The 10 most important paradoxes (and their meaning)

Curious real or hypothetical situations that lead us to contradictory conclusions.

It is likely that on more than one occasion we have encountered some situation or situation or reality that has seemed strange, contradictory or even paradoxical to us.. Although human beings try to seek rationality and logic in everything that happens around them, the truth is that it is often possible to find real or hypothetical events that defy what we would consider logical or intuitive.

We are talking about paradoxes, situations or hypothetical propositions that lead us to a result for which we cannot find a solution, which starts from a correct reasoning but whose explanation is contrary to common sense or even to the statement itself.

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 look at some of the most important we are going to see some of the most important and well-known paradoxeswith a brief explanation.

Some of the most important paradoxes

Below you will find cited the most relevant and popular paradoxes, as well as a brief explanation of why they are considered as such.

1. The Epimenides (or Cretan) Paradox

A well-known paradox is that of Epimenides, which has existed since Ancient Greece and serves as a basis for other similar paradoxes based on the same principle. This paradox is based on logic and reads as follows.

Epimenides of Knossos is a Cretan man, who claims that all Cretans are liars. If this statement is true, then Epimenides is a liar.so it is not true that all Cretans are liars. On the other hand, if he lies, it is not true that the Cretans are liars, so his statement would be true, which in turn would imply that he was lying.

2. Scrödinger's cat

Probably one of the best known paradoxes is Scrödinger's paradox.. This Austrian physicist tried with his paradox to explain the functioning of quantum physics: the momentum 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 the time has elapsed, the cat will die. Is the cat inside the box alive or dead?

This system, from a logical point of view, will make us think that the cat can indeed be dead or alive. However, if we act on the basis of the quantum mechanical perspective and value the system at the moment, the cat is both dead and alive, since on the basis of the function of 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 momentum and lead us to one of the two possible outcomes. Thus, one of the most popular interpretations states that it will be the observation of the system that causes it to change, inevitably in the measurement of what is observed. The momentum or wave function collapses at that time.

3. The grandfather paradox

Being attributed to the writer René Barjavel, the paradox of the grandfather is an example of the application of this type of situation to the field of science fiction, specifically with regard to time travel.specifically with regard to time travel. In fact, it has often been used as an argument for a possible impossibility of time travel.

This paradox states that if a person travels to the past and eliminated one of his grandparents before he conceived one of his parents, the person himself would not be able to be born..

However, the fact that the subject was not born implies that he could not have committed the murder, something that in turn would cause him to be born and be able to commit it. Something that would undoubtedly generate that he could not be born, and so on.

4. Russell's paradox (and the barber)

A paradox widely known in the field of mathematics is the one proposed by Bertrand Russell, in relation to set theory (according to which every predicate defines a set) and to the use of logic as the main element to which most of mathematics can be reduced.

There are numerous variants of Russell's paradox, but all of them are based on this author's discovery that "not belonging to itself" establishes a predicate that contradicts set theory. According to the paradox, the set of sets that are not part of itself can only be part of itself if it is not part of itself. Although it sounds strange, here is a less abstract and more easily understood example, known as the barber's paradox.

"Long ago, in a distant kingdom, there was a shortage of people who were dedicated to being barbers. Faced with this problem, the king of the region ordered the few barbers to shave only and exclusively those people who could not shave for themselves. However, in a small village in the area there was only one barber, who was 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 do not only shaves all those who cannot shave themselvestechnically he would not be able to shave himself by only being able to shave those who cannot. However that automatically makes him unable to shave himself, so he could shave himself. And in turn that would again lead to him not being able to shave himself by not being unable to shave himself. And so on and so forth.

Thus, the only way for the barber to be part of the people he must shave would be precisely if he were not part of the people he must shave, which is Russell's paradox.

5. Paradox of the twins

The so-called twins' paradox is a hypothetical situation originally a hypothetical situation originally posed by Albert Einstein in which it is argued or in which the theory of special relativity is discussed or explored, referring to the relativity of time.

The paradox establishes the existence of two twins, one of which decides to make or participate in a trip to a nearby star from a ship that will move at speeds close to those of light. 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 who stays on Earth as the other twin moves away at near-light speeds. Thus, this one will age sooner.

However, if we look at the situation from the perspective of the twin traveling in the ship, the one who is moving away is not him but the brother who stays on Earth, so time should pass more slowly on Earth and the traveler should age much earlier. 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 reality, in such circumstances the twin that would age before would be the one on Earth: time would pass faster for this one as the twin traveling in the ship would travel at speeds close to light, in a means of transport with a given acceleration.

6. Paradox of the loss of information in black holes.

This paradox is not particularly well known to the majority of the population, but it poses a challenge to physics and science in general even today. challenge to physics and science in general even today (although Stephen Hawkings proposed a seemingly viable theory). (although Stephen Hawkings proposed an apparently viable theory on the subject). It is based on the study of the behavior of black holes and integrates elements of the theory of general relativity and quantum mechanics.

The paradox lies in the assumption that physical information disappears completely in black holes: these are cosmic events that have such intense gravity that not even light is able to escape from them. This implies that no type of 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 believed to be eventually destroyed by the black hole itself and that also implied that the black hole was getting smaller, so that everything that everything that slipped into the black hole would eventually disappear along with it..

However, this contravenes physics and quantum mechanics, according to which the information of any system remains encoded even if its wave function were to collapse. Furthermore, physics proposes that matter is neither created nor destroyed. This implies that the existence and absorption of matter by a black hole may 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 paradoxes linked to psychological and social 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 even though it is something she does not feel like doing since it is a long trip, considering that her opinion will not coincide with that of the others. The husband replies that he is fine with it as long as the mother-in-law is fine with it. The latter also accepts cheerfully. They make the trip, which turns out to be long and unpleasant for everyone.

On their return, one of them insinuates that it was a great trip. To this the mother-in-law replies that she would actually have preferred not to go but agreed because she thought the others wanted to go. The husband responds that it was really just to satisfy the others. His wife indicates that the same thing has happened to her, and the father-in-law says that he only proposed it in case the others were getting bored, although he did not really feel like it.

The paradox is that they all agreed to go even though in reality they would all have preferred not to, but they agreed to go because of theThe paradox is that they all agreed to go even though in reality they would all have preferred not to, but agreed because of a willingness not to contravene the opinion of the group. It speaks of social conformity and groupthink, and is related to a phenomenon called the spiral of silence.

8. Zeno's Paradox (Achilles and the tortoise)

Similar to the fable of the hare and the tortoise, this paradox from antiquity presents us with an attempt to demonstrate an attempt to prove that motion cannot exist..

The paradox presents us with Achilles, the mythological hero nicknamed "the swift-footed", who competes in a race with a tortoise. Considering his speed and the slowness of the tortoise, he decides to give it a fairly considerable head start. However, when he reaches the position where the tortoise was initially, Achilles observes that the tortoise has advanced in the same time that he arrived there and is further ahead.

Likewise, when he manages to overcome this second distance that separates them, the tortoise has advanced a little further, something that will make him have to continue running to reach the point where the tortoise is now. And when he gets there, the tortoise will still be ahead of him, because he continues to move forward without stopping. in such a way that Achilles is always behind it..

This mathematical paradox is highly counterintuitive. Technically it is easy to imagine that Achilles or anyone else would eventually overtake the tortoise relatively quickly, being faster. However, what the paradox proposes is that if the tortoise does not stop, it will continue to advance, so that each time Achilles reaches the position he was in, he will be a little further away, indefinitely (although the times will be shorter and shorter).

This is a mathematical calculation based on the study of convergent series. In fact, although it may seem simple, this paradox has not been proven until recently. has not been able to be contrasted until relatively recently, with the discovery of infinitesimal mathematics..

9. The Sorites paradox

A little known paradox, but nevertheless useful when considering the use of language and the existence of vague concepts. Created by Eubulides of Miletus, this paradox works with the conceptualization of the concept heap..

Specifically, it sets out to elucidate how much sand would be considered a heap. Obviously a grain of sand does not look like a heap of sand. Neither two, nor three. If to any of these quantities we add one more grain (n+1), we will still not have it. If we think in thousands, we will surely consider to be in front of a heap. On the other hand, if we remove one grain at a time (n-1) from this heap of sand, we could not say that we no longer have a heap of sand.

The paradox lies in the difficulty to find at what point we can consider that we are in front of the concept "heap" of something: if we take into account all the above considerations, the same set of grains of sand could be classified as a heap 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, it is Hempel's paradox, which aims to account for the problems linked to the use of induction. problems linked to the use of induction as an element of knowledge. as well as serving as a problem to be evaluated at a statistical level.

Thus, its existence in the past has facilitated the study of probability and various methodologies to increase the reliability of our observations, such as those of the hypothetico-deductive method.

The paradox itself, also known as the raven paradox, states that considering the statement "all ravens are black" to be 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: "all crows are black". This is a case where the probability that our original hypothesis is true increases each time we see a case that does not confirm it.

However, we must bear in mind that the same that would confirm that all crows are black could also confirm that they are of any other color.The same 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.