| **This article or section is missing citations or needs footnotes.** Using inline citations helps guard against copyright violations and factual inaccuracies. | **Critical thinking** consists of mental processes of discernment, analysis and evaluation. It includes all possible processes of reflecting upon a tangible or intangible item in order to form a solid judgment that reconciles scientific evidence with common sense. Image File history File links Emblem-important. ...
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Discernment is a term used in the Catholic Church, and other Christian traditions to describe the process of ascertaining Gods will for ones life. ...
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Tangible Tangible relates to something that can be touched. ...
Intangibles are qualities in an individual or group of individuals, especially those organized in an official group (e. ...
Critical thinkers gather information from all senses, verbal and/or written expressions, reflection, observation, experience and reasoning. Critical thinking has its basis in intellectual criteria that go beyond subject-matter divisions and which include: clarity, credibility, accuracy, precision, relevance, depth, breadth, logic, significance and fairness. Interpersonal communication is the process of sending and receiving information or communication with another person. ...
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Look up Experience in Wiktionary, the free dictionary This article discusses the general concept of experience. ...
Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings. ...
Intelligence is the mental capacity to reason, plan, solve problems, think abstractly, comprehend ideas and language, and learn. ...
Clarity is the property of being clear or transparent. ...
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In the fields of science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. ...
In Wikipedia, precision has the following meanings: In engineering, science, industry and statistics, precision characterises the degree of mutual agreement among a series of individual measurements, values, or results - see accuracy and precision. ...
Relevance is a term used to describe how pertinent, connected, or applicable some information is to a given matter. ...
In general English usage, length (symbols: l, L) is but one particular instance of distance â€“ an objects length is how long the object is â€“ but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth...
Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ...
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## Overview
Fundamentally, critical thinking is a form of judgment, specifically purposeful and reflective judgment. Using critical thinking one makes a decision or solves the problem of judging what to believe or what to do, but does so in a reflective way. That is by giving due consideration to the evidence, the context of judgement, the relevant criteria for making that judgment well, the applicable methods or techniques for forming that judgment, and the applicable theoretical and constructs for understanding the nature of the problem and the question at hand. These elements also happen to be the key defining characteristics of professional fields and academic disciplines. This is why critical thinking can occur within a given subject field (by reference to its specific set of permissible questions, evidence sources, criteria, etc.) and across subject fields in all those spaces where human beings need to interact and make decisions, solve problems, and figure out what to believe and what to do. A useful, brief, and higly readable explanation of the concept of critical thinking, its skills and dispositional dimensions, its relationship to cognitive science, and its practical value in life and learning can be found in the free on-line resource: "Critical Thinking: What It is and Why It Counts" [ http://www.insightassessment.com/articles.html].
Within the framework of scientific skepticism, the process of critical thinking involves acquiring information and evaluating it to reach a well-justified conclusion or answer. Part of critical thinking comprises informal logic. However, a large part of critical thinking goes beyond informal logic and includes assessment of beliefs and identification of prejudice, bias, propaganda, self-deception, distortion, misinformation, etc. Given research in cognitive psychology, some educators believe that schools should focus more on teaching their students critical thinking skills, intellectual standards, and cultivating intellectual traits (such as intellectual humility, intellectual empathy, intellectual integrity, and fair-mindedness) than on memorizing facts by rote learning. As defined in A Greek-English Lexicon the verb *krino-* means to choose, decide or judge. Hence a *krites* is a discerner, judge or arbiter. Those who are *kritikos* have the ability to discern or decide. To meet Wikipedias quality standards, this article or section may require cleanup. ...
Theory of justification is a part of epistemology that attempts to understand the justification of statements and beliefs. ...
Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ...
For with(out) prejudice in law, see Prejudice (law). ...
For other senses of this word, see bias (disambiguation). ...
For other uses, see Propaganda (disambiguation). ...
Cognitive Psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. ...
A skill is an ability, usually learned and acquired through training, to perform actions which achieve a desired outcome. ...
It has been suggested that Rote memory be merged into this article or section. ...
A Greek-English Lexicon is the standard lexicographical work of the ancient Greek language, begun in the nineteenth century and now in its ninth (revised) edition. ...
The word *krino-* also means to separate (winnow) the wheat from the chaff or that which has worth from that which does not. Critical thinking is a pervasive human process, evident in children and adults. It is important, because it enables one to analyze, evaluate, explain, and restructure our thinking, decreasing thereby the risk of acting on, or thinking with, a false premise. However, even with the use of critical thinking skills, mistakes can happen due to a thinker's egocentrism or sociocentrism or failure to be in possession of the full facts. In addition, there is always the possibility of inadvertent human error. This page may meet Wikipedias criteria for speedy deletion. ...
Universal concepts and principles of critical thinking can be applied to any context or case but only by reflecting upon the nature of that application. Critical thinking forms, therefore, a system of related, and overlapping, modes of thought such as anthropological thinking, sociological thinking, historical thinking, political thinking, psychological thinking, philosophical thinking, mathematical thinking, chemical thinking, biological thinking, ecological thinking, legal thinking, ethical thinking, musical thinking, thinking like a painter, sculptor, engineer, business person, etc. In other words, though critical thinking principles are universal, their application to disciplines requires a process of reflective contextualization.
One can regard critical thinking as involving two aspects: *a set of cognitive skills, intellectual standards, and traits of mind* *the disposition or intellectual commitment to use those structures to improve thinking and guide behavior*. Critical thinking does not include simply the acquisition and retention of information, or the possession of a skill-set which one does not use regularly; nor does critical thinking merely exercise skills without acceptance of the results. Cognitive The scientific study of how people obtain, retrieve, store and manipulate information. ...
This article does not cite any references or sources. ...
## What is and is not universal in critical thinking Critical thinking is based on concepts and principles, not on hard and fast, or step-by-step, procedures. ^{[citation needed]} Critical thinking does not assure that one will reach either the truth or correct conclusions. First, one may not have all the relevant information; indeed, important information may remain undiscovered, or the information may not even be knowable. Furthermore, one may make unjustified inferences, use inappropriate concepts, fail to notice important implications, use a narrow or unfair point of view. One may be a victim of self-delusion, egocentricity or sociocentricity, or closed-mindedness. One's thinking may be unclear, inaccurate, imprecise, irrelevant, narrow, shallow, illogical, or trivial. One may be intellectually arrogant, intellectually lazy, or intellectually hypocritical. These are some of the ways that human thinking can be flawed. Further information can be found in the *Thinker's Guide* series by Richard Paul and Linda Elder. Human thinking left to itself often leads to various forms of self-deception, individually and socially; and at the left, right, and mainstream of economic, political, and religious issues. Further analysis and resources about this interaction may be found in Roderick Hindery (2001): *Indoctrination and Self-deception or Free and Critical Thought*.
## The uses of critical thinking Critical thinking is useful only in those situations where human beings need to solve problems, make decisions, or decide in a reasonable and reflective way what to believe or what to do. That is, just about everywhere and all the time. Critical thinking is important wherever the quality of human thinking significantly impacts the quality of life (of any sentient creature). For example, success in human life is tied to success in learning. At the same time, every phase in the learning process is tied to critical thinking. Thus, reading, writing, speaking, and listening can all be done critically or uncritically. Critical thinking is crucial to becoming a close reader and a substantive writer. Expressed most generally, critical thinking is “a way of taking up the problems of life.” (William Graham Sumner, Folkways, 1906) William Graham Sumner (1840-1910) was the leading American advocate of a free-trade industrial society, which is what he believed the socialists meant by capitalism. ...
Irrespective of the sphere of thought, “a well cultivated critical thinker": - raises vital questions and problems, formulating them clearly and precisely;
- gathers and assesses relevant information, using abstract ideas to interpret it effectively
- comes to well-reasoned conclusions and solutions, testing them against relevant criteria and standards;
- thinks open-mindedly within alternative systems of thought, recognizing and assessing, as need be, their assumptions, implications, and practical consequences; and
- communicates effectively with others in figuring out solutions to complex problems.
(Paul, R. and Elder, 2006)
## The affective dimension of critical thinking Critical thinking is about being both willing and able to think. Ideally one developes critical thinking skills and at the same time the disposition to use those skills to solve problems and form good judgments. The dispositional dimension of critical thinking is characterological. Its focus in developing the habitual intention to be truth-seeking, open-minded, systematic, analytical, inquisitive, confident in reasoning, and prudent in making judgments. Those who are ambivalent on one or more of these aspects of the disposition toward critical thinking, or who have the opposite disposition [biased, intolerant, disorganized, heedless of consequences, indifferent toward new information, mistrustful of reasoning, imprudence]are less likely to engage problems using their critical thinking skills. The relationship between critical thinking skills and critical thinking dispositions is an empirical question. Some have both in abundance, some have skills but not the disposition to use them, some are disposed but lack strong skills and some have neither. Two measures of critical thinking dispositions are the California Critical Thinking Disposition Inventory [1]and the CM3 [2]. Critical thinking may be distinguished, but not separated, from emotions, desires, and traits of mind. Failure to recognize the relationship between thinking, feeling, wanting, and traits of mind can easily lead to various forms of self-deception, both individually and collectively. When persons possess intellectual skills alone, without the intellectual traits of mind, *weak sense critical thinking* results. Fair-minded or *strong sense critical thinking* requires intellectual humility, empathy, integrity, perseverance, courage, autonomy, confidence in reason, and other intellectual traits. Thus, critical thinking without essential intellectual traits often results in clever, but manipulative, often unethical, thought. In short, the sophist, the con artist, the manipulator often uses an intellectually defective but effective form of thought---serving unethical purposes. However, whereas critical thinking yields itself to analytical consideration readily and may be considered largely "objective", the notions of socially-based mores and taboos are largely relative and "subjective". For the medieval saint of the same name, see Saint Humility. ...
Not to be confused with Pity, Sympathy, or Compassion. ...
This article is about the ethical concept. ...
Perseverance Perseverance was an early steam locomotive that took part in the Rainhill Trials. ...
For other uses, see Courage (disambiguation). ...
Look up autonomy, autonomous in Wiktionary, the free dictionary. ...
Intellectual virtues are character traits necessary for right action and correct thinking. ...
Further analysis and resources about the interaction between thought, desires, and emotions may be found in Roderick Hindery (2001): *Indoctrination and Self-deception or Free and Critical Thought* and in Paul and Elder (2004): *The Human Mind*.
## Overcoming bias There is no simple way to reduce one's bias. There are, however, ways that one can begin to do so. The most important require developing one's intellectual empathy and intellectual humility. The first requires extensive experience in entering and accurately constructing points of view toward which one has negative feelings. The second requires extensive experience in identifying the extent of one's own ignorance in a wide variety of subjects (ignorance whose admission leads one to say, "I thought I *knew*, but I merely *believed*"). One becomes less biased and more broad-minded when one becomes more intellectually empathic and intellectually humble, and that involves time, deliberate practice and commitment. It involves considerable personal and intellectual development. To develop one's critical thinking abilities, one should learn the art of suspending judgment (for example, when reading a novel, watching a movie, engaging in dialogical or dialectical reasoning). Ways of doing this include adopting a perceptive rather than judgmental orientation; that is, avoiding moving from perception to judgment as one applies critical thinking to an issue. One should become aware of one's own fallibility by: - accepting that everyone has subconscious biases, and accordingly questioning any reflexive judgments.
- adopting an ego-sensitive and, indeed, intellectually humble stance
- recalling previous beliefs that one once held strongly but now rejects
- realizing one still has numerous blind spots, despite the foregoing
An integration of insights from the critical thinking literature and cognitive psychology literature is the "Method of Argument and Heuristic Analysis." This technique illustrates the influeces of heuristics and biases on human decision making along with the influences of thinking critically about reasons and claims. *Thinking and Reasoning in Human Decision Making* [3] See also: Unconscious mind. ...
eGO is a company that builds electric motor scooters which are becoming popular for urban transportation and vacation use. ...
Blind spot can refer to: In ophthalmology, Scotoma, an obscuration of the visual field Optic disc, also known as the anatomical blind spot, the specific region of the retina where the optic nerve and blood vessels pass through to connect to the back of the eye Blind spot (vision), also...
## Critical thinking in the classroom The key to seeing the significance of critical thinking in the classroom is in understanding the significance of critical thinking in learning. To learn is to think. To think poorly is to learn poorly. To think well is to learn well. All content, to be learned, must be intellectually constructed. To learn the content of history, I must engage myself in the process of thinking historically. There are two phases to the learning of content. The first occurs when learners (for the first time) construct in their minds the basic ideas, principles, theories that are inherent in content. This is a process of internalization. The second occurs when learners effectively use those ideas, principles, and theories as they become relevant in learners’ lives. This is a process of application. Good teachers cultivate critical thinking (intellectually engaged thinking) at every stage of learning, including initial learning. This process of intellectual engagement is at the heart of the Oxford and Cambridge tutorials. The tutor questions the students, often in a Socratic manner. Here are some typical Socratic questions: - What do you mean by_______________?
- How did you come to that conclusion?
- What was said in the text?
- What is the source of your information?
- What is the source of information in the report?
- What assumption has led you to that conclusion?
- Suppose you are wrong. What are the implications?
- Why did you make that inference? Is another one more consistent with the data?
- Why is this issue significant?
- How do I know that what you are saying is true?
- What is an alternate explanation for this phenomenon?
Of course, there are many other possible Socratic questions. The key is that the teacher who fosters critical thinking fosters reflectiveness in students by asking questions that stimulate thinking essential to the construction of knowledge. Socratic Questioning is disciplined questioning that can be used to pursue thought in many directions and for many purposes, including: to explore complex ideas, to get to the truth of things, to open up issues and problems, to uncover assumptions, to analyze concepts, to distinguish what we know from what...
As emphasized above, each discipline adapts its use of critical thinking concepts and principles. The core concepts are always there, but they are embedded in subject specific content. For students to learn content, intellectual engagement is crucial. All students must do their own thinking, their own construction of knowledge. Good teachers recognize this and therefore focus on the questions, readings, activities that stimulate the mind to take ownership of key concepts and principles underlying the subject. In the UK school system, the syllabus offers *Critical thinking* as a subject which 16-18 year olds can take as an A-Level. Under the OCR exam board, students can sit two exam papers: "Credibility of Evidence" and "Assessing/Developing Argument". The exam tests candidates not on particular information they have learned during the course, but on their ability to think critically about, and analyze, arguments on their deductive or inductive validity. The full advanced GCE is now available and, though very challenging, is extremely useful for degree courses in politics, philosophy, history or theology (to name but a few), providing the skills required for critical analysis that are useful, for example, in biblical study. The A-level, short for Advanced Level, is a General Certificate of Education qualification in the United Kingdom, usually taken by students during the optional final two years of secondary school (Years 12 & 13, commonly called the Sixth Form), or at a separate sixth form college or further education college...
OCR (Oxford, Cambridge and RSA) is a British examination board that sets examinations and awards qualifications (including GCSEs and A-levels). ...
An examination board is an organisation that sets examinations and is responsible for marking them and distributing results. ...
**Bold text**==Measuring or Assessing Critical Thinking== Several well-researched tools are available to measure critical thinking skills and critical thinking dispositions. Some are designed for younger students, others for college students and adults. While most are developed for use in a general education or every day context, some are tailored for the interests of people in different professional fields. In addition to tests, other tools for assessing critical thinking include rubrics and performance rating forms. For examples and more detailed discussion, and for free materials including the *Holisitic Critical Thinking Scoring Rubric*, visit Insight Assessment. [4]
## Reaching a conclusion Given the nature of the process, critical thinking is never final. One arrives at a tentative conclusion, given the evidence and based on an evaluation. However, the conclusion must always remain subject to further evaluation if new information comes to hand.
## Quotations William Graham Sumner offers a useful summary of critical thinking: William Graham Sumner (1840-1910) was the leading American advocate of a free-trade industrial society, which is what he believed the socialists meant by capitalism. ...
The critical habit of thought, if usual in society, will pervade all its mores, because it is a way of taking up the problems of life. Men educated in it cannot be stampeded by stump orators ... They are slow to believe. They can hold things as possible or probable in all degrees, without certainty and without pain. They can wait for evidence and weigh evidence, uninfluenced by the emphasis or confidence with which assertions are made on one side or the other. They can resist appeals to their dearest prejudices and all kinds of cajolery. **Education in the critical faculty is the only education of which it can be truly said that it makes good citizens**. Martin Luther King said: The function of education, therefore, is to teach one to think intensively and to think critically . . . The complete education gives one not only power of concentration but worthy objectives upon which to concentrate. ## See also An Argument map is a visual representation of the structure of an argument in informal logic. ...
Anthropic bias is the bias arising when your evidence is biased by observation selection effects, according to philosopher Nick Bostrom. ...
This article or section does not cite its references or sources. ...
This article or section does not adequately cite its references or sources. ...
Discourse analysis (DA), or discourse studies, is a general term for a number of approaches to analyzing written, spoken or signed language use. ...
Empirical or a posteriori knowledge is propositional knowledge obtained by experience or sensorial information. ...
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Foundation for Critical Thinking The Center for Critical Thinking and Moral Critique and the Foundation For Critical Thinking, two sister educational non-profit organizations, work closely together to promote educational reform. ...
Political Ideologies Part of the Politics series Politics Portal This box: An ideology is an organized collection of ideas. ...
Indoctrination is the process of inculcating ideas, attitudes, cognitive strategies or a professional methodology. ...
Wikipedia does not yet have an article with this exact name. ...
In logic, an argument is a set of statements, consisting of a number of premises, a number of inferences, and a conclusion, which is said to have the following property: if the premises are true, then the conclusion must be true or highly likely to be true. ...
It has been suggested that this article or section be merged into Fallacy. ...
In psychology and cognitive science, magical thinking is non-scientific causal reasoning (e. ...
The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce. ...
In the Swiss Cheese model, individual weaknesses are modelled as holes in slices of swiss cheese, such as this Emmental. ...
Problem solving forms part of thinking. ...
For other uses, see Propaganda (disambiguation). ...
A typical 18th century phrenology chart. ...
Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings. ...
Relevance is a term used to describe how pertinent, connected, or applicable some information is to a given matter. ...
Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Self-deception is a process of denying or rationalizing away the relevance, significance, or importance of opposing evidence and argument. ...
## References - Facione, P. 1990.
*The Delphi Report "CT: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction" Executive Summary* [5] - Facione, P. 2007.
*Critical Thinking: What It Is and Why It Counts - 2007 Update* [6] - Facione, PA, Facione, NC, and Giancarlo, CA.(2000).
*The Disposition Toward Critical Thinking: Its Character, Measurement, and Relationship to Critical Thinking Skill. Informal Logic*, Volume 20, Number 1, pp 61-84. [7] - B.W. Hamby
*The Philosophy of Anything: Critical Thinking in Context.* Kendall Hunt Publishing Company, Dubuque Iowa, 2007. ISBN 978-0-7575-4724-9 - Vincent F. Hendricks,
*Thought 2 Talk: A Crash Course in Reflection and Expression*, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8 - Richard Paul and Linda Elder 2002.
*Critical Thinking: Tools for Taking Charge of Your Professional and Personal Life*. Published by Financial Times Prentice Hall. ISBN 0-13-064760-8. - Richard Paul and Linda Elder, 2003.
*The Miniature Guide to Analytic Thinking*. Published by the Foundation for Critical Thinking. ISBN 0-944583-19-9 - Linda Elder and Richard Paul, 2004.
*The Miniature Guide to the Human Mind*. Dillon Beach: Foundation for Critical Thinking Press. - Richard Paul and Linda Elder, 2006.
*The Miniature Guide to Critical Thinking: Concepts & Tools*. Published by the Foundation for Critical Thinking. ISBN 0-944583-10-5 - Paul, R., Elder, L., and Bartell T. 1997.
*California Teacher Preparation for Instruction in Critical Thinking: Research Findings and Policy Recommendations*. California Commission on Teacher Credentialing. Foundation for Critical Thinking, Sacramento California. - Twardy, Dr. Charles R. (2003) Argument Maps Improve Critical Thinking.
*Teaching Philosophy* 27:2 June 2004. **Preprints:** [8] [9] - Whyte, J. 2003.
*Bad Thoughts - A Guide to Clear Thinking*. Published by Corvo. ISBN 0-9543255-3-2. - T. Edward Damer. Attacking Faulty Reasoning, 5th Edition, Wadsworth, 2005. ISBN 0-534-60516-8
- Francis Watanabe Dauer. "Critical thinking : an introduction to reasoning"
eat pie Vincent F. Hendricks is a philosopher and logician. ...
Attacking Faulty Reasoning is a textbook on logical fallacies by T. Edward Damer that has been used for many years in a number of college courses on logic, critical thinking, argumentation, and philosophy. ...
## External links - Insight Assessment provides free materials on teaching, free research reports, and some free critical thinking assessment tools.[10]
- Argumentation and Critical Thinking Tutorial by Dr. Jay VerLinden, Humboldt State University -- "Intended to help students in college level critical thinking classes learn some of the basic concepts of the formal logical structure of arguments and informal fallacies."
- Argument Mapping Argument mapping is using graphical methods to display the structure of reasoning and argumentation. The technique is essential for advanced critical thinking. Without mapping, it is very hard to be clear about the structure of evidence; and without such clarity, critical responses usually misfire.
- Argument Mapping Tutorials These six extensive tutorials cover the fundamentals of argument mapping, from elementary inferences through to the most complex arguments. Each tutorial contains concepts, principles, and vocabulary; a quiz; and exercises with model answers.
Logic | Main articles | Reason · History of logic · Philosophical logic · Philosophy of logic · Mathematical logic · Metalogic · Logic in computer science Image File history File links Portal. ...
Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ...
For other uses, see Reason (disambiguation). ...
The history of logic documents the development of logic as it occurs in various rival cultures and traditions in history. ...
Philosophical logic is the application of formal logical techniques to problems that concern philosophers. ...
Philosophy of logic is the branch of philosophy that is concerned with the nature and justification of systems of logic. ...
Mathematical logic is a major area of mathematics, which grew out of symbolic logic. ...
The metalogic of a system of logic is the formal proof supporting its soundness. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
| Key concepts and logics | Reasoning | Deduction · Induction · Abduction Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings. ...
Deductive reasoning is the kind of reasoning where the conclusion is necessitated or implied by previously known premises. ...
Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ...
Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence. ...
| Informal | Proposition · Inference · Argument · Validity · Cogency · Term logic · **Critical thinking** · Fallacies · Syllogism Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ...
This article is about the word proposition as it is used in logic, philosophy, and linguistics. ...
Inference is the act or process of deriving a conclusion based solely on what one already knows. ...
In logic, an argument is a set of statements, consisting of a number of premises, a number of inferences, and a conclusion, which is said to have the following property: if the premises are true, then the conclusion must be true or highly likely to be true. ...
In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ...
An argument is cogent if and only if the truth of the arguments premises would render the truth of the conclusion probable (i. ...
Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ...
Look up fallacy in Wiktionary, the free dictionary. ...
A syllogism (Greek: â€” conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ...
| Mathematical | Set · Syntax · Semantics · Wff · Axiom · Theorem · Consistency · Soundness · Completeness · Decidability · Formal system · Set theory · Proof theory · Model theory · Recursion theory Mathematical logic is a major area of mathematics, which grew out of symbolic logic. ...
In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ...
Syntax in logic is a systematic statement of the rules governing the properly formed formulas (WFFs) of a logical system. ...
The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so conscientious logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. ...
In logic, WFF is an abbreviation for well-formed formula. ...
This article is about a logical statement. ...
Look up theorem in Wiktionary, the free dictionary. ...
In mathematical logic, a formal system is consistent if it does not contain a contradiction, or, more precisely, for no proposition Ï† are both Ï† and Â¬Ï† provable. ...
(This article discusses the soundess notion of informal logic. ...
In mathematical logic, a theory is complete, if it contains either or as a theorem for every sentence in its language. ...
A logical system or theory is decidable if the set of all well-formed formulas valid in the system is decidable. ...
In logic and mathematics, a formal system consists of two components, a formal language plus a set of inference rules or transformation rules. ...
Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ...
In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ...
Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory. ...
| Zeroth-order | Boolean functions · Monadic predicate calculus · Propositional calculus · Logical connectives · Truth tables Zeroth-order logic is a term in popular use among practitioners for the subject matter otherwise known as boolean functions, monadic predicate logic, propositional calculus, or sentential calculus. ...
A Boolean function describes how to determine a Boolean value output based on some logical calculation from Boolean inputs. ...
In logic, the monadic predicate calculus is the fragment of predicate calculus in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters. ...
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows to establish that certain formulas are theorems of the formal system. ...
In logic, a logical connective is a syntactic operation on sentences, or the symbol for such an operation, that corresponds to a logical operation on the logical values of those sentences. ...
Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...
| Predicate | First-order · Quantifiers · Second-order ...
First-order logic (FOL) is a formal deductive system used by mathematicians, philosophers, linguists, and computer scientists. ...
In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ...
In mathematical logic, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. ...
| Modal | Deontic · Epistemic · Temporal · Doxastic In formal logic, a modal logic is any logic for handling modalities: concepts like possibility, existence, and necessity. ...
Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. ...
Michaels the greatest boyfriend in the whole wide world, and Id love to call him in a phonebooth sometime. ...
In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. ...
doxastic logic is a modal logic that is concerned with reasoning about beliefs. ...
| Other non-classical | Computability · Fuzzy · Linear · Relevance · Non-monotonic Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. ...
Introduced by Giorgi Japaridze in 2003, Computability logic is a research programme and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth. ...
Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. ...
In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction. ...
Relevance logic, also called relevant logic, is any of a family of non-classical substructural logics that impose certain restrictions on implication. ...
A non-monotonic logic is a formal logic whose consequence relation is not monotonic. ...
| | Controversies | Paraconsistent logic · Dialetheism · Intuitionistic logic · Paradoxes · Antinomies · Is logic empirical? A paraconsistent logic is a logical system that attempts to deal nontrivially with contradictions. ...
Dialetheism is a paraconsistent logic typified by its tolerance of at least some contradictions. ...
Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ...
Look up paradox in Wiktionary, the free dictionary. ...
Antinomy (Greek anti-, against, plus nomos, law) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction. ...
Is logic empirical? is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic as a consistent logical...
| Key figures | Aristotle · Boole · Cantor · Carnap · Church · Frege · Gentzen · Gödel · Hilbert · Kripke · Peano · Peirce · Putnam · Quine · Russell · Skolem · Tarski · Turing · Whitehead For other uses, see Aristotle (disambiguation). ...
George Boole [], (November 2, 1815 â€“ December 8, 1864) was a British mathematician and philosopher. ...
Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845[1] â€“ January 6, 1918) was a German mathematician. ...
Rudolf Carnap (May 18, 1891, Ronsdorf, Germany â€“ September 14, 1970, Santa Monica, California) was an influential philosopher who was active in central Europe before 1935 and in the United States thereafter. ...
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Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar â€“ 26 July 1925, IPA: ) was a German mathematician who became a logician and philosopher. ...
Gerhard Karl Erich Gentzen (November 24, 1909 â€“ August 4, 1945) was a German mathematician and logician. ...
Kurt GÃ¶del (IPA: ) (April 28, 1906 BrÃ¼nn, Austria-Hungary (now Brno, Czech Republic) â€“ January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher. ...
David Hilbert (January 23, 1862, KÃ¶nigsberg, East Prussia â€“ February 14, 1943, GÃ¶ttingen, Germany) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. ...
Saul Aaron Kripke (born in November 13, 1940 in Bay Shore, New York) is an American philosopher and logician now emeritus from Princeton and teaches as distinguished professor of philosophy at CUNY Graduate Center. ...
Giuseppe Peano Giuseppe Peano (August 27, 1858 â€“ April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ...
Charles Sanders Peirce (IPA: /pÉs/), (September 10, 1839 â€“ April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ...
Hilary Whitehall Putnam (born July 31, 1926) is an American philosopher who has been a central figure in Western philosophy since the 1960s, especially in philosophy of mind, philosophy of language, and philosophy of science. ...
For people named Quine, see Quine (surname). ...
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 â€“ 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ...
Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician. ...
// Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland â€“ October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ...
Alan Mathison Turing, OBE, FRS (23 June 1912 â€“ 7 June 1954) was an English mathematician, logician, and cryptographer. ...
Alfred North Whitehead, OM (February 15, 1861 Ramsgate, Kent, England â€“ December 30, 1947 Cambridge, Massachusetts, USA) was an English-born mathematician who became a philosopher. ...
| Lists | Topics (basic • mathematical logic • basic discrete mathematics • set theory) · Logicians · Rules of inference · Paradoxes · Fallacies · Logic symbols This is a list of topics in logic. ...
For a more comprehensive list, see the List of logic topics. ...
This is a list of mathematical logic topics, by Wikipedia page. ...
This is a list of basic discrete mathematics topics, by Wikipedia page. ...
Set theory Axiomatic set theory Naive set theory Zermelo set theory Zermelo-Fraenkel set theory Kripke-Platek set theory with urelements Simple theorems in the algebra of sets Axiom of choice Zorns lemma Empty set Cardinality Cardinal number Aleph number Aleph null Aleph one Beth number Ordinal number Well...
A logician is a person, such as a philosopher or mathematician, whose topic of scholarly study is logic. ...
This is a list of rules of inference. ...
This is a list of paradoxes, grouped thematically. ...
This is a list of fallacies. ...
In logic, a set of symbols is frequently used to express logical constructs. ...
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