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 ...

In philosophy and logic, the liar paradox or liar's paradox ( pseudomenon in Ancient Greek ) is the statement " this sentence is false.

" Trying to assign to this statement a classical binary truth value leads to a contradiction ( see 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.

The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:

Another reaction to the paradox of ( A ) is to posit, as Graham Priest has, that the statement is both true and false.

The multi-sentence version of the liar paradox generalizes to any circular sequence of such statements ( wherein the last statement asserts the truth / falsity of the first statement ), provided there are an odd number of statements asserting the falsity of their successor ; the following is a three-sentence version, with each statement asserting the falsity of its successor:

An example of a paradox is " This statement is false.

In literature a paradox can be any contradictory or obviously untrue statement, which resolves itself upon later inspection.

; Self-reference: An example is " This statement is false ", a form of the liar paradox.

The apparent paradox is caused by a hasty generalization, for if the surgeon is the boy's father, the statement cannot be true.

The paradox arises when this same process is applied to statement ( 2 ).

Some authors have claimed that the self-referential nature of this statement is the source of the paradox.

Using an equivalent form of the paradox which reduces the length of the week to just two days, he proved that although self-reference is not illegitimate in all circumstances, it is in this case because the statement is self-contradictory.

This objection rests on an understanding of the conclusion to be that the judge's statement is self-contradictory and therefore the source of the paradox.

Finally, Chow suggests that because the statement which the prisoner is supposed to " know " to be true is a statement about his inability to " know " certain things, there is reason to believe that the unexpected hanging paradox is simply a more intricate version of Moore's paradox.

So, to think that omnipotence is an epistemological paradox is like failing to recognize that, when taking the statement, ' I am a liar ' self-referentially, the statement is reduced to an actual failure to lie.

It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.

This work described several now famous results, including Condorcet's jury theorem, which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases as the number of members of the group increases, and Condorcet's paradox, which shows that majority preferences become intransitive with three or more options – it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.

Although the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen independently, the birthday paradox becomes less surprising if a group is thought of in terms of the number of possible pairs, rather than as the number of individuals.

He became known to more than a small group of specialists by formulating his paradox which was extensively use by Poincaré to attack set theory whereupon the advocates of set theory had to refute these attacks.

The Abilene paradox is a paradox in which a group of people collectively decide on a course of action that is counter to the preferences of any of the individuals in the group.

Indeed, if a precise prescriptive definition of " heap " is available then the group consensus will always be unanimous and the paradox does not arise.

Rudy Wade, a member of the group, mentions that the paradox will continue and they'll probably just keep going in circles.

According to the birthday paradox, in a group of 23 ( or more ) randomly chosen people, the probability is more than 50 % that some pair of them will have the same birthday.

This paradox has led Icke, who argues that Christian Patriots are the only Americans who understand the truth about the New World Order ( which he believes is controlled by a race of reptilians known as the " Babylonian Brotherhood "), to reportedly tell a Christian Patriot group:

In group decision-making it is possible for a voting paradox to form.

In 1929, during his work on the Banach – Tarski paradox, John von Neumann defined the concept of amenable groups and showed that no amenable group contains a free subgroup of rank 2.

Including Scott Webb, Jim Levi, Dave Potorti, Jay Newell, Will McRobb, and Tom Hill, the group was guided towards created a series of internal campaigns to emphasize the seeming paradox of a contemporary network setting that programmed reruns from the 1960s.

* Abilene paradox, a form of dysfunctional group dynamics

In addition, Robert Christgau commented on the band's growth from previous efforts, stating that while the group is " devoid of intellectual thrust ," they're " onto something ," and " when it works, it suggests a nice paradox -- relaxed and exciting at the same time.