The statement also points to a classic paradox: The more men turn toward God, who is not only in himself the paradigm of all unity but also the only ground on which human unity can ultimately be established, the more men splinter into groups and set themselves apart from one another.

Swift also recognizes the implications of such a fact in making mercantilist philosophy a paradox: the wealth of a country is based on the poverty of the majority of its citizens.

For example, the Banach – Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition.

In other formulations of the Berry paradox, such as one that instead reads: "... not nameable in less ..." the term " nameable " is also one that has this systematic ambiguity.

Work on " Skilled Memory and Expertise " by Anders Ericsson and James J. Staszewski confronts the paradox of expertise and claims that people not only acquire content knowledge as they practice cognitive skills, they also develop mechanisms that enable them to use a large and familiar knowledge base efficiently.

The fifth and sixth paradoxes are also a single paradox and is usually thought to relate to the vagueness of language.

The paradox is further extended when one considers that – despite his claims of spiritual authority over Philemon – Paul frames himself – and, by extension, both Philemon and Onesimus – as fellow bondservants of Christ, who being their spiritual master, is also their brother and equal.

It is also often seen as the solution to the " Leontief paradox " in international trade.

Moore is also remembered for drawing attention to the peculiar inconsistency involved in uttering a sentence such as " It is raining but I do not believe it is raining "-- a puzzle which is now commonly called " Moore's paradox.

In addition to Moore's own work on the paradox, the puzzle also inspired a great deal of work by Ludwig Wittgenstein, who described the paradox as the most impressive philosophical insight that Moore had ever introduced.

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.

There are also multi-sentence versions of the liar paradox.

In astrophysics and physical cosmology, Olbers ' paradox, named after the German astronomer Heinrich Wilhelm Olbers and also called the " dark night sky paradox ", is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe.

According to Harrison, the first to conceive of anything like the paradox was Thomas Digges, who was also the first to expound the Copernican system in English and may have been the first to postulate an infinite universe with infinitely many stars.

Kepler also posed the problem in 1610, and the paradox took its mature form in the 18th century work of Halley and Cheseaux.

This paradox is explained by the fact that the Big Bang theory also involves the expansion of space which can cause the energy of emitted light to be reduced via redshift.

A consequence to which also introduces another paradox showing how creation would thus be an impossible action to where an omniscient entity could only infinitely know everything with the inability to create or alter anything in or of existence.

However, he was also the first to notice some of the apparently exotic consequences of entanglement, and used them to formulate the Einstein-Podolsky-Rosen paradox in the hope of showing that quantum mechanics had unacceptable implications.

Economist Hyman Minsky also described a " paradox of deleveraging " as financial institutions that have too much leverage ( debt relative to equity ) cannot all de-leverage simultaneously without significant declines in the value of their assets.

The stretching of space also accounts for the apparent paradox that two galaxies can be 40 billion light years apart, although they started from the same point 13. 7 billion years ago and never moved faster than the speed of light.

The voting paradox ( also known as Condorcet's paradox or the paradox of voting ) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic ( i. e. not transitive ), even if the preferences of individual voters are not.

Interestingly, the halting paradox still applies to such machines ; although they determine whether particular Turing machines will halt on particular inputs, they cannot determine, in general, if machines equivalent to themselves will halt.

A similar paradox applies to the vertical resolution in television in general: reducing the bandwidth of the video signal will preserve the vertical resolution, even if the image loses sharpness and is smudged in the horizontal direction.

* if the Sorites paradox applies to the concept or predicate.

The paradox arises, according to this resolution, because we implicitly interpret Nicod's criterion as applying to all predicates when in fact it only applies to natural kinds.

The barber's claim applies to only " men in our town ," so there is no paradox if the barber is a woman ( or a gorilla, or a child, or a man from some other town — or anything other than a " man in our town ").

Such a variation is not considered to be a paradox at all: the true Barber paradox requires the contradiction arising from the situation where the barber's claim applies to himself.

The paradox applies equally well both north and south of the equator.

This version of the paradox applies only to well-ordered sets with a natural order, such as the natural numbers ; the argument would not apply to the real numbers.

As the paradox lies in the definition of " interesting ", it applies only to persons with particular opinions on numbers: if one's view is that all numbers are boring, and one finds uninteresting the observation that 0 is the smallest boring number, there is no paradox.

The Epimenides paradox applies to anything that makes statements, whether they are machines or humans, even Lucas himself, as in:

) As a corollary, they obtain that Braess's paradox is about as likely to occur as not occur ; their result applies to random rather than planned networks and additions.

As the Jevons paradox applies only to technological improvements that increase fuel efficiency, policies that impose conservation standards and increase costs do not display the paradox.

As the Jevons paradox applies only to technological improvements that increase fuel efficiency, the imposition of conservation standards that simultaneously increase costs does not cause an increase in fuel use.

The paradox of perfection — that imperfection is perfect — applies not only to human affairs, but to technology.

The holographic principle resolves the black hole information paradox within the framework of string theory.

It becomes a paradox within a paradox that seems to simply self-nullify a boundless and limitless omniscient being.

Thus, it was important to uncover the hidden patterns of circularity, self-reference and paradox within a given set of statements rather that feign objectivity, as such an investigation might allow new perspectives to have influence and new practices to be sanctioned or adopted.

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.

Astronomers think that the sun had about 70 – 75 % of the present luminosity, yet temperatures appear to have been near modern levels even within 500 Ma of Earth's formation, which is puzzling ( the faint young sun paradox ).

" The paradox of this music was that it was new, using techniques never known before, but it took place within the framework of old-fashioned forms.

Several schools of the philosophy of mathematics ran into difficulties one after the other in the 20th century, as the assumption that mathematics had any foundation that could be consistently stated within mathematics itself was heavily challenged by the discovery of various paradoxes ( such as Russell's paradox ).

An interesting paradox is created within this poem.

It was found that set theory could be formulated as an axiomatized system within the apparatus of first-order logic ( at the cost of several kinds of completeness, but nothing so bad as Russell's paradox ), and this was done ( see Zermelo-Fraenkel set theory ), as sets are vital for mathematics.

Feri witches often see themselves as " fey ": outside social definitions and intentionally living within paradox.

Skolem also pointed out that a consequence of the Löwenheim – Skolem theorem is what is now known as Skolem's paradox: If Zermelo's axioms are consistent, then they must be satisfiable within a countable domain, even though they prove the existence of uncountable sets.

In this case Dasein still authentically chooses the tradition when it is confronted by a paradox within the tradition and must choose to dismiss the tradition or dismiss the experience of being confronted with choice.

The Bertrand paradox is a problem within the classical interpretation of probability theory.

Fitzpatrick's project presented Foster with a paradox: he did not think that electoral politics had much potential for advancing the rights of workers, much less revolutionary goals, and he had even less regard for progressive reformists such as Robert La Follette, Sr .. On the other hand, he was attacked from the left within the party for his relations with Fitzpatrick and the CFL, which were denounced as too conservative.

* A series of jokes is based on a paradox of vulgarity within the " high society " setting.

Scottish Common Sense Realism is a school of philosophy that sought to defend naive realism against philosophical paradox and scepticism, arguing that matters of common sense are within the reach of common understanding and that common-sense beliefs even govern the lives and thoughts of those who hold non-commonsensical beliefs.

The liberal paradox is a logical paradox advanced by Amartya Sen, building on the work of Kenneth Arrow and his impossibility theorem, which showed that within a system of menu-independent social choice, it is impossible to have both a commitment to " Minimal Liberty ", which was defined as the ability to order tuples of choices, and Pareto optimality.

Specially the question of gender, and what is referred to as the gender paradox ( the fact that although Norwegian women are largely represented within the working stock, more so than most countries, the Norwegian job market remains highly segregated in terms of gender ) has provoked controversy.

But suddenly Earth is a threat, its people on the verge of discovering interstellar travel, and with it, of gaining access to Dreenor itself-a paradox within a paradox, not to be permitted.

The Doctor explains to Rose that her actions have caused a paradox that normally the Time Lords would have prevented, but without them, the Reaper are sterilising the wound in time by consuming everyone within it.

The title suggests a paradox: a rural or pastoral place within a modern urban setting.