Common Thinking Errors and Modes of Reasoning

You have called reasoning “the core of human thinking”. How do you define it?

Reasoning is a systematic mental process in which an individual reaches a conclusion from a starting point that depends on a perception, a memory or a set of verbal propositions. Children reason, as do infants even before they can speak, and even other species reason to some degree. When we reason, we aim to draw conclusions that are valid; that is, conclusions whereby if our premises are true, then our conclusions must be true, too.   Of course, we differ in our ability to reason, but the good news is that we can improve our reasoning abilities. 

Inferences are a key element of reasoning.  Please describe how they work.
Inference is a process by which new information is obtained from old, either by transforming the old information or by combining two separate pieces of old information.  There are two key types of inference: implicit and explicit.  Implicit inferences occur as an automatic, non-conscious understanding of the world or descriptions of it, whereas explicit inferences are consciously made in attempts to answer questions or solve problems.  Suppose you were to read in the paper, “There was a fault in the signaling circuit. The crash led to the deaths of 10 passengers.” While the text does not make this assertion, you are likely to make the implicit inference that the passengers were killed in the crash.  However, the story might have continued as follows: “They were arrested when the plane crashed, found to be terrorists, and subsequently shot.” Plainly, you jumped to a conclusion based on the content of the passage and on your store of general knowledge. You made this implicit inference automatically and involuntarily -- perhaps without even being aware that you were making it.  In contrast, suppose that you read the following two assertions:
Al is a blood relative of Ben.
Ben is a blood relative of Cathy.
and you are asked, “Is Al a blood relative of Cathy?” Many people respond, “yes”.  They make an implicit inference based on their model of typical lineal descendants or filial relations.  But, in order to reach the correct answer you need to make an explicit inference.  That is, you need to search for an alternative model that refutes the conclusion  (I’ll tell give you an example of such a model in a moment.) The roots of human rationality may be inherent in this process of searching for a counterexample, i.e., a model in which the premises are true, but the conclusion is false.  It shows that an inference is not valid.   Of course, the claim that we rely on mental models and counterexamples is controversial.  Some psychologists argue to the contrary that deduction depends on following formal rules of inference akin to those in logic.  I believed so once myself, but the experimental evidence led me to the view that we rely on models.  A counterexample to the blood relative inference above is a case in which Al is Ben’s father, and Cath is Ben’s mother.  The premises are true, but the conclusion could well be false, i.e.: Al is not a blood relative of his wife, Cathy.  

There are three main types of reasoning: deductive, inductive and abductive. Describe how they differ.
Deductive inferences are attempts to draw valid inferences.  The conclusion follows necessarily from the premises, and so it holds in all the models of the premises: there are no counterexamples to the conclusion.  For example,
The patient has chicken pox or she has measles.
    She doesn’t have chicken pox.
    Therefore, she has measles.

An induction goes beyond the information in the premises, and so there is no guarantee that its conclusion is true even if its premises are true.  For example,
    The patient has chicken pox or she has measles.
    She has chicken pox.
    Therefore, she doesn’t have measles.

The conclusion is plausible, but it isn’t valid, because the patient may have both diseases at the same time.  As I child, I myself received such a double diagnosis!  A special case of induction is when we make an induction in order to explain something. This is known as an abduction.  For example,
    If someone pulled the trigger, then the pistol fired.
    Someone did pull the trigger but the pistol didn’t fire.
    So, a prudent person must have emptied the pistol and there were no bullets in its chamber.

Some theorists have tried to frame rules for induction in an analogy to the formal rules of logic, but the model theory postulates that the roots of induction and abduction are our intuitive ability to use knowledge to construct mental models of the world.  The difference between the three sorts of inference is accordingly between whether a counterexample to a conclusion is at least possible.  If no counterexample is possible, the inference is a valid deduction.  If a counterexample is possible, it is an induction.  And if an induction yields a putative explanation – typically, a causal one – then the inference is an induction.

Which is the most valuable form of reasoning in today’s environment?
All three tend to work together when we solve problems, whether in daily life, in business, or in science, so they are all valuable.  In my most recent book, I analyzed three case histories of thinking. One was the way in which the Wright brothers succeeded in designing a controllable heavier-than-air craft; the second was the breaking of the Nazi’s enigma code in World War II; and the third was John Snow’s solving the problem of how cholera was communicated from one person to another.  These three case histories concern technology, an application of logic, and science, respectively. In each case, however, we see all three sorts of reasoning going hand in hand in order to solve the problem.  The same is true, I think, when we solve problems in daily life.

You have studied the Wright brothers’ thinking process in great detail.  What was so special about it?
Soon after the Wrights had begun their work, they – or at least Wilbur, who was the intellectual leader – realized that flight was not a single puzzle that could be solved by trial and error. It called for systematic thought about many problems.   They succeeded in achieving controllable flight before their rivals because they were better reasoners.  Many of their contemporaries, for example, thought that the secret of flight was a light and powerful engine. But Wilbur made the induction that an engine was bound to fail sooner or later, so that control of the craft was more important so the pilot could land safely.  With hindsight, it is quite extraordinary that so many pioneers lost their lives because they failed to draw this conclusion.  As owners of a bicycle shop, the Wrights drew many analogies between bicycles aircraft: in many ways, their aircraft was a flying bicycle.   For example, their rivals aimed for flight in a stable equilibrium.  As Wilbur argued, bicycles don’t move in a stable equilibrium like a tramcar.  But, their ‘pilots’ learn to control them.  
The Wrights had a genius for visualization.  This ability should not be confused with the mere formation of visual images.  It depends on the construction of mental models of three-dimensional entities or of more abstract structures, and the ability to manipulate these representations.  The brothers animated their representations to work out the flow of wind over a wing, to design a transmission system, and to solve the design of propellers. They used mental models in imaginative play constrained by their knowledge. They also used models in their reasoning in order to check the consequences of an assumption, to derive a counterexample to a claim, and to diagnose a malfunction. And they were most adroit in using a model of one thing, such as a bicycle, as an analogy for another, such as an aircraft.  Of course they had some luck, great perseverance, and skill in working with their hands, but above all, they were exceptional thinkers.

What causes problematic reasoning?
The biggest source of difficulty with inferences is the need to hold in mind two or three different models that are compatible with the premises.  Individuals differ in this ability, and it likely explains the correlation between reasoning ability and intelligence tests.  When the going gets tough – whenever circumstances make it impossible to cope with multiple mental models -- we all tend to err.  We think that we are drawing a valid conclusion, but we have often overlooked a possibility that may be a counterexample to our conclusion.

In your view, what is the single biggest error in human thinking?
That is easy: we overlook possibilities.  Sometimes, as my previous answer implied, there are too many models for us to hold in our mind.  But when we rely on intuitive thinking, we often depend on a single mental model, and it may be the wrong one.  Studies of human errors that led to disasters illustrate this failure over and over again.  The Herald of Free Enterprise ferry disaster is a classic example.  The vessel was a ‘roll on, roll off’ car ferry: you would drive your car onto it through the open bow doors; and when all the cars were on board, a member of the crew would close the bow doors, and the ship would be put out to sea.  On March 6th 1987, the Herald left Belgium bound for England, sailing out of the Zeebrugge harbor into the North Sea with its bow doors wide open.  It is hard to imagine that such a possibility could occur, but it did, and 188 people drowned as a result.  The human contribution to disasters is almost always a failure to envisage a possibility.

Is there anything that can be done to prevent such errors?
Checklists are one preventative measure.  Their use in airplanes has been routine since the 1930s, and a Professor at Johns Hopkins Medical School, Peter Provonost, has recently shown that they are also very effective in reducing infections in hospital.  His checklist for inserting a catheter into a patient in an ICU is as follows.  
Doctors should:
1. Wash their hands with soap.
2. Clean the patient’s skin with chlorhexidine antiseptic.
3. Put sterile drapes over the entire patient.
4. Wear a sterile mask, hat, gown and gloves.
5. Put a sterile dressing over the catheter site.

In one 18-month study, this simple list is estimated to have saved the lives of over 1,500 patients.  A former PhD student of mine, Victoria Bell has extended the checklist idea to improve reasoning.  She teaches people in about two minutes what she calls ‘the model method’.  Here’s a simplified example to illustrate: suppose you know that a fault has occurred either in your computer or in your printer. Draw a line down the middle of a piece of paper and put ‘computer’ at the head of one column and ‘printer’ at the head of the other. Then, as you receive further information, add it to the relevant column or columns.  Say you discover that the ink cartridge can run out without warning;  you would add that under the ‘Printer’ column.  You keep updating the possibilities as each piece of information comes in; and some information may enable you to delete an entire column, because it is no longer a viable possibility.

As Sherlock Holmes once remarked, “when you have eliminated the impossible, whatever remains -- however improbable -- must be the case.”  This maxim holds for the model method.   When you teach people how to use it, two things happen: they reason much more rapidly, and they reason much more accurately. Once people   master this method, they can use it without paper and pencil -- they can just imagine the possibilities, and they will still outperform those who haven’t been taught the method.

You have said that working memory is at the heart of computational power.  Why is it so important?
The most powerful mental processes are ‘recursive’ in that they depend on loops of mental operations.  An example is mental multiplication: you can't do it unless you can remember the results of your intermediate computations, and so you need working memory to record them.  If you take away someone’s working memory, they can no longer do long multiplication or any other recursive task.  Implicit reasoning, as I said earlier, relies on just a single mental model.  It is not recursive.  But explicit reasoning and the search for alternative models is a recursive process: we need working memory in order to keep in mind alternative models.  Some psychologists have speculated that intelligence depends on working memory and that explicit reasoning also depends on working memory.  Variations in its processing capacity may explain the link between reasoning and intelligence, and the differences in ability from one individual to another.

You have said that a super-human intelligence would not only have an unlimited working memory and the ability to think at great speed, it would also be able to think about both what is true and what is false. What is the importance of this latter ability?
We tend to think in terms of ‘either this happened or else that happened’, considering the truth of one case, and then the truth of the other case.   What we fail to bear in mind is that when one case is true, the other case is false.  This omission reduces the load on working memory, but unfortunately it can lead us into error.  Here’s an example from an experiment that Clare Walsh and I did:

    Either Ann is sitting on the sofa and watching TV or else Eve is standing at the
window and watching the birds.
Ann is sitting on the sofa.
Is she watching TV?

Most people say, ‘yes’, but that inference is invalid.  Suppose that it is true that Eve is standing at the window and watching the birds.  The meaning of ‘or else’ tells us that in this case it is false then Ann is sitting on the sofa and watching TV.  And one way in which this conjunction could be false is that Ann is indeed sitting on the sofa, but she is not watching TV.  So, just because Ann is sitting on the sofa, it doesn’t follow that she has to be watching TV.  We go wrong in our inference because we fail to think about falsity, and in particular about the different ways in which the assertion about Ann can be false given the truth of the assertion about Eve.  This failure to think about falsity is a general shortcoming in human reasoning;  even expert reasoners suffer from it.

What do we stand to gain by working on our reasoning abilities?
The better we reason, the better our lives: chances are that we will be healthier, we will live longer, and we will achieve our goals.  If the theory that I have relied on in my answers is correct, then we use mental models when we reason.  If the theory is wrong, psychologists will discover a series of counterexamples to it.  But, here I can quote from my latest book: the model theory itself argues that counterexamples are fundamental to our reasoning.  As so the theory has at least this to say for itself: as it collapses in the face of systematic counterexamples, it can explain its own demise.

Philip Johnson-Laird is the Stuart Professor of Psychology at Princeton University. His most recent book is How We Reason (Oxford University Press, 2006).

[This article has been reprinted, with permission, from Rotman Management, the magazine of the University of Toronto's Rotman School of Management]