Archive for the ‘Reasoning’ Category

John Stuart Mill, in his classic On Liberty, said

three-fourths of the arguments for every disputed opinion consist in dispelling the appearances which favour some opinion different from it.

In this spirit, the second lesson of our free email course, Argument Mapping: Make Your Case Clear and Compelling covers the importance of anticipating and responding to objections to your position, and shows how you can use argument mapping to organise these arguments.

A participant, Chantal, asked: “My question would be about how to produce objections. You are saying we can train for that. Sometimes I try and no interesting idea will arise :( What type of question should I be asking myself to create this other point of view?”

This is an excellent question.  How might one actually go about identifying the strongest objections to one’s own position?

Here are some things you can try.  Of course not all of these may be feasible in your situation.

1. Ask Opponents, or Bystanders

Perhaps the most obvious strategy is just to ask one or more people who strongly disagree with your position.  Such people are likely to be quite happy to help, and are likely to know the best objections.

If you can’t ask somebody who strongly disagrees, you can try asking somebody who is neutral on the topic.  Having no emotional involvement in the matter, they may find it easier than you do to see the problems with your position.

2. Research the Topic

If your position is on an issue that many people may have considered, a little digital sleuthing will often quickly uncover the main arguments on the other side.  For public issues, it should be easy to find op-eds or magazine articles, government reports, and so on.  For more technical or academic issues, scholar.google.com is a great resource.

3. Adapt Objections to Similar Positions

The best arguments against your position might just be adaptations of the best arguments against similar positions.  For example, if you are proposing that there should be a new freeway to the airport, you could look at proposals for freeways elsewhere to quickly get an idea of the kind of objections you are likely to encounter.

4. Use Standard Form Objections

This is a closely related suggestion.  There are many standard types of objections to positions of various kinds.  For example, any position which involves restricting people’s behavior – e.g., a proposal to ban vaping in public places – will encounter objections from based on individual rights and liberties.  (See the rest of Mill’s On Liberty).  If your position is that your group or team should pursue a certain course of action, there will be objections based on risk, particularly worst-case possible outcomes.  And so on.

5. Construct Objections from Interests

Consider what interests are threatened by your position.  Objections might be direct or indirect expressions of those interests.  For example, if your position is that our future energy needs should be met by large nuclear fusion plants, your position will threaten anyone with an interest (commercial, ideological, or any other type) in standard renewable energy industries such as wind or solar.  Those interests will lead to objections such as the impact on jobs in regional areas.

6. Identify and Challenge Assumptions

Any position will depend on a range of assumptions.  You can identify objections by ferreting out all or most of your assumptions and challenging those yourself.  One way to do that is covered in the email course, Lessons 4 and 5.  This is using principles of logic to expose the hidden assumptions in your own arguments supporting your position.

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Note: this is a draft section of a larger guide.  Comments welcome. 

What is reasoning? Everyone has an intuitive sense, though many would struggle if asked to define it.

A dictionary is usually a good starting point. Merriam-Webster defines reasoning as the process of thinking about something in a logical way in order to form a conclusion or judgment.  

This is OK as far as it goes, but we need to expand and sharpen it quite a bit.  To do this, let’s look at some simple examples.   

Reasoning as a mental activity

Suppose Daniel, someone you know and trust, tells you that a person he knows, Marie, is married.  You now know Marie is in fact married.  Put differently, you are now confident that the claim Marie is married is true.  

Now Daniel asks: does Marie have a husband? Think about that before reading on.


If you’re like most people, you would have quickly thought something like Of course Marie has a husband – she’s married! But then you may well have reflected a bit more.  Why would Daniel ask about this, if the answer is so obvious?  What’s the trick?  

The “trick,” of course, is that Marie could be married to a woman, and so have a wife.  Marie might be lesbian and live in a state allowing same-sex marriage.  Or Marie might in fact be a straight man.  Marie’s being married doesn’t prove she has a husband – though she probably does.    

Your thinking here involved considering various ideas – Marie’s being married, Marie’s being a lesbian, Marie’s being a man, and perhaps others – and arriving at a judgement about Marie’s having a husband.  This is reasoning in the Merriam-Webster sense.

In slightly technical terminology, we say that you considered various claims, and also your confidence in the truth of these claims:

Claims Your confidence in their truth
Marie is married. Certain
Marie is a lesbian, married to a woman. Remote possibility.  
Marie is a man, married to a woman. Remote possibility.

and, given the logical relationships among these claims, you arrived at a level of confidence in another claim:

Claim Your confidence in its truth
Marie has a husband. Probable

So in this sense, reasoning is a mental activity; it is:

  • Understanding the logical relationships, if any, among claims; and  
  • Adjusting your confidence in those claims accordingly.  

However this is not the full story.

Reasoning is also the network of claims

Sometimes the word “reasoning” is used to refer not to the mental activity but to the claims themselves.

For example here are the various claims in the above example, with a few extra words (but, and, so) used to indicate logical relationships among them:

Marie reasoning

This is the sense of “reasoning” we are using when we say things like Show me your reasoning! or The reasoning in the article is flawed.  

Reasoning in this sense is like a social network, except claims replace people, and logical relationships replace personal relationships.  Note that just as some people in a social network have no relationship with to each other, some of the claims in the reasoning might not be logically related at all.

Thus, “reasoning” has two different meanings: the mental activity, and the network of claims.  These are of course closely connected; the network is what the mental activity is about.  

Reasoning can be presented in prose, or in a diagram

A network of logically related claims is an abstract thing.  We always need some way to show or present the network, so that our minds can see and follow it.

The standard way to do this is to express the claims in prose (writing or speech).  Examples abound; just look at the opinion page of any newspaper.  Here’s an example of some reasoning expressed in standard prose:

Religion Reasoning.png

It’s not set out rigidly as in the list for the Marie example above, but it is still expressing logically related claims, aimed at getting you to agree that not all religions deserve equal respect.  (Plus, it’s more fun to read.)

Representing reasoning in text is so common, and so normal, that most people hardly even realise that that is what they are doing.  There is however an alternative.  We can represent a network of claims diagrammatically.  

Here’s a diagram for the religion example:

Religion diagram.png

Note that arrows are used instead of the words like but, and and so in the Marie example; and the claims are arranged left to right in a logical order, though one quite different to the order in which they appeared in the original text.

There are lots of different ways to diagram reasoning, depending on what conventions you choose to adopt.  The diagram above is very minimalist.  In this course, we’ll be using a few different types of diagramming.  

To understand somebody’s reasoning, we must model it.

As mentioned, people almost always present reasoning in ordinary prose.  Consequently, we (the readers) have to interpret the prose in order to understand what their reasoning is.  Sometimes this is simple and effortless.  Other times, it is very difficult.  Often it is not at all obvious exactly what the reasoning is, and we have to make our best guess.  

In this course, such “guesses” or interpretations are called models of reasoning.  The diagram above presents a model of the reasoning in the religion text.

Coming up with this model required:

  • Figuring out what claims were being made as part of the reasoning.  For example, the sentence “Jedi knights, for example?” was interpreted as making the claim It is appropriate to ridicule Jedi Knights.
  • Figuring out what logical relationships, if any, these claims are supposed have to each other.  The arrows show these logical relationships.   Notice that nothing in the original text explicitly specified these particular relationships.  They are a matter of interpretation.  

Now, you may not agree with the model expressed in the diagram.  You may think that the author’s reasoning was different.  You might be right; but that would just highlight that you are coming up with your own model of the reasoning, and that coming up with such models is what we always have to do when we read or listen to prose presentations.  

Religion Model.png

An argument map displays a model of reasoning

In practice, a reasoning model is usually displayed diagrammatically.  In the graphic above, the middle representation, the list of claims and their relationships, was included for a couple of reasons.  First, it emphasises the point that reasoning (in one sense) is a set of claims with logical relationships.  Second, it makes visually clear that the same reasoning can be expressed in prose or displayed in a diagram.  

A diagram displaying a model of reasoning in some text can be thought as a kind of map.   A good analogy here is the classic subway map.  The subway map does not show the subway system exactly as it is in reality.  Rather, it portrays certain aspects of the subway system.  Similarly, a diagram of the reasoning expressed in a piece of prose cannot display the reasoning itself; it can only ever show a model of the reasoning.  

A diagram displaying a model of the reasoning expressed in a text is called an argument map.  

Religion Map.png


We’ve just covered a fair bit of theory, so here is a brief recap.  We defined reasoning as

  1. In one sense, a mental activity, in which we understand the logical relationships among claims, and adjust our confidence in the truth of those claims accordingly.  
  2. In another sense, a network of claims defined by logical relationships.    

Reasoning in the second sense must always be expressed or displayed in some way so that we can see what it is and apply our reasoning capacities to it.  Almost always, reasoning is laid out in prose (speech or writing).  However it is also possible to present reasoning diagrammatically.  A diagram will usually be much better than prose in specifying exactly what the reasoning is.  

Often, it is not easy to identify the reasoning somebody has expressed in prose.  We need to make our best guess as to what that reasoning is; in other words, we need to come up with a model of the reasoning. An argument map is a diagram displaying such a model.






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The question of who actually wrote the works attributed to “William Shakespeare” is a genuine conundrum.  In fact it may be the greatest “whodunnit” of all time.

Although mainstream scholars tend to haughtily dismiss the issue, there are very serious problems with the hypothesis that the author was William Shakspere of Stratford upon Avon. However all other candidates also have serious problems.  For example Edward de Vere died in 1604, but plays kept appearing for another decade or so.  Hence the conundrum.

Recently however this conundrum may have been resolved.  A small group of scholars (James, Rubinstein, Casson) have been arguing the case for Henry Neville.  A new book, Sir Henry Neville Was Shakespeare, presents an “avalanche” of evidence supporting Neville.  Nothing comparable has been available for any other candidate.

Suppose Rubinstein et al are right.  How can the relevant experts, and interested parties more generally, reach rational consensus on this?  How could the matter be decisively established?  How can the process of collective rational resolution be expedited?

A workshop later this month in Melbourne will address this issue.  The first half will involve traditional presentations and discussion, including Rubinstein making the case for Neville.

The second half will be attempting something quite novel.  We will introduce a kind of website – an “arguwiki” where the arguments and evidence can be laid out, discussed and evaluated not as a debate, in any of the standard formats, but as a collaborative project.  The workshop will be a low-key launch of the Shakespeare Authorship Arguwiki; and later, all going well, it will be opened up to the world at large.  Our grand ambition is that the site, or something like it, may prove instrumental in resolving the greatest whodunnit of all time, and more generally be a model for collective rational resolution of difficult issues.

The workshop is open to any interested persons, but there are only a small number of places left.

Register now.  There is no charge for attending.


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OK, I know picking on climate pseudoskeptics is like… well, shooting fish in a barrel.  (Not that I’ve ever shot fish in a barrel – but Mythbusters have shown it is easy to do, and that’s good enough for me.)

But this example illustrates an important general point.

One of the most basic, widespread and damaging thinking errors is: failure to make a relevant comparison.*

Consider this comment by someone I’ll call “Peggy Balfour,” since that’s what she calls herself.

The Europen Union has been carbon trading since 2005. All are industrialised nations.

According to the Mauna Loa air quality measurements Global CO2 was rising at average 1.67ppm per year prior to 2005.

7 years later, 2012, CO2 is still rising at 1.67ppm per year.

Check out ‘Full Mauna Loa CO2 record’ on this site. http://www.esrl.noaa.gov/gmd/ccgg/trends/

E.U carbon trading hasn’t made one whit of difference.

To show that E.U. carbon trading “hasn’t made one whit of difference” Ms Balfour compares C02 levels in 2005 with those in 2012.

Of course, the relevant comparison is CO2 levels in 2012 with what CO2 levels would have been in 2012 had European Union carbon trading not been in place but all else remaining the same.

The relevant comparison for this kind of causal inference is between an actual reading and a hypothetical value, one which can only be estimated using the kinds of complex quantitative global climate models that pseudoskeptics are wont to cavalierly dismiss.

I personally have no idea how much difference EU trading has made.  Maybe its not very much.  But I do know that you can’t properly answer that question, or a host of others, without making relevant comparisons.

* I think Robyn Dawes made something like this point in one of his excellent books.

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An interesting case of what I would call visual deliberation, in the broad sense of “the use of visual aids to support deliberative processes”:

Joe Heller | Green Bay Press Gazette

The carton obviously presents four distinct arguments, using a mix of verbal, pictorial and spatial elements or mechanisms.

However the main argument made by the cartoon is that the arguments against wind power are weak as compared with the arguments against nuclear, oil and coal.   This argument is not explicitly given, whether verbally or pictorially; it is a kind of “conversational implicature” of the presenting of the four arguments.

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Almost everyone agrees that critical thinking skills are important.  Almost everyone agrees that it is worth investing effort (in education, or in workplace training) to improve these skills.   And so it is rather surprising to find that there is, in the academic literature, little clarity, and even less consensus, about one of the most basic  questions you’d need answered if you wanted to generate any sort of gains in critical thinking skills (let alone generate those gains cost-effectively); viz., how are critical thinking skills acquired?

Theories on this matter come in five main kinds:

  • Formal Training. CT skills are simply the exercise of generic thinking power which can be strengthened by intensive training, much as general fitness can be enhanced by running, swimming or weightlifting.  This approach recommends working out in some formal ‘mental gym’ such as chess, mathematics or symbolic logic as the most convenient and effective way to build these mental muscles.
  • Theoretical Instruction. CT skills are acquired by learning the relevant theory (logic, statistics, scientific method, etc.).  This perspective assumes that mastering skills is a matter of gaining the relevant theory.  People with poor CT poor skills lack only a theoretical understanding; if they are taught the theory in sufficient detail, they will automatically be able to exhibit the skills, since exhibiting skills is just a matter of following explicit (or explicable) rules.
  • Situated Cognition. CT is deeply tied to particular domains and can only be acquired through properly “situated” activity in each domain.  Extreme versions deny outright that there are any generic CT skills (e.g. McPeck).  Moderate versions claim, more plausibly, that increasingly general skills are acquired through engaging in domain-specific CT activities.  According to the moderate version general CT skills emerge gradually in a process of consolidation and abstraction from particular, concrete deployments, much as general sporting skills (e.g., hand-eye coordination) are acquired by playing a variety of particular sports in which those general skills are exercised in ways peculiar to those sports.
  • Practice sees CT skills as acquired by directly practicing the general skills themselves, applying them to many particular problems within a wide selection of specific domains and contexts.  The Practice perspective differs from Formal Training in that it is general CT skills themselves which are being practiced rather than formal substitutes, and the practice takes place in non-formal domains.  It differs from Situated Cognition in that it is practice of general skills aimed at improving those general capacities, rather than embedded deployment of skills aimed at meeting some specific challenge within that domain.
  • Evolutionary Psychology views the mind as constituted by an idiosyncratic set of universal, innate, hard-wired cognitive capacities bequeathed by natural selection due to the advantages conferred by those capacities in the particular physical and social environments in which we evolved.  The mind does not possess and cannot attain general-purpose CT skills; rather, it can consolidate strengths in those particular forms or patterns of thinking for which evolution has provided dedicated apparatus.  Cultivating CT is a matter of identifying and nurturing those forms.

Formal training is the oldest and most thoroughly discredited of the perspectives.   It seems now so obvious that teaching latin, chess, music or even formal logic will have little or no impact on general critical thinking skills that it is hard to understand now how this idea could ever have been embraced.   And we also know why it fails: it founders on the rock of transfer.  Skills acquired in playing chess do not transfer to, say, evaluating political debates.  Period.

Theoretical Instruction has almost as old a philosophical pedigree as Formal Training.  It has been implemented in countless college critical thinking classes whose pedagogical modus operandi is to teach students “what they need to know” to be better critical thinkers, by lecturing at them and having them read slabs out of textbooks.   Token homework exercises are assigned primarily as a way of assessing whether they have acquired the relevant knowledge; if they can’t do the exercises, what they need is more rehearsing of theory.   As you can probably tell from the tone of this paragraph, I believe this approach is deeply misguided.  The in-depth explanation was provided by philosophers such as Ryle and Heidegger who established the primacy of knowledge-how over knowledge-that, of skills over theory.

Current educational practice subscribes overwhelmingly (and for the most part unwittingly) to the moderate version of Situated Cognition.  That is, we typically hope and expect that students’ general CT skills will emerge as a consequence of their engaging in learning and thinking as they proceed through secondary and especially tertiary education studying a range of particular subjects.  However, students generally do not reach levels of skill regarded as both desirable and achievable.  As Deanna Kuhn put it, “Seldom has there been such widespread agreement about a significant social issue as there is reflected in the view that education is failing in its most central mission—to teach students to think.”  In my view the weakness of students’ critical thinking skills, after 12 or even 16 years of schooling, is powerful evidence of the inadequacy of the Situated Cognition perspective.

There may be some truth to the Evolutionary Psychology perspective.  However in my view the best argument against it is the fact that another perspective – Practice – actually seems quite promising.   The basic idea behind it is very simple and plausible.   It is a truism that, in general, skills are acquired through practice.   The Practice perspective simply says that generic critical thinking skills are really just like most other skills (that is, most other skills that are acquired, like music or chess or trampolining, rather than skills that are innate and develop naturally, like suckling or walking).

In our work in the Reason Project at the University of Melbourne we refined the Practice perspective into what we called the Quality (or Deliberate) Practice Hypothesis.   This was based on the foundational work of Ericsson and others who have shown that skill acquisition in general depends on extensive quality practice.  We conjectured that this would also be true of critical thinking; i.e. critical thinking skills would be (best) acquired by doing lots and lots of good-quality practice on a wide range of real (or realistic) critical thinking problems.   To improve the quality of practice we developed a training program based around the use of argument mapping, resulting in what has been called the LAMP (Lots of Argument Mapping) approach.   In a series of rigorous (or rather, as-rigorous-as-possible-under-the-circumstances) studies involving pre-, post- and follow-up testing using a variety of tests, and setting our results in the context of a meta-analysis of hundreds of other studies of critical thinking gains, we were able to establish that critical thinking skills gains could be dramatically accelerated, with students reliably improving 7-8 times faster, over one semester, than they would otherwise have done just as university students.   (For some of the detail on the Quality Practice hypothesis and our studies, see this paper, and this chapter.)

So if I had to choose one theory out of the five on offer, I’d choose Practice.  Fortunately however we are not in a forced-choice situation. Practice is enhanced by carefully-placed Theoretical Instruction.  And Practice can be reinforced by Situated Cognition, i.e. by engaging in domain-specific critical thinking activities, even when not framed as deliberate practice of general CT skills.   As one of the greatest critical thinkers said in one of the greatest texts on critical thinking:

“Popular opinions, on subjects not palpable to sense, are often true, but seldom or never the whole truth. They are a part of the truth; sometimes a greater, sometimes a smaller part, but exaggerated, distorted, and disjoined from the truths by which they ought to be accompanied and limited.”

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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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