title: Youth

text: The legal drinking age is the age at which a person can consume or purchase alcoholic beverages. These laws cover a wide range of issues and behaviors, addressing when and where alcohol can be consumed. The minimum age alcohol can be legally consumed can be different from the age when it can be purchased in some countries. These laws vary among different countries and many laws have exemptions or special circumstances. Most laws apply only to drinking alcohol in public places, with alcohol consumption in the home being mostly unregulated (an exception being the UK, which has a minimum legal age of five for supervised consumption in private places). Some countries also have different age limits for different types of alcoholic drinks.


title: Youth

text: Driving age is the age at which a person can apply for a driver's license. Countries with the lowest driving ages (below 17) are Argentina, Australia, Canada, El Salvador, Iceland, Israel, Macedonia, Malaysia, New Zealand, the Philippines, Saudi Arabia, Slovenia, the United Kingdom (Mainland) and the United States. The Canadian province of Alberta and several U.S. states permit youth driving as low as 14. Niger has the highest minimum driving age in the world at 23. In India, driving is legal after getting a license at the age of 18.


title: Youth

text: The legal working age is the minimum age required by law for a person to work in each country or jurisdiction. The threshold of adulthood, or "the age of majority" as recognized or declared in law in most countries, has been set at age 18. Some types of labor are commonly prohibited even for those above the working age, if they have not reached the age of majority. Activities that are dangerous, harmful to the health or that may affect the morals of minors fall into this category.


title: Youth

text: Student rights are those rights, such as civil, constitutional, contractual and consumer rights, which regulate student rights and freedoms and allow students to make use of their educational investment. These include such things as the right to free speech and association, to due process, equality, autonomy, safety and privacy, and accountability in contracts and advertising, which regulate the treatment of students by teachers and administrators.


title: Youth

text: The smoking age is the minimum age a person can buy tobacco and/or smoke in public. Most countries regulate this law at the national level while at some point it is done by the state or province.


title: Youth

text: Young people spend much of their lives in educational settings, and their experiences in schools, colleges and universities can shape much of their subsequent lives. Research shows that poverty and income affect the likelihood for the incompletion of high school. These factors also increase the likelihood for the youth to not go to a college or university. In the United States, 12.3 percent of young people ages 16 to 24 are disconnected, meaning they are neither in school nor working.


title: Youth

text: The leading causes of morbidity and mortality among youth and adults are due to certain health-risk behaviors. These behaviors are often established during youth and extend into adulthood. Since the risk behaviors in adulthood and youth are interrelated, problems in adulthood are preventable by influencing youth behavior.


title: Youth

text: A 2004 mortality study of youth (defined in this study as ages 10–24) mortality worldwide found that 97% of deaths occurred in low to middle-income countries, with the majority in southeast Asia and sub-Saharan Africa. Maternal conditions accounted for 15% of female deaths, while HIV/AIDS and tuberculosis were responsible for 11% of deaths; 14% of male and 5% of female deaths were attributed to traffic accidents, the largest cause overall. Violence accounted for 12% of male deaths. Suicide was the cause of 6% of all deaths.


title: Youth

text: The U.S. Centers for Disease Control and Prevention developed its Youth Risk Behavior Surveillance System (YRBSS) in 2003 to help assess risk behavior. YRBSS monitors six categories of priority health-risk behaviors among youth and young adults. These are behaviors that contribute to unintentional injuries and violence;


title: Youth

text: YRBSS includes a national school-based survey conducted by CDC as well as state and local school-based surveys conducted by education and health agencies.


title: Youth

text: Universal school-based interventions such as formal classroom curricula, behavioural management practices, role‐play, and goal‐setting may be effective in preventing tobacco use, alcohol use, illicit drug use, antisocial behaviour, and improving physical activity of young people.


title: Youth

text: Obesity now affects one in five children in the United States, and is the most prevalent nutritional disease of children and adolescents in the United States. Although obesity-associated morbidities occur more frequently in adults, significant consequences of obesity as well as the antecedents of adult disease occur in obese children and adolescents.


title: Youth

text: Discrimination against overweight children begins early in childhood and becomes progressively institutionalized. Obese children may be taller than their non-overweight peers, in which case they are apt to be viewed as more mature. The inappropriate expectations that result may have an adverse effect on their socialization.


title: Youth

text: Many of the cardiovascular consequences that characterize adult-onset obesity are preceded by abnormalities that begin in childhood. Hyperlipidemia, hypertension, and abnormal glucose tolerance occur with increased frequency in obese children and adolescents. The relationship of cardiovascular risk factors to visceral fat independent of total body fat remains unclear. Sleep apnea, pseudotumor cerebri, and Blount's disease represent major sources of morbidity for which rapid and sustained weight reduction is essential. Although several periods of increased risk appear in childhood, it is not clear whether obesity with onset early in childhood carries a greater risk of adult morbidity and mortality.


title: Youth

text: Bullying among school-aged youth is increasingly being recognized as an important problem affecting well-being and social functioning. While a certain amount of conflict and harassment is typical of youth peer relations, bullying presents a potentially more serious threat to healthy youth development. The definition of bullying is widely agreed on in literature on bullying.


title: Youth

text: The majority of research on bullying has been conducted in Europe and Australia.Considerable variability among countries in the prevalence of bullying has been reported. In an international survey of adolescent health-related behaviors, the percentage of students who reported being bullied at least once during the current term ranged from a low of 15% to 20% in some countries to a high of 70% in others. Of particular concern is frequent bullying, typically defined as bullying that occurs once a week or more. The prevalence of frequent bullying reported internationally ranges from a low of 1.9% among one Irish sample to a high of 19% in a Malta study.


title: Youth

text: Research examining characteristics of youth involved in bullying has consistently found that both bullies and those bullied demonstrate poorer psychosocial functioning than their non-involved peers. Youth who bully others tend to demonstrate higher levels of conduct problems and dislike of school, whereas youth who are bullied generally show higher levels of insecurity, anxiety, depression, loneliness, unhappiness, physical and mental symptoms, and low self-esteem. Males who are bullied also tend to be physically weaker than males in general. The few studies that have examined the characteristics of youth who both bully and are bullied found that these individuals exhibit the poorest psychosocial functioning overall.


title: Youth

text: Globalization and transnational flows have had tangible effects on sexual relations, identities, and subjectivities. In the wake of an increasingly globalized world order under waning Western dominance, within ideologies of modernity, civilization, and programs for social improvement, discourses on population control, 'safe sex', and 'sexual rights'. Sex education programmes grounded in evidence-based approaches are a cornerstone in reducing adolescent sexual risk behaviours and promoting sexual health. In addition to providing accurate information about consequences of Sexually transmitted disease or STIs and early pregnancy, such programmes build life skills for interpersonal communication and decision making. Such programmes are most commonly implemented in schools, which reach large numbers of teenagers in areas where school enrollment rates are high. However, since not all young people are in school, sex education programmes have also been implemented in clinics, juvenile detention centers and youth-oriented community agencies. Notably, some programmes have been found to reduce risky sexual behaviours when implemented in both school and community settings with only minor modifications to the curricula.


title: Youth

text: The Sangguniang Kabataan ("Youth Council" in English), commonly known as SK, was a youth council in each barangay (village or district) in the Philippines, before being put "on hold", but not quite abolished, prior to the 2013 barangay elections. The council represented teenagers from 15 to 17 years old who have resided in their barangay for at least six months and registered to vote. It was the local youth legislature in the village and therefore led the local youth program and projects of the government. The Sangguniang Kabataan was an offshoot of the KB or the "Kabataang Barangay" (Village Youth) which was abolished when the Local Government Code of 1991 was enacted.


title: Youth

text: The vast majority of young people live in developing countries: according to the United Nations, globally around 85 per cent of 15- to 24-year-olds live in developing countries, a figure projected to grow 89.5 per cent by 2025. Moreover, this majority are extremely diverse: some live in rural areas but many inhabit the overcrowded metropolises of India, Mongolia and other parts of Asia and in South America, some live traditional lives in tribal societies, while others participate in global youth culture in ghetto contexts.


title: Youth

text: Many young lives in developing countries are defined by poverty, some suffer from famine and a lack of clean water, while involvement in armed conflict is all common. Health problems are rife, especially due to the prevalence of HIV/AIDS in certain regions. The United Nations estimates that 200 million young people live in poverty, 130 million are illiterate and 10 million live with HIV/AIDS.


title: Pakka Commercial

text: Pakka Commercial () is a 2022 Indian Telugu-language legal action comedy film written and directed by Maruthi and produced by UV Creations and GA2 Pictures. The film stars Gopichand and Raashii Khanna. It was released on 1 July 2022, and received mixed reviews from critics and audience.


title: Pakka Commercial

text: Suryanarayana is a dutiful lawyer, who resigns after being unable to deliver justice to Amulya, who was threatened and blackmailed by the rich man named Vivek and ultimately committed suicide. While he works hard at his shop to provide for his family, his son Ramchand "Lucky" finds his law books and coat, sparking an inspiration to become a lawyer. Years later, Lucky becomes an advocate, who embodies the opposite principles of his father, settling cases outside of the court for his personal profits, which Suryanarayana is unaware. One day, Jhansi an actress whose character, a lawyer in a serial, was killed off to save money requests Lucky so that she can sue the studio. Although their case is rejected, Lucky is impressed by Jhansi's knowledge and qualifications in real-life law and they fall in love with each other.


title: Pakka Commercial

text: Afterwards, Lucky defends a gangster, who killed a lawyer despite extensive evidence against him while Suryanayarana helps a couple file a case against a corrupt developer and politician who is actually Vivek. When Suryanarayana refers the case to him, he instead meets Vivek and agrees to work with him for substantial rewards. Vivek also kidnaps the husband, who exposed his corruption. On the second hearing for the gangster's murder case, Jhansi, who has gotten closer to the family, unexpectedly brings Suryanarayana to the courtroom, forcing Lucky to honestly argue and leading to a guilty verdict for the gangster. Watching through a secret camera, Vivek is impressed by his performances and reaches the court. Vivek's arrival brings all the truths to light, and Suryanaryana is ashamed by Lucky's actions, where he decides to fight for the couple himself.


title: Pakka Commercial

text: Jhansi decides to join Suryanarayana after seeing his drive for justice. At home, they work on the case, splitting the house into halves which they title themselves as "Commercial" (Lucky) and "Non-Commercial" (Suryanaryana and Jhansi). Lucky uses various tricks to hamper Suryanaryana and Jhansi, slanders the couple's names, claiming that he had actually gone to Dubai and had affairs, and nearly gets Suryanaryana disbarred. Meanwhile, Lucky keeps getting gifts from Vivek. Lucky's search for the disappeared husband, ends to no avail and Vivek plans to kill him by putting him in a pillar and casting concrete inside. Lucky also meets a mysterious woman also named Amulya, who is Vivek's wife. Ultimately, Lucky gets a seat as an MLA in Vivek's political party.


title: Pakka Commercial

text: As Vivek prepares to be sworn, the news breaks about the body of a cab driver that Vivek had murdered earlier being found at his farmhouse. It is revealed that Amulya is actually Saira Banu, the cab driver's wife. In retaliation, Vivek kidnaps Suryanarayana and asks Lucky to cover his bail. However, Lucky instead saves Suryanarayana from Vivek's goons and reveals that he had planned everything all along to seek vengeance on Vivek, ever since he saw Suryanarayana's sufferings as a child following his resignation, and had enlisted Saira Banu to seduce and distract Vivek. Vivek attempts to appeal, but his lawyer deserts him after revealing that Lucky used his gifts and conversations to collect his evidence and biometric traits. Finally, Vivek becomes insane and requests the court to provide him a death penalty.


title: Pakka Commercial

text: In January 2021, sources claimed that director Maruthi will collaborate with Gopichand for a new film. The official announcement of the film and its title were announced in February 2021. Principal photography of the film began in March 2021.


title: Pakka Commercial

text: In January 2021, Sai Pallavi was in talks to play the female lead, however, Raashi Khanna, who paired up with Gopichand in "Jil" (2015), and "Oxygen" (2017), was cast in the female lead in February 2021. The film marks the third collaboration between Gopichand and Khanna, and also second collaboration between Maruthi and Khanna after "Prati Roju Pandage" (2019). Eesha Rebba was rumored to be playing second female lead. Anasuya Bharadwaj was roped in for a role. The film shooting has started in Hyderabad in March 2021. In April, due to the second wave of COVID-19 pandemic, the film shooting is postponed. Filming was resumed in August 2021.


title: Pakka Commercial

text: The music rights of the film are sold to Aditya Music. The music of the film is composed by Jakes Bejoy.


title: Pakka Commercial

text: The film was initially planned for a theatrical release on 1 October 2021, but due to the second wave of the COVID-19 pandemic, the filming was delayed, and the film's release was initially planned to 24 February 2022, and pushed to 20 May 2022, but eventually postponed and then finally released on 1 July 2022. The total worldwide theatrical distribution rights of the film were sold at a cost of ₹19.20 crore.


title: Pakka Commercial

text: Digital streaming rights of the film were acquired by Netflix and Aha, whereas the satellite rights were acquired by Star Maa. Digital streaming and satellite rights of the film were sold at a cost of ₹31 crore. The film was premiered on Netflix and Aha on 5 August 2022.


title: Pakka Commercial

text: Neeshita Nyayapati of "The Times of India" rated the film 3 out of 5 stars and wrote "Maruthi has delivered better films, characters and stories in the past; "Pakka Commercial" is really not his best work". Arvind V of "Pinkvilla" rated the film 2.5 out of 5 stars and wrote "Amid a sea of mundane ideas, Pakka Commercial manages to offer a few good ideas". Sangeetha Devi Dundoo of "The Hindu" gave the film a mixed review and said the film is commercial but far from entertaining. Balakrishna Ganeshan of "The News Minute" criticized the film and gave a rating of 1.5 out of 5 stars while stating that "The performances of actors Gopichand, Sathyaraj and Rao Ramesh are convincing. Raashii Khanna however deserves much of the appreciation for experimenting with comedy and succeeding with it". "NTV"'s Kota opined that forced comedy, routine screenplay and film duration are the negatives whereas performances by lead actors are positives of the film.


title: Kantian ethics

text: Kantian ethics refers to a deontological ethical theory developed by German philosopher Immanuel Kant that is based on the notion that: "It is impossible to think of anything at all in the world, or indeed even beyond it, that could be considered good without limitation except a good will." The theory was developed in the context of Enlightenment rationalism. It states that an action can only be moral if (i) it is motivated by a sense of duty and (ii) its maxim may be rationally willed a universal, objective law.


title: Kantian ethics

text: Central to Kant's theory of the moral law is the categorical imperative. Kant formulated the categorical imperative in various ways. His principle of universalizability requires that, for an action to be permissible, it must be possible to apply it to all people without a contradiction occurring. Kant's formulation of humanity, the second section of the categorical imperative, states that as an "end in itself", humans are required never to treat others merely as a "means to an end", but always as "ends in themselves". The formulation of autonomy concludes that rational agents are bound to the moral law by their own will, while Kant's concept of the Kingdom of Ends requires that people act as if the principles of their actions establish a law for a hypothetical kingdom.


title: Kantian ethics

text: The tremendous influence of Kant's moral thought is evident both in the breadth of appropriations and criticisms it has inspired and in the many real world contexts in which it has found application.


title: Kantian ethics

text: Although all of Kant's work develops his ethical theory, it is most clearly defined in "Groundwork of the Metaphysics of Morals", "Critique of Practical Reason", and "Metaphysics of Morals". As part of the Enlightenment tradition, Kant based his ethical theory on the belief that reason should be used to determine how people ought to act. He did not attempt to prescribe specific action, but instructed that reason should be used to determine how to behave.


title: Kantian ethics

text: In his combined works, Kant constructed the basis for an ethical law by the concept of duty. Kant began his ethical theory by arguing that the only virtue that can be unqualifiedly good is a good will. No other virtue has this status because every other virtue can be used to achieve immoral ends (for example, the virtue of loyalty is not good if one is loyal to an evil person). The "good will" is unique in that it is always good and maintains its moral value even when it fails to achieve its moral intentions. Kant regarded the "good will" as a single moral principle that freely chooses to use the other virtues for moral ends.


title: Kantian ethics

text: For Kant, a "good will" is a broader conception than a will that acts from duty. A will that acts from duty is distinguishable as a will that overcomes hindrances in order to keep the moral law. A dutiful will is thus a special case of a "good will" that becomes visible in adverse conditions. Kant argues that only acts performed with regard to duty have moral worth. This is not to say that acts performed merely in accordance with duty are worthless (these still deserve approval and encouragement), but that special esteem is given to acts that are performed out of duty.


title: Kantian ethics

text: Kant's conception of duty does not entail that people perform their duties grudgingly. Although duty often constrains people and prompts them to act against their inclinations, it still comes from an agent's volition: they desire to keep the moral law. Thus, when an agent performs an action from duty it is because the rational incentives matter to them more than their opposing inclinations. Kant wished to move beyond the conception of morality as externally imposed duties, and present an ethics of autonomy, when rational agents freely recognize the claims reason makes upon them.


title: Kantian ethics

text: Applying the categorical imperative, duties arise because failure to fulfill them would either result in a contradiction in conception or in a contradiction in the will. The former are classified as "perfect duties", the latter as "imperfect". A perfect duty always holds true. Kant eventually argues that there is in fact only one "perfect duty" -- The Categorical Imperative. An imperfect duty allows flexibility—beneficence is an imperfect duty because we are not obliged to be completely beneficent at all times, but may choose the times and places in which we are. Kant believed that perfect duties are more important than imperfect duties: if a conflict between duties arises, the perfect duty must be followed.


title: Kantian ethics

text: The foundation of Kant's ethics is the categorical imperative, for which he provides four formulations. Kant made a distinction between categorical and hypothetical imperatives. A hypothetical imperative is one that we must obey if we want to satisfy our desires: 'go to the doctor' is a hypothetical imperative because we are only obliged to obey it if we want to get well. A categorical imperative binds us regardless of our desires: everyone has a duty to not lie, regardless of circumstances and even if it is in our interest to do so. These imperatives are morally binding because they are based on reason, rather than contingent facts about an agent. Unlike hypothetical imperatives, which bind us insofar as we are part of a group or society which we owe duties to, we cannot opt out of the categorical imperative because we cannot opt out of being rational agents. We owe a duty to rationality by virtue of being rational agents; therefore, rational moral principles apply to all rational agents at all times.


title: Kantian ethics

text: Kant defines "maxim" as a "subjective principle of volition," which is distinguished from an "objective principle or 'practical law. While "the latter is valid for every rational being and is a 'principle according to which they ought to act[,]' a maxim 'contains the practical rule which reason determines in accordance with the conditions of the subject (often their ignorance or inclinations) and is thus the principle according to which the subject does act.


title: Kantian ethics

text: Maxims fail to qualify as practical laws if they produce a contradiction in conception or a contradiction in the will when universalized. A contradiction in conception happens when, if a maxim were to be universalized, it ceases to make sense, because the "maxim would necessarily destroy itself as soon as it was made a universal law." For example, if the maxim 'It is permissible to break promises' was universalized, no one would trust any promises made, so the idea of a promise would become meaningless; the maxim would be self-contradictory because, when universalized, promises cease to be meaningful. The maxim is not moral because it is logically impossible to universalize—we could not conceive of a world where this maxim was universalized.


title: Kantian ethics

text: A maxim can also be immoral if it creates a contradiction in the will when universalized. This does not mean a logical contradiction, but that universalizing the maxim leads to a state of affairs that no "rational" being would desire.


title: Kantian ethics

text: Kant believed that morality is the objective law of reason: just as objective physical laws necessitate physical actions (e.g., apples fall down because of gravity), objective rational laws necessitate rational actions. He thus believed that a perfectly rational being must also be perfectly moral, because a perfectly rational being subjectively finds it necessary to do what is rationally necessary. Because humans are not perfectly rational (they partly act by instinct), Kant believed that humans must conform their subjective will with objective rational laws, which he called conformity obligation. Kant argued that the objective law of reason is "a priori", existing externally from rational being. Just as physical laws exist prior to physical beings, rational laws (morality) exist prior to rational beings. Therefore, according to Kant, rational morality is universal and cannot change depending on circumstance.


title: Kantian ethics

text: Some have postulated a similarity between the first formulation of the Categorical Imperative and the Golden Rule. Kant himself criticized the Golden Rule as neither purely formal nor necessarily universally binding.


title: Kantian ethics

text: Kant argued that rational beings can never be treated merely as "means to ends"; they must always also be treated as "ends themselves", requiring that their own reasoned motives must be equally respected. This derives from Kant's claim that the sense of "duty", the rational "respect" for law, motivates morality: it demands that we respect the rationality of all beings. A rational being cannot rationally consent to be used merely as a means to an end, so they must always be treated as an end. Kant justified this by arguing that moral obligation is a rational necessity: that which is rationally willed is morally right. Because all rational agents rationally will themselves to be an end and never merely a means, it is morally obligatory that they are treated as such. This does not mean that we can never treat a human as a means to an end, but that when we do, we also treat them as an end in themselves.


title: Kantian ethics

text: Kant's "formula of autonomy" expresses the idea that an agent is obliged to follow the Categorical Imperative because of their rational will, rather than any outside influence. Kant believed that any moral law motivated by the desire to fulfill some other interest would deny the Categorical Imperative, leading him to argue that the moral law must only arise from a rational will. This principle requires people to recognize the right of others to act autonomously and means that, as moral laws must be universalizable, what is required of one person is required of all.


title: Kantian ethics

text: This formulation requires that actions be considered as if their maxim is to provide a law for a hypothetical Kingdom of Ends. Accordingly, people have an obligation to act upon principles that a community of rational agents would accept as laws. In such a community, each individual would only accept maxims that can govern every member of the community without treating any member merely as a means to an end. Although the Kingdom of Ends is an ideal—the actions of other people and events of nature ensure that actions with good intentions sometimes result in harm—we are still required to act categorically, as legislators of this ideal kingdom.


title: Kantian ethics

text: As Kant explains in the "Groundwork of the Metaphysics of Morals" (and as its title directly indicates), that short 1785 text is "nothing more than the search for and establishment of the "supreme principle of morality."" Kant further states,


title: Kantian ethics

text: just because moral laws are to hold for every rational being as such, to derive them from the universal concept of a rational being as such, and in this way to set forth completely the whole of morals, [a metaphysics of morals] needs anthropology for its "application" to human beings.


title: Kantian ethics

text: His promised "Metaphysics of Morals", however, was much delayed and did not appear until its two parts, The Doctrine of Right and The Doctrine of Virtue, were published separately in 1797 and 1798. In the twelve years between the "Groundwork" and The Doctrine of Right, Kant decided that the metaphysics of morals and its application should, after all, be integrated (though still as distinct from practical anthropology). The distinction between its groundwork (or foundation) and the metaphysics of morals itself, however, continues to apply. Moreover, the account provided in the latter "Metaphysics of Morals" provides "a very different account of ordinary moral reasoning" than the one suggested by the "Groundwork."


title: Kantian ethics

text: The Doctrine of Right deals with "juridical" duties, which are "concerned only with protecting the external freedom of individuals" and indifferent to incentives. (Although we do have a moral duty "to limit ourselves to actions that are right, that duty is not part of [right] itself.") Its basic political idea is that "each person’s entitlement to be his or her own master is only consistent with the entitlements of others if public legal institutions are in place."


title: Kantian ethics

text: The Doctrine of Virtue is concerned with "duties of virtue" or "ends that are at the same time duties." It is here, in the domain of ethics, that "The Metaphysics of Morals"'s greatest innovation is to be found. According to Kant's account, "ordinary moral reasoning is fundamentally teleological – it is reasoning about what ends we are constrained by morality to pursue, and the priorities among these ends we are required to observe." More specifically,


title: Kantian ethics

text: There are two sorts of ends that it is our duty to have: our own perfection and the happiness of others ("MS" 6:385). "Perfection" includes both our natural perfection (the development of our talents, skills, and capacities of understanding) and moral perfection (our virtuous disposition) ("MS" 6:387). A person’s "happiness" is the greatest rational whole of the ends the person set for the sake of her own satisfaction ("MS" 6:387–8).


title: Kantian ethics

text: Kant's elaboration of this teleological doctrine offers up a very different moral theory than the one typically attributed to him on the basis of his foundational works alone.


title: Kantian ethics

text: Biographer of Kant, Manfred Kuhn, suggested that the values Kant's parents held, of "hard work, honesty, cleanliness, and independence”, set him an example and influenced him more than their pietism did. In the "Stanford Encyclopedia of Philosophy", Michael Rohlf suggests that Kant was influenced by his teacher, Martin Knutzen, himself influenced by the work of Christian Wolff and John Locke, and who introduced Kant to the work of English physicist Isaac Newton.


title: Kantian ethics

text: Eric Entrican Wilson and Lara Denis emphasize David Hume's influence on Kant's ethics. Both of them try to reconcile freedom with a commitment to causal determinism and believe that morality’s foundation is independent of religion.


title: Kantian ethics

text: German philosopher Jürgen Habermas has proposed a theory of discourse ethics that he claims is a descendant of Kantian ethics. He proposes that action should be based on communication between those involved, in which their interests and intentions are discussed so they can be understood by all. Rejecting any form of coercion or manipulation, Habermas believes that agreement between the parties is crucial for a moral decision to be reached. Like Kantian ethics, discourse ethics is a cognitive ethical theory, in that it supposes that truth and falsity can be attributed to ethical propositions. It also formulates a rule by which ethical actions can be determined and proposes that ethical actions should be universalizable, in a similar way to Kant's ethics.


title: Kantian ethics

text: Habermas argues that his ethical theory is an improvement on Kant's, and rejects the dualistic framework of Kant's ethics. Kant distinguished between the "phenomena" world, which can be sensed and experienced by humans, and the "noumena", or spiritual world, which is inaccessible to humans. This dichotomy was necessary for Kant because it could explain the autonomy of a human agent: although a human is bound in the phenomenal world, their actions are free in the intelligible world. For Habermas, morality arises from discourse, which is made necessary by their rationality and needs, rather than their freedom.


title: Kantian ethics

text: The social contract theory of political philosopher John Rawls, developed in his work "A Theory of Justice", was influenced by Kant's ethics. Rawls argued that a just society would be fair. To achieve this fairness, he proposed a hypothetical moment prior to the existence of a society, at which the society is ordered: this is the original position. This should take place from behind a veil of ignorance, where no one knows what their own position in society will be, preventing people from being biased by their own interests and ensuring a fair result. Rawls' theory of justice rests on the belief that individuals are free, equal, and moral; he regarded all human beings as possessing some degree of reasonableness and rationality, which he saw as the constituents of morality and entitling their possessors to equal justice. Rawls dismissed much of Kant's dualisms, arguing that the structure of Kantian ethics, once reformulated, is clearer without them—he described this as one of the goals of "A Theory of Justice".


title: Kantian ethics

text: Thomas Nagel has been highly influential in the related fields of moral and political philosophy. Supervised by John Rawls, Nagel has been a long-standing proponent of a Kantian and rationalist approach to moral philosophy. His distinctive ideas were first presented in the short monograph "The Possibility of Altruism," published in 1970. That book seeks by reflection on the nature of practical reasoning to uncover the formal principles that underlie reason in practice and the related general beliefs about the self that are necessary for those principles to be truly applicable to us.


title: Kantian ethics

text: Nagel defends motivated desire theory about the motivation of moral action. According to "motivated desire theory", when a person is motivated to moral action it is indeed true that such actions are motivated—like all intentional actions—by a belief and a desire. But it is important to get the justificatory relations right: when a person accepts a moral judgment he or she is necessarily motivated to act. But it is the reason that does the justificatory work of justifying both the action and the desire. Nagel contrasts this view with a rival view which believes that a moral agent can only accept that he or she has a reason to act if the desire to carry out the action has an independent justification. An account based on presupposing sympathy would be of this kind.


title: Kantian ethics

text: The most striking claim of the book is that there is a very close parallel between prudential reasoning in one's own interests and moral reasons to act to further the interests of another person. When one reasons prudentially, for example about the future reasons that one will have, one allows the reason in the future to justify one's current action without reference to the strength of one's current desires. If a hurricane were to destroy someone's car next year at that point he will want his insurance company to pay him to replace it: that future reason gives him a reason, now, to take out insurance. The strength of the reason ought not to be hostage to the strength of one's current desires. The denial of this view of prudence, Nagel argues, means that one does not really believe that one is one and the same person through time. One is dissolving oneself into distinct person-stages.


title: Kantian ethics

text: Philosopher Onora O'Neill, who studied under John Rawls at Harvard University, is a contemporary Kantian ethicist who supports a Kantian approach to issues of social justice. O'Neill argues that a successful Kantian account of social justice must not rely on any unwarranted idealizations or assumption. She notes that philosophers have previously charged Kant with idealizing humans as autonomous beings, without any social context or life goals, though maintains that Kant's ethics can be read without such an idealization. O'Neill prefers Kant's conception of reason as practical and available to be used by humans, rather than as principles attached to every human being. Conceiving of reason as a tool to make decisions with means that the only thing able to restrain the principles we adopt is that they could be adopted by all. If we cannot will that everyone adopts a certain principle, then we cannot give them reasons to adopt it. To use reason, and to reason with other people, we must reject those principles that cannot be universally adopted. In this way, O'Neill reached Kant's formulation of universalisability without adopting an idealistic view of human autonomy. This model of universalisability does not require that we adopt all universalisable principles, but merely prohibits us from adopting those that are not.


title: Kantian ethics

text: From this model of Kantian ethics, O'Neill begins to develop a theory of justice. She argues that the rejection of certain principles, such as deception and coercion, provides a starting point for basic conceptions of justice, which she argues are more determinate for human beings that the more abstract principles of equality or liberty. Nevertheless, she concedes that these principles may seem to be excessively demanding: there are many actions and institutions that do rely on non-universalisable principles, such as injury.


title: Kantian ethics

text: In his paper "The Schizophrenia of Modern Ethical Theories", philosopher Michael Stocker challenges Kantian ethics (and all modern ethical theories) by arguing that actions from duty lack certain moral value. He gives the example of Smith, who visits his friend in hospital out of duty, rather than because of the friendship; he argues that this visit seems morally lacking because it is motivated by the wrong thing.


title: Kantian ethics

text: Marcia Baron has attempted to defend Kantian ethics on this point. After presenting a number of reasons that we might find acting out of duty objectionable, she argues that these problems only arise when people misconstrue what their duty is. Acting out of duty is not intrinsically wrong, but immoral consequences can occur when people misunderstand what they are duty-bound to do. Duty need not be seen as cold and impersonal: one may have a duty to cultivate their character or improve their personal relationships. Baron further argues that duty should be construed as a secondary motive—that is, a motive that regulates and sets conditions on what may be done, rather than prompt specific actions. She argues that, seen this way, duty neither reveals a deficiency in one's natural inclinations to act, nor undermines the motives and feelings that are essential to friendship. For Baron, being governed by duty does not mean that duty is always the primary motivation to act; rather, it entails that considerations of duty are always action-guiding. A responsible moral agent should take an interest in moral questions, such as questions of character. These should guide moral agents to act from duty.


title: Kantian ethics

text: While Friedrich Schiller appreciated Kant for basing the source of morality on a person's reason rather than on God, he also criticized Kant for not going far enough in the conception of autonomy, as the internal constraint of reason would also take away a person's autonomy by going against their sensuous self. Schiller introduced the concept of the "beautiful soul," in which the rational and non-rational elements within a person are in such harmony that a person can be led entirely by his sensibility and inclinations. "Grace" is the expression in appearance of this harmony. However, given that humans are not naturally virtuous, it is in exercising control over the inclinations and impulses through moral strength that a person displays "dignity." Schiller's main implied criticism of Kant is that the latter only saw dignity while grace is ignored.


title: Kantian ethics

text: Kant responded to Schiller in a footnote that appears in Religion within the Bounds of Bare Reason. While he admits that the concept of duty can only be associated with dignity, gracefulness is also allowed by the virtuous individual as he attempts to meet the demands of the moral life courageously and joyously.


title: Kantian ethics

text: German philosopher G. W. F. Hegel presented two main criticisms of Kantian ethics. He first argued that Kantian ethics provides no specific information about what people should do because Kant's moral law is solely a principle of non-contradiction. He argued that Kant's ethics lack any content and so cannot constitute a supreme principle of morality. To illustrate this point, Hegel and his followers have presented a number of cases in which the Formula of Universal Law either provides no meaningful answer or gives an obviously wrong answer. Hegel used Kant's example of being trusted with another man's money to argue that Kant's Formula of Universal Law cannot determine whether a social system of property is a morally good thing, because either answer can entail contradictions. He also used the example of helping the poor: if everyone helped the poor, there would be no poor left to help, so beneficence would be impossible if universalized, making it immoral according to Kant's model. Hegel's second criticism was that Kant's ethics forces humans into an internal conflict between reason and desire. Because it does not address the tension between self-interest and morality, Kant's ethics cannot give individuals any reason to be moral.


title: Kantian ethics

text: German philosopher Arthur Schopenhauer criticised Kant's belief that ethics should concern what ought to be done, insisting that the scope of ethics should be to attempt to explain and interpret what actually happens. Whereas Kant presented an idealized version of what ought to be done in a perfect world, Schopenhauer argued that ethics should instead be practical and arrive at conclusions that could work in the real world, capable of being presented as a solution to the world's problems. Schopenhauer drew a parallel with aesthetics, arguing that in both cases prescriptive rules are not the most important part of the discipline. Because he believed that virtue cannot be taught—a person is either virtuous or is not—he cast the proper place of morality as restraining and guiding people's behavior, rather than presenting unattainable universal laws.


title: Kantian ethics

text: Philosopher Friedrich Nietzsche criticised all contemporary moral systems, with a special focus on Christian and Kantian ethics. He argued that all modern ethical systems share two problematic characteristics: first, they make a metaphysical claim about the nature of humanity, which must be accepted for the system to have any normative force; and second, the system benefits the interests of certain people, often over those of others. Although Nietzsche's primary objection is not that metaphysical claims about humanity are untenable (he also objected to ethical theories that do not make such claims), his two main targets—Kantianism and Christianity—do make metaphysical claims, which therefore feature prominently in Nietzsche's criticism.


title: Kantian ethics

text: Nietzsche rejected fundamental components of Kant's ethics, particularly his argument that morality, God, and immorality, can be shown through reason. Nietzsche cast suspicion on the use of moral intuition, which Kant used as the foundation of his morality, arguing that it has no normative force in ethics. He further attempted to undermine key concepts in Kant's moral psychology, such as the will and pure reason. Like Kant, Nietzsche developed a concept of autonomy; however, he rejected Kant's idea that valuing our own autonomy requires us to respect the autonomy of others. A naturalist reading of Nietzsche's moral psychology stands contrary to Kant's conception of reason and desire. Under the Kantian model, reason is a fundamentally different motive to desire because it has the capacity to stand back from a situation and make an independent decision. Nietzsche conceives of the self as a social structure of all our different drives and motivations; thus, when it seems that our intellect has made a decision against our drives, it is actually just an alternative drive taking dominance over another. This is in direct contrast with Kant's view of the intellect as opposed to instinct; instead, it is just another instinct. There is thus no self-capable of standing back and making a decision; the decision the self-makes is simply determined by the strongest drive. Kantian commentators have argued that Nietzsche's practical philosophy requires the existence of a self capable of standing back in the Kantian sense. For an individual to create values of their own, which is a key idea in Nietzsche's philosophy, they must be able to conceive of themselves as a unified agent. Even if the agent is influenced by their drives, he must regard them as his own, which undermines Nietzsche's conception of autonomy.


title: Kantian ethics

text: The Utilitarian philosopher John Stuart Mill criticizes Kant for not realizing that moral laws are justified by a moral intuition based on utilitarian principles (that the greatest good for the greatest number ought to be sought). Mill argued that Kant's ethics could not explain why certain actions are wrong without appealing to utilitarianism. As basis for morality, Mill believed that his principle of utility has a stronger intuitive grounding than Kant's reliance on reason, and can better explain why certain actions are right or wrong.


title: Kantian ethics

text: Virtue ethics is a form of ethical theory which emphasizes the character of an agent, rather than specific acts; many of its proponents have criticised Kant's deontological approach to ethics. Elizabeth Anscombe criticised modern ethical theories, including Kantian ethics, for their obsession with law and obligation. As well as arguing that theories which rely on a universal moral law are too rigid, Anscombe suggested that, because a moral law implies a moral lawgiver, they are irrelevant in modern secular society.


title: Kantian ethics

text: In his work After Virtue, Alasdair MacIntyre criticises Kant's formulation of universalisability, arguing that various trivial and immoral maxims can pass the test, such as "Keep all your promises throughout your entire life except one." He further challenges Kant's formulation of humanity as an end in itself by arguing that Kant provided no reason to treat others as means: the maxim "Let everyone except me be treated as a means," though seemingly immoral, can be universalized. Bernard Williams argues that, by abstracting persons from character, Kant misrepresents persons and morality and Philippa Foot identified Kant as one of a select group of philosophers responsible for the neglect of virtue by analytic philosophy.


title: Kantian ethics

text: Roman Catholic priest Servais Pinckaers regarded Christian ethics as closer to the virtue ethics of Aristotle than Kant's ethics. He presented virtue ethics as "freedom for excellence", which regards freedom as acting in accordance with nature to develop one's virtues.


title: Kantian ethics

text: A number of philosophers (including Elizabeth Anscombe, Jean Bethke Elshtain, Servais Pinckaers, Iris Murdoch, and Kevin Knight) have all suggested that the Kantian conception of ethics rooted in autonomy is contradictory in its dual contention that humans are co-legislators of morality and that morality is a priori. They argue that if something is universally a priori (i.e., existing unchangingly prior to experience), then it cannot also be in part dependent upon humans, who have not always existed. On the other hand, if humans truly do legislate morality, then they are not bound by it objectively, because they are always free to change it.


title: Kantian ethics

text: This objection seems to rest on a misunderstanding of Kant's views since Kant argued that morality is dependent upon the "concept" of a rational will (and the related concept of a categorical imperative: an imperative which any rational being must necessarily will for itself). It is not based on contingent features of any being's will, nor upon human wills in particular, so there is no sense in which Kant makes ethics "dependent" upon anything which has not always existed. Furthermore, the sense in which our wills are subject to the law is precisely that if our wills are rational, we must will in a lawlike fashion; that is, we must will according to moral judgments we apply to all rational beings, including ourselves.


title: Kantian ethics

text: This is more easily understood by parsing the term "autonomy" into its Greek roots: auto (self) + nomos (rule or law). That is, an autonomous will, according to Kant, is not merely one which follows its own will, but whose will is lawful-that is, conforming to the principle of universalizability, which Kant also identifies with reason. Ironically, in another passage, willing according to immutable reason is precisely the kind of capacity Elshtain ascribes to God as the basis of his moral authority, and she commands this over an inferior voluntarist version of divine command theory, which would make both morality and God's will contingent. As O'Neill argues, Kant's theory is a version of the first rather than the second view of autonomy, so neither God nor any human authority, including contingent human institutions, play any unique authoritative role in his moral theory. Kant and Elshtain, that is, both agree God has no choice but to conform his will to the immutable facts of reason, including moral truths; humans do have such a choice, but otherwise their relationship to morality is the same as that of God's: they can recognize moral facts, but do not determine their content through contingent acts of will.


title: Kantian ethics

text: Kant believed that the shared ability of humans to reason should be the basis of morality, and that it is the ability to reason that makes humans morally significant. He, therefore, believed that all humans should have the right to common dignity and respect. Margaret L. Eaton argues that, according to Kant's ethics, a medical professional must be happy for their own practices to be used by and on anyone, even if they were the patient themselves. For example, a researcher who wished to perform tests on patients without their knowledge must be happy for all researchers to do so. She also argues that Kant's requirement of autonomy would mean that a patient must be able to make a fully informed decision about treatment, making it immoral to perform tests on unknowing patients. Medical research should be motivated out of respect for the patient, so they must be informed of all facts, even if this would be likely to dissuade the patient.


title: Kantian ethics

text: Jeremy Sugarman has argued that Kant's formulation of autonomy requires that patients are never used merely for the benefit of society, but are always treated as rational people with their own goals. Aaron E. Hinkley notes that a Kantian account of autonomy requires respect for choices that are arrived at rationally, not for choices which are arrived at by idiosyncratic or non-rational means. He argues that there may be some difference between what a purely rational agent would choose and what a patient actually chooses, the difference being the result of non-rational idiosyncrasies. Although a Kantian physician ought not to lie to or coerce a patient, Hinkley suggests that some form of paternalism—such as through withholding information which may prompt a non-rational response—could be acceptable.


title: Kantian ethics

text: In "How Kantian Ethics Should Treat Pregnancy and Abortion", Susan Feldman argues that abortion should be defended according to Kantian ethics. She proposes that a woman should be treated as a dignified autonomous person, with control over their body, as Kant suggested. She believes that the free choice of women would be paramount in Kantian ethics, requiring abortion to be the mother's decision.


title: Kantian ethics

text: Dean Harris has noted that, if Kantian ethics is to be used in the discussion of abortion, it must be decided whether a fetus is an autonomous person. Kantian ethicist Carl Cohen argues that the potential to be rational or participation in a generally rational species is the relevant distinction between humans and inanimate objects or irrational animals. Cohen believes that even when humans are not rational because of age (such as babies or fetuses) or mental disability, agents are still morally obligated to treat them as an "ends in themselves", equivalent to a rational adult such as a mother seeking an abortion.


title: Kantian ethics

text: Kant viewed humans as being subject to the animalistic desires of self-preservation, species-preservation, and the preservation of enjoyment. He argued that humans have a duty to avoid maxims that harm or degrade themselves, including suicide, sexual degradation, and drunkenness. This led Kant to regard sexual intercourse as degrading because it reduces humans to an object of pleasure. He admitted sex only within marriage, which he regarded as "a merely animal union." He believed that masturbation is worse than suicide, reducing a person's status to below that of an animal; he argued that rape should be punished with castration and that bestiality requires expulsion from society.


title: Kantian ethics

text: Feminist philosopher Catharine MacKinnon has argued that many contemporary practices would be deemed immoral by Kant's standards because they dehumanize women. Sexual harassment, prostitution, and pornography, she argues, objectify women and do not meet Kant's standard of human autonomy. Commercial sex has been criticised for turning both parties into objects (and thus using them as a means to an end); mutual consent is problematic because in consenting, people choose to objectify themselves. Alan Soble has noted that more liberal Kantian ethicists believe that, depending on other contextual factors, the consent of women can vindicate their participation in pornography and prostitution.


title: Kantian ethics

text: Because Kant viewed rationality as the basis for being a moral patient—one due moral consideration—he believed that animals have no moral rights. Animals, according to Kant, are not rational, thus one cannot behave immorally towards them. Although he did not believe we have any duties towards animals, Kant did believe being cruel to them was wrong because our behaviour might influence our attitudes toward human beings: if we become accustomed to harming animals, then we are more likely to see harming humans as acceptable.


title: Kantian ethics

text: Ethicist Tom Regan rejected Kant's assessment of the moral worth of animals on three main points: First, he rejected Kant's claim that animals are not self-conscious. He then challenged Kant's claim that animals have no intrinsic moral worth because they cannot make a moral judgment. Regan argued that, if a being's moral worth is determined by its ability to make a moral judgment, then we must regard humans who are incapable of moral thought as being equally undue moral consideration. Regan finally argued that Kant's assertion that animals exist merely as a means to an end is unsupported; the fact that animals have a life that can go well or badly suggests that, like humans, they have their own ends.


title: Kantian ethics

text: Christine Korsgaard has reinterpreted Kantian theory to argue that animal rights are implied by his moral principles.


title: Kantian ethics

text: Kant believed that the Categorical Imperative provides us with the maxim that we ought not to lie in any circumstances, even if we are trying to bring about good consequences, such as lying to a murderer to prevent them from finding their intended victim. Kant argued that, because we cannot fully know what the consequences of any action will be, the result might be unexpectedly harmful. Therefore, we ought to act to avoid the known wrong—lying—rather than to avoid a potential wrong. If there are harmful consequences, we are blameless because we acted according to our duty. Driver argues that this might not be a problem if we choose to formulate our maxims differently: the maxim 'I will lie to save an innocent life' can be universalized. However, this new maxim may still treat the murderer as a means to an end, which we have a duty to avoid doing. Thus we may still be required to tell the truth to the murderer in Kant's example.


title: Jagjit Singh

text: Jagjit Singh (born Jagmohan Singh Dhiman; 8 February 1941 – 10 October 2011) was an Indian composer, singer and musician. He composed and sang in numerous languages and is credited for the revival and popularity of ghazal, an Indian classical art form, by choosing poetry that was relevant to the masses and composing them in a way that laid more emphasis on the meaning of words and melody evoked by them. In terms of Indian classical music, his style of composing and "gayaki" (singing) is considered as "Bol-pradhan", one that lays emphasis on words. He highlighted this in his music for films such as "Prem Geet" (1981), "Arth (1982)", and ""Saath Saath"" (1982), and TV serials "Mirza Ghalib" (1988) and "Kahkashan" (1991). Singh is considered to be the most successful ghazal singer and composer of all time in terms of critical acclaim and commercial success. With a career spanning five decades and many albums, the range and breadth of his work has been regarded as genre-defining.


title: Jagjit Singh

text: Singh's 1987 album, "Beyond Time", was the first digitally recorded release in India. He was regarded as one of India's most influential artists. With sitar player Ravi Shankar and other leading figures of Indian classical music and literature, Singh voiced his concerns over politicisation of arts and culture in India and lack of support experienced by the practitioners of India's traditional art forms, particularly folk artists and musicians. He lent active support to several philanthropic endeavours such as the library at St. Mary's School, Mumbai, Bombay Hospital, CRY, Save the Children and ALMA.


title: Jagjit Singh

text: Singh was awarded the Padma Bhushan by the government of India in 2003 and in February 2014, the government released a set of two postal stamps in his honour.


title: Jagjit Singh

text: Jagjit Singh Dhiman was born at Sri Ganganagar, Rajasthan, India (then Bikaner State). His father, Sardar Amar Singh Dhiman, was a surveyor with the government's Public Works' Department and hailed from village Dalla in Ropar district of Punjab.


title: Jagjit Singh

text: Educated initially at Khalsa High School and Government College in Sri Ganganagar, Singh obtained an arts degree from DAV College, Jalandhar. There, he began his professional career in 1961 by undertaking singing and composing assignments at All India Radio's (AIR) Jalandhar station. Later, he studied to obtain a post-graduate degree in history from Kurukshetra University in Haryana. Throughout this time, and as a consequence of a natural talent that was spotted by his father, Singh learned music initially from a visually impaired master of Indian classical music, "Pandit Chagan Lal Sharma" and later from "Ustad Jamal Khan" of Maihar gharana, who taught and trained him in all the prominent styles of Hindustani Classical vocal tradition such as Khayal, Dhrupad, Thumri and others. Throughout his teenage years, he performed on stage and composed music. Although his father, who was a government employee, had hoped that he would become an engineer, Singh pursued his passion for music relentlessly. Like all parents in Indian middle-class families, his father aspired for him to become a bureaucrat. However, he also encouraged Singh and his siblings to learn music.


title: Jagjit Singh

text: In March 1965, and without the knowledge of his family, Singh moved to Bombay, where there were many opportunities for music artists because of the Hindi film industry. He obtained work initially as a singer of advertising jingles and later progressed to playback singing.


title: Jagjit Singh

text: Singh was still struggling to make a living in 1967 when he met the Bengali-born Chitra Dutta. She divorced her husband and married Singh in December 1969. Following the birth of their son, Vivek, the couple performed as a singing duo but it was not until the 1977 release of the album "The Unforgettable" that they found significant, and surprising, success. In the interval, the primary difficulty for them had been that the ghazal music genre was dominated by Muslim artists and especially those from Pakistan.


title: Jagjit Singh

text: "The Unforgettable", which was the couple's first LP, was an unconventional recording and it turned them into stars. The song "Baat Niklegi" from the album achieved great popularity for the Singhs. "The Independent" described it in 2011 as "ground-breaking ... it became a transformative, before-and-after milestone in the history of Indian popular and ghazals music. It remains that." Using modern arrangements, it consists of ten tracks that include two on which they sang as a duo and the remainder equally split between Jagjit and Chitra singing the lead. "The Independent" further noted that "This format of solo and duet performances from the first commercially successful husband-and-wife team in Indian popular music proved astonishingly successful." Jagjit explained that "I was determined to polish up the genre and make it more acceptable to modern tastes, so chose simple poems and set them to simple tunes. I also introduced western instrumentation to make them livelier." Thereafter, the couple worked both on solo and joint musical projects and performed concerts worldwide. There was success from involvement with the film industry and they amassed considerable wealth.


title: Jagjit Singh

text: Among their subsequent duo recordings of the 1970s were "Shiv Kumar Batalvi – Birha da Sultan" (1978), "Live in Concert at Wembley" (1979) and "Come Alive" (1979). Of those released in the 1980s, "The Latest" by Sudarshan Faakir was the best selling album with his lifetime hit "Woh Kagaz ki Kashti...Woh Baarish ka Paani". It was the first album by the duo with poetry of only one Poet. "Ecstasies" (1984) has also been described as "one of their finest". The joint projects ceased in 1990 when their 20-year-old son, Vivek, died in a road accident. Chitra felt unable to sing following these events. Monica, Chitra's daughter from her first marriage, committed suicide in 2009.


title: Jagjit Singh

text: Although Jagjit continued to work and to have success after Chitra withdrew from public life he, too, was affected by the death of Vivek. "The Guardian" notes that he "suffered from deep depression and his anguish was often evident in his live performances." Aside from occupying himself with solo projects, which he performed in several languages, he collaborated with Lata Mangeshkar on an album titled "Sajda", an Urdu word meaning "prostration".


title: Jagjit Singh

text: Singh's work in film encompassed playback singing for productions such as "Arth", ""Saath Saath"" and "Premgeet". He composed all of the songs for the latter, as well as for the TV serial "Mirza Ghalib" that was based on the life of the eponymous poet, Mirza Ghalib.


title: Jagjit Singh

text: On 10 May 2007, in the presence of numerous political and diplomatic luminaries at an event held in the Central Hall of the Parliament of India, Jagjit Singh rendered Bahadur Shah Zafar's famous ghazal "Lagta nahin hai dil mera" to commemorate the 150th anniversary of the Indian Rebellion of 1857.


title: Jagjit Singh

text: In 1990, Vivek (Jagjit Singh and Chitra's son) died in a road accident at the age of 20. This came as a profound shock to Jagjit and Chitra Singh. They gave up music for a full year after the death. At the end of that period, Jagjit returned slowly to music, but Chitra announced her retirement and declared that she would not sing or record any more songs.


title: Jagjit Singh

text: Singh had suffered from numerous ailments like diabetes and hypertension during his later life, and had undergone two heart bypass surgeries in 1998 and 2007. A chain smoker for decades, he had stopped smoking after his first heart attack.


title: Jagjit Singh

text: Singh turned 70 in February 2011. To celebrate his 70th birthday he committed 70 concerts in different parts of the world. He toured the UK, Singapore, Mauritius, inter alias, in 2011 and was due to perform with Ghulam Ali in Mumbai but suffered a brain haemorrhage on 23 September 2011. He was in coma for over two weeks and died on 10 October at Lilavati Hospital, in Mumbai. He was cremated the following day at Chandanwadi Crematorium near Marine Lines in Mumbai.


title: Jagjit Singh

text: A number of tributes have been paid to Singh after his death, and some tried to cash in on his popularity, which was criticised by his wife.


title: Jagjit Singh

text: A biography of Singh, entitled "Beyond Time" based on about 40 hours of interviews with him, was released in 2012. It was transcribed and edited by Ashrani Mathur.


title: Jagjit Singh

text: A biopic documentary by the name of "Kaagaz Ki Kashti" has been made on the life journey of Jagjit Singh, who broke through the norms and revolutionised the Ghazal scenario. The film traces the struggle and stardom in his musical career, the love & loss in his personal life and the scope and limitations in the music scenario of the times. The film directed by Brahmanand S Singh is currently available on Amazon Prime Video in India and worldwide.


title: Thought experiment

text: A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.


title: Thought experiment

text: The ancient Greek "deiknymi" (), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment.


title: Thought experiment

text: Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the German term ' (lit. thought experiment) circa 1812. Ørsted was also the first to use the equivalent term ' in 1820.


title: Thought experiment

text: By 1883 Ernst Mach used the term "" in a different way, to denote exclusively the conduct of a experiment that would be subsequently performed as a by his students. Physical and mental experimentation could then be contrasted: Mach asked his students to provide him with explanations whenever the results from their subsequent, real, physical experiment differed from those of their prior, imaginary experiment.


title: Thought experiment

text: The English term "thought experiment" was coined (as a calque) from Mach's "", and it first appeared in the 1897 English translation of one of Mach's papers. Prior to its emergence, the activity of posing hypothetical questions that employed subjunctive reasoning had existed for a very long time (for both scientists and philosophers). The irrealis moods are ways to categorize it or to speak about it. This helps explain the extremely wide and diverse range of the application of the term "thought experiment" once it had been introduced into English.


title: Thought experiment

text: Perhaps the key experiment in the history of modern science is Galileo's demonstration that falling objects must fall at the same rate regardless of their masses. This is widely thought to have been a straightforward physical demonstration, involving climbing up the Leaning Tower of Pisa and dropping two heavyweights off it, whereas in fact, it was a logical demonstration, using the 'thought experiment' technique. The 'experiment' is described by Galileo in "Discorsi e dimostrazioni matematiche" (1638) (literally, 'Mathematical Discourses and Demonstrations') thus:


title: Thought experiment

text: Although the extract does not convey the elegance and power of the 'demonstration' terribly well, it is clear that it is a 'thought' experiment, rather than a practical one. Strange then, as Cohen says, that philosophers and scientists alike refuse to acknowledge either Galileo in particular or the thought experiment technique in general for its pivotal role in both science and philosophy. (The exception proves the rule – the iconoclastic philosopher of science, Paul Feyerabend, has also observed this methodological prejudice.) Instead, many philosophers prefer to consider 'Thought Experiments' to be merely the use of a hypothetical scenario to help understand the way things are.


title: Thought experiment

text: The common goal of a thought experiment is to explore the potential consequences of the principle in question:


title: Thought experiment

text: Given the structure of the experiment, it may not be possible to perform it, and even if it could be performed, there need not be an intention to perform it.


title: Thought experiment

text: Examples of thought experiments include Schrödinger's cat, illustrating quantum indeterminacy through the manipulation of a perfectly sealed environment and a tiny bit of radioactive substance, and Maxwell's demon, which attempts to demonstrate the ability of a hypothetical finite being to violate the 2nd law of thermodynamics.


title: Thought experiment

text: Thought experiments, which are well-structured, well-defined hypothetical questions that employ subjunctive reasoning (irrealis moods) – "What might happen (or, what might have happened) if . . . " – have been used to pose questions in philosophy at least since Greek antiquity, some pre-dating Socrates. In physics and other sciences many thought experiments date from the 19th and especially the 20th Century, but examples can be found at least as early as Galileo.


title: Thought experiment

text: In thought experiments, we gain new information by rearranging or reorganizing already known empirical data in a new way and drawing new (a priori) inferences from them or by looking at these data from a different and unusual perspective. In Galileo's thought experiment, for example, the rearrangement of empirical experience consists of the original idea of combining bodies of different weights.


title: Thought experiment

text: Thought experiments have been used in philosophy (especially ethics), physics, and other fields (such as cognitive psychology, history, political science, economics, social psychology, law, organizational studies, marketing, and epidemiology). In law, the synonym "hypothetical" is frequently used for such experiments.


title: Thought experiment

text: Regardless of their intended goal, all thought experiments display a patterned way of thinking that is designed to allow us to explain, predict and control events in a better and more productive way.


title: Thought experiment

text: Thought experiments can produce some very important and different outlooks on previously unknown or unaccepted theories. However, they may make those theories themselves irrelevant, and could possibly create new problems that are just as difficult, or possibly more difficult to resolve.


title: Thought experiment

text: Generally speaking, there are seven types of thought experiments in which one reasons from causes to effects, or effects to causes:


title: Thought experiment

text: "Prefactual (before the fact) thought experiments" – the term prefactual was coined by Lawrence J. Sanna in 1998 — speculate on possible future outcomes, given the present, and ask "What will be the outcome if event E occurs?"


title: Thought experiment

text: "Counterfactual (contrary to established fact) thought experiments" – the term "counterfactual" was coined by Nelson Goodman in 1947, extending Roderick Chisholm's (1946) notion of a "contrary-to-fact conditional" – speculate on the possible outcomes of a different past; and ask "What might have happened if A had happened instead of B?" (e.g., "If Isaac Newton and Gottfried Leibniz had cooperated with each other, what would mathematics look like today?").


title: Thought experiment

text: The study of counterfactual speculation has increasingly engaged the interest of scholars in a wide range of domains such as philosophy, psychology, cognitive psychology, history, political science, economics, social psychology, law, organizational theory, marketing, and epidemiology.


title: Thought experiment

text: "Semifactual thought experiments" – the term "semifactual" was coined by Nelson Goodman in 1947 – speculate on the extent to which things might have remained the same, despite there being a different past; and asks the question Even though X happened instead of E, would Y have still occurred? (e.g., Even if the goalie had moved left, rather than right, could he have intercepted a ball that was traveling at such a speed?).


title: Thought experiment

text: The activity of prediction attempts to project the circumstances of the present into the future. According to David Sarewitz and Roger Pielke (1999, p123), scientific prediction takes two forms:


title: Thought experiment

text: Although they perform different social and scientific functions, the only difference between the qualitatively identical activities of "predicting", "forecasting," and "nowcasting" is the distance of the speculated future from the present moment occupied by the user. Whilst the activity of nowcasting, defined as "a detailed description of the current weather along with forecasts obtained by extrapolation up to 2 hours ahead", is essentially concerned with describing the current state of affairs, it is common practice to extend the term "to cover very-short-range forecasting up to 12 hours ahead" (Browning, 1982, p.ix).


title: Thought experiment

text: The activity of hindcasting involves running a forecast model after an event has happened in order to test whether the model's simulation is valid.


title: Thought experiment

text: The activity of "retrodiction" (or "postdiction") involves moving backward in time, step-by-step, in as many stages as are considered necessary, from the present into the speculated past to establish the ultimate cause of a specific event (e.g., reverse engineering and forensics).


title: Thought experiment

text: Given that retrodiction is a process in which "past observations, events, add and data are used as evidence to infer the process(es) that produced them" and that diagnosis "involve[s] going from visible effects such as symptoms, signs and the like to their prior causes", the essential balance between prediction and retrodiction could be characterized as:


title: Thought experiment

text: regardless of whether the prognosis is of the course of the disease in the absence of treatment, or of the application of a specific treatment regimen to a specific disorder in a particular patient.


title: Thought experiment

text: The activity of "backcasting" – the term "backcasting" was coined by John Robinson in 1982 — involves establishing the description of a very definite and very specific future situation. It then involves an imaginary moving backward in time, step-by-step, in as many stages as are considered necessary, from the future to the present to reveal the mechanism through which that particular specified future could be attained from the present.


title: Thought experiment

text: Thought experiments have been used in a variety of fields, including philosophy, law, physics, and mathematics. In philosophy they have been used at least since classical antiquity, some pre-dating Socrates. In law, they were well known to Roman lawyers quoted in the Digest. In physics and other sciences, notable thought experiments date from the 19th and especially the 20th century, but examples can be found at least as early as Galileo.


title: Thought experiment

text: In philosophy, a thought experiment typically presents an imagined scenario with the intention of eliciting an intuitive or reasoned response about the way things are in the thought experiment. (Philosophers might also supplement their thought experiments with theoretical reasoning designed to support the desired intuitive response.) The scenario will typically be designed to target a particular philosophical notion, such as morality, or the nature of the mind or linguistic reference. The response to the imagined scenario is supposed to tell us about the nature of that notion in any scenario, real or imagined.


title: Thought experiment

text: For example, a thought experiment might present a situation in which an agent intentionally kills an innocent for the benefit of others. Here, the relevant question is not whether the action is moral or not, but more broadly whether a moral theory is correct that says morality is determined solely by an action's consequences (See Consequentialism). John Searle imagines a man in a locked room who receives written sentences in Chinese, and returns written sentences in Chinese, according to a sophisticated instruction manual. Here, the relevant question is not whether or not the man understands Chinese, but more broadly, whether a functionalist theory of mind is correct.


title: Thought experiment

text: It is generally hoped that there is universal agreement about the intuitions that a thought experiment elicits. (Hence, in assessing their own thought experiments, philosophers may appeal to "what we should say," or some such locution.) A successful thought experiment will be one in which intuitions about it are widely shared. But often, philosophers differ in their intuitions about the scenario.


title: Thought experiment

text: Other philosophical uses of imagined scenarios arguably are thought experiments also. In one use of scenarios, philosophers might imagine persons in a particular situation (maybe ourselves), and ask what they would do.


title: Thought experiment

text: For example, in the veil of ignorance, John Rawls asks us to imagine a group of persons in a situation where they know nothing about themselves, and are charged with devising a social or political organization. The use of the state of nature to imagine the origins of government, as by Thomas Hobbes and John Locke, may also be considered a thought experiment. Søren Kierkegaard explored the possible ethical and religious implications of Abraham's binding of Isaac in "Fear and Trembling". Similarly, Friedrich Nietzsche, in "On the Genealogy of Morals", speculated about the historical development of Judeo-Christian morality, with the intent of questioning its legitimacy.


title: Thought experiment

text: An early written thought experiment was Plato's allegory of the cave. Another historic thought experiment was Avicenna's "Floating Man" thought experiment in the 11th century. He asked his readers to imagine themselves suspended in the air isolated from all in order to demonstrate human self-awareness and self-consciousness, and the substantiality of the soul.


title: Thought experiment

text: Scientists tend to use thought experiments as imaginary, "proxy" experiments prior to a real, "physical" experiment (Ernst Mach always argued that these gedankenexperiments were "a necessary precondition for physical experiment"). In these cases, the result of the "proxy" experiment will often be so clear that there will be no need to conduct a physical experiment at all.


title: Thought experiment

text: Scientists also use thought experiments when particular physical experiments are impossible to conduct (Carl Gustav Hempel labeled these sorts of experiment ""theoretical experiments-in-imagination""), such as Einstein's thought experiment of chasing a light beam, leading to special relativity. This is a unique use of a scientific thought experiment, in that it was never carried out, but led to a successful theory, proven by other empirical means.


title: Thought experiment

text: In many thought experiments, the scenario would be nomologically possible, or possible according to the laws of nature. John Searle's Chinese room is nomologically possible.


title: Thought experiment

text: Some thought experiments present scenarios that are not nomologically possible. In his Twin Earth thought experiment, Hilary Putnam asks us to imagine a scenario in which there is a substance with all of the observable properties of water (e.g., taste, color, boiling point), but is chemically different from water. It has been argued that this thought experiment is not nomologically possible, although it may be possible in some other sense, such as metaphysical possibility. It is debatable whether the nomological impossibility of a thought experiment renders intuitions about it moot.


title: Thought experiment

text: In some cases, the hypothetical scenario might be considered metaphysically impossible, or impossible in any sense at all. David Chalmers says that we can imagine that there are zombies, or persons who are physically identical to us in every way but who lack consciousness. This is supposed to show that physicalism is false. However, some argue that zombies are inconceivable: we can no more imagine a zombie than we can imagine that 1+1=3. Others have claimed that the conceivability of a scenario may not entail its possibility.


title: Thought experiment

text: The relation to real experiments can be quite complex, as can be seen again from an example going back to Albert Einstein. In 1935, with two coworkers, he published a paper on a newly created subject called later the EPR effect (EPR paradox). In this paper, starting from certain philosophical assumptions, on the basis of a rigorous analysis of a certain, complicated, but in the meantime assertedly realizable model, he came to the conclusion that "quantum mechanics should be described as "incomplete"". Niels Bohr asserted a refutation of Einstein's analysis immediately, and his view prevailed. After some decades, it was asserted that feasible experiments could prove the error of the EPR paper. These experiments tested the Bell inequalities published in 1964 in a purely theoretical paper. The above-mentioned EPR philosophical starting assumptions were considered to be falsified by the empirical fact (e.g. by the optical "real experiments" of Alain Aspect).


title: Thought experiment

text: Thus "thought experiments" belong to a theoretical discipline, usually to theoretical physics, but often to theoretical philosophy. In any case, it must be distinguished from a real experiment, which belongs naturally to the experimental discipline and has "the final decision on "true" or "not true"", at least in physics.


title: Thought experiment

text: Thought experiments can also be interactive where the author invites people into his thought process through providing alternative paths with alternative outcomes within the narrative, or through interaction with a programmed machine, like a computer program.


title: Thought experiment

text: Thanks to the advent of the Internet, the digital space has lent itself as a new medium for a new kind of thought experiments. The philosophical work of Stefano Gualeni, for example, focuses on the use of virtual worlds to materialize thought experiments and to playfully negotiate philosophical ideas. His arguments were originally presented in his book "Virtual Worlds as Philosophical Tools".


title: Thought experiment

text: Gualeni's argument is that the history of philosophy has, until recently, merely been the history of written thought, and digital media can complement and enrich the limited and almost exclusively linguistic approach to philosophical thought. He considers virtual worlds to be philosophically viable and advantageous in contexts like those of thought experiments, when the recipients of a certain philosophical notion or perspective are expected to objectively test and evaluate different possible courses of action, or in cases where they are confronted with interrogatives concerning non-actual or non-human phenomenologies.


title: Airfoil

text: An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine.


title: Airfoil

text: A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils.


title: Airfoil

text: The lift on an airfoil is primarily the result of its angle of attack. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flowfield about the airfoil has a higher average velocity on the upper surface than on the lower surface. In some situations (e.g. inviscid potential flow) the lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta–Joukowski theorem.


title: Airfoil

text: The wings and stabilizers of fixed-wing aircraft, as well as helicopter rotor blades, are built with airfoil-shaped cross sections. Airfoils are also found in propellers, fans, compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the centerboard, rudder, and keel, are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of fish, and the shape of sand dollars. An airfoil-shaped wing can create downforce on an automobile or other motor vehicle, improving traction.


title: Airfoil

text: When the wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience drag and also an aerodynamic force perpendicular to the wind. This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag. Airfoils are used in the design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering.


title: Airfoil

text: A lift and drag curve obtained in wind tunnel testing is shown on the right. The curve represents an airfoil with a positive camber so some lift is produced at zero angle of attack. With increased angle of attack, lift increases in a roughly linear relation, called the "slope" of the lift curve. At about 18 degrees this airfoil stalls, and lift falls off quickly beyond that. The drop in lift can be explained by the action of the upper-surface boundary layer, which separates and greatly thickens over the upper surface at and past the stall angle. The thickened boundary layer's displacement thickness changes the airfoil's effective shape, in particular it reduces its effective camber, which modifies the overall flow field so as to reduce the circulation and the lift. The thicker boundary layer also causes a large increase in pressure drag, so that the overall drag increases sharply near and past the stall point.


title: Airfoil

text: Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better suit frequent inverted flight as in an aerobatic airplane. In the region of the ailerons and near a wingtip a symmetric airfoil can be used to increase the range of angles of attack to avoid spin–stall. Thus a large range of angles can be used without boundary layer separation. Subsonic airfoils have a round leading edge, which is naturally insensitive to the angle of attack. The cross section is not strictly circular, however: the radius of curvature is increased before the wing achieves maximum thickness to minimize the chance of boundary layer separation. This elongates the wing and moves the point of maximum thickness back from the leading edge.


title: Airfoil

text: Supersonic airfoils are much more angular in shape and can have a very sharp leading edge, which is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness close to the leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic speeds. Generally such transonic airfoils and also the supersonic airfoils have a low camber to reduce drag divergence. Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing.


title: Airfoil

text: Movable high-lift devices, flaps and sometimes slats, are fitted to airfoils on almost every aircraft. A trailing edge flap acts similarly to an aileron; however, it, as opposed to an aileron, can be retracted partially into the wing if not used.


title: Airfoil

text: A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the Navier–Stokes equations in the linear regime shows that a negative pressure gradient along the flow has the same effect as reducing the speed. So with the maximum camber in the middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising speed is possible. However, some surface contamination will disrupt the laminar flow, making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under certain conditions, insect debris on the wing will cause the loss of small regions of laminar flow as well. Before NASA's research in the 1970s and 1980s the aircraft design community understood from application attempts in the WW II era that laminar flow wing designs were not practical using common manufacturing tolerances and surface imperfections. That belief changed after new manufacturing methods were developed with composite materials (e.g. laminar-flow airfoils developed by Professor Franz Wortmann for use with wings made of fibre-reinforced plastic). Machined metal methods were also introduced. NASA's research in the 1980s revealed the practicality and usefulness of laminar flow wing designs and opened the way for laminar-flow applications on modern practical aircraft surfaces, from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic designs.


title: Airfoil

text: Schemes have been devised to define airfoils – an example is the NACA system. Various airfoil generation systems are also used. An example of a general purpose airfoil that finds wide application, and pre–dates the NACA system, is the Clark-Y. Today, airfoils can be designed for specific functions by the use of computer programs.


title: Airfoil

text: Some important parameters to describe an airfoil's shape are its "camber" and its "thickness". For example, an airfoil of the NACA 4-digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness.


title: Airfoil

text: Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are:


title: Airfoil

text: Thin airfoil theory is a simple theory of airfoils that relates angle of attack to lift for incompressible, inviscid flows. It was devised by German mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan.


title: Airfoil

text: Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional inviscid flow:


title: Airfoil

text: As a consequence of (3), the section lift coefficient of a symmetric airfoil of infinite wingspan is:


title: Airfoil

text: Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is:


title: Airfoil

text: Thin airfoil theory does not account for the stall of the airfoil, which usually occurs at an angle of attack between 10° and 15° for typical airfoils. In the mid-late 2000s, however, a theory predicting the onset of leading-edge stall was proposed by Wallace J. Morris II in his doctoral thesis. Morris's subsequent refinements contain the details on the current state of theoretical knowledge on the leading-edge stall phenomenon. Morris's theory predicts the critical angle of attack for leading-edge stall onset as the condition at which a global separation zone is predicted in the solution for the inner flow. Morris's theory demonstrates that a subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil chord, and an inner region, around the nose, that asymptotically match each other. As the flow in the outer region is dominated by classical thin airfoil theory, Morris's equations exhibit many components of thin airfoil theory.


title: Airfoil

text: The airfoil is modeled as a thin lifting mean-line (camber line). The mean-line, "y"("x"), is considered to produce a distribution of vorticity formula_9 along the line, "s". By the Kutta condition, the vorticity is zero at the trailing edge. Since the airfoil is thin, "x" (chord position) can be used instead of "s", and all angles can be approximated as small.


title: Airfoil

text: formula_12 is the location where induced velocity is produced, formula_13 is the location of the vortex element producing the velocity and formula_1 is the chord length of the airfoil.


title: Airfoil

text: Since there is no flow normal to the curved surface of the airfoil, formula_10 balances that from the component of main flow formula_16, which is locally normal to the plate – the main flow is locally inclined to the plate by an angle formula_17. That is:


title: Airfoil

text: The aerodynamic center, AC, is at the quarter-chord point. The AC is where the pitching moment "M"′ does not "vary" with a change in lift coefficient, i.e.,


title: Subset

text: In mathematics, set "A" is a subset of a set "B" if all elements of "A" are also elements of "B"; "B" is then a superset of "A". It is possible for "A" and "B" to be equal; if they are unequal, then "A" is a proper subset of "B". The relationship of one set being a subset of another is called inclusion (or sometimes containment). "A" is a subset of "B" may also be expressed as "B" includes (or contains) "A" or "A" is included (or contained) in "B". A "k"-subset is a subset with "k" elements.


title: Subset

text: The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation.


title: Subset

text: If "A" is a subset of "B", but "A" is not equal to "B" (i.e. there exists at least one element of B which is not an element of "A"), then:


title: Subset

text: The empty set, written formula_5 or formula_6 is a subset of any set "X" and a proper subset of any set except itself, the inclusion relation formula_7 is a partial order on the set formula_8 (the power set of "S"—the set of all subsets of "S") defined by formula_9. We may also partially order formula_8 by reverse set inclusion by defining formula_11


title: Subset

text: We can prove the statement formula_1 by applying a proof technique known as the element argument:Let sets "A" and "B" be given. To prove that formula_15


title: Subset

text: The validity of this technique can be seen as a consequence of Universal generalization: the technique shows formula_16 for an arbitrarily chosen element "c". Universal generalisation then implies formula_17 which is equivalent to formula_15 as stated above.


title: Subset

text: The set of all subsets of formula_19 is called its powerset, and is denoted by formula_20. The set of all formula_21-subsets of formula_19 is denoted by formula_23, in analogue with the notation for binomial coefficients, which count the number of formula_21-subsets of an formula_25-element set. In set theory, the notation formula_26 is also common, especially when formula_21 is a transfinite cardinal number.


title: Subset

text: Some authors use the symbols formula_31 and formula_32 to indicate and respectively; that is, with the same meaning as and instead of the symbols formula_7 and formula_34 For example, for these authors, it is true of every set "A" that formula_35