It is likely that on more than one occasion we have come across some situation or reality that has seemed strange, contradictory or even paradoxical to us . The fact is that although human beings try to search for rationality and logic in everything that happens around them, the truth is that it is often possible to find real or hypothetical events that challenge what we would consider logical or intuitive.
We are talking about paradoxes, situations or hypothetical propositions that lead us to a result of which we cannot find a solution, which starts from a correct reasoning but whose explanation is contrary to common sense or even to the very statement.
There are many great paradoxes that have been created throughout history to try to reflect on different realities. That is why throughout this article we are going to see some of the most important and well-known paradoxes , with a brief explanation about them.
Some of the most important paradoxes
Below you will find the most relevant and popular paradoxes, as well as a brief explanation of why they are considered as such.
1. The Epimenid (or Cretan) Paradox
A well-known paradox is that of Epimenides, which has existed since Ancient Greece and serves as the basis for similar ones based on the same principle. This paradox is based on logic and says the following.
Epimenides of Knossos is a Cretan man, who claims that all Cretans are liars. If this statement is true, then Epimenides is lying , so it is not true that all Cretans are liars. On the other hand if he lies it is not true that Cretans are liars, so his statement would be true which in turn would mean that he was lying.
2. Scrödinger’s cat
Probably one of the best known paradoxes is that of Scrödinger . This physicist from Austria dealt with his paradox to explain the functioning of quantum physics: the moment or wave function in a system. The paradox is as follows:
In an opaque box we put a bottle with a poisonous gas and a small device with radioactive elements with a 50% probability of disintegrating in a given time, and we put a cat in it. If the radioactive particle disintegrates, the device will cause the poison to be released and the cat will die. Given the 50% probability of disintegration, once time has passed , is the cat inside the box alive or dead?
This system, from a logical vision, will make us think that the cat can indeed be alive or dead. However, if we act on the basis of the perspective of quantum mechanics and we value the system in the moment, the cat is dead and alive at the same time, since on the basis of the function we would find two superimposed states in which we cannot predict the final result.
Only if we proceed to check it we will be able to see it, something that would break the moment and lead us to one of the two possible outcomes. Thus, one of the most popular interpretations establishes that it will be the observation of the system that will cause it to be modified, inevitably in the measurement of what is observed. The moment or wave function collapses at that moment.
3. The Grandfather Paradox
Attributed to the writer René Barjavel, the grandfather paradox is an example of the application of this type of situation to the field of science fiction , specifically to what refers to time travel. In fact, it has often been used as an argument for the possible impossibility of time travel.
This paradox states that if a person travels to the past and eliminates one of his grandparents before he conceived one of his parents, the person himself could not be born .
However, the fact that the subject was not born implies that he could not commit the murder, which in turn would cause him to be born and to be able to commit it. Something that would undoubtedly result in him not being able to be born, and so on.
4. The Russell (and Barber) Paradox
A well-known paradox within the field of mathematics is that proposed by Bertrand Russell, in relation to the theory of sets (according to which every predicate defines a set) and the use of logic as the main element to which most mathematics can be reduced.
There are numerous variants of Russell’s paradox, but all of them are based on the author’s discovery that “not belonging to oneself” establishes a predicate that contradicts set theory. According to the paradox, the set of sets that are not part of themselves can only be part of themselves if they are not part of themselves. Although this sounds strange, we leave you with a less abstract and more easily understandable example, known as the barber’s paradox.
“A long time ago, in a faraway kingdom, there was a shortage of people to become barbers. Faced with this problem, the king of the region ordered the few barbers there to shave only those people who could not shave themselves. However, in a small village in the area there was only one barber, who found himself faced with a situation for which he could not find a solution: who would shave him?
The problem is that if the barber only shaves all those who cannot shave themselves , he could not technically shave himself by only being able to shave those who cannot. However, this automatically makes him unable to shave, so he could shave himself. And that in turn would lead back to him not being able to shave because he is not incapable of shaving. And so on.
Thus, the only way for the barber to be part of the people he has to shave would be precisely not to be part of the people he has to shave, which brings us to Russell’s paradox.
5. Twin paradox
The so-called twin paradox is a hypothetical situation originally put forward by Albert Einstein in which the theory of special or special relativity is discussed or explored, with reference to the relativity of time.
The paradox establishes the existence of two twins, one of which decides to make or participate in a journey to a nearby star from a ship that will move at near-light speeds. In principle and according to the theory of special relativity, the passage of time will be different for both twins, passing faster for the twin that stays on Earth as the other twin moves away at speeds close to those of light. Thus, it will age earlier .
However, if we look at the situation from the perspective of the twin who is travelling in the ship, it is not him but the brother who stays on Earth who is going away, so time should pass more slowly on Earth and the traveller should age much sooner. And this is where the paradox lies.
Although it is possible to resolve this paradox with the theory from which it arises, it was not until the theory of general relativity that the paradox could be resolved more easily. In fact, in such circumstances the twin that would age first would be the Earth’s twin: time would pass more quickly for it as the twin travelling in the ship moves at speeds close to light, in a means of transport with a given acceleration.
6. Paradox of information loss in black holes
This paradox is not particularly well known to most people, but poses a challenge to physics and science in general even today (although Stephen Hawkings proposed a seemingly viable theory in this regard). It is based on the study of the behaviour of black holes and integrates elements of the theory of general relativity and quantum mechanics.
The paradox is that physical information is supposed to disappear completely in black holes: these are cosmic events that have such intense gravity that not even light is able to escape from it. This implies that no information could escape from them, so that it ends up disappearing forever.
It is also known that black holes give off radiation, an energy that was thought to be destroyed by the black hole itself and that also implied that the black hole was getting smaller, so that everything that was leaking into it would end up disappearing along with it .
However, this contravenes quantum physics and mechanics, according to which the information of every system remains encoded even if its wave function should collapse. Furthermore, physics proposes that matter is neither created nor destroyed. This implies that the existence and absorption of matter by a black hole can lead to a paradoxical result with quantum physics.
However, with the passage of time Hawkings corrected this paradox, proposing that information was not actually destroyed but remained at the limits of the event horizon of the space-time boundary.
7. The Abilene Paradox
Not only do we find paradoxes within the world of physics, but it is also possible to find some linked to psychological and social elements . One of them is the Abilene paradox, proposed by Harvey.
According to this paradox, a married couple and his parents are playing dominoes in a house in Texas. The husband’s father proposes to visit the city of Abilene, with which the daughter-in-law agrees despite the fact that it is not something she feels like doing because it is a long journey, considering that her opinion will not coincide with that of the others. The husband replies that it is fine with him as long as the mother-in-law agrees. The latter also accepts happily. They make the journey, which is long and unpleasant for everyone.
When one of them comes back, he hints that it’s been a great trip. To this the mother-in-law replies that in reality she would have preferred not to go but accepted because she believed that the others wanted to go. The husband replies that in reality it was only to satisfy the others. His wife indicates that the same thing has happened to her and for the last one the father-in-law refers that he only proposed it in case the others were getting bored, although he didn’t really want to.
The paradox is that everyone agreed to go even though in reality everyone would have preferred not to do so , but they accepted because of the willingness not to contradict the group’s opinion. It speaks to us of social conformity and group thought, and is related to a phenomenon called the spiral of silence.
8. Zeno’s Paradox (Achilles and the Turtle)
Similar to the fable of the hare and the tortoise, this paradox from antiquity presents us with an attempt to demonstrate that movement cannot exist .
The paradox presents us with Achilles, the mythological hero nicknamed “the one with the swift feet”, who competes in a race with a turtle. Considering his speed and the turtle’s slowness, he decides to give it a rather considerable advantage. However, when he gets to the position the turtle was initially in, Achilles notices that the turtle has advanced in the same time that he was arriving there and is now further ahead.
Also, when he manages to overcome this second distance that separates them the turtle has advanced a little more, something that will make him have to continue running to get to the point where the turtle is now. And when he gets there, the tortoise will continue ahead of him, as he keeps advancing without stopping in such a way that Achilles is always behind him .
This mathematical paradox is highly counterintuitive. Technically it is easy to imagine that Achilles or anyone else would end up overtaking the turtle relatively quickly, being faster. However, what the paradox proposes is that if the turtle does not stop, it will continue to advance, so that every time Achilles reaches the position he was in, he will be a little further away, indefinitely (although the times will be shorter and shorter).
It is a mathematical calculation based on the study of converging series. In fact, although it may seem simple, this paradox could not be contrasted until relatively recently, with the discovery of infinitesimal mathematics .
9. The Sorites Paradox
A little known paradox but nevertheless useful when it comes to taking into account the use of language and the existence of vague concepts. Created by Eubulides of Miletus, this paradox works with the conceptualization of the concept pile .
Specifically, it is proposed to elucidate how much sand would be considered a pile. Obviously a grain of sand doesn’t look like a pile of sand. Neither does two, or three. If we add one more grain (n+1) to any of these quantities, we still don’t have it. If we think in thousands, we will surely consider that we are looking at a pile. On the other hand, if we take away grain by grain (n-1) from this pile of sand, we cannot say that we do not have a pile of sand.
The paradox lies in the difficulty of finding out at what point we can consider that we are before the concept “pile” of something: if we take into account all the previous considerations, the same set of sand grains could be classified as a pile or not.
10. Hempel’s paradox
We are coming to the end of this list of the most important paradoxes with one linked to the field of logic and reasoning. Specifically, this is Hempel’s paradox, which aims to account for the problems linked to the use of induction as an element of knowledge as well as serving as a problem to be assessed at a statistical level.
Thus, its existence in the past has facilitated the study of probability and of diverse methodologies to increase the reliability of our observations, such as those of the hypothetical-deductive method.
The paradox itself, also known as the raven paradox, states that considering the statement “all ravens are black” is true implies that “all non-black objects are not ravens”. This implies that everything we see that is not black and is not a crow will reinforce our belief and confirm not only that everything not black is not a crow but also the complementary one: “all crows are black. We are faced with a case in which the probability of our original hypothesis being true increases every time we see a case that does not confirm it.
However, we have to take into account that just as it would confirm that all crows are black, it could also confirm that they are any other color , as well as the fact that only if we knew all the non-black objects to guarantee that they are not crows we could have a real conviction.
- Bolander, T. (2013). Self-Reference. The Metaphysics Research Lab, Stanford University.
- Hughes, P.; Brecht, G. (1975). Vicious Circles and Infinity: A Panoply of Paradoxes. Garden City, New York: Doubleday. pp. 1 – 8.