“All models are wrong. Some models are useful.” — George Box
This Freeman Online article by Max Borders posits that the word model “may be the most dangerous word in the English language right now.”
Models justify a lot of the bad policies that have been, or soon will be, foisted on us. For example, what was used to justify the fiscal policy of the big “stimulus”? That’s right. And as I wrote this, “experts” were using models to gear us up for another one.
More than a year after the original “stimulus,” not only are economists nowhere near consensus about its effects but few if any of the models used to justify it have turned out to be right. Obamanomic adviser Christina Romer, for example, has come under heavy criticism because her team’s plan has performed abysmally. The model behind the plan predicted unemployment would peak at 8.3 percent. It exceeded 10 percent before dropping back slightly. In defending her plan she appealed to counterfactuals—that is, how bad things could have been without it. That her team failed to reach its rosy targets, she says, “prevents people from focusing on the positive impact.” But did Romer ever consider the possibility that her model was just wrong?
When it comes to prediction and explanation, macroeconomic models are often just as bad after the fact as before it.
I suspect the same can be said of most models of complex systems (e.g., climate models).
Specifically regarding macroeconomic models, Borders says that failed models have several traits in common:
They’re rendered either in impenetrable math or with sophisticated computers, requiring a lot of popular (and political) faith.
Politicians and policy wizards hide behind this impenetrability, both to evade public scrutiny and to secure their status as elites.
Models vaguely resemble the real-world phenomena they’re meant to explain but often fail to track with reality when the evidence comes in.
They’re meant to model complex systems, but such systems resist modeling. Complexity makes things inherently hard to predict and forecast.
They’re used by people who fancy themselves planners—not just predictors or describers—of complex phenomena.
I’ve made yet another model. This one is so simple and obvious that it’s arguably not worth making, but that’s never stopped me before.
It’s a simple graph of confidence versus competence:
Fig. 1. A model of confidence versus competence.
Any person can be mapped into this model by plotting the person’s confidence in his/her ability versus the person’s actual level of ability. Those people who fall on the line have a perfect assessment of their own competence. Those who fall above the line have inflated opinions of their abilities and are therefore arrogant. Those who fall below the line have underestimated their abilities and are therefore humble. It should be noted that a person can be arrogant for some abilities and humble in others, just as a person can be competent in some abilities and incompetent in others.
People naturally interpret confidence and decisiveness in others as signs of competence, and conversely interpret uncertainty and a lack of confidence as signs of low ability. The implicit assumption is that a person’s confidence or lack thereof is generally warranted — i.e., people seem to believe that everyone clusters pretty close to the line in my model of confidence/competence, like so:
Fig. 2. People tend to assume that everyone accurately assesses their competence.
But we know from the Dunning-Kruger effect that incompetent individuals tend to overestimate their own abilities and generally fail to recognize their inadequacies. (See here for their full report - pdf.) Moreover, Dunning-Kruger also showed that people who do have true knowledge and ability tend to underestimate their own level of competence.
So in actuality people cluster more like this:
Fig. 3. In reality, incompetent people tend to be arrogant and competent people tend to be humble.
Because of the common and widespread misinterpretation of confidence (shown in Fig. 2), those who are very decisive and confident tend to fool people enough to rise through the ranks, and those who are uncertain and hesitant tend to have a harder time doing so. Now, in the corporate world and in the military, one cannot rise very far on the power of confidence alone. Competence in these environments is rather easily observable, as is its lack, so the arrogant are soon exposed.
But it’s a different story in politics. It is, unfortunately, all too easy for a politician to hide incompetence in most areas as long as the politician is very competent in the single most essential skill of politics: persuasion. (And I do think there is at least a moderate correlation between confidence/arrogance and persuasive powers.) Those who are persuasive can spin their way out of anything, by blaming poor results and unintended negative consequences on other factors (usually on the opposing political party) and by playing on the cognitive biases of their constituents.
High confidence is practically a prerequisite for a politician, because (as Fig. 2 shows) voters believe confidence and decisiveness equates to competence. But sadly we are just electing the arrogant. The truly competent may be too humble to ever run for office.
This model (pdf), by Phillip Armour, appeared in the Oct. 2000 Communications of the ACM (sadly I’ve let my membership lapse). It is really a model of ignorance in the context of building software systems, but informative nonetheless. Armour defines five orders of ignorance:
0th order of ignorance (0OI) — I have 0OI when I know something and can demonstrate my lack of ignorance in some tangible form, such as by building a system that satisfies the user.
1st Order Ignorance (1OI) — Lack of Knowledge. I have 1OI when I don’t know something and can readily identify that fact.
2nd Order Ignorance (2OI) — Lack of Awareness. I have 2OI when I don’t know that I don’t know something. That is to say, not only am I ignorant of something (for instance I have 1OI), I am unaware of this fact. I don’t know enough to know that I don’t know enough.
3rd Order Ignorance (3OI) — Lack of Process. I have 3OI when I don’t know a suitably efficient way to find out I don’t know that I don’t know something. This is lack of process, and it presents me with a major problem: If I have 3OI, I don’t know of a way to find out there are things I don’t know that I don’t know.
4th Order Ignorance (4OI) — Meta Ignorance. I have 4OI when I don’t know about the Five Orders of Ignorance. I no longer have this kind of ignorance, and now, neither, dear reader, do you.
His 2nd order ignorance (2OI) corresponds to what I was calling metaignorance. Interestingly, Armour states: “Example: I cannot give a good example of 2OI (of course).” Heh, maybe this is why I was having difficulty giving a good example. If I knew it enough to make it an example, it wouldn’t be ignorance.
Not a bad model at all.
Jamesh also linked to a page of taxonomies of the unknown, providing several models of uncertainty and ignorance. My favorite is this one:
Domains of Ignorance (Kerwin)
Known Unknowns: All the things you know you don’t know
Unknown Unknowns: All the things you don’t know you don’t know
Errors: All the things you think you know but don’t
Unknown Knowns: All the things you don’t know you know
Taboos: Dangerous, polluting or forbidden knowledge
Denials: All the things too painful to know, so you don’t
“Unknown unknowns” would correspond to my metaignorance.
This model seems to cover all the bases; I can’t think of any ignorance situation that doesn’t map to one of these categories (although that doesn’t mean there aren’t any — hence I’ve avoided the argumentum ad ignorantium fallacy as well as the irony of being metaignorant).
Regular readers will know by now that I have a creepily compulsive INTJ-related need to build models as a means of getting an intellectual handle on a particular phenomenon. See, e.g., here, here, here, here, and here.
Less Wrong (author Yvain) offers a pretty good model for different types of assertions that people make. Yvain lists the following types of assertions:
1. Unsupported assertions about non-controversial topics
Yvain offers as an example assertion: “The Wikipedia featured article today is on Uriel Sebree.” You are justified in believing the claim, because (a) the probability of someone asserting this when it is false is pretty low, and (b) the probability of someone asserting this when it is true is pretty high. There’s just no reason to believe that someone would intentionally lie, or have a wrong opinion, about a simple fact like this.
2. Unsupported assertions about controversial topics
When someone makes an unsupported assertion about a controversial topic, one of the following three cases occurs.
If you are aware the topic is controversial, you would take their assertion with a huge grain of salt. An unsubstantiated assertion on a topic of known controversy does not help you in adjusting your own opinion.
If you don’t know whether the topic is controversial, but you are aware that you don’t know whether the topic is controversial, you could gauge the opinions of others to determine if the topic is controversial. Upon discovering the topic to be controversial, you then know that the unsubstantiated assertion does not help you in adjusting your own opinion.
If you are unaware that the topic is controversial, and are also unaware that you are unaware that the topic is controversial, then you would implicitly assume the topic to be uncontroversial. In this case you would erroneously accept the assertion, since it fits the profile for a non-controversial assertion. This is another example of how metaignorance, as I discussed in yesterday’s post, can lead one to become mistaken.
A caution: Using the opinions of others to gauge whether a topic is controversial may be useful. But if you use the opinions of others to determine what your own opinion should be, you are guilty of the argument from popularity fallacy.
3. Unsupported assertions on extremely unusual topics
Yvain’s example makes clear that he is talking about extraordinary claims here: “I believe that a race of otter-people from Neptune secretly controls the World Cup soccer tournament.”
Carl Sagan said it best: “Extraordinary claims require extraordinary proof.” Absent commensurate extraordinary proof, we should reject an extraordinary claim out of hand.
4. Unsupported assertions by important authorities
There’s a fine line to walk when evaluating expert opinions. We would assign a higher pedigree to an opinion from an expert than from a layman. But we want to avoid falling victim to the appeal to authority fallacy, and keep in mind that experts are often wrong.
5. Assertions supported by unsupported claims of “evidence”
An assertion supported by a claim of evidence, where the claim of evidence itself is an unsupported assertion (i.e., the evidence itself is not offered for examination), is no better than an unsupported assertion. Yvain claims that it at least signals some sanity, but I’m not that forgiving. Many people with no (or poorly pedigreed) evidence still regularly claim their opinions are based on good evidence.
And Yvain left out one more:
6. Assertions supported by evidence
This is the best type of assertion, as we can examine the evidence for ourselves to determine the credibility of the assertion.
In this NY Times op-ed piece, Stewart Brand provides a taxonomy of four types of views on anthropocentric global warming (AGW):
DENIALISTS They are loud, sure and political. Their view is that climatologists and their fellow travelers are engaged in a vast conspiracy to panic the public into following an agenda that is political and pernicious. Senator James Inhofe of Oklahoma and the columnist George Will wave the banner for the hoax-callers.
I would agree that Inhofe fits this definition, but I’m not so sure about George Will. I’d have to re-read some of his editorials first.
SKEPTICS This group is most interested in the limitations of climate science so far: they like to examine in detail the contradictions and shortcomings in climate data and models, and they are wary about any “consensus” in science. To the skeptics’ discomfort, their arguments are frequently quoted by the denialists.
In this mode, Roger Pielke, a climate scientist at the University of Colorado, argues that the scenarios presented by the United Nations Intergovernmental Panel on Climate Change are overstated and underpredictive. Another prominent skeptic is the physicist Freeman Dyson, who wrote in 2007: “I am opposing the holy brotherhood of climate model experts and the crowd of deluded citizens who believe the numbers predicted by the computer models …. I have studied the climate models and I know what they can do. The models solve the equations of fluid dynamics, and they do a very good job of describing the fluid motions of the atmosphere and the oceans. They do a very poor job of describing the clouds, the dust, the chemistry and the biology of fields and farms and forests.”
WARNERS These are the climatologists who see the trends in climate headed toward planetary disaster, and they blame human production of greenhouse gases as the primary culprit. Leaders in this category are the scientists James Hansen, Stephen Schneider and James Lovelock. (This is the group that most persuades me and whose views I promote.)
“If humanity wishes to preserve a planet similar to that on which civilization developed and to which life on earth is adapted,” Mr. Hansen wrote as the lead author of an influential 2008 paper, then the concentration of carbon dioxide in the atmosphere would have to be reduced from 395 parts per million to “at most 350 p.p.m.”
CALAMATISTS There are many environmentalists who believe that industrial civilization has committed crimes against nature, and retribution is coming. They quote the warners in apocalyptic terms, and they view denialists as deeply evil. The technology critic Jeremy Rifkin speaks in this manner, and the writer-turned-activist Bill McKibben is a (fairly gentle) leader in this category.
I’m not sure I see much difference between Brand’s calamatists and warners. Maybe only a difference of degrees. What are the warners warning about, if not calamity? I do appreciate Brand’s efforts to distinguish legitimate climate skeptics from closed-minded deniers (and I’ll give him a pass on using the perjorative term “denier” as he’s defined it). But ultimately this taxonomy falls just a bit short of the mark.
Gnostic Theist - claims certain knowledge that God exists.
Agnostic Theist - knows there is no evidence to support the notion that God exists, but chooses to believe anyway.
Agnostic Atheist - knows there is no evidence to support the notion that God exists, and therefore chooses to not believe in God.
Gnostic Atheist - claims certain knowledge that God does not exist.
For AGW, the Gnostic/Agnostic dimension is analogous to a closed-minded/open-minded continuum — perhaps a better way to put this would be an ideology-driven/truth-driven continuum. This dimension reflects the degree to which one would be willing to alter one’s beliefs about AGW when presented with legitimate countering evidence. The Gnostic position equates to bull-headed closed-mindedness, with a strong emotional attachment to one’s current AGW opinion; the Agnostic position equates to open-mindedness and an interest primarily in the truth. In short, the Gnostic lives in a castle while the Agnostic lives in a tent.
The Theist/Atheist dimension is analogous to belief/skepticism in the “consensus” AGW position that greenhouse gases are the primary cause of recent global warming, along with the mainstream IPCC predictions of what the degree and consequences of that warming are likely to be.
The four points along the spectrum would then be:
AGW Ideologue - a closed-minded AGW believer who claims certain knowledge in the catastrophic consequences of AGW, if drastic measures aren’t taken immediately. Is a smug and shrill ideologue who may exaggerate and cherry-pick from the climate science to support his opinion. Anything and everything is interpreted as confirming evidence of AGW. No hurricanes this year? Caused by global warming. Double the usual number of hurricanes? Global warming. Consequently there is no evidence that could possibly shake him from his belief, short of an ice age.
AGW Proponent - an open-minded AGW believer who is of the informed opinion that the science and evidence supports the notion that greenhouse gases are the primary culprit of AGW and that AGW will continue as predicted by the mainstream/IPCC sanctioned climate models. Could be convinced otherwise by the right evidence. Is primarily motivated by the truth and a desire to maintain scientific integrity.
AGW Skeptic - an open-minded AGW skeptic who is of the informed opinion that the mainstream position on AGW has been overstated, and is wary of claims about a “consensus” and “settled science.” Can raise legitimate concerns about the climate models and scientific methods being used to promote the mainstream position. Could be convinced of mainstream AGW claims by the right evidence. Is primarily motivated by the truth and a desire to maintain scientific integrity.
Anti-AGW Ideologue - a closed-minded AGW skeptic (”denier” would not be an unfair term here) who claims certain knowledge that global warming — if even occurring at all — is not primarily man-caused. Is a smug and shrill ideologue who calls out every bad data point as smoking-gun evidence of a vast global warming conspiracy for political and financial ends. Would not change his mind if the ice caps melted completely and all of Florida went underwater.
The two middle points of the spectrum are characterized by science over politics; the two end points are ideologically driven. The AGW Ideologue roughly corresponds to Brand’s “Calamatist”, and the Anti-AGW Ideologue to his “Denialist”, but I don’t think the two middle points match his “Skeptics” and “Warners” position as well. Note for example that Brand includes James Hansen in his “Warners” group. I’m not so sure he would fit my “AGW Proponent” definition; Hansen seems more interested (see Brand’s quoting of him above, for example) in prescribing solutions to AGW than in maintaining scientific neutrality. I would place Hansen somewhere between AGW Idealogue and AGW Proponent on my spectrum.
What about other prominent folks in the AGW debate? Surely Al Gore is firmly in the AGW Ideologue camp, and James Inhofe is an Anti-AGW Ideologue. Beyond those extremes it’s pretty hard to tell, since the model is based on knowing the underlying motivations (truth versus ideology). A fundamental problem is that the science is so complicated that any underlying ideological motivations can easily be masked by seemingly legitimate scientific arguments, on either side of the issue.
The Alarmed (18% of Americans) — “They are very convinced it is happening, human-caused, and a serious and urgent threat. The Alarmed are already making changes in their own lives and support an aggressive national response.”
The Concerned (33%) — “are also convinced that global warming is a serious problem and support a vigorous national response. Members of this group have signaled their intention to at least engage in consumer action on global warming in the near term, but they are less personally involved in the issue and have taken fewer actions than the Alarmed.”
The Cautious (19%) — “believe that global warming is a problem, although they are less certain that it is happening than the Alarmed or the Concerned. They do not view it as a personal threat, and do not feel a sense of urgency to deal with it.”
The Disengaged (12%) — “do not know and have not thought much about the issue at all and say that they could easily change their minds about global warming.”
The Doubtful (11%) — “are evenly split among those who think global warming is happening, those who think it isn’t, and those who do not know. Many within this group believe that if global warming is happening, it is caused by natural changes in the environment.”
The Dismissive (7%) — “like the Alarmed, are actively engaged in the issue, but are on the opposite end of the spectrum. Most members of this group believe that global warming is not happening, is not a threat to either people or non-human nature, and strongly believe that it does not warrant a national response.”
These percentages come from a 2008 survey conducted jointly by the Yale Project on Climate Change and the George Mason University Center for Climate Change Communication, published in a study dated May 20, 2009.
A project manager must balance the Cost, Schedule, and Scope of a project. (Scope means the overall “magnitude” of the project in terms of the project’s requirements for functionality, features, quality, and so on.) This principle applies to all projects and programs, whether big or small, private or public.
Related to this balance, one of the most fundamental concepts in project management is the “Pick Any Two” rule, which reflects the understanding that you can’t control all three of these factors simultaneously. The rule is simply this: pick any two of these factors — Cost, Schedule, and Scope — and the third will be beyond your control.
For example, if you want your project completed quickly and cheaply, the quality (scope) will suck; if you want it better and quicker, be prepared to pay out the nose (cost); and so on. As an example, the Apollo program had Scope constraints (land a man on the moon and return him safely to Earth, within certain safety requirements) and a Schedule constraint (by the end of the 1960’s), and consequently Cost was not particularly controllable (roughly $145B in 2007 dollars). You can NOT have it faster, cheaper, and better, all at once.
Because I am the Master of Stupid Analogies TM, I’ve always thought of the “Pick Any Two” rule in terms of a big cargo ship. The length of the ship itself represents the Cost of the project. Stacked on deck are cargo crates representing the Scope of the project - the quality, requirements, and so on. The ship’s draft — the depth to which the bottom of the hull rides below the waterline — represents schedule. If you pile more crates on (i.e., add more requirement and/or a higher standard of quality), the ship will ride lower in the water (i.e., the project will take longer to complete). If you want to reduce the draft (schedule) you’ll either have to jettison some cargo (eliminate some requirements) or get a bigger ship (increase cost). And so on.
Now, analogies can be pushed too far, and every analogy has its breaking point. But since I am the Master of Stupid Analogies TM, my analogies are particularly resilient. Watch as I push this one farther.
If you pile a ridiculous amount of cargo on deck without getting a longer ship, the ship sinks. This really is analogous to what happens in a real-world project: the schedule stretches to infinity and the project is never completed.
I’ll push on the analogy just once more. In the real world, it is possible — on rare occasions — to actually have a net improvement to Cost, Schedule, and/or Scope without having to sacrifice any of these three factors. This can happen when the fundamental rules of the game change — for instance, when technology improvements make it possible to do the same work at a lower cost (or shorter schedule, or higher quality), all other things being equal. In my analogy here, the water itself would represent things like technology, the policies and processes in place, regulations and legal issues, and so on. These things constitute the environment in which the project operates, just like the sea is the ship’s environment. Improving any of these things would produce a “sea change” (groan) whereby the water would become denser and the ship more buoyant, thereby enabling the existing Scope to be accomplished at the same Cost with a reduced Schedule (or some other combination thereof).
I think I’ll stop pushing the analogy before we all get seasick.
In a future post I will apply this model to the current proposed plan for health care insurance reform, a.k.a. “Obamacare.”
A model can be more powerful than a mere definition, which may fail to do justice to a complex subject with many interrelated concepts. That’s why I put together my model of critical thinking and my model of belief — to improve the intellectual manageability of the various concepts entailed by showing the structural relationships between them.
In a recent email exchange with The Thinker reader George, he described to me his own model of beliefs in God:
The model is in the form of a spectrum or continuum of beliefs based on two dimensions: gnosticism/agnosticism (i.e., certainty or uncertainty) and theism/atheism (i.e., belief or non-belief).
Thus, according to George’s model:
Gnostic Theist - claims certain knowledge that God exists.
Agnostic Theist - knows there is no evidence to support the notion that God exists, but chooses to believe anyway.
Agnostic Atheist - knows there is no evidence to support the notion that God exists, and therefore chooses to not believe in God.
Gnostic Atheist - claims certain knowledge that God does not exist.
George points out that the two extreme ends of this spectrum are fundamentalist in nature, and governed by black-and-white thinking. Gnostic Theists, for example, include fundamentalist Christians and Muslims. Says George: “Their belief comes first, supplanting factual evidence that may contradict the belief, which is why a Creationists can believe the world is 6,000 years old.”
George claims - and I agree - that the two middle positions are the most reasonable and most in line with good critical thinking.
When he first expressed this model to me I was tempted to suggest it might be better in a table — e.g., with gnosticism/agnosticism across the columns and theism/atheism down the rows. But upon reflection I realized George’s approach is better. A table would have quantized these beliefs into four possible values (albeit better organized along their two separate dimensions), rather than showing them as points along a continuum as George’s model does. For example, there is a point somewhere between Agnostic Theist and Agnostic Atheist where a person knows there is no evidence to support the notion that God exists, and therefore chooses to neither believe nor disbelieve in God.*
It also occurs to me that this type of model - which George calls a “rigidity of belief” model — could be applied to things other than belief in God. For instance, it could be applied to beliefs about global warming, with the “Gnostic Theist” position representing someone with certain knowledge that anthropocentric global warming will doom the planet, and so on.
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* At this point any of my Rush friends reading this will of course be cueing Freewill in their heads: “If you choose not to decide, you still have made a choice.”
I would like to retract this post, wherein I attempted to distinguish between faith-based belief and critical thinking-based belief. In retrospect I chose my words poorly and I’d like to try over, plus add a bit more. In fact, this may end up being a model, rather than a definition, of belief, similar to my model of critical thinking.
So, here goes…
(1) A belief is a conviction that something is true. A belief need not be absolute, but can involve uncertainty. You can believe something provisionally, you can be 75% confident that something is true, and so on.
(2) A faith-based belief is a belief in something for which there is no proof. Faith need not refer to a belief in God, either; one can believe in any number of things for which there is no proof (the tooth fairy, Santa Clause, ghosts, etc.).
(3) A critical thinking-based belief is a belief that is arrived at by applying sound critical thinking in evaluating the evidence. A CT-based belief is almost always a provisional belief since a critical thinker only commits to a belief to the extent that the evidence and logic would justify, which is rarely if ever absolute.
This post on Skeptic’s Play discusses the difference between religion and delusion, and has prompted me to add the following definition to my list:
(4) A delusional belief is a belief that is maintained in spite of evidence to the contrary.
From a critical thinking point of view, delusion is obviously far worse than faith. A faith-based belief is not rational, but neither is it strongly irrational, since there is neither proof nor disproof of the thing’s existence. A delusional belief, however, is irrational.
And looking at my definition of a CT-based belief, it appears there should be a similar one for non-CT based belief:
(5) A bias-based belief is a belief that is arrived at, in large part, due to cognitive biases and logical fallacies. I’m not entirely happy with the label here and reserve the right to change it later.
So, what are the relationships between all these beliefs? I think it would look something like this:
The first thing that should immediately jump out at you is that CT-based belief does not overlap any of the other types of belief. Critical thinking has nothing to do with faith or delusion, and seeks aggressively to avoid all biases and fallacies.
A second note: I suspect that delusional is entirely a subset of bias-based. I’m not sure how it’s possible to hold a delusional belief without cognitive biases and fallacies being at work1. Nevertheless, I may be wrong, so I have drawn them as overlapping sets rather than showing delusional contained entirely within bias-based.
Now let’s examine the overlap areas between the other belief types.
1. Faith-based and bias-based. For example, many people believe in God (faith) due to wishful thinking (a cognitive bias) — they believe in God because the idea that God exists is comforting to them, so they want for God to exist.
2. Bias-based and delusional. For example, those who continue to believe that Obama is not a natural born citizen and hence is ineligible to be the President hold a belief that is both bias-based (a combination of political worldview and wishful thinking) and delusional (believing in something for which there is evidence to the contrary, such as court findings based on review of Obama’s birth certificate).
3. Faith-based and delusional. As I mentioned above, I’m not sure you can hold a delusional belief that is not also bias-based. I certainly can’t come up with an example. I suspect that area #3 (as well as the rest of the delusional bubble outside of bias-based) may be the empty set.
4. Faith-based, bias-based, and delusional. An example would be a strict Creationist, i.e., someone who believes in a literal interpretation of the creation story in the Book of Genesis and disbelieves in evolution. Now, I suppose it is possible for someone to fit my definition here of a strict Creationist without being well aware of the evidence in favor of evolution, and/or based on belief in various pseudo-scientific claims made by the Creationist crowd (see, e.g., the Answers in Genesis and similar websites). In that case the person’s belief is based on cognitive biases and fallacies, and hence is not delusional. I’ll exclude those types of folks from this example. But those folks who are truly deluding themselves fall squarely into area #4.
So there you have it: my initial model of belief types. Feel free to poke holes in this — tell me what I got wrong, what I missed, etc.
In this post I defined critical thinking as “the set of practices and attitudes intended to get us as close as possible to the truth.” But I’m not happy with that definition. It falls a bit short of fully capturing what critical thinking is really all about. Critical thinking is hard to define in a simple statement of meaning, and upon reflection I think a model is warranted rather than a definition.
In today’s post I’d like to introduce my own working model of critical thinking. And by “working” model, I mean it works good enough for now, but I’m not completely happy with it and it’s still a work in progress.
I begin by recognizing that critical thinking involves certain cognitive skills, various characteristic habits, and specific values or commitments, as well as the relationships between these things. For the mathematically inclined, we could formally define critical thinking using set theory notation as:
CT = { {S}, {H}, {V}, {R} }
where {S} is a set of cognitive skills, {H} is a set of characteristic habits, {V} is a set of values/commitments, and {R} is a set of relationships among the various elements in {S}, {H}, and {V}.
The set of cognitive skills include things like logic, analysis, evaluation, inference, interpretation, explanation, and synthesis. Alternatively I could have used Bloom’s taxonomy of cognitive skills or some other list, and/or I could even decompose these into further more specific skills. For instance, analysis can be decomposed into deconstructing, contrasting and comparing, differentiating and discriminating, etc.; synthesis can be decomposed into organizing, classifying, composing, etc.; and so on. The point is that these are all fundamental reasoning skills, regardless of the specific list or taxonomy chosen to represent them.
Next is the set of characteristic habits. I use the term “characteristic habits” because these are the habits that characterize the critical thinker — i.e., the acquired behavior patterns that distinguish the critical thinker from the non-critical thinker. Richard Paul lists these as intellectual humility (an awareness of and willingness to admit to the prejudice of one’s viewpoint and the limits of one’s knowledge and abilities), intellectual courage (a willingness to challenge one’s own beliefs), intellectual empathy (ability and willingness to examine issues from others’ viewpoints in an open-minded manner), intellectual integrity (ability to consistently apply good standards of thinking), intellectual perseverance (willingness to overcome obstacles and adhere to rational principles despite irrational objections from others), faith in reason (belief that quality reasoning leads to quality outcomes), and fair-mindedness (treating all viewpoints equally without regard for one’s own feelings or vested interests). Based on other critical thinking sources, I might choose to also add introspection (routinely examining one’s own thought processes and seeking to overcome biases and errors introduced by human limitations) and possibly other traits such as inquisitiveness, flexibility, prudence, etc.
Last is the set of values/commitments. This is a small set with only one member: a commitment to the truth, or the true best answer, where by “best” I mean the most defensible choice based on the available evidence and reasoning.
At the highest level, the relationships {R} between the cognitive skills, characteristic habits, and values/commitments enable me to loosely assemble these components into a structural model of critical thinking as follows:
Values/commitments provide the foundation for critical thinking. It is the commitment to searching for the truth that motivates the need for intellectual humility, empathy, and the various other critical thinking traits, and these traits in turn regulate the way in which cognitive skills are applied to form opinions, make decisions, and solve problems.
One interesting thing about structuring the model this way is that the vertical axis roughly corresponds to intelligence. Elements towards the top of the model (i.e. cognitive skills) are those that are measured by conventional definitions of intelligence, i.e., IQ, and elements lower down decreasingly depend upon intelligence. As I’ve said before on The Thinker, critical thinking is much more than just IQ. A person’s “practical intelligence” — a person’s intelligence for all practical purposes in the real world, i.e., how well a person can come to the right opinions, make the best decisions, and formulate good solutions to problems in the real world, rather than their ability to solve logic puzzles on an IQ test — is determined more by their intellectual habits and attitudes (characteristic habits) than by their cognitive skills.
So, this is my initial model of critical thinking. It’s pretty austere, but I think it’s a good starting point to build on. In the future I might try to come up with a use for the horizontal axis and decompose each of the three sets (values/commitments, characteristic habits, and cognitive skills) to arrange them along that variable. The model is also only a structural model (showing components and their relationships), and does not show any dynamics or processes that occur during critical thinking; those would be nice additions too.
