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Fernando Leal and colleagues at the University of Guadalajara have released Introducción a la Teoría de la Argumentación, an integrated selection of pieces intended to assist students and their teachers to focus on argumentation when reading and writing academic texts.

The section Parte II: La téchnica de mapeo de argumentos (argument mapping) contains three pieces emerging from work at the University of Melbourne and Austhink:

  • A translation of my article Teaching Critical Thinking: Some Lessons from Cognitive Science
  • A translation of Enhancing our Grasp of Complex Arguments, by Paul Monk and me, a big-picture view of why complex arguments are cognitively challenging and how argument mapping can help.  It has been available as a manuscript since 2004 and been well-received so we are very happy to see it finally appear in print.
  • A new chapter  by Claudia María Álvarez Ortiz, ¿El estudio de le filosofia mejora las habilidades de pensamiento crítico? which extracts some core material from her MA thesis Does Philosophy Improve Reasoning Skills?.  This is the first proper publication of the very important meta-analysis of studies of gains in critical thinking at college.

Well-designed and attractively produced, the appearance of the volume is a significant development in critical thinking pedagogy and theory, particularly in the Spanish-speaking Americas.   Regrettably the language barrier will be a major hurdle to recognition and uptake in the Anglosphere.  Perhaps somebody should undertake a translation of the whole volume into English?


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A few months back I discussed Benjamin Franklin’s “moral algebra,” his simple prescription for good deliberative decision making.  We know of Franklin’s moral algebra only because he succinctly summarized it in a now-famous short letter to his longtime scientific colleague and friend, Joseph Priestley.  In that letter Franklin seemed to suggest that the moral algebra was his own invention, using phrases such as “My way [of making decisions]…”, but he didn’t explicitly claim it as his own creation.

Recently, one FelixM cryptically commented on this blog that

St Ignatius of Loyola (founder of the Jesuits) recommended this approach, about two hundred years earlier. presumably other people used it before him.

This was intriguing.  What was the method that St Ignatius allegedly used?  Was it indeed the same or very similar to Franklin’s moral algebra? And did Franklin know of it?  Was it indeed the original formulation of the method?

I contacted FelixM, who kindly informed me that St Ignatius’ version of the method could be found in his major work The Spiritual Exercises, which to this day remains a key Jesuit text.   The full text of the relevant section is appended below.

Felix was quite right; Franklin’s moral algebra, and Ignatius’ version, which we might call his “spiritual algebra,” are indeed very similar.

The Ignatius version is however expressed in what appears (to us) archaic and floridly religious language. Here’s my take: a contemporary, secular version of St. Ignatius’ spiritual algebra:

  1. Identify the issue you need to decide upon, framed as whether to take a proposed action or not
  2. Identify and keep in mind  your most important values and objectives.
  3. Cultivate an indifference to the outcome.
  4. List and weigh up the pros and cons of acting in the proposed way, and the pros and cons of not acting.
  5. Determine whether acting has the greater net benefit
  6. Choose what to do based on this determination rather than your gut feeling (“inclination of sense”).

The parallels are striking, but there are some differences:

  1. St Ignatius’ step 2 – identify and keep in mind your most important values and objectives – is not mentioned by Franklin
  2. Franklin recommends listing the pros and cons of taking the action only; he doesn’t recommend also listing the pros and cons of not acting.  [Arguably, these are just the inverse of the pros and cons of acting, and so there is no need to list both.]
  3. Franklin provides a heuristic for determining the balance of considerations (i.e. “cancelling out” considerations of equal weight, etc.) whereas St Ignatius simply instructs us to “reckon” the overall balance.

As to whether Franklin knew of St Ignatius’ method, Felix says:

St Ignatius was pretty well known and I wouldn’t be at all surprised if Franklin had read him.  (In fact, perhaps it would be surprising if he hadn’t!)

This may well be right, but I haven’t been able to find any independent evidence for it.


From The Spiritual Exercises of St. Ignatius of Loyola


It contains six Points.

First Point. The first Point is to put before me the thing on which I
want to make election, such as an office or benefice, either to take or
leave it; or any other thing whatever which falls under an election
that can be changed.

Second Point. Second: It is necessary to keep as aim the end for which
I am created, which is to praise God our Lord and save my soul, and,
this supposed, to find myself indifferent, without any inordinate
propensity; so that I be not more inclined or disposed to take the
thing proposed than to leave it, nor more to leave it than to take it,
but find myself as in the middle of a balance, to follow what I feel to
be more for the glory and praise of God our Lord and the salvation of
my soul.

Third Point. Third: To ask of God our Lord to be pleased to move my
will and put in my soul what I ought to do regarding the thing
proposed, so as to promote more His praise and glory; discussing well
and faithfully with my intellect, and choosing agreeably to His most
holy pleasure and will.

Fourth Point. Fourth: To consider, reckoning up, how many advantages
and utilities follow for me from holding the proposed office or
benefice for only the praise of God our Lord and the salvation of my
soul, and, to consider likewise, on the contrary, the disadvantages and
dangers which there are in having it. Doing the same in the second
part, that is, looking at the advantages and utilities there are in not
having it, and likewise, on the contrary, the disadvantages and dangers
in not having the same.

Fifth Point. Fifth: After I have thus discussed and reckoned up on all
sides about the thing proposed, to look where reason more inclines: and
so, according to the greater inclination of reason, and not according
to any inclination of sense, deliberation should be made on the thing

Sixth Point. Sixth, such election, or deliberation, made, the person
who has made it ought to go with much diligence to prayer before God
our Lord and offer Him such election, that His Divine Majesty may be
pleased to receive and confirm it, if it is to His greater service and

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Every issue, the Harvard Business Review contains a “case”, a fictional situation in which a senior executive, usually a CEO, has to make some hard decision.   The situation is presented in an entertaining narrative, and then the decision problem is posed in a succinct question.  Then three or four expert commentators provide insights and recommendations.  

HBR cases are excellent material for business decision mapping.  They are realistic examples of the kind of decision problems for which decision mapping is well suited.   Mapping out the problem can provide useful insight into the case.  Conversely, working on HBR cases is a great way to build experience with and skills in decision mapping.  

The case in the current issue is Who Can Help the CEO? “With pressure mounting for better results, the CEO of TrakVue needs help.  But every avenue he tries turns out to be a dead end…Whom and how can Eliot ask for help?”

Here’s how I mapped the first half of the decision problem, i.e. the who part:


In this case, there were lots of options to choose from.  This made hierarchical grouping of the options particularly useful.  Once the options are properly grouped, it is easy to see how some considerations bear at higher levels (on whole groups of options, e.g. colleagues at TrakVue) while others bear on sub-options at lower levels (e.g., Armory Essler).   Thus this case usefully illustrates it how important it is to get good hierarchical structuring of options, and how a decision map can make this hierarchical structuring visually transparent. 

More interestingly, in this case, the decision map reveals the answer.  If you identify and organise all the options and all the considerations bearing upon them that were provided in the case and the commentaries – and restrict yourself to them – then it is clear where Eliot should be turning.  He should be talking to experienced outsiders – “peer” CEOs in other industries, or experienced mentors.  This is the only category of people for whom the “pros” clearly, and overwhelmingly, outweigh the “cons”.   There are no “red flags” at all down this branch.  

Rarely, in reality, would the answer be so obvious.  Most of the time, any option would have at least some disadvantages.  And, as things currently stand, rarely would decision makers have the benefit of decision maps to guide them.

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Surviving a firestorm

Victoria has been hit this week by the highest temperatures and most intense bushfires in the state’s recorded history.  Around 200 dead, 1800 houses destroyed – and it is far from over.  

As shown in this video, Jim Baruta was caught in the middle of it and managed to survive  in a purpose-built bunker.  

As it happens, he’s also the manager of Quist’s Coffee in Little Collins St. where I’ve been getting my daily fix for the past year or so.  

Watch the video.   It is truly extraordinary, and quite moving.

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A third chunk of the work-in-progress paper.

Draft only. As always, comments welcome.

3.3 Semiformality

A third theme in explaining how using an argument mapping package such as Rationale can improve reasoning centres on the notion of semiformality. In a nutshell, the idea is this: human thinking is typically informal. In certain areas, such as general reasoning and argumentation, it can be improved by moving into a semiformal, rather than formal, mode. Argument mapping is reasoning conducted in a semi-formal mode.

The contrast between formality and informality, in the sense relevant here, is familiar enough. Modes, domains, systems, languages or whatever count as formal to the extent they have characteristics such as:

  • a finite set of basic symbols or primitives
  • are digital (Haugeland)
  • are governed by strict rules or algorithms
  • have well-defined concepts or “semantics”
  • achieve complexity through combination
  • support effective procedures

Mathematics, formal logic, programming languages, artificial intelligence, and many games such as chess are all formal. Natural language, conversation, politics, and humour on the other hand are informal, even if they exhibit a few of the features of formality to some extent.

Now human reasoning and argumentation are standardly informal. There are primitives (words, or propositions), meanings, and principles or norms, but these are not defined with the kind of precision, rigour or reliability one finds in formal modes such as mathematics or chess. In this respect, human reasoning is often reflecting the nature of the domains or issues about which the reasoning is being conducted. For example, politics is an inherently informal domain, and this informality is reflected in the nature of our default intellectual tools for thinking about and debating over political topics.

Noting on one hand the problems associated with ordinary human reasoning and argumentation, and on the other the often impressive achievements of their formal counterparts, the temptation has often been to recommend shifting human reasoning into a formal gear. Thus introductory logic textbooks are usually dominated by elementary formal logic (Aristotelian syllogisms, propositional logic, predicate calculus), making the assumption that people would reason more effectively if they replaced their instinctually informal thinking habits with logical formulae and proofs. This tendency culminates in the aspiration of mainstream artificial intelligence to recreate human-grade intelligence in the formal medium of digital computation.

Unfortunately this generally doesn’t work. AI research has discovered that it is extremely difficult, and perhaps impossible, to engineer formal systems capable of reliably making the mundane inferences underlying everyday conversation or humour, let alone engaging complex argumentation of the kind found, for example, in legal practice. Conversely, when people struggle with everyday reasoning and argumentation, they are not helped by attempting to translate their premises into some logical calculus and draw inferences by reference to its official rules. Indeed for innumerable commonplace reasoning challenges, formal techniques are so hopelessly impractical that recommending their use seems like a kind of sophistical sadism, another sad manifestation of Bacon’s Idols of the Theater.*

There are of course notable exceptions to the claim that human reasoning is not improved through the adoption of formal techniques. Clearly, for example, the proper use of statistical methods can help us draw better conclusions about subtle correlations and causal relationships. Formal modes of thought certainly have broad and important areas of application. The point being made here is that in general our practices of informal reasoning and argumentation cannot be enhanced by transposing into a formal key.

It may be, however, that some degree of formality can be helpful even where full-blown formal modes such as mathematics, formal logic and computation get no useful traction. The distinction between formality and informality is not a binary opposition. Rather, there is a spectrum of cases depending on which of the characteristics of formality are adopted and how those characteristics are manifested.

In the case of reasoning and argumentation, there have been many contexts in which these practices have been made more formal than they would normally be. Consider for example the medieval theory of disputation, which presented a sophisticated framework of rules governing moves in argumentation. Or consider contemporary high-school debating or “forensics;” etc. These sorts of elaborations of our ordinary practices are aimed, at least in part, at improving those practices; i.e., at enabling us to reason and argue more effectively. Implicitly they are proposing that the optimal mode for human reasoning is not the informal or the formal, but rather something intermediate, a “best of both worlds” scenario.

The conjecture, then, is that for general reasoning and argumentation there is a “sweet spot” somewhere on the spectrum between ordinary informal practices at one end, with their sloppiness and disorder, and purely formal techniques at the other, with their rigidity and limited range of application.
Argument mapping pushes reasoning in a formal direction by forcing relatively high level of explicitness and rigour in articulation. It generally requires that:

  • The claims involved be rendered discretely in full grammatical sentences
  • Material not directly involved in the reasoning be stripped away
  • The central contention or point in dispute be identified as such
  • All direct evidential links between claims be specified
  • Unstated claims or “assumptions” be identified and explicitly stated

In Rationale, these activities are scaffolded by providing a graphical format or “syntax” for the articulation of reasoning, with a limited set of “primitives” (claims, reasons, objections etc.) and strict rules about how those primitives can be combined.

Beyond the basic constraints, there are a number of principles of good mapping which cannot be specified as strict, universally-applicable rules. For example there is the principle of abstraction: generally, in a well-developed argument map, claims “higher” in the map (i.e., closer to the main contention) should be more abstract, and claims lower down should be more particular or concrete; and claims at a given level should be approximately the same in their degree of abstraction. While this principle is easy enough to state and understand, and with some practice is easy enough to apply in most cases, it involves inherently vague notions and is subject to a wide variety of exceptions, such that any attempt to articulate in a fully precise way what the principle is and how it applies ends up floundering in a quagmire of uncertainties and exceptions.

The principle of abstraction its ilk depend fundamentally for their successful application on intuitive human judgments based on experience and practice. To the best of our knowledge it is impossible to cash them out as formal rules capable of mechanistic implementation. Thus, argument mapping has irreducibly informal dimensions even as it makes reasoning activities more formal than they would normally be.

So argument mapping is semi-formal; it introduces aspects of formality while acknowledging its limits and retaining essentially informal dimensions.The idea is that disciplining reasoning practices to observe this degree of formality is the most feasible way to, if not eliminate, at least substantially mitigate the typical failures or difficulties standing in the way of good reasoning, argumentation and deliberation, such as:

  • not making reasoning fully explicit, including in particular the failure to articulate key assumptions
  • not applying relevant principles of good reasoning
  • not coping with the complexity of “real world” debates
  • not achieving common understanding among participants in argumentation

From what has already been said it should be clear that argument mapping confronts these failures head-on, which is why we can be optimistic that argument mapping practices, if widely and properly adopted, can lead to better reasoning.

What is the optimal level of formality to introduce into our reasoning practices? Where precisely is the “semi-formal sweet spot”? We don’t yet have definitive answers to these questions. Argument mapping as supported by a package such as Rationale constitutes one take on where the sweet spot is. It may have erred in one direction or the other. However evidence of the kind discussed in section X above suggest that Rationale’s take could well be approximately correct.


* “Lastly, there are idols which have immigrated into men’s minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theater; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion.” From Novum Organum

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With the recent release of Rationale 1.3, we also created a wiki for the Rationale community to create and share resources.

I’ve just uploaded a case study displaying some reasoning quite typical of the sort of argumentation conducted in small law firms.  In this case, the issue is whether tax is payable by the purchasors of a block of land. 

It is a useful case study because it illustrates many aspects of Rationale-style argument mapping all in a single map. 


What also struck me about it – and the reason for this post – is how such mapping can reveal the true complexity of even the most commonplace instances of legal argumentation.

In this case, the inferential chain from the critical piece of supporting evidence (a quote from a tax office decision) to the ultimate conclusion has six steps, including a rebuttal of an objection to a supporting reason for the main argument…

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Toddler logic

How old are people when they first start being able to reason?

I vaguely recall reading somewhere in the psychological literature on the development of reasoning skills that kids are able to reason as early as 4.  However even that may underestimate how early these skills emerge.

Our daughter is 3 years and one month old.  Here’s a conversation we had this evening.

Lillian (singing): “I’m the king of the castle, and you the dirty bascal.”

Us: “Its rascal, not bascal.”

“No, its BASCAL.”

“OK, well, grown-ups say rascal.  Little babies say bascal.”

Lillian ponders for a moment, then smiles. “I’m a baby!”

She had performed the following inference:

Babies say bascal.
I say bascal.
Therefore, I’m a baby.

This of course is an invalid inference; she might be something other than a baby which also says bascal.

However logical perfection is a lot to ask of a three year old.  In context, despite not being deductively valid, it wasn’t a bad inferential move to make.

She’s been making these sorts of inferences for a while – indeed, since well before she was three.  And explicit or verbalised inference was preceded by patterns of behavior which seemed to indicate an implicit understanding of certain inferential patterns.

So we can say the following with certainty: Reasoning abilities of a rudimentary kind are, at least sometimes, exhibited by humans before they turn 3.

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