critical thinking justification

1 Introduction to Critical Thinking

I. what is c ritical t hinking [1].

Critical thinking is the ability to think clearly and rationally about what to do or what to believe.  It includes the ability to engage in reflective and independent thinking. Someone with critical thinking skills is able to do the following:

• Understand the logical connections between ideas.
• Identify, construct, and evaluate arguments.
• Detect inconsistencies and common mistakes in reasoning.
• Solve problems systematically.
• Identify the relevance and importance of ideas.
• Reflect on the justification of one’s own beliefs and values.

Critical thinking is not simply a matter of accumulating information. A person with a good memory and who knows a lot of facts is not necessarily good at critical thinking. Critical thinkers are able to deduce consequences from what they know, make use of information to solve problems, and to seek relevant sources of information to inform themselves.

Critical thinking should not be confused with being argumentative or being critical of other people. Although critical thinking skills can be used in exposing fallacies and bad reasoning, critical thinking can also play an important role in cooperative reasoning and constructive tasks. Critical thinking can help us acquire knowledge, improve our theories, and strengthen arguments. We can also use critical thinking to enhance work processes and improve social institutions.

Some people believe that critical thinking hinders creativity because critical thinking requires following the rules of logic and rationality, whereas creativity might require breaking those rules. This is a misconception. Critical thinking is quite compatible with thinking “out-of-the-box,” challenging consensus views, and pursuing less popular approaches. If anything, critical thinking is an essential part of creativity because we need critical thinking to evaluate and improve our creative ideas.

II. The I mportance of C ritical T hinking

Critical thinking is a domain-general thinking skill. The ability to think clearly and rationally is important whatever we choose to do. If you work in education, research, finance, management or the legal profession, then critical thinking is obviously important. But critical thinking skills are not restricted to a particular subject area. Being able to think well and solve problems systematically is an asset for any career.

Critical thinking is very important in the new knowledge economy.  The global knowledge economy is driven by information and technology. One has to be able to deal with changes quickly and effectively. The new economy places increasing demands on flexible intellectual skills, and the ability to analyze information and integrate diverse sources of knowledge in solving problems. Good critical thinking promotes such thinking skills, and is very important in the fast-changing workplace.

Critical thinking enhances language and presentation skills. Thinking clearly and systematically can improve the way we express our ideas. In learning how to analyze the logical structure of texts, critical thinking also improves comprehension abilities.

Critical thinking promotes creativity. To come up with a creative solution to a problem involves not just having new ideas. It must also be the case that the new ideas being generated are useful and relevant to the task at hand. Critical thinking plays a crucial role in evaluating new ideas, selecting the best ones and modifying them if necessary.

Critical thinking is crucial for self-reflection. In order to live a meaningful life and to structure our lives accordingly, we need to justify and reflect on our values and decisions. Critical thinking provides the tools for this process of self-evaluation.

Good critical thinking is the foundation of science and democracy. Science requires the critical use of reason in experimentation and theory confirmation. The proper functioning of a liberal democracy requires citizens who can think critically about social issues to inform their judgments about proper governance and to overcome biases and prejudice.

Critical thinking is a   metacognitive skill . What this means is that it is a higher-level cognitive skill that involves thinking about thinking. We have to be aware of the good principles of reasoning, and be reflective about our own reasoning. In addition, we often need to make a conscious effort to improve ourselves, avoid biases, and maintain objectivity. This is notoriously hard to do. We are all able to think but to think well often requires a long period of training. The mastery of critical thinking is similar to the mastery of many other skills. There are three important components: theory, practice, and attitude.

III. Improv ing O ur T hinking S kills

If we want to think correctly, we need to follow the correct rules of reasoning. Knowledge of theory includes knowledge of these rules. These are the basic principles of critical thinking, such as the laws of logic, and the methods of scientific reasoning, etc.

Also, it would be useful to know something about what not to do if we want to reason correctly. This means we should have some basic knowledge of the mistakes that people make. First, this requires some knowledge of typical fallacies. Second, psychologists have discovered persistent biases and limitations in human reasoning. An awareness of these empirical findings will alert us to potential problems.

However, merely knowing the principles that distinguish good and bad reasoning is not enough. We might study in the classroom about how to swim, and learn about the basic theory, such as the fact that one should not breathe underwater. But unless we can apply such theoretical knowledge through constant practice, we might not actually be able to swim.

Similarly, to be good at critical thinking skills it is necessary to internalize the theoretical principles so that we can actually apply them in daily life. There are at least two ways to do this. One is to perform lots of quality exercises. These exercises don’t just include practicing in the classroom or receiving tutorials; they also include engaging in discussions and debates with other people in our daily lives, where the principles of critical thinking can be applied. The second method is to think more deeply about the principles that we have acquired. In the human mind, memory and understanding are acquired through making connections between ideas.

Good critical thinking skills require more than just knowledge and practice. Persistent practice can bring about improvements only if one has the right kind of motivation and attitude. The following attitudes are not uncommon, but they are obstacles to critical thinking:

• I prefer being given the correct answers rather than figuring them out myself.
• I don’t like to think a lot about my decisions as I rely only on gut feelings.
• I don’t usually review the mistakes I have made.
• I don’t like to be criticized.

To improve our thinking we have to recognize the importance of reflecting on the reasons for belief and action. We should also be willing to engage in debate, break old habits, and deal with linguistic complexities and abstract concepts.

The  California Critical Thinking Disposition Inventory  is a psychological test that is used to measure whether people are disposed to think critically. It measures the seven different thinking habits listed below, and it is useful to ask ourselves to what extent they describe the way we think:

• Truth-Seeking—Do you try to understand how things really are? Are you interested in finding out the truth?
• Open-Mindedness—How receptive are you to new ideas, even when you do not intuitively agree with them? Do you give new concepts a fair hearing?
• Analyticity—Do you try to understand the reasons behind things? Do you act impulsively or do you evaluate the pros and cons of your decisions?
• Systematicity—Are you systematic in your thinking? Do you break down a complex problem into parts?
• Confidence in Reasoning—Do you always defer to other people? How confident are you in your own judgment? Do you have reasons for your confidence? Do you have a way to evaluate your own thinking?
• Inquisitiveness—Are you curious about unfamiliar topics and resolving complicated problems? Will you chase down an answer until you find it?
• Maturity of Judgment—Do you jump to conclusions? Do you try to see things from different perspectives? Do you take other people’s experiences into account?

Finally, as mentioned earlier, psychologists have discovered over the years that human reasoning can be easily affected by a variety of cognitive biases. For example, people tend to be over-confident of their abilities and focus too much on evidence that supports their pre-existing opinions. We should be alert to these biases in our attitudes towards our own thinking.

IV. Defining Critical Thinking

There are many different definitions of critical thinking. Here we list some of the well-known ones. You might notice that they all emphasize the importance of clarity and rationality. Here we will look at some well-known definitions in chronological order.

1) Many people trace the importance of critical thinking in education to the early twentieth-century American philosopher John Dewey. But Dewey did not make very extensive use of the term “critical thinking.” Instead, in his book  How We Think (1910), he argued for the importance of what he called “reflective thinking”:

…[when] the ground or basis for a belief is deliberately sought and its adequacy to support the belief examined. This process is called reflective thought; it alone is truly educative in value…

Active, persistent and careful consideration of any belief or supposed form of knowledge in light of the grounds that support it, and the further conclusions to which it tends, constitutes reflective thought.

There is however one passage from How We Think where Dewey explicitly uses the term “critical thinking”:

The essence of critical thinking is suspended judgment; and the essence of this suspense is inquiry to determine the nature of the problem before proceeding to attempts at its solution. This, more than any other thing, transforms mere inference into tested inference, suggested conclusions into proof.

2) The  Watson-Glaser Critical Thinking Appraisal  (1980) is a well-known psychological test of critical thinking ability. The authors of this test define critical thinking as:

…a composite of attitudes, knowledge and skills. This composite includes: (1) attitudes of inquiry that involve an ability to recognize the existence of problems and an acceptance of the general need for evidence in support of what is asserted to be true; (2) knowledge of the nature of valid inferences, abstractions, and generalizations in which the weight or accuracy of different kinds of evidence are logically determined; and (3) skills in employing and applying the above attitudes and knowledge.

3) A very well-known and influential definition of critical thinking comes from philosopher and professor Robert Ennis in his work “A Taxonomy of Critical Thinking Dispositions and Abilities” (1987):

Critical thinking is reasonable reflective thinking that is focused on deciding what to believe or do.

4) The following definition comes from a statement written in 1987 by the philosophers Michael Scriven and Richard Paul for the  National Council for Excellence in Critical Thinking (link), an organization promoting critical thinking in the US:

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. In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness. It entails the examination of those structures or elements of thought implicit in all reasoning: purpose, problem, or question-at-issue, assumptions, concepts, empirical grounding; reasoning leading to conclusions, implications and consequences, objections from alternative viewpoints, and frame of reference.

The following excerpt from Peter A. Facione’s “Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction” (1990) is quoted from a report written for the American Philosophical Association:

We understand critical thinking to be purposeful, self-regulatory judgment which results in interpretation, analysis, evaluation, and inference, as well as explanation of the evidential, conceptual, methodological, criteriological, or contextual considerations upon which that judgment is based. CT is essential as a tool of inquiry. As such, CT is a liberating force in education and a powerful resource in one’s personal and civic life. While not synonymous with good thinking, CT is a pervasive and self-rectifying human phenomenon. The ideal critical thinker is habitually inquisitive, well-informed, trustful of reason, open-minded, flexible, fairminded in evaluation, honest in facing personal biases, prudent in making judgments, willing to reconsider, clear about issues, orderly in complex matters, diligent in seeking relevant information, reasonable in the selection of criteria, focused in inquiry, and persistent in seeking results which are as precise as the subject and the circumstances of inquiry permit. Thus, educating good critical thinkers means working toward this ideal. It combines developing CT skills with nurturing those dispositions which consistently yield useful insights and which are the basis of a rational and democratic society.

V. Two F eatures of C ritical T hinking

A. how not what .

Critical thinking is concerned not with what you believe, but rather how or why you believe it. Most classes, such as those on biology or chemistry, teach you what to believe about a subject matter. In contrast, critical thinking is not particularly interested in what the world is, in fact, like. Rather, critical thinking will teach you how to form beliefs and how to think. It is interested in the type of reasoning you use when you form your beliefs, and concerns itself with whether you have good reasons to believe what you believe. Therefore, this class isn’t a class on the psychology of reasoning, which brings us to the second important feature of critical thinking.

B. Ought N ot Is ( or Normative N ot Descriptive )

There is a difference between normative and descriptive theories. Descriptive theories, such as those provided by physics, provide a picture of how the world factually behaves and operates. In contrast, normative theories, such as those provided by ethics or political philosophy, provide a picture of how the world should be. Rather than ask question such as why something is the way it is, normative theories ask how something should be. In this course, we will be interested in normative theories that govern our thinking and reasoning. Therefore, we will not be interested in how we actually reason, but rather focus on how we ought to reason.

In the introduction to this course we considered a selection task with cards that must be flipped in order to check the validity of a rule. We noted that many people fail to identify all the cards required to check the rule. This is how people do in fact reason (descriptive). We then noted that you must flip over two cards. This is how people ought to reason (normative).

• Section I-IV are taken from http://philosophy.hku.hk/think/ and are in use under the creative commons license. Some modifications have been made to the original content. ↵

Critical Thinking Copyright © 2019 by Brian Kim is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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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.

Prevent plagiarism. Run a free check.

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

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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What is Critical Thinking?

Critical thinking is the ability to think clearly and rationally, understanding the logical connection between ideas.  Critical thinking has been the subject of much debate and thought since the time of early Greek philosophers such as Plato and Socrates and has continued to be a subject of discussion into the modern age, for example the ability to recognise fake news .

Critical thinking might be described as the ability to engage in reflective and independent thinking.

In essence, critical thinking requires you to use your ability to reason. It is about being an active learner rather than a passive recipient of information.

Critical thinkers rigorously question ideas and assumptions rather than accepting them at face value. They will always seek to determine whether the ideas, arguments and findings represent the entire picture and are open to finding that they do not.

Critical thinkers will identify, analyse and solve problems systematically rather than by intuition or instinct.

Someone with critical thinking skills can:

Understand the links between ideas.

Determine the importance and relevance of arguments and ideas.

Recognise, build and appraise arguments.

Identify inconsistencies and errors in reasoning.

Approach problems in a consistent and systematic way.

Reflect on the justification of their own assumptions, beliefs and values.

Critical thinking is thinking about things in certain ways so as to arrive at the best possible solution in the circumstances that the thinker is aware of. In more everyday language, it is a way of thinking about whatever is presently occupying your mind so that you come to the best possible conclusion.

Critical Thinking is:

A way of thinking about particular things at a particular time; it is not the accumulation of facts and knowledge or something that you can learn once and then use in that form forever, such as the nine times table you learn and use in school.

The Skills We Need for Critical Thinking

The skills that we need in order to be able to think critically are varied and include observation, analysis, interpretation, reflection, evaluation, inference, explanation, problem solving, and decision making.

Specifically we need to be able to:

Think about a topic or issue in an objective and critical way.

Identify the different arguments there are in relation to a particular issue.

Evaluate a point of view to determine how strong or valid it is.

Recognise any weaknesses or negative points that there are in the evidence or argument.

Notice what implications there might be behind a statement or argument.

Provide structured reasoning and support for an argument that we wish to make.

The Critical Thinking Process

You should be aware that none of us think critically all the time.

Sometimes we think in almost any way but critically, for example when our self-control is affected by anger, grief or joy or when we are feeling just plain ‘bloody minded’.

On the other hand, the good news is that, since our critical thinking ability varies according to our current mindset, most of the time we can learn to improve our critical thinking ability by developing certain routine activities and applying them to all problems that present themselves.

Once you understand the theory of critical thinking, improving your critical thinking skills takes persistence and practice.

Try this simple exercise to help you to start thinking critically.

Think of something that someone has recently told you. Then ask yourself the following questions:

Who said it?

Someone you know? Someone in a position of authority or power? Does it matter who told you this?

What did they say?

Did they give facts or opinions? Did they provide all the facts? Did they leave anything out?

Where did they say it?

Was it in public or in private? Did other people have a chance to respond an provide an alternative account?

When did they say it?

Was it before, during or after an important event? Is timing important?

Why did they say it?

Did they explain the reasoning behind their opinion? Were they trying to make someone look good or bad?

How did they say it?

Were they happy or sad, angry or indifferent? Did they write it or say it? Could you understand what was said?

What are you Aiming to Achieve?

One of the most important aspects of critical thinking is to decide what you are aiming to achieve and then make a decision based on a range of possibilities.

Once you have clarified that aim for yourself you should use it as the starting point in all future situations requiring thought and, possibly, further decision making. Where needed, make your workmates, family or those around you aware of your intention to pursue this goal. You must then discipline yourself to keep on track until changing circumstances mean you have to revisit the start of the decision making process.

However, there are things that get in the way of simple decision making. We all carry with us a range of likes and dislikes, learnt behaviours and personal preferences developed throughout our lives; they are the hallmarks of being human. A major contribution to ensuring we think critically is to be aware of these personal characteristics, preferences and biases and make allowance for them when considering possible next steps, whether they are at the pre-action consideration stage or as part of a rethink caused by unexpected or unforeseen impediments to continued progress.

The more clearly we are aware of ourselves, our strengths and weaknesses, the more likely our critical thinking will be productive.

The Benefit of Foresight

Perhaps the most important element of thinking critically is foresight.

Almost all decisions we make and implement don’t prove disastrous if we find reasons to abandon them. However, our decision making will be infinitely better and more likely to lead to success if, when we reach a tentative conclusion, we pause and consider the impact on the people and activities around us.

The elements needing consideration are generally numerous and varied. In many cases, consideration of one element from a different perspective will reveal potential dangers in pursuing our decision.

For instance, moving a business activity to a new location may improve potential output considerably but it may also lead to the loss of skilled workers if the distance moved is too great. Which of these is the more important consideration? Is there some way of lessening the conflict?

These are the sort of problems that may arise from incomplete critical thinking, a demonstration perhaps of the critical importance of good critical thinking.

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In Summary:

Critical thinking is aimed at achieving the best possible outcomes in any situation. In order to achieve this it must involve gathering and evaluating information from as many different sources possible.

Critical thinking requires a clear, often uncomfortable, assessment of your personal strengths, weaknesses and preferences and their possible impact on decisions you may make.

Critical thinking requires the development and use of foresight as far as this is possible. As Doris Day sang, “the future’s not ours to see”.

Implementing the decisions made arising from critical thinking must take into account an assessment of possible outcomes and ways of avoiding potentially negative outcomes, or at least lessening their impact.

• Critical thinking involves reviewing the results of the application of decisions made and implementing change where possible.

It might be thought that we are overextending our demands on critical thinking in expecting that it can help to construct focused meaning rather than examining the information given and the knowledge we have acquired to see if we can, if necessary, construct a meaning that will be acceptable and useful.

After all, almost no information we have available to us, either externally or internally, carries any guarantee of its life or appropriateness.  Neat step-by-step instructions may provide some sort of trellis on which our basic understanding of critical thinking can blossom but it doesn’t and cannot provide any assurance of certainty, utility or longevity.

Continue to: Critical Thinking and Fake News Critical Reading

See also: Analytical Skills Understanding and Addressing Conspiracy Theories Introduction to Neuro-Linguistic Programming (NLP)

[C01] What is critical thinking?

Module: Critical thinking

• C02. Improve our thinking skills
• C03. Defining critical thinking
• C04. Teaching critical thinking
• C05. Beyond critical thinking
• C06. The Cognitive Reflection Test
• C07. Critical thinking assessment
• C08. Videos and courses on critical thinking
• C09. Famous quotes
• C10. History of critical thinking

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Critical thinking is the ability to think clearly and rationally about what to do or what to believe. It includes the ability to engage in reflective and independent thinking. Someone with critical thinking skills is able to do the following :

• understand the logical connections between ideas
• identify, construct and evaluate arguments
• detect inconsistencies and common mistakes in reasoning
• solve problems systematically
• identify the relevance and importance of ideas
• reflect on the justification of one's own beliefs and values

Critical thinking is not a matter of accumulating information. A person with a good memory and who knows a lot of facts is not necessarily good at critical thinking. A critical thinker is able to deduce consequences from what he knows, and he knows how to make use of information to solve problems, and to seek relevant sources of information to inform himself.

Critical thinking should not be confused with being argumentative or being critical of other people. Although critical thinking skills can be used in exposing fallacies and bad reasoning, critical thinking can also play an important role in cooperative reasoning and constructive tasks. Critical thinking can help us acquire knowledge, improve our theories, and strengthen arguments. We can use critical thinking to enhance work processes and improve social institutions.

Some people believe that critical thinking hinders creativity because it requires following the rules of logic and rationality, but creativity might require breaking rules. This is a misconception. Critical thinking is quite compatible with thinking "out-of-the-box", challenging consensus and pursuing less popular approaches. If anything, critical thinking is an essential part of creativity because we need critical thinking to evaluate and improve our creative ideas.

§1. The importance of critical thinking

Critical thinking is a domain-general thinking skill . The ability to think clearly and rationally is important whatever we choose to do. If you work in education, research, finance, management or the legal profession, then critical thinking is obviously important. But critical thinking skills are not restricted to a particular subject area. Being able to think well and solve problems systematically is an asset for any career.

Critical thinking is very important in the new knowledge economy. The global knowledge economy is driven by information and technology. One has to be able to deal with changes quickly and effectively. The new economy places increasing demands on flexible intellectual skills, and the ability to analyse information and integrate diverse sources of knowledge in solving problems. Good critical thinking promotes such thinking skills, and is very important in the fast-changing workplace.

Critical thinking enhances language and presentation skills . Thinking clearly and systematically can improve the way we express our ideas. In learning how to analyse the logical structure of texts, critical thinking also improves comprehension abilities.

Critical thinking promotes creativity . To come up with a creative solution to a problem involves not just having new ideas. It must also be the case that the new ideas being generated are useful and relevant to the task at hand. Critical thinking plays a crucial role in evaluating new ideas, selecting the best ones and modifying them if necessary

Critical thinking is crucial for self-reflection . In order to live a meaningful life and to structure our lives accordingly, we need to justify and reflect on our values and decisions. Critical thinking provides the tools for this process of self-evaluation.

Good critical thinking is the foundation of science and democracy . Science requires the critical use of reason in experimentation and theory confirmation. The proper functioning of a liberal democracy requires citizens who can think critically about social issues to inform their judgments about proper governance and to overcome biases and prejudice.

§2. The future of critical thinking

The Fourth Industrial Revolution, which includes developments in previously disjointed fields such as artificial intelligence and machine-learning, robotics, nanotechnology, 3-D printing, and genetics and biotechnology, will cause widespread disruption not only to business models but also to labour markets over the next five years, with enormous change predicted in the skill sets needed to thrive in the new landscape.

The top three skills that supposed to be most relevant are thinking skills related to critical thinking, creativity, and their practical application. These are the cognitive skills that our website focuses on.

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• The ideas on this page were discussed in a blog post on edutopia. The author uses the critical thinking framework here to apply to K-12 education. Very relevant to school teachers!

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Open Access

Peer-reviewed

Research Article

Fostering Critical Thinking, Reasoning, and Argumentation Skills through Bioethics Education

* E-mail: [email protected]

Affiliation Northwest Association for Biomedical Research, Seattle, Washington, United States of America

Affiliation Center for Research and Learning, Snohomish, Washington, United States of America

• Jeanne Ting Chowning, 
• Joan Carlton Griswold, 
• Dina N. Kovarik, 
• Laura J. Collins

• Published: May 11, 2012
• https://doi.org/10.1371/journal.pone.0036791
• Reader Comments

Developing a position on a socio-scientific issue and defending it using a well-reasoned justification involves complex cognitive skills that are challenging to both teach and assess. Our work centers on instructional strategies for fostering critical thinking skills in high school students using bioethical case studies, decision-making frameworks, and structured analysis tools to scaffold student argumentation. In this study, we examined the effects of our teacher professional development and curricular materials on the ability of high school students to analyze a bioethical case study and develop a strong position. We focused on student ability to identify an ethical question, consider stakeholders and their values, incorporate relevant scientific facts and content, address ethical principles, and consider the strengths and weaknesses of alternate solutions. 431 students and 12 teachers participated in a research study using teacher cohorts for comparison purposes. The first cohort received professional development and used the curriculum with their students; the second did not receive professional development until after their participation in the study and did not use the curriculum. In order to assess the acquisition of higher-order justification skills, students were asked to analyze a case study and develop a well-reasoned written position. We evaluated statements using a scoring rubric and found highly significant differences (p<0.001) between students exposed to the curriculum strategies and those who were not. Students also showed highly significant gains (p<0.001) in self-reported interest in science content, ability to analyze socio-scientific issues, awareness of ethical issues, ability to listen to and discuss viewpoints different from their own, and understanding of the relationship between science and society. Our results demonstrate that incorporating ethical dilemmas into the classroom is one strategy for increasing student motivation and engagement with science content, while promoting reasoning and justification skills that help prepare an informed citizenry.

Citation: Chowning JT, Griswold JC, Kovarik DN, Collins LJ (2012) Fostering Critical Thinking, Reasoning, and Argumentation Skills through Bioethics Education. PLoS ONE 7(5): e36791. https://doi.org/10.1371/journal.pone.0036791

Editor: Julio Francisco Turrens, University of South Alabama, United States of America

Received: February 7, 2012; Accepted: April 13, 2012; Published: May 11, 2012

Copyright: © 2012 Chowning et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: The “Collaborations to Understand Research and Ethics” (CURE) program was supported by a Science Education Partnership Award grant ( http://ncrrsepa.org ) from the National Center for Research Resources and the Division of Program Coordination, Planning, and Strategic Initiatives of the National Institutes of Health through Grant Number R25OD011138. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

While the practice of argumentation is a cornerstone of the scientific process, students at the secondary level have few opportunities to engage in it [1] . Recent research suggests that collaborative discourse and critical dialogue focused on student claims and justifications can increase student reasoning abilities and conceptual understanding, and that strategies are needed to promote such practices in secondary science classrooms [2] . In particular, students need structured opportunities to develop arguments and discuss them with their peers. In scientific argument, the data, claims and warrants (that relate claims to data) are strictly concerned with scientific data; in a socio-scientific argument, students must consider stakeholder perspectives and ethical principles and ideas, in addition to relevant scientific background. Regardless of whether the arguments that students employ point towards scientific or socio-scientific issues, the overall processes students use in order to develop justifications rely on a model that conceptualizes arguments as claims to knowledge [3] .

Prior research in informal student reasoning and socio-scientific issues also indicates that most learners are not able to formulate high-quality arguments (as defined by the ability to articulate justifications for claims and to rebut contrary positions), and highlights the challenges related to promoting argumentation skills. Research suggests that students need experience and practice justifying their claims, recognizing and addressing counter-arguments, and learning about elements that contribute to a strong justification [4] , [5] .

Proponents of Socio-scientific Issues (SSI) education stress that the intellectual development of students in ethical reasoning is necessary to promote understanding of the relationship between science and society [4] , [6] . The SSI approach emphasizes three important principles: (a) because science literacy should be a goal for all students, science education should be broad-based and geared beyond imparting relevant content knowledge to future scientists; (b) science learning should involve students in thinking about the kinds of real-world experiences that they might encounter in their lives; and (c) when teaching about real-world issues, science teachers should aim to include contextual elements that are beyond traditional science content. Sadler and Zeidler, who advocate a SSI perspective, note that “people do not live their lives according to disciplinary boundaries, and students approach socio-scientific issues with diverse perspectives that integrate science and other considerations” [7] .

Standards for science literacy emphasize not only the importance of scientific content and processes, but also the need for students to learn about science that is contextualized in real-world situations that involve personal and community decision-making [7] – [10] . The National Board for Professional Teaching Standards stresses that students need “regular exposure to the human contexts of science [and] examples of ethical dilemmas, both current and past, that surround particular scientific activities, discoveries, and technologies” [11] . Teachers are mandated by national science standards and professional teaching standards to address the social dimensions of science, and are encouraged to provide students with the tools necessary to engage in analyzing bioethical issues; yet they rarely receive training in methods to foster such discussions with students.

The Northwest Association for Biomedical Research (NWABR), a non-profit organization that advances the understanding and support of biomedical research, has been engaging students and teachers in bringing the discussion of ethical issues in science into the classroom since 2000 [12] . The mission of NWABR is to promote an understanding of biomedical research and its ethical conduct through dialogue and education. The sixty research institutions that constitute our members include academia, industry, non-profit research organizations, research hospitals, professional societies, and volunteer health organizations. NWABR connects the scientific and education communities across the Northwestern United States and helps the public understand the vital role of research in promoting better health outcomes. We have focused on providing teachers with both resources to foster student reasoning skills (such as activities in which students practice evaluating arguments using criteria for strong justifications), as well as pedagogical strategies for fostering collaborative discussion [13] – [15] . Our work draws upon socio-scientific elements of functional scientific literacy identified by Zeidler et al. [6] . We include support for teachers in discourse issues, nature of science issues, case-based issues, and cultural issues – which all contribute to cognitive and moral development and promote functional scientific literacy. Our Collaborations to Understand Research and Ethics (CURE) program, funded by a Science Education Partnership Award from the National Institutes of Health (NIH), promotes understanding of translational biomedical research as well as the ethical considerations such research raises.

Many teachers find a principles-based approach most manageable for introducing ethical considerations. The principles include respect for persons (respecting the inherent worth of an individual and his or her autonomy), beneficence/nonmaleficence (maximizing benefits/minimizing harms), and justice (distributing benefits/burdens equitably across a group of individuals). These principles, which are articulated in the Belmont Report [16] in relation to research with human participants (and which are clarified and defended by Beauchamp and Childress [17] ), represent familiar concepts and are widely used. In our professional development workshops and in our support resources, we also introduce teachers to care, feminist, virtue, deontological and consequentialist ethics. Once teachers become familiar with principles, they often augment their teaching by incorporating these additional ethical approaches.

The Bioethics 101 materials that were the focus of our study were developed in conjunction with teachers, ethicists, and scientists. The curriculum contains a series of five classroom lessons and a culminating assessment [18] and is described in more detail in the Program Description below. For many years, teachers have shared with us the dramatic impacts that the teaching of bioethics can have on their students; this research study was designed to investigate the relationship between explicit instruction in bioethical reasoning and resulting student outcomes. In this study, teacher cohorts and student pre/post tests were used to investigate whether CURE professional development and the Bioethics 101 curriculum materials made a significant difference in high school students’ abilities to analyze a case study and justify their positions. Our research strongly indicates that such reasoning approaches can be taught to high school students and can significantly improve their ability to develop well-reasoned justifications to bioethical dilemmas. In addition, student self-reports provide additional evidence of the extent to which bioethics instruction impacted their attitudes and perceptions and increased student motivation and engagement with science content.

Program Description

Our professional development program, Ethics in the Science Classroom, spanned two weeks. The first week, a residential program at the University of Washington (UW) Pack Forest Conference Center, focused on our Bioethics 101 curriculum, which is summarized in Table S1 and is freely available at http://www.nwabr.org . The curriculum, a series of five classroom lessons and a culminating assessment, was implemented by all teachers who were part of our CURE treatment group. The lessons explore the following topics: (a) characteristics of an ethical question; (b) bioethical principles; (c) the relationship between science and ethics and the roles of objectivity/subjectivity and evidence in each; (d) analysis of a case study (including identifying an ethical question, determining relevant facts, identifying stakeholders and their concerns and values, and evaluating options); and (e) development of a well-reasoned justification for a position.

Additionally, the first week focused on effective teaching methods for incorporating ethical issues into science classrooms. We shared specific pedagogical strategies for helping teachers manage classroom discussion, such as asking students to consider the concerns and values of individuals involved in the case while in small single and mixed stakeholder groups. We also provided participants with background knowledge in biomedical research and ethics. Presentations from colleagues affiliated with the NIH Clinical and Translational Science Award program, from the Department of Bioethics and Humanities at the UW, and from NWABR member institutions helped participants develop a broad appreciation for the process of biomedical research and the ethical issues that arise as a consequence of that research. Topics included clinical trials, animal models of disease, regulation of research, and ethical foundations of research. Participants also developed materials directly relevant and applicable to their own classrooms, and shared them with other educators. Teachers wrote case studies and then used ethical frameworks to analyze the main arguments surrounding the case, thereby gaining experience in bioethical analysis. Teachers also developed Action Plans to outline their plans for implementation.

The second week provided teachers with first-hand experiences in NWABR research institutions. Teachers visited research centers such as the Tumor Vaccine Group and Clinical Research Center at the UW. They also had the opportunity to visit several of the following institutions: Amgen, Benaroya Research Institute, Fred Hutchinson Cancer Research Center, Infectious Disease Research Institute, Institute for Stem Cells and Regenerative Medicine at the UW, Pacific Northwest Diabetes Research Institute, Puget Sound Blood Center, HIV Vaccine Trials Network, and Washington National Primate Research Center. Teachers found these experiences in research facilities extremely valuable in helping make concrete the concepts and processes detailed in the first week of the program.

We held two follow-up sessions during the school year to deepen our relationship with the teachers, promote a vibrant ethics in science education community, provide additional resources and support, and reflect on challenges in implementation of our materials. We also provided the opportunity for teachers to share their experiences with one another and to report on the most meaningful longer-term impacts from the program. Another feature of our CURE program was the school-year Institutional Review Board (IRB) and Institutional Animal Care and Use Committee (IACUC) follow-up sessions. Teachers chose to attend one of NWABR’s IRB or IACUC conferences, attend a meeting of a review board, or complete NIH online ethics training. Some teachers also visited the UW Embryonic Stem Cell Research Oversight Committee. CURE funding provided substitutes in order for teachers to be released during the workday. These opportunities further engaged teachers in understanding and appreciating the actual process of oversight for federally funded research.

Participants

Most of the educators who have been through our intensive summer workshops teach secondary level science, but we have welcomed teachers at the college, community college, and even elementary levels. Our participants are primarily biology teachers; however, chemistry and physical science educators, health and career specialists, and social studies teachers have also used our strategies and materials with success.

The research design used teacher cohorts for comparison purposes and recruited teachers who expressed interest in participating in a CURE workshop in either the summer of 2009 or the summer of 2010. We assumed that all teachers who applied to the CURE workshop for either year would be similarly interested in ethics topics. Thus, Cohort 1 included teachers participating in CURE during the summer of 2009 (the treatment group). Their students received CURE instruction during the following 2009–2010 academic year. Cohort 2 (the comparison group) included teachers who were selected to participate in CURE during the summer of 2010. Their students received a semester of traditional classroom instruction in science during the 2009–2010 academic year. In order to track participation of different demographic groups, questions pertaining to race, ethnicity, and gender were also included in the post-tests.

Using an online sample size calculator http://www.surveysystem.com/sscalc.htm , a 95% Confidence Level, and a Confidence Interval of 5, it was calculated that a sample size of 278 students would be needed for the research study. For that reason, six Cohort 1 teachers were impartially chosen to be in the study. For the comparison group, the study design also required six teachers from Cohort 2. The external evaluator contacted all Cohort 2 teachers to explain the research study and obtain their consent, and successfully recruited six to participate.

Ethics Statement

This study was conducted according to the principles expressed in the Declaration of Helsinki. Prior to the study, research processes and materials were reviewed and approved by the Western Institutional Review Board (WIRB Study #1103180). CURE staff and evaluators received written permission from parents to have their minor children participate in the Bioethics 101 curriculum, for the collection and subsequent analysis of students’ written responses to the assessment, and for permission to collect and analyze student interview responses. Teachers also provided written informed consent prior to study participation. All study participants and/or their legal guardians provided written informed consent for the collection and subsequent analysis of verbal and written responses.

Research Study

Analyzing a case study: cure and comparison students..

Teacher cohorts and pre/post tests were used to investigate whether CURE professional development and curriculum materials made a significant difference in high school students’ abilities to analyze a case study and justify their positions. Cohort 1 teachers (N = 6) received CURE professional development and used the Bioethics 101 curriculum with their students (N = 323); Cohort 2 teachers (N = 6) did not receive professional development until after their participation in the study and did not use the curriculum with their students (N = 108). Cohort 2 students were given the test case study and questions, but with only traditional science instruction during the semester. Each Cohort was further divided into two groups (A and B). Students in Group A were asked to complete a pre-test prior to the case study, while students in Group B did not. All four student groups completed a post-test after analysis of the case study. This four-group model ( Table 1 ) allowed us to assess: 1) the effect of CURE treatment relative to conventional education practices, 2) the effect of the pre-test relative to no pre-test, and 3) the interaction between the pre-test and CURE treatment condition. Random assignment of students to treatment and comparison groups was not possible; consequently we used existing intact classes. In all, 431 students and 12 teachers participated in the research study ( Table 2 ).

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In order to assess the acquisition of higher-order justification skills, students used the summative assessment provided in our curriculum as the pre- and post-test. We designed the curriculum to scaffold students’ ability to write a persuasive bioethical position; by the time they participated in the assessment, Cohort 1 students had opportunities to discuss the elements of a strong justification as well as practice in analyzing case studies. For our research, both Cohort 1 and 2 students were asked to analyze the case study of “Ashley X” ( Table S2 ), a young girl with a severe neurological impairment whose parents wished to limit her growth through a combination of interventions so that they could better care for her. Students were asked to respond to the ethical question: “Should one or more medical interventions be used to limit Ashley’s growth and physical maturation? If so, which interventions should be used and why?” In their answer, students were encouraged to develop a well-reasoned written position by responding to five questions that reflected elements of a strong justification. One difficulty in evaluating a multifaceted science-related learning task (analyzing a bioethical case study and justifying a position) is that a traditional multiple-choice assessment may not adequately reflect the subtlety and depth of student understanding. We used a rubric to assess student responses to each of the following questions (Q) on a scale of 1 to 4; these questions represent key elements of a strong justification for a bioethical argument:

• Q1: Student Position: What is your decision?
• Q2: Factual Support: What facts support your decision? Is there missing information that could be used to make a better decision?
• Q3: Interests and Views of Others: Who will be impacted by the decision and how will they be impacted?
• Q4: Ethical Considerations: What are the main ethical considerations?
• Q5: Evaluating Alternative Options: What are some strengths and weaknesses of alternate solutions?

In keeping with our focus on the process of reasoning rather than on having students draw any particular conclusion, we did not assess students on which position they took, but on how well they stated and justified the position they chose.

We used a rubric scoring guide to assess student learning, which aligned with the complex cognitive challenges posed by the task ( Table S3 ). Assessing complex aspects of student learning is often difficult, especially evaluating how students represent their knowledge and competence in the domain of bioethical reasoning. Using a scoring rubric helped us more authentically score dimensions of students’ learning and their depth of thinking. An outside scorer who had previously participated in CURE workshops, has secondary science teaching experience, and who has a Masters degree in Bioethics blindly scored all student pre- and post-tests. Development of the rubric was an iterative process, refined after analyzing a subset of surveys. Once finalized, we confirmed the consistency and reliability of the rubric and grading process by re-testing a subset of student surveys randomly selected from all participating classes. The Cronbach alpha reliability result was 0.80 [19] .

The rubric closely followed the framework introduced through the curricular materials and reinforced through other case study analyses. For example, under Q2, Factual Support , a student rated 4 out of 4 if their response demonstrated the following:

• The justification uses the relevant scientific reasons to support student’s answer to the ethical question.
• The student demonstrates a solid understanding of the context in which the case occurs, including a thoughtful description of important missing information.
• The student shows logical, organized thinking. Both facts supporting the decision and missing information are presented at levels exceeding standard (as described above).

An example of a student response that received the highest rating for Q2 asking for factual support is: “Her family has a history of breast cancer and fibrocystic breast disease. She is bed-bound and completely dependent on her parents. Since she is bed-bound, she has a higher risk of blood clots. She has the mentality of an infant. Her parents’ requests offer minimal side effects. With this disease, how long is she expected to live? If not very long then her parents don’t have to worry about growth. Are there alternative measures?”

In contrast, a student rated a 1 for responses that had the following characteristics:

• Factual information relevant to the case is incompletely described or is missing.
• Irrelevant information may be included and the student demonstrates some confusion.

An example of a student response that rated a 1 for Q2 is: “She is unconscious and doesn’t care what happens.”

All data were entered into SPSS (Statistical Package for the Social Sciences) and analyzed for means, standard deviations, and statistically significant differences. An Analysis of Variance (ANOVA) was used to test for significant overall differences between the two cohort groups. Pre-test and post-test composite scores were calculated for each student by adding individual scores for each item on the pre- and post-tests. The composite score on the post-test was identical in form and scoring to the composite score on the pre-test. The effect of the CURE treatment on post-test composite scores is referred to as the Main Effect, and was determined by comparing the post-test composite scores of the Cohort 1 (CURE) and Cohort 2 (Comparison) groups. In addition, Cohort 1 and Cohort 2 means scores for each test question (Questions 1–5) were compared within and between cohorts using t-tests.

CURE student perceptions of curriculum effect.

During prior program evaluations, we asked teachers to identify what they believed to be the main impacts of bioethics instruction on students. From this earlier work, we identified several themes. These themes, listed below, were further tested in our current study by asking students in the treatment group to assess themselves in these five areas after participation in the lesson, using a retrospective pre-test design to measure self-reported changes in perceptions and abilities [20] .

• Interest in the science content of class (before/after) participating in the Ethics unit.
• Ability to analyze issues related to science and society and make well-justified decisions (before/after) participating in the Ethics unit.
• Awareness of ethics and ethical issues (before/after) participating in the Ethics unit.
• Understanding of the connection between science and society (before/after) participating in the Ethics unit.
• Ability to listen to and discuss different viewpoints (before/after) participating in the Ethics unit.

After Cohort 1 (CURE) students participated in the Bioethics 101 curriculum, we asked them to indicate the extent to which they had changed in each of the theme areas we had identified using Likert-scale items on a retrospective pre-test design [21] , with 1 =  None and 5 =  A lot!. We used paired t-tests to examine self-reported changes in their perceptions and abilities. The retrospective design avoids response-shift bias that results from overestimation or underestimation of change since both before and after information is collected at the same time [20] .

Student Demographics

Demographic information is provided in Table 3 . Of those students who reported their gender, a larger number were female (N = 258) than male (N = 169), 60% and 40%, respectively, though female students represented a larger proportion of Cohort 1 than Cohort 2. Students ranged in age from 14 to 18 years old; the average age of the students in both cohorts was 15. Students were enrolled in a variety of science classes (mostly Biology or Honors Biology). Because NIH recognizes a difference between race and ethnicity, students were asked to respond to both demographic questions. Students in both cohorts were from a variety of ethnic and racial backgrounds.

https://doi.org/10.1371/journal.pone.0036791.t003

Pre- and Post-Test Results for CURE and Comparison Students

Post-test composite means for each cohort (1 and 2) and group (A and B) are shown in Table 4 . Students receiving CURE instruction earned significantly higher (p<0.001) composite mean scores than students in comparison classrooms. Cohort 1 (CURE) students (N = 323) post-test composite means were 10.73, while Cohort 2 (Comparison) students (N = 108) had post-test composite means of 9.16. The ANOVA results ( Table 5 ) showed significant differences in the ability to craft strong justifications between Cohort 1 (CURE) and Cohort 2 (Comparison) students F (1, 429) = 26.64, p<0.001.

https://doi.org/10.1371/journal.pone.0036791.t004

https://doi.org/10.1371/journal.pone.0036791.t005

We also examined if the pre-test had a priming effect on the students’ scores because it provides an opportunity to practice or think about the content. The pre-test would not have this effect on the comparison group because they were not exposed to CURE teaching or materials. If the pre-test provides a practice or priming effect, this would result in higher post-test performance by CURE students receiving the pre-test than by CURE students not receiving the pre-test. For this comparison, the F (1, 321) = 0.10, p = 0.92. This result suggests that the differences between the CURE and comparison groups are attributable to the treatment condition and not a priming effect of the pre-test.

After differences in main effects were investigated, we analyzed differences between and within cohorts on individual items (Questions 1–5) using t-tests. The Mean scores of individual questions for each cohort are shown in Figure 1 . There were no significant differences between Cohort 1 (CURE) and Cohort 2 (Comparison) on pre-test scores. In fact, for Q5, the mean pre-test scores for the Cohort 2 (Comparison) group were slightly higher (1.8) than the Cohort 1 (CURE) group (1.6). On the post-test, the Cohort 1 (CURE) students significantly outscored the Cohort 2 (Comparison) students on all questions; Q1, Q3, and Q4 were significant at p<0.001, Q2 was significant at p<0.01, and Q5 was significant at p<0.05. The largest post-test difference between Cohort 1 (CURE) students and Cohort 2 (Comparison) students was for Q3, with an increase of 0.6; all the other questions showed changes of 0.3 or less. Comparing Cohort 1 (CURE) post-test performance on individual questions yields the following results: scores were highest for Q1 (mean = 2.8), followed by Q3 (mean = 2.2), Q2 (mean = 2.1), and Q5 (mean = 1.9). Lowest Cohort 1 (CURE) post-test scores were associated with Q4 (mean = 1.8).

Mean scores for individual items of the pre-test for each cohort revealed no differences between groups for any of the items (Cohort 1, CURE, N = 323; Cohort 2, Comparison, N = 108). Post-test gains of Cohort 1 (CURE) relative to Cohort 2 (Comparison) were statistically significant for all questions. (Question (Q) 1) What is your decision? (Q2) What facts support your decision? Is there missing information that could be used to make a better decision? (Q3) Who will be impacted by the decision and how will they be impacted? (Q4) What are the main ethical considerations? and (Q5)What are some strengths and weaknesses of alternate solutions? Specifically: (Q1), (Q3), (Q4) were significant at p<0.001 (***); (Q2) was significant at p<0.01 (**); and (Q5) was significant at p<0.05 (*). Lines represent standard deviations.

https://doi.org/10.1371/journal.pone.0036791.g001

Overall, across all four groups, mean scores for Q1 were highest (2.6), while scores for Q4 were lowest (1.6). When comparing within-Cohort scores on the pre-test versus post-test, Cohort 2 (Comparison Group) showed little to no change, while CURE students improved on all test questions.

CURE Student Perceptions of Curriculum Effect

After using our resources, Cohort 1 (CURE) students showed highly significant gains (p<0.001) in all areas examined: interest in science content, ability to analyze socio-scientific issues and make well-justified decisions, awareness of ethical issues, understanding of the connection between science and society, and the ability to listen to and discuss viewpoints different from their own ( Figure 2 ). Overall, students gave the highest score to their ability to listen to and discuss viewpoints different than their own after participating in the CURE unit (mean = 4.2). Also highly rated were the changes in understanding of the connection between science and society (mean = 4.1) and the awareness of ethical issues (mean = 4.1); these two perceptions also showed the largest change pre-post (from 2.8 to 4.1 and 2.7 to 4.1, respectively).

Mean scores for individual items of the retrospective items on the post-test for Cohort 1 students revealed significant gains (p<0.001) in all self-reported items: Interest in science (N = 308), ability to Analyze issues related to science and society and make well-justified decisions (N = 306), Awareness of ethics and ethical issues (N = 309), Understanding of the connection between science and society (N = 308), and the ability to Listen and discuss different viewpoints (N = 308). Lines represent standard deviations.

https://doi.org/10.1371/journal.pone.0036791.g002

NWABR’s teaching materials provide support both for general ethics and bioethics education, as well as for specific topics such as embryonic stem cell research. These resources were developed to provide teachers with classroom strategies, ethics background, and decision-making frameworks. Teachers are then prepared to share their understanding with their students, and to support their students in using analysis tools and participating in effective classroom discussions. Our current research grew out of a desire to measure the effectiveness of our professional development and teaching resources in fostering student ability to analyze a complex bioethical case study and to justify their positions.

Consistent with the findings of SSI researchers and our own prior anecdotal observations of teacher classrooms and student work, we found that students improve in their analytical skill when provided with reasoning frameworks and background in concepts such as beneficence, respect, and justice. Our research demonstrates that structured reasoning approaches can be effectively taught at the secondary level and that they can improve student thinking skills. After teachers participated in a two-week professional development workshop and utilized our Bioethics 101 curriculum, within a relatively short time period (five lessons spanning approximately one to two weeks), students grew significantly in their ability to analyze a complex case and justify their position compared to students not exposed to the program. Often, biology texts present a controversial issue and ask students to “justify their position,” but teachers have shared with us that students frequently do not understand what makes a position or argument well-justified. By providing students with opportunities to evaluate sample justifications, and by explicitly introducing a set of elements that students should include in their justifications, we have facilitated the development of this important cognitive skill.

The first part of our research examined the impact of CURE instruction on students’ ability to analyze a case study. Although students grew significantly in all areas, the highest scores for the Cohort 1 (CURE) students were found in response to Q1 of the case analysis, which asked them to clearly state their own position, and represented a relatively easy cognitive task. This question also received the highest score in the comparison group. Not surprisingly, students struggled most with Q4 and Q5, which asked for the ethical considerations and the strengths and weaknesses of different solutions, respectively, and which tested specialized knowledge and sophisticated analytical skills. The area in which we saw the most growth in Cohort 1 (CURE) (both in comparison to the pre-test and in relation to the comparison group) was in students’ ability to identify stakeholders in a case and state how they might be impacted by a decision (Q3). Teachers have shared with us that secondary students are often focused on their own needs and perspectives; stepping into the perspectives of others helps enlarge their understanding of the many views that can be brought to bear upon a socio-scientific issue.

Many of our teachers go far beyond these introductory lessons, revisiting key concepts throughout the year as new topics are presented in the media or as new curricular connections arise. Although we have observed this phenomenon for many years, it has been difficult to evaluate these types of interventions, as so many teachers implement the concepts and ideas differently in response to their unique needs. Some teachers have used the Bioethics 101 curriculum as a means for setting the tone and norms for the entire year in their classes and fostering an atmosphere of respectful discussion. These teachers note that the “opportunity cost” of investing time in teaching basic bioethical concepts, decision-making strategies, and justification frameworks pays off over the long run. Students’ understanding of many different science topics is enhanced by their ability to analyze issues related to science and society and make well-justified decisions. Throughout their courses, teachers are able to refer back to the core ideas introduced in Bioethics 101, reinforcing the wide utility of the curriculum.

The second part of our research focused on changes in students’ self-reported attitudes and perceptions as a result of CURE instruction. Obtaining accurate and meaningful data to assess student self-reported perceptions can be difficult, especially when a program is distributed across multiple schools. The traditional use of the pretest-posttest design assumes that students are using the same internal standard to judge attitudes or perceptions. Considerable empirical evidence suggests that program effects based on pre-posttest self-reports are masked because people either overestimate or underestimate their pre-program perceptions [20] , [22] – [26] . Moore and Tananis [27] report that response shift can occur in educational programs, especially when they are designed to increase students’ awareness of a specific construct that is being measured. The retrospective pre-test design (RPT), which was used in this study, has gained increasing prominence as a convenient and valid method for measuring self-reported change. RPT has been shown to reduce response shift bias, providing more accurate assessment of actual effect. The retrospective design avoids response-shift bias that results from overestimation or underestimation of change since both before and after information is collected at the same time [20] . It is also convenient to implement, provides comparison data, and may be more appropriate in some situations [26] . Using student self-reported measures concerning perceptions and attitudes is also a meta-cognitive strategy that allows students to think about their learning and justify where they believe they are at the end of a project or curriculum compared to where they were at the beginning.

Our approach resulted in a significant increase in students’ own perceived growth in several areas related to awareness, understanding, and interest in science. Our finding that student interest in science can be significantly increased through a case-study based bioethics curriculum has implications for instruction. Incorporating ethical dilemmas into the classroom is one strategy for increasing student motivation and engagement with science content. Students noted the greatest changes in their own awareness of ethical issues and in understanding the connection between science and society. Students gave the highest overall rating to their ability to listen to and discuss viewpoints different from their own after participation in the bioethics unit. This finding also has implications for our future citizenry; in an increasingly diverse and globalized society, students need to be able to engage in civil and rational dialogue with others who may not share their views.

Conducting research studies about ethical learning in secondary schools is challenging; recruiting teachers for Cohort 2 and obtaining consent from students, parents, and teachers for participation was particularly difficult, and many teachers faced restraints from district regulations about curriculum content. Additional studies are needed to clarify the extent to which our curricular materials alone, without accompanying teacher professional development, can improve student reasoning skills.

Teacher pre-service training programs rarely incorporate discussion of how to address ethical issues in science with prospective educators. Likewise, with some noticeable exceptions, such as the work of the University of Pennsylvania High School Bioethics Project, the Genetic Science Learning Center at the University of Utah, and the Kennedy Institute of Ethics at Georgetown University, relatively few resources exist for high school curricular materials in this area. Teachers have shared with us that they know that such issues are important and engaging for students, but they do not have the experience in either ethical theory or in managing classroom discussion to feel comfortable teaching bioethics topics. After participating in our workshops or using our teaching materials, teachers shared that they are better prepared to address such issues with their students, and that students are more engaged in science topics and are better able to see the real-world context of what they are learning.

Preparing students for a future in which they have access to personalized genetic information, or need to vote on proposals for stem cell research funding, necessitates providing them with the tools required to reason through a complex decision containing both scientific and ethical components. Students begin to realize that, although there may not be an absolute “right” or “wrong” decision to be made on an ethical issue, neither is ethics purely relative (“my opinion versus yours”). They come to realize that all arguments are not equal; there are stronger and weaker justifications for positions. Strong justifications are built upon accurate scientific information and solid analysis of ethical and contextual considerations. An informed citizenry that can engage in reasoned dialogue about the role science should play in society is critical to ensure the continued vitality of the scientific enterprise.

“I now bring up ethical issues regularly with my students, and use them to help students see how the concepts they are learning apply to their lives…I am seeing positive results from my students, who are more clearly able to see how abstract science concepts apply to them.” – CURE Teacher “In ethics, I’ve learned to start thinking about the bigger picture. Before, I based my decisions on how they would affect me. Also, I made decisions depending on my personal opinions, sometimes ignoring the facts and just going with what I thought was best. Now, I know that to make an important choice, you have to consider the other people involved, not just yourself, and take all information and facts into account.” – CURE Student

Supporting Information

Bioethics 101 Lesson Overview.

https://doi.org/10.1371/journal.pone.0036791.s001

Case Study for Assessment.

https://doi.org/10.1371/journal.pone.0036791.s002

Grading Rubric for Pre- and Post-Test: Ashley’s Case.

https://doi.org/10.1371/journal.pone.0036791.s003

Acknowledgments

We thank Susan Adler, Jennifer M. Pang, Ph.D., Leena Pranikay, and Reitha Weeks, Ph.D., for their review of the manuscript, and Nichole Beddes for her assistance scoring student work. We also thank Carolyn Cohen of Cohen Research and Evaluation, former CURE Evaluation Consultant, who laid some of the groundwork for this study through her prior work with us. We also wish to thank the reviewers of our manuscript for their thoughtful feedback and suggestions.

Author Contributions

Conceived and designed the experiments: JTC LJC. Performed the experiments: LJC. Analyzed the data: LJC JTC DNK. Contributed reagents/materials/analysis tools: JCG. Wrote the paper: JTC LJC DNK JCG. Served as Principal Investigator on the CURE project: JTC. Provided overall program leadership: JTC. Led the curriculum and professional development efforts: JTC JCG. Raised funds for the CURE program: JTC.

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• 26. Klatt J, Taylor-Powell E (2005) Synthesis of literature relative to the retrospective pretest design. Presentation to the 2005 Joint CES/AEA Conference, Toronto.

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• v.22(4); 2014 Aug

Critical Thinking: The Development of an Essential Skill for Nursing Students

Ioanna v. papathanasiou.

1 Nursing Department, Technological Educational Institute of Thessaly, Greece

Christos F. Kleisiaris

2 Nursing Department, Technological Educational Institute of Crete, Greece

Evangelos C. Fradelos

3 State Mental Hospital of Attica “Daphne”, Greece

Katerina Kakou

Lambrini kourkouta.

4 Nursing Department, Alexander Technological Educational Institute of Thessaloniki, Greece

Critical thinking is defined as the mental process of actively and skillfully perception, analysis, synthesis and evaluation of collected information through observation, experience and communication that leads to a decision for action. In nursing education there is frequent reference to critical thinking and to the significance that it has in daily clinical nursing practice. Nursing clinical instructors know that students face difficulties in making decisions related to clinical practice. The main critical thinking skills in which nursing students should be exercised during their studies are critical analysis, introductory and concluding justification, valid conclusion, distinguish of facts and opinions, evaluation the credibility of information sources, clarification of concepts and recognition of conditions. Specific behaviors are essentials for enhancing critical thinking. Nursing students in order to learn and apply critical thinking should develop independence of thought, fairness, perspicacity in personal and social level, humility, spiritual courage, integrity, perseverance, self-confidence, interest for research and curiosity. Critical thinking is an essential process for the safe, efficient and skillful nursing practice. The nursing education programs should adopt attitudes that promote critical thinking and mobilize the skills of critical reasoning.

1. INTRODUCTION

Critical thinking is applied by nurses in the process of solving problems of patients and decision-making process with creativity to enhance the effect. It is an essential process for a safe, efficient and skillful nursing intervention. Critical thinking according to Scriven and Paul is the mental active process and subtle perception, analysis, synthesis and evaluation of information collected or derived from observation, experience, reflection, reasoning or the communication leading to conviction for action ( 1 ).

So, nurses must adopt positions that promote critical thinking and refine skills of critical reasoning in order a meaningful assessment of both the previous and the new information and decisions taken daily on hospitalization and use of limited resources, forces you to think and act in cases where there are neither clear answers nor specific procedures and where opposing forces transform decision making in a complex process ( 2 ).

Critical thinking applies to nurses as they have diverse multifaceted knowledge to handle the various situations encountered during their shifts still face constant changes in an environment with constant stress of changing conditions and make important decisions using critical thinking to collect and interpret information that are necessary for making a decision ( 3 ).

Critical thinking, combined with creativity, refine the result as nurses can find specific solutions to specific problems with creativity taking place where traditional interventions are not effective. Even with creativity, nurses generate new ideas quickly, get flexible and natural, create original solutions to problems, act independently and with confidence, even under pressure, and demonstrate originality ( 4 ).

The aim of the study is to present the basic skills of critical thinking, to highlight critical thinking as a essential skill for nursing education and a fundamental skill for decision making in nursing practice. Moreover to indicate the positive effect and relation that critical thinking has on professional outcomes.

2. CRITICAL THINKING SKILLS

Nurses in their efforts to implement critical thinking should develop some methods as well as cognitive skills required in analysis, problem solving and decision making ( 5 ). These skills include critical analysis, introductory and concluding justification, valid conclusion, distinguishing facts and opinions to assess the credibility of sources of information, clarification of concepts, and recognition conditions ( 6 , 7 ).

Critical analysis is applied to a set of questions that relate to the event or concept for the determination of important information and ideas and discarding the unnecessary ones. It is, thus, a set of criteria to rationalize an idea where one must know all the questions but to use the appropriate one in this case ( 8 ).

The Socratic Method, where the question and the answer are sought, is a technique in which one can investigate below the surface, recognize and examine the condition, look for the consequences, investigate the multiple data views and distinguish between what one knows and what he simply believes. This method should be implemented by nurses at the end of their shifts, when reviewing patient history and progress, planning the nursing plan or discussing the treatment of a patient with colleagues ( 9 ).

The Inference and Concluding justification are two other critical thinking skills, where the justification for inductive generalizations formed from a set of data and observations, which when considered together, specific pieces of information constitute a special interpretation ( 10 ). In contrast, the justification is deduced from the general to the specific. According to this, nurse starts from a conceptual framework–for example, the prioritization of needs by Maslow or a context–evident and gives descriptive interpretation of the patient’s condition with respect to this framework. So, the nurse who uses drawing needs categorizes information and defines the problem of the patient based on eradication, nutrition or need protection.

In critical thinking, the nurses still distinguish claims based on facts, conclusions, judgments and opinions. The assessment of the reliability of information is an important stage of critical thinking, where the nurse needs to confirm the accuracy of this information by checking other evidence and informants ( 10 ).

The concepts are ideas and opinions that represent objects in the real world and the importance of them. Each person has developed its own concepts, where they are nested by others, either based on personal experience or study or other activities. For a clear understanding of the situation of the patient, the nurse and the patient should be in agreement with the importance of concepts.

People also live under certain assumptions. Many believe that people generally have a generous nature, while others believe that it is a human tendency to act in its own interest. The nurse must believe that life should be considered as invaluable regardless of the condition of the patient, with the patient often believing that quality of life is more important than duration. Nurse and patient, realizing that they can make choices based on these assumptions, can work together for a common acceptable nursing plan ( 11 ).

3. CRITICAL THINKING ENHANCEMENT BEHAVIORS

The person applying critical thinking works to develop the following attitudes and characteristics independence of thought, fairness, insight into the personal and public level, humble intellect and postpone the crisis, spiritual courage, integrity, perseverance, self-confidence, research interest considerations not only behind the feelings and emotions but also behind the thoughts and curiosity ( 12 ).

Independence of Thought

Individuals who apply critical thinking as they mature acquire knowledge and experiences and examine their beliefs under new evidence. The nurses do not remain to what they were taught in school, but are “open-minded” in terms of different intervention methods technical skills.

Impartiality

Those who apply critical thinking are independent in different ways, based on evidence and not panic or personal and group biases. The nurse takes into account the views of both the younger and older family members.

Perspicacity into Personal and Social Factors

Those who are using critical thinking and accept the possibility that their personal prejudices, social pressures and habits could affect their judgment greatly. So, they try to actively interpret their prejudices whenever they think and decide.

Humble Cerebration and Deferral Crisis

Humble intellect means to have someone aware of the limits of his own knowledge. So, those who apply critical thinking are willing to admit they do not know something and believe that what we all consider rectum cannot always be true, because new evidence may emerge.

Spiritual Courage

The values and beliefs are not always obtained by rationality, meaning opinions that have been researched and proven that are supported by reasons and information. The courage should be true to their new ground in situations where social penalties for incompatibility are strict. In many cases the nurses who supported an attitude according to which if investigations are proved wrong, they are canceled.

Use of critical thinking to mentally intact individuals question their knowledge and beliefs quickly and thoroughly and cause the knowledge of others so that they are willing to admit and appreciate inconsistencies of both their own beliefs and the beliefs of the others.

Perseverance

The perseverance shown by nurses in exploring effective solutions for patient problems and nursing each determination helps to clarify concepts and to distinguish related issues despite the difficulties and failures. Using critical thinking they resist the temptation to find a quick and simple answer to avoid uncomfortable situations such as confusion and frustration.

Confidence in the Justification

According to critical thinking through well motivated reasoning leads to reliable conclusions. Using critical thinking nurses develop both the inductive and the deductive reasoning. The nurse gaining more experience of mental process and improvement, does not hesitate to disagree and be troubled thereby acting as a role model to colleagues, inspiring them to develop critical thinking.

Interesting Thoughts and Feelings for Research

Nurses need to recognize, examine and inspect or modify the emotions involved with critical thinking. So, if they feel anger, guilt and frustration for some event in their work, they should follow some steps: To restrict the operations for a while to avoid hasty conclusions and impulsive decisions, discuss negative feelings with a trusted, consume some of the energy produced by emotion, for example, doing calisthenics or walking, ponder over the situation and determine whether the emotional response is appropriate. After intense feelings abate, the nurse will be able to proceed objectively to necessary conclusions and to take the necessary decisions.

The internal debate, that has constantly in mind that the use of critical thinking is full of questions. So, a research nurse calculates traditions but does not hesitate to challenge them if you do not confirm their validity and reliability.

4. IMPLEMENTATION OF CRITICAL THINKING IN NURSING PRACTICE

In their shifts nurses act effectively without using critical thinking as many decisions are mainly based on habit and have a minimum reflection. Thus, higher critical thinking skills are put into operation, when some new ideas or needs are displayed to take a decision beyond routine. The nursing process is a systematic, rational method of planning and providing specialized nursing ( 13 ). The steps of the nursing process are assessment, diagnosis, planning, implementation, evaluation. The health care is setting the priorities of the day to apply critical thinking ( 14 ). Each nurse seeks awareness of reasoning as he/she applies the criteria and considerations and as thinking evolves ( 15 ).

Problem Solving

Problem solving helps to acquire knowledge as nurse obtains information explaining the nature of the problem and recommends possible solutions which evaluate and select the application of the best without rejecting them in a possible appeal of the original. Also, it approaches issues when solving problems that are often used is the empirical method, intuition, research process and the scientific method modified ( 16 ).

Experiential Method

This method is mainly used in home care nursing interventions where they cannot function properly because of the tools and equipment that are incomplete ( 17 ).

Intuition is the perception and understanding of concepts without the conscious use of reasoning. As a problem solving approach, as it is considered by many, is a form of guessing and therefore is characterized as an inappropriate basis for nursing decisions. But others see it as important and legitimate aspect of the crisis gained through knowledge and experience. The clinical experience allows the practitioner to recognize items and standards and approach the right conclusions. Many nurses are sensing the evolution of the patient’s condition which helps them to act sooner although the limited information. Despite the fact that the intuitive method of solving problems is recognized as part of nursing practice, it is not recommended for beginners or students because the cognitive level and the clinical experience is incomplete and does not allow a valid decision ( 16 ).

Research Process / Scientifically Modified Method

The research method is a worded, rational and systematic approach to problem solving. Health professionals working in uncontrolled situations need to implement a modified approach of the scientific method of problem solving. With critical thinking being important in all processes of problem solving, the nurse considers all possible solutions and decides on the choice of the most appropriate solution for each case ( 18 ).

The Decision

The decision is the selection of appropriate actions to fulfill the desired objective through critical thinking. Decisions should be taken when several exclusive options are available or when there is a choice of action or not. The nurse when facing multiple needs of patients, should set priorities and decide the order in which they help their patients. They should therefore: a) examine the advantages and disadvantages of each option, b) implement prioritization needs by Maslow, c) assess what actions can be delegated to others, and d) use any framework implementation priorities. Even nurses make decisions about their personal and professional lives. The successive stages of decision making are the Recognition of Objective or Purpose, Definition of criteria, Calculation Criteria, Exploration of Alternative Solutions, Consideration of Alternative Solutions, Design, Implementation, Evaluation result ( 16 ).

The contribution of critical thinking in decision making

Acquiring critical thinking and opinion is a question of practice. Critical thinking is not a phenomenon and we should all try to achieve some level of critical thinking to solve problems and make decisions successfully ( 19 - 21 ).

It is vital that the alteration of growing research or application of the Socratic Method or other technique since nurses revise the evaluation criteria of thinking and apply their own reasoning. So when they have knowledge of their own reasoning-as they apply critical thinking-they can detect syllogistic errors ( 22 – 26 ).

5. CONCLUSION

In responsible positions nurses should be especially aware of the climate of thought that is implemented and actively create an environment that stimulates and encourages diversity of opinion and research ideas ( 27 ). The nurses will also be applied to investigate the views of people from different cultures, religions, social and economic levels, family structures and different ages. Managing nurses should encourage colleagues to scrutinize the data prior to draw conclusions and to avoid “group thinking” which tends to vary without thinking of the will of the group. Critical thinking is an essential process for the safe, efficient and skillful nursing practice. The nursing education programs should adopt attitudes that promote critical thinking and mobilize the skills of critical reasoning.

CONFLICT OF INTEREST: NONE DECLARED.

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Justification Logic

You may say, “I know that Abraham Lincoln was a tall man. ” In turn you may be asked how you know. You would almost certainly not reply semantically, Hintikka-style, that Abraham Lincoln was tall in all situations compatible with your knowledge. Instead you would more likely say, “I read about Abraham Lincoln’s height in several books, and I have seen photographs of him next to other people. ” One certifies knowledge by providing a reason, a justification. Hintikka semantics captures knowledge as true belief. Justification logics supply the missing third component of Plato’s characterization of knowledge as justified true belief.

1.1 Epistemic Tradition

1.2 mathematical logic tradition, 1.3 hyperintensionality, 2.1 the language of justification logic, 2.2 basic justification logic \(\mathsf{j}_{0}\), 2.3 logical awareness and constant specifications, 2.4 extending basic justification logic, 2.5 factivity, 2.6 positive introspection, 2.7 negative introspection, 2.8 geach logics and more, 3.1 single-agent possible world justification models for \(\mathsf{j}\), 3.2 weak and strong completeness, 3.3 the single-agent family, 3.4 single world justification models, 3.5 ontologically transparent semantics, 3.6 connections with awareness models, 4. realization theorems, 5.1 mixing explicit and implicit knowledge, 5.2 multi-agent possible world justification models, 6. russell’s example: induced factivity, 7. self-referentiality of justifications, 8. quantifiers in justification logic, 9. historical notes, other internet resources, related entries, 1. why justification logic.

Justification logics are epistemic logics which allow knowledge and belief modalities to be ‘unfolded’ into justification terms : instead of \(\Box X\) one writes \(t : X\), and reads it as “\(X\) is justified by reason \(t\)”. One may think of traditional modal operators as implicit modalities, and justification terms as their explicit elaborations which supplement modal logics with finer-grained epistemic machinery. The family of justification terms has structure and operations. Choice of operations gives rise to different justification logics. For all common epistemic logics their modalities can be completely unfolded into explicit justification form. In this respect Justification Logic reveals and uses the explicit, but hidden, content of traditional Epistemic Modal Logic.

Justification logic originated as part of a successful project to provide a constructive semantics for intuitionistic logic—justification terms abstracted away all but the most basic features of mathematical proofs. Proofs are justifications in perhaps their purest form. Subsequently justification logics were introduced into formal epistemology. This article presents the general range of justification logics as currently understood. It discusses their relationships with conventional modal logics. In addition to technical machinery, the article examines in what way the use of explicit justification terms sheds light on a number of traditional philosophical problems. The subject as a whole is still under active development.

The roots of justification logic can be traced back to many different sources, two of which are discussed in detail: epistemology and mathematical logic.

The properties of knowledge and belief have been a subject for formal logic at least since von Wright and Hintikka, (Hintikka 1962, von Wright 1951). Knowledge and belief are both treated as modalities in a way that is now very familiar— Epistemic Logic . But of Plato’s three criteria for knowledge, justified, true, belief , (Gettier 1963, Hendricks 2005), epistemic logic really works with only two of them. Possible worlds and indistinguishability model belief—one believes what is so under all circumstances thought possible. Factivity brings a trueness component into play—if something is not so in the actual world it cannot be known, only believed. But there is no representation for the justification condition. Nonetheless, the modal approach has been remarkably successful in permitting the development of a rich mathematical theory and applications, (Fagin, Halpern, Moses, and Vardi 1995, van Ditmarsch, van der Hoek, and Kooi 2007). Still, it is not the whole picture.

The modal approach to the logic of knowledge is, in a sense, built around the universal quantifier: \(X\) is known in a situation if \(X\) is true in all situations indistinguishable from that one. Justifications, on the other hand, bring an existential quantifier into the picture: \(X\) is known in a situation if there exists a justification for \(X\) in that situation. This universal/existential dichotomy is a familiar one to logicians—in formal logics there exists a proof for a formula \(X\) if and only if \(X\) is true in all models for the logic. One thinks of models as inherently non-constructive, and proofs as constructive things. One will not go far wrong in thinking of justifications in general as much like mathematical proofs. Indeed, the first justification logic was explicitly designed to capture mathematical proofs in arithmetic, something which will be discussed further in Section 1.2.

In Justification Logic, in addition to the category of formulas, there is a second category of justifications . Justifications are formal terms, built up from constants and variables using various operation symbols. Constants represent justifications for commonly accepted truths—typically axioms. Variables denote unspecified justifications. Different justification logics differ on which operations are allowed (and also in other ways too). If \(t\) is a justification term and \(X\) is a formula, \(t : X\) is a formula, and is intended to be read:

\(t\) is a justification for X.

One operation, common to all justification logics, is application , written like multiplication. The idea is, if \(s\) is a justification for \(A \rightarrow B\) and \(t\) is a justification for \(A\), then [\(s\cdot t\)] is a justification for \(B\) [ 1 ] . That is, the validity of the following is generally assumed:

This is the explicit version of the usual distributivity of knowledge operators, and modal operators generally, across implication:

In fact, formula (2) is behind many of the problems of logical omniscience . It asserts that an agent knows everything that is implied by the agent’s knowledge—knowledge is closed under consequence. While knowable-in-principle, knowability, is closed under consequence, the same cannot be said for any plausible version of actual knowledge. The distinction between (1) and (2) can be exploited in a discussion of the paradigmatic Red Barn Example of Goldman and Kripke; here is a simplified version of the story taken from (Dretske 2005).

Suppose I am driving through a neighborhood in which, unbeknownst to me, papier-mâché barns are scattered, and I see that the object in front of me is a barn. Because I have barn-before-me percepts, I believe that the object in front of me is a barn. Our intuitions suggest that I fail to know barn. But now suppose that the neighborhood has no fake red barns, and I also notice that the object in front of me is red, so I know a red barn is there. This juxtaposition, being a red barn, which I know, entails there being a barn, which I do not, “is an embarrassment”.

In the first formalization of the Red Barn Example, logical derivation will be performed in a basic modal logic in which \(\Box\) is interpreted as the ‘belief’ modality. Then some of the occurrences of \(\Box\) will be externally interpreted as ‘knowledge’ according to the problem’s description. Let \(B\) be the sentence ‘the object in front of me is a barn’, and let \(R\) be the sentence ‘the object in front of me is red’.

• \(\Box B\), ‘I believe that the object in front of me is a barn’;
• \(\Box ( B \wedge R)\), ‘I believe that the object in front of me is a red barn’.

At the metalevel, 2 is actually knowledge, whereas by the problem description, 1 is not knowledge.

• \(\Box ( B \wedge R \rightarrow B)\), a knowledge assertion of a logical axiom.

Within this formalization, it appears that epistemic closure in its modal form (2) is violated: line 2, \(\Box ( B \wedge R )\), and line 3, \(\Box ( B \wedge R \rightarrow B)\) are cases of knowledge whereas \(\Box B\) (line 1) is not knowledge. The modal language here does not seem to help resolving this issue.

Next consider the Red Barn Example in Justification Logic where \(t : F\) is interpreted as ‘I believe \(F\) for reason \(t\)’. Let \(u\) be a specific individual justification for belief that \(B\), and \(v\), for belief that \(B \wedge R\). In addition, let \(a\) be a justification for the logical truth \(B \wedge R \rightarrow B\). Then the list of assumptions is:

• \(u : B\), ‘\(u\) is a reason to believe that the object in front of me is a barn’;
• \(v :( B \wedge R)\), ‘\(v\) is a reason to believe that the object in front of me is a red barn’;
• \(a :( B \wedge R \rightarrow B)\).

On the metalevel, the problem description states that 2 and 3 are cases of knowledge, and not merely belief, whereas 1 is belief which is not knowledge. Here is how the formal reasoning goes:

• \(a :( B \wedge R \rightarrow B ) \rightarrow ( v :( B \wedge R ) \rightarrow [ a\cdot v ]: B)\), by principle (1);
• \(v :( B \wedge R ) \rightarrow [ a \cdot v ]: B\), from 3 and 4, by propositional logic;
• [\(a\cdot v ]: B\), from 2 and 5, by propositional logic.

Notice that conclusion 6 is [\(a\cdot v ]: B\), and not \(u : B\) ; epistemic closure holds. By reasoning in justification logic it was concluded that [\(a\cdot v ]: B\) is a case of knowledge, i.e., ‘I know \(B\) for reason \(a\cdot v\)’. The fact that \(u : B\) is not a case of knowledge does not spoil the closure principle, since the latter claims knowledge specifically for [\(a\cdot v ]: B\). Hence after observing a red façade, I indeed know \(B\), but this knowledge has nothing to do with 1, which remains a case of belief rather than of knowledge. The justification logic formalization represents the situation fairly.

Tracking justifications represents the structure of the Red Barn Example in a way that is not captured by traditional epistemic modal tools. The Justification Logic formalization models what seems to be happening in such a case; closure of knowledge under logical entailment is maintained even though ‘barn’ is not perceptually known. [ 2 ]

According to Brouwer, truth in constructive (intuitionistic) mathematics means the existence of a proof, cf. (Troelstra and van Dalen 1988). In 1931–34, Heyting and Kolmogorov gave an informal description of the intended proof-based semantics for intuitionistic logic (Kolmogorov 1932, Heyting 1934), which is now referred to as the Brouwer-Heyting-Kolmogorov (BHK) semantics . According to the BHK conditions, a formula is ‘true’ if it has a proof. Furthermore, a proof of a compound statement is connected to proofs of its components in the following way:

• a proof of \(A \wedge B\) consists of a proof of proposition \(A\) and a proof of proposition \(B\);
• a proof of \(A \vee B\) is given by presenting either a proof of \(A\) or a proof of \(B\);
• a proof of \(A \rightarrow B\) is a construction transforming proofs of \(A\) into proofs of \(B\);
• falsehood \(\bot\) is a proposition which has no proof, \(\neg A\) is shorthand for \(A \rightarrow \bot\) .

Kolmogorov explicitly suggested that the proof-like objects in his interpretation (“problem solutions”) came from classical mathematics (Kolmogorov 1932). Indeed, from a foundational point of view it does not make much sense to understand the ‘proofs’ above as proofs in an intuitionistic system which these conditions are supposed to be specifying.

The fundamental value of the BHK semantics is that informally but unambiguously it suggests treating justifications, here mathematical proofs, as objects with operations.

In (Gödel 1933), Gödel took the first step towards developing a rigorous proof-based semantics for intuitionism. Gödel considered the classical modal logic \(\mathsf{S4}\) to be a calculus describing properties of provability:

• Axioms and rules of classical propositional logic;
• \(\Box ( F \rightarrow G ) \rightarrow ( \Box F \rightarrow \Box G)\);
• \(\Box F \rightarrow F\);
• \(\Box F \rightarrow \Box \Box F\);
• Rule of necessitation: if \(\vdash F\), then \(\vdash \Box F\).

Based on Brouwer’s understanding of logical truth as provability, Gödel defined a translation tr\((F)\) of the propositional formula \(F\) in the intuitionistic language into the language of classical modal logic: tr\((F)\) is obtained by prefixing every subformula of \(F\) with the provability modality \(\Box\). Informally speaking, when the usual procedure of determining classical truth of a formula is applied to tr\((F)\), it will test the provability (not the truth) of each of \(F\)’s subformulas, in agreement with Brouwer’s ideas. From Gödel’s results and the McKinsey-Tarski work on topological semantics for modal logic, it follows that the translation tr\((F)\) provides a proper embedding of the Intuitionistic Propositional Calculus, \(\mathsf{IPC}\), into \(\mathsf{S4}\), i.e., an embedding of intuitionistic logic into classical logic extended by the provability operator.

Still, Gödel’s original goal of defining intuitionistic logic in terms of classical provability was not reached, since the connection of \(\mathsf{S4}\) to the usual mathematical notion of provability was not established. Moreover, Gödel noted that the straightforward idea of interpreting modality \(\Box F\) as F is provable in a given formal system T contradicted Gödel’s second incompleteness theorem. Indeed, \(\Box ( \Box F \rightarrow F)\) can be derived in \(\mathsf{S4}\) by the rule of necessitation from the axiom \(\Box F \rightarrow F\). On the other hand, interpreting modality \(\Box\) as the predicate of formal provability in theory \(T\) and \(F\) as contradiction, converts this formula into a false statement that the consistency of \(T\) is internally provable in \(T\).

The situation after (Gödel 1933) can be described by the following figure where ‘\(X \hookrightarrow Y\)’ should be read as ‘\(X\) is interpreted in \(Y\)’

In a public lecture in Vienna in 1938, Gödel observed that using the format of explicit proofs:

can help in interpreting his provability calculus \(\mathsf{S4}\) (Gödel 1938). Unfortunately, Gödel’s work (Gödel 1938) remained unpublished until 1995, by which time the Gödelian logic of explicit proofs had already been rediscovered, and axiomatized as the Logic of Proofs \(\mathsf{LP}\) and supplied with completeness theorems connecting it to both \(\mathsf{S4}\) and classical proofs (Artemov 1995).

The Logic of Proofs \(\mathsf{LP}\) became the first in the Justification Logic family. Proof terms in \(\mathsf{LP}\) are nothing but BHK terms understood as classical proofs. With \(\mathsf{LP}\), propositional intuitionistic logic received the desired rigorous BHK semantics:

For further discussion of the mathematical logic tradition, see the Section 1 of the supplementary document Some More Technical Matters .

The hyperintensional paradox was formulated by Cresswell in 1975.

It is well known that it seems possible to have a situation in which there are two propositions \(p\) and \(q\) which are logically equivalent and yet are such that a person may believe the one but not the other. If we regard a proposition as a set of possible worlds then two logically equivalent propositions will be identical, and so if ‘\(x\) believes that’ is a genuine sentential functor, the situation described in the opening sentence could not arise. I call this the paradox of hyperintensional contexts. Hyperintensional contexts are simply contexts which do not respect logical equivalence.

Starting with Cresswell himself, several ways of dealing with this have been proposed. Generally these involve adding more layers to familiar possible world approaches so that some way of distinguishing between logically equivalent sentences is available. Cresswell suggested that the syntactic form of sentences be taken into account. Justification Logic, in effect, takes sentence form into account through its mechanism for handling justifications for sentences. Thus Justification Logic addresses some of the central issues of hyperintensionality and, as a bonus, we automatically have an appropriate proof theory, model theory, complexity estimates and a broad variety of applications.

A good example of a hyperintensional context is the informal language used by mathematicians conversing with each other. Typically when a mathematician says he or she knows something, the understanding is that a proof is at hand. But as the following illustrates, this kind of knowledge is essentially hyperintensional.

Fermat’s Last Theorem, FLT, is logically equivalent to \(0=0\) since both are provable, and hence denote the same proposition. However, the context of proofs distinguishes them immediately: a proof \(t\) of \(0=0\) is not necessarily a proof of FLT, and vice versa.

To formalize mathematical speech the justification logic \({\textsf{LP}}\) is a natural choice since \(t{:}X\) was designed to have characteristics of “\(t\) is a proof of \(X\).”

The fact that propositions \(X\) and \(Y\) are equivalent in \({\textsf{LP}}\), \(X\leftrightarrow Y\), does not warrant the equivalence of the corresponding justification assertions and typically \(t{:}X\) and \(t{:}Y\) are not equivalent, \(t{:}X\not\leftrightarrow t{:}Y\).

Going further \({\textsf{LP}}\), and Justification Logic in general, is not only sufficiently refined to distinguish justification assertions for logically equivalent sentences, it provides a flexible machinery to connect justifications of equivalent sentences and hence to maintain constructive closure properties necessary for a quality logic system. For example, let \(X\) and \(Y\) be provably equivalent, i.e., there is a proof \(u\) of \(X\leftrightarrow Y\), and so \(u{:}(X\leftrightarrow Y)\) is provable in \({\textsf{LP}}\). Suppose also that \(v\) is a proof of \(X\), and so \(v{:}X\). It has already been mentioned that this does not mean \(v\) is a proof of \(Y\)—this is a hyperintensional context. However within the framework of Justification Logic, building on the proofs of \(X\) and of \(X\leftrightarrow Y\), we can construct a proof term \(f(u,v)\) which represents the proof of \(Y\) and so \(f(u,v){:}Y\) is provable. In this respect, Justification Logic goes beyond Cresswell’s expectations: logically equivalent sentences display different but constructively controlled epistemic behavior.

2. The Basic Components of Justification Logic

In this section the syntax and axiomatics of the most common systems of justification logic are presented.

In order to build a formal account of justification logics one must make a basic structural assumption: justifications are abstract objects which have structure and operations on them . A good example of justifications is provided by formal proofs, which have long been objects of study in mathematical logic and computer science (cf. Section 1.2).

Justification Logic is a formal logical framework which incorporates epistemic assertions \(t : F\), standing for ‘\(t\) is a justification for \(F\)’. Justification Logic does not directly analyze what it means for \(t\) to justify \(F\) beyond the format \(t : F\), but rather attempts to characterize this relation axiomatically. This is similar to the way Boolean logic treats its connectives, say, disjunction: it does not analyze the formula \(p \vee q\) but rather assumes certain logical axioms and truth tables about this formula.

There are several design decisions made. Justification Logic starts with the simplest base: classical Boolean logic , and for good reasons. Justifications provide a sufficiently serious challenge on even the simplest level. The paradigmatic examples by Russell, Goldman-Kripke, Gettier and others, can be handled with Boolean Justification Logic. The core of Epistemic Logic consists of modal systems with a classical Boolean base ( K, T, K4, S4, K45, KD45, S5 , etc.), and each of them has been provided with a corresponding Justification Logic companion based on Boolean logic. Finally, factivity of justifications is not always assumed. This makes it possible to capture the essence of discussions in epistemology involving matters of belief and not knowledge.

The basic operation on justifications is application . The application operation takes justifications \(s\) and \(t\) and produces a justification \(s\cdot t\) such that if \(s :( F \rightarrow G)\) and \(t : F\), then [\(s\cdot t ]: G\). Symbolically,

This is a basic property of justifications assumed in combinatory logic and \(\lambda\) -calculi (Troelstra and Schwichtenberg 1996), Brouwer-Heyting-Kolmogorov semantics (Troelstra and van Dalen 1988), Kleene realizability (Kleene 1945), the Logic of Proofs \(\mathsf{LP}\), etc.

Another common operation on justifications is sum: it has been introduced to make explicit the modal logic reasoning (Artemov 1995). However, some meaningful justification logics like \({\mathsf{J}}^{-}\) (Artemov and Fitting 2019) or \({\mathsf{JNoC}}^{-}\) (Faroldi, Ghari, Lehmann, and Studer 2024) do not use the operation sum. With sum, any two justifications can safely be combined into something with broader scope. If \(s : F\), then whatever evidence \(t\) may be, the combined evidence \(s\) + \(t\) remains a justification for \(F\). More properly, the operation ‘+’ takes justifications \(s\) and \(t\) and produces \(s\) + \(t\), which is a justification for everything justified by \(s\) or by \(t\).

As motivation, one might think of \(s\) and \(t\) as two volumes of an encyclopedia, and \(s\) + \(t\) as the set of those two volumes. Imagine that one of the volumes, say \(s\), contains a sufficient justification for a proposition \(F\), i.e., \(s : F\) is the case. Then the larger set \(s\) + \(t\) also contains a sufficient justification for \(F\), [\(s\) + \(t ]: F\). In the Logic of Proofs \(\mathsf{LP}\), Section 1.2, ‘\(s + t\)’ can be interpreted as a concatenation of proofs \(s\) and \(t\).

Justification terms are built from justification variables \(x , y , z\), … and justification constants \(a , b , c\), … (with indices \(i\) = 1, 2, 3, … which are omitted whenever it is safe) by means of the operations ‘\(\cdot\) ’ and ‘+’. More elaborate logics considered below also allow additional operations on justifications. Constants denote atomic justifications which the system does not analyze; variables denote unspecified justifications. The Basic Logic of Justifications, \(\mathsf{J}_{0}\) is axiomatized by the following.

\(\mathsf{J}_{0}\) is the logic of general (not necessarily factive) justifications for an absolutely skeptical agent for whom no formula is provably justified, i.e., \(\mathsf{J}_{0}\) does not derive \(t : F\) for any \(t\) and \(F\). Such an agent is, however, capable of drawing relative justification conclusions of the form

With this capacity \(\mathsf{J}_{0}\) is able to adequately emulate many other Justification Logic systems in its language.

The Logical Awareness principle states that logical axioms are justified ex officio : an agent accepts logical axioms as justified (including the ones concerning justifications). As just stated, Logical Awareness may be too strong in some epistemic situations. However Justification Logic offers the flexible mechanism of Constant Specifications to represent varying shades of Logical Awareness.

Of course one distinguishes between an assumption and a justified assumption. In Justification Logic constants are used to represent justifications of assumptions in situations where they are not analyzed any further. Suppose it is desired to postulate that an axiom \(A\) is justified for the knower. One simply postulates \(e_{1} : A\) for some evidence constant \(e_{1}\) (with index 1). If, furthermore, it is desired to postulate that this new principle \(e_{1} : A\) is also justified, one can postulate \(e_{2} :( e_{1} : A)\) for a constant \(e_{2}\) (with index 2). And so on. Keeping track of indices is not necessary, but it is easy and helps in decision procedures (Kuznets 2008). The set of all assumptions of this kind for a given logic is called a Constant Specification . Here is the formal definition:

A Constant Specification \(CS\) for a given justification logic \(\mathcal{L}\) is a set of formulas of the form

where \(A\) is an axiom of \(\mathcal{L}\), and \(e_{1} , e_{2}, \ldots, e_{n}\) are similar constants with indices 1, 2, …, \(n\). It is assumed that \(CS\) contains all intermediate specifications, i.e., whenever \(e_{n} : e_{n- 1}:\ldots:e_{1} : A\) is in \(CS\), then \(e_{n- 1}:\ldots:e_{1} : A\) is in \(CS\), too.

There are a number of special conditions that have been placed on constant specifications in the literature. The following are the most common.

We may now specify:

Logic of Justifications : \(\mathsf{J}\) is the logic \(\mathsf{J}_{0}\) + Axiom Internalization Rule . The new rule states:

For each axiom \(A\) and any constants \(e_{1} , e_{2}, \ldots, e_{n}\) infer \(e_{n} : e_{n- 1} : \ldots : e_{1} : A\).

The latter embodies the idea of unrestricted Logical Awareness for \(\mathsf{J}\). A similar rule appeared in the Logic of Proofs \(\mathsf{LP}\), and has also been anticipated in Goldman’s (Goldman 1967). Logical Awareness, as expressed by axiomatically appropriate Constant Specifications, is an explicit incarnation of the Necessitation Rule in Modal Logic: \(\vdash F \Rightarrow\, \vdash \Box F\), but restricted to axioms. Note that \(\mathsf{J}\) coincides with \(\mathsf{J}_{TCS}\).

The key feature of Justification Logic systems is their ability to internalize their own derivations as provable justification assertions within their languages. This property was anticipated in (Gödel 1938).

Theorem 1 : For each axiomatically appropriate constant specification \(CS\), J\(_{CS}\) enjoys Internalization:

If \(\vdash F\), then \(\vdash p : F\) for some justification term \(p\).

Proof. Induction on derivation length. Suppose \(\vdash\)  \(F\). If \(F\) is a member of \(\mathsf{J}_{0}\), or a member of \(CS\), there is a constant \(e_{n}\) (where \(n\) might be 1) such that \(e_{n} : F\) is in \(CS\), since \(CS\) is axiomatically appropriate. Then \(e_{n} : F\) is derivable. If \(F\) is obtained by Modus Ponens from \(X \rightarrow F\) and \(X\), then, by the Induction Hypothesis, \(\vdash s :( X \rightarrow F)\) and \(\vdash t : X\) for some \(s , t\). Using the Application Axiom, \(\vdash [ s\cdot t ]: F\).

See Section 2 of the supplementary document Some More Technical Matters for examples of concrete syntactic derivations in justification logic.

The basic justification logic \({\textsf{J}}_0\), and its extension with a constant specification \({\textsf{J}}_{CS}\), is an explicit counterpart of the smallest normal modal logic \({\textsf{K}}\). A proper definition of counterpart will be given in Section 4 because the notion of realization is central, but some hints are already apparent at this stage of our presentation. For instance, it was noted in Section 1.1 that (1), \(s{:}(A\rightarrow B)\rightarrow(t{:}A\rightarrow [s\cdot t]{:}B)\), is an explicit version of the familiar modal principle (2), \({\square}(A\rightarrow B) \rightarrow ({\square}A\rightarrow {\square}B)\). In a similar way the first justification logic \(\textsf{LP}\) is an explicit counterpart of modal \({\textsf{S4}}\). It turns out that many modal logics have justification logic counterparts—indeed, generally more than one. In what follows we begin by discussing some very familiar logics, leading up to \({\textsf{S4}}\) and \(\textsf{LP}\). Up to this point much of our original motivation applies—we have justification logics that are interpretable in arithmetic. Then we move on to a broader family of modal logics, and the arithmetic motivation is no longer applicable. The phenomenon of having a modal logic with a justification logic counterpart has turned out to be unexpectedly broad.

In almost all cases, one must add operations to the \(+\) and \(\cdot\) of \({\textsf{J}}_0\), along with axioms capturing their intended behavior. The exception is factivity, discussed next, for which no additional operations are required, though additional axioms are. It is always understood that constant specifications cover axioms from the enlarged set. We continue using the terminology of Section 2.3; for instance a constant specification is axiomatically appropriate if it meets the condition as stated there, for all axioms including any that have been added to the original set. Theorem 1 from Section 2.3 continues to apply to our new justification logics, and with the same proof: if we have a justification logic \(\textsf{JL}_{CS}\) with an axiomatically appropriate constant specification, Internalization holds.

Factivity states that justifications are sufficient for an agent to conclude truth. This is embodied in the following.

Factivity Axiom \(t : F \rightarrow F\).

The Factivity Axiom has a similar motivation to the Truth Axiom of Epistemic Logic, \(\Box F \rightarrow F\), which is widely accepted as a basic property of knowledge.

Factivity of justifications is not required in basic Justification Logic systems, which makes them capable of representing both partial and factive justifications. The Factivity Axiom appeared in the Logic of Proofs \(\mathsf{LP}\), Section 1.2, as a principal feature of mathematical proofs. Indeed, in this setting Factivity is clearly valid: if there is a mathematical proof \(t\) of \(F\), then \(F\) must be true.

The Factivity Axiom is adopted for justifications that lead to knowledge. However, factivity alone does not warrant knowledge, as has been demonstrated by the Gettier examples (Gettier 1963).

Logic of Factive Justifications :

• \(\mathsf{JT}_{0} = \mathsf{J}_{0}\) + Factivity;
• \(\mathsf{JT} = \mathsf{J}\) + Factivity.

Systems \(\mathsf{JT}_{CS}\) corresponding to Constant Specifications \(CS\) are defined as in Section 2.3.

One of the common principles of knowledge is identifying knowing and knowing that one knows . In a modal setting, this corresponds to \(\Box F \rightarrow \Box \Box F\). This principle has an adequate explicit counterpart: the fact that an agent accepts \(t\) as sufficient evidence for \(F\) serves as sufficient evidence for \(t : F\). Often such ‘meta-evidence’ has a physical form: a referee report certifying that a proof in a paper is correct; a computer verification output given a formal proof \(t\) of \(F\) as an input; a formal proof that \(t\) is a proof of \(F\), etc. A Positive Introspection operation ‘!’ may be added to the language for this purpose; one then assumes that given \(t\), the agent produces a justification !\(t\) of \(t : F\) such that \(t : F \rightarrow ! t :( t : F)\). Positive Introspection in this operational form first appeared in the Logic of Proofs \(\mathsf{LP}\).

Positive Introspection Axiom : \(t : F \rightarrow ! t :( t : F)\).

We then define:

• \(\mathsf{J4} := \mathsf{J}\) + Positive Introspection;
• \(\mathsf{LP} := \mathsf{JT}\) + Positive Introspection. [ 3 ]

Logics \(\mathsf{J4}_{0} , \mathsf{J4}_{CS} , \mathsf{LP}_{0}\), and \(\mathsf{LP}_{CS}\) are defined in the natural way (cf. Section 2.3).

In the presence of the Positive Introspection Axiom, one can limit the scope of the Axiom Internalization Rule to internalizing axioms which are not of the form \(e : A\). This is how it was done in \(\mathsf{LP}\): Axiom Internalization can then be emulated by using !!\(e :(! e :( e : A))\) instead of \(e_{3} :( e_{2} :( e_{1} : A))\), etc. The notion of Constant Specification can also be simplified accordingly. Such modifications are minor and they do not affect the main theorems and applications of Justification Logic.

(Pacuit 2006, Rubtsova 2006) considered the Negative Introspection operation ‘?’ which verifies that a given justification assertion is false. A possible motivation for considering such an operation is that the positive introspection operation ‘!’ may well be regarded as capable of providing conclusive verification judgments about the validity of justification assertions \(t : F\), so when \(t\) is not a justification for \(F\), such a ‘!’ should conclude that \(\neg t : F\). This is normally the case for computer proof verifiers, proof checkers in formal theories, etc. This motivation is, however, nuanced: the examples of proof verifiers and proof checkers work with both \(t\) and \(F\) as inputs, whereas the Pacuit-Rubtsova format ?\(t\) suggests that the only input for ‘?’ is a justification \(t\), and the result ?\(t\) is supposed to justify propositions \(\neg t : F\) uniformly for all \(F\)s for which \(t : F\) does not hold. Such an operation ‘?’ does not exist for formal mathematical proofs since ?\(t\) should then be a single proof of infinitely many propositions \(\neg t : F\), which is impossible. The operation ‘?’ was, historically, the first example that did not fit into the original framework in which justifications were abstract versions of formal proofs.

Negative Introspection Axiom \(\neg t : F \rightarrow ? t :( \neg t : F)\)

We define the systems:

• \(\mathsf{J45} = \mathsf{J4}\) + Negative Introspection;
• \(\mathsf{JD45} = \mathsf{J45}\) + \(\neg t : \bot\) ;
• \(\mathsf{JT45} = \mathsf{J45}\) + Factivity

and naturally extend these definitions to \(\mathsf{J}45_{CS} , \mathsf{JD}45_{CS}\), and \(\mathsf{JT}45_{CS}\).

Justification logics involving \(?\) were the first examples that went beyond sublogics of \({\textsf{LP}}\). More recently it has been discovered that there is an infinite family of modal logics that have justification counterparts, but for which the connection with arithmetic proofs is weak or missing. We discuss a single case in some detail, and sketch others.

Peter Geach proposed the axiom scheme \({\lozenge}{\square}X{\rightarrow}{\square}{\lozenge}X\). When added to axiomatic \({\textsf{S4}}\) it yields an interesting logic known as \(\textsf{S4.2}\). Semantically, Geach’s scheme imposes confluence on frames. That is, if two possible worlds, \(w_1\) and \(w_2\) are accessible from the same world \(w_0\), there is a common world \(w_4\) accessible from both \(w_1\) and \(w_2\). Geach’s scheme was generalized in Lemmon and Scott (1977) and a corresponding notation was introduced: \({\textsf{G}}^{k,l,m,n}\) is the scheme \({\lozenge}^k{\square}^l X {\rightarrow}{\square}^m{\lozenge}^n X\), where \(k, l, m, n\geq 0\). Semantically these schemes correspond to generalized versions of confluence. Some people have begun referring to the schemes as Geach schemes , and we will follow this practice. More generally, we will call a modal logic a Geach logic if it can be axiomatized by adding a finite set of Geach schemes to \({\textsf{K}}\). The original Geach scheme is \({\textsf{G}}^{1,1,1,1}\), but also note that \({\square}X{\rightarrow}X\) is \({\textsf{G}}^{0,1,0,0}\), \({\square}X{\rightarrow}{\square}{\square}X\) is \({\textsf{G}}^{0,1,2,0}\), \({\lozenge}X{\rightarrow}{\square}{\lozenge}X\) is \({\textsf{G}}^{1,0,1,1}\), and \(X{\rightarrow}{\square}{\lozenge}X\) is \({\textsf{G}}^{0,0,1,1}\), so Geach logics include the most common of the modal logics. Geach logics constitute an infinite family.

Every Geach logic has a justification counterpart. Consider the original Geach logic, with axiom scheme \(\textsf{G}^{1,1,1,1}\), \({\lozenge}{\square}X{\rightarrow}{\square}{\lozenge}X\) added to a system for \(\textsf{S4}\)—the system \(\textsf{S4.2}\) mentioned above. We build a justification counterpart for \(\textsf{S4.2}\) axiomatically by starting with \({\textsf{LP}}\). Then we add two function symbols, \(f\) and \(g\), each two-place, and adopt the following axiom scheme, calling the resulting justification logic \(\textsf{J4.2}\).

There is some informal motivation for this scheme. In \({\textsf{LP}}\), because of the axiom scheme \(t{:}X{\rightarrow}X\), we have provability of \((t{:}X\land u{:}\lnot X){\rightarrow}\bot\) for any \(t\) and \(u\), and thus provability of \(\lnot t{:}X \lor\lnot u{:}\lnot X\). In any context one of the disjuncts must hold. The scheme above is equivalent to \(f(t,u){:}\lnot t{:}X \lor g(t,u){:}\lnot u{:}\lnot X\), which informally says that in any context we have means for computing a justification for the disjunct that holds. It is a strong assumption, but not implausible at least in some circumstances.

A realization theorem connects \(\textsf{S4.2}\) and \(\textsf{J4.2}\), though it is not known if this has a constructive proof.

As another example, consider \({\textsf{G}}^{1,2,2,1}\), \({\lozenge}{\square}{\square}X{\rightarrow}{\square}{\square}{\lozenge}X\), or equivalently \({\square}\lnot{\square}{\square}X \lor {\square}{\square}\lnot{\square}X\). It has as a corresponding justification axiom scheme the following, where \(f\), \(g\), and \(h\) are three-place function symbols.

An intuitive interpretation for \(f\), \(g\), and \(h\) is not as clear as it is for \(\textsf{G}^{1,1,1,1}\), but formally things behave quite well.

Even though the Geach family is infinite, these logics do not cover the full range of logics with justification counterparts. For instance, the normal modal logic using the axiom scheme \({\square}({\square}X{\rightarrow}X)\), sometimes called shift reflexivity , is not a Geach logic, but it does have a justification counterpart. Add a one-place function symbol \(k\) to the machinery building up justification terms, and adopt the justification axiom scheme \(k(t){:}(t{:}X{\rightarrow}X)\). A Realization Theorem holds; this is shown in Fitting (2014b) . We speculate that all logics axiomatized with Sahlquist formulas will have justification counterparts, but this remains a conjecture at this point.

3. Semantics

The now-standard semantics for justification logic originates in (Fitting 2005)—the models used are generally called Fitting models in the literature, but will be called possible world justification models here. Possible world justification models are an amalgam of the familiar possible world semantics for logics of knowledge and belief, due to Hintikka and Kripke, with machinery specific to justification terms, introduced by Mkrtychev in (Mkrtychev 1997), (cf. Section 3.4).

To be precise, a semantics for \(\mathsf{J}_{CS}\), where \(CS\) is any constant specification, is to be defined. Formally, a possible world justification logic model for \(\mathsf{J}_{CS}\) is a structure \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) . Of this, \(\langle \mathcal{G} , \mathcal{R}\rangle\) is a standard \(\mathsf{K}\) frame, where \(\mathcal{G}\) is a set of possible worlds and \(\mathcal{R}\) is a binary relation on it. \(\mathcal{V}\) is a mapping from propositional variables to subsets of \(\mathcal{G}\), specifying atomic truth at possible worlds.

The new item is \(\mathcal{E}\), an evidence function , which originated in (Mkrtychev 1997). This maps justification terms and formulas to sets of worlds. The intuitive idea is, if the possible world \(\Gamma\) is in \(\mathcal{E} ( t , X)\), then \(t\) is relevant or admissible evidence for \(X\) at world \(\Gamma\) . One should not think of relevant evidence as conclusive. Rather, think of it as more like evidence that can be admitted in a court of law: this testimony, this document is something a jury should examine, something that is pertinent, but something whose truth-determining status is yet to be considered. Evidence functions must meet certain conditions, but these are discussed a bit later.

Given a \(\mathsf{J}_{CS}\) possible world justification model \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) , truth of formula \(X\) at possible world \(\Gamma\) is denoted by \(\mathcal{M} , \Gamma \Vdash X\), and is required to meet the following standard conditions:

For each \(\Gamma \in \mathcal{G}\):

• \(\mathcal{M} , \Gamma \Vdash P\) iff \(\Gamma \in \mathcal{V} ( P)\) for \(P\) a propositional letter;
• it is not the case that \(\mathcal{M} , \Gamma \Vdash \bot\) ;
• \(\mathcal{M} , \Gamma \Vdash X \rightarrow Y\) iff it is not the case that \(\mathcal{M} , \Gamma \Vdash X\) or \(\mathcal{M} , \Gamma \Vdash Y\).

These just say that atomic truth is specified arbitrarily, and propositional connectives behave truth-functionally at each world. The key item is the next one.

• \(\mathcal{M} , \Gamma \Vdash ( t : X)\) if and only if \(\Gamma \in \mathcal{E} ( t , X)\) and, for every \(\Delta \in \mathcal{G}\) with \(\Gamma \mathcal{R} \Delta\) , we have that \(\mathcal{M} , \Delta \Vdash X\).

This condition breaks into two parts. The clause requiring that \(\mathcal{M} , \Delta \Vdash X\) for every \(\Delta \in \mathcal{G}\) such that \(\Gamma \mathcal{R} \Delta\) is the familiar Hintikka/Kripke condition for \(X\) to be believed, or be believable, at \(\Gamma\) . The clause requiring that \(\Gamma \in \mathcal{E} ( t , X)\) adds that \(t\) should be relevant evidence for \(X\) at \(\Gamma\) . Then, informally, \(t : X\) is true at a possible world if \(X\) is believable at that world in the usual sense of epistemic logic, and \(t\) is relevant evidence for \(X\) at that world.

It is important to realize that, in this semantics, one might not believe something for a particular reason at a world either because it is simply not believable, or because it is but the reason is not appropriate.

Some conditions must still be placed on evidence functions, and the constant specification must also be brought into the picture. Suppose one is given \(s\) and \(t\) as justifications. One can combine these in two different ways: simultaneously use the information from both; or use the information from just one of them, but first choose which one. Each gives rise to a basic operation on justification terms, \(\cdot\) and +, introduced axiomatically in Section 2.2.

Suppose \(s\) is relevant evidence for an implication and \(t\) is relevant evidence for the antecedent. Then \(s\) and \(t\) together provides relevant evidence for the consequent. The following condition on evidence functions is assumed:

With this condition added, the validity of

is secured.

If \(s\) and \(t\) are items of evidence, one might say that something is justified by one of \(s\) or \(t\), without bothering to specify which, and this will still be evidence. The following requirement is imposed on evidence functions.

Not surprisingly, both

Finally, the Constant Specification \(CS\) should be taken into account. Recall that constants are intended to represent reasons for basic assumptions that are accepted outright. A model \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) meets Constant Specification \(CS\) provided: if \(c : X \in CS\) then \(\mathcal{E}\)( c,X ) = \(\mathcal{G}\).

Possible World Justification Model A possible world justification model for \(\mathsf{J}_{CS}\) is a structure \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) satisfying all the conditions listed above, and meeting Constant Specification \(CS\).

Despite their similarities, possible world justification models allow a fine-grained analysis that is not possible with Kripke models. See Section 3 of the supplementary document Some More Technical Matters for more details.

A formula \(X\) is valid in a particular model for \(\mathsf{J}_{CS}\) if it is true at all possible worlds of the model. Axiomatics for \(\mathsf{J}_{CS}\) was given in Sections 2.2 and 2.3. A completeness theorem now takes the expected form.

Theorem 2 : A formula \(X\) is provable in \(\mathsf{J}_{CS}\) if and only if \(X\) is valid in all \(\mathsf{J}_{CS}\) models.

The completeness theorem as just stated is sometimes referred to as weak completeness. It maybe a bit surprising that it is significantly easier to prove than completeness for the modal logic \(\mathsf{K}\). Comments on this point follow. On the other hand it is very general, working for all Constant Specifications.

In (Fitting 2005) a stronger version of the semantics was also introduced. A model \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) is called fully explanatory if it meets the following condition. For each \(\Gamma \in \mathcal{G}\), if \(\mathcal{M} , \Delta \Vdash X\) for all \(\Delta \in \mathcal{G}\) such that \(\Gamma \mathcal{R} \Delta\) , then \(\mathcal{M} , \Gamma \Vdash t : X\) for some justification term \(t\). Note that the condition, \(\mathcal{M} , \Delta \Vdash X\) for all \(\Delta \in \mathcal{G}\) such that \(\Gamma \mathcal{R} \Delta\) , is the usual condition for \(X\) being believable at \(\Gamma\) in the Hintikka/Kripke sense. So, fully explanatory really says that if a formula is believable at a possible world, there is a justification for it.

Not all weak models meet the fully explanatory condition. Models that do are called strong models. If constant specification \(CS\) is rich enough so that an Internalization theorem holds, then one has completeness with respect to strong models meeting \(CS\). Indeed, in an appropriate sense completeness with respect to strong models is equivalent to being able to prove Internalization.

The proof of completeness with respect to strong models bears a close similarity to the proof of completeness using canonical models for the modal logic \(\mathsf{K}\). In turn, strong models can be used to give a semantic proof of the Realization Theorem (cf. Section 4).

So far a possible world semantics for one justification logic has been discussed, for \(\mathsf{J}\), the counterpart of \(\mathsf{K}\). Now things are broadened to encompass justification analogs of other familiar modal logics.

Simply by adding reflexivity of the accessibility relation \(\mathcal{R}\) to the conditions for a model in Section 3.1, one gains the validity of \(t{:}X \rightarrow X\) for every \(t\) and \(X\), and obtains a semantics for \(\mathsf{JT}\), the justification logic analog of the modal logic \({\textsf{T}}\), the weakest logic of knowledge. Indeed, if \({\mathcal{M},\Gamma{\Vdash}t{:}X}\) then, in particular, \(X\) is true at every state accessible from \(\Gamma\). Since the accessibility relation is required to be reflexive, \({\mathcal{M},\Gamma{\Vdash}X}\). Weak and strong completeness theorems are provable using the same machinery that applied in the case of \(\textsf{J}\), and a semantic proof of a Realization Theorem connecting \(\mathsf{JT}\) and \({\textsf{T}}\) is also available. The same applies to the logics discussed below.

For a justification analog of \({\textsf{K4}}\) an additional unary operator ‘!’ is added to the term language, see Section 2.5. Recall this operator maps justifications to justifications, where the idea is that if \(t\) is a justification for \(X\), then \(!t\) should be a justification for \(t{:}X\). Semantically this adds conditions to a model \(\mathcal{M} = \langle \mathcal{G},\mathcal{R},\mathcal{E},\mathcal{V}\rangle\), as follows.

First, of course, \(\mathcal{R}\) should be transitive, but not necessarily reflexive. Second, a monotonicity condition on evidence functions is required:

\[\mbox{If } \Gamma \mathcal{R} \Delta \mbox{ and } \Gamma\in \mathcal{E}(t,X) \mbox{ then } \Delta \in \mathcal{E}(t,X)\] And finally, one more evidence function condition is needed.

\[\mathcal{E}(t,X) \subseteq \mathcal{E}(!t,t{:}X)\] These conditions together entail the validity of \(t{:}X \rightarrow !t{:}t{:}X\) and produce a semantics for \(\mathsf{J4}\), a justification analog of \(\mathsf{K4}\), with a Realization Theorem connecting them. Adding reflexivity leads to a logic that is called \({\textsf{LP}}\) for historical reasons.

We have discussed justification logics that are sublogics of \({\textsf{LP}}\), corresponding to sublogics of the modal logic \(\textsf{S4}\). The first examples that went beyond \({\textsf{LP}}\) were those discussed in Section 2.7, involving a negative introspection operator, ‘?’. Models for justification logics that include this operator add three conditions. First R is symmetric. Second, one adds a condition that has come to be known as strong evidence : \({\mathcal{M},\Gamma{\Vdash}t{:}X}\) for all \(\Gamma\in \mathcal{E}(t, X)\). Finally, there is a condition on the evidence function:

If this machinery is added to that for \(\mathsf{J4}\) we get the logic \(\mathsf{J45}\), a justification counterpart of \(\mathsf{K45}\). Axiomatic soundness and completeness can be proved. In a similar way, related logics \(\mathsf{JD45}\) and \(\mathsf{JT45}\) can be formulated semantically. A Realization Theorem taking the operator \(?\) into account was shown in (Rubtsova 2006).

Moving to Geach logics as introduced in Section 2.8, a semantic model for \(\textsf{J4.2}\) can also be specified. Suppose \(G = \langle \mathcal{G}, \mathcal{R}, \mathcal{E}, \mathcal{V}\rangle\) is an \({\textsf{LP}}\) model. We add the following requirements. First, the frame must be convergent, as with \(\textsf{S4.2}\). Second, as with \(?\), \(\mathcal{E}\) must be a strong evidence function. And third, \(\mathcal{E}(f(t,u), \lnot t{:}X)\cup \mathcal{E}(g(t,u), \lnot u{:}\lnot X) = \mathcal{G}\). Completeness and soundness results follow in the usual way.

In a similar way every modal logic axiomatized by Geach schemes in this family has a justification counterpart, with a Fitting semantics and a realization theorem connecting the justification counterpart with the corresponding modal logic. In particular, this tells us that the justification logic family is infinite, and certainly much broader than it was originally thought to be. It is also the case that some modal logics not previously considered, and not in this family, have justification counterparts as well. Investigating the consequences of all this is still work in progress.

Single world justification models were developed considerably before the more general possible world justification models we have been discussing, (Mkrtychev 1997). Today they can most simply be thought of as possible world justification models that happen to have a single world. The completeness proof for \(\mathsf{J}\) and the other justification logics mentioned above can easily be modified to establish completeness with respect to single world justification models, though of course this was not the original argument. What completeness with respect to single world justification models tells us is that information about the possible world structure of justification models can be completely encoded by the admissible evidence function, at least for the logics discussed so far. Mkrtychev used single world justification models to establish decidability of \(\mathsf{LP}\), and others have made fundamental use of them in setting complexity bounds for justification logics, as well as for showing conservativity results for justification logics of belief (Kuznets 2000, Kuznets 2008, Milnikel 2007, Milnikel 2009). Complexity results have further been used to address the problem of logical omniscience (Artemov and Kuznets 2014).

The formal semantics for Justification Logic described above in 3.1–3.4 defines truth value at a given world \(\Gamma\) the same way it is done in Awareness Models: \(t{:}F\) holds at \(\Gamma\) iff

\(F\) holds at all worlds accessible from \(\Gamma\) and

\(t\) is admissible evidence for \(F\) according to the given evidence function.

In addition, there is a different kind of semantics, so-called modular semantics, which focuses on making more transparent the ontological status of justifications. Within modular semantics propositions receive the usual classical truth values and justifications are interpreted syntactically as sets of formulas. We retain a classical interpretation \(\ast\) of the propositional formulas \(Fm\), which, in the case of a single world, reduces to \[\ast: Fm \mapsto\ \ \{0,1\}\] i.e., each formula gets a truth value 0 (false) or 1 (true), with the usual Boolean conditions: \({\Vdash}A\rightarrow B\) iff \(\not\Vdash A\) or \({\Vdash}B\), etc. The principal issue is how to interpret justification terms. For sets of formulas \(X\) and \(Y\), we define \[X\cdot Y = \{ F \mid G{\rightarrow}F \in X\ \mbox{and} \ G \in Y\ \mbox{for some}\ G\}.\] Informally, \(X\cdot Y\) is the result of applying Modus Ponens once between all members of \(X\) and of \(Y\) (in that order). Justification terms Tm are interpreted as subsets of the set of formulas: \[\ast: Tm \mapsto\ \ 2^{Fm}\] such that \[(s\cdot t)^\ast\supseteq s^\ast\cdot t^\ast \ \ \mbox{and}\ \ \ (s+t)^\ast\supseteq s^\ast\cup t^\ast .\] These conditions correspond to the basic justification logic \(\textsf{J}\); other systems require additional closure properties of \(\ast\). Note that whereas propositions in modular models are interpreted semantically, as truth values, justifications are interpreted syntactically, as sets of formulas. This is a principal hyperintensional feature: a modular model may treat distinct formulas \(F\) and \(G\) as equal in the sense that \(F^\ast = G^\ast\), but still be able to distinguish justification assertions \(t{:}F\) and \(t{:}G\), for example when \(F \in t^\ast\) but \(G\not\in t^\ast\) yielding \({\Vdash}t{:}F\) but \(\not\Vdash t{:}G\). In the general possible world setting, formulas are interpreted classically as subsets of the set \(W\) of possible worlds, \[\ast: Fm \mapsto\ \ 2^W ,\] and justification terms are interpreted syntactically as sets of formulas at each world \[\ast: W\times Tm \mapsto\ \ 2^{Fm}.\] Soundness and completeness of Justification Logic systems with respect to modular models have been demonstrated in (Artemov 2012; Kuznets and Studer 2012) .

The logical omniscence problem is that in epistemic logics all tautologies are known and knowledge is closed under consequence, which is unreasonable. In Fagin and Halpern (1988) a simple mechanism for avoiding the problems was introduced. One adds to the usual Kripke model structure an awareness function \(\cal A\) indicating for each world which formulas the agent is aware of at this world. Then a formula is taken to be known at a possible world \(\Gamma\) if 1) the formula is true at all worlds accessible from \(\Gamma\) (the Kripkean condition for knowledge) and 2) the agent is aware of the formula at \(\Gamma\). Awareness functions can serve as a practical tool for blocking knowledge of an arbitrary set of formulas. However as logical structures, awareness models can exhibit unusual behavior due to the lack of natural closure properties. For example, the agent can know \(A\wedge B\) but be aware of neither \(A\) nor \(B\) and hence not know either.

Possible world justification logic models use a forcing definition reminiscent of the one from the awareness models: for any given justification \(t\) the justification assertion \(t{:}F\) holds at world \(\Gamma\) iff 1) \(F\) holds at all worlds \(\Delta\) accessible from \(\Gamma\) and 2) \(t\) is admissible evidence for \(F\) at \(\Gamma\), \(\Gamma\in{\cal E}(t,F)\). The principal difference is in the operations on justifications and corresponding closure conditions on admissible evidence function \(\cal E\) in Justification Logic models, which may hence be regarded as a dynamic version of awareness models which necessary closure properties specified. This idea has been explored in Sedlár (2013) which worked with the language of \(\textsf{LP}\), thinking of it as a multi-agent modal logic, and taking justification terms as agents (more properly, actions of agents). This shows that Justification Logic models absorb the usual epistemic themes of awareness, group agency and dynamics in a natural way.

The natural modal epistemic counterpart of the evidence assertion \(t : F\) is \(\Box F\), read for some x, x :\(F\). This observation leads to the notion of forgetful projection which replaces each occurrence of \(t : F\) by \(\Box F\) and hence converts a Justification Logic sentence \(S\) to a corresponding Modal Logic sentence \(S^{o}\). The forgetful projection extends in the natural way from sentences to logics.

Obviously, different Justification Logic sentences may have the same forgetful projection, hence \(S^{o}\) loses certain information that was contained in \(S\). However, it is easily observed that the forgetful projection always maps valid formulas of Justification Logic (e.g., axioms of \(\mathsf{J})\) to valid formulas of a corresponding Epistemic Logic \((\mathsf{K}\) in this case). The converse also holds: any valid formula of Epistemic Logic is the forgetful projection of some valid formula of Justification Logic. This follows from the Correspondence Theorem 3.

Theorem 3 : \(\mathsf{J}^{o} = \mathsf{K}\).

This correspondence holds for other pairs of Justification and Epistemic systems, for instance \(\mathsf{J4}\) and \(\mathsf{K4}\), or \(\mathsf{LP}\) and \(\mathsf{S4}\), and many others. In such extended form, the Correspondence Theorem shows that major modal logics such as \(\mathsf{K} , \mathsf{T} , \mathsf{K4} , \mathsf{S4} , \mathsf{K45} , \mathsf{S5}\) and some others have exact Justification Logic counterparts.

At the core of the Correspondence Theorem is the following Realization Theorem.

Theorem 4 : There is an algorithm which, for each modal formula \(F\) derivable in \(\mathsf{K}\), assigns evidence terms to each occurrence of modality in \(F\) in such a way that the resulting formula \(F^{r}\) is derivable in \(\mathsf{J}\). Moreover, the realization assigns evidence variables to the negative occurrences of modal operators in \(F\), thus respecting the existential reading of epistemic modality.

Known realization algorithms which recover evidence terms in modal theorems use cut-free derivations in the corresponding modal logics. Alternatively, the Realization Theorem can be established semantically by Fitting’s method or its proper modifications. In principle, these semantic arguments also produce realization procedures which are based on exhaustive search.

It would be a mistake to draw the conclusion that any modal logic has a reasonable Justification Logic counterpart. For example the logic of formal provability, \(\mathsf{GL}\), (Boolos 1993) contains the Löb Principle :

which does not seem to have an epistemically acceptable explicit version. Consider, for example, the case where \(F\) is the propositional constant \(\bot\) for false . If an analogue of Theorem 4 would cover the Löb Principle there would be justification terms \(s\) and \(t\) such that \(x :( s : \bot \rightarrow \bot ) \rightarrow t : \bot\) . But this is intuitively false for factive justification. Indeed, \(s : \bot \rightarrow \bot\) is an instance of the Factivity Axiom. Apply Axiom Internalization to obtain \(c :( s : \bot \rightarrow \bot )\) for some constant \(c\). This choice of \(c\) makes the antecedent of \(c :( s : \bot \rightarrow \bot ) \rightarrow t : \bot\) intuitively true and the conclusion false [ 4 ] . In particular, the Löb Principle (5) is not valid for the proof interpretation (cf. (Goris 2007) for a full account of which principles of \(\mathsf{GL}\) are realizable).

The Correspondence Theorem gives fresh insight into epistemic modal logics. Most notably, it provides a new semantics for the major modal logics. In addition to the traditional Kripke-style ‘universal’ reading of \(\Box F\) as F holds in all possible situations , there is now a rigorous ‘existential’ semantics for \(\Box F\) that can be read as there is a witness (proof, justification) for F .

Justification semantics plays a similar role in Modal Logic to that played by Kleene realizability in Intuitionistic Logic. In both cases, the intended semantics is existential : the Brouwer-Heyting-Kolmogorov interpretation of Intuitionistic Logic (Heyting 1934, Troelstra and van Dalen 1988, van Dalen 1986) and Gödel’s provability reading of \(\mathsf{S4}\) (Gödel 1933, Gödel 1938). In both cases there is a possible-world semantics of universal character which is a highly potent and dominant technical tool. It does not, however, address the existential character of the intended semantics. It took Kleene realizability (Kleene 1945, Troelstra 1998) to reveal the computational semantics of Intuitionistic Logic and the Logic of Proofs to provide exact BHK semantics of proofs for Intuitionistic and Modal Logic.

In the epistemic context, Justification Logic and the Correspondence Theorem add a new ‘justification’ component to modal logics of knowledge and belief. Again, this new component was, in fact, an old and central notion which has been widely discussed by mainstream epistemologists but which remained out of the scope of classical epistemic logic. The Correspondence Theorem tells us that justifications are compatible with Hintikka-style systems and hence can be safely incorporated into the foundation for Epistemic Modal Logic.

See Section 4 of the supplementary document Some More Technical Matters for more on Realization Theorems.

5. Generalizations

So far in this article only single-agent justification logics, analogous to single-agent logics of knowledge, have been considered. Justification Logic can be thought of as logic of explicit knowledge, related to more conventional logics of implicit knowledge. A number of systems beyond those discussed above have been investigated in the literature, involving multiple agents, or having both implicit and explicit operators, or some combination of these.

Since justification logics provide explicit justifications, while conventional logics of knowledge provide an implicit knowledge operator, it is natural to consider combining the two in a single system. The most common joint logic of explicit and implicit knowledge is \(\mathsf{S4LP}\) (Artemov and Nogina 2005). The language of \(\mathsf{S4LP}\) is like that of \(\mathsf{LP}\), but with an implicit knowledge operator added, written either \(\mathbf{K}\) or \(\Box\) . The axiomatics is like that of \(\mathsf{LP}\), combined with that of \(\mathsf{S4}\) for the implicit operator, together with a connecting axiom, \(t : X \rightarrow \Box X\), anything that has an explicit justification is knowable.

Semantically, possible world justification models for \(\mathsf{LP}\) need no modification, since they already have all the machinery of Hintikka/Kripke models. One models the \(\Box\) operator in the usual way, making use of just the accessibility relation, and one models the justification terms as described in Section 3.1 using both accessibility and the evidence function. Since the usual condition for \(\Box X\) being true at a world is one of the two clauses of the condition for \(t : X\) being true, this immediately yields the validity of \(t : X \rightarrow \Box X\), and soundness follows easily. Axiomatic completeness is also rather straightforward.

In \(\mathsf{S4LP}\) both implicit and explicit knowledge is represented, but in possible world justification model semantics a single accessibility relation serves for both. This is not the only way of doing it. More generally, an explicit knowledge accessibility relation could be a proper extension of that for implicit knowledge. This represents the vision of explicit knowledge as having stricter standards for what counts as known than that of implicit knowledge. Using different accessibility relations for explicit and implicit knowledge becomes necessary when these epistemic notions obey different logical laws, e.g., \(\mathsf{S5}\) for implicit knowledge and \(\mathsf{LP}\) for explicit. The case of multiple accessibility relations is commonly known in the literature as Artemov-Fitting models, but will be called multi-agent possible world models here. (cf. Section 5.2).

Curiously, while the logic \(\mathsf{S4LP}\) seems quite natural, a Realization Theorem has been problematic for it: no such theorem can be proved if one insists on what are called normal realizations (Kuznets 2010). Realization of implicit knowledge modalities in \(\mathsf{S4LP}\) by explicit justifications which would respect the epistemic structure remains a major challenge in this area.

Interactions between implicit and explicit knowledge can sometimes be rather delicate. As an example, consider the following mixed principle of negative introspection (again \(\Box\) should be read as an implicit epistemic operator),

From the provability perspective, it is the right form of negative introspection. Indeed, let \(\Box F\) be interpreted as F is provable and \(t : F\) as t is a proof of F in a given formal theory \(T\), e.g., in Peano Arithmetic \(\mathsf{PA}\). Then (6) states a provable principle. Indeed, if \(t\) is not a proof of \(F\) then, since this statement is decidable, it can be established inside \(T\), hence in \(T\) this sentence is provable. On the other hand, the proof \(p\) of ‘\(t\) is not a proof of \(F\)’ depends on both \(t\) and \(F , p = p ( t , F)\) and cannot be computed given \(t\) only. In this respect, \(\Box\) cannot be replaced by any specific proof term depending on \(t\) only and (6) cannot be presented in an entirely explicit justification-style format.

The first examples of explicit/implicit knowledge systems appeared in the area of provability logic. In (Sidon 1997, Yavorskaya (Sidon) 2001), a logic \(\mathsf{LPP}\) was introduced which combined the logic of provability \(\mathsf{GL}\) with the logic of proofs \(\mathsf{LP}\), but to ensure that the resulting system had desirable logical properties some additional operations from outside the original languages of \(\mathsf{GL}\) and \(\mathsf{LP}\) were added. In (Nogina 2006, Nogina 2007) a complete logical system, \(\mathsf{GLA}\), for proofs and provability was offered, in the sum of the original languages of \(\mathsf{GL}\) and \(\mathsf{LP}\). Both \(\mathsf{LPP}\) and \(\mathsf{GLA}\) enjoy completeness relative to the class of arithmetical models, and also relative to the class of possible world justification models.

Another example of a provability principle that cannot be made completely explicit is the Löb Principle (5). For each of \(\mathsf{LPP}\) and \(\mathsf{GLA}\), it is easy to find a proof term \(l ( x)\) such that

holds. However, there is no realization which makes all three \(\Box\) s in (5) explicit. In fact, the set of realizable provability principles is the intersection of \(\mathsf{GL}\) and \(\mathsf{S4}\) (Goris 2007).

In multi-agent possible world justification models multiple accessibility relations are employed, with connections between them, (Artemov 2006). The idea is, there are multiple agents, each with an implicit knowledge operator, and there are justification terms, which each agent understands. Loosely, everybody understands explicit reasons; these amount to evidence-based common knowledge .

An \(n\)-agent possible world justification model is a structure \(\langle \mathcal{G} , \mathcal{R}_{1}\), …,\(\mathcal{R}_{n} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) meeting the following conditions. \(\mathcal{G}\) is a set of possible worlds. Each of \(\mathcal{R}_{1}\),…,\(\mathcal{R}_{n}\) is an accessibility relation, one for each agent. These may be assumed to be reflexive, transitive, or symmetric, as desired. They are used to model implicit agent knowledge for the family of agents. The accessibility relation \(\mathcal{R}\) meets the \(\mathsf{LP}\) conditions, reflexivity and transitivity. It is used in the modeling of explicit knowledge. \(\mathcal{E}\) is an evidence function, meeting the same conditions as those for \(\mathsf{LP}\) in Section 3.3. \(\mathcal{V}\) maps propositional letters to sets of worlds, as usual. There is a special condition imposed: for each \(i\) = 1, …,\(n , \mathcal{R}_{i} \subseteq \mathcal{R}\).

If \(\mathcal{M} = \langle \mathcal{G} , \mathcal{R}_{1}\), …,\(\mathcal{R}_{n} , \mathcal{R} , \mathcal{E} , \mathcal{V}\rangle\) is a multi-agent possible world justification model a truth-at-a-world relation, \(\mathcal{M} , \Gamma \Vdash X\), is defined with most of the usual clauses. The ones of particular interest are these:

• \(\mathcal{M} , \Gamma \Vdash K_{i}X\) if and only if, for every \(\Delta \in \mathcal{G}\) with \(\Gamma \mathcal{R}_{i} \Delta\), we have that \(\mathcal{M} , \Delta \Vdash X\).
• \(\mathcal{M} , \Gamma \Vdash t : X\) if and only if \(\Gamma \in \mathcal{E} ( t , X)\) and, for every \(\Delta \in \mathcal{G}\) with \(\Gamma \mathcal{R} \Delta\), we have that \(\mathcal{M} , \Delta \Vdash X\).

The condition \(\mathcal{R}_{i} \subseteq \mathcal{R}\) entails the validity of \(t : X \rightarrow K_{i}X\), for each agent \(i\). If there is only a single agent, and the accessibility relation for that agent is reflexive and transitive, this provides another semantics for \(\mathsf{S4LP}\). Whatever the number of agents, each agent accepts explicit reasons as establishing knowledge.

A version of \(\mathsf{LP}\) with two agents was introduced and studied in (Yavorskaya (Sidon) 2008), though it can be generalized to any finite number of agents. In this, each agent has its own set of justification operators, variables, and constants, rather than having a single set for everybody, as above. In addition some limited communication between agents may be permitted, using a new operator that allows one agent to verify the correctness of the other agent’s justifications. Versions of both single world and more general possible world justification semantics were created for the two-agent logics. This involves a straightforward extension of the notion of an evidence function, and for possible world justification models, using two accessibility relations. Realization theorems have been proved syntactically, though presumably a semantic proof would also work.

Multi-agent models (where each agent has its own set of justification operators) with explicit and implicit knowledge can be used to epistemically analyze zero-knowledge proofs (Lehnherr, Ognjanovic, and Studer 2022). Zero-knowledge proofs are protocols by which one agent (the prover) can prove to another agent (the verifier) that the prover has certain knowledge (e.g., knows a password) without conveying any information beyond the mere fact of the possession of knowledge (e.g., without revealing the password). The following formulas can be used to describe the situation after the execution of the protocol, where the term \(s\) justifies the verifier’s knowledge that results from the protocol: \[ s:_V K_P F, \] meaning the protocol yields a justification \(s\) to the verifier \(V\) that the prover \(P\) knows \(F\); and \[ \lnot s:_V t:_P F \text{ for any term t,} \] i.e., for no term \(t\) the protocol justifies that the verifier could know that \(t\) justifies the prover’s knowledge of \(F\). That is, the protocol justifies that the prover knows \(F\) but it does not justify any possible evidence for that knowledge.

There has been some exploration of the role of public announcements in multi-agent justification logics (Renne 2008, Renne 2009).

There is more on the notion of evidence-based common knowledge in Section 5 of the supplementary document Some More Technical Matters .

Besides multi-agent epistemic logics, there are other justification logics that feature two types of terms. Kuznets, Marin, and Strassburger (2021) introduce an explicit version of constructive modal logic. There, the \(\Box\)-modality is realized by proof terms like in \(\mathsf{LP}\). To realize the \(\Diamond\)-modality, a second kind of terms is introduced, which are called witness terms. In constructive modal logic, the formula \(\Diamond F\) means \(F\) is consistent . In its realization \(s:F\), the witness term \(s\) represents an abstract witnessing model for the formula \(F\).

Another example is dyadic deontic logic (DDL), which can be axiomatized by two modalities \(\Box\) and \(\bigcirc\). The formula \(\Box F\) means \(F\) is settled true , and the conditional \(\bigcirc(F/G)\) means \(F\) is obligatory given G . Faroldi, Rohani, and Studer (2023) consider an explicit version of DDL. Again, \(\Box F\) is realized by a proof term as in \(\mathsf{LP}\), whereas \(\bigcirc(F/G)\) is realized by making use of a new type of terms that represent deontic reasons.

There is a technique for using Justification Logic to analyze different justifications for the same fact, in particular when some of the justifications are factive and some are not. To demonstrate the technique consider a well-known example:

If a man believes that the late Prime Minister’s last name began with a ‘B,’ he believes what is true, since the late Prime Minister was Sir Henry Campbell Bannerman [ 5 ] . But if he believes that Mr. Balfour was the late Prime Minister [ 6 ] , he will still believe that the late Prime Minister’s last name began with a ‘B,’ yet this belief, though true, would not be thought to constitute knowledge. (Russell 1912)

As in the Red Barn Example, discussed in Section 1.1, here one has to deal with two justifications for a true statement, one of which is correct and one of which is not. Let \(B\) be a sentence (propositional atom), \(w\) be a designated justification variable for the wrong reason for \(B\) and \(r\) a designated justification variable for the right (hence factive) reason for \(B\). Then, Russell’s example prompts the following set of assumptions [ 7 ] :

Somewhat counter to intuition, one can logically deduce factivity of \(w\) from \(\mathcal{R}\):

• \(r : B\) (assumption)
• \(r : B \rightarrow B\) (assumption)
• \(B\) (from 1 and 2 by Modus Ponens)
• \(B \rightarrow ( w : B \rightarrow B)\) (propositional axiom)
• \(w : B \rightarrow B\) (from 3 and 4 by Modus Ponens)

However, this derivation utilizes the fact that \(r\) is a factive justification for \(B\) to conclude \(w : B \rightarrow B\), which constitutes a case of ‘induced factivity’ for \(w : B\). The question is, how can one distinguish the ‘real’ factivity of \(r : B\) from the ‘induced factivity’ of \(w : B\) ? Some sort of evidence-tracking is needed here, and Justification Logic is an appropriate tool. The natural approach is to consider the set of assumptions without \(r : B\), i.e.,

and establish that factivity of \(w\), i.e., \(w : B \rightarrow B\) is not derivable from \(\mathcal{S}\). Here is a possible world justification model \(\mathcal{M}\) = \((\mathcal{G} , \mathcal{R} , \mathcal{E} , \mathcal{V})\) in which \(\mathcal{S}\) holds but \(w : B \rightarrow B\) does not:

• \(\mathcal{G} = \{\mathbf{1}\}\),
• \(\mathcal{R} = \varnothing\) ,
• \(\mathcal{V} ( B)\) = \(\varnothing\) (and so not-\(\mathbf{1} \Vdash B)\),
• \(\mathcal{E} ( t , F)\) = \(\{\mathbf{1}\}\) for all pairs \((t , F)\) except \((r , B)\),and
• \(\mathcal{E} ( r , B)\) = \(\varnothing\) .

It is easy to see that the closure conditions Application and Sum on \(\mathcal{E}\) are fulfilled. At \(\mathbf{1} , w : B\) holds, i.e.,

since \(w\) is admissible evidence for \(B\) at \(\mathbf{1}\) and there are no possible worlds accessible from \(\mathbf{1}\). Furthermore,

since, according to \(\mathcal{E} , r\) is not admissible evidence for \(B\) at \(\mathbf{1}\). Hence:

On the other hand,

since \(B\) does not hold at \(\mathbf{1}\).

The Realization algorithms sometimes produce Constant Specifications containing self-referential justification assertions \(c : A ( c)\), that is, assertions in which the justification (here \(c)\) occurs in the asserted proposition (here \(A ( c))\).

Self-referentiality of justifications is a new phenomenon which is not present in the conventional modal language. In addition to being intriguing epistemic objects, such self-referential assertions provide a special challenge from the semantical viewpoint because of the built-in vicious circle. Indeed, to evaluate \(c\) one would expect first to evaluate \(A\) and then assign a justification object for \(A\) to \(c\). However, this cannot be done since \(A\) contains \(c\) which is yet to be evaluated. The question of whether or not modal logics can be realized without using self-referential justifications was a major open question in this area.

The principal result by Kuznets in (Brezhnev and Kuznets 2006) states that self-referentiality of justifications is unavoidable in realization of \(\mathsf{S4}\) in \(\mathsf{LP}\). The current state of things is given by the following theorem due to Kuznets:

Theorem 5 : Self-referentiality can be avoided in realizations of modal logics \(\mathsf{K}\) and \(\mathsf{D}\). Self-referentiality cannot be avoided in realizations of modal logics \(\mathsf{T} , \mathsf{K4} , \mathsf{D4}\) and \(\mathsf{S4}\).

This theorem establishes that a system of justification terms for \(\mathsf{S4}\) will necessarily be self-referential. This creates a serious, though not directly visible, constraint on provability semantics. In the Gödelian context of arithmetical proofs, the problem was coped with by a general method of assigning arithmetical semantics to self-referential assertions \(c : A ( c)\) stating that \(c\) is a proof of \(A ( c)\). In the Logic of Proofs \(\mathsf{LP}\) it was dealt with by a non-trivial fixed-point construction.

Self-referentiality gives an interesting perspective on Moore’s Paradox. See Section 6 of the supplementary document Some More Technical Matters for details.

The question of the self-referentiality of BHK-semantics for intuitionistic logic \(\mathsf{IPC}\) has been answered by Junhua Yu (Yu 2014). Extending Kuznets’ method, he established

Theorem 6 : Each \(\mathsf{LP}\) realization of the intuitionistic law of double negation \(\neg\neg(\neg\neg p \rightarrow p)\) requires self referential constant specifications.

While the investigation of propositional Justification Logic is far from complete, there has also been some work on first-order versions. Quantified versions of Modal Logic already offer complexities beyond standard first-order logic. Quantification has an even broader field to play when Justification Logics are involved. Classically one quantifies over ‘objects,’ and models are equipped with a domain over which quantifiers range. Modally one might have a single domain common to all possible worlds, or one might have separate domains for each world. The role of the Barcan formula is well-known here. Both constant and varying domain options are available for Justification Logic as well. In addition there is a possibility that has no analog for Modal Logic: one might quantify over justifications themselves.

Initial results concerning the possibility of Quantified Justification Logic were notably unfavorable. The arithmetical provability semantics for the Logic of Proofs \(\mathsf{LP}\), naturally generalizes to a first-order version with conventional quantifiers, and to a version with quantifiers over proofs. In both cases, axiomatizability questions were answered negatively.

Theorem 7 : The first-order logic of proofs is not recursively enumerable (Artemov and Yavorskaya (Sidon) 2001). The logic of proofs with quantifiers over proofs is not recursively enumerable (Yavorsky 2001).

Although an arithmetic semantics is not possible, in (Fitting 2008) a possible world semantics, and an axiomatic proof theory, was given for a version of \(\mathsf{LP}\) with quantifiers ranging over justifications. Soundness and completeness were proved. At this point possible world semantics separates from arithmetic semantics, which may or may not be a cause for alarm. It was also shown that \(\mathsf{S4}\) embeds into the quantified logic by translating \(\Box Z\) as “there exists a justification \(x\) such that \(x : Z^{*}\),” where \(Z^{*}\) is the translation of \(Z\). While this logic is somewhat complicated, it has found applications, e.g., in (Dean and Kurokawa 2009b) it is used to analyze the Knower Paradox, though objections have been raised to this analysis in (Arlo-Costa and Kishida 2009).

A First-Order Logic of Proofs, \(\textsf{FOLP}\), with quantifiers over individual variables, has been presented in Artemov and Yavorskaya (Sidon) (2011) . In \(\textsf{FOLP}\) proof assertions are represented by formulas of the form \(t{:}_X A\) where \(X\) is a finite set of individual variables that are considered global parameters open for substitution. All occurrences of variables from \(X\) that are free in \(A\) are also free in \(t{:}_X A\). All other free variables of \(A\) are considered local and hence bound in \(t{:}_X A\). For example, if \(A(x,y)\) is an atomic formula, then in \(p{:}_{\{x\}} A(x,y)\) variable \(x\) is free and variable \(y\) is bound. Likewise, in \(p{:}_{\{x,y\}} A(x,y)\) both variables are free, and in \(p{:}_{\emptyset} A(x,y)\) neither \(x\) nor \(y\) is free.

Proofs (justifications) are represented by proof terms which do not contain individual variables. In addition to \(\textsf{LP}\) operations there is one more series of operations on proof terms, \({\sf gen}_x(t)\), corresponding to generalization over individual variable \(x\). The new axiom that governs this operation is \(t{:}_X A {\rightarrow}{\sf gen{:}_x(t)}_X\forall x A\), with \(x\not\in X\). The complete list of \(\textsf{FOLP}\) principles along with realization of First-Order \(\textsf{S4}\) can be found in Artemov and Yavorskaya (Sidon) (2011) . A semantics for \(\textsf{FOLP}\) has been developed in Fitting (2014a) .

The initial Justification Logic system, the Logic of Proofs \(\mathsf{LP}\), was introduced in 1995 in (Artemov 1995) (cf. also (Artemov 2001)) where such basic properties as Internalization, Realization, arithmetical completeness, were first established. \(\mathsf{LP}\) offered an intended provability semantics for Gödel’s provability logic \(\mathsf{S4}\), thus providing a formalization of Brouwer-Heyting-Kolmogorov semantics for intuitionistic propositional logic. Epistemic semantics and completeness (Fitting 2005) were first established for \(\mathsf{LP}\). Symbolic models and decidability for \(\mathsf{LP}\) are due to Mkrtychev (Mkrtychev 1997). Complexity estimates first appeared in (Brezhnev and Kuznets 2006, Kuznets 2000, Milnikel 2007). A comprehensive overview of all decidability and complexity results can be found in (Kuznets 2008). Systems \(\mathsf{J} , \mathsf{J4}\), and \(\mathsf{JT}\) were first considered in (Brezhnev 2001) under different names and in a slightly different setting. \(\mathsf{JT45}\) appeared independently in (Pacuit 2006) and (Rubtsova 2006), and \(\mathsf{JD45}\) in (Pacuit 2006). The logic of uni-conclusion proofs has been found in (Krupski 1997). A more general approach to common knowledge based on justified knowledge was offered in (Artemov 2006). Game semantics of Justification Logic and Dynamic Epistemic Logic with justifications were studied in (Renne 2008, Renne 2009). Connections between Justification Logic and the problem of logical omniscience were examined in (Artemov and Kuznets 2009, Artemov and Kuznets 2014, Wang 2009). The name Justification Logic was introduced in (Artemov 2008), in which Kripke, Russell, and Gettier examples were formalized; this formalization has been used for the resolution of paradoxes, verification, hidden assumption analysis, and eliminating redundancies. In (Dean and Kurokawa 2009a), Justification Logic was used for the analysis of Knower and Knowability paradoxes.

The first two monographs on Justification Logic were published in 2019 (Artemov and Fitting 2019, Kuznets and Studer 2019).

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• Justification Logic Bibliography , a complete bibliography of material on justification logic up to February 2014. Maintained by Roman Kuznets.

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7.3 Justification

Learning objectives.

By the end of this section, you will be able to:

• Explain what justification means in the context of epistemology.
• Explain the difference between internal and external theories of justification.
• Describe the similarities and differences between coherentism and foundationalism.
• Classify beliefs according to their source of justification.

Much of epistemology in the latter half of the 20th century was devoted to the question of justification . Questions about what knowledge is often boil down to questions about justification. When we wonder whether knowledge of the external world is possible, what we really question is whether we can ever be justified in accepting as true our beliefs about the external world. And as previously discussed, determining whether a defeater for knowledge exists requires knowing what could undermine justification.

We will start with two general points about justification. First, justification makes beliefs more likely to be true. When we think we are justified in believing something, we think we have reason to believe it is true. How justification does this and how to think about the reasons will be discussed below. Second, justification does not always guarantee truth . Justification makes beliefs more likely to be true, which implies that justified beliefs could still be false. The fallibility of justification will be addressed at the end of this section.

The Nature of Justification

Justification makes a belief more likely to be true by providing reasons in favor of the truth of the belief. A natural way to think of justification is that it provides logical support. Logic is the study of reasoning, so logical support is strong reasoning. If I am reasoning correctly, I am justified in believing that my dog is a mammal because all dogs are mammals. And I am justified in believing that 3 1332 = 444 3 1332 = 444 if I did the derivation correctly. But what if I used a calculator to derive the result? Must I also have reasons for believing the calculator is reliable before being justified in believing the answer? Or can the mere fact that calculators are reliable justify my belief in the answer? These questions get at an important distinction between the possible sources of justification—whether justification is internal or external to the mind of the believer.

Internalism and Externalism

Theories of justification can be divided into two different types: internal and external. Internalism is the view that justification for belief is determined solely by factors internal to a subject’s mind. The initial appeal of internalism is obvious. A person’s beliefs are internal to them, and the process by which they form beliefs is also an internal mental process. If you discover that someone engaged in wishful thinking when they came to the belief that the weather would be nice today, even if it turns out to be true, you can determine that they did not know that it would be nice today. You will believe they did not have that knowledge because they had no reasons or evidence on which to base their belief. When you make this determination, you reference that person’s mental state (the lack of reasons).

But what if a person had good reasons when they formed a belief but cannot currently recall what those reasons were? For example, I believe that Aristotle wrote about unicorns, although I cannot remember my reasons for believing this. I assume I learned it from a scholarly text (perhaps from reading Aristotle himself), which is a reliable source. Assuming I did gain the belief from a reliable source, am I still justified given that I cannot now recall what that source was? Internalists contend that a subject must have cognitive access to the reasons for belief in order to have justification. To be justified, the subject must be able to immediately or upon careful reflection recall their reasons. Hence, according to internalism , I am not justified in believing that Aristotle wrote about unicorns.

On the other hand, an externalist would say my belief about Aristotle is justified because of the facts about where I got the belief. Externalism is the view that at least some part of justification can rely on factors that are not internal or accessible to the mind of the believer. If I once had good reasons, then I am still justified, even if I cannot now cite those reasons. Externalist theories about justification usually focus on the sources of justification, which include not only inference but also testimony and perception. The fact that a source is reliable is what matters. To return to the calculator example, the mere fact that a calculator is reliable can function as justification for forming beliefs based on its outputs.

An Example of Internalism: Ruling Out Relevant Alternatives

Recall that the “no defeaters” theory of knowledge requires that there exist no evidence that, if known by the subject, would undermine their justification. The evidence is not known by the subject, which makes the evidence external. The fourth condition could instead be an internal condition. Rather than require that there exist no evidence, one could say that S needs to rule out any relevant alternatives to their belief. The “no relevant alternatives” theory adds to the traditional account of knowledge the requirement that a person rule out any competing hypotheses for their belief. Ruling out refers to a subject’s conscious internal mental state, which makes this condition internal in nature. Like the “no defeaters” condition, the “no relevant alternatives” condition is meant to solve the Gettier problem . It does so by broadening the understanding of justification so that justification requires ruling out relevant alternatives. However, it still doesn’t solve the Gettier problem. Returning to the barn example, the possibility that there are barn facades is not a relevant alternative to the belief that one is looking at a barn. Unless one is in Hollywood, one would not think that facades are a distinct possibility.

An Example of Externalism: Causal Theories

Externalists hold that a subject need not have access to why their true beliefs are justified. But some theorists, such as American philosopher Alvin Goldman (b. 1938), argue that the justification condition in the account of knowledge should be replaced with a more substantial and thorough condition that effectively explains what justification is . Goldman argues that beliefs are justified if they are produced by reliable belief-forming processes (Goldman 1979). Importantly, it is the process that confers justification, not one’s ability to recount that process. Goldman’s account of knowledge is that a true belief is the result of a reliable belief-forming process .

Goldman’s theory is called historical reliabilism — historical because the view focuses on the past processes that led to a belief, and reliabilism because, according to the theory, processes that reliably produce true beliefs confer justification on those beliefs. Reliable belief-forming processes include perception, memory, strong or valid reasoning, and introspection. These processes are functional operations whose outputs are beliefs and other cognitive states. For example, reasoning is an operation that takes as input prior beliefs and hypotheses and outputs new beliefs, and memory is a process that “takes as input beliefs or experiences at an earlier time and generates as output beliefs at a later time” (Goldman 1979, 12). Usually, memory is reliable in the sense that it is more likely to produce true beliefs than false ones.

Because Goldman ’s approach is externalist, the justification-conferring process need not be cognitively accessible to the believer. His view has also been called causal because he focuses on the causes of belief. If a belief is caused in the right way (by a reliable belief-forming processes), then it is justified. One virtue of this approach is that it accounts for the intuition that someone could have a justified belief without being able to cite all the reasons for holding that belief. However, this view is not without fault. The original impetus behind revising Plato’s traditional JTB analysis was to solve the Gettier problem , and Goldman’s account cannot do this. Consider again Henry and the barn. Henry looks at a real barn and forms the belief that it is a barn. Henry’s belief that he is looking at a barn is caused by a reliable belief-forming process (perception), so according to Goldman’s account, Henry does have knowledge. Yet many philosophers think that Henry doesn’t have knowledge given the lucky nature of his belief.

Theories of Justification

So far, we have looked at theories of justification as applied to individual beliefs. But beliefs are not always justified in isolation. Usually, the justification of one belief depends on the justification of other beliefs. I must be justified in trusting my perception to then be justified in believing that there is a bird outside of my office window. Thus, some theories focus on the structure of justification—that is, how a system or set of beliefs is structured. The theories on the structure of justification aim to illustrate how the structure of a system of beliefs leads to knowledge, or true beliefs.

Foundationalism

Much of what a subject justifiably believes is inferred from other justified beliefs . For example, Ella justifiably believes the Battle of Hastings occurred in 1066 because her history professor told her this. But the justification for her belief doesn’t end there. Why is Ella justified in believing that her history professor is a good source? Furthermore, why is she even justified in believing that her history professor told her this? To the second question, Ella would reply that she is justified because she remembers her professor telling her. But then one can ask, Why is the reliance on memory justifiable? Justified beliefs rest on other justified beliefs. The question is whether the chain of justification ever ends. Foundationalists hold that justification must terminate at some point.

Foundationalism is the view that all justified beliefs ultimately rest on a set of foundational, basic beliefs. Consider a house. Most of what people see of a house is the superstructure—the main floor, columns, and roof. But the house must rest on a foundation that stabilizes and props up the parts of the house people can see. According to foundationalists, most beliefs are like the superstructure of the house—the frame, roof, and walls. The majority of people’s beliefs are inferential beliefs , or beliefs based on inference. And according to foundationalism, all beliefs rest on a foundation of basic beliefs (Hasan and Fumerton 2016). One of Ella’s foundational beliefs could be that her memory is reliable. If this belief is justified, then all of Ella’s justified beliefs derived from memory will rest on this foundational belief.

But what justifies basic beliefs? If basic beliefs function so as to justify other beliefs, then they too must be justified. If the foundation is not justified, then none of the beliefs that rest on it are justified. According to foundationalism, the beliefs that make up the foundation are justified beliefs, but they are justified non-inferential beliefs. Foundational beliefs must be non-inferential (not based on inference) because if they were inferential, they would get their justification from another source, and they would no longer be foundational. Foundational beliefs are supposed to be where the justification stops.

What is a basic belief, and what are the reasons for thinking basic beliefs are justified? French philosopher René Descartes (1596–1650) was a foundationalist, and he held that people’s basic beliefs are indubitable (Descartes 2008). An indubitable belief is one that cannot be mistaken. Clearly, if the foundation is made of beliefs that cannot be mistaken, then it is justified. But why think that foundational beliefs cannot be mistaken? Descartes thought that whatever a subject can clearly and distinctly conceive of in their mind, they can take to be true because God would not allow them to be fooled. As an illustration of how some beliefs might be indubitable, recall that knowledge by acquaintance is direct and unmediated knowledge. Acquaintance is unmediated by other ways of knowing, including inference, so beliefs gained though acquaintance are non-inferential, which is what the foundationalist wants. Beliefs gained via acquaintance are also justified, which is why Russell deems them knowledge . As an example, imagine that you see a green orb in your field of vision. You may not know whether the green orb is due to something in your environment, but you cannot be mistaken about the fact that you visually experience the green orb. Hence, knowledge by acquaintance is a possible candidate for the foundation of beliefs.

Coherentism is the view that justification, and thus knowledge, is structured not like a house but instead like a web. More precisely, coherentism argues that a belief is justified if it is embedded in a network of coherent, mutually supported beliefs. Think of a web. Each strand in a web is not that strong by itself, but when the strands are connected to multiple other strands and woven together, the result is a durable network. Similarly, a subject’s justification for individual beliefs, taken alone, is not that strong. But when those beliefs are situated in a system of many mutually supporting beliefs, the justification grows stronger. Justification emerges from the structure of a belief system (BonJour 1985).

Within foundationalism , the justifications for some beliefs can proceed in a completely linear fashion. Ella believes the Battle of Hastings occurred in 1066 because her professor told her, and she believes that her professor told her because she remembers it and thinks her memory is justifiable. One belief justifies another, which justifies another, and so on, until the foundation is reached. Yet very few beliefs are actually structured in this manner. People often look for support for their beliefs in multiple other beliefs while making sure that they are also consistent. Figure 7.5 offers a simplified visual of the two different structures of belief.

Often, when we think of the justification for our beliefs, we don’t just consider the original source of a belief. We also think about how that belief fits into our other beliefs. If a belief does not cohere with other beliefs, then its justification appears weak, even if the initial justification for the belief seemed strong. Suppose you need to go to the bank, and on your way out the door, your roommate tells you not to waste your time because they drove by the bank earlier and it was closed. Your roommate’s testimony seems like enough reason to believe the bank is closed. However, it is a weekday, and the bank is always open during the week. Furthermore, it is not a holiday. You check the bank’s website, and it states that the bank is open. Hence, the belief that the bank is closed does not cohere with your other beliefs. The lack of coherence with other beliefs weakens the justification for believing what your otherwise reliable roommate tells you.

To be fair, foundationalists also consider coherence of beliefs in determining justification. However, as long as a belief is consistent with other beliefs and rests on the foundation, it is justified. But consistency is not the same thing as logical support. The beliefs that there is a bird in that tree, it is November, and a person is hungry are all consistent with one another, but they do not support one another. And for coherentists, logical consistency alone does not make a system of belief justified. Justification arises from a system of beliefs that mutually reinforce one another. Support can happen in many ways: beliefs can deductively entail one another, they can inductively entail one another, and they can cohere by explaining one another. Suppose I am trying to remember where my friend Faruq is from. I believe he is from Tennessee but am not sure. But then I remember that Faruq often wears a University of Tennessee hat and has a Tennessee Titans sticker on this car. He also speaks with a slight southern twang and has told stories about hiking in the Smoky Mountains, which are partially in Tennessee. That Faruq is from Tennessee can explain these further beliefs. Note that I can get more assurance for my belief that Faruq is from Tennessee by considering my other beliefs about him. When beliefs mutually reinforce one another, they acquire more justification.

Coherentism more naturally reflects the actual structure of belief systems, and it does so without relying on the notion of basic, justified, non-inferential beliefs. However, coherentism has weaknesses. One objection to coherentism is that it can result in circularity. Within a system of beliefs, any belief can play a roundabout role in its own justification. Figure 7.6 illustrates this problem.

Another objection to coherentism is called the isolation objection . A network of beliefs can mutually explain and support one another, thus giving them justification . However, it is not guaranteed that these beliefs are connected to reality. Imagine a person, Dinah, who is trapped in a highly detailed virtual reality. Dinah has been trapped for so long that she believes her experiences are of the real world. Because of the detailed nature of Dinah’s virtual reality, most of her beliefs are consistent with and support one another, just as your beliefs about the real world do. As long as Dinah’s beliefs are consistent and coherent, she will be justified in believing that her experience is of real objects and real people. So Dinah has justification even though all her beliefs concerning the reality of her world are false. Dinah’s situation reveals an important feature of justification: while justification makes beliefs more likely to be true, it does not always guarantee that they are true. Justification is often fallible.

The Fallible Nature of Justification

The sources of beliefs are varied. Perception, reason, hope, faith, and wishful thinking can all result in belief. Yet just because something results in belief, that does not mean that the belief is justified. Beliefs that result from wishful thinking are not justified because wishful thinking does not make a belief more likely to be true. A source of justification is a reliable basis for belief. Yet while justification is a reliable source, notice that this does not mean that the belief is true; it just makes it more likely. Justified beliefs can turn out to be false. In order to drive this point home, we will briefly look at four different sources of belief. As you will see, each source is fallible.

One source of belief is memory . Memory is not always reliable. First of all, that you do not remember something in your past does not mean that it did not happen. Second, when you do remember something, does that guarantee that it happened the way you remember it? Because people can misremember, philosophers distinguish between remembering and seeming to remember. When you actually remember P, then this justifies believing P. When you seem to remember P, this does not justify believing P. The problem is that remembering and seeming to remember often feel the same to the person trying to remember.

Most beliefs are the product of inference. When you use reason to come to belief, the justification you have is inferential; hence, inferential justification is equivalent to logical justification. But as discussed in the chapter on logic, not all forms of inference can guarantee truth. Inductive reasoning , which is the most common source of beliefs, is only probable even when done well. Furthermore, people often make mistakes in reasoning. Just because someone reasoned their way to a belief doesn’t mean they reasoned well. But assume for a moment that a person comes to a belief using deductive reasoning, which can guarantee truth, and they reason well. Is it still possible that their belief is false? Yes. Deductive reasoning takes as its input other beliefs to then derive conclusions. In good inductive reasoning, if the premises are true (the input beliefs), then the conclusion is true. If the input beliefs are false, then even good deductive reasoning cannot guarantee true beliefs.

Another source of belief is testimony . When you gain beliefs based on the stated beliefs of others, you rely on testimony. Testimony is usually considered something that happens only in a court of law, but in philosophy, the term testimony is used much more broadly. Testimony is any utterance, spoken or written, occurring in normal communication conditions. Instances of testimony include news magazines, nonfiction books, personal blogs, professors’ lectures, and opinions volunteered in casual conversation. Often, testimony is a reliable source of information and so can be justified. When you form beliefs based on the testimony of experts, it is justified. But even when justified, those beliefs could be false because experts are vulnerable to all of the weaknesses of justification covered in this section. More will be said about testimony in the section on social epistemology.

Last, perception can be used as a source of justification. Perception includes the information received from the senses (smell, taste, touch, sight, hearing). People often automatically form beliefs based on perception. However, not all beliefs that follow from perception are guaranteed to be true, as the possibility of knowledge by acquaintance shows. As discussed earlier, Russell maintained that the only automatically justified beliefs gained from perception are about the existence of sense data (Russell 1948). When looking at the bird outside of my office window, I only have knowledge by acquaintance of the experience of seeing the bird on a branch in my visual field. I know that it seems to me that there’s a bird. But how do I get from those sense data to the justified belief that there really is bird on the branch? I must rely on another belief about the reliability of my perception—a belief that I can only get by inference, specifically induction . I reason from past instances where I believe my perception is reliable to the general belief that it is reliable. And of course, induction is fallible. Whenever one moves from knowledge by acquaintance to further beliefs—such as the belief that sense data is caused by actually existing objects—there is room for error.

Not all philosophers agree that all perceptual beliefs are mediated through sense data (Crane and French 2021). The view called direct realism states that people have direct access to objects in the external world via perception. While direct realism holds that one can directly perceive the external world, it still cannot guarantee that beliefs about it are true, for both hallucinations and illusions are still possible. Figure 7.7 is an example of an illusion.

If you focus only on the top two lines, it appears as though they are of different lengths. Yet the bottom two lines indicate that this appearance is illusory—the lines are actually of equal length. Illusions function as evidence that perception sometimes misrepresents reality. Even direct realists have to contend with the possibility that beliefs gained through sense perception could be wrong. Hence, sources of beliefs, even when they are usually justified, are nevertheless fallible. The possibility that the subject could be wrong is what gives rise to philosophical skepticism—the view that knowledge in some or all domains is impossible.

Think Like a Philosopher

Think critically about the sources of justification explained above. Which of these is more reliable than the others? For each source, identify one instance in which it is reliable and one instance in which it is not.

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Critical Thinking and Justification

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Critical Thinking: 25 Performance Review Phrases Examples

By Status.net Editorial Team on July 15, 2023 — 8 minutes to read

Critical thinking skills are an essential aspect of an employee’s evaluation: the ability to solve problems, analyze situations, and make informed decisions is crucial for the success of any organization.

Questions that can help you determine an employee’s rating for critical thinking:

• Does the employee consistently analyze data and information to identify patterns and trends?
• Does the employee proactively identify potential problems and develop solutions to mitigate them?
• Has the employee demonstrated the ability to think creatively and come up with innovative ideas or approaches?
• Does the employee actively seek out feedback and input from others to inform their decision-making process?
• Has the employee demonstrated the ability to make sound decisions based on available information and data?

Performance Review Phrases and Paragraphs Examples For Critical Thinking

5 – outstanding.

Employees with outstanding critical thinking skills are exceptional at identifying patterns, making connections, and using past experiences to inform their decisions.

Phrases Examples

• Consistently demonstrates exceptional critical thinking abilities
• Always finds creative and innovative solutions to complex problems
• Skilfully analyzes information and data to make well-informed decisions
• Frequently provides valuable insights and perspectives that benefit the team
• Continuously seeks out new learning opportunities to sharpen their critical thinking skills
• Demonstrates exceptional ability to identify and analyze complex issues
• Consistently develops innovative solutions to problems
• Skillfully connects disparate ideas to create coherent arguments
• Effectively communicates well-reasoned conclusions
• Exceptional ability to recognize trends in data
• Expertly applies existing knowledge to new situations
• Consistently anticipates potential challenges and develops solution

Paragraph Example 1

“Jane consistently demonstrates outstanding critical thinking skills in her role. She not only engages in deep analysis of complex information, but she also presents unique solutions to problems that have a significant positive impact on the team’s performance. Her ability to make well-informed decisions and offer valuable insights has led to numerous successes for the organization. Moreover, Jane’s dedication to improvement and learning demonstrates her commitment to personal and professional growth in the area of critical thinking.”

Paragraph Example 2

“Jessica consistently displays outstanding critical thinking skills. She is able to identify and analyze complex issues with ease and has demonstrated her ability to develop innovative solutions. Her skill in connecting disparate ideas to create coherent arguments is impressive, and she excels at communicating her well-reasoned conclusions to the team.”

Paragraph Example 3

“Melanie consistently demonstrates an exceptional ability to recognize patterns and trends in data, which has significantly contributed to the success of our projects. Her critical thinking skills allow her to apply her extensive knowledge and experience in creative and innovative ways, proactively addressing potential challenges and developing effective solutions.”

4 – Exceeds Expectations

Employees exceeding expectations in critical thinking skills are adept at analyzing information, making sound decisions, and providing thoughtful recommendations. They are also effective at adapting their knowledge to novel situations and displaying confidence in their abilities.

• Excellent analytical capabilities
• Provides well-reasoned recommendations
• Demonstrates a solid understanding of complex concepts
• Regularly demonstrates the ability to think analytically and critically
• Effectively identifies and addresses complex problems with well-thought-out solutions
• Shows exceptional skill in generating innovative ideas and solutions
• Exhibits a consistently high level of decision-making based on sound reasoning
• Proactively seeks out new information to improve critical thinking skills
• Routinely identifies potential challenges and provides solutions
• Typically recognizes and prioritizes the most relevant information
• Logical thinking is evident in daily decision-making
• Often weighs the pros and cons of multiple options before selecting a course of action

“Eric’s critical thinking skills have consistently exceeded expectations throughout his tenure at the company. He is skilled at reviewing and analyzing complex information, leading him to provide well-reasoned recommendations and insights. Eric regularly demonstrates a deep understanding of complicated concepts, which allows him to excel in his role.”

“In this evaluation period, Jane has consistently demonstrated an exceptional ability to think critically and analytically. She has repeatedly shown skill in identifying complex issues while working on projects and has provided well-thought-out and effective solutions. Her innovative ideas have contributed significantly to the success of several key initiatives. Moreover, Jane’s decision-making skills are built on sound reasoning, which has led to positive outcomes for the team and organization. Additionally, she actively seeks opportunities to acquire new information and apply it to her work, further strengthening her critical thinking capabilities.”

“John consistently exceeds expectations in his critical thinking abilities. He routinely identifies potential challenges and provides thoughtful solutions. He is skilled at recognizing and prioritizing the most relevant information to make well-informed decisions. John regularly weighs the pros and cons of various options and selects the best course of action based on logic.”

3 – Meets Expectations

Employees meeting expectations in critical thinking skills demonstrate an ability to analyze information and draw logical conclusions. They are effective at problem-solving and can make informed decisions with minimal supervision.

• Capable of processing information and making informed decisions
• Displays problem-solving skills
• Demonstrates logical thinking and reasoning
• Consistently demonstrates the ability to analyze problems and find possible solutions.
• Actively engages in group discussions and contributes valuable ideas.
• Demonstrates the ability to draw conclusions based on logical analysis of information.
• Shows willingness to consider alternative perspectives when making decisions.
• Weighs the pros and cons of a situation before reaching a decision.
• Usually identifies relevant factors when faced with complex situations
• Demonstrates an understanding of cause and effect relationships
• Generally uses sound reasoning to make decisions
• Listens to and considers different perspectives

“Sarah consistently meets expectations in her critical thinking skills, successfully processing information and making informed decisions. She has shown her ability to solve problems effectively and displays logical reasoning when approaching new challenges. Sarah continues to be a valuable team member thanks to these critical thinking skills.”

“Jane is a team member who consistently meets expectations in regards to her critical thinking skills. She demonstrates an aptitude for analyzing problems within the workplace and actively seeks out potential solutions by collaborating with her colleagues. Jane is open-minded and makes an effort to consider alternative perspectives during decision-making processes. She carefully weighs the pros and cons of the situations she encounters, which helps her make informed choices that align with the company’s objectives.”

“David meets expectations in his critical thinking skills. He can usually identify the relevant factors when dealing with complex situations and demonstrates an understanding of cause and effect relationships. David’s decision-making is generally based on sound reasoning, and he listens to and considers different perspectives before reaching a conclusion.”

2 – Needs Improvement

Employees in need of improvement in critical thinking skills may struggle with processing information and making logical conclusions. They may require additional guidance when making decisions or solving problems.

• Struggles with analyzing complex information
• Requires guidance when working through challenges
• Difficulty applying past experiences to new situations
• With some guidance, Jane is able to think critically, but she struggles to do so independently.
• John tends to jump to conclusions without analyzing a situation fully.
• Sarah’s problem-solving skills need improvement, as she often overlooks important information when making decisions.
• David’s critical thinking skills are limited and need further development to enhance his overall work performance.
• Occasionally struggles to identify and analyze problems effectively
• Inconsistently uses logic to make decisions
• Often overlooks important information or perspectives
• Requires guidance in weighing options and making judgments

“Bob’s critical thinking skills could benefit from further development and improvement. He often struggles when analyzing complex information and tends to need additional guidance when working through challenges. Enhancing Bob’s ability to apply his past experiences to new situations would lead to a notable improvement in his overall performance.”

“Jenny is a valuable team member, but her critical thinking skills need improvement before she will be able to reach her full potential. In many instances, Jenny makes decisions based on her first impressions without questioning the validity of her assumptions or considering alternative perspectives. Her tendency to overlook key details has led to several instances in which her solutions are ineffective or only partly beneficial. With focused guidance and support, Jenny has the potential to develop her critical thinking skills and make more informed decisions in the future.”

“Tom’s critical thinking skills require improvement. He occasionally struggles to identify and analyze problems effectively, and his decision-making is inconsistent in its use of logic. Tom often overlooks important information or perspectives and may require guidance in weighing options and making judgments.”

1 – Unacceptable

Employees with unacceptable critical thinking skills lack the ability to analyze information effectively, struggle with decision-making, and fail to solve problems without extensive support from others.

• Fails to draw logical conclusions from information
• Incapable of making informed decisions
• Unable to solve problems without extensive assistance
• Fails to analyze potential problems before making decisions
• Struggles to think critically and ask relevant questions
• Cannot effectively identify alternative solutions
• Lacks the ability to apply logic and reason in problem-solving situations
• Does not consistently seek input from others or gather information before making a decision
• Regularly fails to recognize or address important issues
• Makes hasty decisions without considering potential consequences
• Lacks objectivity and often relies on personal biases
• Resistant to alternative viewpoints and constructive feedback

“Unfortunately, Sue’s critical thinking skills have been consistently unacceptable. She fails to draw logical conclusions from available information and is incapable of making informed decisions. Sue has also shown that she is unable to solve problems without extensive assistance from others, which significantly impacts her performance and the team’s productivity.”

“Jane’s performance in critical thinking has been unacceptable. She often fails to analyze potential problems before making decisions and struggles to think critically and ask relevant questions. Jane’s inability to effectively identify alternative solutions and apply logic and reason in problem-solving situations has negatively impacted her work. Furthermore, she does not consistently seek input from others or gather information before making a decision. It is crucial for Jane to improve her critical thinking skills to become a more effective and valuable team member.”

“Susan’s critical thinking skills are unacceptable. She regularly fails to recognize and address important issues, and her decision-making is often hasty and without considering potential consequences. Susan frequently lacks objectivity and tends to rely on personal biases. She is resistant to alternative viewpoints and constructive feedback, which negatively affects her work performance.”

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