First published in 1982, Kripke's Wittgenstein on Rules and Private Language contends that the central argument of Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of our ever following rules in our use of language.

The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever following rules in our use of language.

However, most traditional bows are not center-shot and the arrow has to deflect around the handle in the archer's paradox ; such bows tend to give most consistent results with a narrower range of arrow spine that allows the arrow to deflect correctly around the bow.

This paradox is often spun around backwards, to illustrate that pleasure and happiness cannot be reverse-engineered.

Something similar can be said around the well-known Russell's paradox ( Does the set of all those sets that do not contain themselves contain itself?

With a more sophisticated understanding of relative velocity time dilation, this seeming twin paradox turns out not to be a paradox at all ( the resolution of the paradox involves a jump in time, as a result of the accelerated observer turning around ).

This paradox of youth is even more remarkable for stars that are on very tight orbits around Sagittarius A *, such as S2.

Zane Grey describes him as a gentle-voiced, sad-faced man who was a hater and killer of Mormons ; together, these characteristics appear to be a paradox for the people around him.

As the newly named Tropical Storm Gay strengthened, it " presented a paradox to forecasters " according to Lieutenant Dianne K. Crittenden ; synoptic data from Malaysia and Thailand indicated decreasing wind speeds and increasing barometric pressures around the storm, but these observations were later interpreted as increased subsidence.

Paradox soon takes his leave as Jaden explains to Yusei what Paradox's true intentions are: He plans to kill Pegasus around the time he was creating Duel Monsters, thus preventing the events of all 3 series from ever occurring & causing a time paradox.

His travels around the galaxy uncover information about the Fermi paradox ( see below ).

It is thus now possible again to reason about sets in a non-axiomatic fashion without running afoul of Russell's paradox, namely by reasoning about the elements of V. Whether it is appropriate to think of sets in this way is a point of contention among the rival points of view on the philosophy of mathematics.

" The Mapplethorpe trial and the paradox of its formalist and liberal defense: sights of contention.

In general relativity theory, it is still possible for the paradox to hold in a finite universe: though the sky would not be infinitely bright, every point in the sky would still be like the surface of a star.

In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of which makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.

However, this scenario can be resolved within the standard framework of special relativity ( because the twins are not equivalent ; the space twin experienced additional, asymmetrical acceleration when switching direction to return home ), and therefore is not a paradox in the sense of a logical contradiction.

Einstein considered this to be a natural consequence of special relativity, not a paradox as some suggested, and in 1911, he restated and elaborated on this result as printed below, ( with physicist Robert Resnick's comments following Einstein's ):

The standard textbook approach treats the twin paradox as a straightforward application of special relativity.

In a theory like general relativity, which presumes a single space-time continuum, the paradox may be blocked.

In each case, where general relativity fails as the curvature of space-time invokes singularities from its equations at t = 0, the statistically " gray " nature of quantum cosmology tends to allow a scientific rationale to account for each paradox, and in so doing allows for a scientific perspective on previously theistic terrain.

* Bell's spaceship paradox ( special relativity )

* Ladder paradox ( special relativity )

* Twin paradox ( special relativity )

The basic plot line is derived from a 1911 thought experiment in special relativity, commonly called the twin paradox, proposed by French physicist Paul Langevin.

Initially Dingle argued that, contrary to the usual understanding of the famous twin paradox, special relativity did not predict unequal aging of twins, one of whom makes a high-speed voyage and returns to Earth, but he then came to realize and acknowledge that his understanding had been mistaken.

Several solutions have been proposed to solve this kind of paradox, all of them in agreement with special relativity.

Because the pairs of putatively simultaneous moments are identified differently by different observers ( as illustrated in the twin paradox article ), each can treat the other clock as being the slow one without relativity being self-contradictory.

Local realism is a significant feature of classical mechanics, of general relativity, and of electrodynamics ; but quantum mechanics largely rejects this principle due to the theory of distant quantum entanglements, an interpretation rejected by Einstein in the EPR paradox but subsequently apparently quantified by Bell's inequalities.

During his career, Paul Langevin also did much to spread the theory of relativity in France and created what is now called the twin paradox.

The black hole information paradox results from the combination of quantum mechanics and general relativity.

The ladder paradox ( or barn-pole paradox ) is a thought experiment in special relativity.

The paradox has also been studied by George Matsas, who used mathematical methods from general relativity to remove Supplee's assumptions.

Relativistic phase is often overlooked by students of special relativity, but if it is understood, then phenomena such as the twin paradox are easier to understand.

For example, special relativity has traditionally yielded two common paradoxes: the twin paradox and the ladder paradox.

Another paradox associated with relativity is Supplee's paradox which seems to describe two reference frames that are irreconcilable.

After the appearance of Leontief's paradox, many researchers tried to save the Heckscher-Ohlin theory, either by new methods of measurement, or either by new interpretations.

This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence, a concept related to the law of the excluded middle.

In 1950, the idea was independently revived by Dutch astronomer Jan Hendrik Oort as a means to resolve a paradox: over the course of the Solar System's existence, the orbits of comets are unstable ; eventually, dynamics dictate that a comet must either collide with the Sun or a planet, or else be ejected from the Solar System by planetary perturbations.

This question results in a paradox because, according to the statement above, he can either be shaven by:

But a paradox may either refer to a surprising but true result in a given formal theory, or to an informal argument leading to a contradiction, so that a candidate theory where a formalization of the argument might be attempted must disallow at least one of its steps ; in this case the problem is to find a satisfying theory without contradiction.

" In support of this, he referred to " the paradox of Rush Limbaugh, ensconced in a Palm Beach mansion massaging the resentments across the country of white-knuckled wage earners, who are barely making ends meet in no small part because of the corporate and ideological forces for whom Rush has been a hero .... As Eric Alterman reports in his recent book — a book that I'm proud to have helped make happen — part of the red meat strategy is to attack mainstream media relentlessly, knowing that if the press is effectively intimidated, either by the accusation of liberal bias or by a reporter's own mistaken belief in the charge's validity, the institutions that conservatives revere — corporate America, the military, organized religion, and their own ideological bastions of influence — will be able to escape scrutiny and increase their influence over American public life with relatively no challenge.

* The Smith set can have more than one candidate, either because of pair-wise ties or because of cycles, such as in Condorcet's paradox.

( The same paradox arises if we make it discrete: the side is either exactly 3 cm, 4 cm, or 5 cm, mutatis mutandis.

Stefan Pernar argues along the lines of Meno's paradox against the usefulness of Yudkowsky's approach by pointing out that attempting to solve the FAI problem is either pointless or hopeless depending on whether one assumes a universe that exhibits moral realism or not.

" Socrates rephrases the question, which has come to be the canonical statement of the paradox: " man cannot search either for what he knows or for what he does not know He cannot search for what he knows -- since he knows it, there is no need to search -- nor for what he does not know, for he does not know what to look for.

Unlike more general concepts of autology and self-reference, this particular distinction and opposition of " autological " and " heterological words " is uncommon in linguistics for describing linguistic phenomena or classes of words, but is current in logic and philosophy where it was introduced by Kurt Grelling and Leonard Nelson for describing a semantic paradox, later known as Grelling's paradox or the Grelling-Nelson paradox .< ref > Grelling and Nelson used the following definition when first publishing their paradox in 1908: " Let < big > φ </ big >( M ) be the word that denotes the concept defining M. This word is either an element of M or not.

Two events would merge into the nearest event which does not produce a paradox ( a dead grandfather in one universe but not in another would either create a dead grandfather in both universes, but alter the person's heritage so as to allow this, merge both timelines so that the person would fade from all timelines upon return, or produce a mean between life and death such as a coma ).

Since the uncertainty principle says that either of them can be determined, but both cannot be determined at the same time, he faces a paradox.

The Ellsberg paradox is based on the difference between these two types of risk, and the problems it poses for utility theory – one is faced with an urn that contains 30 red balls and 60 balls that are either all yellow or all black, and one then draws a ball from the urn.

Unlike the Bertrand paradox, the situation of both companies charging zero-profit prices is not an equilibrium, since either company can raise its price and generate profits.