Archive for the ‘Rationale’ Category

The free online magazine The Reasoner has recently published an interview with me in their February 2010 issue.  Much of it is discussing argument mapping and its uses.  However the first third or so of the interview covers my earlier work in the foundations of cognitive science (distributed representation, dynamical systems and such topics).

Thanks to Kevin Korb for initiating and conducting the interview.


KK: What are argument maps and why are they important?

TvG: Typically an argument map is a box-and-arrow or node-and-link diagram showing the relationships among propositions in some piece of informal reasoning or argumentation. Argument mapping is thus “semi- formal”, blending formal graph structure with natural language. You can think of argument mapping as addressing a design challenge: come up with a maximally transparent way of representing informal reasoning and argumentation for human thinkers, one that makes the reasoning as explicit, rigorous and yet easily comprehensible and communicable as possible.  From this point of view, the various forms of argument mapping around today—such as the one embodied in the Rationale software—as particular attempts to come up with that optimal format. No doubt improved schemes, supported by more sophisticated technologies, will arise in coming years.

KK: How does your understanding of their importance relate to what you know about human cognition?
TvG: The diagrammatic format of typical argument maps is useful for humans with cognitive machinery dominated by powerful visual systems. Diagrammatic argument maps complement the idiosyncratic strengths and weaknesses of our evolutionarily-endowed cognitive equipment. For example, argument maps compensate for our limited short-term memory, providing a stable external representation of complex inferential webs. At the same time they facilitate access to this externally represented information by exploiting our powerful visual scanning capacities. In computer terms, our eyes constitute the high-capacity bus connecting the argument map, stored in external RAAM, to our brains as the CPU…

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I have recently been involved in a series of tutorials with a team from a law firm, involving mapping the arguments found in Federal or High Court judgements in the area of competition law.   For example we mapped the arguments presented by Chief Justice Gibbs of the High Court in the case Castlemaine Tooheys Ltd v Williams and Hodgson Transport Pty Ltd (1986) 68 ALR 376.  Here is the map in Rationale format:


Figure 1.  View full size image, or the Rationale file.

Mapping these judgements is quite hard work.   This is due in part to the complexity of the arguments and their often turning on subtle conceptual distinctions.  However the difficulty is also largely due to the manner of expression, i.e. the way in which judges present complex legal arguments in traditional legal prose.  In a number of ways, this style of writing makes it very challenging to determine what the arguments are, at least at the level of clarity and rigour required for a well-developed argument map.

Sparse use of logical language

When we we present arguments in prose, we can use logical language to clearly indicate the logical connections between the parts of the argument.  So for example I might say

A brewer cannot sell beer on the condition that the buyer engage a particular transport firm for delivery.  The reason is that this would amount to exclusive dealing.

Here I have used the locution “The reason is” to help the reader understand that what follows is an argument for the preceding proposition.

However if you look closely at the Gibbs judgement, you’ll find that there is surprisingly little logical language of this kind.   Argument pieces are provided, but with little clear and explicit flagging of their logical relationships.  For example:

It is even more clear that there was no exclusive dealing of the kind mentioned in s.47(7).  The appellant did not refuse to supply the beer to any retailer.  It was already ready to supply any retailer, either by delivering it from the brewery to North Queensland, or by allowing it to be picked up from a regional depot.

The phrase “it is even more clear that” does suggest that the following proposition (there was no exclusive dealing…) is a point being established or supported.  The following sentences constitute (in part) the argument for that proposition.  Note however that those sentences are simply stated immediately after the proposition to be established.  There is no explicit verbal flag that they constitute an/the argument.   You, the reader, are supposed to just “see” that.  The cue is contextual (proximity) rather than verbal.  Gibbs could have said something like “This is because…” – but he didn’t; he relied on non-verbal cues instead.  The trouble is that non-verbal cues to logical relationships are generally quite weak and ambiguous, and impose a heavy interpretative burden – and hence cognitive load – on the reader.

Diverse or unclear logical language

Even when logical language is used, there are innumerable different forms, with subtle differences in meaning.   Readers would have a much easier time identifying complex arguments if there were standard, unambiguous verbal conventions for signposting logical relations.  Unfortunately, there are not.  Of course there are some locutions that are used more often than others and are relatively unambiguous – e.g. “It follows that”.  But you also find obscure or archaic expressions like “does not gainsay”, and use of ambiguous terms like “however” and “but”.  Both of these common expressions can be functioning as argument structure indicators, but might be playing quite different role.

Missing premises

Another problem is that only some pieces of the argument are actually presented in the prose.  The rest are left unstated, with the expectation that the reader will be able to fill in the gaps.

Consider again the passage quoted above.  What’s missing – at the very least – from this presentation of the argument is something like

Exclusive dealing of the kind mentioned in s.47(7) would require the appellant to refuse to supply beer.

Gibbs is assuming that the reader will understand that some proposition of this kind is part of the argument.  In this case it may seem a reasonable enough assumption.  However we know in general that people find it very hard to identify these missing parts, and when they try, there is huge variation in what they come up with.   In other words, it is dangerous to assume that readers will properly “read in” the missing pieces.  Even if they can do it correctly, it often takes signficant mental effort (though it is worth noting that very often, in simple cases, filling in the missing pieces is seemingly effortless).

Missing intermediate pieces (“leaps of logic”)

There are at least two kinds of missing pieces.  The first, just illustrated, is unstated co-premises; in other words, the argument is enthymematic.  The other kind are intermediate steps in the argument.  Here, in Rationale format, is an alternative rendering of the argument, making clear that between the general conclusion Gibbs is drawing (no exclusive dealing) and the  particular fact offered by way of proof (no refusal to supply beer) there is really an intermediate level of argument.


Figure 2.  Click on the thumbnail to view full-size version.

In other words, judges often expect readers to fill in missing pieces both alongside and between the pieces that are provided.

In fact, the first premise at the intermediate level had been provided, but many pages  before.  It was not (re)stated in the immediate context of the argument, though it did appear in the text, in a rather remote location, with many other pieces of the larger argument appearing in between.   Which brings up the next point…


Consider an argument structure of the kind displayed in Figure 1.  Suppose you had to present that argument in ordinary prose.   Ordinary prose is essentially just a “linear” sequence of sentences – one sentence after another – though of course we can use some formatting to break up the monotony.    An issue you would be forced to address is: in what order do you present the pieces of the argument?

There is a systematic way to map a hierarchical structure into a sequence.  In fact there are many such ways.  However, every such way necessarily involves placing items adjacent in the sequence when they are not adjacent in the hierarchy.  This is simply a topological fact, with an interesting consequence for presenting arguments in prose.  It means that pieces of the argument with no direct relationship to each other must end up adjacent to each other in the text (though there may be other material, not part of the pure argument structure, separating them).  In other words, the prose will “bounce around” the argument structure.

puzzledWhen we study real examples of presentation of complex arguments in prose, such as the Gibbs judgement, and we look carefully at the order of presentation of pieces, we find that the author “bounces around” even more than is required mathematically.  In other words, in terms purely of ordering, the pieces are all “jumbled up”, almost as if pieces of a jigsaw had been thrown in a bag and drawn out one by one.

Of course, there will generally be some kind of logic in the madness; the author is trying to present the pieces in an order which, with the surrounding text, will help the reader understand the argument.  The issue is whether the author has done as well as he could in this.   Other things being equal, the more the “dis-order” or jumbling, the more trouble the reader will have in reassembling the hierarchical structure.


Intermingling with other material – and purposes

Another problem is that a written judgement is not solely concerned with transparently presenting the argument.   First, there is other material needing to be presented.  For example, there are the facts of the case, including both the facts that are immediately involved in the argument as well as other information providing important context.  Also there will be related issues which the judge may feel should be discussed, even though they are not part of the core arguments.

The trouble is that the presentation of the argument is intermingled with all this other material.  This means that the reader must pull apart what is argument, what is background, what is peripheral, etc..

On a related point, the judge has purposes in addition to transparent presentation of argument.  There is a certain amount of rhetoric involved in presenting a judgement, since the goal is to persuade others such as the parties to the case, their lawyers, and other judges.  Further, most judges would like to think that their written judgements are well-crafted, readable, perhaps somewhat entertaining, and possibly even literary, in a legal fashion.   It turns out that these goals are somewhat in tension with the goal of presenting the argument transparently.   It is certainly possible to present complex arguments in prose in such a way as a suitably trained reader can see, without inordinate effort or doubt, exactly what the argument is.  The problem is that such text is not pleasant to read, and it may not be as persuasive as more mellifluous discourse.   It requires a true master of argumentative writing to simultaneously reward the reader’s taste for literature or entertainment, and their desire to understand a complex argument with crystal clarity.

Argument Structure vs Essence

I’ve been writing as if judges’ primary ambition, in drafting written judgements, is to transparently display a complex argument structure.  But often when reading these judgements it seems that the authors are  more concerned to convey the “conceptual essence” of the argument – the key insight(s) such that, if the reader get that insight, then they’ve grasped the real heart of the argument.  The key that unlocks the case.   How exactly that essence is embedded in a larger structure of argument may not be so important.   So you find judges “talking around” that key insight or argument step, doing multiple “takes” on the presenting the point so that if the reader doesn’t quite get it one way, they’ll get it another, gaining understanding through a kind of triangulation.

Clearly conveying the conceptual essence of the case is of course a very important thing to do.  However it that is what the judge is primarily trying to do, then the effort devoted to this may be at the expense of, or even interfere with, transparent display of the rest of the case.

Summing up

Judges use written judgements to convey the complex set of arguments supporting their decision.  However it is difficult to extract the arguments from those written judgements, at the level of clarity and rigour demanded by good-quality argument mapping.   This difficulty is due in large part to various aspects of traditional legal prose.

  • Judges make surprisingly little use of verbal indicators of logical structure, and often use obscure or vague indicators
  • Judges present only some pieces of the arguments, expecting the reader to fill in the rest
  • The pieces necessarily appear in the text in a “disrupted” order, compared with their proper relationships in the argument structure
  • When producing their written judgements, judges have multiple purposes in addition to clearly conveying a complex structure; and the argument is intermingled, in the text, with other material
  • Judges may be more focused on conveying the conceptual essence of the argument than the full argument structure.

These observations are based on a fairly small sample – a handful of judgements in the current round of tutorials, plus my occasional experience over the past few decades  grappling with similar legal writings.  Still, I’m confident that the factors listed would be in play in most legal argumentative writing, and indeed almost any time an author attempts to convey a complex argument in prose.

If this is right, then if we’re faced with the challenge of presenting a complex argument in prose, we can help our readers by:

  • Making generous use of logical structure indicators, and trying to use a limited range of relatively standard, unambiguous ones
  • Explicitly stating more pieces of the argument
  • Trying to present the pieces in as coherent an order as possible, given the logical relationships among the pieces
  • Being aware of one’s purposes, and trying to avoid compromising the clear expression of the argument by other purposes
  • Disentangling the presentation of the argument from presentation of other material
  • Not neglecting overall argument structure while conveying the conceptual essence.

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I’ve been engaged (with a great team) in building argument mapping software for over a decade now.  Its been an uphill battle most of the way.  The acid test of success is sales, but there are other measures, such as positive, insightful feedback from users who “get it,” i.e. understand what we’ve done.  Such as the feedback which arrived today:

“I could go on at length about how much I like Rationale.  Where to start.  Where it end.  First of all a big sincere thanks to the designers – developers.  Your product is superlative.  It functions flawlessly, doesn’t crash, no small accomplishment.  The conceptual method of Rationale diagramming is really great.  It is easy and fun to use.  If more readers were aware of the methodology gently introduced in Rationale’s tutorials, they would reach more intelligent conclusions and be more demanding of writers.  I am just starting the final exercise sets in Rationale.  They appear to have a pretty good dose of philosophy, a fair stretch made easy by your excellent tutorials. Rationale is a truly different, truly useful product.”

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[originally posted to BlogCisive]

To a first approximation, all deliberative judgements (i.e., those that turn on to-some-degree careful consideration of the relevant arguments) can be usefully sorted into three kinds.

These are the three Ds of judgement.

1. Decision

Decision is a matter of choosing from among options, particularly where those options are possible actions.  The question here is “What should I (we) do?”

2. Diagnosis

Diagnostic judgements concern what is going on.   The question is “What is happening?” or “What’s the situation?”  The term diagnosis has medical connotations, but here I’m widening its use to include various kinds of investigation, hypothesis testing,  and problem-solving.  All diagnostic judgements involve hypotheses (conjectures) as to what is actually happening.  A good example of diagnostic judgement in this sense is the assessment in intelligence analysis.

3. Debate

Debate is trying to determine the truth of some proposition by presenting the arguments for or against it.  The question is “Is it true?”

Austhink has two products – Rationale, and bCisive.  Rationale, the argument mapping tool, supports debate.  bCisive, the business decision mapping tool, has been positioned as supporting decision.  We haven’t had a tool for diagnosis, and have tended to recommend that people wanting to make diagnostic judgements use some variant of the “Analysis of Competing Hypotheses” (ACH) method.

However, just as argument mapping supports debate, and business decision mapping supports decision, so “hypothesis mapping,” an alternative to ACH, supports diagnosis.  Further, hypothesis mapping is quite easily handled in bCisive as it stands.

Austhink is currently working on a “Pro” version of bCisive which will include crucial features needed for supporting both deliberation and diagnosis.

This means that one tool will help users map the thinking behind all three major kinds of deliberative judgement.

The tool should be available in a few months.

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Draft magazine piece.  Comments welcome.

In the late 1950s, a young engineer by the name of Douglas Engelbart made a decision that was to have a immense effect on all of our lives. Engelbart realised that the massive challenges faced by humanity, such as hunger or nuclear war, would place unprecedented demands on our thinking capacities – indeed, they may be so complex that our finite human brains may be unable to find solutions. With youthful idealism, he wondered how he could fix this problem.

As an engineer, his natural inclination was to build something – in this case, something that could expand our innate thinking capacities, much as a shovel or an excavator can greatly extend our digging capacities. In short, his mission in life became building tools which augment human intelligence. Over the following decades, he and his co-workers developed the key aspects of the personal computer, including innovations such as the mouse, hyper-linking and videoconferencing. Via Apple and Microsoft, these innovations rapidly became a standard part of every office worker’s equipment.

These days it seems hard to imagine how a management consultant could function without spreadsheets, presentation software, email, and so forth, all incorporating the basic functionality developed by Engelbart. These tools obviously help speed up various activities, thereby helping us get more done. An email or an instant message is immensely faster than “snail mail,” so turnaround is quicker and results can be delivered earlier.

However a focus on speed and convenience obscures the most profound change here. A consultant with a spreadsheet can perform analyses that would have been practically impossible fifty years ago. The spreadsheet magnifies the consultant’s effective thinking capacities. The sum of consultant plus spreadsheet is more intelligent than the consultant – or spreadsheet – alone. This is Engelbart’s dream become reality.

Yet, as profound as the changes to date have been, they are probably only the beginning. There is still plenty of scope for human intelligence, in its diverse manifestations, to be further augmented.

This is of great significance for management consulting, since consulting is, more than any other profession or industry, a matter of applied intelligence.

It is a curious fact that the computer aids or “cognitive prosthetics” used by management consultants are for the most part the same as those used by other knowledge workers. Excel and PowerPoint are found on most office computers, not just those of consultants.

To be sure, management consultants have some distinctive conceptual tools; the McKinsey 7S framework, the BCG matrix, and the Minto Pyramid Principle are well known examples. Yet as useful as these may be, they are not realised in hardware in the way a spreadsheet is and so can’t share the cognitive workload in the same way. Bluntly, they don’t “do” anything. We are now, however, starting to see new thinking tools which dovetail well with consulting work, and which may be adopted earlier in the consulting domain than in most others.

One characteristic intellectual skill of the management consultant is hierarchical structuring. Whether it is building logic trees, issue diagrams, pyramid structures, or any other type of “tree,” hierarchical structuring can bring rigour and depth to thinking, and experienced consultants develop facility with this technique. While hierarchical structuring can to some extent be done in the head, when things get complex it helps to lay them out visually – hence the familiar tree structures on whiteboards, with sticky notes, or on-screen using presentation or drawing tools.

But these aids, while handy, have their limitations. Most importantly, diagrams created by these manual methods are not easily modified. Organising information hierarchically is a process. A good hierarchical analysis typically evolves through a number of drafts; observing one attempt suggests a better way it might be done. The more quickly you can reshape the structure, the more quickly your thinking advances. But with whiteboards, sticky notes and generic drawing tools, this reshaping can be slow and frustrating; thinking is interrupted, and thinking has lost “flow.”

New tools designed specifically for hierarchical structuring largely remove these speedbumps. When you can build and modify a visual tree structure almost as fast as you can think, the visual representation becomes like an extension of your own cognitive equipment – a “mind’s eye” that just happens to be outside the head. A consultant using such a tool produces a logic tree better and faster than a similar consultant working on a whiteboard. The net result is that the former consultant is, for practical purposes, smarter.

Another area where new thinking tools can augment consultants’ high-level thinking is in argument construction. Very often a consultant’s primary task is to provide recommendations backed by compelling arguments. Those arguments consist of information organised in evidential or logical relationships. As with hierarchical structures, when it helps to lay arguments out in diagrams when they become complicated.

Back in 1962, in a landmark report, Engelbart described a system in which a user could, on a screen, organise propositions into complex argument structures. To have envisaged such a system well before computers even had monitors, let alone contemporary graphical user interfaces, was a remarkable achievement. Fast forward to this decade, and research teams at universities and software companies around the world are exploring argument visualisation and developing new software applications for this unique task. Just as spreadsheets support calculation, new commercial-grade “argument mapping” applications are supporting argumentation.

In a consulting context, argument mapping applications can be used to construct, refine, evaluate and present the thinking behind a recommendation. The visual display reduces the cognitive load involved in maintaining a complex argument structure in one’s head alone — freeing up mental resources for the more interesting and valuable thinking tasks involved in improving or critiquing an argument.

You can see for easily yourself how powerful this effect can be. Play a game of tic-tac-toe with a friend or colleague. No problem. But then play again, this time without using pen & paper or anything similar. Each player should hold the state of the board in her mind and call out her move in turn. Played the normal way, the game is trivial. Played without visual aids, it is far more laborious and error prone.

Remarkably, consultants usually carry out one of their most central tasks – the development of clear, compelling arguments – either without a “board” at all (i.e., in their heads), or by making do with generic tools such as word processors and presentation software. It is a bit like a carpenter trying to work without a saw.

The main reason for this is that until recently the “saw” for argument construction had not been developed. Going forward, however, we will see consultants increasingly using argument visualisation to augment their inbuilt reasoning abilities. A particular benefit of argument mapping is that, once an argument has been laid out diagrammatically, simple, almost mechanical checks can uncover hidden assumptions which might be critical weaknesses in the case. Extensive research at the University of Melbourne and elsewhere has shown that practise based on argument mapping can dramatically accelerate critical thinking skill gains in university students. This suggests another role for these new thinking tools.

A major challenge for consulting firms is helping new recruits come to “think like a consultant.” There are many aspects to this, but cultivating the two skills already discussed – hierarchical structuring and argument construction – is at the heart of it. Introducing suitably-designed software tools into training can speed up the process whereby new consultants develop understanding and mastery of these skills. The intuitive visual format promotes comprehension, the interactivity supports “hands on” practice, and inbuilt assistance helps provide guidance.

Finally, using these tools can help consultants collaborate on solving tough thinking problems. Traditionally, each consultant on a team holds in her head her own “take” on the evolving state of the group’s thinking about an issue. The trouble is that each take may be somewhat different, leading to confusion, error and wasted time. A better way is to have the thinking shared in a visual display, on a screen or projected onto a wall, with every contribution immediately and transparently incorporated into the common understanding. Such software can make this happen.

Management consulting has long had a reputation for snapping up the best and the brightest. The raw human intelligence of these young minds is greatly magnified as they come to master consulting’s “tools of the trade”. Despite the kind of inertial and conservative tendencies found in any profession, this toolkit does evolve over time. The latest additions are increasingly aiding consultants in some of the most distinctive of their intellectual tasks.

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 Check it out

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Spotted at the Creation Museum:


Q: Are human bones found with dinosaur fossils?

A: None have been discovered yet.  However, if human bones aren’t found with dinosaur bones, it simply means they weren’t buried together.  Humans have come in contact with lots of animals, like crocodiles and coelecanths, but they aren’t buried with humans.

The obvious thing to say about this is that it is flagrant “confirmation bias” – seeking or treating evidence in such a way as to confirm one’s cherished beliefs rather than to evaluate or test them.

From an argument analysis perspective, though, it is a nice example of what, technically, we’d call an “inference rebuttal” – an objection to an primary objection which targets not any of the stated premises of the primary objection but rather the inference from the primary objection to the falsity of the main contention.

That’s quite a mouthful, but the basic idea is simple enough, and can be easily illustrated.

Doing so will help explain one of the most distinctive – but subtle – features of the Rationale software.

On the face of it, the fact that human bones have not been discovered with dinosaur fosils is an objection to the standard Creationist story, which includes the idea that humans and dinosaurs once both roamed the earth at the same time.


The premise of the objection is a blunt fact, and so the Creationist has to accept it:


However the Creationist still wants to defuse the objection, and can do it by arguing that the premise, though true, doesn’t show that the contention is false.

To represent this kind of move, Rationale allows a lower-level objection to be connected to the primary objection itself rather than to any of its premises.  Graphically, the lower-level objection points to the word “opposes”:


Evaluating this argument as a Creationist presumably would, the objection has been defused:


There is however another way to read the Creationist’s argument.  This way of framing things probably better reflects the Creationist’s underlying mindset.   From this perspective, creationist “science” combined with the basic facts imply an interesting “discovery”: those humans who did (supposedly) coexist with dinosaurs never buried themselves with said dinosaurs:


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