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 an ideal " perfect hash function ", no bucket should have more than one record ; but a small number of collisions is virtually inevitable, even if n is much larger than m – see the birthday paradox ).

An opposite iterated technique, counting down rather than up, is found in the Sorites paradox, where one argued that if 1, 000, 000 grains of sand formed a heap, and removing one grain from a heap left it a heap, then a single grain of sand ( or even no grains ) forms a heap.

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.

This would not resolve the paradox given the following argument: According to the laws of thermodynamics, the intermediate matter must eventually heat up ( or cool down, if it was initially hotter ) until it is in thermal equilibrium with the surrounding stars.

They both postulated that if the stars in the universe were distributed in a hierarchical fractal cosmology ( e. g., similar to Cantor dust )— the average density of any region diminishes as the region considered increases — it would not be necessary to rely on the Big Bang theory to explain Olbers ' paradox.

A paradox is a statement or group of statements that leads to a contradiction or a situation which ( if true ) defies logic or reason, similar to circular reasoning.

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 is resolved if it is revealed that the surgeon is a woman, the boy's mother.

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.

The grandfather paradox, for example, would arise if a time traveler were to kill his own grandfather before his mother or father was conceived, thereby preventing his own birth.

Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays, if he was born on a leap day.

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 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.

Stated simply, the Novikov consistency principle asserts that if an event exists that would give rise to a paradox, or to any " change " to the past whatsoever, then the probability of that event is zero.

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology, a self-evident truth that cannot possibly be false, because if you make the assumption that it is false this would lead to a logical paradox.

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.

The prisoner's reasoning, which gives rise to the paradox, is able to get off the ground because the prisoner tacitly assumes that on Monday evening, he will ( if he is still alive ) know S1, S2, and S3 to be true.

While stating that if time travel is possible it would be impossible to violate the grandfather paradox, it goes further to state that any action taken that itself negates the time travel event cannot occur.

On the other hand, if one traveled back and did something else that as a result prevented the death of someone else's parents, then such an event would be successful, because the reason for the journey and therefore the journey itself remains unchanged preventing a paradox.

The paradox states that: if a being can perform any action, then it should be able to create a task which this being is unable to perform ; hence, this being cannot perform all actions.

" ere's the interesting paradox: The reputation economy creates an incentive to be more open, not less.

An interesting paradox is created within this poem.

The interesting number paradox is a semi-humorous paradox that arises from attempting to classify natural numbers as " interesting " or " dull ".

The paradox states that all natural numbers are interesting.

Since the definition of interesting is usually a subjective, intuitive notion of " interesting ", it should be understood as a half-humorous application of self-reference in order to obtain a paradox.

One proposed resolution of the paradox asserts that only the first uninteresting number is made interesting by that fact.

However, this resolution is invalid, since the paradox is proved by contradiction: assuming that there is any uninteresting number, we arrive to the fact that that same number is interesting, hence no number can be uninteresting ; its aim is not in particular to identify the interesting or uninteresting numbers, but to speculate whether any number can in fact exhibit such properties.

However, assuming this predicate is defined with a finite, definite list of " interesting properties of positive integers ", and is defined self-referentially to include the smallest number not in such a list, a paradox arises.

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.

This creates a rather interesting continuity paradox.

This is an interesting paradox: there has been a gradual increase in brain volume as we progressed along the Human timeline of evolution ( see Homininae ), starting from about in Homo habilis up to in Homo sapiens neanderthalensis.

The interesting paradox is that the Doomsday argument is probably wrong even assuming it to be completely right ( in its 95 % estimate ).

An interesting paradox develops here because Divine Assassins are designed to be immortal, to always survive, a concept developed in episode 18 of season 4, " The Game.