At the same time, I am aware that my recoil could be interpreted by readers of the tea leaves at the bottom of my psyche as an incestuous sign, since theirs is a science of paradox: if one hates, they say it is because one loves ; ;

It is an understandable paradox that most American history and most American literature is today written from an essentially egocentric and isolationistic point of view at the very time America is spreading her dominion over palm and pine.

The pattern here pictured is clearly not peculiar to Notre Dame: it is simply that the paradox involved in this kind of control of the institution by `` the organization which actually owns '' it, becomes more obvious where there is a larger and more distinguished `` outside '' faculty.

The paradox implicit in the whole affair is shown by the demand of the government, after the conviction, that General Electric sign a wide-open consent decree that it would not reduce prices so low as to compete seriously with its fellows.

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.

The source of this paradox is not difficult to identify.

The technique of reality confusion -- the use of paradox and riddles to shake the mind's grip on reality -- originated with fourth and third century B.C. Chinese Quietism: the koan is not basically a new device.

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.

One example is the Banach – Tarski paradox which says that it is possible to decompose (" carve up ") the 3-dimensional solid unit ball into finitely many pieces and, using only rotations and translations, reassemble the pieces into two solid balls each with the same volume as the original.

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.

This feature is known as the archer's paradox.

This is related to Cesare Burali-Forti's " paradox " that there can be no greatest ordinal number.

A paradox in metabolism is that, while the vast majority of complex life on Earth requires oxygen for its existence, oxygen is a highly reactive molecule that damages living organisms by producing reactive oxygen species.

If nature cannot err, then there are no paradoxes in it ; to Hobbes, the paradox is a form of the absurd, which is inconsistency: " Natural sense and imagination, are not subject to absurdity " and " For error is but a deception ...

One of the secular peculiarities of the Epistle to Titus is the inclusion of text which has become known as the Epimenides paradox.

EPR tried to set up a paradox to question the range of true application of Quantum Mechanics: Quantum theory predicts that both values cannot be known for a particle, and yet the EPR thought experiment purports to show that they must all have determinate values.

Moore is best known today for his defence of ethical non-naturalism, his emphasis on common sense in philosophical method, and the paradox that bears his name.

Both the number of base pairs and the number of genes vary widely from one species to another, and there is only a rough correlation between the two ( an observation known as the C-value paradox ).

It leads to a difficulty known as the Gibbs paradox.

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.

Harrison argues that the first to set out a satisfactory resolution of the paradox was Lord Kelvin, in a little known 1901 paper, and that Edgar Allan Poe's essay Eureka ( 1848 ) curiously anticipated some qualitative aspects of Kelvin's argument:

This sentence is false is an example of the famous liar paradox: it is a sentence which cannot be consistently interpreted as true or false, because if it is known to be false then it is known that it must be true, and if it is known to be true then it is known that it must be false.

He produced a series of objections to the theory, the most famous of which has become known as the Einstein-Podolsky-Rosen paradox.

The name " quine " was coined by Douglas Hofstadter, in his popular science book Gödel, Escher, Bach: An Eternal Golden Braid, in the honor of philosopher Willard Van Orman Quine ( 1908 – 2000 ), who made an extensive study of indirect self-reference, and in particular for the following paradox-producing expression, known as Quine's paradox:

There has been much discussion about the exact nature of the drive phase, because it has now been shown scientifically that the quadriceps have no activity after the supporting phase ; this has become known as the extensor paradox in running.

Edmund Halley ( 1720 ) and Jean-Philippe de Cheseaux ( 1744 ) noted independently that the assumption of an infinite space filled uniformly with stars would lead to the prediction that the nighttime sky would be as bright as the sun itself ; this became known as Olbers ' paradox in the 19th century.

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.

It is also known as the Race Course paradox.

In the arrow paradox ( also known as the fletcher's paradox ), Zeno states that for motion to occur, an object must change the position which it occupies.

The Raven paradox, also known as Hempel's paradox or Hempel's ravens is a paradox proposed by the logician Carl Gustav Hempel in the 1940s to illustrate a problem where inductive logic violates intuition.

Statements such as the Banach – Tarski paradox can be rephrased as conditional statements, for example, " If AC holds, the decomposition in the Banach – Tarski paradox exists.

** The Banach – Tarski paradox.

# redirect Banach – Tarski paradox

Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry ( 1867 – 1928 ), a junior librarian at Oxford's Bodleian library, who had suggested the more limited paradox arising from the expression " the first undefinable ordinal ".

EPR ( Einstein – Podolsky – Rosen ) paradox

The Epimenides paradox appears explicitly in " Mathematical Logic as Based on the Theory of Types ", by Bertrand Russell, in the American Journal of Mathematics, volume 30, number 3 ( July, 1908 ), pages 222 – 262, which opens with the following:

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.

Bell, On the Einstein – Poldolsky – Rosen paradox, Physics 1 195-200 ( 1964 ).

The Jeffreys – Lindley paradox shows how different interpretations, applied to the same data set, can lead to different conclusions about the ' statistical significance ' of a result.

A more detailed examination of the implications of the topic began with a paper by Michael H. Hart in 1975, and it is sometimes referred to as the Fermi – Hart paradox.

The first aspect of the paradox, " the argument by scale ", is a function of the raw numbers involved: there are an estimated 200 – 400 billion ( 2 – 4 × 10 < sup > 11 </ sup >) stars in the Milky Way and 70 sextillion ( 7 × 10 < sup > 22 </ sup >) in the visible universe.

He did not abandon mathematics completely, however, lecturing on the paradoxes of set theory ( Burali-Forti paradox, Cantor's paradox, and Russell's paradox ) to a meeting of the Deutsche Mathematiker – Vereinigung in 1903, and attending the International Congress of Mathematicians at Heidelberg in 1904.