On PARADOXES

One dictionary defines a paradox as

1. a statement that is seemingly contradictory or opposed to common sense yet is perhaps true;
2. a self-contradictory statement that at first seems true;
3. an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises.

Paradoxes have been a central part of philosophical thinking for centuries, and are always ready to challenge our interpretation of otherwise simple situations, turning what we might think to be true on its head and presenting us with provably plausible situations that are in fact just as provably impossible.

I have given in this essay, some of the most famous paradoxes of all time

THE TIGER PARADOX

1. A tiger snatched a baby from its mother, and offered to return it if the mother could correctly answer the question “Will I eat your baby?” If the mother had said “no” there would have been no problem, but she was clever enough to say ‘yes’ (If the tiger were now to eat the baby proving the mother right, he would be contradicting his offer to return the baby if the mother answered correctly).

2. Epimenides the Cretan says, ‘that all the Cretans are liars,’ but Epimenides is himself a Cretan; If he is telling the truth he is lying and if he is lying, he is telling the truth.

THE BARBER OF SEVILLE

The barber of Seville shaves all those, and those only, who do not shave themselves. The question is, “does the barber of Seville shave himself?”

Any answer to this question results in a contradiction. The barber cannot shave himself, as he only shaves those who do not shave themselves. Thus, if he shaves himself he ceases to be the barber specified. Conversely, if the barber does not shave himself, he fits into the group of people who would be shaved by the specified barber, and thus, as that barber, he must shave himself.

THE SOCRATES PARADOX

Socrates. says whatever Plato says is false. Plato replies “Socrates has spoken truly”. This means that the statement of Socrates that whatever Plato says is false, is false!

ACHILLES AND THE TORTOISE

Achilles is in a footrace with a tortoise. Achilles allows the tortoise a head start of 200 meters, for example. Suppose that Achilles as well as the tortoise start running at some constant speed, with of course Achilles faster than the tortoise. After some finite time, Achilles will have run 200 meters, bringing him to the tortoise’s starting point. During this time, the tortoise would have run a much shorter distance, say 4 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise. So he can never overtake the tortoise

THE BULLET PARADOX

A man is shot through the heart during the last half of a minute by A. B shoots him during the heart during the preceding one quarter minute, C during the one eighth minute before that, ad infinitum. Assuming that each shot kills instantly (if the man were alive) the man must be already dead before each shot. Thus he cannot be said to have died of a bullet wound.

THE PUNISHMENT PARADOX

Poaching on the hunting preserves of a powerful prince was punishable by death. But the prince further decreed that anyone caught poaching was to be given the privilege of deciding whether he would be hanged or beheaded. The culprit was permitted to make a statement – if it were false he has to be hanged; if it were true he was to be beheaded. One logical rogue availed himself of this dubious prerogative- to be hanged if he didn’t and beheaded if he did- by stating “I shall be hanged”. Here was a dilemma not anticipated. For as the poacher put it ” If you now hang me you break the laws made by the prince for my statement is true and I ought to be beheaded”; but if you beheaded me you are also breaking the laws for then what I said was false and I should therefore be hanged

ZENO’S PARADOX

Whatever exists is in a place. Therefore place exists. The place is in a place and so on ad infinitude.

THE SELF- PARADOX

There are forms of self-reference which approach the paradoxical state. A good example of this type of contradiction is a signpost which says “IGNORE THIS NOTICE.” To do as it says, you must not have done as it says.

THE MAP PARADOX

Let us imagine that a portion of the soil of India, has been levelled off perfectly, and on that a cartographer traces the map of India; the job is perfect; there is no detail of the soil of India, no matter how minute that is not registered on the map: everything there has its correspondence. This map in such a case, should contain a map of the map, which should contain a map of the map of the map and so on to infinity.

The CAT PARADOX

In quantum mechanics, Schrödinger’s cat is a thought experiment, sometimes described as a paradox, of quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead, while it is unobserved in a closed box, as a result of its fate being linked to a random subatomic event that may or may not occur. This thought experiment was devised by physicist Erwin Schrödinger in 1935 in a discussion with Albert Einstein to illustrate what Schrödinger saw as the problems of the Copenhagen interpretation of quantum mechanics.

Schrödinger’s cat: a cat, a flask of poison, and a radioactive source connected to a Geiger counter are placed in a sealed box. As illustrated, the objects are in a state of superposition: the cat is both alive and dead.

In Schrödinger’s original formulation, a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal radiation monitor (e.g. a Geiger counter) detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. The Copenhagen interpretation implies that, after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality resolves into one possibility or the other.

Although originally a critique on the Copenhagen interpretation, Schrödinger’s seemingly paradoxical thought experiment became part of the foundation of quantum mechanics. The scenario is often featured in theoretical discussions of the interpretations of quantum mechanics, particularly in situations involving the measurement problem. As a result, Schrödinger’s cat has had enduring appeal in popular culture. The experiment is not intended to be actually performed on a cat, but rather as an easily understandable illustration of the behavior of atoms. Experiments at the atomic scale have been carried out, showing that very small objects may exist as superpositions; but superimposing an object as large as a cat would pose a considerable challenge.

THE ISLAND/LAKE PARADOX

The dictionaries define island as ” a body of land completely surrounded by water” and a lake as a body of water completely surrounded by land. But suppose the Northern Hemisphere were all land and the Southern Hemisphere all water, would you call the Northern Hemisphere an island or would you call the Southern Hemisphere a lake.

The grandfather paradox.

The following hypothetical coincidence is very interesting: Sometime since it was announced that a man at Titusville, Pennsylvania, committed suicide for the strange reason that he had discovered that he was his own grandfather. He gave his own explanation of the mixed-up condition of his kinsfolk in his own words. He says, ‘I married a widow who had a grown-up daughter. My father visited our house very often, fell in love with my stepdaughter, and married her. So my father became my son-in law, and my step-daughter my mother, because she was my father’s wife. Some time afterwards, my wife gave birth to a son; he was my father’s brother-in-law, and my uncle, for he was the brother of my step-mother. My father’s wife — i.e. my step-daughter — had also a son; he was, of course, my brother, and in the mean time my grandchild, for he was the son of my daughter. My wife was my grandmother, because she was my mother’s mother. I was my wife’s husband and the grandchild at the same time. And as the husband of a person’s grandmother is his grandfather, I was my own grandfather.’ After this logical conclusion, we are not surprised that the unfortunate man should have taken refuge in oblivion. It was the most married family and the worst mixed up relationship that we ever heard of.

MOST BIZARRE SUICIDE ONE CAN THINK OF

The mother of all paradoxes is 1994’s MOST BIZARRE SUICIDE, believed to be fictional (or just another urban legend?*)

At the 1994 annual awards dinner given by the American Association for Forensic Science, AAFS President Don Harper Mills astounded his audience in San Diego with the legal complications of a bizarre death. Here is the story.

“On 23 March 1994, the medical examiner viewed the body of Ronald Opus and concluded that he died from a shotgun wound of the head. The decedent had jumped from the top of a ten-story building intending to commit suicide (he left a note indicating his despondency). As he fell past the ninth floor, his life was interrupted by a shotgun blast through a window, which killed him instantly. Neither the shooter nor the decedent was aware that a safety net had been erected at the eighth floor level to protect some window washers and that Opus would not have been able to complete his suicide anyway because of this.”

“Ordinarily,” Dr. Mills continued, “a person who sets out to commit suicide ultimately succeeds, even though the mechanism might not be what he intended.

That Opus was shot on the way to certain death nine stories below probably would not have changed his mode of death from suicide to homicide. But the fact that his suicidal intent would not have been successful caused the medical examiner to feel that he had homicide on his hands.

“The room on the ninth floor whence the shotgun blast emanated was occupied by an elderly man and his wife. They were arguing and he was threatening her with the shotgun. He was so upset that, when he pulled the trigger, he completely missed his wife and the pellets went through the a window striking Opus.

“When one intends to kill subject A but kills subject B in the attempt, one is guilty of the murder of subject B. When confronted with this charge, the old man and his wife were both adamant that neither knew that the shotgun was loaded. The old man said it was his long-standing habit to threaten his wife with the unloaded shotgun. He had no intention to murder her -therefore, the killing of Opus appeared to be an accident. That is, the gun had been accidentally loaded.

“The continuing investigation turned up a witness who saw the old couple’s son loading the shotgun approximately six weeks prior to the fatal incident. It transpired that the old lady had cut off her son’s financial support and the son, knowing the propensity of his father to use the shotgun threateningly, loaded the gun with the expectation that his father would shoot his mother.

The case now becomes one of murder on the part of the son for the death of Ronald Opus.

There was an exquisite twist.

“Further investigation revealed that the son [Ronald Opus] had become increasingly despondent over the failure of his attempt to engineer his mother’s murder. This led him to jump off the ten-story building on March 23, only to be killed by a shotgun blast through a ninth story window.

“The medical examiner closed the case as a suicide

The following sentences approach paradoxes,

“Never say never”

“All rules have exceptions”

“It is forbidden to forbid”

THE JAIL PARADOX

 The following resolution was passed by the Board of Councilmen, in Canton, Mississippi.

A) Resolved by this council that we build a new Jail

B) Resolved that the new Jail will be built out of the materials of old jail,

C) Resolved that the old jail will be used until the new jail is finished.

THE SHIP PARADOX

The ship paradox was invented by the British logician Philip Jourdain in the early 1900s.Theseus was a mythical king and the hero of Athens. (He was the guy who slayed the Minotaur, amongst other feats.) He did a lot of sailing, and his famed ship was eventually kept in an Athenian harbour as a sort of memorial/museum piece. As time went on, the ship’s wood began to rot in various places. Those wooden pieces were replaced, one by one. Gradually more pieces needed replacing. The process of replacing rotten planks with new ones continued, at least in modern versions of the paradox, until the entire ship was made up of new pieces of wood. This thought experiment asks the question: Is this completely refurbished vessel still the ship of Theseus?

Let’s take it a step further: What if someone else took all of the discarded, original pieces of wood and reassembled them into a ship. Would this object be Theseus’s ship? And if so, what do we make of the restored ship sitting in the harbour? Which is they original ship?

This paradox is all about the nature of identity over time, which asks whether an object remains the same after all the aggregate parts have been replaced. 

The LAWYER PARADOX

How can a witness reply to a lawyer who says “Please answer yes or no to the following question-

“will the next word you speak be no?”

THE LIAR PARADOX

One of Eubulides of Miletus’s more famous paradoxes, the Liar Paradox, is still discussed today. It has a very simple premise but a very mind-boggling result. Here it is:

This sentence is false.

Think about it for a moment. If the statement is true, then that means that the sentence is in fact false, as it claims. But that would then mean that the sentence is false. And if the sentence “this sentence is false” is false, then that means it’s true. But, if it’s true that it’s false, then—you get the picture. It goes on and on, forever.