Critical Thinking for Educators

"Pick any article from the newspaper," I would say to my students. "Bring it in and we'll analyze it." This was one of my favourite - and my most effective - activities in my critical thinking classes. I never knew what the students would bring in. With each article we would have to begin afresh. I was not merely teaching critical thinking, I was modeling it with them.

As the classes progressed the students would contribute more. Over time we would develop and grow our toolbox of analytical methods, evaluative devices, and argumentation strategies. It didn't matter what the subject was, what the newspaper was - we would get to the heart of what was being said and make it our own.

Educators, of course, are told a lot about critical thinking. Sometimes, if they are lucky, they take a critical thinking course in university and learn first-hand about the practice. Or they may be given a demonstration at an educational conference. Sometimes they are informed about critical thinking during discussions of pedagogy and policy. Or sometimes they simply read about it in magazines and journals.

I've focused this article on critical thinking for educators because I am concerned that teachers and school administrators are exposed to a lot of misinformation about critical thinking. Various writers have developed 'their own' approach to critical thinking, which sometimes muddies the waters. Others confuse critical thinking with creativity, various literacies, lateral thinking, or rhetoric.

For some examples of what critical thinking is not, take a look at this edutopia article. We are told:
Critical thinking is:
  • "Seeing both sides of an issue." -- Daniel Willingham
Sorry, no. Critical thinking is none of those things. Some of these might be outcomes of critical thinking - you might develop a reflective and reasonable thought process, for example. But that's not what it is.

If I had to define critical thinking (which I don't) I would say something like this: critical thinking is the method of application of logic and reasoning to thought. But as with most definitions, this doesn't really tell us what it is, it merely distinguishes it from other things. It's like saying 'carpentry is the process of creating things out of wood'. There's a lot more to the story of carpentry than that!

In this article I'll talk about some of the key concepts of critical thinking. It will help you recognize critical thinking when you see it, and more importantly, be able to recognize when something is not critical thinking.

Why is this important? Educators hear a lot of things from a lot of sources (including the Edutopia article above) about critical thinking. Indeed, just the other day we saw an article called Why schools should not teach general critical-thinking skills published in Aeon saying that "teaching students generic ‘thinking skills’ separate from the rest of their curriculum is meaningless and ineffective."

From where I sit, this is nonsense. As I tweeted in response, "Not teaching general critical thinking skills would be like teaching math for retail separately from math for engineering. Or teaching grammar for sports writing separately from grammar for history essays. It shows a basic misunderstanding of how knowledge works." But to understand why this is the case, you have to understand what critical thinking is. Hence this article.

Basic Concepts

Most critical thinking texts (I provide a list below) begin by identifying the parts of an argument. They do this because they are usually written for philosophers, and philosophers work mostly through argumentation. I'm actually going to start a few steps before that, because these texts take for granted some key concepts that may not have already been introduced.

One of these is the concept of the proposition. A proposition is essentially the assertion that something is the case.
  • If I say 'Paris is the capital of France," that is a proposition. 
  • If I ask, "Where am I?" that is not a proposition; it is a question.
  • If I say "Get out of here!" that is not a proposition; it is an order. 
  • If I say "Peter" that is not a proposition, it is a name.
Usually we will express a proposition with a sentence, and for that reason critical thinking focuses on language. But we can also express propositions through our actions, expressions, or habits.

Another key concept is the concept of truth. Truth is a property of a proposition, and more specifically:
  • If I say a proposition is the case, then the proposition is true.
  • If I say a proposition is not the case, then the proposition is false.
Why would I say that a proposition is or is not the case? I might have many reasons: I might have seen something happen, I might have a theory describing the world, or I might believe in a faith. At this point it doesn't matter; I'm just talking about what truth is, not how we get to it.

Finally I want to introduce the idea of fact and opinion. I will define these very simply. If I say a proposition is true, then it is a fact. In other words, facts are true propositions. Alternatively, if I do not say that a proposition is true, then it is an opinion. An opinion might be true, or it might not be true. We don't know. We can ask, "what makes something a fact?" That's like asking, "what makes something true?" At this point it doesn't matter. I'm just defining what a 'fact' is, not how to create one.

This now brings us to the concept of the argument. An argument is the presentation of one or more propositions as reasons to believe that another proposition is true. These propositions are called the premises and the other proposition is called the conclusion. We typically say that the conclusion 'follows' from the premises, or is 'supported by' the premises.

This is a very common form of discourse. We use reasons all the time. Any time we present evidence for something, or perform a mathematical calculation to get a result, or classify something as one type of thing or another, we are using argumentation. If you are trying to convince a child to eat his vegetables, or are trying to get an A instead of a B, or trying to say we should teach critical thinking in the classroom, we are using argumentation.

A key think to keep in mind about an argument is that typically it proceeds from premises that are facts to a conclusion that is an opinion. We are using propositions we already think are true in order to conclude that a new proposition is true.


The first and most fundamental aspect of critical thinking is the capacity to comprehend what has been said. When I taught critical thinking I often spent more time on this than on any other aspect of the discipline. If you don't get this part right, then the rest of critical thinking isn't of much use to you.

To comprehend an article is to recognize the major elements of that article. When I am looking at newspaper and magazine articles, for example, I might recognize part of it as an argument. This in turn leads me to identify the premises and the conclusion. Being able to recognize an argument is a core skill, because it allows you to recognize what the author is trying to get you to believe is true.

An experienced critical thinker will have a range of tools and methods allowing them to recognize arguments. I'll present a simple tool here, the concept of indicator words.

We typically use indicator words to indicate the presence of a premise or a conclusion. I like to think of indicator words as signposts in a piece of writing which guide us to its structure. There are two types of indicator words: premise indicators, and conclusion indicators. They work like this:
  • [premise indicator] premise, premise, premise
  • [conclusion indicator] conclusion
 Often, the indicator words will help us find both parts of an argument. You might see them like this:
  • conclusion [premise indicator] premise, premise, premise
  • premise, premise, premise [conclusion indicator] conclusion
As I said, premise indicators and conclusion indicators are words or phrases. A word or a phrase is an ordered sequence of letters intended to perform a specific function . In this case, the function is to indicate the presence of a premise or a conclusion. Here are some examples of indicator words:

Premise IndicatorsConclusion Indicators
for the reason thatso

These indicator words are in English, but other languages have their own indicator words. Knowing these indicator words in other languages can help you even if you don't know the language. Here is a famous argument:
 Cogito ergo sum.
It's expressed in Latin. But even if we speak no Latin (except for 'ergo', which is a conclusion indicator) we can comprehend the structure of the argument: 'cogito' is the premise, and 'sum' is the conclusion.

Not only do we now have a tool that generalizes across different disciplines, we have a tool that generalizes across languages. And this is just the beginning.


I'm going to skip ahead past a lot of further discussion about comprehension. In particular, I haven't talked at all about complex arguments, explanations, definitions, names and descriptions. What I will say here is only that, just as we learned how to recognize arguments, we can learn to recognize each of these other major elements.

So far we have talked about propositions as though they were simple things. We didn't look at all into the structure of a proposition. There are some interesting things we can recognize here as well.

The first are elements of what we call propositional logic. These are ways of combining simple propositions into complex propositions. There are four major propositional operators. Here they are, with their most common indicator words:
  • negation - not
  • disjunction - either, or
  • conjunction - both, and
  • conditional - if, then
As I said, these are ways of creating complex propositions out of simple propositions. Let's suppose I have two propositions: P: 'Paris is the capital of France' and Q: 'Lyon is the capital of France'. Then we have:
  • not P - Paris is not the capital of France
  • P or QEither Paris is the capital of France or Lyon is the capital of France
  • P and Q - Paris is the capital of France and Lyon is the capital of France
  • if P then Q - If Paris is the capital of France then Lyon is the capital of France
What's important about these complex propositions is that the truth of the complex proposition depends on the truth of the simple propositions. It is a fact, for example, that Paris is the capital of France, and Lyon is not the capital of France. Because we know this, we know that three of the complex propositions (the first, third and fourth) are not true, while the second one is true. This is important. It means that the structure of an argument matters.

If I understand how to recognize propositional operators, I can understand the structure of the complex propositions in an argument. So now I am able to understand not only what the conclusion is that the person is trying to convince me to believe, I can understand how the argument is structured: I can see how a complex proposition might lead to a simple one, or how simple propositions work together to form a complex proposition, or how complex propositions work together.

There is a lot more to say about propositional logic (and any good textbook will cover all of this) and in teaching the subject I'd cover a lot of different ways to say 'not', 'or', 'and' and 'if'. But I want to move to another type of structure, quantificational logic.

You already know some very complex quantificational logic, called mathematics, but I want to focus on a much simpler form of quantificational logic involving only two major terms: 'all', and 'some'. We will also employ a concept we already encountered in propositional logic: the negation. These taken together allow us to recognize a very common (and very old) form of reasoning, categorical logic.

This requires that I introduce another concept, that of the 'category'. A category is a set or collection on things created by virtue of the fact that they have some property in common. We create categories through a process of classification: that is, we list a set of properties, then organize things into different categories based on those properties. We use categories in language and reasoning a lot.

Interestingly, we don't need to know what the properties are to know that someone is talking about categories. All we have to do is to recognize the indicator words 'all' and 'some'. And in particular, we can recognize four characteristic types of statement:
  • Universal Affirmative: All [something] are [something]
  • Universal Negative: All [something] are not [something] (or: No [something] are [something])
  • Particular Affirmative: Some [something] are [something]
  • Particular Negative: Some [something] are not [something]
Just as with all the other elements, there are many ways to express universals and particulars. Some are straightforward ("All men are mortal", "Frank is a man."). Some are trickier ("Everybody loves somebody sometime.")

And just with propositional logic, there are relations between the different types of statements. If I say that "All men are mortal" is true, then I am also saying that "Some men are not mortal" is not true. If I say that "some metals glitter" is true, I am saying that "no metals glitter" is not true. As well, arguments can be created from combinations of statements (we call these 'categorical syllogisms'). For example, I could argue that "All men are mortal" and "some Republicans are men" to prove that "some Republicans are mortal."

Again, when I can recognize the indicator words (in this case 'all', 'every', 'some', 'no') then I can recognize the type of argument that is being used here. And as with propositional logic, there are many ways of expressing categorical statements, and it is a matter of considerable practice and experience to be able to recognize them.

If we combine categorical logic and propositional logic then we get a complex form of logic called predicate calculus. I won't say much about it here, except to say this: the statements "All A are B" and the statement "For all x, if x is a A, then x is a B" are equivalent.

Another major branch of logic is inductive logic. This branch of reasoning includes probability and statistics, as well as scientific inference, hypothesis formation, and more. It is based on the idea that if you know something about some of the things, then you can know something (with varying degrees of confidence) about all or most of the things.

There are three sets of indicator words that help identify inductive arguments. The first set refers to the sample that is being used as evidence in the premise. The second refers to things being discussed in the conclusion. And the third (and often the most useful) refers to the degree of confidence. We can call these 'population', 'prediction' and 'confidence'. Here are some typical indicator words:
  • population: most, many, x percent, usually, in the past
  • prediction: will, is projected, the next, the rest
  • confidence: probably, likely, generally
When we recognize an inductive argument by recognizing any of the indicator words, experience teaches us to look for the other parts of the argument. If someone says, for example, "it will probably be sunny tomorrow", then we look for a reason like "it has been sunny all week" or "it's July and July is generally sunny".

Most arguments in day-to-day discourse will be one of the types listed above, which means that we can deploy some very powerful tools for comprehension with a limited toolbox. Further expertise in critical thinking will lead to other interesting and complex types of logic. I've already mentioned probability theory. There's also modal logic, which deals with the logic of necessity and possibility (and you can probably figure out your own indicator words). Deontic logic deals with obligation and permission. Fuzzy logic deals with multiple truth values. Computational logic deals with processes and algorithms. And so it goes.


In what I wrote above I talked several times about how the truth of one proposition is related to the truth of another proposition. For example, in propositional logic, if P is true and Q is false, then the proposition 'P and Q' is false. In categorical logic I said that if 'All A are B' is true, then 'Some A is not B' is false. Similar statements can be made about all forms of logic. But why do we believe them?

This is the question that semantics answers. When I talk about semantics, I am talking about the theory of truth being employed by the argument. Above, I used a very simple theory of truth: "a proposition P is true if I say that 'P is true'". Most people would not accept this as a theory of truth (but it works for me).

The popular conception of truth is usually something akin to Tarski's theory of truth. We say that a proposition P is true if and only if what it says about the world is in fact the case in the world. Or as Tarski would say, "The proposition 'snow is white' is true if and only if snow is white." Most of the time this is a pretty good theory of truth, because we can agree that snow is white. But what if we don't agree? Or what if we don't know?

What makes logic and reasoning so powerful is that they don't depend on our knowing ahead of time whether something is true or not. All reasoning is based on the idea of the preservation of truth. If we have a premise, and the premise is true, then if the argument is well formed, then the conclusion must be true (or, in the case of an inductive argument, must be probably true).

It's useful to think of reasoning as though it were plumbing, and truth as though it were water. If your plumbing is good, then if you put water in the top, it will come out the bottom. But if the plumbing is bad, then even if you put water in the top, it won't come out the bottom. And this works not just for water but any type of liquid or even gas! You don't need to know what's going in; you can imagine it's water, and ask yourself what would happen. If it looks like the water would leak, then it's poor plumbing.

That's what semantics is. We create a model of the world. We then create statements that have meaning with reference to that model, and then use the model to determine whether or not arguments using them in different ways preserve truth.

Critical thinking is the use of these models to assess what people are saying about the world. The model is a toolbox that helps us look at different forms of argumentation (and explanation, definition and description) and assess them for truth-preservation (or other principles which we'll discuss below).

Assessment of Arguments

A core concept of argumentation is validity. The objective of an argument is to lead you to believe that the conclusion is true, in other words, to accept the conclusion as a fact. The way we do that is to use propositions we already believe are facts, and to say that from these facts, the conclusion follows as a fact. The idea here is that, because the premises are true, then if the argument is properly constructed, the conclusion should be true as well.

This gives us two key ways to evaluate an argument:
  • We can say that the premises are not true. If the premises are not true, then the premises don't give us any reason to believe that the conclusion is true.
  • We can say that the argument is not valid. This means that even if the premises are true, we still have no reason to believe that the conclusion is true.
If we don't know that the premises are not true, and our interlocutor also agrees that we don't know that the premises are not true, then we can stop there. The whole point of an argument is, as I said, truth-preservation, and if there's no truth to preserve, we don't have an argument worth considering.

This, though, is almost never the case. Even if you or I don't know whether or not the premises are true, we can assume that the person advancing the argument believes that they are true (or at least wants us to act as though they were true). So unless we want to do some research and find out how to prove the premises are true or false we have only the form of the argument to reply upon, and specifically, the question of whether or not the argument is valid.

The way we do this is that we build a model of the argument, then we assess whether or not arguments of this type are valid.

Let's use an actual argument from the Aeon paper to illustrate this process. Carl Hendrick writes:
If you put a left-back in a striker’s position or a central midfielder in goal, the players would be lost. For them to make excellent, split-second decisions, and to enact robust and effective strategies, they need thousands of specific mental models – and thousands of hours of practice to create those models – all of which are specific and exclusive to a position.

Our first move is to comprehend what is being said. We can see that it is an inductive argument with the following conclusion:
Let's reconstruct the premises, simplifying a bit for clarity:
  • At a professional level, if you put a player in someone else's position, the player would be lost, because
  • In a football team, for example, there are different ‘domains’ or positions
  • they need mental models, all of which are specific and exclusive to a position
Knowing about categorical logic allows us to reconstruct the argument into a nice simple model:
All of the models are specific, so none of the models are non-specific, so the player would be lost (that is, would not have a model).
Well this is valid. If it is true that 'all the models are specific', then it is certainly true that 'none of the models are non-specific', and thus that the player would be lost (that is, would have no model to guide his or her actions).

Why do I say that this argument is valid? The employment of some very specific terms (including: "If you put...", "all of which..." and "they need," among others) tells the reader the sort of reasoning the author intends us to follow. By using this language, he shows us how his argument is truth-preserving, and he is by the use of this language employing a system of logic that we share, one we can verify for ourselves by doing the semantics ourselves.

Logical Fallacies

If I had to define 'logical fallacies' generally (which I don't) I would say something like "a logical fallacy is a way for an argument to be invalid." In other words, logical fallacies are types of arguments that are not truth preserving, where (recall) an argument uses the truth of one proposition (the premises) to give us a reason to believe the truth of a different proposition (the conclusion).

I've authored an extensive list of logical fallacies. These are based on the of the critical thinking textbooks I've consulted over the years and supported, of course, by the semantics governing the various forms of fallacies. The logic of fallacies is the same logic as the logic of inference. Except in this case the model shows how the premise could be true while the conclusion is still false. That is, it shows that the form of argument used is not truth preserving.

Let me highlight a few fallacies by giving an example and then doing some simple semantics to show that the argument is invalid.

Non-sequiter: in an argument "P therefore Q" the conclusion Q can be false even if the premise P is true. For example: "Paris is the capital of France, therefore, rice is a mammal." It is true that Paris is the capital of France in this world, even though rice is not a mammal.

Affirming the consequent: the argument is "If Lyon is the capital of France then Lyon is in France; Lyon is in France; therefore, Lyon is the capital of France." We can create a model of France where Paris is the capital (it looks a lot like the real world) such that both the premises are true, and yet the conclusion is false.

Undistributed middle: "All sharks are fish. All salmon are fish. Therefore, all salmon are sharks." We can create a model in which sharks and salmon are different types of fish (it looks a lot like the real world) and where it is nonetheless true that all salmon are fish and all sharks are fish.

Unrepresentative sample: "Most of the people in this building, the Republican National Convention, are Republicans, therefore, probably most people are Republicans." We can create a model consisting of two buildings, one housing the Republican National Convention, the other housing the Democratic National Convention, such that the premise is true and the conclusion is probably false.

Begging the question: "There are no general models, because all the models are specific." This has the form "P, therefore, P". The proposition "No S are P" is equivalent to the proposition "All S are not P." If I did not believe that "All S are not P", then I would not believe (and for the same reasons) that "No S are P."

What's important to understand here is that the content has nothing to do with whether or not the argument is valid. What makes the argument invalid is that it can be represented using a model of an invalid argument. Or, to put the same point more simply, it is invalid because it has an invalid form.

This is important, because it allows us to spot logical fallacies even if we don't know (or don't understand) the content of the argument. Logical fallacies use the same indicator words as valid arguments. So spotting and correcting a logical fallacy is a two-step process: first, recognizing the sort of model that applies (is it propositional? categorical? inductive?) and then second testing whether it fits an invalid model.

In my Guide to the Logical Fallacies I show people first how to spot the argument form (using the definition of the fallacy) and then how to demonstrate that the argument is invalid (by applying the proof).


An advantage of employing the strategies outlinesd above is that it helps you address the soundness of the argument as well.

We say that an argument is sound if and only if it is valid (as discussed above) and its premises are true. When we have a sound argument, we have a good reason to believe that the conclusion is true.

The reason the strategies help us address the soundness of the argument is that they help us clearly understand how the argument is structured and therefore to understand just what the premises actually are. Very often, the actual premises can be difficult to isolate unless we've analyzed the argument. But once we have the argument fully reconstructed, then even if the argument is valid, if there is a false premise, it might show up pretty clearly.

Let's return, for example, to the argument above.
Now, strictly speaking, this argument begs the question. It says there are no general models because all the models are specific and exclusive to a position. If I don't believe all the models are specific and exclusive to a position, I am not very likely to believe that the player will have no models to draw upon when in a different position.

But because we have analyzed this argument, we can examine this one premise in isolation: "they need mental models, all of which are specific and exclusive to a position."Is it true that all mental models in football are exclusive to a position?

Even not knowing much about football, it's hard to imagine how that could be the case. The rules (or most of them) are the same for each position, right? You can't bash the other player with a club. You can't play with the ball out of bounds. If you score a goal at one position, that's the same as scoring a goal at another position.

Indeed, still not knowing much about football, it would seem that there are some general skills that apply, aren't there? The same sort of ball is used by players in each position, so the mechanics of kicking it and heading it would be the same. The principles of how to run are the same. You use the same language to communicate with other players. Right?

Now of course I could be wrong about all of this. I don't know anything about football. But I do know about baseball. And I know (as people have said) that baseball is a simple game. You throw the ball. You hit the ball. You catch the ball. Sure, there are specializations, and not all skills transfer well. A shortstop can't pitch. A right fielder won't be as strong at shortstop. But any professional player at any position will be a lot better than me because they throw better catch better, and hit better. Yes, even pitchers.

Indeed, one of the things that baseball announcers like to say is that baseball players are, in general, better athletes than most people. Professional baseball players typically majored in more than one sport, often choosing a professional career in baseball over an equally promising career in basketball or football. Sure, Michael Jordan was a failure as a professional ball player, but he still made double A, which is way better than I could have done.

So, yeah, maybe there's something special about football. But if so, it's not a very good analogy for professional activities in general. My thinking, based on similar sorts of things I do know about is that while professionals specialize, that's not what makes them special.


Much of what we read in the popular literature about 'critical thinking' addresses what might generally be called critical thinking strategies. These strategies are useful, but they are not themselves critical thinking. It's important to appreciate the difference, because this difference is what informs us how the strategy works and what it is supposed to do.

These strategies are important mostly because you can't use logical terminology and shorthand in casual conversations or articles. Telling someone that they are begging the question won't change anyone's mind. It will just insult them. To be effective in critical reasoning it is wiser therefore to employ one or another strategy.

Other strategies are more methodological. It's not easy to get to the best and most correct result, even if you have the full array of facts and arguments and your disposal. These methodological principles are not employed as an alternative to logic and reasoning, but as an accompaniment to them.

The Reductio

The full name for this strategy is reduction ad absurdum - reduction to the absurd. This is where you take a statement or an argument that someone has provided and show that if we accept it at face value, it results in a pretty obvious contradiction. Almost everybody will agree that a contradiction is a bad result, and so the reductio is a very powerful tool.

Here's a simple example. We both agree that gold glitters, right? But you have an expression you apply all the time, "all that glitters is not gold." I want you to stop using that expression because it's nonsensical. Look, I say. If  'all that glitters is not gold' then 'nothing that is gold glitters'. So you're saying that gold glitters, and that gold doesn't glitter. That's absurd.

A special case of the reduction is used to prove invalidity. I employed it above. You present me with some premises and a conclusion. I set up an example where your conclusion is false, and show that your premises could still be true. This means that your premises allow your conclusion to be both true and not true, which is absurd.

The Non-Sequiter

I described the non-sequiter above as an argument "P therefore Q" where the conclusion Q can be false even if the premise P is true. I didn't talk about the way this usually happens.

In most (almost all!) non-sequiters the conclusion does not follow from the premises because the premises are talking about different things than the conclusion. If my premises are about frogs, my conclusion had better be about frogs. If my premises are about 17th century Spanish philosophers, then my conclusion had better be about 17th century Spanish philosophers.

It doesn't matter what you're talking about. If you talk about one thing, and draw a conclusion about something different, then the argument is a non-sequiter.

This makes tracking the topic of an argument a very powerful technique. Look at the following argument:
Donald Trump says Chinese trade policies are unfair. But he is a buffoon and a bigot.
So are Chinese trade policies unfair? That's the topic of the first sentence. But the second sentence says nothing about Chinese trade policies. It simply talks about Donald Trump. And while Donald Trump might be a buffoon and a bigot, he might also be right about Chinese trade policies. We just don't know.

This is a special type of non-sequiter called an argumentum ad hominem. Or as I like to call it, 'attacking the person.' It uses personal insults instead of reasons. Now of course we all dislike personal insults. But what makes it a fallacy is that it talks about one thing in the premise and another thing in the conclusion.

The Principle of Charity

This principle states that, when interpreting someone's argument, that you should use the most charitable interpretation possible. That is to say, when you have an option between a weak reading of the argument and a strong reading, you should choose the strong reading.

The reason for this is that you are attempting to determine whether you have been given a good reason to believe that the conclusion is true. It's not about 'defeating' the other person - this has nothing to do with critical thinking. And the only way to determine whether you have a reason to believe the conclusion is true is to find the best case for it.

There's a common fallacy, called the 'straw man', where a person finds (or worse, makes up) a weak version of an argument, and then proceeds to defeat it. The term comes from the idea of making yourself look good by defeating opponents made of straw rather than real humans. This may be effective in jousting (I wouldn't know) but it is not effective in critical thinking.

There's a lot to the principle of charity that I won't go into here. It can be hard to make some arguments look good. But the better you are at it, the more you will be loved (and the better at reasoning you will be).

Requirement of Total Evidence

I sometimes refer to this as Carnap's principle, since Rudolf Carnap has the clearest statement of it, but it's a commonly held principle. The purpose of the principle is to suggest that you have at hand all the relevant premises in support (or opposed to) a conclusion.

The reason for this is that in some domains of logic (and especially inductive logic) having more evidence - and more diverse evidence - can impact the validity of the argument (by contrast, having more evidence does not change the validity of a deductive argument at all - that's why I might want many sources of evidence about climate change, but I don't need a second opinion on whether 2+2=4).

For example, you might know that most bank tellers live in London, so if you meet Tessie the bank teller, you would infer that she probably lives in London. However, if you discover that Tessie is a Latvian bank teller, then your inference is no longer valid, because even if something is true of most bank tellers, it doesn't follow that it is true of most Latvian bank tellers (who are, in fact most likely to live in Riga).

Ockham's razor

William of Ockham was a medieval philosopher who argued against people who believed that abstract things (like colours and shapes and moral virtues) existed independently of the objects that instantiated them. His principle was originally, therefore, "do not multiply entities beyond necessity". In today's world we have recast the principle as "adopt the simplest explanation possible."

This is a methodological principle. There's nothing to suggest that the more complex principle might be the better one. But all else being equal, the simple principle is preferred (if for no other reason than it's easier to write).

The 'all other things being equal' part is important. Simplicity is not a logical principle, so simplicity does not count against actual reasons to believe one thing over another. We use it when there is no evidence to count for or against one or another theory.

With a nod to Ockham, let me give you an example: suppose your terrier Yappy is in the front room. Now we ask, is there one thing or two things in the front room. One way of looking at the world would be to say that Yappy is the terrier, so there's one thing. But a different, and equally valid, way of looking at the world would be to say that there are two things, one which is 'what I named Yappy' and the other which is 'the thing that is a terrier'. Since there's no logical connection between the two, I can consistently say they are two separate things.  But it wouldn't be very convenient. So we say there's just one thing.

On Why We Should Teach Critical Thinking

In my tweetstorm the other day I said the following (I've corrected the spelling):
It's simply not true that critical thinking cannot be detached from context. What do you think mathematics is? Probability theory? Logic? How do you think we teach language and grammar? If we could not generalize without context, we would have no abstract reasoning at all.

Indeed, if a person says critical thinking cannot be detached from context, then this tells me that the person does not understand what critical thinking is. Critical thinking is not factual recall or provision of implicit premises. It's based on form, not content.


With skill in critical thinking I can spot errors and deception even in fields I have not studied. If you say 1+1=3 you're wrong. If you affirm the consequent of a conditional, your reasoning is unsound. It doesn't matter what the content was. 

I think I have made the case here that what I tweeted is true. I think I have shown, by showing what critical thinking actually is, how critical thinking can be generalized without context, how it's based on form and not content, how it doesn't make sense to teach it separately in separate disciplines, and how I can use it to spot errors and deceptions even when I don't understand the subject being discussed.

It really is a wonderful all-purpose toolbox.

But what about the people who argue that critical thinking can not and should not be taught in schools. Well, as I suggested, I think that they don't understand what critical thinking actually is, or at the very least, they misrepresent what it is and what it can be used for.

There has been a lot of this sort of argumentation over the years so I'll focus only on the most recent offering, even thought its origins can be traced to other people (whose own views I would be happy to take on any time and in any forum). So let's look at the Carl Hendrick article in Aeon.

Hendrick begins by telling us about the very demanding job done by air traffic controllers and a recent study exploring whether "they had a general enhanced ability to ‘keep track of a number of things at once' and whether that skill could be applied to other situations." It turns out that they have no more ability than anyone else in the "set of generic memory-based tasks with shapes and colours."

This makes sense. It is well-established that perceptual ability and recall are improved with specialization. That's why wine tasters can recognize "a hint of orange pekoe" when all I recognize is "drunk".  It's why a painter can discern (let alone remember) several dozen different shades of what I only know as "'white'. The concept is called perceptual narrowing and, as I said, is well established.

Why is that important? It's because as I think I have amply demonstrated in the several thousand preceding words that critical thinking is not the same as generic memory-based tasks such as those characterized by perceptual narrowing. These are two very different things.

Hendrick, though uses this to introduce his criticism of critical thinking. He writes:
schools have become ever more captivated by the idea that students must learn a set of generalised thinking skills to flourish in the contemporary world – and especially in the contemporary job market. Variously called ‘21st-century learning skills’ or ‘critical thinking’, the aim is to equip students with a set of general problem-solving approaches that can be applied to any given domain; these are lauded by business leaders as an essential set of dispositions for the 21st century.
This again suggests that Hendrick either does not understand or is misrepresenting critiical thinking. Specifically, critical thinking is none of the following:
  • generalised thinking skills
  • 21st-century learning skills
  • problem-solving approaches
  • a set of disposition
As I suggested above, critical thinking is "critical thinking is the method of application of logic and reasoning to thought." This is clearly not a problem-solving approach (though it would be useful in solving problems). It is not the same as "21st century learning skills" (though often included among them). And then though critical thinking can be applied generally, it does not follow that it is "generalized thinking skills". And though critical thinking is a good habit to get into, it does not follow that critical thinking is a set of dispositions.

All of this aside, the core of the Hendrick argument now follows:
 There are several concepts all rolled into one here, so it's important to unpack them:
  • the idea of being good in a specific domain
  • the idea of knowing a lot about it (aka, the 'content-knowledge' argument)
  • the idea that skills do not 'translate' to other areas
Each of these is a special sort of mistake.

First of all, there are many things that constitute 'being good' in a specific domain. Nobody would ever say that if you know critical thinking you are (by that fact alone) good in any (let alone every) domain. Being good at critical thinking is like being good at math or good at grammar: it helps a lot, but by itself won't make you good at anything. And nobody says it does.

Second, being good at critical thinking does not require 'content knowledge' over and above critical thinking, not even if critical thinking is applied in a specific domain. If a football player reasons "he can't score on me because he's a jerk" then I can say that the football player's reasoning is flawed even if I know nothing about football. Maybe you do need 'content knowledge' to become proficient in a certain domain, or maybe you don't. That's an argument for another day. But the 'content knowledge' argument does not apply to critical thinking.

Finally, the presumption that skills must be 'translated' from one area to another has its own problems. In  order to be true, it must be true that there are no skills that are common to different areas. But we know this to be false. This is why, when designing an education system, we focus on certain skills we think are common to most areas, and focus on specialized disciplines only later in life. So children are taught to read and write, they are taught basic mathematics, they are taught some common principles of physics, biology and chemistry, they are taught about their own bodies and they are taught about society and geography around them.

Why? Because even if you're a professional footballer it's still useful to be able to read the rulebook and follow instructions, to communicate with teammates, to understand basic addition and even some geometry, to know some physics, to be able to understand their bodies, and to know that London is in England, not Wales.

The idea, in other words, that expertise in any profession consists only of skills that 'do not translate' to other areas seems, on the face of it, absurd. The real question is, is critical thinking one of those skills that applies in multiple domains. I believe I have made the case that it is.

Hendrick quotes Daniel Willingham, who has been vocal on this subject on numerous occasions:

The advice to "look at an issue from multiple perspectives" is at its most charitably understood as a methodological principle, akin to the others I described above. What it is not is 'critical thinking'. It is true that looking at an issue from multiple perspectives is good advice. But it's not core to any of what I have described thus far. The fact that it is good advice does not mean it is a part of critical thinking.

We could also ask whether a person cannot think of an issue from multiple perspectives when they don't know very much about it. Let's take the example of an argument expressed in an unfamiliar language. Cogito ergo sum, say. Several alternative perspectives suggest themselves. perhaps Sum ergo cogito. Or perhaps recasting the argument as a hypothetical: if cogito then sum.

More to the point, if I don't know a lot about something, and I want to consider alternative perspectives, a very simply strategy is presented to me: ask. Getting multiple perspectives isn't a question of content, it's a question of talking to multiple people. By pursuing the strategy of asking, it is possible to learn about things.

Some of the other things Hendrick mentions in this article:
  • "brain-training games that claim to help kids become smarter, more alert and able to learn faster" - these have quite rightly been denounced, but it should be noted that (a) these games no not teach critical thinking, and (b) critical thinking does not promise to make people "smarter, more alert and able to learn faster".
  • "teaching ‘dispositions’ such as the ‘growth mindset’ (focusing on will and effort as opposed to inherent talent) or ‘grit’ (determination in the face of obstacles)" - again, none of these bears any resemblance to critical thinking.
  • "know which hypothesis to focus on and which variables to discount" - critical thinking is not a hypothesis-selection tool. It isn't intended to "unlock the unique, intricate mysteries of each subject." No doubt there is a certain skill required to comprehend, say, Mary Shelly. But if you commit a logical fallacy while interpreting Frankenstein it's still a fallacy even if you are a Shelly scholar.

The suggestion that critical thinking is not a skill that can be learned, not a skill that can be applied in numerous disciplines, and not a skill that should be taught, is a suggestion that is pernicious and wrong, and should be disputed and disregarded at all levels.


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