title: Newcastle, New South Wales

text: Winters are generally mild with drier conditions than summer on average. Cold fronts affect the area and sometimes bring strong westerly winds behind them, but due to the foehn effect they generally provide clear conditions as the region lies leeward of the Great Dividing Range. The lowest temperature ever recorded was in July 1986. East coast lows also impact Newcastle, sometimes delivering winds well above and torrential rainfall, usually lasting a couple of days. The east coast low in May 1974, the June 2007 Hunter Region and Central Coast storms and April 2015 are extreme examples of this type of weather.


title: Newcastle, New South Wales

text: In the 2021 Australian Census updated population figures on the Newcastle and Hunter Region were provided. What is generally labeled as the 'Greater Newcastle Area' includes the LGAs of Newcastle, Lake Macquarie, Maitland, Cessnock and Port Stephens. In 2021 this region had a total population of 619,653.


title: Newcastle, New South Wales

text: 83.6% of people in the Newcastle metropolitan area were born in Australia. The next most common countries of birth were England 2.3%, New Zealand 1.0%, China 0.7%, India 0.5% and Philippines 0.4%. Aboriginal and Torres Strait Islander people made up 3.8% of the population. 88.2% of people spoke only English at home. Other languages spoken at home included Mandarin 0.7%, Macedonian 0.5%, Italian 0.4%, Greek 0.3% and Cantonese 0.3%. The most common responses for religion in Newcastle were No Religion 31.1%, Catholic 21.7% and Anglican 19.2%.


title: Newcastle, New South Wales

text: Newcastle is often quoted as being the seventh largest city in Australia. This is misleading as the area represented extends well beyond both the City of Newcastle and the Newcastle metropolitan area. The area, officially the Newcastle Statistical District, is referred to as Greater Newcastle or the Lower Hunter Region, which includes most parts of the Newcastle, Lake Macquarie, Cessnock, Maitland and Port Stephens local government areas and, as of 30 June 2009, has an estimated population of 540,796. Despite their proximity, all of the LGAs in the region maintain their own individual identities, separate from Newcastle.


title: Newcastle, New South Wales

text: The demonym for the people of Newcastle is "Novocastrian", derived from Latin "novus" (new) and "castra" (castle or fort).


title: Newcastle, New South Wales

text: The oldest state school in the area is Newcastle East Public School, a primary school established in 1816. Newcastle East Public School is the oldest continuously operating school in Australia, and celebrated its bicentenary in 2016.


title: Newcastle, New South Wales

text: Newcastle High School, which was formed by the merger of three schools, traces its lineage to a secondary school section initially founded on the grounds of Newcastle East Public School.


title: Newcastle, New South Wales

text: The two main independent schools in Newcastle are Newcastle Grammar School and St Philip's Christian College, both coeducational K-12 schools.


title: Newcastle, New South Wales

text: The local area is also home to two Steiner schools: the Newcastle Waldorf School at Glendale in Lake Macquarie, and the Linuwel Steiner School in East Maitland.


title: Newcastle, New South Wales

text: The city's main provider of tertiary education is the University of Newcastle. It was established in 1951 as a satellite campus of the University of New South Wales and obtained autonomy in 1965. The University now offers over 150 undergraduate and graduate courses to a student population of more than 38,000, including 7,000 international students from more than 113 countries. The main campus is in the suburb of Callaghan about from the CBD.


title: Newcastle, New South Wales

text: There are three campuses of the Hunter Institute of TAFE, one located in the Newcastle CBD, one in the suburb of Hamilton East and the other located in the suburb of Tighes Hill. The Tighes Hill campus is the network's largest campus and offers courses in business, hospitality and various trades.


title: Newcastle, New South Wales

text: The Newcastle Regional Show is held in the Newcastle Showground annually. There are a mixture of typical regional show elements such as woodchopping displays, showbags, rides and stalls and usually fireworks to complement the events in the main arena.


title: Newcastle, New South Wales

text: The Mattara festival, founded in 1961, is the official festival of Newcastle with a more traditional "country fair" type program that combines a parade, rides, sporting events, band competitions and portrait and landscape painting exhibitions. Mattara means "hand of friendship" in the local Awabakal language. Originally held at Civic Park and then moved to Newcastle foreshore in 2006 In 2017 the festival was moved to Wallsend Park.


title: Newcastle, New South Wales

text: The Newcastle Jazz Festival is held across three days in August, and attracts performers and audiences from all over Australia. The first festival was held in September 1988 as part the NSW Bicentenital Festival of Music which was organised by the Newcastle Jazz Action Society.


title: Newcastle, New South Wales

text: The Shoot Out 24 Hour Filmmaking Festival, first started in Newcastle in 1999. This is the film festival where film-makers come together in one place to make a short film in 24 hours. It is run annually in July.


title: Newcastle, New South Wales

text: This Is Not Art is a national festival of new media and arts held in Newcastle each year over the October long weekend. Since its humble beginnings in 1998, it has become one of the leading arts festivals in Australia dedicated to the work and ideas of communities not included in other major Australian arts festivals. The umbrella program includes the independent festivals Electrofringe, the National Young Writers' Festival, Critical Animals, Sound Summit, Crack Theatre Festival and other projects that vary from year to year.


title: Newcastle, New South Wales

text: The Newcastle Entertainment Centre, located inside the Newcastle Showground is a popular venue for regular events including wrestling, concerts and monster truck shows.


title: Newcastle, New South Wales

text: Newcastle has an active youth music culture, as well as a Conservatorium of Music which is part of the University of Newcastle. It continues to support local bands and has a large underground music scene. The members of Silverchair, the highly successful Australian band, hail from Newcastle, as do the Australian bands The Screaming Jets and Vacations. It has a fertile punk rock and hardcore scene, which has spawned successful local acts and national acts. Newcastle was also home to the short-lived band Velvet Underground which featured future AC/DC guitarist Malcolm Young.


title: Newcastle, New South Wales

text: Notable modernist artists associated with Newcastle are seascape sketcher Shay Docking (1928–1998), the cubist influenced abstract painter William Rose (1929–1999), landscape painter John Olsen, who was born in Newcastle in 1928, still- life painter Margaret Olley, portraitist William Dobell and figurative painter John Montefiore lived at Lake Macquarie to the south of the city. Art collector William Bowmore resided in Newcastle and collected Brett Whiteley paintings as well as owning a large collection of international art and artefacts. The Von Bertouch Galleries was a commercial gallery founded by Anne Von Bertouch and for more than forty years from 1963 exhibited nationally and locally known artists.


title: Newcastle, New South Wales

text: The Newcastle Art Gallery is home to one of Australia's most substantial public art collections outside a major capital city, and its extensive collection of works by contemporary and historical Australian visual artists presents an overview of Australian art. Due to an ongoing space issue, the gallery is planning a major redevelopment. The Lock Up is a multidisciplinary contemporary art space located in the inner city and hosts local, national and international artists to exhibit in the historic former Newcastle Police station.


title: Newcastle, New South Wales

text: Newcastle has a variety of smaller theatres, but the main theatre in the CBD is now the "Civic", at Wheeler Place, (seating capacity about 1500), one of Australia's great historic theatres built during 1929 in Art Deco style. It hosts a wide range of musicals, plays, concerts, dance and other events each year. Newcastle previously boasted several large theatres, among them the oldest purpose-built theatre in Australia, the Victoria Theatre on Perkins Street (built 1876, capacity 1750), saw touring international opera companies such as the D'Oyly Carte Opera Company, and other troupes, and played host to some of the greatest stars of the age, such as Dame Nellie Melba, Gladys Moncrieff, and Richard Tauber, (it is now closed and derelict); the "Century", Nineways, Broadmeadow, (built 1941, capacity 1800) although largely used as a cinema was a popular Symphony orchestra venue (demolished 1990 after being severely damaged by the 1989 earthquake); the "Hunter" (capacity 1,000) at The Junction, had advanced modern stage facilities, but was eventually sold and demolished to make way for a motel that was destroyed by the 1989 earthquake. The decline in theatres and cinemas from the 1960s onwards was blamed on television.


title: Newcastle, New South Wales

text: Newcastle has also been home to noted Australian actors, comedians and entertainers, including Sarah Wynter, John Doyle (part of comic act Roy & HG), Susie Porter, Celia Ireland, Yahoo Serious and Jonathan Biggins. The cast of the Tap Dogs show also come from Newcastle.


title: Newcastle, New South Wales

text: Newcastle is home to the Octapod Association, a New Media Arts collective established in 1996. Octapod presents the annual This Is Not Art Festival and is also home to the Podspace Gallery.


title: Newcastle, New South Wales

text: The Newcastle Museum was founded in 1988 in the former headquarters of the Great Northern Railway and stewards local history, culture, industry, and science. It features permanent exhibitions relating to coal mining and steel production, aboriginal history and the area's history, as well as a hands-on science centre.


title: Newcastle, New South Wales

text: Newcastle has had two teams in the National Basketball League, the Newcastle Falcons and The Hunter Pirates. Both teams folded due to financial difficulties. The city co-hosted the 1985 FIBA Oceania Championship where Australia's national basketball team won its seventh straight title.


title: Newcastle, New South Wales

text: A bid for Newcastle to establish a 2012 team in the national Twenty20 competition the Big Bash League, with games played at either Hunter Stadium or No.1 Sports Ground was unsuccessful.


title: Newcastle, New South Wales

text: Several different football codes are popular sports in Newcastle, with at least one having been played since the mid-1800s.


title: Newcastle, New South Wales

text: Rugby league is the most popular sport in Newcastle by a wide margin. Newcastle sports teams playing in national competitions include the Newcastle Knights, a team that plays in Australia's premier rugby league competition, the National Rugby League. The Knights play at McDonald Jones Stadium, situated in the suburb of . After an upgrade, the stadium now has capacity for almost 27,000 spectators. In May 2008, the NSW state government agreed to provide a further $20 million for further upgrades to increase the crowd capacity to 33,000 by end of 2010.


title: Newcastle, New South Wales

text: The Newcastle Rugby League holds local club competition and has done so since the early 1900s. Touring domestic and international teams would play against Newcastle's representative team which was made up of players from this League. The Newcastle & Hunter Rugby League is a community competition also based in the city which was created from a merger in 2007 of leagues which ran under various names since the mid 20th Century, and is the largest community Rugby League competition anywhere in the world. It generally features smaller teams compared to the Newcastle Rugby League.


title: Newcastle, New South Wales

text: Rugby union is a football code that has been played in Newcastle since at least 1869, with the Newcastle Football Club formed in 1877. Newcastle and Hunter Rugby Union is the main body overseeing the sport in the region. In 2019, the New South Wales Waratahs of the professional Super Rugby competition played a competition match in Newcastle at Hunter Stadium for the first time.


title: Newcastle, New South Wales

text: The Newcastle Jets Football Club, which plays in Australia's highest level soccer competition, the A-League, also play at McDonald Jones Stadium. The Newcastle Jets won the A-League competition in their third season, defeating local rivals the Central Coast Mariners in the grand final. The Jets are playing in the 2015/16 A-League season, and their eleventh in the Australian National Competition.


title: Newcastle, New South Wales

text: The city also played host to 4 games of the 2015 AFC Asian Cup, including the semi-final between Australia and the United Arab Emirates, as well as the 3rd place playoff between the United Arab Emirates and Iraq.


title: Newcastle, New South Wales

text: Newcastle Racecourse is in the suburb of Broadmeadow. It is home to the Newcastle Jockey Club, established in 1907, which () races 35 times annually at the spacious turf track with a home straight. It is the venue for three Group 3 races: in March is the Newcastle Newmarket Handicap; and in September the 1400-metre Cameron Handicap, and the Newcastle Gold Cup. In 2015 work an inner track, known as the Beaumont Track, was added.


title: Newcastle, New South Wales

text: Aboriginal jockey Merv Maynard commenced his career at Newcastle Racecourse, under Keith Tinson. Maynard enjoyed his first success in the 1948–49 season there, and went on to have a career spanning 50 years, winning the Newcastle Premiership twice, along with 1500 winning rides in four countries.


title: Newcastle, New South Wales

text: The Newcastle North Stars are Newcastle's representatives in the Australian Ice Hockey League championships. Originally based in Newcastle West in the 1970-80s, the North Stars now play out of the Hunter Ice Skating Stadium in Warners Bay.


title: Newcastle, New South Wales

text: Newcastle hosted the final round of the Supercars Championship in 2017. The Newcastle 500 is held on the Newcastle Street Circuit in the East End of the city. The city previously hosted the Mattara Hillclimb which was held in King Edward Park, and has hosted the F1 Offshore Powerboats in the harbour.


title: Newcastle, New South Wales

text: The Hunter Jaegers (Commonwealth Bank Trophy – Netball) were based at the Newcastle Entertainment Centre. They became defunct in 2007 after merging with the Sydney Swifts to become the NSW Swifts. Officially opened in June 1992, the Entertainment Centre offers 5,000 square metres of clear span floor space and is capable of catering for capacities from 2,000 to 6,500 for entertainment style events. The Centre was built to house the now defunct Newcastle Falcons National Basketball League team and was also home to the Hunter Pirates before a lack of sponsorship forced them to close after the 2005–06 season, with the licence sold to the Singapore Slingers. The Slingers played one home game at the Centre during the 2006–07 season.


title: Newcastle, New South Wales

text: Newcastle has an abundance of beaches and surf breaks for which the city is internationally well known. Newcastle hosts the annual surfing contest Surfest on the world professional surfing tour. Four time world champion surfer Mark Richards grew up surfing at Newcastle's Merewether Beach, and is a local icon, appearing at many local functions, and supporting local charities. Nobbys Beach is a very popular kitesurfing spot, especially during the warm summer months when there are northeasterly sea breezes.


title: Newcastle, New South Wales

text: Newcastle is served by a daily tabloid, "The Herald" (formerly "The Newcastle Morning Herald and Miners' Advocate" and then "The Newcastle Herald"), several weeklies including the "Newcastle Star", "The Post" and the bi-monthly "The Hunter Advocate".


title: Newcastle, New South Wales

text: Other alternative media in the city include the university's student publications Opus and Yak Magazine, Newcastle Mirage (a local arts and culture zine) and Urchin (a zine published by the media and arts organisation Octapod).


title: Newcastle, New South Wales

text: The city is also served by several local radio stations, including those owned by the Australian Broadcasting Corporation and SBS.


title: Newcastle, New South Wales

text: NBN produces an evening news bulletin combining local, state, national and international news screening nightly at 6.00 pm on Channel 9, due to NBN being an owner and operator of the network, Nine News' Sydney-based bulletin at 6 is not relayed on this station, but stories from the bulletin are shown on NBN News. Seven, Nine and WIN Television produce short local updates throughout the day to fulfil local content quotas.


title: Newcastle, New South Wales

text: Like most major cities, the Newcastle metropolitan area has an extensive system of both road links and road based public transport services (bus, taxi etc.) which cover most areas of both Newcastle and Lake Macquarie and which extend beyond the metropolitan area itself. Rail transport, however, is accessible to only a relatively small percentage of the population along the major rail transport routes and ferry services are restricted to those commuting between Newcastle and Stockton. Within the metropolitan area the car remains the dominant form of transportation. At the time of the 2001 Census, less than 4% of the population caught public transport, of which around 2.5% travelled by bus and 1% used the train or ferry to commute to work. On the other hand, over 72% of the population travelled by car to and from work. Newcastle, like all major Australian urban centres, had a tram system, but it was closed in 1950. In February 2019, trams returned to the city with the opening of the Newcastle Light Rail.


title: Newcastle, New South Wales

text: Newcastle is connected to surrounding cities by the Pacific Motorway (south), Hunter Expressway (west), New England Highway (west) and the Pacific Highway (north and south). Hunter Street is the main shopping street in the Newcastle CBD and, along with King Street, is one of the major links to the Pacific Highway from the CBD. King Street provides direct access to the Newcastle Link Road and then the Pacific Motorway and Hunter Expressway.


title: Newcastle, New South Wales

text: Bus services within Newcastle are operated by Newcastle Transport. Prior to July 2017, these were operated by Newcastle Buses & Ferries. Hunter Valley Buses, Port Stephens Coaches and Rover Coaches also operate services into the CBD from other parts of the Hunter Region.


title: Newcastle, New South Wales

text: The network radiates from a bus terminal near Newcastle railway station, on the waterfront of Newcastle's CBD. Major interchanges are located at the University of Newcastle, Wallsend, Glendale, Warners Bay, Belmont, Charlestown Square and Westfield Kotara.


title: Newcastle, New South Wales

text: The Newcastle area is serviced by two NSW TrainLink intercity lines providing local and regional commuter services terminating at Newcastle Interchange along the Newcastle line. The Central Coast & Newcastle Line has twice-hourly train services to Sydney and the Central Coast. The Hunter Line has twice-hourly services to Maitland and less frequently to Scone and Dungog. Two long-distance lines operate through the Newcastle area using Broadmeadow station. These provide services to Moree, Armidale, Brisbane and Sydney.


title: Newcastle, New South Wales

text: Newcastle once had rail passenger services to Belmont and Toronto, on Lake Macquarie, Wallsend, Kurri Kurri and several towns and villages between Maitland and Cessnock on the South Maitland Railway, but these lines have been closed. In the late-1990s there was intense debate about the future of the rail line into central Newcastle.


title: Newcastle, New South Wales

text: In December 2014, the Newcastle line was curtailed to Hamilton. A new Newcastle Interchange opened on 15 October 2017. The Newcastle Light Rail line also operates from here.


title: Newcastle, New South Wales

text: From 1924 until 1994, Broadmeadow Locomotive Depot was the main railway centre for the Hunter region. Cardiff Locomotive Workshops opened in 1928, primarily as a major repair centre for New South Wales Government Railways locomotives, although it did build twelve 38 class and two 58 class locomotives. Today it is operated by Downer Rail and along with UGL Rail's Broadmeadow plant, remains active as a locomotive and rolling stock manufacturer and repairer.


title: Newcastle, New South Wales

text: The Port of Newcastle is crucial to the economic life of Newcastle and the Hunter Valley region beyond. Over 90 million tonnes of coal is shipped through the facility each year – making it the largest coal exporting port in the world. The Port of Newcastle claims to be Australia's first port. Coal was first exported from the harbour in 1799.


title: Newcastle, New South Wales

text: Newcastle Transport operates a ferry service across the Hunter River between Newcastle's CBD and Stockton.


title: Newcastle, New South Wales

text: Newcastle Airport is located north of the Newcastle CBD ( by road). The airport, which is a joint venture between Newcastle City Council and Port Stephens Council, has experienced rapid growth since 2000 as a result of an increase in low-cost airline operations. The airport is located at RAAF Base Williamtown, a Royal Australian Air Force base on land leased from the Department of Defence.


title: Newcastle, New South Wales

text: The suburb of Broadmeadow is home to the base of the Westpac Life Saver Rescue Helicopter Service. The Helicopter service is one of the longest running services of this type in the world. Two helicopters operate out of this base and operate 24 hours a day.


title: Newcastle, New South Wales

text: The closure of Belmont Airport, commonly referred to as Aeropelican, in the Lake Macquarie suburb of Marks Point has caused Williamtown to become Newcastle's only major airport and residents in the south of the Newcastle metropolitan area must commute up to by car to reach Williamtown.


title: Employment

text: Employment is a relationship between two parties regulating the provision of paid labour services. Usually based on a contract, one party, the employer, which might be a corporation, a not-for-profit organization, a co-operative, or any other entity, pays the other, the employee, in return for carrying out assigned work. Employees work in return for wages, which can be paid on the basis of an hourly rate, by piecework or an annual salary, depending on the type of work an employee does, the prevailing conditions of the sector and the bargaining power between the parties. Employees in some sectors may receive gratuities, bonus payments or stock options. In some types of employment, employees may receive benefits in addition to payment. Benefits may include health insurance, housing, disability insurance. Employment is typically governed by employment laws, organisation or legal contracts.


title: Employment

text: An employee contributes labour and expertise to an endeavor of an employer or of a person conducting a business or undertaking (PCB) and is usually hired to perform specific duties which are packaged into a job. In a corporate context, an employee is a person who is hired to provide services to a company on a regular basis in exchange for compensation and who does not provide these services as part of an independent business.


title: Employment

text: An issue that arises in most companies, especially the ones that are in the gig economy, is the classification of workers. A lot of workers that fulfill gigs are often hired as "independent contractors".


title: Employment

text: To categorize a worker as an independent contractor rather than an employee, an independent contractor must agree with the client on what the finished work product will be and then the contractor controls the means and manner of achieving the desired outcome. Secondly, an independent contractor offers services to the public at large, not just to one business, and is responsible for disbursing payments from the client, paying unreimbursed expenses, and providing his or her own tools to complete the job. Third, the relationship of the parties is often evidenced by a written agreement that specifies that the worker is an independent contractor and is not entitled to employee benefits; the services provided by the worker are not key to the business; and the relationship is not permanent.


title: Employment

text: As a general principle of employment law, in the United States, there is a difference between an agent and an independent contractor. The default status of a worker is an employee unless specific guidelines are met, which can be determined by the ABC test. Thus, clarifying whether someone who performs work is an independent contractor or an employee from the beginning, and treating them accordingly, can save a company from trouble later on.


title: Employment

text: Provided key circumstances, including ones such as that the worker is paid regularly, follows set hours of work, is supplied with tools from the employer, is closely monitored by the employer, acting on behalf of the employer, only works for one employer at a time, they are considered an employee, and the employer will generally be liable for their actions and be obliged to give them benefits. Similarly, the employer is the owner of any invention created by an employee “hired to invent,” even in the absence of an assignment of inventions. In contrast, a company commissioning a work by an independent contractor will not own the copyright unless the company secures either a written contract stating that it is a “work made for hire” or a written assignment of the copyright. In order to stay protected and avoid lawsuits, an employer has to be aware of that distinction.


title: Employment

text: Employer and managerial control within an organization rests at many levels and has important implications for staff and productivity alike, with control forming the fundamental link between desired outcomes and actual processes. Employers must balance interests such as decreasing wage constraints with a maximization of labor productivity in order to achieve a profitable and productive employment relationship.


title: Employment

text: The main ways for employers to find workers and for people to find employers are via jobs listings in newspapers (via classified advertising) and online, also called job boards. Employers and job seekers also often find each other via professional recruitment consultants which receive a commission from the employer to find, screen and select suitable candidates. However, a study has shown that such consultants may not be reliable when they fail to use established principles in selecting employees. A more traditional approach is with a "Help Wanted" sign in the establishment (usually hung on a window or door or placed on a store counter). Evaluating different employees can be quite laborious but setting up different techniques to analyze their skills to measure their talents within the field can be best through assessments. Employer and potential employee commonly take the additional step of getting to know each other through the process of a job interview.


title: Employment

text: Training and development refers to the employer's effort to equip a newly hired employee with the necessary skills to perform at the job, and to help the employee grow within the organization. An appropriate level of training and development helps to improve employee's job satisfaction.


title: Employment

text: There are many ways that employees are paid, including by hourly wages, by piecework, by yearly salary, or by gratuities (with the latter often being combined with another form of payment). In sales jobs and real estate positions, the employee may be paid a commission, a percentage of the value of the goods or services that they have sold. In some fields and professions ("e.g.", executive jobs), employees may be eligible for a bonus if they meet certain targets. Some executives and employees may be paid in shares or stock options, a compensation approach that has the added benefit, from the company's point of view, of helping to align the interests of the compensated individual with the performance of the company.


title: Employment

text: Under the faithless servant doctrine, a doctrine under the laws of a number of states in the United States, and most notably New York State law, an employee who acts unfaithfully towards his employer must forfeit all of the compensation he received during the period of his disloyalty.


title: Employment

text: Employee benefits are various non-wage compensation provided to employees in addition to their wages or salaries. The benefits can include: housing (employer-provided or employer-paid), group insurance (health, dental, life etc.), disability income protection, retirement benefits, daycare, tuition reimbursement, sick leave, vacation (paid and non-paid), social security, profit sharing, funding of education, and other specialized benefits. In some cases, such as with workers employed in remote or isolated regions, the benefits may include meals. Employee benefits can improve the relationship between employee and employer and lowers staff turnover.


title: Employment

text: Organizational justice is an employee's perception and judgement of employer's treatment in the context of fairness or justice. The resulting actions to influence the employee-employer relationship is also a part of organizational justice.


title: Employment

text: Employees can organize into trade or labor unions, which represent the workforce to collectively bargain with the management of organizations about working, and contractual conditions and services.


title: Employment

text: Usually, either an employee or employer may end the relationship at any time, often subject to a certain notice period. This is referred to as at-will employment. The contract between the two parties specifies the responsibilities of each when ending the relationship and may include requirements such as notice periods, severance pay, and security measures. A contract forbidding an employee from leaving their employment, under penalty of a surety bond, is referred to as an employment bond. In some professions, notably teaching, civil servants, university professors, and some orchestra jobs, some employees may have tenure, which means that they cannot be dismissed at will. Another type of termination is a layoff.


title: Employment

text: Wage labor is the socioeconomic relationship between a worker and an employer, where the worker sells their labor under a formal or informal employment contract. These transactions usually occur in a labor market where wages are market-determined. In exchange for the wages paid, the work product generally becomes the undifferentiated property of the employer, except for special cases such as the vesting of intellectual property patents in the United States where patent rights are usually vested in the original personal inventor. A wage laborer is a person whose primary means of income is from the selling of his or her labor in this way.


title: Employment

text: In modern mixed economies such as that of the OECD countries, it is currently the dominant form of work arrangement. Although most work occurs following this structure, the wage work arrangements of CEOs, professional employees, and professional contract workers are sometimes conflated with class assignments, so that "wage labor" is considered to apply only to unskilled, semi-skilled or manual labor.


title: Employment

text: Wage labor, as institutionalized under today's market economic systems, has been criticized, especially by socialists, using the pejorative term wage slavery. Socialists draw parallels between the trade of labor as a commodity and slavery. Cicero is also known to have suggested such parallels.


title: Employment

text: The American philosopher John Dewey posited that until "industrial feudalism" is replaced by "industrial democracy", politics will be "the shadow cast on society by big business". Thomas Ferguson has postulated in his investment theory of party competition that the undemocratic nature of economic institutions under capitalism causes elections to become occasions when blocs of investors coalesce and compete to control the state plus cities.


title: Employment

text: Bangladesh Association of International Recruiting Agencies (BAIRA) is an association of national level with its international reputation of co-operation and welfare of the migrant workforce as well as its approximately 1200 members agencies in collaboration with and support from the Government of Bangladesh.


title: Employment

text: In the Canadian province of Ontario, formal complaints can be brought to the Ministry of Labour. In the province of Quebec, grievances can be filed with the Commission des normes du travail.


title: Employment

text: Two of the prominent examples of work and employment contracts in Germany are the Werksvertrag or the Arbeitsvertrag, which is a form of Dienstleistungsvertrag (service-oriented contract). An Arbeitsvertrag can also be temporary, whereas a temporary worker is working under Zeitarbeit or Leiharbeit. Another employment setting is Arbeitnehmerüberlassung (ANÜ).


title: Employment

text: India has options for a fixed term contract or a permanent contract. Both contracts are entitled to minimum wages, fixed working hours and social security contributions.


title: Employment

text: Pakistan has no contract Labor, Minimum Wage and Provident Funds Acts. Contract labor in Pakistan must be paid minimum wage and certain facilities are to be provided to labor. However, the Acts are not yet fully implemented.


title: Employment

text: There are no laws about minimum salary in Sweden. Instead, there are agreements between employer organizations and trade unions about minimum salaries, and other employment conditions.


title: Employment

text: There is a type of employment contract which is common but not regulated in law, and that is Hour employment ("swe: Timanställning"), which can be Normal employment (unlimited), but the work time is unregulated and decided per immediate need basis. The employee is expected to be answering the phone and come to work when needed, e.g. when someone is ill and absent from work. They will receive salary only for actual work time and can in reality be fired for no reason by not being called anymore. This type of contract is common in the public sector.


title: Employment

text: In the United Kingdom, employment contracts are categorized by the government into the following types:


title: Employment

text: For purposes of U.S. federal income tax withholding, 26 U.S.C. § 3401(c) provides a definition for the term "employee" specific to chapter 24 of the Internal Revenue Code:


title: Employment

text: "For purposes of this chapter, the term "employee" includes an officer, employee, or elected official of the United States, a State, or any political subdivision thereof, or the District of Columbia, or any agency or instrumentality of any one or more of the foregoing. The term "employee" also includes an officer of a corporation." This definition does not exclude all those who are commonly known as 'employees'. "Similarly, Latham’s instruction which indicated that under 26 U.S.C. § 3401(c) the category of ‘employee’ does not include privately employed wage earners is a preposterous reading of the statute. It is obvious that within the context of both statutes the word ‘includes’ is a term of enlargement not of limitation, and the reference to certain entities or categories is not intended to exclude all others."


title: Employment

text: Employees are often contrasted with independent contractors, especially when there is dispute as to the worker's entitlement to have matching taxes paid, workers compensation, and unemployment insurance benefits. However, in September 2009, the court case of "Brown v. J. Kaz, Inc." ruled that independent contractors are regarded as employees for the purpose of discrimination laws if they work for the employer on a regular basis, and said employer directs the time, place, and manner of employment.


title: Employment

text: In non-union work environments, in the United States, unjust termination complaints can be brought to the United States Department of Labor.


title: Employment

text: Labor unions are legally recognized as representatives of workers in many industries in the United States. Their activity today centers on collective bargaining over wages, benefits, and working conditions for their membership, and on representing their members in disputes with management over violations of contract provisions. Larger unions also typically engage in lobbying activities and electioneering at the state and federal level.


title: Employment

text: Most unions in America are aligned with one of two larger umbrella organizations: the AFL–CIO created in 1955, and the Change to Win Federation which split from the AFL–CIO in 2005. Both advocate policies and legislation on behalf of workers in the United States and Canada, and take an active role in politics. The AFL–CIO is especially concerned with global trade issues.


title: Employment

text: American business theorist Jeffrey Pfeffer posits that contemporary employment practices and employer commonalities in the United States, including toxic working environments, job insecurity, long hours and increased performance pressure from management, are responsible for 120,000 excess deaths annually, making the workplace the fifth leading cause of death in the United States.


title: Employment

text: Young workers are at higher risk for occupational injury and face certain occupational hazards at a higher rate; this is generally due to their employment in high-risk industries. For example, in the United States, young people are injured at work at twice the rate of their older counterparts. These workers are also at higher risk for motor vehicle accidents at work, due to less work experience, a lower use of seat belts, and higher rates of distracted driving. To mitigate this risk, those under the age of 17 are restricted from certain types of driving, including transporting people and goods under certain circumstances.


title: Employment

text: High-risk industries for young workers include agriculture, restaurants, waste management, and mining. In the United States, those under the age of 18 are restricted from certain jobs that are deemed dangerous under the Fair Labor Standards Act.


title: Employment

text: Youth employment programs are most effective when they include both theoretical classroom training and hands-on training with work placements.


title: Employment

text: In the conversation of employment among younger aged workers, youth unemployment has also been monitored. Youth unemployment rates tend to be higher than the adult rates in every country in the world.


title: Employment

text: Those older than the statutory defined retirement age may continue to work, either out of enjoyment or necessity. However, depending on the nature of the job, older workers may need to transition into less-physical forms of work to avoid injury. Working past retirement age also has positive effects, because it gives a sense of purpose and allows people to maintain social networks and activity levels. Older workers are often found to be discriminated against by employers.


title: Employment

text: Employment is no guarantee of escaping poverty, the International Labour Organization (ILO) estimates that as many as 40% of workers are poor, not earning enough to keep their families above the $2 a day poverty line. For instance, in India most of the chronically poor are wage earners in formal employment, because their jobs are insecure and low paid and offer no chance to accumulate wealth to avoid risks. According to the UNRISD, increasing labor productivity appears to have a negative impact on job creation: in the 1960s, a 1% increase in output per worker was associated with a reduction in employment growth of 0.07%, by the first decade of this century the same productivity increase implies reduced employment growth by 0.54%. Both increased employment opportunities and increased labor productivity (as long as it also translates into higher wages) are needed to tackle poverty. Increases in employment without increases in productivity leads to a rise in the number of "working poor", which is why some experts are now promoting the creation of "quality" and not "quantity" in labor market policies. This approach does highlight how higher productivity has helped reduce poverty in East Asia, but the negative impact is beginning to show. In Vietnam, for example, employment growth has slowed while productivity growth has continued. Furthermore, productivity increases do not always lead to increased wages, as can be seen in the United States, where the gap between productivity and wages has been rising since the 1980s.


title: Employment

text: Researchers at the Overseas Development Institute argue that there are differences across economic sectors in creating employment that reduces poverty. 24 instances of growth were examined, in which 18 reduced poverty. This study showed that other sectors were just as important in reducing unemployment, such as manufacturing. The services sector is most effective at translating productivity growth into employment growth. Agriculture provides a safety net for jobs and economic buffer when other sectors are struggling.


title: Employment

text: Scholars conceptualize the employment relationship in various ways. A key assumption is the extent to which the employment relationship necessarily includes conflicts of interests between employers and employees, and the form of such conflicts. In economic theorizing, the labor market mediates all such conflicts such that employers and employees who enter into an employment relationship are assumed to find this arrangement in their own self-interest. In human resource management theorizing, employers and employees are assumed to have shared interests (or a unity of interests, hence the label “unitarism”). Any conflicts that exist are seen as a manifestation of poor human resource management policies or interpersonal clashes such as personality conflicts, both of which can and should be managed away. From the perspective of pluralist industrial relations, the employment relationship is characterized by a plurality of stakeholders with legitimate interests (hence the label “pluralism), and some conflicts of interests are seen as inherent in the employment relationship (e.g., wages v. profits). Lastly, the critical paradigm emphasizes antagonistic conflicts of interests between various groups (e.g., the competing capitalist and working classes in a Marxist framework) that are part of a deeper social conflict of unequal power relations. As a result, there are four common models of employment:


title: Employment

text: These models are important because they help reveal why individuals hold differing perspectives on human resource management policies, labor unions, and employment regulation. For example, human resource management policies are seen as dictated by the market in the first view, as essential mechanisms for aligning the interests of employees and employers and thereby creating profitable companies in the second view, as insufficient for looking out for workers’ interests in the third view, and as manipulative managerial tools for shaping the ideology and structure of the workplace in the fourth view.


title: Employment

text: Literature on the employment impact of economic growth and on how growth is associated with employment at a macro, sector and industry level was aggregated in 2013.


title: Employment

text: Researchers found evidence to suggest growth in manufacturing and services have good impact on employment. They found GDP growth on employment in agriculture to be limited, but that value-added growth had a relatively larger impact. The impact on job creation by industries/economic activities as well as the extent of the body of evidence and the key studies. For extractives, they again found extensive evidence suggesting growth in the sector has limited impact on employment. In textiles, however, although evidence was low, studies suggest growth there positively contributed to job creation. In agri-business and food processing, they found impact growth to be positive.


title: Employment

text: They found that most available literature focuses on OECD and middle-income countries somewhat, where economic growth impact has been shown to be positive on employment. The researchers didn't find sufficient evidence to conclude any impact of growth on employment in LDCs despite some pointing to the positive impact, others point to limitations. They recommended that complementary policies are necessary to ensure economic growth's positive impact on LDC employment. With trade, industry and investment, they only found limited evidence of positive impact on employment from industrial and investment policies and for others, while large bodies of evidence does exist, the exact impact remains contested.


title: Employment

text: Researchers have also explored the relationship between employment and illicit activities. Using evidence from Africa, a research team found that a program for Liberian ex-fighters reduced work hours on illicit activities. The employment program also reduced interest in mercenary work in nearby wars. The study concludes that while the use of capital inputs or cash payments for peaceful work created a reduction in illicit activities, the impact of training alone is rather low.


title: Employment

text: The balance of economic efficiency and social equity is the ultimate debate in the field of employment relations. By meeting the needs of the employer; generating profits to establish and maintain economic efficiency; whilst maintaining a balance with the employee and creating social equity that benefits the worker so that he/she can fund and enjoy healthy living; proves to be a continuous revolving issue in westernized societies.


title: Employment

text: Globalization has affected these issues by creating certain economic factors that disallow or allow various employment issues. Economist Edward Lee (1996) studies the effects of globalization and summarizes the four major points of concern that affect employment relations:


title: Employment

text: What also results from Lee's (1996) findings is that in industrialized countries an average of almost 70 per cent of workers are employed in the service sector, most of which consists of non-tradable activities. As a result, workers are forced to become more skilled and develop sought after trades, or find other means of survival. Ultimately this is a result of changes and trends of employment, an evolving workforce, and globalization that is represented by a more skilled and increasing highly diverse labor force, that are growing in non standard forms of employment (Markey, R. et al. 2006).


title: Employment

text: Various youth subcultures have been associated with not working, such as the hippie subculture in the 1960s and 1970s (which endorsed the idea of "dropping out" of society) and the punk subculture.


title: Employment

text: One of the alternatives to work is engaging in post-secondary education at a college, university or professional school. One of the major costs of obtaining a post-secondary education is the opportunity cost of forgone wages due to not working. At times when jobs are hard to find, such as during recessions, unemployed individuals may decide to get post-secondary education, because there is less of an opportunity cost.


title: Employment

text: In some countries, individuals who are not working can receive social assistance support (e.g., welfare or food stamps) to enable them to rent housing, buy food, repair or replace household goods, maintenance of children and observe social customs that require financial expenditure.


title: Employment

text: Workers who are not paid wages, such as volunteers who perform tasks for charities, hospitals or not-for-profit organizations, are generally not considered employed. One exception to this is an internship, an employment situation in which the worker receives training or experience (and possibly college credit) as the chief form of compensation.


title: Employment

text: Those who work under obligation for the purpose of fulfilling a debt, such as indentured servants, or as property of the person or entity they work for, such as slaves, do not receive pay for their services and are not considered employed. Some historians suggest that slavery is older than employment, but both arrangements have existed for all recorded history. Indentured servitude and slavery are not considered compatible with human rights or with democracy.


title: Mathematical logic

text: Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.


title: Mathematical logic

text: Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.


title: Mathematical logic

text: The "Handbook of Mathematical Logic" in 1977 makes a rough division of contemporary mathematical logic into four areas:


title: Mathematical logic

text: Additionally, sometimes the field of computational complexity theory is also included as part of mathematical logic. Each area has a distinct focus, although many techniques and results are shared among multiple areas. The borderlines amongst these fields, and the lines separating mathematical logic and other fields of mathematics, are not always sharp. Gödel's incompleteness theorem marks not only a milestone in recursion theory and proof theory, but has also led to Löb's theorem in modal logic. The method of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics.


title: Mathematical logic

text: The mathematical field of category theory uses many formal axiomatic methods, and includes the study of categorical logic, but category theory is not ordinarily considered a subfield of mathematical logic. Because of its applicability in diverse fields of mathematics, mathematicians including Saunders Mac Lane have proposed category theory as a foundational system for mathematics, independent of set theory. These foundations use toposes, which resemble generalized models of set theory that may employ classical or nonclassical logic.


title: Mathematical logic

text: Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics. "Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last [nineteenth] century with the aid of an artificial notation and a rigorously deductive method." Before this emergence, logic was studied with rhetoric, with "calculationes", through the syllogism, and with philosophy. The first half of the 20th century saw an explosion of fundamental results, accompanied by vigorous debate over the foundations of mathematics.


title: Mathematical logic

text: Theories of logic were developed in many cultures in history, including China, India, Greece and the Islamic world. Greek methods, particularly Aristotelian logic (or term logic) as found in the "Organon", found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic. In 18th-century Europe, attempts to treat the operations of formal logic in a symbolic or algebraic way had been made by philosophical mathematicians including Leibniz and Lambert, but their labors remained isolated and little known.


title: Mathematical logic

text: In the middle of the nineteenth century, George Boole and then Augustus De Morgan presented systematic mathematical treatments of logic. Their work, building on work by algebraists such as George Peacock, extended the traditional Aristotelian doctrine of logic into a sufficient framework for the study of foundations of mathematics. Charles Sanders Peirce later built upon the work of Boole to develop a logical system for relations and quantifiers, which he published in several papers from 1870 to 1885.


title: Mathematical logic

text: Gottlob Frege presented an independent development of logic with quantifiers in his "Begriffsschrift", published in 1879, a work generally considered as marking a turning point in the history of logic. Frege's work remained obscure, however, until Bertrand Russell began to promote it near the turn of the century. The two-dimensional notation Frege developed was never widely adopted and is unused in contemporary texts.


title: Mathematical logic

text: From 1890 to 1905, Ernst Schröder published "Vorlesungen über die Algebra der Logik" in three volumes. This work summarized and extended the work of Boole, De Morgan, and Peirce, and was a comprehensive reference to symbolic logic as it was understood at the end of the 19th century.


title: Mathematical logic

text: Concerns that mathematics had not been built on a proper foundation led to the development of axiomatic systems for fundamental areas of mathematics such as arithmetic, analysis, and geometry.


title: Mathematical logic

text: In logic, the term "arithmetic" refers to the theory of the natural numbers. Giuseppe Peano published a set of axioms for arithmetic that came to bear his name (Peano axioms), using a variation of the logical system of Boole and Schröder but adding quantifiers. Peano was unaware of Frege's work at the time. Around the same time Richard Dedekind showed that the natural numbers are uniquely characterized by their induction properties. Dedekind proposed a different characterization, which lacked the formal logical character of Peano's axioms. Dedekind's work, however, proved theorems inaccessible in Peano's system, including the uniqueness of the set of natural numbers (up to isomorphism) and the recursive definitions of addition and multiplication from the successor function and mathematical induction.


title: Mathematical logic

text: In the mid-19th century, flaws in Euclid's axioms for geometry became known. In addition to the independence of the parallel postulate, established by Nikolai Lobachevsky in 1826, mathematicians discovered that certain theorems taken for granted by Euclid were not in fact provable from his axioms. Among these is the theorem that a line contains at least two points, or that circles of the same radius whose centers are separated by that radius must intersect. Hilbert developed a complete set of axioms for geometry, building on previous work by Pasch. The success in axiomatizing geometry motivated Hilbert to seek complete axiomatizations of other areas of mathematics, such as the natural numbers and the real line. This would prove to be a major area of research in the first half of the 20th century.


title: Mathematical logic

text: The 19th century saw great advances in the theory of real analysis, including theories of convergence of functions and Fourier series. Mathematicians such as Karl Weierstrass began to construct functions that stretched intuition, such as nowhere-differentiable continuous functions. Previous conceptions of a function as a rule for computation, or a smooth graph, were no longer adequate. Weierstrass began to advocate the arithmetization of analysis, which sought to axiomatize analysis using properties of the natural numbers. The modern (ε, δ)-definition of limit and continuous functions was already developed by Bolzano in 1817, but remained relatively unknown.


title: Mathematical logic

text: Cauchy in 1821 defined continuity in terms of infinitesimals (see Cours d'Analyse, page 34). In 1858, Dedekind proposed a definition of the real numbers in terms of Dedekind cuts of rational numbers, a definition still employed in contemporary texts.


title: Mathematical logic

text: Georg Cantor developed the fundamental concepts of infinite set theory. His early results developed the theory of cardinality and proved that the reals and the natural numbers have different cardinalities. Over the next twenty years, Cantor developed a theory of transfinite numbers in a series of publications. In 1891, he published a new proof of the uncountability of the real numbers that introduced the diagonal argument, and used this method to prove Cantor's theorem that no set can have the same cardinality as its powerset. Cantor believed that every set could be well-ordered, but was unable to produce a proof for this result, leaving it as an open problem in 1895.


title: Mathematical logic

text: In the early decades of the 20th century, the main areas of study were set theory and formal logic. The discovery of paradoxes in informal set theory caused some to wonder whether mathematics itself is inconsistent, and to look for proofs of consistency.


title: Mathematical logic

text: In 1900, Hilbert posed a famous list of 23 problems for the next century. The first two of these were to resolve the continuum hypothesis and prove the consistency of elementary arithmetic, respectively; the tenth was to produce a method that could decide whether a multivariate polynomial equation over the integers has a solution. Subsequent work to resolve these problems shaped the direction of mathematical logic, as did the effort to resolve Hilbert's "Entscheidungsproblem", posed in 1928. This problem asked for a procedure that would decide, given a formalized mathematical statement, whether the statement is true or false.


title: Mathematical logic

text: Ernst Zermelo gave a proof that every set could be well-ordered, a result Georg Cantor had been unable to obtain. To achieve the proof, Zermelo introduced the axiom of choice, which drew heated debate and research among mathematicians and the pioneers of set theory. The immediate criticism of the method led Zermelo to publish a second exposition of his result, directly addressing criticisms of his proof. This paper led to the general acceptance of the axiom of choice in the mathematics community.


title: Mathematical logic

text: Skepticism about the axiom of choice was reinforced by recently discovered paradoxes in naive set theory. Cesare Burali-Forti was the first to state a paradox: the Burali-Forti paradox shows that the collection of all ordinal numbers cannot form a set. Very soon thereafter, Bertrand Russell discovered Russell's paradox in 1901, and Jules Richard discovered Richard's paradox.


title: Mathematical logic

text: Zermelo provided the first set of axioms for set theory. These axioms, together with the additional axiom of replacement proposed by Abraham Fraenkel, are now called Zermelo–Fraenkel set theory (ZF). Zermelo's axioms incorporated the principle of limitation of size to avoid Russell's paradox.


title: Mathematical logic

text: In 1910, the first volume of "Principia Mathematica" by Russell and Alfred North Whitehead was published. This seminal work developed the theory of functions and cardinality in a completely formal framework of type theory, which Russell and Whitehead developed in an effort to avoid the paradoxes. "Principia Mathematica" is considered one of the most influential works of the 20th century, although the framework of type theory did not prove popular as a foundational theory for mathematics.


title: Mathematical logic

text: Fraenkel proved that the axiom of choice cannot be proved from the axioms of Zermelo's set theory with urelements. Later work by Paul Cohen showed that the addition of urelements is not needed, and the axiom of choice is unprovable in ZF. Cohen's proof developed the method of forcing, which is now an important tool for establishing independence results in set theory.


title: Mathematical logic

text: Leopold Löwenheim and Thoralf Skolem obtained the Löwenheim–Skolem theorem, which says that first-order logic cannot control the cardinalities of infinite structures. Skolem realized that this theorem would apply to first-order formalizations of set theory, and that it implies any such formalization has a countable model. This counterintuitive fact became known as Skolem's paradox.


title: Mathematical logic

text: In his doctoral thesis, Kurt Gödel proved the completeness theorem, which establishes a correspondence between syntax and semantics in first-order logic. Gödel used the completeness theorem to prove the compactness theorem, demonstrating the finitary nature of first-order logical consequence. These results helped establish first-order logic as the dominant logic used by mathematicians.


title: Mathematical logic

text: In 1931, Gödel published "On Formally Undecidable Propositions of Principia Mathematica and Related Systems", which proved the incompleteness (in a different meaning of the word) of all sufficiently strong, effective first-order theories. This result, known as Gödel's incompleteness theorem, establishes severe limitations on axiomatic foundations for mathematics, striking a strong blow to Hilbert's program. It showed the impossibility of providing a consistency proof of arithmetic within any formal theory of arithmetic. Hilbert, however, did not acknowledge the importance of the incompleteness theorem for some time.


title: Mathematical logic

text: Gödel's theorem shows that a consistency proof of any sufficiently strong, effective axiom system cannot be obtained in the system itself, if the system is consistent, nor in any weaker system. This leaves open the possibility of consistency proofs that cannot be formalized within the system they consider. Gentzen proved the consistency of arithmetic using a finitistic system together with a principle of transfinite induction. Gentzen's result introduced the ideas of cut elimination and proof-theoretic ordinals, which became key tools in proof theory. Gödel gave a different consistency proof, which reduces the consistency of classical arithmetic to that of intuitionistic arithmetic in higher types.


title: Mathematical logic

text: The first textbook on symbolic logic for the layman was written by Lewis Carroll, author of "Alice in Wonderland", in 1896.


title: Mathematical logic

text: Beginning in 1935, a group of prominent mathematicians collaborated under the pseudonym Nicolas Bourbaki to publish "Éléments de mathématique", a series of encyclopedic mathematics texts. These texts, written in an austere and axiomatic style, emphasized rigorous presentation and set-theoretic foundations. Terminology coined by these texts, such as the words "bijection", "injection", and "surjection", and the set-theoretic foundations the texts employed, were widely adopted throughout mathematics.


title: Mathematical logic

text: The study of computability came to be known as recursion theory or computability theory, because early formalizations by Gödel and Kleene relied on recursive definitions of functions. When these definitions were shown equivalent to Turing's formalization involving Turing machines, it became clear that a new concept – the computable function – had been discovered, and that this definition was robust enough to admit numerous independent characterizations. In his work on the incompleteness theorems in 1931, Gödel lacked a rigorous concept of an effective formal system; he immediately realized that the new definitions of computability could be used for this purpose, allowing him to state the incompleteness theorems in generality that could only be implied in the original paper.


title: Mathematical logic

text: Numerous results in recursion theory were obtained in the 1940s by Stephen Cole Kleene and Emil Leon Post. Kleene introduced the concepts of relative computability, foreshadowed by Turing, and the arithmetical hierarchy. Kleene later generalized recursion theory to higher-order functionals. Kleene and Georg Kreisel studied formal versions of intuitionistic mathematics, particularly in the context of proof theory.


title: Mathematical logic

text: At its core, mathematical logic deals with mathematical concepts expressed using formal logical systems. These systems, though they differ in many details, share the common property of considering only expressions in a fixed formal language. The systems of propositional logic and first-order logic are the most widely studied today, because of their applicability to foundations of mathematics and because of their desirable proof-theoretic properties. Stronger classical logics such as second-order logic or infinitary logic are also studied, along with Non-classical logics such as intuitionistic logic.


title: Mathematical logic

text: First-order logic is a particular formal system of logic. Its syntax involves only finite expressions as well-formed formulas, while its semantics are characterized by the limitation of all quantifiers to a fixed domain of discourse.


title: Mathematical logic

text: Early results from formal logic established limitations of first-order logic. The Löwenheim–Skolem theorem (1919) showed that if a set of sentences in a countable first-order language has an infinite model then it has at least one model of each infinite cardinality. This shows that it is impossible for a set of first-order axioms to characterize the natural numbers, the real numbers, or any other infinite structure up to isomorphism. As the goal of early foundational studies was to produce axiomatic theories for all parts of mathematics, this limitation was particularly stark.


title: Mathematical logic

text: Gödel's completeness theorem established the equivalence between semantic and syntactic definitions of logical consequence in first-order logic. It shows that if a particular sentence is true in every model that satisfies a particular set of axioms, then there must be a finite deduction of the sentence from the axioms. The compactness theorem first appeared as a lemma in Gödel's proof of the completeness theorem, and it took many years before logicians grasped its significance and began to apply it routinely. It says that a set of sentences has a model if and only if every finite subset has a model, or in other words that an inconsistent set of formulas must have a finite inconsistent subset. The completeness and compactness theorems allow for sophisticated analysis of logical consequence in first-order logic and the development of model theory, and they are a key reason for the prominence of first-order logic in mathematics.


title: Mathematical logic

text: Gödel's incompleteness theorems establish additional limits on first-order axiomatizations. The first incompleteness theorem states that for any consistent, effectively given (defined below) logical system that is capable of interpreting arithmetic, there exists a statement that is true (in the sense that it holds for the natural numbers) but not provable within that logical system (and which indeed may fail in some non-standard models of arithmetic which may be consistent with the logical system). For example, in every logical system capable of expressing the Peano axioms, the Gödel sentence holds for the natural numbers but cannot be proved.


title: Mathematical logic

text: Here a logical system is said to be effectively given if it is possible to decide, given any formula in the language of the system, whether the formula is an axiom, and one which can express the Peano axioms is called "sufficiently strong." When applied to first-order logic, the first incompleteness theorem implies that any sufficiently strong, consistent, effective first-order theory has models that are not elementarily equivalent, a stronger limitation than the one established by the Löwenheim–Skolem theorem. The second incompleteness theorem states that no sufficiently strong, consistent, effective axiom system for arithmetic can prove its own consistency, which has been interpreted to show that Hilbert's program cannot be reached.


title: Mathematical logic

text: Many logics besides first-order logic are studied. These include infinitary logics, which allow for formulas to provide an infinite amount of information, and higher-order logics, which include a portion of set theory directly in their semantics.


title: Mathematical logic

text: The most well studied infinitary logic is formula_1. In this logic, quantifiers may only be nested to finite depths, as in first-order logic, but formulas may have finite or countably infinite conjunctions and disjunctions within them. Thus, for example, it is possible to say that an object is a whole number using a formula of formula_1 such as


title: Mathematical logic

text: Higher-order logics allow for quantification not only of elements of the domain of discourse, but subsets of the domain of discourse, sets of such subsets, and other objects of higher type. The semantics are defined so that, rather than having a separate domain for each higher-type quantifier to range over, the quantifiers instead range over all objects of the appropriate type. The logics studied before the development of first-order logic, for example Frege's logic, had similar set-theoretic aspects. Although higher-order logics are more expressive, allowing complete axiomatizations of structures such as the natural numbers, they do not satisfy analogues of the completeness and compactness theorems from first-order logic, and are thus less amenable to proof-theoretic analysis.


title: Mathematical logic

text: Another type of logics are s that allow inductive definitions, like one writes for primitive recursive functions.


title: Mathematical logic

text: One can formally define an extension of first-order logic — a notion which encompasses all logics in this section because they behave like first-order logic in certain fundamental ways, but does not encompass all logics in general, e.g. it does not encompass intuitionistic, modal or fuzzy logic.


title: Mathematical logic

text: Lindström's theorem implies that the only extension of first-order logic satisfying both the compactness theorem and the downward Löwenheim–Skolem theorem is first-order logic.


title: Mathematical logic

text: Modal logics include additional modal operators, such as an operator which states that a particular formula is not only true, but necessarily true. Although modal logic is not often used to axiomatize mathematics, it has been used to study the properties of first-order provability and set-theoretic forcing.


title: Mathematical logic

text: Intuitionistic logic was developed by Heyting to study Brouwer's program of intuitionism, in which Brouwer himself avoided formalization. Intuitionistic logic specifically does not include the law of the excluded middle, which states that each sentence is either true or its negation is true. Kleene's work with the proof theory of intuitionistic logic showed that constructive information can be recovered from intuitionistic proofs. For example, any provably total function in intuitionistic arithmetic is computable; this is not true in classical theories of arithmetic such as Peano arithmetic.


title: Mathematical logic

text: Algebraic logic uses the methods of abstract algebra to study the semantics of formal logics. A fundamental example is the use of Boolean algebras to represent truth values in classical propositional logic, and the use of Heyting algebras to represent truth values in intuitionistic propositional logic. Stronger logics, such as first-order logic and higher-order logic, are studied using more complicated algebraic structures such as cylindric algebras.


title: Mathematical logic

text: Set theory is the study of sets, which are abstract collections of objects. Many of the basic notions, such as ordinal and cardinal numbers, were developed informally by Cantor before formal axiomatizations of set theory were developed. The first such axiomatization, due to Zermelo, was extended slightly to become Zermelo–Fraenkel set theory (ZF), which is now the most widely used foundational theory for mathematics.


title: Mathematical logic

text: Other formalizations of set theory have been proposed, including von Neumann–Bernays–Gödel set theory (NBG), Morse–Kelley set theory (MK), and New Foundations (NF). Of these, ZF, NBG, and MK are similar in describing a cumulative hierarchy of sets. New Foundations takes a different approach; it allows objects such as the set of all sets at the cost of restrictions on its set-existence axioms. The system of Kripke–Platek set theory is closely related to generalized recursion theory.


title: Mathematical logic

text: Two famous statements in set theory are the axiom of choice and the continuum hypothesis. The axiom of choice, first stated by Zermelo, was proved independent of ZF by Fraenkel, but has come to be widely accepted by mathematicians. It states that given a collection of nonempty sets there is a single set "C" that contains exactly one element from each set in the collection. The set "C" is said to "choose" one element from each set in the collection. While the ability to make such a choice is considered obvious by some, since each set in the collection is nonempty, the lack of a general, concrete rule by which the choice can be made renders the axiom nonconstructive. Stefan Banach and Alfred Tarski showed that the axiom of choice can be used to decompose a solid ball into a finite number of pieces which can then be rearranged, with no scaling, to make two solid balls of the original size. This theorem, known as the Banach–Tarski paradox, is one of many counterintuitive results of the axiom of choice.


title: Mathematical logic

text: The continuum hypothesis, first proposed as a conjecture by Cantor, was listed by David Hilbert as one of his 23 problems in 1900. Gödel showed that the continuum hypothesis cannot be disproven from the axioms of Zermelo–Fraenkel set theory (with or without the axiom of choice), by developing the constructible universe of set theory in which the continuum hypothesis must hold. In 1963, Paul Cohen showed that the continuum hypothesis cannot be proven from the axioms of Zermelo–Fraenkel set theory. This independence result did not completely settle Hilbert's question, however, as it is possible that new axioms for set theory could resolve the hypothesis. Recent work along these lines has been conducted by W. Hugh Woodin, although its importance is not yet clear.


title: Mathematical logic

text: Contemporary research in set theory includes the study of large cardinals and determinacy. Large cardinals are cardinal numbers with particular properties so strong that the existence of such cardinals cannot be proved in ZFC. The existence of the smallest large cardinal typically studied, an inaccessible cardinal, already implies the consistency of ZFC. Despite the fact that large cardinals have extremely high cardinality, their existence has many ramifications for the structure of the real line. "Determinacy" refers to the possible existence of winning strategies for certain two-player games (the games are said to be "determined"). The existence of these strategies implies structural properties of the real line and other Polish spaces.


title: Mathematical logic

text: Model theory studies the models of various formal theories. Here a theory is a set of formulas in a particular formal logic and signature, while a model is a structure that gives a concrete interpretation of the theory. Model theory is closely related to universal algebra and algebraic geometry, although the methods of model theory focus more on logical considerations than those fields.


title: Mathematical logic

text: The set of all models of a particular theory is called an elementary class; classical model theory seeks to determine the properties of models in a particular elementary class, or determine whether certain classes of structures form elementary classes.


title: Mathematical logic

text: The method of quantifier elimination can be used to show that definable sets in particular theories cannot be too complicated. Tarski established quantifier elimination for real-closed fields, a result which also shows the theory of the field of real numbers is decidable. He also noted that his methods were equally applicable to algebraically closed fields of arbitrary characteristic. A modern subfield developing from this is concerned with o-minimal structures.


title: Mathematical logic

text: Morley's categoricity theorem, proved by Michael D. Morley, states that if a first-order theory in a countable language is categorical in some uncountable cardinality, i.e. all models of this cardinality are isomorphic, then it is categorical in all uncountable cardinalities.


title: Mathematical logic

text: A trivial consequence of the continuum hypothesis is that a complete theory with less than continuum many nonisomorphic countable models can have only countably many. Vaught's conjecture, named after Robert Lawson Vaught, says that this is true even independently of the continuum hypothesis. Many special cases of this conjecture have been established.


title: Mathematical logic

text: Recursion theory, also called computability theory, studies the properties of computable functions and the Turing degrees, which divide the uncomputable functions into sets that have the same level of uncomputability. Recursion theory also includes the study of generalized computability and definability. Recursion theory grew from the work of Rózsa Péter, Alonzo Church and Alan Turing in the 1930s, which was greatly extended by Kleene and Post in the 1940s.


title: Mathematical logic

text: Classical recursion theory focuses on the computability of functions from the natural numbers to the natural numbers. The fundamental results establish a robust, canonical class of computable functions with numerous independent, equivalent characterizations using Turing machines, λ calculus, and other systems. More advanced results concern the structure of the Turing degrees and the lattice of recursively enumerable sets.


title: Mathematical logic

text: Generalized recursion theory extends the ideas of recursion theory to computations that are no longer necessarily finite. It includes the study of computability in higher types as well as areas such as hyperarithmetical theory and α-recursion theory.


title: Mathematical logic

text: Contemporary research in recursion theory includes the study of applications such as algorithmic randomness, computable model theory, and reverse mathematics, as well as new results in pure recursion theory.


title: Mathematical logic

text: An important subfield of recursion theory studies algorithmic unsolvability; a decision problem or function problem is algorithmically unsolvable if there is no possible computable algorithm that returns the correct answer for all legal inputs to the problem. The first results about unsolvability, obtained independently by Church and Turing in 1936, showed that the Entscheidungsproblem is algorithmically unsolvable. Turing proved this by establishing the unsolvability of the halting problem, a result with far-ranging implications in both recursion theory and computer science.


title: Mathematical logic

text: There are many known examples of undecidable problems from ordinary mathematics. The word problem for groups was proved algorithmically unsolvable by Pyotr Novikov in 1955 and independently by W. Boone in 1959. The busy beaver problem, developed by Tibor Radó in 1962, is another well-known example.


title: Mathematical logic

text: Hilbert's tenth problem asked for an algorithm to determine whether a multivariate polynomial equation with integer coefficients has a solution in the integers. Partial progress was made by Julia Robinson, Martin Davis and Hilary Putnam. The algorithmic unsolvability of the problem was proved by Yuri Matiyasevich in 1970.


title: Mathematical logic

text: Proof theory is the study of formal proofs in various logical deduction systems. These proofs are represented as formal mathematical objects, facilitating their analysis by mathematical techniques. Several deduction systems are commonly considered, including Hilbert-style deduction systems, systems of natural deduction, and the sequent calculus developed by Gentzen.


title: Mathematical logic

text: The study of constructive mathematics, in the context of mathematical logic, includes the study of systems in non-classical logic such as intuitionistic logic, as well as the study of predicative systems. An early proponent of predicativism was Hermann Weyl, who showed it is possible to develop a large part of real analysis using only predicative methods.


title: Mathematical logic

text: Because proofs are entirely finitary, whereas truth in a structure is not, it is common for work in constructive mathematics to emphasize provability. The relationship between provability in classical (or nonconstructive) systems and provability in intuitionistic (or constructive, respectively) systems is of particular interest. Results such as the Gödel–Gentzen negative translation show that it is possible to embed (or "translate") classical logic into intuitionistic logic, allowing some properties about intuitionistic proofs to be transferred back to classical proofs.


title: Mathematical logic

text: Recent developments in proof theory include the study of proof mining by Ulrich Kohlenbach and the study of proof-theoretic ordinals by Michael Rathjen.


title: Mathematical logic

text: "Mathematical logic has been successfully applied not only to mathematics and its foundations (G. Frege, B. Russell, D. Hilbert, P. Bernays, H. Scholz, R. Carnap, S. Lesniewski, T. Skolem), but also to physics (R. Carnap, A. Dittrich, B. Russell, C. E. Shannon, A. N. Whitehead, H. Reichenbach, P. Fevrier), to biology (J. H. Woodger, A. Tarski), to psychology (F. B. Fitch, C. G. Hempel), to law and morals (K. Menger, U. Klug, P. Oppenheim), to economics (J. Neumann, O. Morgenstern), to practical questions (E. C. Berkeley, E. Stamm), and even to metaphysics (J. [Jan] Salamucha, H. Scholz, J. M. Bochenski). Its applications to the history of logic have proven extremely fruitful (J. Lukasiewicz, H. Scholz, B. Mates, A. Becker, E. Moody, J. Salamucha, K. Duerr, Z. Jordan, P. Boehner, J. M. Bochenski, S. [Stanislaw] T. Schayer, D. Ingalls)." "Applications have also been made to theology (F. Drewnowski, J. Salamucha, I. Thomas)."


title: Mathematical logic

text: The study of computability theory in computer science is closely related to the study of computability in mathematical logic. There is a difference of emphasis, however. Computer scientists often focus on concrete programming languages and feasible computability, while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.


title: Mathematical logic

text: The theory of semantics of programming languages is related to model theory, as is program verification (in particular, model checking). The Curry–Howard correspondence between proofs and programs relates to proof theory, especially intuitionistic logic. Formal calculi such as the lambda calculus and combinatory logic are now studied as idealized programming languages.


title: Mathematical logic

text: Computer science also contributes to mathematics by developing techniques for the automatic checking or even finding of proofs, such as automated theorem proving and logic programming.


title: Mathematical logic

text: Descriptive complexity theory relates logics to computational complexity. The first significant result in this area, Fagin's theorem (1974) established that NP is precisely the set of languages expressible by sentences of existential second-order logic.


title: Mathematical logic

text: In the 19th century, mathematicians became aware of logical gaps and inconsistencies in their field. It was shown that Euclid's axioms for geometry, which had been taught for centuries as an example of the axiomatic method, were incomplete. The use of infinitesimals, and the very definition of function, came into question in analysis, as pathological examples such as Weierstrass' nowhere-differentiable continuous function were discovered.


title: Mathematical logic

text: Cantor's study of arbitrary infinite sets also drew criticism. Leopold Kronecker famously stated "God made the integers; all else is the work of man," endorsing a return to the study of finite, concrete objects in mathematics. Although Kronecker's argument was carried forward by constructivists in the 20th century, the mathematical community as a whole rejected them. David Hilbert argued in favor of the study of the infinite, saying "No one shall expel us from the Paradise that Cantor has created."


title: Mathematical logic

text: Mathematicians began to search for axiom systems that could be used to formalize large parts of mathematics. In addition to removing ambiguity from previously naive terms such as function, it was hoped that this axiomatization would allow for consistency proofs. In the 19th century, the main method of proving the consistency of a set of axioms was to provide a model for it. Thus, for example, non-Euclidean geometry can be proved consistent by defining "point" to mean a point on a fixed sphere and "line" to mean a great circle on the sphere. The resulting structure, a model of elliptic geometry, satisfies the axioms of plane geometry except the parallel postulate.


title: Mathematical logic

text: With the development of formal logic, Hilbert asked whether it would be possible to prove that an axiom system is consistent by analyzing the structure of possible proofs in the system, and showing through this analysis that it is impossible to prove a contradiction. This idea led to the study of proof theory. Moreover, Hilbert proposed that the analysis should be entirely concrete, using the term "finitary" to refer to the methods he would allow but not precisely defining them. This project, known as Hilbert's program, was seriously affected by Gödel's incompleteness theorems, which show that the consistency of formal theories of arithmetic cannot be established using methods formalizable in those theories. Gentzen showed that it is possible to produce a proof of the consistency of arithmetic in a finitary system augmented with axioms of transfinite induction, and the techniques he developed to do so were seminal in proof theory.


title: Mathematical logic

text: A second thread in the history of foundations of mathematics involves nonclassical logics and constructive mathematics. The study of constructive mathematics includes many different programs with various definitions of "constructive". At the most accommodating end, proofs in ZF set theory that do not use the axiom of choice are called constructive by many mathematicians. More limited versions of constructivism limit themselves to natural numbers, number-theoretic functions, and sets of natural numbers (which can be used to represent real numbers, facilitating the study of mathematical analysis). A common idea is that a concrete means of computing the values of the function must be known before the function itself can be said to exist.


title: Mathematical logic

text: In the early 20th century, Luitzen Egbertus Jan Brouwer founded intuitionism as a part of philosophy of mathematics . This philosophy, poorly understood at first, stated that in order for a mathematical statement to be true to a mathematician, that person must be able to "intuit" the statement, to not only believe its truth but understand the reason for its truth. A consequence of this definition of truth was the rejection of the law of the excluded middle, for there are statements that, according to Brouwer, could not be claimed to be true while their negations also could not be claimed true. Brouwer's philosophy was influential, and the cause of bitter disputes among prominent mathematicians. Later, Kleene and Kreisel would study formalized versions of intuitionistic logic (Brouwer rejected formalization, and presented his work in unformalized natural language). With the advent of the BHK interpretation and Kripke models, intuitionism became easier to reconcile with classical mathematics.


title: Nondualism

text: Nondualism, also called nonduality and nondual awareness, is a fuzzy concept originating in Indian philosophy and religion for which many definitions can be found, including: nondual awareness, the nonduality of seer and seen or nondifference of subject and object; the identity of conventional phenomena and ultimate reality, or the "nonduality of duality and nonduality"; metaphysical monism, the nonplurality of the world and "the interconnection of all things." It may also refer to a negation of dualistic thinking; and to the mystical unity with God or with Ultimate reality.


title: Nondualism

text: The English term is derived from Sanskrit terms such as "advaita" (अद्वैत), "not-two" or "one without a second," which in various Hindu philosophies refers to the identity of "Atman" and "Brahman"; and "advaya", also meaning "not two," but referring to various Buddhist ideas such as the identity of conventional and ultimate reality. In Indian philosophy, these terms refer to several, related strands of thought, and there is no single definition for the English word "nonduality". According to David Loy, it is best to speak of various "nondualities" or theories of nonduality.


title: Nondualism

text: Regarding the metaphysics of interconnectedness, or the "nonpluraility of the world", the first millennium CE saw various Indian philosophies postulating an underlying "basis of unity," "single substrate" or "underlying principle", both in Mahayana Buddhism, and in Hinduism.


title: Nondualism

text: In Buddhist philosophy, non-duality ("advaya") is associated with the teachings of the Madhyamaka school on interdependence, emptiness ("śūnyatā") and the non-duality of absolute and relative truth. The term is also found in the idealist Yogachara philosophy of "mind only" ("citta-matra"), which holds that everything is a transformation of consciousness ("vijñana-parinama"). These teachings, coupled with the doctrine of Buddha-nature, have been influential concepts in the subsequent development of Buddhist thought in India, East Asia and Tibet.


title: Nondualism

text: In Hindu philosophy, non-duality ("advaita") generally refers to the nonduality of Atman (the individual self) and Brahman (the ultimate universal principle). In a metaphysical sense, the term refers to various forms of monism, "the interconnectedness of everything which is dependent upon the nondual One, Transcendent Reality", "the singular wholeness of existence that suggests that the personal self is an illusion". There are various schools of Hindu philosophy which interpret the idea in different ways, from the illusionistic monism of the Advaita Vedanta school (which sees the world as an unreal illusion) to the more realistic qualified non-dualism of the Vishistadvaita school or the realistic monism of Kashmir Shaivism (in which the world is a real transformation of universal consciousness).


title: Nondualism

text: The term non-duality can also be used to describe an experience of "nondual awareness", also called "pure awareness" or "pure consciousness" and the "non-difference of subject and object," is self-luminous awareness or witness-consciousness, a "primordial, natural awareness" which is described as the essence of being, 'centerless' and without dichotomies. Indian ideas of nondual awareness developed in various religious milieus in the 1st millennium BCE. In the Indian traditions, the realisation of a primordial consciousness (variously called "Purusha" or "Turiya" in Hinduism and "pariniṣpanna" or luminous mind in Buddhism), witnessing but disengaged from the entanglements of the ordinary mind and "samsara", is considered moksha or nirvana, a total release from all suffering and reincarnation.


title: Nondualism

text: Ideas of nondual awareness can also be found in other religious traditions, such as Sufism (see: Wahdat al Wujud, Fanaa, and Haqiqah), as well as in Christian mysticism and Neoplatonism (henosis, mystical union). Western Neoplatonism is an essential element of both Christian contemplation, Islamic Dhikr, mysticism, Western esotericism and modern spirituality, especially Unitarianism, Transcendentalism, Universalism and Perennialism.


title: Nondualism

text: "Dual" comes from Latin "duo," two, prefixed with "non-" meaning "not"; "non-dual" means "not-two." When referring to nondualism, Hinduism generally uses the Sanskrit term "Advaita," while Buddhism uses "Advaya" (Tibetan: "gNis-med," Chinese: "pu-erh," Japanese: "fu-ni")"."


title: Nondualism

text: "Advaita" (अद्वैत) is from Sanskrit roots "a", not; "dvaita", dual. As "Advaita", it means "not-two." or "one without a second," and is usually translated as "nondualism", "nonduality" and "nondual". The term "nondualism" and the term ""advaita"" from which it originates are polyvalent terms.


title: Nondualism

text: "Advaya" (अद्वय) is also a Sanskrit word that means "identity, unique, not two, without a second," and typically refers to the two truths doctrine of Mahayana Buddhism, especially Madhyamaka.


title: Nondualism

text: The English term "nondual" was informed by early translations of the Upanishads in Western languages other than English from 1775. These terms have entered the English language from literal English renderings of "advaita" subsequent to the first wave of English translations of the Upanishads. These translations commenced with the work of Müller (1823–1900), in the monumental "Sacred Books of the East" (1879). Max Müller rendered "advaita" as "Monism", as have many recent scholars. However, some scholars state that "advaita" is not really monism.


title: Nondualism

text: Nondualism is a fuzzy concept, for which many definitions can be found. According to David Loy, since there are similar ideas and terms in a wide variety of spiritualities and religions, ancient and modern, no single definition for the English word "nonduality" can suffice, and perhaps it is best to speak of various "nondualities" or theories of nonduality. Loy sees non-dualism as a common thread in Taoism, Mahayana Buddhism, and Advaita Vedanta, distinguishes "Five Flavors Of Nonduality":


title: Nondualism

text: Brahmanical and non-Brahmanical ascetic traditions of the first millennium BCE developed in close interaction, utilizing proto-Samkhya enumerations (lists) analyzing experience in the context of meditative practices providing liberating insight into the nature of experience. The first millennium CE saw a movement towards postulating an underlying "basis of unity," both in the Buddhist Madhyamaka and Yogacara schools, and in Advaita Vedanta, collapsing phenomenal reality into a "single substrate or underlying principle."


title: Nondualism

text: Nondual awareness refers to "a primordial, natural awareness without subject or object". According to Hanley, Nakamura and Garland, nondual awareness is central to contemplative wisdom traditions, "a state of consciousness that rests in the background of all conscious experiencing – a background field of awareness that is unified, immutable, and empty of mental content, yet retains a quality of cognizant bliss [...] This field of awareness is thought to be ever present, yet typically unrecognized, obscured by discursive thought, emotion, and perception." According to Josipovic, "consciousness-as-such is a non-conceptual nondual awareness, whose essential property is non-representational reflexivity. This property makes consciousness-as-such phenomenologically, cognitively and neurobiologically a unique kind, different from and irreducible to any contents, functions and states." It is the pure consciousness or witness-consciousness of the Purusha of Samkhya and the Atman of Advaita Vedanta, which is aware of prakriti, the entanglements of the muddled mind and cognitive apparatus.


title: Nondualism

text: According to Espín and Nickoloff, referring to monism, "nondualism" is the thought in some Hindu, Buddhist and Taoist schools, which, generally speaking, "teaches that the multiplicity of the universe is reducible to one essential reality." The idea of nondualism as monism is typically contrasted with dualism, with dualism defined as the view that the universe and the nature of existence consists of two realities, such as the God and the world, or as God and Devil, or as mind and matter, and so on. In Advaita Vedanta, nonduality refers to monism, the nonduality of Atman and Brahman.