List paradoxes

This article is restricted to give briefly the majority of the famous Paradoxe S. These paradoxes are generally treated in a more exhaustive way in articles which theirs are devoted into clean.

The Paradoxe S are gathered here for convenience of reading. It goes without saying this classification is arbitrary and constestable; but if it enables you to find the paradox more quickly than you seek, its goal is reached.

Other paradoxes related to the restricted Relativité are present in the article which is devoted to him, under the designation of Petites experiments of thought .

Autoreferential paradoxes

Paradox of the liar

The paradox of the liar is derived from the paradox of the crétois (or paradox of Épiménide Crétois). In its most concise form, it is stated

I lie!

One can see there two interpretations

* as a statement, this sentence known as: “ This sentence is false. ”

* as matter, it is necessary to include/understand: “ I lie now. ”

In other words, this paradox appears clearly in the following proposal:

If I say that I lie, I do say the truth?

Paradox of Russell

The whole of all the units which are not members of themselves, is member of itself if and only if it is not it. This paradox was found in the axiomatic of Gottlob Frege by Bertrand Russell.

Paradox of the barber

“In the kingdom of Razibus, the king issued the following edict: " The barber must shave only the men who do not shave themselves but it must shave all these derniers" ” Question: who shaves the barber?
Possible solution: nobody shaves the barber because the barber is a woman or a robot.

Paradox of Grelling-Nelson

Is named heterologic a word which does not describe itself. For example: “long” heterologic in this is a word which it is not “long”.

Thus according to this definition, the word “ heterologic ” is autologic if and only if it is not it.

(Even explanation that the Paradox of the liar.)

Paradox of Richard

If one numbers all the definable real numbers in a finished number of words, then one can build, by using the Argument of the diagonal of Cantor a real number out of this list. However this number was defined in a finished number of words.

Paradox of Berry

“Smallest Whole not-describable naturalness by an expression of fifteen words or less. ”

Paradox of the lawyer

Euathlos, if it gains its first lawsuit, must pay Protagoras. However, it is Protagoras itself which decides to attack Euathlos. Therefore, the judgment and the possible damage will be inevitably in direction opposed so that the agreement envisaged.

Semantic paradoxes

Paradox of Moore

It rains outside, but I do not believe that it rains.

G.E.Moore highlighted the inconsistency of this type of sentences.

Paradox of the syllogism in Camestres

Saccheri proposed the Syllogisme in Camestres (AEE of the first figure) according to, built starting from the rules of constructions of the syllogisms (it is implied that the syllogism is first figure):

Any syllogism having major universal and a minor affirmative is conclusive
No syllogism in AEE does not have major universal and a minor affirmative
Donc no syllogism in AEE is not conclusive

However precisely this syllogism is in AEE.

Paradoxes based on a syllogism in A-A-A

This type of paradox draws its name from the Syllogisme S known as as a Barbara , (A-A-A = two universal premises and conclusion and affirmatives):

The paradox of " the emmental" is the most famous example:

Plus there is emmental, more there are holes
gold more there are holes, less there is emmental
thus more there is emmental, less there is emmental.

Another paradox of the same kind, mentioned in almanacs of pre-war period:

a horse good-market is rare.
gold what is rare is expensive
thus a horse good-market is expensive.

(See Theory of the types, to also see page of discussion)

Paradox sorite

An isolated grain does not constitute a heap. The addition of a grain does not make a not-heap, a heap. One from of deduced that one cannot constitute a heap by the accumulation of grains.

Paradox of bearded the

One can remove a hair of barb to bearded, it will remain bearded; however, after a certain number of removed hairs it will not be it any more. Starting from how much hairs it will change statute?

Paradox of egg and the hen

The paradox of egg and the hen is one of oldest and most representative of the vicious circles:

“What appeared in first: the egg or the hen? ”.

Thanks to advanced phylogenesis one knows from now on that only the gamètes and the embryos " evolve/move " and thus that the egg came before hen.

Mathematical paradoxes

No " paradoxe" presented here a real mathematical paradox does not constitute. This is why the Paradoxe of Russell is absent from this list. Some of these " paradoxes" are actually theorems particularly surprising even against-intuitive. Others must be apprehended like simple formative exercises of type: seek the error. They are thus built false results of subtle errors of reasoning. One will find other examples in the article Pseudo-demonstration of equality between numbers. Historically, such errors of reasoning contributed to the formalization of mathematics and the clarification of the concepts used. Let us note as a preliminary that what one calls mathematical paradoxes is not today any more (except the new ones, of course). Indeed, the old paradoxes all were based on a lack of assumptions, or rather must-one-to say, on a lack of total references. One works today in mathematics only by taking care well to define of which elements we speak, and in particular of the space of reference (for the experts, a relation can be paradoxical at the base because is applied in an unspecified space. It is not paradoxical any more as soon as you bring back yourselves to a space of reference, like Banach.) -->

Paradox of Wedge

It is a small underhand geometrical construction, aiming has to show that a triangle can have two different surfaces.

Paradox of the equality between 0,9999… and 1

0,9999… =1. This result is a qualified mathematical curiosity of Paradoxe because of its against-intuitive character, in fact an important result induced by the decimal developments. Indeed let us use for example this reasoning: x=0.9999999 ...... an infinity of 9 then 10x=9.99999 ....... either 10x=9+x thus 9x=9 or x=1? however x=0.99999 ......

Paradox of Galileo or Georg Cantor

There are as many integers than of square numbers because one can make them correspond one by one (1 with 1,2 with 4,3 with 9, etc) whereas the integers contain the square numbers strictly.

In fact, the “number” of entireties as well as of squares is the transfinite first cardinal, $\ aleph_0$ . The laws of composition of transfinite are not those of the finished numbers which compose them. $\ aleph_0$ with the square is equal to $\ aleph_0$ .

Paradoxes on the complex numbers

The mathematicians of the 18th century tried to apply the rules of calculation to the real numbers to the complex numbers, for example:

$\ sqrt {- 2} \ times \ sqrt {- 3} = \ sqrt {- 2 \ times -3} = \ sqrt {6}$ but $\ sqrt {- 2} = \ sqrt {2} \ times I$ and $\ sqrt {- 3} = \ sqrt {3} \ times I$ thus $\ sqrt {- 2} \ times \ sqrt {- 3} = \ sqrt {6} \ times i^2 = - \ sqrt {6}$
ln (- 1) +ln (- 1) =ln ((- 1) 2 ) =ln (1) =0 thus of the same ln (I) =0 thus by taking the Exponential , E ln (I) =e 0 that is to say i=1 since exp∘ln =Id.

These two paradoxes are due to the lack of precision in the definition of the complex numbers and to the loss of properties of certain operations at the time of the passage to the complex numbers. However , it should be held account that these " égalités" " bring into play; ln (- 1) " who are not correct since the function ln is defined only on] 0; +inf

Moreover the square root does not exist in ℂ since there exist two square roots of any complex number. In the same way the logarithm of a complex number is defined except for 2iπ. See further the paradox from “I”.

one can use this paradox while requiring to calculate I I

- I I = (E iπ/2 ) I = (E (iπ/2) I ) = E - π/2 < E

- I I = (E - i3π/2 ) I = (E (- i3π/2) I ) = E 3π/2 > E

thus e>e.

e: forgery! === One obtains exp (- Pi/2) < E and E < exp (3Pi/2), that is to say: exp (- Pi/2) < E < exp (3Pi/2) and nothing more. -->

Paradox of Bertrand

Joseph Bertrand proposed into 1888 to estimate the probability that a cord traced randomly in a given circle is length higher than the side of the registered equilateral triangle. Paradoxically, answers 1/2, 1/3, 1/4 can be all three justified.

Paradox of Burali-Forti

The whole of all the ordinal ones does not have itself of ordinal owing to the fact that this ordinal must be necessarily larger than or at least of size equal to (for a cardinal ℵ) each member of this unit which, consequently and in spite of its definition, does not contain this ordinal.

Paradox of Skolem

The Théorème of Löwenheim-Skolem says that any system of axioms of a countable language, if it has a infinite model, has a countable model . If one applies it to the Set theory ZFC, or to another axiomatic theory intended to found the theorems of Cantor, one obtains a countable universe of all the units defined in ZFC. But one can prove in ZFC which there exist indénombrables units. In other words ZFC affirms that there exist more units than it cannot about it define. Such is the paradox of Skolem. (see also: Theorem of complétude of Gödel)

Paradox of Banach-Tarski

In the space of dimension 3, it is possible to cut out a ball in a finished number of parts, so that by moving these parts one recomposes two of the same balls cuts than the first ball. Cutting is of course not realizable physically; in other words, " morceaux" have forms inimaginablement irregular.

Paradox of “I” or the two square roots

“The Complex numbers are defined compared to a named value I and whose square is defined like -1. But there exists necessarily two such values, because if X has as a square X, - X has the same one. Comment to know about which about the two values we speak? ”

the lifting of this paradox is a very beautiful illustration of the principle of Symétrie: it consists in noticing quite simply that when we said that the square of I is -1, we already said all that there is to say on I . Undoubtedly, the square of - I will be also -1, but that does to nothing but indicate us that any true relation where number I the remainder appears if one replaces it by - I : one cannot indeed carry out functional distinction between - I and I. They have difference only in opposition one to the other (see the vintage and cooks it).

It is left on the initiative it reader check that E - iπ = -1.

Paradox of Potato

Statement of the problem: We have 100 kg from potatoes which consist of 99 liters of water and 1 kg of dry matter. One wants to decrease the water content of our potatoes to obtain potatoes made up of water 98%. For that, one heats apples (only water evaporates) until obtaining the good ratio. The question is: Which is the remaining potato total weight?

the answer is: 50 kg.

Step of the answer: There thus remains to us 98% of water and per complement 2% of dry matter. The matter 2% always account for 1 kg of dry matter. By applying the rule of three simply, one from of deduced that water represents 49 kg. And that the total weight remaining is of 50 kg.

Bad interpretation: The error classically made at the time of the resolution of this paradox is to consider that one removed water 1% compared to the initial total weight. It is concluded whereas the final weight is of 99 kg.

The paradox lies in the confusion which the statement causes. The concepts of percentage are not easy to handle.

Paradoxes related to the Theory of knowledge

Paradox of Hempel

If I say “All the corbels are black”, this sentence is logically equivalent to “All the not-blacks objects are not-corbels”. To reinforce by a process of induction my conviction that “All the not-blacks objects are not-corbels”, I can extremely well remain in my room, to find ten thousand objects nonblack, and check there that they all are well of the not-corbels. Isn't a law which is checked on ten thousand observations without the least exception is certainly valid?

Answer: Not. All that was established, it is that all the objects not-blacks contained in my room are not-corbels. In logical inductive, it is always necessary to specify the context of an observation (see Inférence bayésienne and Conditional probability).

Paradox of Goodman

It is a thorny question on the manner of apprehending certain considerations such as the “" couleur" vleu”:

is “vleu” green object a “until a certain date and blue then”.

Paradox of the life on Ganymède

If one literally takes an old definition of the probability like report/ratio of the number of outcomes successful to the number of possible cases, one arrives at curious results.

Thus are there men on the satellite (of Jupiter) Ganymède? If we take the definition of the probability without precaution, we could be tried to suppose that there is a chance on two!

In this case, the probability that there are around Ganymède neither men, neither cats, neither dogs, neither hens, neither cockroaches, neither ground worms, neither fish, nor birds can be returned as near to 0 as it is wanted (1/2) NR , NR being the number of species considered.

It goes without saying one cannot take the problem in this way. Number of formulas being prided to show that there exists quasi-certainement of the life elsewhere than on Earth have this type of approach however. See also Paradox of Fermi.

Paradox of the surprised interrogation

A professor announces with his pupils: “There will be a surprised interrogation the next week. ”

Paradox of Newcomb

Experiment of thought utilizing a player and a soothsayer able to envisage the choice of the player.

Paradoxes of traditional physics

Paradox of Achilles or the arrow

( See Zénon d' Élée, Paradoxes of Zénon )

“It is impossible that Achille catches up with a tortoise in front of him: during a time T, Achille advances X (the distance separating Achille from the tortoise at the beginning) and the tortoise advances X. Then, starting from these new positions, during time T1, the tortoise advances x1 and Achille de X1. The distance between Achilles and the tortoise are smaller. One thus continues so on. In the same way, an arrow drawn from an arc will never reach a tree” .

Whoever knows the geometrical sums of continuations will know that this series (T, t/n, t/2n… with n=réel since Achille and the tortoise has uniform speeds) converges and that there is no paradox. Just an easily calculable moment of meeting.

More precisely, a illusion of paradox is created if one operates a confusion between:

an algorithm describing by an infinite series of stages a process finished

and

a process itself of infinite duration

what does not have a direct report/ratio.

What one cannot fix, it is a number given of iteration of the process who will give exact time, even if this time is in what relates to it given with all the precision that one will want.

Let us note in the passing that the process used for description is conceived in order not to allow the consideration of any posterior moment the meeting, and thus presents a version of reality amputated by construction .

Paradox of Olbers known as “of the sky of fire”

If it is supposed that the universe infinite, and is uniformly populated stars, it is shown easily that a half-line on the basis of the observer in an unspecified direction always ends up meeting one of them. The night sky should thus be as brilliant as the surface of stars. However, it is obviously not the case.

Paradoxes of modern physics

See with the Small experiments of thought, illustrations of the article restricted Relativity.

Paradox of the twins

The paradox of the twins is a Expérience of thought in restricted Relativité imagined by Paul Langevin in 1911. Its paradoxical aspect is highlighted as follows:

When a twin travels (very quickly), there returns younger than his twin brother remained fixed.

Paradox of the train

There exists a paradoxical property of the restricted Relativité, which has as a consequence that a train can appear more or less long that a tunnel, according to the position (and the speed) of the observer.

Paradox of Ehrenfest

The paradox of Ehrenfest is a paradox noted in the study of the revolving reference marks and more especially here in the study of the revolving discs. When one takes into account the restricted Relativité it is noted that the geometry seems different in the inertial reference mark and the turning reference mark whereas it is about the same physical space.

Paradox of Selleri

The paradox of Selleri describes a situation where, while reasoning in a revolving reference mark, one shows that the transformations of the coordinates must obey the transformations of Galileo. A reasoning apparently without fault then results in invalidating postulates of the restricted Relativité.

Paradox EPR

The paradox EPR (Einstein, Podolsky, Rosen) show that the assumptions

impossibility for a signal of exceeding the speed '' C '' (relativistic causality);
quantum mechanics complete and is entirely described reality (not of hidden variables);
the two distant particles form elements independent of reality (locality)

mênent with a contradiction. It is the assumption of locality which made the expenses of them.

Paradox of the cat of Schrödinger

In quantum mechanics, the state of a system is unspecified as long as one did not carry out measurement: there are not “hidden variables”, even the atom “does not know” not which is its state before measurement. The paradox, it is that at the macroscopic level this is not true: a cat locked up in a box died well or living independently of the observation of an experimenter, even if this death is dependant on a quantum phenomenon (in the experiment of thought: the disintegration of an atom which would cause the release of a poison).

Is paradox “which the cause of Big Bang? ”

Orthodoxe interpretation (pure RG)

Big Bang representing in the standard model (G and 1/c nonnull, H neglected) the absolute origin of time in our universe, the question of wondering in this model what there was before does not have there more direction than to ask which are the points of terrestrial surface more in North that the north pole. If Big Bang existed, all that one can say is that it could exist, and it is not necessary to wonder which event was chronologically the cause since, always within the framework of the standard model , time started with him. One cannot speak about causes which would be former ; at most reasons (logical and noncausal) for which it was not autocontradictoire.

Interpretations under consideration within framework RG+MQ

In the cases of the theories other than the standard model (see Gabriele Veneziano) one can of course put the question again; except that if a time preexists, then it in the classical sense of the term does not act any more a Big Bang .

It is in particular the case if one takes into account the value of H, which is not null and cannot certainly be neglected taking into account the short distances considered. There is not in this case not a possible “singularity” by construction , and supposed “the Big bang” would be only one kind of bottleneck; to date (2005) these other models are under study, many and of course speculative.

See Big bang

probabilistic Paradoxes

Argument of the apocalypse

According to the date of the Apocalypse, the number of human having lived can vary from a factor 1000. But if one takes a man randomly, the fact of knowing itself born before the date nearest for doesn't the Apocalypse consolidate the date nearest?

Law of Godwin

In 1990, Mike Godwin stated the empirical rule following: “More one discussion on Usenet lasts a long time, plus the probability of finding there a comparison with the Nazi S or with Hitler approaches 1”

Paradox of the birthdays

the paradox of the birthdays is actually a simple result surprising in Probabilité. This result answers the question:

“How much people at least does one have to join together to have a chance on two that two people of this group have their birthday the same day? ”

Paradox of the trucks prospectors

This paradox (of appearance only) is treated in the article Probabilité in the sub-section erroneous Idée that a probability is necessarily objective .

Paradox of the two envelopes

Two envelopes contain each one a certain amount, one doubles other. If a candidate chooses an envelope of value NR among both proposed, then it will evaluate its hope of profit (if it changes envelope) with 0,5 × 2N + 0,5 × N/2, is 1,25 NR. It will want with any blow to thus change envelope.

Paradox of the three coins

Which is the probability, when three coins are launched, that all three fall down on the same side? (The answer is 1/4, and not 1/2 as an error of reasoning would let it believe)

Paradox of the two children

Knowing what does a family have two children and who one of them is a boy, which is the probability that the other is a boy too?

Paradox of the prisoners

One says to three prisoners whom they are condemned but that one of them will be pardoned. One of them requires of a guard: “Can you show me one of my companions who will be carried out? ”. The guard is carried out and the prisoner answers him then: “Thank you, front, I had a chance on three to be pardoned, and now, I have a chance on two. ”

Paradox of Monty Hall

This problem was born from a television game where a player hopes to gain a car hidden behind one of the three doors in front of him. After it chose a door, the presenter who knows where the car is, opens one second door not hiding it; then proposes to the player to modify his choice. Although vis-a-vis two doors remained closed, the chances of success of the player could not be 1/2. What does it have to make?

Paradox of Beautiful with wood sleeping

Sleeping Beauty is used here as guinea-pig. Being always amnesic with its alarm clock, it is reminded to him that it must guess the result of a pulling with pile-or-face. Which are its chances of success if it is specified to him that it was agreed to awake it once if face fell, twice if not?

“Paradox” of Benford

Announced by Frank Benford in 1939: Why the pages of the old tables of logarithms are all the more worn as they are close to the beginning? ( to see Law of Benford )

By studying numerical tables of values of very diverse origins (BTP, resistance of materials, chemistry, mechanics of the fluids, astronomy…), one finds in fact a remarkably regular distribution of the first figure (not-no one) of the values which are contained there:

the 1 appears with a frequency of 30%
the 2 appears with a frequency of 18%
the 9 appears with a frequency of 5%

and, in a more general way, each figure NR appears in first position with the probability:

p (NR) = log (1+1/N)

That is due to the fact that a general distribution, if it exists, must remain invariant by a change of units (for example that the tables are expressed in inches or centimetres, in °F, °C or Kelvins, etc the only distribution remaining invariant in a multiplication of all its terms by a constant is that which precedes.

You will most probably observe the same distribution in the numbers of streets present in your address book (but not those of telephone, where the plan of classification of the telephone operators plays the part of anti-chance).

Paradox of Borel

The paradox of Borel (sometimes called the paradox of Borel-Kolmogorov ) is a technical result of the Theory of probability. It expresses that the functions of Densité of conditional probability are not invariant by change of variable.

Paradox of Saint-Pétersbourg

This paradox highlights that a Espérance of profit positive, even infinite, is not a sufficient reason to play.

Paradox of Parrondo

This paradox highlights that it is possible to find a strategy gaining on plays known as " perdants" . Mathematically that can be summarized by:

Being given 2 plays, each one having a probability of loss larger than that of profit, it is possible alternatively to build a strategy gaining by playing the 2 games.

Paradox of the electoral systems

Paradox of Alabama

This paradox of Alabama presents a situation where, by increasing the number of seats to be provided, one decreases the number of seats acquired by a party. It was born from a situation concretes in 1880, in the state of the Alabama to the the United States.

Paradox of Condorcet

Statement in 1785, by Nicolas of ''' Condorcet ''', this paradox describes the possible Intransitivité of the majority: among the same electorate, and at the time of the same election, it is possible that a majority prefers has with B, that another majority prefers B with C, and that a third majority prefers C with A.

Paradox of Simpson

The paradox of Simpson or effect Yule-Simpson is a singular result in Statistique, in which the success of several groups seems to be reversed when the groups are combined.

temporal Paradox

Paradox of the grandfather

The paradox of the grandfather is an experiment of thought of which the goal is to give an account of the problematic or improbable character of the Voyage in time: an human being turns over in the past and kills his/her grandfather before even as this last does not have children.

Paradox of the writer

The paradox of the writer is to some extent reciprocal precedent: a temporal traveller dispatches with his me past a book which it is supposed to have written, and which it publishes finally without nobody never having to dig the head so that its text exists.

Extension of the Paradox of Fermi

Stephen Hawking and other physicists propose to employ the paradox of Fermi like argument against the temporal voyages: if they were possible, a man of the future would have appeared (even by supposing that the laws of the future prohibit it).

Other paradoxes

Paradox of Abilene

The paradox reported on the sociologist Jerry Harvey relates to the relation with decision making within a group. It is an illustration of the difficulty of a group of making a decision and of managing its agreement collectively. In this fable morderne none of the 4 members of a group wished to go to Abilene but by fear to offend themselves and to contradict themselves mutually, they finish all there! Paradox of Abilene

Paradox of the ass of Buridan

Ass which, according to the legend, died of hunger and thirst between its ration of oats for oats and its water bucket, fault of choosing by what to start…

Paradox of water and diamond

“There is nothing more useful than water, but it can almost nothing buy; hardly is there average to have something in exchange. A diamond, on the contrary, does not have almost any value as for the use, but one will frequently find to exchange it against a very great quantity of other goods. ”

Paradox of Fermi

According to Fermi: “If the extraterrestrial ones exist, taking into account the very long lifespan of the Univers and the Galaxie, why sums us not already in contact? ”

Paradox of the compressor

When was launched by IBM the system OS/2, the CD readers were not generalized and the system was provided on 17 diskettes, which made from there the installation painful. To a request of the direction anxious to know if one could reduce this size, the legend says that the answer would have been: " We can make it hold compressed in only one diskette, but using a compressor so complex that it will occupy sixteen of it ". It was the famous initial paradox there.

Paradox of the absolute power

“If God is the Almighty, can it create a rock so heavy which it would not be able to raise it ? If it cannot create it, it is not the Almighty, and if it creates it as specified and cannot raise it then, he is not the Almighty either”.

This question ignited the spirits with the Middle Ages with some others which of it are derived.

According to Thomas d' Aquin, God entirely occupies the space of possibilities in conformity with his nature, which is of coherence. The preceding example would not mean that God does not exist, but simply that the Autocontradiction belongs to what is not him and who it of it is by nature free. Let us notice moreover that the paradox suggested presupposes that God has a temporal nature, but in the majority of the religions monotheists, it is on the contrary atemporel (omnipresent in time).

Paradox of Eliezer

Eliezer is the right-hand man of Abraham. The numerical value of its Hebrew name is of 318.

In an episode of the bible, Loth is prisoner. Abraham releases it accompanied by its 318 men what makes say to the rabbis that Abraham was accompanied only by Eliezer.

What is paradoxical is an opposite proposal with logic. How to fight an army and to release a prisoner with only one man? This account is thus a metaphysical paradox because as one cannot deny the truth of the writings nor the result of the studies of those by the rabbis, there is a conflict of comprehension. Is this value 318 plurality or not?

Paradox of the club of Groucho

Groucho Marx declares:

Jamais I would not agree to belong to a club which would accept me like member. The exact quotation is " people like moi" (" people like me" in the text). See The joy off Yiddish of Leo Rosten.

It is simply a Jewish joke of autodérision where Groucho gives a pretext not to be made embrigader in some mobility that it is.

From a logical point of view, there is not a real paradox: this assertion only amounts saying that Groucho refuses to belong to any club, and that it has a high idea neither others nor of itself.

This assertion leaves on the other hand open the possibility that Groucho wishes to be solicited to take part in clubs in order to be able to refuse this invitation: paradoxical wish but altogether rather widespread.

Paradox of Labelle

In certain countries, the suicide is liable to the capital punishment.

Paradox of Tristan

In its novel Breaking news of Beyond the, Frédérick Tristan written: " This morning, when Mr Némo awoke, he realized that he was mort." If he realizes that he died, it is that he is not it. On the other hand, if he died he cannot wake up. A third assumption is possible: in death there would exist a possibility of knowledge of its state, but this assumption is unverifiable. This sentence uses what one names speculative Pensée. The idea is also present at Jean d' Ormesson like in a song of Gilbert Bécaud:

I died this morning at six hours minus the quart
To die, they is three times nothing, it is after it is odd

( Welcome among us )

Paradox of the tie

“Jewish” history:

The mother offers two ties to her son. To please to him, it puts one of them to visit him. What attracts the following remark to him:

“Why ace you put the tie (the other) that I offered to you? ”

The paradox, it is that the son is in front of two solutions (two ties) which both lead it to the fault.

Paul Watzlawick enjoys to tell this history to illustrate the Paradoxes and double constraint of a pair of paradoxical injunctions supplied with third implicit or clarifies named by Yves Barel of " injunction-cliquet" who prohibits any refusal to obey to impossible choices and any comment on this nonsense. Apart from a relation of authority or domination real or interiorized by social training, there would not be a double constraint, but only one pleasant joke.

A mother returns visit to her child and offers two ties to him, blue and a red. To the following visit, the child presents himself with the red tie.

The mother says to him: “You do not like the blue tie? ” To the following visit, the child presents himself with the blue tie.

To the following visit still, the child presents himself with the two ties blue and red with the collar and his/her mother says to him:

“It is not astonishing that you would be placed in pédopsychiatrie! ”

Paradox of the cigar surprised

The general promised with each one of his men a cigar and a surprise. However the surprise, it is that there was no cigar.

Origin of the paradox: whereas one expects that the two terms are independent one of the other and cumulate positively, the second term is in fact only one function of cancellation of the first, and the end result is null.

Paradox of the masked ball

It is about a famous case of mystification of the reader, appearing in the comic news of Alphonse Allais entitled a quite Parisian drama.

Paradox of the paradise

" A very pious mother is allowed with the paradise; she has all that she wants. As a good mother, once installed well, it encquiert of the fate of his/her John son. She learns that he is suffering atrociously in hell. How our mother can be happy with the Paradise? "

There will be unhappy people with the Paradise, the place of supreme happiness.

Lexical paradox

The teacher of maths to his pupils: " The next week you will have a duty. This time, you will not have any problem. But you will have nevertheless problèmes."

Small experiments of thought

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