critical analysis and critical thinking are the same true or false

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Critical Thinking

Critical thinking is a widely accepted educational goal. Its definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. Conceptions differ with respect to the scope of such thinking, the type of goal, the criteria and norms for thinking carefully, and the thinking components on which they focus. Its adoption as an educational goal has been recommended on the basis of respect for students’ autonomy and preparing students for success in life and for democratic citizenship. “Critical thinkers” have the dispositions and abilities that lead them to think critically when appropriate. The abilities can be identified directly; the dispositions indirectly, by considering what factors contribute to or impede exercise of the abilities. Standardized tests have been developed to assess the degree to which a person possesses such dispositions and abilities. Educational intervention has been shown experimentally to improve them, particularly when it includes dialogue, anchored instruction, and mentoring. Controversies have arisen over the generalizability of critical thinking across domains, over alleged bias in critical thinking theories and instruction, and over the relationship of critical thinking to other types of thinking.

2.1 Dewey’s Three Main Examples

2.2 dewey’s other examples, 2.3 further examples, 2.4 non-examples, 3. the definition of critical thinking, 4. its value, 5. the process of thinking critically, 6. components of the process, 7. contributory dispositions and abilities, 8.1 initiating dispositions, 8.2 internal dispositions, 9. critical thinking abilities, 10. required knowledge, 11. educational methods, 12.1 the generalizability of critical thinking, 12.2 bias in critical thinking theory and pedagogy, 12.3 relationship of critical thinking to other types of thinking, other internet resources, related entries.

Use of the term ‘critical thinking’ to describe an educational goal goes back to the American philosopher John Dewey (1910), who more commonly called it ‘reflective thinking’. He defined it as

active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it, and the further conclusions to which it tends. (Dewey 1910: 6; 1933: 9)

and identified a habit of such consideration with a scientific attitude of mind. His lengthy quotations of Francis Bacon, John Locke, and John Stuart Mill indicate that he was not the first person to propose development of a scientific attitude of mind as an educational goal.

In the 1930s, many of the schools that participated in the Eight-Year Study of the Progressive Education Association (Aikin 1942) adopted critical thinking as an educational goal, for whose achievement the study’s Evaluation Staff developed tests (Smith, Tyler, & Evaluation Staff 1942). Glaser (1941) showed experimentally that it was possible to improve the critical thinking of high school students. Bloom’s influential taxonomy of cognitive educational objectives (Bloom et al. 1956) incorporated critical thinking abilities. Ennis (1962) proposed 12 aspects of critical thinking as a basis for research on the teaching and evaluation of critical thinking ability.

Since 1980, an annual international conference in California on critical thinking and educational reform has attracted tens of thousands of educators from all levels of education and from many parts of the world. Also since 1980, the state university system in California has required all undergraduate students to take a critical thinking course. Since 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions in conjunction with the divisional meetings of the American Philosophical Association (APA). In 1987, the APA’s Committee on Pre-College Philosophy commissioned a consensus statement on critical thinking for purposes of educational assessment and instruction (Facione 1990a). Researchers have developed standardized tests of critical thinking abilities and dispositions; for details, see the Supplement on Assessment . Educational jurisdictions around the world now include critical thinking in guidelines for curriculum and assessment.

For details on this history, see the Supplement on History .

2. Examples and Non-Examples

Before considering the definition of critical thinking, it will be helpful to have in mind some examples of critical thinking, as well as some examples of kinds of thinking that would apparently not count as critical thinking.

Dewey (1910: 68–71; 1933: 91–94) takes as paradigms of reflective thinking three class papers of students in which they describe their thinking. The examples range from the everyday to the scientific.

Transit : “The other day, when I was down town on 16th Street, a clock caught my eye. I saw that the hands pointed to 12:20. This suggested that I had an engagement at 124th Street, at one o’clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o’clock.” (Dewey 1910: 68–69; 1933: 91–92)

Ferryboat : “Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river is a long white pole, having a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere on the boat two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

“I then tried to imagine all possible purposes of the pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

“In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot’s position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly.” (Dewey 1910: 69–70; 1933: 92–93)

Bubbles : “In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat, or by decrease of pressure, or both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside. But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse” (Dewey 1910: 70–71; 1933: 93–94).

Dewey (1910, 1933) sprinkles his book with other examples of critical thinking. We will refer to the following.

Weather : A man on a walk notices that it has suddenly become cool, thinks that it is probably going to rain, looks up and sees a dark cloud obscuring the sun, and quickens his steps (1910: 6–10; 1933: 9–13).

Disorder : A man finds his rooms on his return to them in disorder with his belongings thrown about, thinks at first of burglary as an explanation, then thinks of mischievous children as being an alternative explanation, then looks to see whether valuables are missing, and discovers that they are (1910: 82–83; 1933: 166–168).

Typhoid : A physician diagnosing a patient whose conspicuous symptoms suggest typhoid avoids drawing a conclusion until more data are gathered by questioning the patient and by making tests (1910: 85–86; 1933: 170).

Blur : A moving blur catches our eye in the distance, we ask ourselves whether it is a cloud of whirling dust or a tree moving its branches or a man signaling to us, we think of other traits that should be found on each of those possibilities, and we look and see if those traits are found (1910: 102, 108; 1933: 121, 133).

Suction pump : In thinking about the suction pump, the scientist first notes that it will draw water only to a maximum height of 33 feet at sea level and to a lesser maximum height at higher elevations, selects for attention the differing atmospheric pressure at these elevations, sets up experiments in which the air is removed from a vessel containing water (when suction no longer works) and in which the weight of air at various levels is calculated, compares the results of reasoning about the height to which a given weight of air will allow a suction pump to raise water with the observed maximum height at different elevations, and finally assimilates the suction pump to such apparently different phenomena as the siphon and the rising of a balloon (1910: 150–153; 1933: 195–198).

Diamond : A passenger in a car driving in a diamond lane reserved for vehicles with at least one passenger notices that the diamond marks on the pavement are far apart in some places and close together in others. Why? The driver suggests that the reason may be that the diamond marks are not needed where there is a solid double line separating the diamond lane from the adjoining lane, but are needed when there is a dotted single line permitting crossing into the diamond lane. Further observation confirms that the diamonds are close together when a dotted line separates the diamond lane from its neighbour, but otherwise far apart.

Rash : A woman suddenly develops a very itchy red rash on her throat and upper chest. She recently noticed a mark on the back of her right hand, but was not sure whether the mark was a rash or a scrape. She lies down in bed and thinks about what might be causing the rash and what to do about it. About two weeks before, she began taking blood pressure medication that contained a sulfa drug, and the pharmacist had warned her, in view of a previous allergic reaction to a medication containing a sulfa drug, to be on the alert for an allergic reaction; however, she had been taking the medication for two weeks with no such effect. The day before, she began using a new cream on her neck and upper chest; against the new cream as the cause was mark on the back of her hand, which had not been exposed to the cream. She began taking probiotics about a month before. She also recently started new eye drops, but she supposed that manufacturers of eye drops would be careful not to include allergy-causing components in the medication. The rash might be a heat rash, since she recently was sweating profusely from her upper body. Since she is about to go away on a short vacation, where she would not have access to her usual physician, she decides to keep taking the probiotics and using the new eye drops but to discontinue the blood pressure medication and to switch back to the old cream for her neck and upper chest. She forms a plan to consult her regular physician on her return about the blood pressure medication.

Candidate : Although Dewey included no examples of thinking directed at appraising the arguments of others, such thinking has come to be considered a kind of critical thinking. We find an example of such thinking in the performance task on the Collegiate Learning Assessment (CLA+), which its sponsoring organization describes as

a performance-based assessment that provides a measure of an institution’s contribution to the development of critical-thinking and written communication skills of its students. (Council for Aid to Education 2017)

A sample task posted on its website requires the test-taker to write a report for public distribution evaluating a fictional candidate’s policy proposals and their supporting arguments, using supplied background documents, with a recommendation on whether to endorse the candidate.

Immediate acceptance of an idea that suggests itself as a solution to a problem (e.g., a possible explanation of an event or phenomenon, an action that seems likely to produce a desired result) is “uncritical thinking, the minimum of reflection” (Dewey 1910: 13). On-going suspension of judgment in the light of doubt about a possible solution is not critical thinking (Dewey 1910: 108). Critique driven by a dogmatically held political or religious ideology is not critical thinking; thus Paulo Freire (1968 [1970]) is using the term (e.g., at 1970: 71, 81, 100, 146) in a more politically freighted sense that includes not only reflection but also revolutionary action against oppression. Derivation of a conclusion from given data using an algorithm is not critical thinking.

What is critical thinking? There are many definitions. Ennis (2016) lists 14 philosophically oriented scholarly definitions and three dictionary definitions. Following Rawls (1971), who distinguished his conception of justice from a utilitarian conception but regarded them as rival conceptions of the same concept, Ennis maintains that the 17 definitions are different conceptions of the same concept. Rawls articulated the shared concept of justice as

a characteristic set of principles for assigning basic rights and duties and for determining… the proper distribution of the benefits and burdens of social cooperation. (Rawls 1971: 5)

Bailin et al. (1999b) claim that, if one considers what sorts of thinking an educator would take not to be critical thinking and what sorts to be critical thinking, one can conclude that educators typically understand critical thinking to have at least three features.

• It is done for the purpose of making up one’s mind about what to believe or do.
• The person engaging in the thinking is trying to fulfill standards of adequacy and accuracy appropriate to the thinking.
• The thinking fulfills the relevant standards to some threshold level.

One could sum up the core concept that involves these three features by saying that critical thinking is careful goal-directed thinking. This core concept seems to apply to all the examples of critical thinking described in the previous section. As for the non-examples, their exclusion depends on construing careful thinking as excluding jumping immediately to conclusions, suspending judgment no matter how strong the evidence, reasoning from an unquestioned ideological or religious perspective, and routinely using an algorithm to answer a question.

If the core of critical thinking is careful goal-directed thinking, conceptions of it can vary according to its presumed scope, its presumed goal, one’s criteria and threshold for being careful, and the thinking component on which one focuses. As to its scope, some conceptions (e.g., Dewey 1910, 1933) restrict it to constructive thinking on the basis of one’s own observations and experiments, others (e.g., Ennis 1962; Fisher & Scriven 1997; Johnson 1992) to appraisal of the products of such thinking. Ennis (1991) and Bailin et al. (1999b) take it to cover both construction and appraisal. As to its goal, some conceptions restrict it to forming a judgment (Dewey 1910, 1933; Lipman 1987; Facione 1990a). Others allow for actions as well as beliefs as the end point of a process of critical thinking (Ennis 1991; Bailin et al. 1999b). As to the criteria and threshold for being careful, definitions vary in the term used to indicate that critical thinking satisfies certain norms: “intellectually disciplined” (Scriven & Paul 1987), “reasonable” (Ennis 1991), “skillful” (Lipman 1987), “skilled” (Fisher & Scriven 1997), “careful” (Bailin & Battersby 2009). Some definitions specify these norms, referring variously to “consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey 1910, 1933); “the methods of logical inquiry and reasoning” (Glaser 1941); “conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication” (Scriven & Paul 1987); the requirement that “it is sensitive to context, relies on criteria, and is self-correcting” (Lipman 1987); “evidential, conceptual, methodological, criteriological, or contextual considerations” (Facione 1990a); and “plus-minus considerations of the product in terms of appropriate standards (or criteria)” (Johnson 1992). Stanovich and Stanovich (2010) propose to ground the concept of critical thinking in the concept of rationality, which they understand as combining epistemic rationality (fitting one’s beliefs to the world) and instrumental rationality (optimizing goal fulfillment); a critical thinker, in their view, is someone with “a propensity to override suboptimal responses from the autonomous mind” (2010: 227). These variant specifications of norms for critical thinking are not necessarily incompatible with one another, and in any case presuppose the core notion of thinking carefully. As to the thinking component singled out, some definitions focus on suspension of judgment during the thinking (Dewey 1910; McPeck 1981), others on inquiry while judgment is suspended (Bailin & Battersby 2009, 2021), others on the resulting judgment (Facione 1990a), and still others on responsiveness to reasons (Siegel 1988). Kuhn (2019) takes critical thinking to be more a dialogic practice of advancing and responding to arguments than an individual ability.

In educational contexts, a definition of critical thinking is a “programmatic definition” (Scheffler 1960: 19). It expresses a practical program for achieving an educational goal. For this purpose, a one-sentence formulaic definition is much less useful than articulation of a critical thinking process, with criteria and standards for the kinds of thinking that the process may involve. The real educational goal is recognition, adoption and implementation by students of those criteria and standards. That adoption and implementation in turn consists in acquiring the knowledge, abilities and dispositions of a critical thinker.

Conceptions of critical thinking generally do not include moral integrity as part of the concept. Dewey, for example, took critical thinking to be the ultimate intellectual goal of education, but distinguished it from the development of social cooperation among school children, which he took to be the central moral goal. Ennis (1996, 2011) added to his previous list of critical thinking dispositions a group of dispositions to care about the dignity and worth of every person, which he described as a “correlative” (1996) disposition without which critical thinking would be less valuable and perhaps harmful. An educational program that aimed at developing critical thinking but not the correlative disposition to care about the dignity and worth of every person, he asserted, “would be deficient and perhaps dangerous” (Ennis 1996: 172).

Dewey thought that education for reflective thinking would be of value to both the individual and society; recognition in educational practice of the kinship to the scientific attitude of children’s native curiosity, fertile imagination and love of experimental inquiry “would make for individual happiness and the reduction of social waste” (Dewey 1910: iii). Schools participating in the Eight-Year Study took development of the habit of reflective thinking and skill in solving problems as a means to leading young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18, 81). Harvey Siegel (1988: 55–61) has offered four considerations in support of adopting critical thinking as an educational ideal. (1) Respect for persons requires that schools and teachers honour students’ demands for reasons and explanations, deal with students honestly, and recognize the need to confront students’ independent judgment; these requirements concern the manner in which teachers treat students. (2) Education has the task of preparing children to be successful adults, a task that requires development of their self-sufficiency. (3) Education should initiate children into the rational traditions in such fields as history, science and mathematics. (4) Education should prepare children to become democratic citizens, which requires reasoned procedures and critical talents and attitudes. To supplement these considerations, Siegel (1988: 62–90) responds to two objections: the ideology objection that adoption of any educational ideal requires a prior ideological commitment and the indoctrination objection that cultivation of critical thinking cannot escape being a form of indoctrination.

Despite the diversity of our 11 examples, one can recognize a common pattern. Dewey analyzed it as consisting of five phases:

• suggestions , in which the mind leaps forward to a possible solution;
• an intellectualization of the difficulty or perplexity into a problem to be solved, a question for which the answer must be sought;
• the use of one suggestion after another as a leading idea, or hypothesis , to initiate and guide observation and other operations in collection of factual material;
• the mental elaboration of the idea or supposition as an idea or supposition ( reasoning , in the sense on which reasoning is a part, not the whole, of inference); and
• testing the hypothesis by overt or imaginative action. (Dewey 1933: 106–107; italics in original)

The process of reflective thinking consisting of these phases would be preceded by a perplexed, troubled or confused situation and followed by a cleared-up, unified, resolved situation (Dewey 1933: 106). The term ‘phases’ replaced the term ‘steps’ (Dewey 1910: 72), thus removing the earlier suggestion of an invariant sequence. Variants of the above analysis appeared in (Dewey 1916: 177) and (Dewey 1938: 101–119).

The variant formulations indicate the difficulty of giving a single logical analysis of such a varied process. The process of critical thinking may have a spiral pattern, with the problem being redefined in the light of obstacles to solving it as originally formulated. For example, the person in Transit might have concluded that getting to the appointment at the scheduled time was impossible and have reformulated the problem as that of rescheduling the appointment for a mutually convenient time. Further, defining a problem does not always follow after or lead immediately to an idea of a suggested solution. Nor should it do so, as Dewey himself recognized in describing the physician in Typhoid as avoiding any strong preference for this or that conclusion before getting further information (Dewey 1910: 85; 1933: 170). People with a hypothesis in mind, even one to which they have a very weak commitment, have a so-called “confirmation bias” (Nickerson 1998): they are likely to pay attention to evidence that confirms the hypothesis and to ignore evidence that counts against it or for some competing hypothesis. Detectives, intelligence agencies, and investigators of airplane accidents are well advised to gather relevant evidence systematically and to postpone even tentative adoption of an explanatory hypothesis until the collected evidence rules out with the appropriate degree of certainty all but one explanation. Dewey’s analysis of the critical thinking process can be faulted as well for requiring acceptance or rejection of a possible solution to a defined problem, with no allowance for deciding in the light of the available evidence to suspend judgment. Further, given the great variety of kinds of problems for which reflection is appropriate, there is likely to be variation in its component events. Perhaps the best way to conceptualize the critical thinking process is as a checklist whose component events can occur in a variety of orders, selectively, and more than once. These component events might include (1) noticing a difficulty, (2) defining the problem, (3) dividing the problem into manageable sub-problems, (4) formulating a variety of possible solutions to the problem or sub-problem, (5) determining what evidence is relevant to deciding among possible solutions to the problem or sub-problem, (6) devising a plan of systematic observation or experiment that will uncover the relevant evidence, (7) carrying out the plan of systematic observation or experimentation, (8) noting the results of the systematic observation or experiment, (9) gathering relevant testimony and information from others, (10) judging the credibility of testimony and information gathered from others, (11) drawing conclusions from gathered evidence and accepted testimony, and (12) accepting a solution that the evidence adequately supports (cf. Hitchcock 2017: 485).

Checklist conceptions of the process of critical thinking are open to the objection that they are too mechanical and procedural to fit the multi-dimensional and emotionally charged issues for which critical thinking is urgently needed (Paul 1984). For such issues, a more dialectical process is advocated, in which competing relevant world views are identified, their implications explored, and some sort of creative synthesis attempted.

If one considers the critical thinking process illustrated by the 11 examples, one can identify distinct kinds of mental acts and mental states that form part of it. To distinguish, label and briefly characterize these components is a useful preliminary to identifying abilities, skills, dispositions, attitudes, habits and the like that contribute causally to thinking critically. Identifying such abilities and habits is in turn a useful preliminary to setting educational goals. Setting the goals is in its turn a useful preliminary to designing strategies for helping learners to achieve the goals and to designing ways of measuring the extent to which learners have done so. Such measures provide both feedback to learners on their achievement and a basis for experimental research on the effectiveness of various strategies for educating people to think critically. Let us begin, then, by distinguishing the kinds of mental acts and mental events that can occur in a critical thinking process.

• Observing : One notices something in one’s immediate environment (sudden cooling of temperature in Weather , bubbles forming outside a glass and then going inside in Bubbles , a moving blur in the distance in Blur , a rash in Rash ). Or one notes the results of an experiment or systematic observation (valuables missing in Disorder , no suction without air pressure in Suction pump )
• Feeling : One feels puzzled or uncertain about something (how to get to an appointment on time in Transit , why the diamonds vary in spacing in Diamond ). One wants to resolve this perplexity. One feels satisfaction once one has worked out an answer (to take the subway express in Transit , diamonds closer when needed as a warning in Diamond ).
• Wondering : One formulates a question to be addressed (why bubbles form outside a tumbler taken from hot water in Bubbles , how suction pumps work in Suction pump , what caused the rash in Rash ).
• Imagining : One thinks of possible answers (bus or subway or elevated in Transit , flagpole or ornament or wireless communication aid or direction indicator in Ferryboat , allergic reaction or heat rash in Rash ).
• Inferring : One works out what would be the case if a possible answer were assumed (valuables missing if there has been a burglary in Disorder , earlier start to the rash if it is an allergic reaction to a sulfa drug in Rash ). Or one draws a conclusion once sufficient relevant evidence is gathered (take the subway in Transit , burglary in Disorder , discontinue blood pressure medication and new cream in Rash ).
• Knowledge : One uses stored knowledge of the subject-matter to generate possible answers or to infer what would be expected on the assumption of a particular answer (knowledge of a city’s public transit system in Transit , of the requirements for a flagpole in Ferryboat , of Boyle’s law in Bubbles , of allergic reactions in Rash ).
• Experimenting : One designs and carries out an experiment or a systematic observation to find out whether the results deduced from a possible answer will occur (looking at the location of the flagpole in relation to the pilot’s position in Ferryboat , putting an ice cube on top of a tumbler taken from hot water in Bubbles , measuring the height to which a suction pump will draw water at different elevations in Suction pump , noticing the spacing of diamonds when movement to or from a diamond lane is allowed in Diamond ).
• Consulting : One finds a source of information, gets the information from the source, and makes a judgment on whether to accept it. None of our 11 examples include searching for sources of information. In this respect they are unrepresentative, since most people nowadays have almost instant access to information relevant to answering any question, including many of those illustrated by the examples. However, Candidate includes the activities of extracting information from sources and evaluating its credibility.
• Identifying and analyzing arguments : One notices an argument and works out its structure and content as a preliminary to evaluating its strength. This activity is central to Candidate . It is an important part of a critical thinking process in which one surveys arguments for various positions on an issue.
• Judging : One makes a judgment on the basis of accumulated evidence and reasoning, such as the judgment in Ferryboat that the purpose of the pole is to provide direction to the pilot.
• Deciding : One makes a decision on what to do or on what policy to adopt, as in the decision in Transit to take the subway.

By definition, a person who does something voluntarily is both willing and able to do that thing at that time. Both the willingness and the ability contribute causally to the person’s action, in the sense that the voluntary action would not occur if either (or both) of these were lacking. For example, suppose that one is standing with one’s arms at one’s sides and one voluntarily lifts one’s right arm to an extended horizontal position. One would not do so if one were unable to lift one’s arm, if for example one’s right side was paralyzed as the result of a stroke. Nor would one do so if one were unwilling to lift one’s arm, if for example one were participating in a street demonstration at which a white supremacist was urging the crowd to lift their right arm in a Nazi salute and one were unwilling to express support in this way for the racist Nazi ideology. The same analysis applies to a voluntary mental process of thinking critically. It requires both willingness and ability to think critically, including willingness and ability to perform each of the mental acts that compose the process and to coordinate those acts in a sequence that is directed at resolving the initiating perplexity.

Consider willingness first. We can identify causal contributors to willingness to think critically by considering factors that would cause a person who was able to think critically about an issue nevertheless not to do so (Hamby 2014). For each factor, the opposite condition thus contributes causally to willingness to think critically on a particular occasion. For example, people who habitually jump to conclusions without considering alternatives will not think critically about issues that arise, even if they have the required abilities. The contrary condition of willingness to suspend judgment is thus a causal contributor to thinking critically.

Now consider ability. In contrast to the ability to move one’s arm, which can be completely absent because a stroke has left the arm paralyzed, the ability to think critically is a developed ability, whose absence is not a complete absence of ability to think but absence of ability to think well. We can identify the ability to think well directly, in terms of the norms and standards for good thinking. In general, to be able do well the thinking activities that can be components of a critical thinking process, one needs to know the concepts and principles that characterize their good performance, to recognize in particular cases that the concepts and principles apply, and to apply them. The knowledge, recognition and application may be procedural rather than declarative. It may be domain-specific rather than widely applicable, and in either case may need subject-matter knowledge, sometimes of a deep kind.

Reflections of the sort illustrated by the previous two paragraphs have led scholars to identify the knowledge, abilities and dispositions of a “critical thinker”, i.e., someone who thinks critically whenever it is appropriate to do so. We turn now to these three types of causal contributors to thinking critically. We start with dispositions, since arguably these are the most powerful contributors to being a critical thinker, can be fostered at an early stage of a child’s development, and are susceptible to general improvement (Glaser 1941: 175)

8. Critical Thinking Dispositions

Educational researchers use the term ‘dispositions’ broadly for the habits of mind and attitudes that contribute causally to being a critical thinker. Some writers (e.g., Paul & Elder 2006; Hamby 2014; Bailin & Battersby 2016a) propose to use the term ‘virtues’ for this dimension of a critical thinker. The virtues in question, although they are virtues of character, concern the person’s ways of thinking rather than the person’s ways of behaving towards others. They are not moral virtues but intellectual virtues, of the sort articulated by Zagzebski (1996) and discussed by Turri, Alfano, and Greco (2017).

On a realistic conception, thinking dispositions or intellectual virtues are real properties of thinkers. They are general tendencies, propensities, or inclinations to think in particular ways in particular circumstances, and can be genuinely explanatory (Siegel 1999). Sceptics argue that there is no evidence for a specific mental basis for the habits of mind that contribute to thinking critically, and that it is pedagogically misleading to posit such a basis (Bailin et al. 1999a). Whatever their status, critical thinking dispositions need motivation for their initial formation in a child—motivation that may be external or internal. As children develop, the force of habit will gradually become important in sustaining the disposition (Nieto & Valenzuela 2012). Mere force of habit, however, is unlikely to sustain critical thinking dispositions. Critical thinkers must value and enjoy using their knowledge and abilities to think things through for themselves. They must be committed to, and lovers of, inquiry.

A person may have a critical thinking disposition with respect to only some kinds of issues. For example, one could be open-minded about scientific issues but not about religious issues. Similarly, one could be confident in one’s ability to reason about the theological implications of the existence of evil in the world but not in one’s ability to reason about the best design for a guided ballistic missile.

Facione (1990a: 25) divides “affective dispositions” of critical thinking into approaches to life and living in general and approaches to specific issues, questions or problems. Adapting this distinction, one can usefully divide critical thinking dispositions into initiating dispositions (those that contribute causally to starting to think critically about an issue) and internal dispositions (those that contribute causally to doing a good job of thinking critically once one has started). The two categories are not mutually exclusive. For example, open-mindedness, in the sense of willingness to consider alternative points of view to one’s own, is both an initiating and an internal disposition.

Using the strategy of considering factors that would block people with the ability to think critically from doing so, we can identify as initiating dispositions for thinking critically attentiveness, a habit of inquiry, self-confidence, courage, open-mindedness, willingness to suspend judgment, trust in reason, wanting evidence for one’s beliefs, and seeking the truth. We consider briefly what each of these dispositions amounts to, in each case citing sources that acknowledge them.

• Attentiveness : One will not think critically if one fails to recognize an issue that needs to be thought through. For example, the pedestrian in Weather would not have looked up if he had not noticed that the air was suddenly cooler. To be a critical thinker, then, one needs to be habitually attentive to one’s surroundings, noticing not only what one senses but also sources of perplexity in messages received and in one’s own beliefs and attitudes (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Habit of inquiry : Inquiry is effortful, and one needs an internal push to engage in it. For example, the student in Bubbles could easily have stopped at idle wondering about the cause of the bubbles rather than reasoning to a hypothesis, then designing and executing an experiment to test it. Thus willingness to think critically needs mental energy and initiative. What can supply that energy? Love of inquiry, or perhaps just a habit of inquiry. Hamby (2015) has argued that willingness to inquire is the central critical thinking virtue, one that encompasses all the others. It is recognized as a critical thinking disposition by Dewey (1910: 29; 1933: 35), Glaser (1941: 5), Ennis (1987: 12; 1991: 8), Facione (1990a: 25), Bailin et al. (1999b: 294), Halpern (1998: 452), and Facione, Facione, & Giancarlo (2001).
• Self-confidence : Lack of confidence in one’s abilities can block critical thinking. For example, if the woman in Rash lacked confidence in her ability to figure things out for herself, she might just have assumed that the rash on her chest was the allergic reaction to her medication against which the pharmacist had warned her. Thus willingness to think critically requires confidence in one’s ability to inquire (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Courage : Fear of thinking for oneself can stop one from doing it. Thus willingness to think critically requires intellectual courage (Paul & Elder 2006: 16).
• Open-mindedness : A dogmatic attitude will impede thinking critically. For example, a person who adheres rigidly to a “pro-choice” position on the issue of the legal status of induced abortion is likely to be unwilling to consider seriously the issue of when in its development an unborn child acquires a moral right to life. Thus willingness to think critically requires open-mindedness, in the sense of a willingness to examine questions to which one already accepts an answer but which further evidence or reasoning might cause one to answer differently (Dewey 1933; Facione 1990a; Ennis 1991; Bailin et al. 1999b; Halpern 1998, Facione, Facione, & Giancarlo 2001). Paul (1981) emphasizes open-mindedness about alternative world-views, and recommends a dialectical approach to integrating such views as central to what he calls “strong sense” critical thinking. In three studies, Haran, Ritov, & Mellers (2013) found that actively open-minded thinking, including “the tendency to weigh new evidence against a favored belief, to spend sufficient time on a problem before giving up, and to consider carefully the opinions of others in forming one’s own”, led study participants to acquire information and thus to make accurate estimations.
• Willingness to suspend judgment : Premature closure on an initial solution will block critical thinking. Thus willingness to think critically requires a willingness to suspend judgment while alternatives are explored (Facione 1990a; Ennis 1991; Halpern 1998).
• Trust in reason : Since distrust in the processes of reasoned inquiry will dissuade one from engaging in it, trust in them is an initiating critical thinking disposition (Facione 1990a, 25; Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001; Paul & Elder 2006). In reaction to an allegedly exclusive emphasis on reason in critical thinking theory and pedagogy, Thayer-Bacon (2000) argues that intuition, imagination, and emotion have important roles to play in an adequate conception of critical thinking that she calls “constructive thinking”. From her point of view, critical thinking requires trust not only in reason but also in intuition, imagination, and emotion.
• Seeking the truth : If one does not care about the truth but is content to stick with one’s initial bias on an issue, then one will not think critically about it. Seeking the truth is thus an initiating critical thinking disposition (Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001). A disposition to seek the truth is implicit in more specific critical thinking dispositions, such as trying to be well-informed, considering seriously points of view other than one’s own, looking for alternatives, suspending judgment when the evidence is insufficient, and adopting a position when the evidence supporting it is sufficient.

Some of the initiating dispositions, such as open-mindedness and willingness to suspend judgment, are also internal critical thinking dispositions, in the sense of mental habits or attitudes that contribute causally to doing a good job of critical thinking once one starts the process. But there are many other internal critical thinking dispositions. Some of them are parasitic on one’s conception of good thinking. For example, it is constitutive of good thinking about an issue to formulate the issue clearly and to maintain focus on it. For this purpose, one needs not only the corresponding ability but also the corresponding disposition. Ennis (1991: 8) describes it as the disposition “to determine and maintain focus on the conclusion or question”, Facione (1990a: 25) as “clarity in stating the question or concern”. Other internal dispositions are motivators to continue or adjust the critical thinking process, such as willingness to persist in a complex task and willingness to abandon nonproductive strategies in an attempt to self-correct (Halpern 1998: 452). For a list of identified internal critical thinking dispositions, see the Supplement on Internal Critical Thinking Dispositions .

Some theorists postulate skills, i.e., acquired abilities, as operative in critical thinking. It is not obvious, however, that a good mental act is the exercise of a generic acquired skill. Inferring an expected time of arrival, as in Transit , has some generic components but also uses non-generic subject-matter knowledge. Bailin et al. (1999a) argue against viewing critical thinking skills as generic and discrete, on the ground that skilled performance at a critical thinking task cannot be separated from knowledge of concepts and from domain-specific principles of good thinking. Talk of skills, they concede, is unproblematic if it means merely that a person with critical thinking skills is capable of intelligent performance.

Despite such scepticism, theorists of critical thinking have listed as general contributors to critical thinking what they variously call abilities (Glaser 1941; Ennis 1962, 1991), skills (Facione 1990a; Halpern 1998) or competencies (Fisher & Scriven 1997). Amalgamating these lists would produce a confusing and chaotic cornucopia of more than 50 possible educational objectives, with only partial overlap among them. It makes sense instead to try to understand the reasons for the multiplicity and diversity, and to make a selection according to one’s own reasons for singling out abilities to be developed in a critical thinking curriculum. Two reasons for diversity among lists of critical thinking abilities are the underlying conception of critical thinking and the envisaged educational level. Appraisal-only conceptions, for example, involve a different suite of abilities than constructive-only conceptions. Some lists, such as those in (Glaser 1941), are put forward as educational objectives for secondary school students, whereas others are proposed as objectives for college students (e.g., Facione 1990a).

The abilities described in the remaining paragraphs of this section emerge from reflection on the general abilities needed to do well the thinking activities identified in section 6 as components of the critical thinking process described in section 5 . The derivation of each collection of abilities is accompanied by citation of sources that list such abilities and of standardized tests that claim to test them.

Observational abilities : Careful and accurate observation sometimes requires specialist expertise and practice, as in the case of observing birds and observing accident scenes. However, there are general abilities of noticing what one’s senses are picking up from one’s environment and of being able to articulate clearly and accurately to oneself and others what one has observed. It helps in exercising them to be able to recognize and take into account factors that make one’s observation less trustworthy, such as prior framing of the situation, inadequate time, deficient senses, poor observation conditions, and the like. It helps as well to be skilled at taking steps to make one’s observation more trustworthy, such as moving closer to get a better look, measuring something three times and taking the average, and checking what one thinks one is observing with someone else who is in a good position to observe it. It also helps to be skilled at recognizing respects in which one’s report of one’s observation involves inference rather than direct observation, so that one can then consider whether the inference is justified. These abilities come into play as well when one thinks about whether and with what degree of confidence to accept an observation report, for example in the study of history or in a criminal investigation or in assessing news reports. Observational abilities show up in some lists of critical thinking abilities (Ennis 1962: 90; Facione 1990a: 16; Ennis 1991: 9). There are items testing a person’s ability to judge the credibility of observation reports in the Cornell Critical Thinking Tests, Levels X and Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). Norris and King (1983, 1985, 1990a, 1990b) is a test of ability to appraise observation reports.

Emotional abilities : The emotions that drive a critical thinking process are perplexity or puzzlement, a wish to resolve it, and satisfaction at achieving the desired resolution. Children experience these emotions at an early age, without being trained to do so. Education that takes critical thinking as a goal needs only to channel these emotions and to make sure not to stifle them. Collaborative critical thinking benefits from ability to recognize one’s own and others’ emotional commitments and reactions.

Questioning abilities : A critical thinking process needs transformation of an inchoate sense of perplexity into a clear question. Formulating a question well requires not building in questionable assumptions, not prejudging the issue, and using language that in context is unambiguous and precise enough (Ennis 1962: 97; 1991: 9).

Imaginative abilities : Thinking directed at finding the correct causal explanation of a general phenomenon or particular event requires an ability to imagine possible explanations. Thinking about what policy or plan of action to adopt requires generation of options and consideration of possible consequences of each option. Domain knowledge is required for such creative activity, but a general ability to imagine alternatives is helpful and can be nurtured so as to become easier, quicker, more extensive, and deeper (Dewey 1910: 34–39; 1933: 40–47). Facione (1990a) and Halpern (1998) include the ability to imagine alternatives as a critical thinking ability.

Inferential abilities : The ability to draw conclusions from given information, and to recognize with what degree of certainty one’s own or others’ conclusions follow, is universally recognized as a general critical thinking ability. All 11 examples in section 2 of this article include inferences, some from hypotheses or options (as in Transit , Ferryboat and Disorder ), others from something observed (as in Weather and Rash ). None of these inferences is formally valid. Rather, they are licensed by general, sometimes qualified substantive rules of inference (Toulmin 1958) that rest on domain knowledge—that a bus trip takes about the same time in each direction, that the terminal of a wireless telegraph would be located on the highest possible place, that sudden cooling is often followed by rain, that an allergic reaction to a sulfa drug generally shows up soon after one starts taking it. It is a matter of controversy to what extent the specialized ability to deduce conclusions from premisses using formal rules of inference is needed for critical thinking. Dewey (1933) locates logical forms in setting out the products of reflection rather than in the process of reflection. Ennis (1981a), on the other hand, maintains that a liberally-educated person should have the following abilities: to translate natural-language statements into statements using the standard logical operators, to use appropriately the language of necessary and sufficient conditions, to deal with argument forms and arguments containing symbols, to determine whether in virtue of an argument’s form its conclusion follows necessarily from its premisses, to reason with logically complex propositions, and to apply the rules and procedures of deductive logic. Inferential abilities are recognized as critical thinking abilities by Glaser (1941: 6), Facione (1990a: 9), Ennis (1991: 9), Fisher & Scriven (1997: 99, 111), and Halpern (1998: 452). Items testing inferential abilities constitute two of the five subtests of the Watson Glaser Critical Thinking Appraisal (Watson & Glaser 1980a, 1980b, 1994), two of the four sections in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), three of the seven sections in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), 11 of the 34 items on Forms A and B of the California Critical Thinking Skills Test (Facione 1990b, 1992), and a high but variable proportion of the 25 selected-response questions in the Collegiate Learning Assessment (Council for Aid to Education 2017).

Experimenting abilities : Knowing how to design and execute an experiment is important not just in scientific research but also in everyday life, as in Rash . Dewey devoted a whole chapter of his How We Think (1910: 145–156; 1933: 190–202) to the superiority of experimentation over observation in advancing knowledge. Experimenting abilities come into play at one remove in appraising reports of scientific studies. Skill in designing and executing experiments includes the acknowledged abilities to appraise evidence (Glaser 1941: 6), to carry out experiments and to apply appropriate statistical inference techniques (Facione 1990a: 9), to judge inductions to an explanatory hypothesis (Ennis 1991: 9), and to recognize the need for an adequately large sample size (Halpern 1998). The Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) includes four items (out of 52) on experimental design. The Collegiate Learning Assessment (Council for Aid to Education 2017) makes room for appraisal of study design in both its performance task and its selected-response questions.

Consulting abilities : Skill at consulting sources of information comes into play when one seeks information to help resolve a problem, as in Candidate . Ability to find and appraise information includes ability to gather and marshal pertinent information (Glaser 1941: 6), to judge whether a statement made by an alleged authority is acceptable (Ennis 1962: 84), to plan a search for desired information (Facione 1990a: 9), and to judge the credibility of a source (Ennis 1991: 9). Ability to judge the credibility of statements is tested by 24 items (out of 76) in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) and by four items (out of 52) in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). The College Learning Assessment’s performance task requires evaluation of whether information in documents is credible or unreliable (Council for Aid to Education 2017).

Argument analysis abilities : The ability to identify and analyze arguments contributes to the process of surveying arguments on an issue in order to form one’s own reasoned judgment, as in Candidate . The ability to detect and analyze arguments is recognized as a critical thinking skill by Facione (1990a: 7–8), Ennis (1991: 9) and Halpern (1998). Five items (out of 34) on the California Critical Thinking Skills Test (Facione 1990b, 1992) test skill at argument analysis. The College Learning Assessment (Council for Aid to Education 2017) incorporates argument analysis in its selected-response tests of critical reading and evaluation and of critiquing an argument.

Judging skills and deciding skills : Skill at judging and deciding is skill at recognizing what judgment or decision the available evidence and argument supports, and with what degree of confidence. It is thus a component of the inferential skills already discussed.

Lists and tests of critical thinking abilities often include two more abilities: identifying assumptions and constructing and evaluating definitions.

In addition to dispositions and abilities, critical thinking needs knowledge: of critical thinking concepts, of critical thinking principles, and of the subject-matter of the thinking.

We can derive a short list of concepts whose understanding contributes to critical thinking from the critical thinking abilities described in the preceding section. Observational abilities require an understanding of the difference between observation and inference. Questioning abilities require an understanding of the concepts of ambiguity and vagueness. Inferential abilities require an understanding of the difference between conclusive and defeasible inference (traditionally, between deduction and induction), as well as of the difference between necessary and sufficient conditions. Experimenting abilities require an understanding of the concepts of hypothesis, null hypothesis, assumption and prediction, as well as of the concept of statistical significance and of its difference from importance. They also require an understanding of the difference between an experiment and an observational study, and in particular of the difference between a randomized controlled trial, a prospective correlational study and a retrospective (case-control) study. Argument analysis abilities require an understanding of the concepts of argument, premiss, assumption, conclusion and counter-consideration. Additional critical thinking concepts are proposed by Bailin et al. (1999b: 293), Fisher & Scriven (1997: 105–106), Black (2012), and Blair (2021).

According to Glaser (1941: 25), ability to think critically requires knowledge of the methods of logical inquiry and reasoning. If we review the list of abilities in the preceding section, however, we can see that some of them can be acquired and exercised merely through practice, possibly guided in an educational setting, followed by feedback. Searching intelligently for a causal explanation of some phenomenon or event requires that one consider a full range of possible causal contributors, but it seems more important that one implements this principle in one’s practice than that one is able to articulate it. What is important is “operational knowledge” of the standards and principles of good thinking (Bailin et al. 1999b: 291–293). But the development of such critical thinking abilities as designing an experiment or constructing an operational definition can benefit from learning their underlying theory. Further, explicit knowledge of quirks of human thinking seems useful as a cautionary guide. Human memory is not just fallible about details, as people learn from their own experiences of misremembering, but is so malleable that a detailed, clear and vivid recollection of an event can be a total fabrication (Loftus 2017). People seek or interpret evidence in ways that are partial to their existing beliefs and expectations, often unconscious of their “confirmation bias” (Nickerson 1998). Not only are people subject to this and other cognitive biases (Kahneman 2011), of which they are typically unaware, but it may be counter-productive for one to make oneself aware of them and try consciously to counteract them or to counteract social biases such as racial or sexual stereotypes (Kenyon & Beaulac 2014). It is helpful to be aware of these facts and of the superior effectiveness of blocking the operation of biases—for example, by making an immediate record of one’s observations, refraining from forming a preliminary explanatory hypothesis, blind refereeing, double-blind randomized trials, and blind grading of students’ work. It is also helpful to be aware of the prevalence of “noise” (unwanted unsystematic variability of judgments), of how to detect noise (through a noise audit), and of how to reduce noise: make accuracy the goal, think statistically, break a process of arriving at a judgment into independent tasks, resist premature intuitions, in a group get independent judgments first, favour comparative judgments and scales (Kahneman, Sibony, & Sunstein 2021). It is helpful as well to be aware of the concept of “bounded rationality” in decision-making and of the related distinction between “satisficing” and optimizing (Simon 1956; Gigerenzer 2001).

Critical thinking about an issue requires substantive knowledge of the domain to which the issue belongs. Critical thinking abilities are not a magic elixir that can be applied to any issue whatever by somebody who has no knowledge of the facts relevant to exploring that issue. For example, the student in Bubbles needed to know that gases do not penetrate solid objects like a glass, that air expands when heated, that the volume of an enclosed gas varies directly with its temperature and inversely with its pressure, and that hot objects will spontaneously cool down to the ambient temperature of their surroundings unless kept hot by insulation or a source of heat. Critical thinkers thus need a rich fund of subject-matter knowledge relevant to the variety of situations they encounter. This fact is recognized in the inclusion among critical thinking dispositions of a concern to become and remain generally well informed.

Experimental educational interventions, with control groups, have shown that education can improve critical thinking skills and dispositions, as measured by standardized tests. For information about these tests, see the Supplement on Assessment .

What educational methods are most effective at developing the dispositions, abilities and knowledge of a critical thinker? In a comprehensive meta-analysis of experimental and quasi-experimental studies of strategies for teaching students to think critically, Abrami et al. (2015) found that dialogue, anchored instruction, and mentoring each increased the effectiveness of the educational intervention, and that they were most effective when combined. They also found that in these studies a combination of separate instruction in critical thinking with subject-matter instruction in which students are encouraged to think critically was more effective than either by itself. However, the difference was not statistically significant; that is, it might have arisen by chance.

Most of these studies lack the longitudinal follow-up required to determine whether the observed differential improvements in critical thinking abilities or dispositions continue over time, for example until high school or college graduation. For details on studies of methods of developing critical thinking skills and dispositions, see the Supplement on Educational Methods .

12. Controversies

Scholars have denied the generalizability of critical thinking abilities across subject domains, have alleged bias in critical thinking theory and pedagogy, and have investigated the relationship of critical thinking to other kinds of thinking.

McPeck (1981) attacked the thinking skills movement of the 1970s, including the critical thinking movement. He argued that there are no general thinking skills, since thinking is always thinking about some subject-matter. It is futile, he claimed, for schools and colleges to teach thinking as if it were a separate subject. Rather, teachers should lead their pupils to become autonomous thinkers by teaching school subjects in a way that brings out their cognitive structure and that encourages and rewards discussion and argument. As some of his critics (e.g., Paul 1985; Siegel 1985) pointed out, McPeck’s central argument needs elaboration, since it has obvious counter-examples in writing and speaking, for which (up to a certain level of complexity) there are teachable general abilities even though they are always about some subject-matter. To make his argument convincing, McPeck needs to explain how thinking differs from writing and speaking in a way that does not permit useful abstraction of its components from the subject-matters with which it deals. He has not done so. Nevertheless, his position that the dispositions and abilities of a critical thinker are best developed in the context of subject-matter instruction is shared by many theorists of critical thinking, including Dewey (1910, 1933), Glaser (1941), Passmore (1980), Weinstein (1990), Bailin et al. (1999b), and Willingham (2019).

McPeck’s challenge prompted reflection on the extent to which critical thinking is subject-specific. McPeck argued for a strong subject-specificity thesis, according to which it is a conceptual truth that all critical thinking abilities are specific to a subject. (He did not however extend his subject-specificity thesis to critical thinking dispositions. In particular, he took the disposition to suspend judgment in situations of cognitive dissonance to be a general disposition.) Conceptual subject-specificity is subject to obvious counter-examples, such as the general ability to recognize confusion of necessary and sufficient conditions. A more modest thesis, also endorsed by McPeck, is epistemological subject-specificity, according to which the norms of good thinking vary from one field to another. Epistemological subject-specificity clearly holds to a certain extent; for example, the principles in accordance with which one solves a differential equation are quite different from the principles in accordance with which one determines whether a painting is a genuine Picasso. But the thesis suffers, as Ennis (1989) points out, from vagueness of the concept of a field or subject and from the obvious existence of inter-field principles, however broadly the concept of a field is construed. For example, the principles of hypothetico-deductive reasoning hold for all the varied fields in which such reasoning occurs. A third kind of subject-specificity is empirical subject-specificity, according to which as a matter of empirically observable fact a person with the abilities and dispositions of a critical thinker in one area of investigation will not necessarily have them in another area of investigation.

The thesis of empirical subject-specificity raises the general problem of transfer. If critical thinking abilities and dispositions have to be developed independently in each school subject, how are they of any use in dealing with the problems of everyday life and the political and social issues of contemporary society, most of which do not fit into the framework of a traditional school subject? Proponents of empirical subject-specificity tend to argue that transfer is more likely to occur if there is critical thinking instruction in a variety of domains, with explicit attention to dispositions and abilities that cut across domains. But evidence for this claim is scanty. There is a need for well-designed empirical studies that investigate the conditions that make transfer more likely.

It is common ground in debates about the generality or subject-specificity of critical thinking dispositions and abilities that critical thinking about any topic requires background knowledge about the topic. For example, the most sophisticated understanding of the principles of hypothetico-deductive reasoning is of no help unless accompanied by some knowledge of what might be plausible explanations of some phenomenon under investigation.

Critics have objected to bias in the theory, pedagogy and practice of critical thinking. Commentators (e.g., Alston 1995; Ennis 1998) have noted that anyone who takes a position has a bias in the neutral sense of being inclined in one direction rather than others. The critics, however, are objecting to bias in the pejorative sense of an unjustified favoring of certain ways of knowing over others, frequently alleging that the unjustly favoured ways are those of a dominant sex or culture (Bailin 1995). These ways favour:

• reinforcement of egocentric and sociocentric biases over dialectical engagement with opposing world-views (Paul 1981, 1984; Warren 1998)
• distancing from the object of inquiry over closeness to it (Martin 1992; Thayer-Bacon 1992)
• indifference to the situation of others over care for them (Martin 1992)
• orientation to thought over orientation to action (Martin 1992)
• being reasonable over caring to understand people’s ideas (Thayer-Bacon 1993)
• being neutral and objective over being embodied and situated (Thayer-Bacon 1995a)
• doubting over believing (Thayer-Bacon 1995b)
• reason over emotion, imagination and intuition (Thayer-Bacon 2000)
• solitary thinking over collaborative thinking (Thayer-Bacon 2000)
• written and spoken assignments over other forms of expression (Alston 2001)
• attention to written and spoken communications over attention to human problems (Alston 2001)
• winning debates in the public sphere over making and understanding meaning (Alston 2001)

A common thread in this smorgasbord of accusations is dissatisfaction with focusing on the logical analysis and evaluation of reasoning and arguments. While these authors acknowledge that such analysis and evaluation is part of critical thinking and should be part of its conceptualization and pedagogy, they insist that it is only a part. Paul (1981), for example, bemoans the tendency of atomistic teaching of methods of analyzing and evaluating arguments to turn students into more able sophists, adept at finding fault with positions and arguments with which they disagree but even more entrenched in the egocentric and sociocentric biases with which they began. Martin (1992) and Thayer-Bacon (1992) cite with approval the self-reported intimacy with their subject-matter of leading researchers in biology and medicine, an intimacy that conflicts with the distancing allegedly recommended in standard conceptions and pedagogy of critical thinking. Thayer-Bacon (2000) contrasts the embodied and socially embedded learning of her elementary school students in a Montessori school, who used their imagination, intuition and emotions as well as their reason, with conceptions of critical thinking as

thinking that is used to critique arguments, offer justifications, and make judgments about what are the good reasons, or the right answers. (Thayer-Bacon 2000: 127–128)

Alston (2001) reports that her students in a women’s studies class were able to see the flaws in the Cinderella myth that pervades much romantic fiction but in their own romantic relationships still acted as if all failures were the woman’s fault and still accepted the notions of love at first sight and living happily ever after. Students, she writes, should

be able to connect their intellectual critique to a more affective, somatic, and ethical account of making risky choices that have sexist, racist, classist, familial, sexual, or other consequences for themselves and those both near and far… critical thinking that reads arguments, texts, or practices merely on the surface without connections to feeling/desiring/doing or action lacks an ethical depth that should infuse the difference between mere cognitive activity and something we want to call critical thinking. (Alston 2001: 34)

Some critics portray such biases as unfair to women. Thayer-Bacon (1992), for example, has charged modern critical thinking theory with being sexist, on the ground that it separates the self from the object and causes one to lose touch with one’s inner voice, and thus stigmatizes women, who (she asserts) link self to object and listen to their inner voice. Her charge does not imply that women as a group are on average less able than men to analyze and evaluate arguments. Facione (1990c) found no difference by sex in performance on his California Critical Thinking Skills Test. Kuhn (1991: 280–281) found no difference by sex in either the disposition or the competence to engage in argumentative thinking.

The critics propose a variety of remedies for the biases that they allege. In general, they do not propose to eliminate or downplay critical thinking as an educational goal. Rather, they propose to conceptualize critical thinking differently and to change its pedagogy accordingly. Their pedagogical proposals arise logically from their objections. They can be summarized as follows:

• Focus on argument networks with dialectical exchanges reflecting contesting points of view rather than on atomic arguments, so as to develop “strong sense” critical thinking that transcends egocentric and sociocentric biases (Paul 1981, 1984).
• Foster closeness to the subject-matter and feeling connected to others in order to inform a humane democracy (Martin 1992).
• Develop “constructive thinking” as a social activity in a community of physically embodied and socially embedded inquirers with personal voices who value not only reason but also imagination, intuition and emotion (Thayer-Bacon 2000).
• In developing critical thinking in school subjects, treat as important neither skills nor dispositions but opening worlds of meaning (Alston 2001).
• Attend to the development of critical thinking dispositions as well as skills, and adopt the “critical pedagogy” practised and advocated by Freire (1968 [1970]) and hooks (1994) (Dalgleish, Girard, & Davies 2017).

A common thread in these proposals is treatment of critical thinking as a social, interactive, personally engaged activity like that of a quilting bee or a barn-raising (Thayer-Bacon 2000) rather than as an individual, solitary, distanced activity symbolized by Rodin’s The Thinker . One can get a vivid description of education with the former type of goal from the writings of bell hooks (1994, 2010). Critical thinking for her is open-minded dialectical exchange across opposing standpoints and from multiple perspectives, a conception similar to Paul’s “strong sense” critical thinking (Paul 1981). She abandons the structure of domination in the traditional classroom. In an introductory course on black women writers, for example, she assigns students to write an autobiographical paragraph about an early racial memory, then to read it aloud as the others listen, thus affirming the uniqueness and value of each voice and creating a communal awareness of the diversity of the group’s experiences (hooks 1994: 84). Her “engaged pedagogy” is thus similar to the “freedom under guidance” implemented in John Dewey’s Laboratory School of Chicago in the late 1890s and early 1900s. It incorporates the dialogue, anchored instruction, and mentoring that Abrami (2015) found to be most effective in improving critical thinking skills and dispositions.

What is the relationship of critical thinking to problem solving, decision-making, higher-order thinking, creative thinking, and other recognized types of thinking? One’s answer to this question obviously depends on how one defines the terms used in the question. If critical thinking is conceived broadly to cover any careful thinking about any topic for any purpose, then problem solving and decision making will be kinds of critical thinking, if they are done carefully. Historically, ‘critical thinking’ and ‘problem solving’ were two names for the same thing. If critical thinking is conceived more narrowly as consisting solely of appraisal of intellectual products, then it will be disjoint with problem solving and decision making, which are constructive.

Bloom’s taxonomy of educational objectives used the phrase “intellectual abilities and skills” for what had been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others (Bloom et al. 1956: 38). Thus, the so-called “higher-order thinking skills” at the taxonomy’s top levels of analysis, synthesis and evaluation are just critical thinking skills, although they do not come with general criteria for their assessment (Ennis 1981b). The revised version of Bloom’s taxonomy (Anderson et al. 2001) likewise treats critical thinking as cutting across those types of cognitive process that involve more than remembering (Anderson et al. 2001: 269–270). For details, see the Supplement on History .

As to creative thinking, it overlaps with critical thinking (Bailin 1987, 1988). Thinking about the explanation of some phenomenon or event, as in Ferryboat , requires creative imagination in constructing plausible explanatory hypotheses. Likewise, thinking about a policy question, as in Candidate , requires creativity in coming up with options. Conversely, creativity in any field needs to be balanced by critical appraisal of the draft painting or novel or mathematical theory.

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• What Is Critical Thinking? | Definition & Examples

What Is Critical Thinking? | Definition & Examples

Published on May 30, 2022 by Eoghan Ryan . Revised on May 31, 2023.

Critical thinking is the ability to effectively analyze information and form a judgment .

To think critically, you must be aware of your own biases and assumptions when encountering information, and apply consistent standards when evaluating sources .

Critical thinking skills help you to:

• Identify credible sources
• Evaluate and respond to arguments
• Assess alternative viewpoints
• Test hypotheses against relevant criteria

Table of contents

Why is critical thinking important, critical thinking examples, how to think critically, other interesting articles, frequently asked questions about critical thinking.

Critical thinking is important for making judgments about sources of information and forming your own arguments. It emphasizes a rational, objective, and self-aware approach that can help you to identify credible sources and strengthen your conclusions.

Critical thinking is important in all disciplines and throughout all stages of the research process . The types of evidence used in the sciences and in the humanities may differ, but critical thinking skills are relevant to both.

In academic writing , critical thinking can help you to determine whether a source:

• Is free from research bias
• Provides evidence to support its research findings
• Considers alternative viewpoints

Outside of academia, critical thinking goes hand in hand with information literacy to help you form opinions rationally and engage independently and critically with popular media.

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Critical thinking can help you to identify reliable sources of information that you can cite in your research paper . It can also guide your own research methods and inform your own arguments.

Outside of academia, critical thinking can help you to be aware of both your own and others’ biases and assumptions.

Academic examples

However, when you compare the findings of the study with other current research, you determine that the results seem improbable. You analyze the paper again, consulting the sources it cites.

You notice that the research was funded by the pharmaceutical company that created the treatment. Because of this, you view its results skeptically and determine that more independent research is necessary to confirm or refute them. Example: Poor critical thinking in an academic context You’re researching a paper on the impact wireless technology has had on developing countries that previously did not have large-scale communications infrastructure. You read an article that seems to confirm your hypothesis: the impact is mainly positive. Rather than evaluating the research methodology, you accept the findings uncritically.

Nonacademic examples

However, you decide to compare this review article with consumer reviews on a different site. You find that these reviews are not as positive. Some customers have had problems installing the alarm, and some have noted that it activates for no apparent reason.

You revisit the original review article. You notice that the words “sponsored content” appear in small print under the article title. Based on this, you conclude that the review is advertising and is therefore not an unbiased source. Example: Poor critical thinking in a nonacademic context You support a candidate in an upcoming election. You visit an online news site affiliated with their political party and read an article that criticizes their opponent. The article claims that the opponent is inexperienced in politics. You accept this without evidence, because it fits your preconceptions about the opponent.

There is no single way to think critically. How you engage with information will depend on the type of source you’re using and the information you need.

However, you can engage with sources in a systematic and critical way by asking certain questions when you encounter information. Like the CRAAP test , these questions focus on the currency , relevance , authority , accuracy , and purpose of a source of information.

When encountering information, ask:

• Who is the author? Are they an expert in their field?
• What do they say? Is their argument clear? Can you summarize it?
• When did they say this? Is the source current?
• Where is the information published? Is it an academic article? Is it peer-reviewed ?
• Why did the author publish it? What is their motivation?
• How do they make their argument? Is it backed up by evidence? Does it rely on opinion, speculation, or appeals to emotion ? Do they address alternative arguments?

Critical thinking also involves being aware of your own biases, not only those of others. When you make an argument or draw your own conclusions, you can ask similar questions about your own writing:

• Am I only considering evidence that supports my preconceptions?
• Is my argument expressed clearly and backed up with credible sources?
• Would I be convinced by this argument coming from someone else?

If you want to know more about ChatGPT, AI tools , citation , and plagiarism , make sure to check out some of our other articles with explanations and examples.

• ChatGPT vs human editor
• ChatGPT citations
• Is ChatGPT trustworthy?
• Using ChatGPT for your studies
• What is ChatGPT?
• Chicago style
• Paraphrasing

 Plagiarism

• Types of plagiarism
• Self-plagiarism
• Avoiding plagiarism
• Academic integrity
• Consequences of plagiarism
• Common knowledge

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Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.

Like information literacy , it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.

Critical thinking skills include the ability to:

You can assess information and arguments critically by asking certain questions about the source. You can use the CRAAP test , focusing on the currency , relevance , authority , accuracy , and purpose of a source of information.

Ask questions such as:

• Who is the author? Are they an expert?
• How do they make their argument? Is it backed up by evidence?

A credible source should pass the CRAAP test  and follow these guidelines:

• The information should be up to date and current.
• The author and publication should be a trusted authority on the subject you are researching.
• The sources the author cited should be easy to find, clear, and unbiased.
• For a web source, the URL and layout should signify that it is trustworthy.

Information literacy refers to a broad range of skills, including the ability to find, evaluate, and use sources of information effectively.

Being information literate means that you:

• Know how to find credible sources
• Use relevant sources to inform your research
• Understand what constitutes plagiarism
• Know how to cite your sources correctly

Confirmation bias is the tendency to search, interpret, and recall information in a way that aligns with our pre-existing values, opinions, or beliefs. It refers to the ability to recollect information best when it amplifies what we already believe. Relatedly, we tend to forget information that contradicts our opinions.

Although selective recall is a component of confirmation bias, it should not be confused with recall bias.

On the other hand, recall bias refers to the differences in the ability between study participants to recall past events when self-reporting is used. This difference in accuracy or completeness of recollection is not related to beliefs or opinions. Rather, recall bias relates to other factors, such as the length of the recall period, age, and the characteristics of the disease under investigation.

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Critical Thinking: an essential skill

Jean-Marie Buchilly

It's Your Turn

A quite formal definition of what critical thinking is:

“Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.” — The Foundation for Critical Thinking

Another one that is the much shortest I could find is the one below:

“Critical thinking is the analysis of facts to form a judgment” — Wikipedia

Anyway, both refer to the same process and skills.

And “Critical Thinking: Proven Strategies to Improve Decision Making Skills, Increase Intuition and Think Smarter” by Simon Bradley and Nicole Price is a short book (less than 100 pages) that I thought was both useful and urgent to read during this troubled time.

Basically, critical thinking is a key skill for problem solving and decision making, which are themselves key competencies for innovators, entrepreneurs, intrapreneurs, leaders and managers.

After exploring the history and highlighting the evolution of critical thinking through the ages, the author focus on different types of statements.

From the least to the most debatable, we have:

• Assumptions (Judgments)

Not all statements have the same value. It’s not true to consider that we can have an opinion about everything.

In fact, as you can see in the list above, the opinion is the weakest card.

As an example, I cannot have an opinion about something that is proven by a fact (eg. “Today is Thursday!”).

And when opinions are opposed to each others, the ones that are backed by knowledge and experiences are the strongest ones.

It’s not as easy as just saying “this is my opinion and it’s my right to have it!” Not every opinions have equal value.

Considering the differences between all these statements, Simon Bradley then describes the attitudes that are important to critical thinking. They are listed below:

• Clarity of Thought
• Fair-Mindness
• Intellectual Courage
• Intellectual Humility
• Perseverance
• Independence

They all make part of the equation, however the two that I wrote in bold are the ones essential to challenge the mainstream thinking.

Challenging the mainstream thinking is one of the mission of critical thinkers. They are the ones who are not limited in their analysis of the situation by a short term view that only allows to perceive the obvious consequences, especially when ones undergo a bias related to ones emotions. On the opposite, they have the ability to to get an holistic view, considering the short, middle and long term challenges, and their complicated and complex interconnections, at the same time with a capacity to overcome the emotional debate.

That is what critical thinkers do.

Without courage, they would not ask the questions that could first sound unethical, amoral or outrageous. But asking a question with the right mindset (eg. to get a better view of the whole situation) cannot be outrageous, only the answer can be.

Without independence, they would propose non-credibles answers to the questions they raise.

The conditions for critical thinking are not as frequently met as one might think. Because in general, the population tends to be satisfied with general information proposed by the traditional media. The depth of information and knowledge is therefore lacking here. On the side of stakeholders who are much better informed because they benefit from more solid and complete sources, it is often independence that is lacking because they most often have their own interests. As a result, there are places to take for critical thinkers who are both capable of gathering a maximum of high level information and statements while having no particular interest in the subject. These people add lots of value to the debate.

The main curiosity marker we can detect in good critical thinkers is the fact that they ask tons of questions. They do it to eliminate vagueness and confusion and also to streamline their thinking.

The best devising questions:

• Enhance our knowledge
• Enhance our comprehension of the situation
• Enable us to analyze and evaluate the facts at our disposal
• Help in synthesizing the information available for use

Considering all the skills needed to be a good critical thinker, it would be tempting to consider that critical thinking is a hindrance to creativity. This is totally wrong. If we believe this, we would be implying that creative people are basically illogical and shallow as well. On the opposite, creative poeple are vastly informed and often critical. You often don’t get “thinking out of the box” by whirling aimlessly like the wind — it is usually after a session of critical thinking.

Another false belief about critical thinkers would be that they do not have their own worldviews and beliefs. Again, this is false. They tell themselves stories and make assertions. They just put them in perspective in order to transform their opinions in more solid statements. They do not immediately take decisions or act on their own ideas or on what they hear or read in the last article, but they use these elements to build a global vision of the situation and make the most informed decision, supported by solid facts and assumptions.

To give more concrete examples, critical thinking can help defining if the cure is worse than the disease, considering the whole situation.

It can also help finding the opportunities in a difficult situation.

Failure to think critically in this type of situations could prevent us from perceiving the complexity and the full scope of possibilities.

As you can see, the ultimate goal of critical thinkers is not to think (even critically). It is to make the best possible decisions and take informed actions.

PS: Here below you can find a list of questions proposed by the author to evaluate your critical thinking skills:

• You find yourself becoming more reliant on reasoning than emotions
• You are comfortable evaluating issues from varying perspectives and not just your own point of view
• You find yourself with an open mind when other people are telling their side of the story
• You are comfortable accepting new evidence, findings and fresh explanations even after you have undergone a complete phase evaluating an issue
• You are receptive to the idea of re-assessing information already received
• You are able to ignore personal biases as well as prejudices
• You find yourself open to different options
• You do not succumb to the temptation of making hasty conclusions and judgments

Written by Jean-Marie Buchilly

Jean-Marie is an engineer. And a wine lover. And a runner. And the father of a 11 years old girl. And he thinks he can change the world. And he is trying. Now.

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Defining Critical Thinking

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• Sumner’s Definition of Critical Thinking
• Research in Critical Thinking
• Critical Societies: Thoughts from the Past

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Critical Thinking and Decision-Making  - What is Critical Thinking?

Critical thinking and decision-making  -, what is critical thinking, critical thinking and decision-making what is critical thinking.

Critical Thinking and Decision-Making: What is Critical Thinking?

Lesson 1: what is critical thinking, what is critical thinking.

Critical thinking is a term that gets thrown around a lot. You've probably heard it used often throughout the years whether it was in school, at work, or in everyday conversation. But when you stop to think about it, what exactly is critical thinking and how do you do it ?

Watch the video below to learn more about critical thinking.

Simply put, critical thinking is the act of deliberately analyzing information so that you can make better judgements and decisions . It involves using things like logic, reasoning, and creativity, to draw conclusions and generally understand things better.

This may sound like a pretty broad definition, and that's because critical thinking is a broad skill that can be applied to so many different situations. You can use it to prepare for a job interview, manage your time better, make decisions about purchasing things, and so much more.

The process

As humans, we are constantly thinking . It's something we can't turn off. But not all of it is critical thinking. No one thinks critically 100% of the time... that would be pretty exhausting! Instead, it's an intentional process , something that we consciously use when we're presented with difficult problems or important decisions.

Improving your critical thinking

In order to become a better critical thinker, it's important to ask questions when you're presented with a problem or decision, before jumping to any conclusions. You can start with simple ones like What do I currently know? and How do I know this? These can help to give you a better idea of what you're working with and, in some cases, simplify more complex issues.  

Real-world applications

Let's take a look at how we can use critical thinking to evaluate online information . Say a friend of yours posts a news article on social media and you're drawn to its headline. If you were to use your everyday automatic thinking, you might accept it as fact and move on. But if you were thinking critically, you would first analyze the available information and ask some questions :

• What's the source of this article?
• Is the headline potentially misleading?
• What are my friend's general beliefs?
• Do their beliefs inform why they might have shared this?

After analyzing all of this information, you can draw a conclusion about whether or not you think the article is trustworthy.

Critical thinking has a wide range of real-world applications . It can help you to make better decisions, become more hireable, and generally better understand the world around you.

/en/problem-solving-and-decision-making/why-is-it-so-hard-to-make-decisions/content/

Frontiers and Advances in Positive Learning in the Age of InformaTiOn (PLATO) pp 89–106 Cite as

A Three-Level Model for Critical Thinking: Critical Alertness, Critical Reflection, and Critical Analysis

• Fritz K. Oser 2 &
• Horst Biedermann 3  
• First Online: 03 January 2020

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Based on the idea of measuring Critical Thinking (CT) through a new performance test (the kidney story) we outline why critical thinking is not the same skill as logical or general thinking. After proposing a three-level model of CT we analyze strengths and weaknesses and of the US and European tradition. We finally propose—on the basis of looking to some classical tests on CT—a test form in which the student has to question, deconstruct, model, and rebuild societal problems from a moral, ethos-oriented, political, and religious point of view. The generic part of CT thus relates to questions going beyond the knowing of the technical and functional side of a modern societal problem. CT is seen as an authentic daily-life-oriented and comprehensive competence that exceeds pure intelligence and fluid thinking.

• Critical thinking
• Critical alertness
• Performance test
• Critical thinking and social domains

And don’t criticize What you can’t understand… (From Bob Dylan: The times they are a-changin’)

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Oser, F.K., Biedermann, H. (2019). A Three-Level Model for Critical Thinking: Critical Alertness, Critical Reflection, and Critical Analysis. In: Zlatkin-Troitschanskaia, O. (eds) Frontiers and Advances in Positive Learning in the Age of InformaTiOn (PLATO). Springer, Cham. https://doi.org/10.1007/978-3-030-26578-6_7

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Chapter 17 Sections

• Section 1. An Introduction to the Problem-Solving Process
• Section 3. Defining and Analyzing the Problem
• Section 4. Analyzing Root Causes of Problems: The "But Why?" Technique
• Section 5. Addressing Social Determinants of Health and Development
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• Main Section

What is critical thinking?

Why is critical thinking important, who can (and should) learn to think critically, how do you help people learn to think critically.

Suppose an elected official makes a speech in which he says, "The government doesn't need to be involved in cleaning up pollution from manufacturing. Business can take care of this more efficiently." What's your reaction?

There are a lot of questions you can be asking here, some of which you may already know the answers to. First, what are the assumptions behind this person's statement? How does he view the job of government, for instance? What's his attitude toward business? Does he believe pollution is a real threat to the environment?

Next, you might want to consider the official's biases. What party does this politician belong to, and what's that party's position on pollution regulation? What state is he from -- one with a lot of industry that contributes to acid rain and other pollution? What's his voting record on environmental issues? Is he receiving contributions from major polluters? Does he live in a place that's seriously affected by pollution? What does he know about the science involved? (What do you know about the science involved?) Does he have any knowledge or expertise in this area at all?

Finally, you might want answers to some questions about the context of the statement. What's the record of private industry over the last 10 years in cleaning up its own pollution without government intervention, for instance? What does pollution look like now, as compared to before the government regulated it? For that matter, when did government regulation start? What effect did it have? Perhaps even more important, who will benefit if these ideas are accepted? Who will lose? What will the result be if things are changed in the direction this politician suggests? Are those results good for the country?

If you ask the kinds of questions suggested here when you see new information, or consider a situation or a problem or an issue, you're using critical thinking. Critical thinking is tremendously important in health, human service, and community work because it allows you to understand the actual issues involved, and to come up with an approach that is likely to address them effectively.

There are many definitions of critical thinking. Some see it as a particular way of handling information. Others look at it as a specific set of skills and abilities. People interested in political and social change see it as challenging and providing alternatives to the generally accepted beliefs and values of the power structure. They're all right to an extent: critical thinking is all of these things, and more.

Critical thinking is the process of examining, analyzing, questioning, and challenging situations, issues, and information of all kinds. We use it when we raise questions about:

• Survey results
• Personal comments
• Media stories
• Our own personal relationships
• Scientific research
• Political statements
• And (especially) conventional wisdom, general assumptions, and the pronouncements of authority

Critical thinking is an important tool in solving community problems and in developing interventions or initiatives in health, human services, and community development.

Elements of critical thinking

There are a number of ways to look at the process of critical thinking. Brookfield presents several, with this one being perhaps the simplest.

• Problem/goal identification : What is the real issue here?
• Diagnosis: Given all the information we have, what's the best way to deal with this issue?
• Exploration: How do we do what we decided on, and who will make it happen?
• Action: Do it!
• Reflection: Did it work? If so, how can it work better? If not, what went wrong, and how can we fix it? What have we learned here that might be valuable in the future?

Reflection leads you to the consideration of another problem or goal, and the cycle begins again.

Critical thinking involves being thrown into the questioning mode by an event or idea that conflicts with your understanding of the world and makes you uncomfortable. If you allow yourself to respond to the discomfort -- that's partially an issue of personal development -- you'll try to figure out where it comes from, and to come up with other ways to understand the situation. Ultimately, if you persist, you'll have a new perspective on the event itself, and will have broken through to a more critical understanding.

Goals of critical thinking

• Truth: to separate what is true from what is false, or partially true, or incomplete, or slanted, or based on false premises, or assumed to be true because "everyone says so."
• Context: to consider the context and history of issues, problems, or situations.
• Assumptions: to understand the assumptions and purposes behind information or situations.
• Alternatives: to create ways of approaching problems, issues, and situations that address the real, rather than assumed or imagined, factors that underlie or directly cause them -- even when those factors turn out to be different from what you expected.

The word "critical" here means approaching everything as if you were a critic -- questioning it, analyzing it, putting it in context, looking at its origins. The aim is to understand it on its deepest level. "Everything" includes yourself: thinking critically includes identifying, admitting, and examining your own assumptions and prejudices, and understanding how they change your reactions to and your interpretation of information. It also means being willing to change your ideas and conclusions -- and actions -- if an objective view shows that they're wrong or ineffective. This last point is important. In health, human service, and community work, the main goal of thinking critically is almost always to settle on an action that will have some desired effect. Critical examination of the situation and the available information could lead to anything from further study to organizing a strike, but it should lead to something. Once you've applied critical thinking to an issue, so that you understand what's likely to work, you have to take action to change the situation.

Without thinking critically, you're only looking at the surface of things. When you come across a politician's statement in the media, do you accept it at face value? Do you accept some people's statements and not others'? The chances are you exercise at least some judgment, based on what you know about the particular person, and whether you generally agree with her or not.

Knowing whether or not you agree with someone is not necessarily the same as critical thinking, however. Your reaction may be based on emotion ("I hate that guy!"), or on the fact that this elected official supports programs that are in your interest, even though they may not be in the best interests of everyone else. What's important about critical thinking is that it helps you to sort out what's accurate and what's not, and to give you a solid, factual base for solving problems or addressing issues.

Specific reasons for the importance of critical thinking:

• It identifies bias. Critical thinking identifies both the bias in what it looks at (its object), and the biases you yourself bring to it. If you can address these honestly, and adjust your thinking accordingly, you'll be able to see the object in light of the way it's slanted, and to understand your own biases in your reaction to it.

A bias is not necessarily bad: it is simply a preferred way of looking at things. You can be racially biased, but you can also be biased toward looking at all humans as one family. You can be biased toward a liberal or conservative political point of view, or toward or against tolerance. Regardless of whether most of us would consider a particular bias good or bad, not seeing it can limit how we resolve a problem or issue.

• It's oriented toward the problem, issue, or situation that you're addressing. Critical thinking focuses on analyzing and understanding its object. It eliminates, to the extent possible, emotional reactions, except where they become part of an approach or solution.

It's just about impossible to eliminate emotions, or to divorce them from your own deeply-held assumptions and beliefs. You can, however, try to understand that they're present, and to analyze your own emotional reactions and those of others in the situation. There are different kinds of emotional reactions. If all the evidence points to something being true, your emotional reaction that it's not true isn't helpful, no matter how badly you want to believe it. On the other hand, if a proposed solution involves harming a particular group of people "for the good of the majority", an emotional reaction that says "we can't let this happen" may be necessary to change the situation so that its benefits can be realized without harm to anyone. Emotions that allow you to deny reality generally produce undesirable results; emotions that encourage you to explore alternatives based on principles of fairness and justice can produce very desirable results.

• It gives you the whole picture. Critical thinking never considers anything in a vacuum. Its object has a history, a source, a context. Thinking critically allows you to bring these into play, thus getting more than just the outline of what you're examining, and making a realistic and effective solution to a problem more likely.
• It brings in other necessary factors. Some of the things that affect the object of critical thought -- previous situations, personal histories, general assumptions about an issue -- may need to be examined themselves. Critical thinking identifies them and questions them as well.

During the mid-90's debate in the United States over welfare reform, much fuss was made over the amount of federal money spent on welfare. Few people realized, however, that the whole entitlement program accounted for less than 2% of the annual federal budget. During the height of the debate, Americans surveyed estimated the amount of their taxes going to welfare at as much as 60%. Had they examined the general assumptions they were using, they might have thought differently about the issue.

• It considers both the simplicity and complexity of its object. A situation or issue may have a seemingly simple explanation or resolution, but it may rest on a complex combination of factors. Thinking critically unravels the relationships among these, and determines what level of complexity needs to be dealt with in order to reach a desired conclusion.
• It gives you the most nearly accurate view of reality. The whole point of critical thinking is to construct the most objective view available. 100% objectivity may not be possible, but the closer you can get, the better.
• Most important, for all the above reasons, it is most likely to help you get the results you want. The closer you are to dealing with things as they really are, the more likely you are to be able to address a problem or issue with some hope of success.

In more general terms, the real value of critical thinking is that it's been at the root of all human progress. The first ancestor of humans who said to himself, "We've always made bone tools, but they break awfully easily. I bet we could make tools out of something else. What if I tried this rock?" was using critical thinking. So were most of the social, artistic, and technological groundbreakers who followed. You'd be hard pressed to find an advance in almost any area of humanity's development that didn't start with someone looking at the way things were and saying "It doesn't have to be that way. What if we looked at it from another angle?"

The answer here is everyone, from children to senior citizens. Even small children can learn about such things as cause and effect -- a specific event having a specific result -- through a combination of their own experimentation and experience and of being introduced to more complex ideas by others.

Accepted wisdom, perhaps dispensed by a teacher or other authority figure, is, however, often the opposite of critical thinking, which relies on questioning. In many schools, for example, critical thinkers are, if not punished, stifled because of their "disruptive " need to question (and thereby challenge authority). Interestingly enough, the more a school costs -- whether it's a well-funded public school in an affluent community, or an expensive private school -- the more apt it is to encourage and teach critical thinking. Such schools see themselves, and are seen by their students' parents, as trainers of leaders...and leaders need to know how to think.

Many adults exercise critical thinking as a matter of course. Many more know how, but for various reasons -- fear, perceived self-interest, deeply held prejudices or unexamined beliefs -- choose not to. Still more, perhaps a majority, are capable of learning to think critically, but haven't been taught or exposed to the experiences that would have allowed them to learn on their own.

It is this last group that is both most in need of, and most receptive to, learning to think critically. It often includes people with relatively low levels of education and income who see themselves as powerless. Once they grasp the concept of critical thought, it can change their whole view of the world. Often, the experience of being involved in a community initiative or intervention provides the spur for that learning.

Critical thinking requires the capacity for abstract thought. This is the ability to think about what's not there -- to foresee future consequences and possibilities, to think about your own thinking, to imagine scenarios that haven't yet existed. Most people are capable of learning to think in this way, if given the encouragement and opportunity.

Learning to think critically is more often than not a long process. Many people have to learn to think abstractly -- itself a long process -- before they can really apply the principles of critical thinking. Even those who already have that ability are often slowed, or even stopped, by the developmental and psychological -- and sometimes the actual -- consequences of what they're being asked to do. Often, it takes a crisis of some sort, or a series of negative experiences to motivate people to be willing to think in a different way. Even then, developing the capacity for critical thinking doesn't necessarily make things better. It can alter family relationships, change attitudes toward work and community issues, and bring discord into a life where none was recognized before. Learning it takes courage. The point of all this is that, although there's a series of what we believe are effective how-to steps laid out in this section, teaching critical thinking is not magic. The reason we keep using the words "develop" and "process" is that critical thinking, if it takes root, develops over time. Don't be frustrated if many people don't seem to get it immediately: they won't.

Helping others learn to think critically can take place in a classroom -- it's essentially what higher education is all about -- but it's probably even more common in other situations. Community interventions of all kinds provide opportunities for learning, both because participants are usually involved over a period of time, and because they are often experiencing difficulties that make it clear to them that their world view isn't adequate to solve the problems they face. Many are ready to change, and welcome the chance to challenge the way things are and learn new ways of thinking.

By the same token, learning to think critically can be a frightening process. It leads you to question ideas that you may have taken for granted all your life, and to challenge authority figures whom you may have held in awe. It may push you to tackle problems you thought were insoluble. It's the intellectual equivalent of bungee jumping: once you've leaped off the bridge, there's no going back, and you have to trust that the cord will hold you.

As a result, facilitating critical thinking -- whether formally or informally -- requires more than just a knowledge of the process. It demands that you be supportive, encouraging, and honest, and that you act as role model, constantly demonstrating the process as you discuss it.

There are really three aspects of helping people develop critical thinking: how to be a facilitator for the process; how to help people develop the "critical stance," the mindset that leads them to apply critical thinking all the time; and how to help people learn to apply critical thinking to dealing with community problems and issues.

How to be a critical thinking facilitator

Stephen Brookfield has developed a 10-point guideline for facilitators of critical thinking that focuses both on the learner and the facilitator herself.

• Affirm learners' self-worth. Critical thinking is an intellectual exercise, but it is also a matter of confidence and courage. Learners need to have the self -esteem to believe that authority figures or established beliefs could be wrong, and to challenge them. Facilitators need to encourage that self-esteem by confirming that learners' opinions matter and are worthy of respect, that they themselves have and deserve a voice.
• Listen attentively to learners. Repeat back their words and ideas, so they know they've been heard. What they say can reveal hidden conflicts and assumptions that can then be questioned.
• Show your support for critical thinking efforts. Reward learners for challenging assumptions, even when they're your own.
• Reflect and mirror learners' ideas and actions. That will help to identify assumptions and biases they may not be aware of.
• Motivate people to think critically, but help them to understand when it's appropriate to voice critical ideas and when it's not. The wrong word to the boss could get a learner fired, for example. It's important that he understand the possible consequences of talking about his conclusions before he does it.
• Regularly evaluate progress with learners. Critical thinking involves reflection as well as action, and part of that reflection should be on the process itself.
• Help learners create networks of support. These can include both other learners and others in the community who are learning to or who already practice and support critical thinking.
• Be a critical teacher. Model the critical thinking process in everything you do (particularly, if you're a teacher, in the way you teach), encourage learners to challenge your assumptions and ideas, and challenge them yourself.
• Make people aware of how they learn critical thinking. Discuss learning and thinking styles, intrinsic and extrinsic motivation, learning methods, the role of previous experience, etc. The more conscious you can make people of their preferred ways of learning, the easier it will be for them to understand how they're approaching ideas and situations and to adjust if necessary.
• Model critical thinking. Approach ideas and situations critically and, to the extent possible, explain your thinking so learners can see the process you've used to arrive at your conclusions.

How to encourage the critical stance

Developing the critical stance -- the generalized ability and disposition to apply critical thinking to whatever you encounter -- is a crucial element in teaching critical thinking. It includes recognizing assumptions -- your own and others' -- applying that recognition to questioning information and situations, and considering their context.

Recognize assumptions. Each of us has a set of assumptions -- ideas or attitudes or "facts" we take for granted -- that underlies our thinking. Only when you're willing to look at these assumptions and realize how they color your conclusions can you examine situations, problems, or issues objectively.

Assumptions are based on a number of factors -- physical, environmental, psychological, and experiential -- that we automatically, and often unconsciously, bring to bear on anything we think about. One of the first steps in encouraging the critical stance is to try to make these factors conscious. Besides direct discussion, role plays, discussions of hypothetical or relatively non-threatening real situations, and self -revelation on the facilitator's part ("Some of my own assumptions are...") can all be ways to help people think about the preconceptions they bring to any situation.

Sources of assumptions are numerous and overlapping, but the most important are:

• Senses. The impact of the senses is so elemental that we sometimes react to it without realizing we're doing so. You may respond to a person based on smells you're barely aware of, for instance.
• Experience. Each of us has a unique set of experiences, and they influence our responses to what we encounter. Ultimately, as critical thinkers, we have to understand both how past experience might limit our thinking in a situation, and how we can use it to see things more clearly.
• Values. Values are deeply held beliefs -- often learned from families, schools, and peers -- about how the world should be. These "givens" may be difficult even to recognize, let alone reject. It further complicates matters that values usually concern the core issues of our lives: personal and sexual relationships, morality, gender and social roles, race, social class, and the organization of society, to name just a few.
• Emotion. Recognizing our emotional reactions is vital to keeping them from influencing our conclusions. Anger at child abusers may get in the way of our understanding the issue clearly, for example. We can't control whether emotions come up, but we can understand how we react to them.
• Self interest. Whether we like it or not, each of us sometimes injects what is best for ourselves into our decisions. We have to be aware when self interest gets in the way of reason, or of looking at the other interests in the situation.
• Culture. The culture we grew up in, the culture we've adopted, the predominant culture in the society -- all have their effects on us, and push us into thinking in particular ways. Understanding how culture acts upon our and others' thinking makes it possible to look at a problem or issue in a different light.
• History. Community history, the history of our organization or initiative, and our own history in dealing with particular problems and issues will all have an impact on the way we think about the current situation.
• Religion. Our own religious backgrounds -- whether we still practice religion or not -- may be more powerful than we realize in influencing our thinking.
• Biases. Very few of us, regardless of what we'd like to believe, are free of racial or ethnic prejudices of some sort, or of political, moral, and other biases that can come into play here.
• Prior knowledge. What we know about a problem or issue, from personal experience, from secondhand accounts, or from theory, shapes our responses to it. We have to be sure, however, that what we "know" is in fact true, and relevant to the issue at hand.
• Conventional wisdom. All of us have a large store of information "everybody knows" that we apply to new situations and problems. Unfortunately, the fact that everybody knows it doesn't make it right. Conventional wisdom is often too conventional: it usually reflects the simplest way of looking at things. We may need to step outside the conventions to look for new solutions.

This is often the case when people complain that "common sense" makes the solution to a problem obvious. Many people believe, for instance, that it is "common sense " that sex education courses for teens encourage them to have sex. The statistics show that, in fact, teens with adequate sexual information tend to be less sexually active than their uninformed counterparts.

Examine information for accuracy, assumptions, biases, or specific interests. Helping learners discuss and come up with the kinds of questions that they need to subject information to is probably the best way to facilitate here. Using current examples -- comparing various newspaper and TV news stories, for instance, to see what different aspects are emphasized, or to see how all ignore the same issues -- can also be a powerful way of demonstrating what needs to be asked. Some basic questions are:

• What's the source of the information? Knowing where information originates can tell you a lot about what it's meant to make you believe.
• Does the source generally produce accurate information?
• What are the source's assumptions about the problem or issue? Does the source have a particular interest or belong to a particular group that will allow you to understand what it believes about the issue the information refers to?
• Does the source have biases or purposes that would lead it to slant information in a particular way, or to lie outright? Politicians and political campaigns often "spin" information so that it seems to favor them and their positions. People in the community may do the same, or may "know" things that don't happen to be true.
• Does anyone in particular stand to benefit or lose if the information is accepted or rejected? To whose advantage is it if the information is taken at face value?
• Is the information complete? Are there important pieces missing? Does it tell you everything you need to know? Is it based on enough data to be accurate?

Making sure you have all the information can make a huge difference. Your information might be that a certain approach to this same issue worked well in a similar community. What you might not know or think to ask, however, is whether there's a reason that the same approach wouldn't work in this community. If you investigated, you might find it had been tried and failed for reasons that would doom it again. You'd need all the information before you could reasonably address the issue.

• Is the information logically consistent? Does it make sense? Do arguments actually prove what they pretend to prove? Learning how to sort out logical and powerful arguments from inconsistent or meaningless ones is perhaps the hardest task for learners. Some helpful strategies here might include mock debates, where participants have to devise arguments for the side they disagree with; analysis of TV news programs, particularly those like "Meet the Press," where political figures defend their positions; and after-the-fact discussions of community or personal situations.

Just about anyone can come up with an example that "proves" a particular point: There's a woman down the block who cheats on welfare, so it's obvious that most welfare recipients cheat. You can't trust members of that ethnic group, because one of them stole my wallet. Neither of these examples "proves" anything, because it's based on only one instance, and there's no logical reason to assume it holds for a larger group. A former president was particularly fond of these kinds of "proofs", and as a result often proposed simplistic solutions to complex social problems. Without information that's logically consistent and at least close to complete, you can't draw conclusions that will help you effectively address an issue.

• Is the information clear? Do you understand what you're seeing?
• Is the information relevant to the current situation? Information may be accurate, complete, logically consistent, powerful...and useless, because it has nothing to do with what you're trying to deal with.

An AIDS prevention initiative, for instance, may find that a particular neighborhood has a large number of gay residents. However, if the HIV-positive rate in the gay community is nearly nonexistent, and the real AIDS problem in town is among IV drug users, the location of the gay community is irrelevant information.

• Most important, is the information true? Outright lies and made-up "facts" are not uncommon in politics, community work, and other situations. Knowing the source and its interests, understanding the situation, and being sensibly skeptical can help to protect learners from acting on false information.

Consider the context of the information, problem, or issue. Examining context, in most instances, is easier to approach than the other elements of the critical stance. It involves more concrete and "objective" information, and, at least in the case of community issues, it is often information that learners already know.

Facilitating techniques might include brainstorming to identify context elements; discussing how context issues affected real situations that learners are familiar with; and asking small groups of learners to make up their own examples. The real task is making sure that they include as many different factors as possible. Some areas to be examined in considering a community issue, for instance, are:

• The nature of the community. A big city is likely to present different solutions to a problem than a small town, and both differ from a suburb or a rural area. Understanding the resources, challenges, and peculiarities of a community is important to addressing its issues.
• The social situation. A community may be divided among several mutually hostile ethnic or political groups, or among groups that simply have different ideas about how things should be done. There may be class, race, or other issues to deal with.
• Individuals. Individuals can strongly influence the workings of a community, often in ways that aren't immediately apparent. People can spread or squelch rumors, create harmony or dissension, lead others toward constructive solutions or toward disorganization and ineffectiveness.
• Cultures. Cultures -- which can be based on ethnic ties, religion, class, or other factors (think of the jocks, preppies, punks, skaters, and other groups in a high school)-- can create alliances or divisions, and heavily influence how different groups see an issue and its implications.
• Physical environment. A trash-filled, crumbling urban neighborhood can breed despair and fear. Changing the face of that neighborhood may do a great deal to change the situation of people who live there as well, giving them hope and pride of ownership, as well as diminishing violence and crime by increasing light and accessibility. The role of the physical environment is one that has to be examined in any community issue.
• History. It's crucial to examine the history of a problem or issue, as well as efforts to deal with it. The perfect solution you just came up with may have already ended in disaster five years ago. The person you depend on to explain the situation may have been prominent on one side of a huge conflict, and her presence may alienate anyone who was on the other. Bad feelings over real or perceived slights or dishonesty can persist for decades, and if you don't know about them, they can suddenly rise up, seemingly out of nowhere. Not only getting the history, but getting it from a number of different perspectives, is necessary to success in dealing with any problem or issue.

A group trying to bring public transportation to a rural area started by arranging a meeting between the select boards of the towns involved and the local regional transit authority. What the group didn't know was that, several years before, a small non -profit transportation company -- the chair of whose board was a revered local figure -- had been put out of business through some shady dealings by the regional transit authority. As a result, the towns refused to deal with the transit authority, even though it was now under completely new -- and ethical -- management.

• The interests involved. If there is a conflict, what are the needs and aims of the various factions? Who stands to gain, and who stands to lose? What are the best interests of the community -- or can you determine that at all?

Facilitating problem solving using critical thinking

Actually using critical thinking to solve problems and address issues is, of course, the reason for learning it. Brookfield suggests one problem-solving sequence that can be used in many situations involving community issues. Once people have learned the critical stance, they can apply its principles using this sequence.

Identify the assumptions behind the problem. By asking people to clarify their statements, and by probing for specifics, you can help them look at what is behind their thinking. Some clarifications that you can ask for, accompanied by some of the questions you might ask:

There are actually two sets of assumptions that are important here. One is the set of assumptions that each of us brings to any problem or information, those described above under "How to encourage the critical stance." The other is the set of assumptions about the particular problem -- what the situation is, what the problem consists of, what a solution would look like, and how to achieve that solution. In fact, those two sets of assumptions are inseparable, and both need to be considered. The emphasis in what follows is on the second set of assumptions, that which refers to the problem itself. One of the assumptions of the Tool Box, however, is that you'll deal with both in a real situation.

• The current situation. What exactly do you mean when you say things are bad? What things? How are they bad? What would be happening if they were good?
• The problem itself. Can you describe another situation in which the same problem existed? What was happening then? Can you describe a situation in which things were good, and the problem didn't exist? What was happening then? What are the differences here?
• Potential solutions to the problem. If we were able to solve this problem, what would that look like? What would be happening? Who would be involved?
• Actions that would lead to the solution. How would what you're suggesting lead to a solution? What exactly would happen?

Challenge those assumptions. Once you've clarified the assumptions, everyone needs to question them.

• The current situation. Are you sure that everything is bad? Are there good aspects to the situation? What about it specifically do you think is bad? Could that be interpreted in another way? Who might interpret it differently? Why? Are we even looking at the right aspects of the situation? Are we missing something important?
• The problem itself. What exactly is the problem we're talking about? Are you sure that's really the problem? Could the problem be defined in another (this other) way? What's the actual concern here?
• Potential solutions to the problem. What are the actual results we need here? (If we're trying to reduce the teen pregnancy rate in the community, for instance, are we aiming to provide a particular number of teens with information about birth control? With condoms and other birth control devices? Or are we aiming at an actual reduction in the teen pregnancy rate within a particular period...say, two years?)
• Actions that would lead to the solution. Would what you're proposing actually accomplish what you expect it to? Would it really make a difference even if it did?

Imagine alternatives to what you started with. There are a number of ways you can construct different ways to deal with the problem. Two are:

• Brainstorming. Everyone comes up with every alternative she can think of, no matter how silly it seems at the time. After all the ideas have been recorded, the group goes through them, and sorts out what seems worth pursuing. Sometimes the ideas that seem totally silly at first turn out to be the most valuable, which is why it's important to encourage people to blurt out whatever they think of.
• Starting with the ideal endpoint. Determine what everything would look like if the ideal solution were achieved, then work backward from there to understand what you'd have to do to get there.

In dealing with teen pregnancy again, for instance, the ideal might be a community in which there were no teen pregnancies because all youth clearly understood the physical and emotional consequences of having sex; had adequate sexual information and access to birth control; and felt valued and empowered enough to respect one another and to maintain control over their own bodies. You might determine that that situation would require that there be sex education available through a variety of sources; that condom dispensers should be placed in various public places, and that pharmacies and convenience stores display birth control devices in ways attractive to teens; that every teen needed to have at least one caring adult in his or her life; and that the community valued youth and their contributions. In order for those things to happen, there might need to be a community education process, mechanisms for youth to become more integrated into the community as contributing members, as well as a group of adult volunteers who would act as mentors and friends to youth who had no positive relationships with adults. In order for those things to happen, you'd need to identify teens who had no positive adult role models...etc. If you followed all of this through to its end, you'd have a picture of the ideal solution to the problem and a road map telling you how to get there.

Critique the alternatives. Develop criteria on which you can judge the alternative solutions you've come up with. Some possibilities:

• Effectiveness
• Feasibility
• Consistency with community needs
• Consistency with the values of the group
• Inclusiveness

Once you've selected criteria, another critical thinking exercise is to decide which are most important. In a particular situation, cost might have to be the most important factor. In another, you may be able to weight costs, benefits, and effectiveness together. In others, other criteria may be weighted more heavily.

Finally, apply the criteria to the alternatives you've come up with, and decide which is most likely to achieve the results you want.

Reframe the problem and solution. At this point, learners have come up with a solution. The point of reframing is to look at the problem in the light of all the work they've done. They've perhaps discovered that it was different from what they first thought, or that they needed to view it differently. Reframing solidifies that mindset, and ensures that they approach the problem as they've found it to be in actuality, rather than as they initially saw it.

• The current situation. Start by restating the current situation, as you understand it after critical analysis, in the clearest and most specific terms possible.
• The problem itself. Restate the actual problem as you now understand it.
• Potential solutions to the problem. Explain what changes a solution would bring about, and what things would be like with the problem solved.
• Actions that would lead to the solution. Lay out the alternative you've arrived at.

By and large, people learn critical thinking best when they're approaching real problems that affect their lives in real ways. That's one reason why community interventions and initiatives provide fertile ground for the development of critical thinking.

Critical thinking is a vital skill in health, human service, and community work. It is the process of questioning, examining, and analyzing situations, issues, problems, people (in hiring decisions, for instance) and information of all kinds -- survey results, theories, personal comments, media stories, history, scientific research, political statements, etc.-- from every possible angle. This will give you a view that's as nearly objective as possible, making it more likely that you'll be able to interpret information accurately and resolve problems and issues effectively.

Teaching critical thinking, whether formally or informally, requires a supportive and encouraging presence, and a willingness to both model and be the subject of critical analysis. It entails teaching the critical stance -- how to recognize and analyze your own and others' assumptions, question information, and examine the context of any information, situation, problem, or issue. Finally, it requires helping people to apply the critical stance to a problem and learn how to come up with a solution that is effective because it addresses the real issues involved. Once learners can do that, they're well on their way to successfully addressing the concerns of their communities.

Online Resources

Critical Thinking Across the Curriculum . Internal and external resources on critical thinking from Longview Community College, Lee's Summit, MO.

The Foundation for Critical Thinking .  Articles, references, links, lesson plans, etc. School and college oriented, but lots of good general material.

Mission Critical , an on-line course in critical thinking from an English professor at San Jose (CA) State University.

Print Resources

Brookfield, Stephen D. (1991). Developing Critical Thinkers, Reprint Edition, San Francisco, CA: Jossey-Bass, Inc.

Brookfield, Stephen D. (2012). Teaching for Critical Thinking, San Francisco, CA: John Wiley & Sons, Inc.

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Analytical thinking: what it is and why it matters more than ever

January 30, 2024

Welcome back to our high-impact workplace skills series. We really enjoyed the conversations happening in the comments section of last week’s top skills of 2023 issue, so be sure to check those out for perspectives and insights from fellow members of our Career Chat community.

One comment that’s been on our mind came from Kendra Vivian Lewis , who asked some thoughtful questions about the comparative importance of workplace and technical skills and if there’s a way to forecast which skills will be important in the coming years. This week’s topic—analytical thinking, the number one skill on the list—is a great example as we explore both questions. Be sure to read to the end to discover a special offer that we’re running on Coursera Plus subscriptions through September 21.

What it means to think analytically

Analytical thinking involves using data to understand problems, identify potential solutions, and suggest the solution that’s most likely to have the desired impact. It’s similar to critical thinking skills , which are the skills you use to interpret information and make decisions.

In order to succeed as a strong analytical thinker, you also need to have strong technical skills in your field. Remember: technical skills describe the things you do, while workplace skills describe how you do them. So your workplace skills, used effectively, enhance your technical skills. That’s why we consider them to be high-impact—they stand to make your work more impactful than it would have been had you only used your technical skills.

To illustrate, suppose you just started a job as a data analyst for a think tank focused on climate change, and you’ve been tasked with raising community engagement in future climate action efforts.

You might start with your technical data analysis skills as you gather data from a few sources. Then, you’ll use your analytical thinking skills to determine the validity of each data source. Perhaps you’ll discard one source when you learn the research was funded by a firm with a financial stake in fossil fuel consumption. Your technical skills lead again as you clean data, and then you’ll return to your analytical thinking skills to analyze and interpret your findings, ultimately leading to your recommendation to start a transparency campaign to display water and energy use in the community.

Tell us in the comments: How do you use your analytical skills alongside your technical skills in your day-to-day work?

Why analytical skills top the list

To develop the skills list, the World Economic Forum surveyed 800+ global employers on their views of skills and jobs over the next five years, so this list is forward-looking. According to the Future of Jobs Report , employers believe analytical thinking skills will grow in importance by 72 percent in this timeframe.

The reason employers are keen to hire employees with strong analytical thinking skills is informed by trends in automation and technological advancements. While technical data analysis becomes easier with automation, reasoning and decision-making automation is advancing at a much slower pace—meaning employers anticipate that, within the next five years, we’ll have a wealth of data at our fingertips and too few people to interpret what that data means.

Where to begin

For a crash course in critical thinking, try the University of California, Davis’s Critical Thinking Skills for the Professional course. You can finish this beginner-level course in about 7 hours.

For a more comprehensive exploration into analytical thinking , try Duke University’s Introduction to Logic and Critical Thinking Specialization . Over four courses, you’ll learn how to effectively argue and reason using logic.

For a technical process to guide your analytical thinking, try Google’s Data Analytics Professional Certificate . Ground your analytical thinking skills in technical know-how in this eight-course series.

Interested in multiple programs? Don’t miss this special offer!

Through September 21, we’re offering $100 off annual Coursera Plus subscriptions for new subscribers. With this offer, you’ll pay less than $25 per month for one year of access to 6,100 courses, Specializations, and Professional Certificates with flexibility to start new courses and move between programs at your pace.

This offer is a great choice if you are frequently tempted to enroll in multiple courses at once or plan to complete a Specialization or Professional Certificate within the next year. If that sounds like you, take a closer look at the offer and the Coursera Plus course catalog.

That’s all for this week! Join us next week to talk about motivation and self-awareness skills.

Keep reading

• Job search tips for a career change
• The latest courses, Specializations, and Professional Certifications in UX design, generative AI, real estate, and cybersecurity
• Job search tips for entry-level roles

Pasco-Hernando State College

Finding and Evaluating Sources (Critical Analysis)

• Traditional Sources
• Electronic Library Resources
• Internet Sources
• Synthesizing Information from Sources
• MLA Documentation
• APA Documentation
• Writing a Research Paper

Related Pages

• The Writing Process
• Proving the Thesis - General Principles
• Proving the Thesis - Logic
• Proving the Thesis - Logical Fallacies and Appeals

Fi nding Sources

Identify the research question.

Before you can start research, you must first identify the research question. Your instructor will either assign a specific research question or a research topic.

If you are assigned a question or can select from a list of questions, it is easy to identify your question. You can start with  focused  research looking for sources that would help to answer the question. Don’t select a source by the title. It is critical that you read through possible sources to see if they will help with the question. For example, if your question asks whether pesticides in foods are harmful, don’t just select any source that has to do with pesticides. There are pesticide issues with the environment, for example, that have nothing to do with this question.

If you are assigned a topic, you will start with  exploratory  research. Exploratory research is where you explore various aspects of the topic and after learning something about it, you focus on a particular question of your choice. This is called narrowing the topic. Then, your research becomes focused research on that particular question.

Either way, before doing research for a research paper, you must identify a research question. The research question is critical since all of the content of the research essay follows from the question.

Primary and Secondary Sources

A primary source is where the author is presenting his or her own information either based on professional knowledge or research. This is the best type of source to use when conducting research.

A secondary source is where the author is reporting information presented from other people. This means that there could be a misunderstanding or misinterpretation or the information, and it is not considered as reliable as primary sources.

Traditional Sources, Electronic Library Resources, and Internet Sources

Traditional sources are tangible sources as existed before the Internet: books, newspapers, magazines, film, interviews,  works of art, and so on. Then with the Internet, a new source of information has become available in the website. In addition, many traditional sources have been collected and made available online. Electronic Library Resources (available to PHSC students through a link in Canvas) provides many originally hard-print sources electronically.

Evaluating Sources

General considerations.

It is important to first make sure you understand your assignment as to how many sources are required and any restrictions on where they may be from.  There might be a requirement to use at least one type of specific source such as a book, article from a journal, magazine, or newspaper, or page from a website. 

Don't simply select a source by the title. You must review to be sure the content will help answer the question. For example, if your research question or topic is about how the moon affects earth's tides, the source must have information on that specific area. Some articles on the moon might talk about space exploration or its geography or its climate, none of which will help with a paper about tides.

Once you have screened for appropriateness, the content should be reviewed for reading level. If the paper is too technical, it may not be understandable enough to work with. You should be able to understand it and make notes on the main points.

Then, a closer look is needed.  

Critical Analysis

The term critical doesn't always mean finding the problems or being judgmental.  A movie critic, for example, reviews a movie for strengths and weaknesses. We have to be critics ourselves when we review our own writing and when we review information for our papers. We shouldn't just believe everything we see, hear, or read. We have to be particularly careful when that information comes from a purportedly legitimate source. We generally think that documentaries have true and accurate information, but sometimes they don't present all viewpoints or are biased towards one.  Here are a number of considerations:

• credibility  – is the source believable?; is the source created by a person or organization that knows about the subject matter.  Determining credibility of online sources can be a challenge since it is not always clear who created or published what we are looking at. If a person is named as author, is that person a professional in the field?
• facts  – does the source include the truth; is information based on evidence
• opinion  –  is the content a personal evaluation of the author and not necessarily based on specific, accurate, or credible evidence?
• evidence  – is there support such as examples, statistics, descriptions, comparisons, and illustrations; evidence is also called proof, support, or supporting evidence.  
• bias and slanted language  – is there a  preference for one side over the other; is there slanted language which is language shows a bias or preference for one position over another.
• tone  – what is the tone?  Words can be used to create a feeling such as a happy tone or sarcastic tone or angry tone. Tone can be used to persuade.
• stereotype  – the generalization that a person or situation in a certain category has certain attributes such as because a person is old, he or she is a bad drive. Stereotyping is faulty logic.
• preconceived ideas  – ideas that we already have; in doing research, it is very important to look for sources that present all of the perspectives on a question, not just those that prove what we think we know.
• logic  – evidence should be evaluated for logic; does the evidence have any logical fallacies.  
• valid argument  – is the argument valid? A valid argument is based on logical analysis of information, but if the information is not accurate, the conclusion is not necessarily true.
• sound argument  – an argument based on a syllogism that has accurate major and minor premises. An argument can be sound, but it is not necessarily true since the information on which it is based may not be accurate.
• Toulmin Logic  – a form of logic that uses claim, grounds, and warrant for analyzing the logic of an argument.
• logical fallacies (flawed logic) – faulty logic; includes sweeping generalization, argument to the person (ad hominem), non sequitur, either/or fallacy, begging the question, and bandwagon argument.  
• appeals  – use of language to sway the reader by appealing to emotions, logic, or ethics. 
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7.5: Logical Analysis using Truth Tables

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Truth tables, which we introduced in the last section, are primarily useful in a different way. Instead of just using them to tell us what the different logical operators mean, we can use them to do some in depth analysis of the logical form of a statement, a set of statements, or an inference.

What’s a logical analysis? A logical analysis is a set of things we can do to learn something about a particular logical structure. The statement “I’ll go if you don’t go or if we can get a babysitter and it’s not too expensive for both of us to go” has a particular logical form—something like

[(B \(\wedge\) ~E) \(\rightarrow\) I] . If we do a logical analysis of this logical form, we’ll find out certain things. For instance: when is this statement true? That is, what must the world be like for this statement to turn out to be true? Is this statement always true? Is it always false? What is its relationship with other similar logical forms like [~(B \(\wedge\) E) \(\rightarrow\) I] ? [~(B \(\wedge\) ~E) \(\rightarrow\) ~I] ? [(B \(\wedge\) E) \(\rightarrow\) ~I] ? Is it possible that all of these statements could be true at the same time? That is, are they consistent? We can find out the answers to all of these questions using Truth Tables.

Conceptually speaking, we’re doing the following when we build a truth table:

1. Collecting all of the possible combinations of truth values and listing them out.

• That is, we’re finding out all of the different ways that T and F can be combined for our atomic sentence letters.

2. Using each set of possible truth values to calculate the output truth value for a complex formula (or a set of complex formulas).

• That is, we’re doing what we did in Computing Truth Values : we’re taking the truth values of atomic sentence letters as an input and calculating the single truth value output.

3. Analyzing the results.

• That is, we’re looking at the resulting output and trying to figure out what it tells us about the logical formulas in question.

The goal is to see what possible conditions of the world (what combinations of true and false for the atomic propositions, each of which either describes the world correctly or incorrectly) give what sorts of truth values for the complex formulas we’re analyzing and then to look for patterns in the outputs to tell us something about the individual statement, the set of statements, or the argument we’re analyzing.

That’s not terribly illuminating, though, about how to actually go about building a truth table. Let’s look more concretely at what to do.

First, I must point out a new notation that will be unfamiliar to you. Well, you will have seen it before lots of times, but not here in logic. The forward slash!

If you see this:

[\(\neg\)[D \(\leftrightarrow\) \(\neg\)(X\(\rightarrow\) (Z \(\bullet\) Q))] \(\vee\) P] / (X\(\rightarrow\) (Z \(\bullet\) Q))]

That means there are two formulas here:

[\(\neg\)[D \(\leftrightarrow\) \(\neg\)(X\(\rightarrow\) (Z \(\bullet\) Q))] \(\vee\) P]

(X\(\rightarrow\) (Z \(\bullet\) Q))]

The forward slash (/) has no logical meaning. It simply separates formulas from one another so we can list them on a single line without it seeming like they are parts of the same formula.

Building a Truth Table

Building a truth table is very straightforward, but that doesn’t mean it’s not going to take some getting used to. Let’s divide it into a series of steps.

Step One: Figure out what size you need

How many unique sentence letters are in the formula or set of formulas? Just count ‘em up, counting each unique letter only once (so two B’s just count as one). Here are some examples:

• [~(B\(\wedge\)E)\(\rightarrow\)I] has 3 unique letters: B, E, and I
• [~(B\(\wedge\)E)\(\rightarrow\)B] has 2 unique letter: B and E
• [~(I\(\wedge\)I)\(\rightarrow\)I] has 1 unique letter: I
• [~(B\(\wedge\)E)\(\rightarrow\)I] / [(B\(\wedge\)E)\(\rightarrow\)~I] have 3 unique letters all together: B, E, and I
• [\(\neg\)[D \(\leftrightarrow\) \(\neg\)(X\(\rightarrow\) (Z \(\bullet\) Q))] \(\vee\) P] / Z / (P \(\bullet\) Q) has 5 unique letters: D, X, Z, Q, and P

Once you’ve figure out this magic number, you plug it into a magic formula: 2 n , where n is the magic number: the number of unique sentence letters in the set of propositions the truth table is for. The result of this mathematical formula is the number of rows you’ll need in your truth table.

Here are a set of truth table sizes:

Notice the pattern? The nice thing is that chances are, your instructor will only assign at most a 4-letter truth table, so 16 rows is the absolute most you’ll usually need to work with. Most instructors stick to 1, 2, and 3-letter truth tables.

The downside of truth tables is that it doesn’t take long before you have to start making tables with 32, 64, 128, 256, 512, 65,536 rows! That’s too much to really make making a truth table worthwhile. This is called the problem of Combinatorial Explosion because all of the combinations that are possible “explode” to astronomical numbers . Nevertheless, they are quite useful for relatively simple problems.

Step Two: Make a truth table

A truth table is a table with a column for each unique sentence letter (usually in the order in which they show up in the formulas you are analyzing) and then a column for each formula you are analyzing. Here are some examples:

Notice how each column gets its own label and there’s a bigger border separating the individual sentence letters (the inputs) from the complex formulas (the outputs). So far so good.

Step Three: Fill in the input side

This step is always the same no matter what the columns labels are. There are basically 3 different tables you’ll make, and for bigger tables you can extrapolate the same basic pattern. Remember that the goal when filling in the input side is to make a list of all of the possible combinations of the two truth values T and F.

So when we only have one unique sentence letter. The two possibilities are that the letter is True and the letter is False:

It’s a bit more complicated if we have two unique sentence letters:

Each row in the table is a possible set of truth values. The possible combos are TT, TF, FT, and FF. See how that works?

Before moving onto an eight row truth table, let’s think about the pattern here. We’ve started on the right nearest the thick line separating the inputs from the outputs and alternated going down: TFTF. For the first table, we alternated too, but just had to do it once: TF. On the second table, we alternated TF going down the R column, and then just repeated so the downward pattern would be TFTF.

Then we moved left and alternated every 2, so the Q column reads TTFF. Why would we do this? Well, we have R is true and R is false, then we need to test for when Q is True with both of these possibilities, and then test again for when Q is false. The result is something like the following:

It may even be helpful to think of it in these terms:

This way, we’re getting all the possible combinations of Q:true, Q:false, R:true, and R:false. If this little explanation is confusing for you, it’s probably best to move on. Perhaps it will make more sense later, and even if it doesn’t, it’s okay since this is sort of conceptual background work rather than something that is vital to understanding the truth table. What you need to understand at minimum is simply that by following this procedure, you’re creating all of the possible combinations of T and F for the atomic sentence letters in the formulas you are trying to analyze using the truth table.

Now let’s look at an eight row table. The first thing we do is start on the rightmost input (sentence letter) column, and alternate T and F every one row. Like so:

Then we move one column to the left and alternate every two . Like this:

Finally, we move to the left again and alternate every four rows so that we double the amount we are alternating by each time we move to the left. Like this:

The result is a truth table that’s totally ready to solve: we have our columns labeled, our rows easily distinguishable, and most importantly we have all of the input side filled in in the standard way. This input side will be basically the same for every truth table. That is, you always follow this pattern:

Start below the rightmost atomic sentence letter and alternate every one row. Then move to the left one column and alternate going down every two rows. Finally, move to the left one last column and alternate going down that column every four rows. Extrapolate for bigger tables.

Solving a Truth Table

There are two methods to solving a truth table—filling in the right side or output side of the truth table. On the Brute Force method, you simply calculate each cell in the table by plugging the truth values of the sentence letters and working your way from the inside out. On the Intuitive method, you use your intuitive understanding of the operators to save yourself some work.

Brute Force Method

The Brute Force method to solving a truth table is simply to plug in the truth value for each individual letter by carrying them over from the input side and then calculating the truth value of each complex proposition given the truth values of the input side. This method is safer, so if you feel lost or lose confidence, then just revert back to the brute force method. It does have two downsides, though: a) It requires a lot more work and so takes more time, and b) it involves more individual steps and so the probably of making a simple mistake increases a bit. The second problem is probably balanced out by the riskiness of the Intuitive Method.

Write the truth value of each * letter * as it appears on the left side of the table under each letter as it appears on the right side

1. Starting with the “inner most” operators (inside the most parentheses) calculate the truth value of the whole relationship.

2. Then work your way out until you’ve calculated the truth value of the main operator.

So, step 0 is to make the truth table, as discussed in Basic Symbolization :

Step 1 is to fill in the truth values on the right side for the sentence letters

Step 2 is to find the inner most operators (the ones with the most amount of parentheses outside of them.

And then solve for those values using the truth tables that we use to define each operator.

Repeat the steps in 2 (working from “in” to “out”) until you’ve solved the truth value of the main operators (the operators that are only inside the outermost parentheses. Keep in mind that if there are no outermost parentheses, then they are implied).

So Q \(\leftrightarrow\) (P\(\vee\)Q) is actually supposed to read: (Q \(\leftrightarrow\) (P\(\vee\)Q))

Repeat in each row:

Then you analyze the results by looking at the right side of the truth table!

Intuitive Method

The Intuitive Method to solving a truth table uses our intuitive understanding of the logical operators and their individual truth tables to save as much work as possible. We can often eliminate half of our work for one column in a single swoop.

It is a faster method, but also increases the chances that we’ll make a mistake by moving too quickly and missing something or being overconfident and ignoring important details.

How does it work? Let’s start with an example and then we’ll look at how it works a bit more.

Starting with the first column, we ask ourselves what we know about the main operator (\(\rightarrow\)). I notice that there is only one atomic letter as the antecedent to this conditional. I know that if the antecedent to a conditional is false the whole conditional is true (since it’s only false when T\(\rightarrow\)F and if it’s F\(\rightarrow\)?, then it’s certainly not T\(\rightarrow\)F!). So I just need to find the rows on which P is false and I know the whole first formula will be True!

Then we solve the rest more-or-less using the Brute Force method. When is (Q\(\leftrightarrow\)P) true? When they’re the same! It’s false if they’re different.

Now we look at the second column. When is a conjunction true? It’s only true in one case: when both conjuncts are true. So if Q is false...? Then the whole second formula (Q \(\wedge\) \(\neg\)(P\(\vee\)Q)) is false.

Now that we know Q is true in the remaining cells of the second output column, we need to ask ourselves when \(\neg\)(P\(\vee\)Q) is true. It says “neither P nor Q are true”. When would that be true? Only when P and Q are both false (remember it would be equivalent to (\(\neg\)P\(\wedge\)\(\neg\)Q)). Are both false in rows 1 or 3? Nopers. So that means that \(\neg\)(P\(\vee\)Q) is false in both of our remaining rows. If just one conjunct is false, the whole conjunction is false. So:

Okay, final column. Another way of doing the intuitive method is simply to understand what the formula says in a more intuitive way than the logical formula. (Q \(\wedge\) \(\neg\)P) says something like “Q is true and P is false.” When we understand it this way, it’s easier to figure out on which row(s) it will be true: we’re looking for the row(s) where Q is true and P is false. Which row is that?

Now we just fill in the rest as false since we know that on those rows P isn’t true while Q is false.

Okay, now that we’ve gone through the intuitive method, let’s take a look at some of the rules which we can use while doing the intuitive method. Here are the rules I use:

• Antecedent F or Consequent T \(\rightarrow\) Whole Implication T
• One disjunct T \(\rightarrow\) Whole Disjunction T
• One conjunct F \(\rightarrow\) Whole Conjunction F
• So “(\(\neg\)P\(\bullet\)Q)” means “P is false and Q is true ”

These four rules can save you loads of time. Just identify which is simplest in a formula (surrounding the main operator ): an antecedent? A consequent? A disjunct? A conjunct? Then you identify when that element fits the intuitive rule and eliminate lots of work!

Analyzing a Truth Table

Classification.

If you’re being asked to analyze a single proposition using a truth table, then you automatically know that the answer will be one of three options. This is called a Classification problem because you’re classifying a single proposition.

1) Tautology/Tautologous : the column under the proposition is filled only with Ts.

A “Logical Truth” or Tautology is a statement that, regardless of how the world turns out to be, will be true. Think of “we’ll either have a democratic president or we won’t have a democratic president.” Even if the world ends and we have no president at all, that disjunctive statement is still true!

Example \(\PageIndex{1}\)

2) Self-Contradiction/Self-Contradictory : the column under the proposition is filled only with F’s.

A self-contradiction is always false no matter how the world ends up being. Think of the example “Kamala Harris is going to be our next president, but luckily we won’t have to have Kamala Harris as our next president.” It doesn’t matter what actually happens in the world, this statement will always be false. It can’t possibly be true because it contradicts itself.

Example \(\PageIndex{2}\)

3) Contingent : the column under the proposition is filled with a mixture of “T”s and “F”s.

Contingent propositions are true or false depending on how the world is. The simplest contingent propositions are atomic propositions, which either describe the world accurately or don’t describe the world accurately.

Example \(\PageIndex{3}\)

If you’re being asked to analyze a set of propositions using a truth table, then you know that the answer will be one of the following four options. This is called a Comparison problem because you’re comparing multiple propositions with one another in order to determine what logical relation holds between them. This is the most complex type of truth table analysis problem.

1) Logically Equivalent : each row of the output side of the truth table is the same on each column. So each row is a homogeneous set of either all T’s or all F’s. Logically equivalent propositions are true and false in exactly the same states of the world: they give the same output every time.

Example \(\PageIndex{4}\)

2) Contradictory : the truth values are the opposite on each row of the output side of the truth table. Notice that, since we only have two truth values (T and F), that means that we could only ever have contradictory pairs of statements. A set of three or more couldn’t possibly be contradictory.

Example \(\PageIndex{5}\)

3) Consistent : Once you’ve determined that a set of statements is neither contradictory nor logically equivalent, you should check to see whether it is consistent. A consistent set of propositions is one where the logical form or structure of those propositions allows them to all be true at the same time. If the world is a certain way, then all of the statements will end up being true. So when testing for consistency, you’re simply looking at the output side of the truth table for a row completely filled with T’s. If you find it, then that set is consistent: they can all be true at the same time.

Example \(\PageIndex{6}\)

4) Inconsistent : The last option is to call a set of propositions inconsistent. If you never find that row filled completely with T’s, then the propositions you are analyzing are inconsistent: they cannot, as a matter of logical structure, be true at the same time, no matter the state of the world.

Example \(\PageIndex{7}\)

Note that a set of logically equivalent propositions is likely to be consistent since it’s likely to have one line on which all propositions are true. Furthermore, every contradictory pair of propositions is inconsistent. For the sake of the class, instructors will often require that you choose only one o f the four options on a multiple-choice quiz or exam, though, so how do you decide?

Easy: just test for these four relations in order. Start by asking “are they logically equivalent?” Then, when you’ve found a line on which they have different truth values, as yourself “could they be contradictory?” Next, if you decide that they aren’t contradictory (or couldn’t be because it’s a set of 3 or more), go hunting for one row on which all of the columns have a T. If you find it, then the set is consistent. If you never find such a row, then the set is inconsistent.

In short : always answer with the strongest answer available. If a set of statements is both logically equivalent and consistent, then the correct answer on a multiple-choice test is “Logically Equivalent” since that’s a stronger claim (it’s a claim about every row rather than just one row).

Testing for Validity

If you’re being asked to analyze an argument or inference , then you know that there are only two possible answers: Valid and Invalid. It’s easier to start by discussing an invalid inference:

1) Invalid : an inference or argument is invalid if you find a row of the output side of the truth table where all of the premises are true, but the conclusion is false. So this, depending on how many propositions make up the argument, will typically be a row that looks like TTTTF, TTF, TF, TTTF, etc. If you find even just one row where the output side looks like this, then you’ve proven that the argument is invalid. I like to think of it as searching for a radioactive row. If you find one with *all* true premises and a false conclusion, then you’ve found a radioactive row and therefore you’ve found out that the argument is invalid.

I like to think of the counterexample line—the line that tells you the inference is invalid— as a sort of “radioactive” line you’re searching for. Think of it like this: you’ve got your Geiger counter and you’re scanning through the truth table for radiation. If you find a radioactive line, then the argument is bad (invalid). If you don’t find a radioactive line, then the argument is clean (valid).

2) Valid : If you look through the whole output side of a truth table and never see a row where *every* premise is true and the conclusion is false, then you’ve found a valid argument. Remember that rows where one premise is false don’t count and rows where it’s all false premises and a true conclusion don’t count. Everything is safe except rows somewhat similar to TTF or TTTTF or the like, depending on how many premises and conclusions there are.

Validity means it’s impossible that the premises would be true while the conclusion is false. So if you find a row (even just one!) in a truth table telling you that if the world is like this (what you see on the input side of the row) then the premises will be true while the conclusion is false. This would never happen with a valid argument, so it follows that the argument you’ve found is an invalid argument.

The Reverse Truth Table Method

What happens if we symbolize or translate an argument and we end up with 5, 6, or more atomic sentence letters? Are we doomed to create a truth table with 32, 64, or more rows? That would be a fate worse than many things!

Fear not, dear student. We have a method for directly testing the validity of an inference without having to build a complete truth table. It’s called the indirect or reverse truth table method. The basic idea is to assign “invalid” truth values to the premises and conclusions, figure out what we need the atomic sentence letters to be in order for those truth values to obtain, and then see if we can consistently apply truth values to the atomic sentence letters in order to create a counterexample (a line with all true premises and a false conclusion). So, basically, we’re looking for that “radioactive” row (TF, TTF, TTTF, etc.) from the complete truth table from the previous section, but instead of building a whole truth table, we’re simply going right to the end and testing if there could be such a row. We’re testing to see if a radioactive row is even possible.

So, let’s walk through an example, and then we’ll come up with a set of steps for doing the reverse truth table method. Here’s the English argument:

If you don’t pass the driver’s license written test, then you won’t have a driver's license (until you are able to pass it). But I don’t have a driver’s license, so that means I didn’t pass the driver’s license written test?

Consider how confusing this would be to someone who has passed the written portion of the test, but hasn’t yet completed the driving test. They did pass the written test, but still don’t have a driver’s license! This is confusing, because this argument is what is called “Affirming the Consequent”. It’s a formal fallacy, or an invalid argument that might appear to be valid. Let’s symbolize it (ignoring the parenthetical):

~W \(\rightarrow\) ~L

\(\therefore\) ~W

Remember that “\(\therefore\)” means “therefore"

In order to run the reverse truth table method of analysis on this argument, we’ll first want to set up as if we are doing the output side of a truth table. We’ll want to give ourselves lots of room to work with:

(~W \(\rightarrow\) ~L) / ~L // ~W

Now, the next thing to do is to assign truth values to each whole proposition so that we have a radioactive row or counterexample row. In this case, there are two premises and a conclusion, so the counterexample row will be TTF:

(~W \(\underset{\bf{T}}{\rightarrow}\) ~L) / ~\(\underset{\bf{T}}{L}\) // \(\underset{\bf{F}}{\sim W}\)

The setup part is done. Now we need to do the hard work: actually work out if we can consistently apply truth values to the atomic sentence letters. We’ll go one step at a time, starting with the conclusion. Why start with the conclusion? It's typically easier to make a sentence false given the truth tables for disjunction, negation, and conditional; so the conclusion generally is the easier place to start. Can you figure out why the rules for these operators make establishing falsehood easier?

(~W \(\underset{\text{T}}{\rightarrow}\) ~L) / ~\(\underset{\text{T}}{L}\) // \(\underset{\text{F}}{\sim \overset{\bf{T}}{W}}\)

The conclusion is false, so W will need to be true since the conclusion is ~W. So then we assign T to every W that appears in the argument:

(~\(\overset{\bf{T}}{W}\) \(\underset{\text{T}}{\rightarrow}\) ~L) / ~\(\underset{\text{T}}{L}\) // \(\underset{\text{F}}{\overset{\bf{F}}{\sim }\overset{\bf{T}}{W}}\)

And then work out how that affects the formulas containing the atomic letters I just assigned truth values to. In this case, if W is true, then ~W is false, and if an antecedent is false, then the whole conditional is true. The main operator is the conditional, and so no problems with the first premise:

(\(\overset{\bf{F}}{\sim }\overset{\bf{T}}{W}\overset{\bf{T}}{\underset{\text{T}}{\rightarrow}}\) ~L) / ~\(\underset{\text{T}}{L}\) // \(\underset{\text{F}}{\overset{\bf{F}}{\sim }\overset{\bf{T}}{W}}\)

What about the second premise? Well, since we haven’t yet been forced to assign a truth value to L, we can assign whatever we want to it, so we’ll make it false! The result will be that ~L is true.

(\(\overset{\bf{F}}{\sim }\overset{\bf{T}}{W}\overset{\bf{T}}{\underset{\text{T}}{\rightarrow}}\) ~L) / \(\overset{\bf{T}}{\sim }\underset{\text{T}}{\overset{\bf{F}}{L}}\) // \(\underset{\text{F}}{\overset{\bf{F}}{\sim }\overset{\bf{T}}{W}}\)

At this point, we’ve symbolized the argument, put it in a row as if we were going to make a truth table out of it, and then tried assigning truth values to the atomic sentence letters to make a radioactive row (in this case TTF). Since we were able to do so without coming across a contradiction, we know that the inference is invalid .

Here’s a sort of algorithm for the reverse truth table method of analysis:

1. Symbolize the inference and write out in a single row using slashes between formulas.

2. Assign truth values to each complete formula such that all premises are true and the conclusion is false.

3. Then calculate the truth value of each atomic sentence letter given the truth value of the whole formula. Start with the most restrictive formulas. If you run into a case where multiple truth values would work, then start a new line for each possibility and test each going forward.

4. Then transfer the atomic sentence letter truth value(s) to the other instances throughout the whole inference (transfer the truth values of, for example, ‘A’ to all other A’s throughout the formula).

5. Then calculate whether it is possible to continue assigning truth values to atomic sentence letters and transferring those values to other instances without running into a contradiction (that is, where a single letter must be both T and F) .

6. If you run into no contradiction , then the inference is invalid because the radioactive row is possible . The process is over.

If you run into a contradiction , then possibly the inference is valid. Complete all lines you’ve started to ensure that there is no possible consistent assignment of truth values. You only need one possible row where there is no contradiction to prove that the inference is invalid; whereas you need to eliminate every possible row that could have true premises and a false conclusion before you can know it’s valid.

Okay, let’s try a more complex one:

Lila: We’re either going home or I’m going home alone unless you both assure me you will drive us home later and will phone the babysitter.

Diego: I can’t assure you that I’ll be sober enough to drive us home later.

Lila: Well, I’m not going home alone and you’re not staying the night here.

Diego: Well, then, I guess either we’re both going home now or we’re getting a motel room.

If we conceive of the whole exchange as one big inference, we can symbolize it the following way:

(H \(\vee\) (I \(\vee\) (A \(\wedge\) P))) / ~A / (~I \(\wedge\) ~S) // (H \(\vee\) M)

Now, we assign truth values to the premises and conclusion so that they’ll be radioactive.

Here, I’ve gone ahead and put them under the main operators:

(H \(\underset{\bf{T}}{\vee}\) (I \(\vee\) (A \(\wedge\) P))) / \(\underset{\bf{T}}{\sim }\)A / (~I \(\underset{\bf{T}}{\wedge}\) ~S) // (H \(\underset{\bf{F}}{\vee}\) M)

Next, I’m going to start looking for some simpler formulas to assign truth values to. I’m eyeing the conclusion and the ~A. The conclusion will only admit of one set of truth values: both H and M must be false for the \(\vee\) to be false. A must be false for ~A to be true.

(H \(\underset{\text{T}}{\vee}\) (I \(\vee\) (A \(\wedge\) P))) / \(\underset{\bf{T}}{\sim }\underset{\text{F}}{A}\) / (~I \(\underset{\text{T}}{\wedge}\) ~S) // (\(\underset{\bf{F}}{H}\underset{\text{F}}{\vee} \underset{\bf{F}}{M}\))

Next, you transfer truth values from the ones you just assigned to all identical letters.

Notice how I’d need the right disjunct (I \(\vee\) (A \(\wedge\) P)) to be true for the first premise to turn out true.

But we already know that A is false from premise 2. So that means the conjunction (A \(\wedge\) P) must be false. Now that we know this, we must conclude that I is true for the first premise to turn out true. So we can conclude that I is true.

(\(\underset{\text{F}}{H} \underset{\text{T}}{\vee} (\underset{\bf{T}}{I} \vee (\underset{\text{F}}{A} \underset{\bf{F}}{\wedge}\) P))) / \(\underset{\text{T}}{\sim }\underset{\text{F}}{A}\) / (~I \(\underset{\text{T}}{\wedge}\) ~S) // (\(\underset{\text{F}}{H}\underset{\text{F}}{\vee} \underset{\text{F}}{M}\))

Now we transfer the new atomic truth value:

Now let’s try to work out that third premise. First we can process the negation on I:

(\(\underset{\text{F}}{H} \underset{\text{T}}{\vee} (\underset{\text{T}}{I} \vee (\underset{\text{F}}{A} \underset{\text{F}}{\wedge}\) P))) / \(\underset{\text{T}}{\sim }\underset{\text{F}}{A}\) / (\(\underset{\bf{F}}{\sim }\underset{\text{T}}{I} \underset{\text{T}}{\wedge}\) ~S) // (\(\underset{\text{F}}{H}\underset{\text{F}}{\vee} \underset{\text{F}}{M}\))

We’ve already got a contradiction!!! Ouch! ~I would have had to be true for (~I \(\wedge\) ~S) to turn out true. Both conjuncts need to be true. But ~I is false according to our assignment of false to I. Bummer dude!

What now? We’ve reached a contradiction! At this point we ask ourselves: “was there any step I made that I wasn’t forced to make?” In this case, no, we didn’t arbitrarily choose true or false for any letter, so every step we took was forced by logic. That means there aren’t any alternative assignments to consider and therefore the radioactive counterexample is impossible . Our inference is valid .

You could have also assigned values to I and S given the third premise, but I chose to finishing the first premise. Either way would’ve resulted in a contradiction. This is not an example of an alternative assignment . We’ll cover alternative assignments below:

Here's a handy flow chart for you:

Let’s try a quick example with alternative assignments possible:

(H \(\underset{\text{T}}{\vee}\) (I \(\vee\) (A \(\wedge\) P))) / \(\underset{\text{T}}{\sim }\)A / (H \(\underset{\text{T}}{\vee}\) M) // (~I \(\underset{\text{F}}{\wedge}\) ~S)

There are many ways for Premise 1 to be true, many ways for Premise 3 to be true, and many ways for the Conclusion to be false (an exception to the generalization I made earlier). So we’re not being forced as much as we were in the previous example. Arguments where the conclusion has more than one way of being false are typically the hardest arguments to do using the reverse truth table method. Hardest, that is, in terms of how much work is involved. Remember that this isn’t difficult in the sense of it being a complicated procedure. It’s not like playing chess. We could program a computer to do this whole method in an afternoon. It does, though, sometimes take a bit of work to work out the answer. Let’s start with what we are forced to do:

(H \(\underset{\text{T}}{\vee}\) (I \(\vee\) (\(\underset{\bf{F}}{A}\) \(\wedge\) P))) / \(\underset{\bf{T}}{\sim }\underset{\text{F}}{A}\) / (H \(\underset{\text{T}}{\vee}\) M) // (~I \(\underset{\text{F}}{\wedge}\) ~S)

A must be false because ~A is true. At this point, we aren’t forced to do anything for Premise 1 since there are still many ways for it to come out true. Nothing has changed for Premise 3 and the Conclusion. At this point we need to split our line into all possible successful assignments. I’m going to start with the conclusion (I chose this more or less arbitrarily). Here’s what I do:

\[\begin{array}{} &(H &\vee (I \vee (&A& \wedge P))) / &\sim &A / (H &\vee M) // (&\sim I& \wedge& \sim S) &&\\ \text{Possibility 1} & \rightarrow &T &F &F &T &F &T &\textbf{T} &F &\textbf{F}&&\\\text{Possibility 2} & \rightarrow &T &F &F &T &F &T &\textbf{F} &F &\textbf{T}&&\\\text{Possibility 3} & \rightarrow &T &F &F &T &F &T &\textbf{F} &F &\textbf{F} && \end{array} \nonumber\]

If you focus on the conclusion, it looks sort of like a truth table now, doesn’t it? Now we complete the process for each possible line:

\[\begin{array}{} (H &\vee (I \vee (&A& \wedge P))) / &\sim &A / (H &\vee M) // (&\sim &I& \wedge& \sim &S) \\& T &F &F &T &F &T &T&\textbf{F} &F &F&\textbf{T}\\ &T &F &F &T &F &T &F&\textbf{T} &F &T&\textbf{F}\\ &T &F &F &T &F &T &F&\textbf{T} &F &F&\textbf{T} \end{array} \nonumber\]

Now I’m transferring truth values:

And then calculate what needs to happen given the changes you’ve made. I’ve changed the first premise, so now I notice that (A \(\wedge\) P) is false and now I is false in my first row, so that means H must be true. In the other rows, nothing has yet forced me to assign anything to H.

\[\begin{array}{} (H &\vee (&I \vee (&A& \wedge P))) / &\sim &A / (H &\vee M) // (&\sim &I& \wedge& \sim &S) \\T& T &F &F &F &T &F &T&T &F &F&F &T\\ &T &T &F &F &T &F &F&F &T &F&T &F\\ &T &T &F &F &T &F &F&F &T &F&F &T \end{array} \nonumber\]

Then transfer that H:

At this point, nothing is forcing my hand. If you look carefully, you’ll see that there is no single letter on any single line that must be a given truth value for the truth values we’ve assigned the complete formulas to obtain. So now what???

If we are free to assign any truth values we want, then we aren’t going to run into any contradictions. It follows that there are no contradictions in these three rows and there is therefore at least one row where there are no contradictions. This inference is invalid .

All we need is one row where there are no contradictions to prove that the inference is invalid.

That’s all! That’s how we do the reverse truth table method. One can imagine how to use this to test even super complex sets of sentences for consistency: just assign “true” to each individual sentence and then look for a contradiction. One line with no contradiction? You’ve got a consistent set of sentences.