The 10 Most Important Paradoxes (and Their Meaning)
It is likely that on more than one occasion we have encountered any situation or reality that seemed strange, contradictory or even paradoxical to us And although human beings try to look 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 for which we cannot find a solution, which is based on correct reasoning but whose explanation is contrary to common sense or even 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 Let’s see some of the most important and well-known paradoxes with a brief explanation about it.
Below you will find the most relevant and popular paradoxes cited, as well as a brief explanation of why they are considered such.
1. The paradox of Epimenides (or the Cretan)
A well-known paradox is that of Epimenides, which has existed since Ancient Greece and which serves as the basis for other 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 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 place 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 decays, 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 perspective, will make us think that the cat can indeed be alive or dead. However, if we act based on the perspective of quantum mechanics and evaluate the system at the moment, the cat is dead and alive at the same time, since based on the function of we would find two superimposed states in which we cannot predict the final result.
Only if we proceed to check it can we 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 modify, inevitably in the measurement of what is observed. The momentum or wave function collapses at that moment.
3. The grandfather paradox
Being 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 regarding 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 eliminates one of their grandparents before they conceive one of their parents, the person themselves could not be born
However, the fact that the subject has not been born implies that he has not been able to commit the murder, something that in turn would cause him to be born and could commit it. Something that would undoubtedly result in him not being able to be born, and so on.
4. Russell’s Paradox (and the Barber)
a paradox widely known within the field of mathematics It is the one 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 of mathematics can be reduced.
There are numerous variants of Russell’s paradox, but all of them are based on Russell’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 saying this sounds strange, below we leave you with a less abstract and more easily understood example, known as the barber’s 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 themselves. However, in a small town 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 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 means that he cannot shave, so he could shave himself. And in turn that would lead him back to not being able to shave by not being incapable of shaving. And so on.
In this way, 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 why we find Russell’s paradox.
5. Twin Paradox
The so-called twin paradox is a hypothetical situation originally posed by Albert Einstein in which the theory of restricted or special relativity is discussed or explored, making reference 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 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 speeds close to those of light. So, this one will age sooner
However, if we look at the situation from the perspective of the twin traveling on 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 he should age. long before the 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 resolved more easily. In reality, in these circumstances the twin that would age first would be the one on Earth: time would pass faster for it as the twin traveling in the ship moves at speeds close to light, in a means of transport with a certain acceleration.
This paradox is not especially known by the majority of the population, but It represents a challenge for physics and science in general even today (although Stephen Hawkings proposed a seemingly viable theory on this). 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 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 type of information could escape them, in such a way that it ends up disappearing forever.
It is also known that black holes give off radiation, an energy that was believed 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 what was sneaking inside him would end up disappearing along with him
However, this contravenes physics and quantum mechanics, according to which the information of every system remains encoded even if its wave function were to collapse. 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, as time went by Hawkings corrected this paradox, proposing that the information was not actually destroyed but rather 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 their parents are playing dominoes in a house in Texas. The husband’s father proposes visiting the city of Abilene, with which the daughter-in-law agrees despite it being something that he does not fancy since it is a long trip, considering that his opinion will not coincide with that of the others. The husband responds that he is fine with it as long as the mother-in-law is fine with it. The latter also happily accepts. They make the trip, which is long and unpleasant for everyone.
When they return, one of them suggests that it has been a great trip. To this, the mother-in-law responds that in reality she would have preferred not to go but she accepted because she believed that the others wanted to go. The husband responds that he really only went to satisfy others. Her wife indicates that the same thing has happened to her, and lastly, her father-in-law says that he only proposed it in case the others were getting bored, even though 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 group’s opinion. It tells us about social conformity and groupthink, and is related to a phenomenon called 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 prove that movement cannot exist
The paradox introduces us to Achilles, the mythological hero nicknamed “the one with swift feet,” who competes in a race with a tortoise. Considering his speed and the turtle’s slowness, he decides to give her a fairly considerable advantage. However, when he reaches the position where the tortoise was initially, Achilles observes that it 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 turtle has advanced a little further, something that will mean that he will have to continue running to reach the point where the turtle is now. 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 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 every time Achilles reaches the position he was in, he will be a little further away, indefinitely (although the times will be increasingly shorter.
It is a mathematical calculation based on the study of convergent series. In fact, although this paradox may seem simple 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 which is nevertheless 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 concept heap
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 quantities, we will still not have it. If we think of thousands, we surely consider ourselves to be facing a lot. On the other hand, if we take away from this pile of sand grain by grain (n-1), we could not say that we are ceasing to have a pile of sand.
The paradox lies in the difficulty of finding at what point we can consider that we are dealing with the concept “heap” of something: if we take into account all the previous considerations, the same set of grains of sand could either be classified as a heap or not.
10. Hempel’s paradox
We are reaching 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 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 crow paradox, states that considering the statement “all crows are black” to be true implies that “all non-black objects are not crows.” 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 that is not black is not a crow but also the complementary: “all crows are black.” We are faced with 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 not crows could we have real conviction.
