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 (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.
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 is a mini-album released by the Japanese horror punk band Balzac.
The Yes Album is the third studio album from the English progressive rock band Yes, released on 19 February 1971 on Atlantic Records. It is their first album with guitarist Steve Howe who replaced Peter Banks in 1970, and their last in the 1970s to feature keyboardist Tony Kaye.
The album was the first by the group not to feature any cover versions, which had been a staple of their material until that point. The band spent mid-1970 writing and rehearsing new material at a farmhouse in South Molton, Devon, and the new songs were recorded at Advision Studios in the autumn. While the album retained close harmony singing, Kaye's Hammond organ and Chris Squire's melodic bass, as heard on earlier releases, the new material also covered further styles including jazz piano, funk and acoustic music, with all band members contributing ideas, and tracks were extended in length to allow music to develop. Howe contributed a variety of guitar styles, including a Portuguese guitar, and recorded a solo acoustic guitar piece, "Clap", live at the Lyceum Theatre, London.