Paradox

A paradox is a statement that apparently contradicts itself and yet might be true (or wrong at the same time). Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.

Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, are not yet resolved.

Examples outside logic include the Ship of Theseus from philosophy (questioning whether a ship repaired over time by replacing each of its wooden parts would remain the same ship). Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.

Paradox (horse)

Paradox (1882–1890) was a British Thoroughbred racehorse and sire. In a career that lasted from October 1884 until October 1885 he ran eight times and won six races. Despite running only twice in 1884, he proved himself to be one of the best two-year-olds of his generation by winning the Dewhurst Plate. In the following year he won five of his six races including the 2,000 Guineas, the Grand Prix de Paris, the Sussex Stakes and the Champion Stakes. His only defeat came when he was narrowly beaten by Melton in the Epsom Derby.

The final phase of the colt's racing career was marked by controversy and recrimination following his withdrawal from the Cambridgeshire Handicap in the autumn of 1885 and he was retired from racing in 1886. Paradox had little opportunity to establish himself at stud, dying in 1890 at the age of eight.

Background

Paradox was a strongly-built bay horse bred by the Graham brothers at the Yardley Stud near Birmingham. He was sired by the 2,000 Guineas runner-up Sterling out of Casuistry, an undistinguished racehorse who had been sold cheaply at the end of her racing career by Lord Rosebery. Casuistry became an important broodmare, being the direct female ancestor of notable thoroughbreds such as Humorist, Royal Palace and Spend a Buck. As a yearling Paradox was bought for 700 guineas by the trainer John Porter on behalf of his associate, Captain Bowling. Porter trained the colt at his stable at Kingsclere.

Paradox (Balzac album)

Paradox is a mini-album released by the Japanese horror punk band Balzac.

Track listing

Credits

Additional recording members

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External links

Doctor of Philosophy

A Doctor of Philosophy degree (PhD or Ph.D. or DPhil) or a Doctorate of Philosophy, from the Latin Doctor Philosophiae (for DPhil) or Philosophiae Doctor (for PhD or Ph.D.), is a type of doctorate awarded by universities in many countries.

The degree varies considerably according to the country, institution, and time period, from entry-level research degrees to higher doctorates. A person who attains a doctorate of philosophy is automatically awarded the academic title of doctor. During the studies that lead to the degree, the student is called doctoral student or PhD student, but also "doctoral candidate" at the appropriate stage.

In the context of academic degrees, the term philosophy does not refer solely to the field of philosophy, but is used in a broader sense in accordance with its original Greek meaning, which is "love of wisdom". In most of Europe, all fields (history, philosophy, social sciences, mathematics and natural philosophy/natural sciences) other than theology, law, and medicine (the so-called professional, vocational, or technical curriculum) were traditionally known as philosophy, and in Germany and elsewhere in Europe the basic faculty of liberal arts was known as the faculty of philosophy.