect on CT is that AMs present information in a hierarchical manner, which also facilitates the organization of information for promoting CT. When arguing from a central claim, one may present any number of argument levels which need to be adequately represented for the argument to be properly conveyed. For example, an argument that provides a (1) support for a (2) support for a (3) support for a (4) claim has four levels in its hierarchical structure. More complex or ‘deeper’ arguments (e.g. with three or more argument levels beneath a central claim) are difficult to represent in text due to its linear nature; and yet it is essential that these complex argument structures are understood by a student if their goal is to analyze and evaluate the argument, to infer their own conclusions. The hierarchical nature of AM allows the reader to choose and follow a specific branch of the argument in which each individual proposition is integrated with other relevant propositions in terms of their inferential relationship.

Moreover, asking students to produce AMs can provide educators with valuable insights into a student’s ‘mental model of the argument in question’ (Butchart et al., 2009). Such information can be used to support teachers in offering feedback to students or scaffolding student learning from simple to complex levels of argument comprehension, analysis, and evaluation. Logically, as expertise in AM grows, so does the ability to present a well-structured argument, which allows for improvement in writing ability as well.

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Christopher Dwyer, Ph.D., is a lecturer at the Technological University of the Shannon in Athlone, Ireland.

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Computer-based argument mapping greatly enhances student critical thinking, more than tripling absolute gains made by other methods. I describe the method and my experience as an outsider. Argument mapping often showed precisely how students were erring (for example: confusing helping premises for separate reasons), making it much easier for them to fix their errors.

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van Gelder, T. J. (2001). How to improve critical thinking using educational technology. In G. Kennedy, M. Keppell, C. McNaught, & T. Petrovic (Eds.), Meeting at the Crossroads. Proceedings of the 18th Annual Conference of the Australian Society for Computers In Learning In Tertiary Education (ASCILITE 2001) (pp. 539 548). Melbourne: Biomedical Multimedia Unit, The University of Melbourne. (http://www.medfac.unimelb.edu.au/ascilite2001/ pdf/papers/vang%eldert.pdf)

van Gelder, T. J. (2002). Argument mapping with Reason!Able. American Philosophical Association Newsletter on Philosophy and Computers.

van Gelder, T. J., & Cumming, G. (forthcoming). Change in critical thinking skills during college: A meta-analysis.

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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.

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• © 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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Concept mapping, mind mapping and argument mapping: what are the differences and do they matter?

• Published: 27 November 2010
• Volume 62 , pages 279–301, ( 2011 )

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In recent years, academics and educators have begun to use software mapping tools for a number of education-related purposes. Typically, the tools are used to help impart critical and analytical skills to students, to enable students to see relationships between concepts, and also as a method of assessment. The common feature of all these tools is the use of diagrammatic relationships of various kinds in preference to written or verbal descriptions. Pictures and structured diagrams are thought to be more comprehensible than just words, and a clearer way to illustrate understanding of complex topics. Variants of these tools are available under different names: “concept mapping”, “mind mapping” and “argument mapping”. Sometimes these terms are used synonymously. However, as this paper will demonstrate, there are clear differences in each of these mapping tools. This paper offers an outline of the various types of tool available and their advantages and disadvantages. It argues that the choice of mapping tool largely depends on the purpose or aim for which the tool is used and that the tools may well be converging to offer educators as yet unrealised and potentially complementary functions.

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Stimulating reflection and self-correcting reasoning through argument mapping: three approaches, studying and constructing concept maps: a meta-analysis.

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My thanks to Tim Beaumont and two anonymous reviewers from the journal for useful comments on earlier versions of this paper.

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LESSWRONG LW

Argument maps improve critical thinking.

Charles R. Twardy provides evidence that a course in argrument mapping, using a particular software tool improves critical thinking. The improvement in critical thinking is measured by performance on a specific multiple choice test ( California Critical Thinking Skills Test ). This may not be the best way to measure rationality, but my point is that unlike almost everybody else, there was measurement and statistical improvement!

Also, his paper is the best, methodologically, that I've seen in the field of "individual rationality augmentation research".

To summarize my (clumsy) understanding of the activity of argument mapping:

One takes a real argument in natural language. ( op-eds  are a good source of short arguments, philosophy is a source of long arguments). Then elaborate it into a tree structure, with the main conclusion at the root of the tree. The tree has two kinds of nodes (it is a bipartite graph ). The root conclusion is a "claim" node. Every claim node has approximately one sentence of english text associated. The children of a claim are "reasons", which do NOT have english text associated. The children of a reason are claims. Unless I am mistaken, the intended meaning of the connection from a claim's child (a reason) to the parent is implication, and the meaning of a reason is the conjunction of its children.

In elaborating the argument, it's often necessary to insert implicit claims. This should be done abiding by the "Principle of Charity", that you should interpret the argument in such a way as to make it the strongest argument possible. 

There are two syntactic rules which can easily find flaws in argument maps:

The Rabbit Rule: Informally, "You can't conclude something about rabbits if you haven't been talking about rabbits". Formally, "Every meaningful term in the conclusion must appear at least once in every reason."

The Holding Hands Rule: Informally, "We can't be connected unless we're holding hands". Formally, "Every meaningful term in one premise of a reason must appear at least once in another premise of that reason, or in the conclusion".

I have tried the Rationale tool, and it seems afflicted with creeping featurism. My guess is the open-source tool Freemind  could support argument mapping as described in Twardy's article, if the user is disciplined about it.

I'd love comments offering alternative rationality-improvement tools. I'd prefer tools intended for solo use (that is, prediction markets are awesome but not what I'm looking for) and downloadable rather than web services, but anything would be great.

New to LessWrong?

Getting Started

Thanks for the vote of confidence. I should say that while I think my paper presents things well, I cannot take credit for the statistics or experimental design. Tim van Gelder already had the machinery in place to measure pre-post gains, and had done so for several semesters. The results were published in Donohue et al. 2002. The difference here was that I took over teaching, and we continued the pre-post tests.

Although argument maps are usually used to map existing natural language arguments, one could start with the map. I like to think that the more people use these maps, the more their thinking naturally follows such a structure. I'm sure I could use more practice myself.

Just a note on terminology: the tree does have two kinds of nodes, but by virtue of being a tree, it is not a bipartite graph .

I think arguments in argument maps can be made probabilistic and converted to Bayesian networks. But as it is, it takes long enough just to make an argument map. I've recently discovered Gheorghe Tecuci's work. He's just down the hall from me, but I didn't know his work until I heard him give a talk recently. He has an elaborate system that helps analysts create structures very much like argument maps by filling in schemas, and then reasons quantitatively with them. The tree structure and the simplicity of the combination rules (min, max, average, etc.) are more limited than a full Bayesian network, but it seems to be a very nice extension of argument maps.

Here is a tool that will help figure out whether you are overconfident, underconfident, or neither.

Here is a good puzzle involving rationality. See the discussion here on Less Wrong once you've completed it.

those set kind of a low bar. don't we have a test that more rigorously examines whether you infer correctly from data or not?

if anyone wants some fun (not making any claims about whether solving these indicate rationality, just for fun) try the blue eyes problem http://www.xkcd.com/blue_eyes.html and the "hardest logic puzzle in the world" http://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever

the blue eyes puzzle in particular I enjoyed immensely.

This looks like a formalised general version of an Intervention Logic, a tool used in government to explain how a proposed policy will achieve a desired policy goal.

Tell us more about this Intervention Logic.

What I've described below is the ideal, naturally as soon as politics gets involved in anything you can move away from the ideal rapidly and there's no way of getting politics out of policy formation.

Say you have a policy problem to solve or a policy goal to meet (reducing road fatalities, improving high school graduation rates etc.) and you have a policy you think will work to solve the problem, but you want to check your reasoning or develop a formalised explanation so you can convince another analyst or agency. One way to do this is develop an intervention logic.

The basic format of an intervention logic is a flowchart that outlines the causal relationship between your policy and the desired outcome "This policy will cause A, which causes B, which causes C, which results in outcome Z".

Its not a perfect system, it violates one of the cardinal rules of rationality since its generally used to justify a pre-reasoned position rather than reasoning from scratch and there's inevitably a certain amount of handwaving involved since the causal factors involved in most policy work are very hard to get a grip on, but at least it forces the person using it to state their assumptions and logic explictily.

Semi-OT: what about software for drawing Pearlean causal graphs that permit counterfactual surgery?

Oddly enough, Twardy's research in philosophy (as opposed to philosophy education) is related to Pearlean counterfactuals. He worked somewhat with Lucas Hope on a tool called "Causal Reckoner".

http://portal.acm.org/citation.cfm?id=1082172&dl=GUIDE&coll=GUIDE&CFID=49488126&CFTOKEN=18921351

http://www.springerlink.com/content/30m8ac6uafkxu9k3/

However, my google-fu is not strong enough to find the software itself. Possibly contacting the various individuals involved would be necessary.

Luke Hope and Karl Axnick did most of the work on Causal Reckoner. I have used it, but I did very little to develop it. However, I believe it is GPL, so it could be posted.

I think so. The intervention paper links to the providing site, but the straight link is down with a server error; poking around the site reveals no other mirrors or mentions of the causal reckoner. The Internet Archive shows the pages fine, but the only download page is about getting the source via CVS - and not anonymous CVS! The CVS server doesn't seem to expose any HTTP files either (SSH seems to be the onlyway in).

It's too bad - I kept thinking about Eliezer's old post about 'what would ordinary things like sight be like if they were RPG powers/abilities', and it seems to me like a cool concept to try out would be a game where you can literally see the causal decision graphs governing the actions of characters. Perhaps another power could be snipping branches or modifying weights to manipulate characters into doing your bidding or simply getting out of the way. (One could start off trapped in a jail cell... :)

But I've tried a couple ways to view the PDF and I can't seem to see the screenshot of the GUI! Now that's annoying.

I don't suppose there are any non-paywall versions?

Let me google that for you:

http://crpit.com/confpapers/CRPITV38Marriott.pdf

http://www.csse.monash.edu.au/~korb/pubs/intervene.pdf

Very-OT: have you guys seen the awesome lmgtfy ?

I've heard of the game WFF'n'Proof ever since it was invented, but I've never had any closer knowledge of it. However, the publisher's website claims dramatic improvements in IQ and mathematical performance from playing that and their other games.

WFF'n'Proof and Equations are the ultimate geek games. Fun, too, with the right crowd.

Here's an absolutely phenomenal tool for creating diagrams of whatever level complexity. yEd Graph Editor even has auto-layout which creates graphs with least overlap. http://www.yworks.com/en/products_yed_about.html

I think focusing on the tool here is misleading. It is the process of creating something like a dependency graph representing the entire argument (and knowing how to analyze that graph) that is the important point, and people have been doing that for almost as long as philosophy has been around. Every critical thinking class teaches such techniques.