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  Encyclopedia of Keywords > Information > Science > Mathematics > Set Theory > Paradox   Michael Charnine

Keywords and Sections
HISTORY
ETHICS DEBATES
CENTRAL PARADOX
BIRTHDAY PARADOX
GOTTLOB FREGE
ANTINOMY
ONTOLOGICAL PARADOX
SKOLEM PARADOX
CESARE BURALI-FORTI
EPIMENIDES PARADOX
PETERSBURG PARADOX
PARADOX ENTERTAINMENT
DIAMOND-WATER PARADOX
ZERMELO SET THEORY
AXIOMATIC SET THEORY
BLACK HOLE INFORMATION PARADOX
BANACH-TARSKI PARADOX
BURALI-FORTI PARADOX
TARSKI PARADOX
EPR PARADOX
LIAR PARADOX
CAUSALITY
GRANDFATHER PARADOX
DISAMBIGUATION
SESTET
POEM
COURSE
ARISTOTLE
PROPOSITION
WHETHER
ARGUING
CONSEQUENCE
EXISTENCE
ROWLING
PUZZLE
SOLVING
NAMELY
DISCUSSION
QUESTION
GEORG CANTOR
MATHEMATICIANS
TIMELINE
THREE TYPES
SELF-REFERENCE
REASONING
AVOIDING
Review of Short Phrases and Links

    This Review contains major "Paradox"- related terms, short phrases and links grouped together in the form of Encyclopedia article.

Definitions

  1. A paradox is a proposition that is or appears to be contradictory but expresses some measure of truth.
  2. A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition.
  3. A paradox is a set of statements that are apparently true but, when compared with each other, indicate a contradiction that is intuitively untrue.
  4. A paradox (from the Greek word meaning "contrary to expectation") is a statement that seems self-contradictory but may be true. (Web site)
  5. A paradox is an idea which appears to be in contradiction on the surface, but in harmony at deeper levels of understanding.

History

  1. History of Condorcet and an example of the paradox of Condorcet from a vote in congress in 1956. (Web site)

Ethics Debates

  1. In moral philosophy, paradox plays a central role in ethics debates.
  2. Moral paradox In moral philosophy, paradox plays a central role in ethics debates. (Web site)

Central Paradox

  1. Yet, and this is a central paradox of the Nation of Islam, in the face of this destruction all action taken is constructive.

Birthday Paradox

  1. For example, the Birthday paradox is more of a surprise than a paradox, while the resolution of Curry's paradox is still a matter of contention. (Web site)
  2. Flip side of the birthday paradox, Mancur Olson, logic of collective action.

Gottlob Frege

  1. Gottlob Frege on Russell s paradox [45] The B method, and formal methods in general, are based on formal logic and set theory.

Antinomy

  1. However, if any paradox, dilemma, or antinomy were to be true of the world, it would stop. (Web site)

Ontological Paradox

  1. It is very closely related to the ontological paradox and usually occurs at the same time.

Skolem Paradox

  1. A set theory called intuitive set theory is introduced in which the Skolem Paradox does not appear.

Cesare Burali-Forti

  1. In 1897 the first published paradox appeared, published by Cesare Burali-Forti. (Web site)
  2. The Burali-Forti paradox is named after Cesare Burali-Forti, who discovered it in 1897. (Web site)

Epimenides Paradox

  1. Since that time, the Epimenides paradox has been commonly employed in discussions of logic. (Web site)

Petersburg Paradox

  1. The St. Petersburg paradox and the theory of marginal utility have been highly disputed in the past.
  2. The expected utility model was first proposed by Daniel Bernoulli as a solution to the St. Petersburg paradox. (Web site)

Paradox Entertainment

  1. This division is, as of 2005, separated from Paradox Entertainment and is known as Paradox Interactive.
  2. Hearts of Iron (HoI) is a grand strategy computer game developed by Paradox Entertainment and Strategy First, set in the years 1936-1948. (Web site)

Diamond-Water Paradox

  1. Menger resolved the Diamond-Water Paradox posed by Adam Smith.Menger did this by showing how exchange values in markets to derive from marginal value in use. (Web site)

Zermelo Set Theory

  1. One important method of resolving this paradox was proposed by Ernst Zermelo.[ 111] Zermelo set theory was the first axiomatic set theory.

Axiomatic Set Theory

  1. The Banach-Tarski paradox was a major contribution to the work being done on axiomatic set theory around this period. (Web site)

Black Hole Information Paradox

  1. The black hole information paradox is a very poorly understood problem. (Web site)
  2. This runs counter to the rules of quantum mechanics and is known as the black hole information paradox.

Banach-Tarski Paradox

  1. In fact, proving the necessary properties is harder than proving the Pythagorean theorem itself (see Lebesgue measure and Banach-Tarski paradox). (Web site)
  2. In axiomatic set theory, if one chooses to accept the axiom of choice, axiomatics allows such results as the Banach-Tarski paradox. (Web site)
  3. This theorem, known as the Banach-Tarski paradox, is one of many counterintuitive results of the axiom of choice.

Burali-Forti Paradox

  1. Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number which is smaller than itself. (Web site)
  2. This much is certain — ZFC is immune to the classic paradoxes of naive set theory: Russell's paradox, the Burali-Forti paradox, and Cantor's paradox. (Web site)
  3. The first modern paradox appeared with Cesare Burali-Forti 's 1897 A question on transfinite numbers[ 3] and would become known as the Burali-Forti paradox. (Web site)

Tarski Paradox

  1. One example is the Banach–Tarski paradox, a theorem widely considered to be nonintuitive.

Epr Paradox

  1. He produced a series of objections to the theory, the most famous of which has become known as the EPR paradox. (Web site)

Liar Paradox

  1. The liar paradox and other paradoxes were studied in medieval times under the heading insolubilia. (Web site)
  2. An analysis of several attempted resolutions of the Epimenides Paradox (also known as the Liar Paradox), showing how they all fail.
  3. Many philosophers, attempting to explain the liar paradox, concluded that the problem was with the word "this". (Web site)

Causality

  1. It is only perceived as a paradox because it goes against conventional expectations and assumptions about causality. (Web site)

Grandfather Paradox

  1. What happens if you try to go back in time and kill your grandfather?—see grandfather paradox.
  2. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence.
  3. The best examples of this are the grandfather paradox and the idea of autoinfanticide. (Web site)

Disambiguation

  1. For other uses, see Paradox (disambiguation).
  2. For other uses, see Arrow paradox (disambiguation). (Web site)

Sestet

  1. The paradox is carried over and developed further in the sestet.
  2. Often the octet will pose a problem or paradox which the sestet will resolve. (Web site)

Poem

  1. Thus the paradox that is developed all through the poem reaches its final statement in this line.

Course

  1. Quine's classification, of course, is useful only once a paradox has a clear resolution.
  2. This is of course a paradox only when we insist on visualizing abstract sets as something that exists in the physical world. (Web site)

Aristotle

  1. Aristotle had fallen into the paradox of resolving a mental act into verbal elements. (Web site)

Proposition

  1. He also mused about a proposition which is now referred to as the " Fermi Paradox ".

Whether

  1. When one thinks about whether the barber should shave himself or not, the paradox begins to emerge. (Web site)
  2. The great paradox of modern musical life, whether in the classical or pop arena, is that we both worship our idols and, in a way, straitjacket them.

Arguing

  1. David Ricardo (seconded by Marx) responded to this paradox by arguing that Smith had confused labor with wages. (Web site)

Consequence

  1. In consequence, vagueness gives rise to the Paradox of the heap. (Web site)

Existence

  1. Epicurean paradox (or Problem of Evil): The existence of evil is incompatible with the existence of an omnipotent and caring God.
  2. Thus the Fermi Paradox cannot logically be raised as an objection to the existence of ETI until these major observational deficiencies have been corrected. (Web site)
  3. The best-known paradoxes such as the Banach–Tarski paradox and Hausdorff paradox are based on the existence of non-measurable sets. (Web site)

Rowling

  1. In the course of the second book, Rowling established the paradox that Voldemort hated non-pure blood wizards, despite being a half-blood himself. (Web site)

Puzzle

  1. Necktie Paradox Necktie paradox The necktie paradox is a puzzle or paradox within the subjectivistic interpretation of probability theory. (Web site)

Solving

  1. The first step in solving a paradox is to understand it.

Namely

  1. Explores the paradox of utility: namely, if being useful means serving a further end, then the ultimate end of utility can only be useless.
  2. The paradox shows up in two episodes of The Fairly OddParents cartoon series, namely The Secret Origin of Denzel Crocker and Father Time. (Web site)

Discussion

  1. The World of Paradox - Site containing some well-known paradoxes, together with a discussion of each. (Web site)

Question

  1. Without a resolution to this paradox the basic theory of mathematics was in question. (Web site)
  2. An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. (Web site)
  3. The emerging field of astrobiology has brought an interdisciplinary approach to the Fermi paradox and the question of extraterrestrial life. (Web site)

Georg Cantor

  1. This paradox is named for Georg Cantor, who is often credited with first identifying it in 1899 (or between 1895 and 1897).

Mathematicians

  1. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. (Web site)
  2. Most mathematicians agree that the Skolem paradox creates no contradiction. (Web site)

Timeline

  1. In this demo you will see the oscillations of both outcomes of the paradox on the timeline and on the field.
  2. Another classical paradox and a striking proof that you don't need a machine which transports your complete body into the past to mix up the timeline.
  3. Interesting, the watch causes a "time paradox", it has no start in the timeline.

Three Types

  1. This engaging book includes fifty puzzles and focuses on three types of paradox.

Self-Reference

  1. Once we properly understand this sort of self-reference, they claimed, the paradox no longer arises.

Reasoning

  1. A paradox which is in neither class may be an antinomy, which reaches a self-contradictory result by properly applying accepted ways of reasoning.

Avoiding

  1. Thus, it may be tempting to think that the paradox is avoidable by avoiding the law of excluded middle, as with intuitionistic logic.
  2. In 1908, two ways of avoiding the paradox were proposed, Russell's type theory and the Zermelo set theory, the first constructed axiomatic set theory. (Web site)
  3. All expressions in Z notation are typed, thereby avoiding some of the paradox es of naive set theory.

Categories

  1. Information > Science > Mathematics > Set Theory
  2. Earth > Continents > Europe > Russell
  3. Cantor
  4. Encyclopedia of Keywords > Thought > Philosophy > Logic
  5. Condorcet

Subcategories

Russell`s Paradox

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      Originally created: April 11, 2005.
      Links checked: May 10, 2013.
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