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145-503: The term critique derives, via French, from the Greek word κριτική ( kritikē ), meaning "the faculty of judging", that is, discerning the value of persons or things. Critique is also known as major logic , as opposed to minor logic or dialectics . Philosophy is the application of critical thought, and is the disciplined practice of processing the theory/praxis problem . In philosophical contexts, such as law or academics, critique

290-501: A r y ) ∧ Q ( J o h n ) ) {\displaystyle \exists Q(Q(Mary)\land Q(John))} " . In this case, the existential quantifier is applied to the predicate variable " Q {\displaystyle Q} " . The added expressive power is especially useful for mathematics since it allows for more succinct formulations of mathematical theories. But it has drawbacks in regard to its meta-logical properties and ontological implications, which

435-444: A countable noun , the term "a logic" refers to a specific logical formal system that articulates a proof system . Logic plays a central role in many fields, such as philosophy , mathematics , computer science , and linguistics . Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to

580-562: A political pedagogy that built on McLaren's revolutionary critical pedagogy but took "a distanced and expository position" to link the project more explicitly to communism. Yet he later abandoned that as a starting point and instead turned his attention to educational forms . Joe L. Kincheloe and Shirley R. Steinberg have created the Paulo and Nita Freire Project for International Critical Pedagogy at McGill University . In line with Kincheloe and Steinberg's contributions to critical pedagogy,

725-445: A central role in many arguments found in everyday discourse and the sciences. Ampliative arguments are not automatically incorrect. Instead, they just follow different standards of correctness. The support they provide for their conclusion usually comes in degrees. This means that strong ampliative arguments make their conclusion very likely while weak ones are less certain. As a consequence, the line between correct and incorrect arguments

870-480: A certain cost: the premises support the conclusion in the sense that they make its truth more likely but they do not ensure its truth. This means that the conclusion of an ampliative argument may be false even though all its premises are true. This characteristic is closely related to non-monotonicity and defeasibility : it may be necessary to retract an earlier conclusion upon receiving new information or in light of new inferences drawn. Ampliative reasoning plays

1015-518: A class-based society". While prominent figures within Critical Pedagogy include Paulo Freire , Henry Giroux , Peter McLaren , bell hooks , and others, it is important to note that their work on critical pedagogy varies in focus. For example, some approach critical pedagogy from a Marxist perspective with a focus on socioeconomic class. Paulo Freire, on the other hand, writes about how critical pedagogy can lead to liberty and freedom of

1160-573: A complex argument to be successful, each link of the chain has to be successful. Arguments and inferences are either correct or incorrect. If they are correct then their premises support their conclusion. In the incorrect case, this support is missing. It can take different forms corresponding to the different types of reasoning . The strongest form of support corresponds to deductive reasoning . But even arguments that are not deductively valid may still be good arguments because their premises offer non-deductive support to their conclusions. For such cases,

1305-425: A conclusion. Logic is interested in whether arguments are correct, i.e. whether their premises support the conclusion. These general characterizations apply to logic in the widest sense, i.e., to both formal and informal logic since they are both concerned with assessing the correctness of arguments. Formal logic is the traditionally dominant field, and some logicians restrict logic to formal logic. Formal logic

1450-465: A distinction suggest that there is some ambiguity that is still unresolved. Marx's work inspired the ' Frankfurt School ' of critical theory , now best exemplified in the work of Jürgen Habermas . This, in turn, helped inspire the cultural studies form of social critique, which uses cultural products and their reception to record and inspire change regarding wider social ills such as racism or gender bias . Social critique has been further extended in

1595-510: A formal language together with a set of axioms and a proof system used to draw inferences from these axioms. In logic, axioms are statements that are accepted without proof. They are used to justify other statements. Some theorists also include a semantics that specifies how the expressions of the formal language relate to real objects. Starting in the late 19th century, many new formal systems have been proposed. A formal language consists of an alphabet and syntactic rules. The alphabet

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1740-686: A formal language while informal logic investigates them in their original form. On this view, the argument "Birds fly. Tweety is a bird. Therefore, Tweety flies." belongs to natural language and is examined by informal logic. But the formal translation "(1) ∀ x ( B i r d ( x ) → F l i e s ( x ) ) {\displaystyle \forall x(Bird(x)\to Flies(x))} ; (2) B i r d ( T w e e t y ) {\displaystyle Bird(Tweety)} ; (3) F l i e s ( T w e e t y ) {\displaystyle Flies(Tweety)} "

1885-415: A given argument is valid. Because of the reliance on formal language, natural language arguments cannot be studied directly. Instead, they need to be translated into formal language before their validity can be assessed. The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, a logic is a logical formal system. Distinct logics differ from each other concerning

2030-551: A given conclusion based on a set of premises. This distinction does not just apply to logic but also to games. In chess , for example, the definitory rules dictate that bishops may only move diagonally. The strategic rules, on the other hand, describe how the allowed moves may be used to win a game, for instance, by controlling the center and by defending one's king . It has been argued that logicians should give more emphasis to strategic rules since they are highly relevant for effective reasoning. A formal system of logic consists of

2175-402: A great variety of topics. They include metaphysical theses about ontological categories and problems of scientific explanation. But in a more narrow sense, it is identical to term logic or syllogistics. A syllogism is a form of argument involving three propositions: two premises and a conclusion. Each proposition has three essential parts: a subject , a predicate, and a copula connecting

2320-406: A just, progressive, creative, and democratic society demands both dimensions of this pedagogical progress. One of the major texts taking on the intersection between critical pedagogy and Indigenous knowledge(s) is Sandy Grande's, Red Pedagogy: Native American Social and Political Thought (Rowman and Littlefield, 2004). In agreement with this perspective, Four Arrows, aka Don Trent Jacobs, challenges

2465-614: A logical connective like "and" to form a new complex proposition. In Aristotelian logic, the subject can be universal , particular , indefinite , or singular . For example, the term "all humans" is a universal subject in the proposition "all humans are mortal". A similar proposition could be formed by replacing it with the particular term "some humans", the indefinite term "a human", or the singular term "Socrates". Aristotelian logic only includes predicates for simple properties of entities. But it lacks predicates corresponding to relations between entities. The predicate can be linked to

2610-442: A perspective from which to critically analyze American culture and institutions. Ironically, the same tradition is now regarded as oppressive. The texts once served an unmasking function; now we are told that it is the texts which must be unmasked. In 1992, Maxine Hairston took a hard line against critical pedagogy in the first year college composition classroom and argued, "everywhere I turn I find composition faculty, both leaders in

2755-432: A position of authority and then demonstrate that authority in their actions in supports of students... [A]s teachers relinquish the authority of truth providers, they assume the mature authority of facilitators of student inquiry and problem-solving. In relation to such teacher authority, students gain their freedom--they gain the ability to become self-directed human beings capable of producing their own knowledge. And due to

2900-462: A realization of the emancipatory goals of critical pedagogy. The theory is influenced by Karl Marx who believed that inequality is a result of socioeconomic differences and that all people need to work toward a socialized economy. More recently, critical pedagogy can also be traced back to Paulo Freire 's best-known 1968 work, The Pedagogy of the Oppressed . Freire, a professor of history and

3045-514: A role in further expanding and enriching Freire's original ideas about a critical pedagogy, shifting its main focus on social class to include issues pertaining to religion , military identification , race , gender , sexuality , nationality , ethnicity , and age. Much of the work also draws on anarchism , György Lukács , Wilhelm Reich , postcolonialism , and the discourse theories of Edward Said , Antonio Gramsci , Gilles Deleuze ( rhizomatic learning ) and Michel Foucault . Radical Teacher

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3190-664: A sentence like "yesterday was Sunday and the weather was good". It is only true if both of its input variables, p {\displaystyle p} ("yesterday was Sunday") and q {\displaystyle q} ("the weather was good"), are true. In all other cases, the expression as a whole is false. Other important logical connectives are ¬ {\displaystyle \lnot } ( not ), ∨ {\displaystyle \lor } ( or ), → {\displaystyle \to } ( if...then ), and ↑ {\displaystyle \uparrow } ( Sheffer stroke ). Given

3335-400: A social movement for the creation of a democratic socialist alternative to capitalism. Curry Malott and Derek R. Ford's first collaborative book, Marx, Capital, and Education built on McLaren's revolutionary pedagogy by connecting it to the global class struggle and the history of the actually-existing workers' movements. As Curry Malott noted, "Critical pedagogy was created as a break from

3480-514: A struggle for ownership of themselves. He states that students have previously been lulled into a sense of complacency by the circumstances of everyday life and that through the processes of the classroom, they can begin to envision and strive for something different for themselves. Of course, achieving such a goal is not automatic nor easy, as he suggests that the role of the teacher is critical to this process. Students need to be helped by teachers to separate themselves from unconditional acceptance of

3625-410: A teacher and their students would be served by Standards-based education where there is "only be one correct way to teach" as "[e]veryone is assumed to be the same regardless of race, class, or gender". Donald Schön 's concept of "indeterminate zones of practice" illustrates how any practice, especially ones with human subjects at their center, are infinitely complex and highly contested, which amplify

3770-420: Is sound when its proof system cannot derive a conclusion from a set of premises unless it is semantically entailed by them. In other words, its proof system cannot lead to false conclusions, as defined by the semantics. A system is complete when its proof system can derive every conclusion that is semantically entailed by its premises. In other words, its proof system can lead to any true conclusion, as defined by

3915-465: Is a magazine dedicated to critical pedagogy and issues of interest to critical educators. Many contemporary critical pedagogues have embraced Postmodern , anti-essentialist perspectives of the individual, of language, and of power, "while at the same time retaining the Freirean emphasis on critique, disrupting oppressive regimes of power/knowledge, and social change". Like critical theory itself,

4060-476: Is a red planet". For most types of logic, it is accepted that premises and conclusions have to be truth-bearers . This means that they have a truth value : they are either true or false. Contemporary philosophy generally sees them either as propositions or as sentences . Propositions are the denotations of sentences and are usually seen as abstract objects . For example, the English sentence "the tree

4205-441: Is a restricted version of classical logic. It uses the same symbols but excludes some rules of inference. For example, according to the law of double negation elimination, if a sentence is not not true, then it is true. This means that A {\displaystyle A} follows from ¬ ¬ A {\displaystyle \lnot \lnot A} . This is a valid rule of inference in classical logic but it

4350-416: Is also known as symbolic logic and is widely used in mathematical logic . It uses a formal approach to study reasoning: it replaces concrete expressions with abstract symbols to examine the logical form of arguments independent of their concrete content. In this sense, it is topic-neutral since it is only concerned with the abstract structure of arguments and not with their concrete content. Formal logic

4495-453: Is an example of the existential quantifier " ∃ {\displaystyle \exists } " applied to the individual variable " x {\displaystyle x} " . In higher-order logics, quantification is also allowed over predicates. This increases its expressive power. For example, to express the idea that Mary and John share some qualities, one could use the formula " ∃ Q ( Q ( M

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4640-433: Is at the expense of proficiency of student writing skills in the composition classroom. To this end, O'Dair explained that "recently advocated working-class pedagogies privilege activism over "language instruction." Jeff Smith argued that students want to gain, rather than to critique, positions of privilege, as encouraged by critical pedagogues. Scholars who have worked in the field of critical pedagogy have also critiqued

4785-415: Is blurry in some cases, such as when the premises offer weak but non-negligible support. This contrasts with deductive arguments, which are either valid or invalid with nothing in-between. The terminology used to categorize ampliative arguments is inconsistent. Some authors, like James Hawthorne, use the term " induction " to cover all forms of non-deductive arguments. But in a more narrow sense, induction

4930-421: Is commonly defined in terms of arguments or inferences as the study of their correctness. An argument is a set of premises together with a conclusion. An inference is the process of reasoning from these premises to the conclusion. But these terms are often used interchangeably in logic. Arguments are correct or incorrect depending on whether their premises support their conclusion. Premises and conclusions, on

5075-532: Is considered an inherently political act to the critical pedagogue, a more critical element of teacher education becomes addressing implicit biases (also known as implicit cognition or implicit stereotypes) that can subconsciously affect a teacher's perception of a student's ability to learn. Advocates of critical pedagogy insist that teachers, then, must become learners alongside their students, as well as students of their students. They must become experts beyond their field of knowledge , and immerse themselves in

5220-407: Is controversial because it belongs to the field of psychology , not logic, and because appearances may be different for different people. Fallacies are usually divided into formal and informal fallacies. For formal fallacies, the source of the error is found in the form of the argument. For example, denying the antecedent is one type of formal fallacy, as in "if Othello is a bachelor, then he

5365-453: Is deductively valid. For deductive validity, it does not matter whether the premises or the conclusion are actually true. So the argument "(1) all frogs are mammals; (2) no cats are mammals; (3) therefore no cats are frogs" is also valid because the conclusion follows necessarily from the premises. According to an influential view by Alfred Tarski , deductive arguments have three essential features: (1) they are formal, i.e. they depend only on

5510-484: Is drawn between 'critique' and ' criticism ': the two words both translate as critique , Kritik , and critica , respectively. In the English language, according to philosopher Gianni Vattimo , criticism is used more frequently to denote literary criticism or art criticism , that is, the interpretation and evaluation of literature and art; while critique may refer to more general and profound writing as Kant 's Critique of Pure Reason . Another proposed distinction

5655-412: Is established by verification using a proof. Intuitionistic logic is especially prominent in the field of constructive mathematics , which emphasizes the need to find or construct a specific example to prove its existence. Critical pedagogy Critical pedagogy is a philosophy of education and social movement that developed and applied concepts from critical theory and related traditions to

5800-610: Is green" is different from the German sentence "der Baum ist grün" but both express the same proposition. Propositional theories of premises and conclusions are often criticized because they rely on abstract objects. For instance, philosophical naturalists usually reject the existence of abstract objects. Other arguments concern the challenges involved in specifying the identity criteria of propositions. These objections are avoided by seeing premises and conclusions not as propositions but as sentences, i.e. as concrete linguistic objects like

5945-432: Is interested in deductively valid arguments, for which the truth of their premises ensures the truth of their conclusion. This means that it is impossible for the premises to be true and the conclusion to be false. For valid arguments, the logical structure of the premises and the conclusion follows a pattern called a rule of inference . For example, modus ponens is a rule of inference according to which all arguments of

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6090-415: Is invalid in intuitionistic logic. Another classical principle not part of intuitionistic logic is the law of excluded middle . It states that for every sentence, either it or its negation is true. This means that every proposition of the form A ∨ ¬ A {\displaystyle A\lor \lnot A} is true. These deviations from classical logic are based on the idea that truth

6235-447: Is male; Othello is not a bachelor; therefore Othello is not male". But most fallacies fall into the category of informal fallacies, of which a great variety is discussed in the academic literature. The source of their error is usually found in the content or the context of the argument. Informal fallacies are sometimes categorized as fallacies of ambiguity, fallacies of presumption, or fallacies of relevance. For fallacies of ambiguity,

6380-444: Is most influenced by Kant 's use of the term to mean a reflective examination of the validity and limits of a human capacity or of a set of philosophical claims. This has been extended in modern philosophy to mean a systematic inquiry into the conditions and consequences of a concept , a theory , a discipline , or an approach and/or attempt to understand the limitations and validity of that. A critical perspective , in this sense,

6525-688: Is necessary, then it is also possible. This means that ◊ A {\displaystyle \Diamond A} follows from ◻ A {\displaystyle \Box A} . Another principle states that if a proposition is necessary then its negation is impossible and vice versa. This means that ◻ A {\displaystyle \Box A} is equivalent to ¬ ◊ ¬ A {\displaystyle \lnot \Diamond \lnot A} . Other forms of modal logic introduce similar symbols but associate different meanings with them to apply modal logic to other fields. For example, deontic logic concerns

6670-518: Is necessary. For example, if the formula B ( s ) {\displaystyle B(s)} stands for the sentence "Socrates is a banker" then the formula ◊ B ( s ) {\displaystyle \Diamond B(s)} articulates the sentence "It is possible that Socrates is a banker". To include these symbols in the logical formalism, modal logic introduces new rules of inference that govern what role they play in inferences. One rule of inference states that, if something

6815-407: Is not the best or most likely explanation. Not all arguments live up to the standards of correct reasoning. When they do not, they are usually referred to as fallacies . Their central aspect is not that their conclusion is false but that there is some flaw with the reasoning leading to this conclusion. So the argument "it is sunny today; therefore spiders have eight legs" is fallacious even though

6960-541: Is only one type of ampliative argument alongside abductive arguments . Some philosophers, like Leo Groarke, also allow conductive arguments as another type. In this narrow sense, induction is often defined as a form of statistical generalization. In this case, the premises of an inductive argument are many individual observations that all show a certain pattern. The conclusion then is a general law that this pattern always obtains. In this sense, one may infer that "all elephants are gray" based on one's past observations of

7105-512: Is right are to be found in what John Dewey has referred to as the tensions between traditional and progressive education . Searle argued that critical pedagogy's objections to the Western canon are misplaced and/or disingenuous: Precisely by inculcating a critical attitude, the "canon" served to demythologize the conventional pieties of the American bourgeoisie and provided the student with

7250-430: Is studied by formal logic. The study of natural language arguments comes with various difficulties. For example, natural language expressions are often ambiguous, vague, and context-dependent. Another approach defines informal logic in a wide sense as the normative study of the standards, criteria, and procedures of argumentation. In this sense, it includes questions about the role of rationality , critical thinking , and

7395-399: Is that critique is never personalized nor ad hominem , but is instead the analyses of the structure of the thought in the content of the item critiqued. This analysis then offers by way of the critique method either a rebuttal or a suggestion of further expansion upon the problems presented by the topic of that specific written or oral argumentation. Even authors that believe there might be

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7540-496: Is the opposite of a dogmatic one. Kant wrote: We deal with a concept dogmatically ... if we consider it as contained under another concept of the object which constitutes a principle of reason and determine it in conformity with this. But we deal with it merely critically if we consider it only in reference to our cognitive faculties and consequently to the subjective conditions of thinking it, without undertaking to decide anything about its object. Later thinkers such as Hegel used

7685-425: Is the product of praxis at the collective level." Critical pedagogue Ira Shor , who was mentored by and worked closely with Freire from 1980 until Freire's death in 1997, defines critical pedagogy as: Habits of thought, reading, writing, and speaking which go beneath surface meaning, first impressions, dominant myths, official pronouncements, traditional clichés, received wisdom, and mere opinions, to understand

7830-410: Is the set of basic symbols used in expressions . The syntactic rules determine how these symbols may be arranged to result in well-formed formulas. For instance, the syntactic rules of propositional logic determine that " P ∧ Q {\displaystyle P\land Q} " is a well-formed formula but " ∧ Q {\displaystyle \land Q} " is not since

7975-528: Is the study of correct reasoning . It includes both formal and informal logic . Formal logic is the study of deductively valid inferences or logical truths . It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies , critical thinking , and argumentation theory . Informal logic examines arguments expressed in natural language whereas formal logic uses formal language . When used as

8120-432: Is to study the criteria according to which an argument is correct or incorrect. A fallacy is committed if these criteria are violated. In the case of formal logic, they are known as rules of inference . They are definitory rules, which determine whether an inference is correct or which inferences are allowed. Definitory rules contrast with strategic rules. Strategic rules specify which inferential moves are necessary to reach

8265-540: Is unable to address. Both provide criteria for assessing the correctness of arguments and distinguishing them from fallacies. Many characterizations of informal logic have been suggested but there is no general agreement on its precise definition. The most literal approach sees the terms "formal" and "informal" as applying to the language used to express arguments. On this view, informal logic studies arguments that are in informal or natural language. Formal logic can only examine them indirectly by translating them first into

8410-415: Is used in the classroom. He develops these themes in looking at the use of Freirean teaching methods in the context of the everyday life of classrooms, in particular, institutional settings. He suggests that the whole curriculum of the classroom must be re-examined and reconstructed. He favors a change of role of the student from object to active, critical subject. In doing so, he suggests that students undergo

8555-599: Is used to represent the ideas of knowing something in contrast to merely believing it to be the case. Higher-order logics extend classical logic not by using modal operators but by introducing new forms of quantification. Quantifiers correspond to terms like "all" or "some". In classical first-order logic, quantifiers are only applied to individuals. The formula " ∃ x ( A p p l e ( x ) ∧ S w e e t ( x ) ) {\displaystyle \exists x(Apple(x)\land Sweet(x))} " ( some apples are sweet)

8700-431: Is why first-order logic is still more commonly used. Deviant logics are logical systems that reject some of the basic intuitions of classical logic. Because of this, they are usually seen not as its supplements but as its rivals. Deviant logical systems differ from each other either because they reject different classical intuitions or because they propose different alternatives to the same issue. Intuitionistic logic

8845-540: The Human rights movement , Civil rights movement , Disability rights movement , Indigenous rights movement, postmodern theory , feminist theory , postcolonial theory , and queer theory . Critical Pedagogy is believed to have its roots in the critical theory of the Frankfurt School , which was established in 1923. As an outgrowth of critical theory, critical pedagogy is intended to educate and work towards

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8990-424: The banking model of education outlined by Freire where the structures of knowledge are left unexamined. To the critical pedagogue, the teaching act must incorporate social critique alongside the cultivation of intellect. Joe L. Kincheloe argues that this is in direct opposition to the epistemological concept of positivism , where "social actions should proceed with law-like predictability". In this philosophy,

9135-456: The culture , customs, and lived experiences of the students they aim to teach. Critical pedagogy has been the subject of varied debates inside and outside the field of education. Philosopher John Searle characterized the goal of Giroux's form of critical pedagogy "to create political radicals", thus highlighting the antagonistic moral and political grounds of the ideals of citizenship and "public wisdom." These varying moral perspectives of what

9280-810: The philosophy of education at the Federal University of Pernambuco in Brazil, sought in this and other works to develop a philosophy of adult education that demonstrated a solidarity with the poor in their common struggle to survive by engaging them in a dialog of greater awareness and analysis. Although his family had suffered loss and hunger during the Great Depression , the poor viewed him and his formerly middle-class family "as people from another world who happened to fall accidentally into their world". His intimate discovery of class and their borders "led, invariably, to Freire's radical rejection of

9425-490: The Freire's notion that a pursuit of social change alone could promote anti-intellectualism, promotes a more balanced approach to education than postmodernists. We cannot simply attempt to cultivate the intellect without changing the unjust social context in which such minds operate. Critical educators cannot just work to change the social order without helping to educate a knowledgeable and skillful group of students. Creating

9570-417: The Greek word "logos", which has a variety of translations, such as reason , discourse , or language . Logic is traditionally defined as the study of the laws of thought or correct reasoning , and is usually understood in terms of inferences or arguments . Reasoning is the activity of drawing inferences. Arguments are the outward expression of inferences. An argument is a set of premises together with

9715-523: The Marxism of Freire's Pedagogy of the Oppressed and Bowles and Gintis' Schooling in Capitalist America . Even though it is true that critical pedagogy has become increasingly domesticated and watered down, it's birth was an act of counterrevolution itself." In particular, they argued for a critical pedagogy that simultaneously pursued communism and national liberation. Malott and Ford were

9860-1175: The ability to take constructive action". Freire wrote the introduction to his 1988 work, Teachers as Intellectuals: Toward a Critical Pedagogy of Learning. Another leading critical pedagogy theorist who Freire called his "intellectual cousin", Peter McLaren , wrote the foreword. McLaren and Giroux co-edited one book on critical pedagogy and co-authored another in the 1990s. Among its other leading figures in no particular order are bell hooks (Gloria Jean Watkins), Joe L. Kincheloe , Patti Lather, Myles Horton, Antonia Darder , Gloria Ladson-Billings , Peter McLaren , Khen Lampert , Howard Zinn , Donaldo Macedo , Dermeval Saviani , Sandy Grande, Michael Apple , and Stephanie Ledesma. Educationalists including Jonathan Kozol and Parker Palmer are sometimes included in this category. Other critical pedagogues known more for their Anti-schooling , unschooling , or deschooling perspectives include Ivan Illich , John Holt , Ira Shor , John Taylor Gatto , and Matt Hern. Critical pedagogy has several other strands and foundations. Postmodern , anti-racist , feminist , postcolonial , queer , and environmental theories all play

10005-418: The ambiguity and vagueness of natural language are responsible for their flaw, as in "feathers are light; what is light cannot be dark; therefore feathers cannot be dark". Fallacies of presumption have a wrong or unjustified premise but may be valid otherwise. In the case of fallacies of relevance, the premises do not support the conclusion because they are not relevant to it. The main focus of most logicians

10150-521: The anthropocentrism of critical pedagogy and writes that to achieve its transformative goals there are other differences between Western and Indigenous worldview that must be considered. Approaching the intersection of Indigenous perspectives and pedagogy from another perspective, critical pedagogy of place examines the impacts of place. Ira Shor , a professor at the City University of New York , provides for an example of how critical pedagogy

10295-399: The assessment of arguments. Premises and conclusions are the basic parts of inferences or arguments and therefore play a central role in logic. In the case of a valid inference or a correct argument, the conclusion follows from the premises, or in other words, the premises support the conclusion. For instance, the premises "Mars is red" and "Mars is a planet" support the conclusion "Mars

10440-495: The basic principles of classical logic. They introduce additional symbols and principles to apply it to fields like metaphysics , ethics , and epistemology . Modal logic is an extension of classical logic. In its original form, sometimes called "alethic modal logic", it introduces two new symbols: ◊ {\displaystyle \Diamond } expresses that something is possible while ◻ {\displaystyle \Box } expresses that something

10585-487: The best explanation, for example, when a doctor concludes that a patient has a certain disease which explains the symptoms they suffer. Arguments that fall short of the standards of correct reasoning often embody fallacies . Systems of logic are theoretical frameworks for assessing the correctness of arguments. Logic has been studied since antiquity . Early approaches include Aristotelian logic , Stoic logic , Nyaya , and Mohism . Aristotelian logic focuses on reasoning in

10730-645: The claim "either it is raining, or it is not". These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q " is a logical truth. Formal logic uses formal languages to express and analyze arguments. They normally have a very limited vocabulary and exact syntactic rules . These rules specify how their symbols can be combined to construct sentences, so-called well-formed formulas . This simplicity and exactness of formal logic make it capable of formulating precise rules of inference. They determine whether

10875-658: The classroom in the United States has resulted in an unprecedented amount of linguistic and cultural diversity. In order to respond to these changes, advocates of critical pedagogy call into question the focus on practical skills of teacher credential programs. "[T]his practical focus far too often occurs without examining teachers' own assumptions, values, and beliefs and how this ideological posture informs, often unconsciously, their perceptions and actions when working with linguistic-minority and other politically, socially, and economically subordinated students." As teaching

11020-495: The color of elephants. A closely related form of inductive inference has as its conclusion not a general law but one more specific instance, as when it is inferred that an elephant one has not seen yet is also gray. Some theorists, like Igor Douven, stipulate that inductive inferences rest only on statistical considerations. This way, they can be distinguished from abductive inference. Abductive inference may or may not take statistical observations into consideration. In either case,

11165-502: The conclusion "I don't have to work". Premises and conclusions express propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions are made up of simpler propositions linked by logical vocabulary like ∧ {\displaystyle \land } ( and ) or → {\displaystyle \to } ( if...then ). Simple propositions also have parts, like "Sunday" or "work" in

11310-511: The conclusion "all ravens are black". A further approach is to define informal logic as the study of informal fallacies . Informal fallacies are incorrect arguments in which errors are present in the content and the context of the argument. A false dilemma , for example, involves an error of content by excluding viable options. This is the case in the fallacy "you are either with us or against us; you are not with us; therefore, you are against us". Some theorists state that formal logic studies

11455-458: The conclusion is true. Some theorists, like John Stuart Mill , give a more restrictive definition of fallacies by additionally requiring that they appear to be correct. This way, genuine fallacies can be distinguished from mere mistakes of reasoning due to carelessness. This explains why people tend to commit fallacies: because they have an alluring element that seduces people into committing and accepting them. However, this reference to appearances

11600-591: The conditional proposition p → q {\displaystyle p\to q} , one can form truth tables of its converse q → p {\displaystyle q\to p} , its inverse ( ¬ p → ¬ q {\displaystyle \lnot p\to \lnot q} ) , and its contrapositive ( ¬ q → ¬ p {\displaystyle \lnot q\to \lnot p} ) . Truth tables can also be defined for more complex expressions that use several propositional connectives. Logic

11745-478: The conditions of their own existence. Once this separation is achieved, then students may be prepared for critical re-entry into an examination of everyday life. In a classroom environment that achieves such liberating intent, one of the potential outcomes is that the students themselves assume more responsibility for the class. Power is thus distributed amongst the group and the role of the teacher becomes much more mobile, not to mention more challenging. This encourages

11890-438: The contrast between necessity and possibility and the problem of ethical obligation and permission. Similarly, it does not address the relations between past, present, and future. Such issues are addressed by extended logics. They build on the basic intuitions of classical logic and expand it by introducing new logical vocabulary. This way, the exact logical approach is applied to fields like ethics or epistemology that lie beyond

12035-452: The critical pedagogue's unwillingness to apply universal practices. Furthermore, bell hooks , who is greatly influenced by Freire, points out the importance of engaged pedagogy and the responsibility that teachers, as well as students, must have in the classroom: Teachers must be aware of themselves as practitioners and as human beings if they wish to teach students in a non-threatening, anti-discriminatory way. Self-actualisation should be

12180-470: The deep meaning, root causes, social context, ideology, and personal consequences of any action, event, object, process, organization, experience, text, subject matter, policy, mass media, or discourse. ( Empowering Education , 129) Critical pedagogy explores the dialogic relationships between teaching and learning. Its proponents claim that it is a continuous process of what they call "unlearning", "learning", and "relearning", "reflection", "evaluation", and

12325-451: The depth level. But they can be highly informative on the surface level by making implicit information explicit. This happens, for example, in mathematical proofs. Ampliative arguments are arguments whose conclusions contain additional information not found in their premises. In this regard, they are more interesting since they contain information on the depth level and the thinker may learn something genuinely new. But this feature comes with

12470-498: The effect that these actions have on the students, in particular students whom they believe have been historically and continue to be disenfranchised by what they call "traditional schooling". The educational philosophy has since been developed by Henry Giroux and others since the 1980s as a praxis -oriented "educational movement, guided by passion and principle, to help students develop a consciousness of freedom, recognize authoritarian tendencies, and connect knowledge to power and

12615-409: The example. The truth of a proposition usually depends on the meanings of all of its parts. However, this is not the case for logically true propositions. They are true only because of their logical structure independent of the specific meanings of the individual parts. Arguments can be either correct or incorrect. An argument is correct if its premises support its conclusion. Deductive arguments have

12760-527: The fact that throughout the eighteenth century, which Kant, in Critique of Pure Reason , labeled "in especial degree, the age of criticism" and to which our use of "critique", today remains largely indebted, critique was above all critique of prejudice and established authority, and hence was intimately tied to a conception of the human being as capable of self-thinking, hence authonomous, and free from religious and political authorities. Logic Logic

12905-592: The field of education and the study of culture. It insists that issues of social justice and democracy are not distinct from acts of teaching and learning . The goal of critical pedagogy is emancipation from oppression through an awakening of the critical consciousness , based on the Portuguese term conscientização . When achieved, critical consciousness encourages individuals to effect change in their world through social critique and political action in order to self-actualize . Critical pedagogy

13050-525: The field of critical pedagogy continues to evolve. Contemporary critical educators, such as bell hooks and Peter McLaren , discuss in their criticisms the influences of many varied concerns, institutions, and social structures, "including globalization, the mass media, and race/spiritual relations", while citing reasons for resisting the possibilities to change. McLaren has developed a social movement based version of critical pedagogy that he calls revolutionary critical pedagogy, emphasizing critical pedagogy as

13195-434: The field of ethics and introduces symbols to express the ideas of obligation and permission , i.e. to describe whether an agent has to perform a certain action or is allowed to perform it. The modal operators in temporal modal logic articulate temporal relations. They can be used to express, for example, that something happened at one time or that something is happening all the time. In epistemology, epistemic modal logic

13340-473: The first authors to bring Harry Haywood's work into critical pedagogy. They believed that critical pedagogy had been divorced from its radical roots. Yet when Malott went to re-investigate those roots, he decided that they were not revolutionary at all. In fact, he argued that they were permeated by anti-communism and hostility to any actually-existing struggles of oppressed peoples. As a result, both Malott and Ford moved away from critical pedagogy. Ford developed

13485-485: The form "(1) p , (2) if p then q , (3) therefore q " are valid, independent of what the terms p and q stand for. In this sense, formal logic can be defined as the science of valid inferences. An alternative definition sees logic as the study of logical truths . A proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true in all possible worlds and under all interpretations of its non-logical terms, like

13630-513: The form of syllogisms . It was considered the main system of logic in the Western world until it was replaced by modern formal logic, which has its roots in the work of late 19th-century mathematicians such as Gottlob Frege . Today, the most commonly used system is classical logic . It consists of propositional logic and first-order logic . Propositional logic only considers logical relations between full propositions. First-order logic also takes

13775-523: The form of the premises and the conclusion: how they have to be structured for the inference to be valid. Arguments that do not follow any rule of inference are deductively invalid. The modus ponens is a prominent rule of inference. It has the form " p ; if p , then q ; therefore q ". Knowing that it has just rained ( p {\displaystyle p} ) and that after rain the streets are wet ( p → q {\displaystyle p\to q} ), one can use modus ponens to deduce that

13920-419: The form of the premises and the conclusion; (2) they are a priori, i.e. no sense experience is needed to determine whether they obtain; (3) they are modal, i.e. that they hold by logical necessity for the given propositions, independent of any other circumstances. Because of the first feature, the focus on formality, deductive inference is usually identified with rules of inference. Rules of inference specify

14065-421: The general form of arguments while informal logic studies particular instances of arguments. Another approach is to hold that formal logic only considers the role of logical constants for correct inferences while informal logic also takes the meaning of substantive concepts into account. Further approaches focus on the discussion of logical topics with or without formal devices and on the role of epistemology for

14210-464: The goal of creating not only a better learning environment but also a better world. Freire himself maintained that this was not merely an educational technique but a way of living in our educative practice. Freire endorses students' ability to think critically about their education situation; this method of thinking is thought by practitioners of critical pedagogy to allow them to "recognize connections between their individual problems and experiences and

14355-532: The goal of the teacher as well as the students. Students sometimes resist critical pedagogy. Student resistance to critical pedagogy can be attributed to a variety of reasons. Student objections may be due to ideological reasons, religious or moral convictions, fear of criticism, or discomfort with controversial issues. Kristen Seas argues: "Resistance in this context thus occurs when students are asked to shift not only their perspectives, but also their subjectivities as they accept or reject assumptions that contribute to

14500-458: The growth of each student's intellectual character rather than a mere "mimicry of the professorial style." Teachers, however, do not simply abdicate their authority in a student-centered classroom. In the later years of his life, Freire grew increasingly concerned with what he felt was a major misinterpretation of his work and insisted that teachers cannot deny their position of authority. Critical teachers, therefore, must admit that they are in

14645-406: The internal parts of propositions into account, like predicates and quantifiers . Extended logics accept the basic intuitions behind classical logic and apply it to other fields, such as metaphysics , ethics , and epistemology . Deviant logics, on the other hand, reject certain classical intuitions and provide alternative explanations of the basic laws of logic. The word "logic" originates from

14790-407: The internal structure of propositions. This happens through devices such as singular terms, which refer to particular objects, predicates , which refer to properties and relations, and quantifiers, which treat notions like "some" and "all". For example, to express the proposition "this raven is black", one may use the predicate B {\displaystyle B} for the property "black" and

14935-522: The logical conjunction ∧ {\displaystyle \land } requires terms on both sides. A proof system is a collection of rules to construct formal proofs. It is a tool to arrive at conclusions from a set of axioms. Rules in a proof system are defined in terms of the syntactic form of formulas independent of their specific content. For instance, the classical rule of conjunction introduction states that P ∧ Q {\displaystyle P\land Q} follows from

15080-483: The movement from various angles. In 2016, Curry Stephenson Malott, who had written several books about critical pedagogy and identified as a critical pedagogue, renounced and critiqued his previous work. In History and Education: Engaging the Global Class War , he writes about his "long journey of self-reflection and de-indoctrination" that culminated in the break. Malott writes that "the term critical pedagogy

15225-487: The oppressed and marginalized. bell hooks applies a feminist perspective to critical pedagogy and Ira Shor , for example, advocates for the need of moving the theoretical framework of critical pedagogy to a more practical one. The influential works of Freire made him arguably the most celebrated critical educator. He seldom used the term "critical pedagogy" himself when describing this philosophy. His initial focus targeted adult literacy projects in Brazil and later

15370-409: The other hand, are true or false depending on whether they are in accord with reality. In formal logic, a sound argument is an argument that is both correct and has only true premises. Sometimes a distinction is made between simple and complex arguments. A complex argument is made up of a chain of simple arguments. This means that the conclusion of one argument acts as a premise of later arguments. For

15515-444: The other hand, do not have propositional parts. But they can also be conceived as having an internal structure: they are made up of subpropositional parts, like singular terms and predicates . For example, the simple proposition "Mars is red" can be formed by applying the predicate "red" to the singular term "Mars". In contrast, the complex proposition "Mars is red and Venus is white" is made up of two simple propositions connected by

15660-584: The pedagogical arguments being constructed." Karen Kopelson asserts that resistance to new information or ideologies , introduced in the classroom, is a natural response to persuasive messages that are unfamiliar. Resistance is often, at the least, understandably protective: As anyone who can remember her or his own first uneasy encounters with particularly challenging new theories or theorists can attest, resistance serves to shield us from uncomfortable shifts or all-out upheavals in perception and understanding-shifts in perception which, if honored, force us to inhabit

15805-485: The premises P {\displaystyle P} and Q {\displaystyle Q} . Such rules can be applied sequentially, giving a mechanical procedure for generating conclusions from premises. There are different types of proof systems including natural deduction and sequent calculi . A semantics is a system for mapping expressions of a formal language to their denotations. In many systems of logic, denotations are truth values. For instance,

15950-413: The premises offer support for the conclusion because the conclusion is the best explanation of why the premises are true. In this sense, abduction is also called the inference to the best explanation . For example, given the premise that there is a plate with breadcrumbs in the kitchen in the early morning, one may infer the conclusion that one's house-mate had a midnight snack and was too tired to clean

16095-470: The premises. But this point is not always accepted since it would mean, for example, that most of mathematics is uninformative. A different characterization distinguishes between surface and depth information. The surface information of a sentence is the information it presents explicitly. Depth information is the totality of the information contained in the sentence, both explicitly and implicitly. According to this view, deductive inferences are uninformative on

16240-725: The profession and new voices, asserting that they have not only the right, but the duty, to put ideology and radical politics at the center of their teaching." Hairston further confers, When classes focus on complex issues such as racial discrimination, economic injustices, and inequities of class and gender, they should be taught by qualified faculty who have the depth of information and historical competence that such critical social issues warrant. Our society's deep and tangled cultural conflicts can neither be explained nor resolved by simplistic ideological formulas. Sharon O'Dair (2003) said that compositionists "focus [...] almost exclusively on ideological matters", and further argues that this focus

16385-445: The project attempts to move the field to the next phase of its evolution. In this second phase, critical pedagogy seeks to become a worldwide, decolonizing movement dedicated to listening to and learning from diverse discourses of people from around the planet. Kincheloe and Steinberg also embrace Indigenous knowledges in education as a way to expand critical pedagogy and to question educational hegemony. Joe L. Kincheloe, in expanding on

16530-485: The propositional connective "and". Whether a proposition is true depends, at least in part, on its constituents. For complex propositions formed using truth-functional propositional connectives, their truth only depends on the truth values of their parts. But this relation is more complicated in the case of simple propositions and their subpropositional parts. These subpropositional parts have meanings of their own, like referring to objects or classes of objects. Whether

16675-406: The propositions are formed. For example, the syllogism "all men are mortal; Socrates is a man; therefore Socrates is mortal" is valid. The syllogism "all cats are mortal; Socrates is mortal; therefore Socrates is a cat", on the other hand, is invalid. Classical logic is distinct from traditional or Aristotelian logic. It encompasses propositional logic and first-order logic. It is "classical" in

16820-417: The psychology of argumentation. Another characterization identifies informal logic with the study of non-deductive arguments. In this way, it contrasts with deductive reasoning examined by formal logic. Non-deductive arguments make their conclusion probable but do not ensure that it is true. An example is the inductive argument from the empirical observation that "all ravens I have seen so far are black" to

16965-436: The rules of inference they accept as valid and the formal languages used to express them. Starting in the late 19th century, many new formal systems have been proposed. There are disagreements about what makes a formal system a logic. For example, it has been suggested that only logically complete systems, like first-order logic , qualify as logics. For such reasons, some theorists deny that higher-order logics are logics in

17110-492: The scope of mathematics. Propositional logic comprises formal systems in which formulae are built from atomic propositions using logical connectives . For instance, propositional logic represents the conjunction of two atomic propositions P {\displaystyle P} and Q {\displaystyle Q} as the complex formula P ∧ Q {\displaystyle P\land Q} . Unlike predicate logic where terms and predicates are

17255-418: The semantics for classical propositional logic assigns the formula P ∧ Q {\displaystyle P\land Q} the denotation "true" whenever P {\displaystyle P} and Q {\displaystyle Q} are true. From the semantic point of view, a premise entails a conclusion if the conclusion is true whenever the premise is true. A system of logic

17400-604: The semantics. Thus, soundness and completeness together describe a system whose notions of validity and entailment line up perfectly. Systems of logic are theoretical frameworks for assessing the correctness of reasoning and arguments. For over two thousand years, Aristotelian logic was treated as the canon of logic in the Western world, but modern developments in this field have led to a vast proliferation of logical systems. One prominent categorization divides modern formal logical systems into classical logic , extended logics, and deviant logics . Aristotelian logic encompasses

17545-518: The sense that it is based on basic logical intuitions shared by most logicians. These intuitions include the law of excluded middle , the double negation elimination , the principle of explosion , and the bivalence of truth. It was originally developed to analyze mathematical arguments and was only later applied to other fields as well. Because of this focus on mathematics, it does not include logical vocabulary relevant to many other topics of philosophical importance. Examples of concepts it overlooks are

17690-404: The simple proposition "Mars is red", are true or false. In such cases, the truth is called a logical truth: a proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true under all interpretations of its non-logical terms. In some modal logics , this means that the proposition is true in all possible worlds. Some theorists define logic as

17835-415: The simple proposition they form is true depends on their relation to reality, i.e. what the objects they refer to are like. This topic is studied by theories of reference . Some complex propositions are true independently of the substantive meanings of their parts. In classical logic, for example, the complex proposition "either Mars is red or Mars is not red" is true independent of whether its parts, like

17980-870: The singular term r {\displaystyle r} referring to the raven to form the expression B ( r ) {\displaystyle B(r)} . To express that some objects are black, the existential quantifier ∃ {\displaystyle \exists } is combined with the variable x {\displaystyle x} to form the proposition ∃ x B ( x ) {\displaystyle \exists xB(x)} . First-order logic contains various rules of inference that determine how expressions articulated this way can form valid arguments, for example, that one may infer ∃ x B ( x ) {\displaystyle \exists xB(x)} from B ( r ) {\displaystyle B(r)} . Extended logics are logical systems that accept

18125-474: The smallest units, propositional logic takes full propositions with truth values as its most basic component. Thus, propositional logics can only represent logical relationships that arise from the way complex propositions are built from simpler ones. But it cannot represent inferences that result from the inner structure of a proposition. First-order logic includes the same propositional connectives as propositional logic but differs from it because it articulates

18270-431: The social contexts in which they are embedded". Realizing one's consciousness (" conscientization ", " conscientização" ) is then a needed first step of " praxis ", which is defined as the power and know-how to take action against oppression while stressing the importance of liberating education. "Praxis involves engaging in a cycle of theory, application, evaluation, reflection, and then back to theory. Social transformation

18415-418: The streets are wet ( q {\displaystyle q} ). The third feature can be expressed by stating that deductively valid inferences are truth-preserving: it is impossible for the premises to be true and the conclusion to be false. Because of this feature, it is often asserted that deductive inferences are uninformative since the conclusion cannot arrive at new information not already present in

18560-437: The strict sense. When understood in a wide sense, logic encompasses both formal and informal logic. Informal logic uses non-formal criteria and standards to analyze and assess the correctness of arguments. Its main focus is on everyday discourse. Its development was prompted by difficulties in applying the insights of formal logic to natural language arguments. In this regard, it considers problems that formal logic on its own

18705-550: The strongest form of support: if their premises are true then their conclusion must also be true. This is not the case for ampliative arguments, which arrive at genuinely new information not found in the premises. Many arguments in everyday discourse and the sciences are ampliative arguments. They are divided into inductive and abductive arguments. Inductive arguments are statistical generalizations, such as inferring that all ravens are black based on many individual observations of black ravens. Abductive arguments are inferences to

18850-513: The student-centeredness that critical pedagogy insists upon, there are inherent conflicts associated with the "large collections of top-down content standards in their disciplines". Critical pedagogy advocates insist that teachers themselves are vital to the discussion about Standards-based education reform in the United States because a pedagogy that requires a student to learn or a teacher to teach externally imposed information exemplifies

18995-438: The study of logical truths. Truth tables can be used to show how logical connectives work or how the truth values of complex propositions depends on their parts. They have a column for each input variable. Each row corresponds to one possible combination of the truth values these variables can take; for truth tables presented in the English literature, the symbols "T" and "F" or "1" and "0" are commonly used as abbreviations for

19140-700: The subject in two ways: either by affirming it or by denying it. For example, the proposition "Socrates is not a cat" involves the denial of the predicate "cat" to the subject "Socrates". Using combinations of subjects and predicates, a great variety of propositions and syllogisms can be formed. Syllogisms are characterized by the fact that the premises are linked to each other and to the conclusion by sharing one predicate in each case. Thus, these three propositions contain three predicates, referred to as major term , minor term , and middle term . The central aspect of Aristotelian logic involves classifying all possible syllogisms into valid and invalid arguments according to how

19285-417: The subject to the predicate. For example, the proposition "Socrates is wise" is made up of the subject "Socrates", the predicate "wise", and the copula "is". The subject and the predicate are the terms of the proposition. Aristotelian logic does not contain complex propositions made up of simple propositions. It differs in this aspect from propositional logic, in which any two propositions can be linked using

19430-423: The symbols displayed on a page of a book. But this approach comes with new problems of its own: sentences are often context-dependent and ambiguous, meaning an argument's validity would not only depend on its parts but also on its context and on how it is interpreted. Another approach is to understand premises and conclusions in psychological terms as thoughts or judgments. This position is known as psychologism . It

19575-409: The table. This conclusion is justified because it is the best explanation of the current state of the kitchen. For abduction, it is not sufficient that the conclusion explains the premises. For example, the conclusion that a burglar broke into the house last night, got hungry on the job, and had a midnight snack, would also explain the state of the kitchen. But this conclusion is not justified because it

19720-399: The term ampliative or inductive reasoning is used. Deductive arguments are associated with formal logic in contrast to the relation between ampliative arguments and informal logic. A deductively valid argument is one whose premises guarantee the truth of its conclusion. For instance, the argument "(1) all frogs are amphibians; (2) no cats are amphibians; (3) therefore no cats are frogs"

19865-430: The then-current models of economic theory and thought of that time. Further critique can then be applied after the fact, by using thorough critique as a basis for new argument. The idea of critique is elemental to legal, aesthetic, and literary theory and such practices, such as in the analysis and evaluation of writings such as pictorial, musical, or expanded textual works. In French, German, or Italian, no distinction

20010-479: The truth values "true" and "false". The first columns present all the possible truth-value combinations for the input variables. Entries in the other columns present the truth values of the corresponding expressions as determined by the input values. For example, the expression " p ∧ q {\displaystyle p\land q} " uses the logical connective ∧ {\displaystyle \land } ( and ). It could be used to express

20155-462: The word 'critique' in a broader way than Kant's sense of the word, to mean the systematic inquiry into the limits of a doctrine or set of concepts. This referential expansion led, for instance, to the formulation of the idea of social critique, such as arose after Karl Marx 's theoretical work delineated in his A Contribution to the Critique of Political Economy (1859), which was a critique of

20300-446: The work of Michel Foucault and of Catholic philosopher Alasdair MacIntyre . In their different and radically contrasting ways, MacIntyre and Foucault go well beyond the original Kantian meaning of the term critique in contesting legitimatory accounts of social power. Critique as critical theory has also led to the emergence of critical pedagogy , exemplified by Paulo Freire , bell hooks , and others. Let us also remind ourselves of

20445-465: The world in fundamentally new and different ways. Kristen Seas further explains: "Students [often] reject the teacher's message because they see it as coercive, they do not agree with it, or they feel excluded by it." Karen Kopelson concludes "that many if not most students come to the university in order to gain access to and eventual enfranchisement in 'the establishment,' not to critique and reject its privileges." The rapidly changing demographics of

20590-431: Was adapted to deal with a wide range of social and educational issues. Freire's pedagogy revolved around an anti-authoritarian and interactive approach aimed to examine issues of relational power for students and workers. The center of the curriculum used the fundamental goal based on social and political critiques of everyday life. Freire's praxis required implementation of a range of educational practices and processes with

20735-469: Was created by Henry Giroux (1981) as an attempt to dismiss socialism and the legacy of Karl Marx." During the same period, Derek R. Ford also broke with critical pedagogy, claiming that it was "at a dead end." While Ford is not concerned with "proficiency" like O'Dair, he agrees that the focus on critique at the expense of imagination and actual political engagement serves to produce the critical pedagogue as "the enlightened and isolated researcher that reveals

20880-405: Was discussed at length around the turn of the 20th century but it is not widely accepted today. Premises and conclusions have an internal structure. As propositions or sentences, they can be either simple or complex. A complex proposition has other propositions as its constituents, which are linked to each other through propositional connectives like "and" or "if...then". Simple propositions, on

21025-457: Was founded by the Brazilian philosopher and educator Paulo Freire , who promoted it through his 1968 book, Pedagogy of the Oppressed . It subsequently spread internationally, developing a particularly strong base in the United States, where proponents sought to develop means of using teaching to combat racism , sexism , and oppression . As it grew, it incorporated elements from fields like

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