The 10 most important paradoxes (and their meaning)

It is likely that on more than one occasion we have met some situation or reality that has seemed strange, contradictory or even paradoxical to us. And it is that although the human being tries to look for rationality and logic in everything that happens around him, 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 of which we cannot find a solution, which is based on correct reasoning but whose explanation is contrary to common sense or even to one's own 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 it.

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Some of the most important paradoxes

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

1. The paradox of Epimenides (or of the Cretan)

A highly known paradox is that of Epimenides, which has existed since Ancient Greece and serves as the basis for other similar ones based on the same principle. This paradox is based on the logic and he 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 the Cretans are liars, so his statement would be true, which in turn would mean that he was lying.

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2. Scrodinger's cat

Probably one of the best known paradoxes is that of Scrödinger. This physicist from Austria dealt with the paradox of explaining how quantum physics works: the momentum or wave function in a system. The paradox is the following:

In an opaque box we have a bottle with a poisonous gas and a small device with elements radioactive with a 50% probability of disintegrating in a certain time, and we put in it a cat. 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 passed Is the cat inside the box dead or alive?

This system, from a logical point of view, will make us think that the cat can actually be alive or dead. However, if we act from the perspective of quantum mechanics and value the system at the moment, the cat is dead and alive at the same time, given that based on the function we would find two superimposed states in which we cannot predict the outcome final.

Only if we proceed to check it will we 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 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. 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 back in time and eliminates one of his grandparents before he conceived one of his parents, the person itself could not be born.

However, the fact that the subject was not born implies that he could not commit the murder, something that in turn would cause him to be born and to commit it. Something that would certainly cause him to be unable to 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 to a set) and the use of logic as the main element to which most of the math.

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

“A long time ago, in a distant kingdom, there was a shortage of people who dedicated themselves to being barbers. Faced with this problem, the king of the region ordered that the few barbers that there were shave only and exclusively those people who cannot shave for themselves. However, in a small town 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 just shave everyone who can't shave themselves, he technically couldn't shave himself by only being able to shave those who can't. However, this automatically makes him unable to shave, so he can shave himself. And in turn that would lead back to not being able to shave by not being unable to shave. And so on.

In this way, the only way for the barber to be part of the people he must shave would be precisely that he was not part of the people that he must shave, with which we find ourselves with the paradox by Russell.

5. twins paradox

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

The paradox establishes the existence of two twins, one of whom decides to make or participate in a trip to a nearby star from a ship that will move at speeds close to the speed 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 that stays on Earth as it moves away at near-light speeds the other twin. A) Yes, this will get old sooner.

However, if we look at the situation from the perspective of the twin traveling on the ship, it is not he who is moving away but the brother who stays on Earth, so time should pass more slowly on Earth and he should age much sooner. traveler. 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 more easily resolved. Actually, in such circumstances the twin that would age first would be the one on Earth: time would pass faster for this one. when moving the twin that travels in the ship at speeds close to light, in a means of transport with an acceleration determined.

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6. Paradox of information loss in black holes

This paradox is not especially known by the majority of the population, but is a challenge for physics and science in general even today (although Stephen Hawkings proposed an apparently viable theory about it). 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 is that physical information is supposed to completely disappear in black holes: These are cosmic events that have a gravity so intense that not even light is able to escape from it. This implies that no type of information could escape from them, in such a way that it ends up disappearing forever.

Black holes are also known to give off radiation, an energy that was thought to end up being destroyed by the black hole itself and which also implied that it was getting smaller, in such a way that everything whatever sneaked into him would end up disappearing along with him.

However, this contravenes quantum physics and mechanics, according to which the information of any system remains encoded even if its wave function collapses. In addition to this, 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, over time Hawkings corrected this paradox, proposing that the information was not actually destroyed but remained on the fringes of the frontier event horizon space time.

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 their 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 being something that he does not feel like it as it is a long trip, considering that his opinion will not coincide with that of the the rest. The husband replies that he is fine with him as long as the mother-in-law is fine with him. The latter also happily accepts. They make the journey, which is long and unpleasant for everyone.

When one of them returns, he insinuates that it has been a great trip. To this the mother-in-law replies that she actually would have preferred not to go but she accepted because she believed that the others wanted to go. The husband replies that he really only went to satisfy the others. Her wife indicates that the same thing has happened to her and for the last one the father-in-law mentions that he only proposed it in case the others were getting bored, although he didn't really feel like it.

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

8. Zeno paradox (Achilles and the tortoise)

Similar to the fable of the hare and the tortoise, this paradox from ancient times presents us with an attempt to show that motion cannot exist.

The paradox introduces us to Achilles, the mythological hero nicknamed "he of the swift feet", who competes in a race with a tortoise. Considering his speed and the turtle's slowness, he decides to give him a pretty sizable advantage. However, when he reaches the position where the tortoise was initially, Achilles observes that the tortoise has advanced in the same time that he got there and is further ahead.

Likewise, when he manages to overcome this second distance that separates them, the tortoise has advanced a little more, something that will make you have to continue running to get to the point where the tortoise. And when you get there, the turtle will continue ahead, because it keeps moving forward without stopping in such a way that Achilles is always behind her.

This mathematical paradox is highly counterintuitive. Technically it is easy to imagine that Achilles or anyone else would end up overtaking the tortoise relatively quickly, being faster. However, what the paradox proposes is that if the tortoise does not stop, it will continue to advance, in such a way that each time Achilles reaches the position it was in, it will be a little further, indefinitely (although the times will be more and more short.

It is a mathematical calculation based on the study of convergent series. In fact, although this paradox may seem simple could not be contrasted until relatively recently, with the discovery of infinitesimal mathematics.

9. the paradox sorites

A little known paradox but nevertheless it is useful when 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 heap concept.

Specifically, it is proposed to elucidate how much sand would be considered a heap. Obviously a grain of sand does not look like a pile of sand. Not two, or three. If we add one more grain (n+1) to any of these amounts, we will still not have it. If we think of thousands, surely we will consider being in front of a lot. On the other hand, if we remove grain by grain from this pile of sand (n-1), we cannot say that we are no longer having a pile of sand.

The paradox is found in the difficulty to find at what point we can consider that we are before 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. do it.

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 as an element of knowledge in addition to serving as a problem to assess 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 method hypothetical-deductive.

The paradox itself, also known as the raven paradox, states that holding 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 raven will reinforce our belief and will confirm not only that everything that is not black is not a raven but also the complementary one: “all ravens are blacks”. We are facing a case in which the probability that our original hypothesis is true increases every time we see a case that does not confirm it.

However, it must be taken into account that the same thing that would confirm that all crows are black 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 non-ravens could we have a real conviction.