A paradox is always an amusing situation that contradicts itself in many ways. A phenomenon that may exist in reality, but has no logical explanation. Common sense is alien to the paradoxes that surround us, nevertheless they are very valuable for the development of critical thinking. We find new ways to explain various mysterious phenomena, moving further and further towards knowledge of the world. Teasing your mind and asking difficult questions is part of a lot of intellectual activity. And the more closely you look at the things around you, the more you will find surprising and inexplicable.
Here are some of the most exciting paradoxes you should know about today. Enjoy! If you know any more, share in the comments.
1. Fermi paradox
Physicist Enrico Fermi, apparently, did not like the series "The X-Files", and for him the presence of extraterrestrial life, and technologically advanced, is a very dubious idea. The notorious Drake equation inspires hope in ufologists, logically justifying the high chances of encountering alien intelligence. But Enrico Fermi just can't be fooled, and he asks: “Then where are they? Why are we not seeing any traces of intelligent extraterrestrial life, such as probes, spaceships or radio transmissions? " This very question formulates the paradox:
On the one hand, numerous arguments are put forward that a significant number of technologically advanced civilizations should exist in the Universe. On the other hand, there are no observations that would confirm this. The situation is paradoxical and leads to the conclusion that either our understanding of nature or our observations are incomplete and erroneous.
2. The paradox of Theseus' ship
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Briefly described, it sounds like this: an object, all components of which are replaced, can it remain the same object?
This classical paradox was retold by Plutarch. According to myths, the ship on which Theseus returned from Crete to Athens was kept by the Athenians until the era of Demetrius of Phaler and was annually sent with a sacred embassy to Delos. But here's the point. Each time before shipment, the boards were replaced in it. And now a dispute arose between the ancient philosophers, whether this is the ship on which Theseus sailed the seas, or not already? And if you build the same ship from old boards, then which one will be real?
The new version of this paradox replaces the ship with the brain, thereby asking the unknown: "If a person is transplanted the brain of his clone, will the person remain himself?"
3. The paradox of the murdered grandfather
Science fiction writer Rene Bergevel loved to write about time travel, but one day, in 1943, he described the following paradox.
Let's first assume that time travel is possible, and you have a dedicated time machine for that. You went back in time and killed your biological grandfather before he met your grandmother. Why would you do this, we do not know. You may be a mentally ill psychopath who hates all people over 60. But that's not the point. So, you killed your grandfather, as a result of which one of your parents was never born, which means that you were not born either. It turns out that in the end you would not be able to travel in time, because you are not, which means that your grandfather would remain alive, and you, accordingly, would be born, and this would allow you to travel in time, and therefore kill your grandfather. Such is the explosion of the brain.
4. The paradox of almighty God
In general, there is a whole family of such paradoxes, but they all boil down to what an omnipotent being can do, and can his omnipotence limit the ability to perform God's actions?
The simplest example is: "Can Almighty God create a stone that he himself is not able to lift?"
Richard Dawkins, meanwhile, notes that the omnipotence and omniscience of God also come into conflict with each other: either God knows what he will do tomorrow, or he has the freedom (opportunity) to do whatever.
5. The Liar's paradox
A common paradox that has several subspecies. It was not without the Greeks, as the greatest lovers of asking questions to which there is no single answer. Here, for example, is the theme about Epimenides, an ancient Greek priest and seer. The paradox, by the way, can be read in the New Testament of the Apostle Paul. It sounds like this: "The Cretan Epimenides claimed that all Cretans are liars." It turns out that if Epimenides is right, then all Cretans are really liars, but he is a liar, which means that the statement is false. If he turns out to be a liar, then, paradoxically, he is telling the truth.
6. The Barber's Paradox
It is very similar to the previous paradox, and in fact is an interpretation of Russell's paradox, which demonstrates the inconsistency of Frege's logical system, which is an early attempt to formalize G. Cantor's naive set theory. But we will not delve into logic and philosophy, but we will reveal the essence of the paradox through the situation that Russell himself proposed.
Imagine that the council of a village set a directive for its hairdresser: to shave all the men in the village who do not shave themselves, and only those men. Should this barber then shave himself? If so, he will refer to those who shave himself, which means he should not shave himself. As a result, the barber shaves himself when he does not shave himself. This is impossible. On the other hand, this paradox violates an important law of logic - the law of identity, which was formulated by Aristotle in his treatise Metaphysics. Actually, this is why many people perceive the paradox of the barber as a pseudo-paradox.
7. Curry's paradox
You've heard about him, we think. It's as simple as a bacon sandwich: "If this is true, then mermaids exist." Instead of mermaids, you can specify a pasta monster, cthulhu, a dragon, and the like.
The train of thought that leads to the paradox is as follows:
- let us denote by S the statement: "If S is true, then the macaroni monster exists";
- we do not know if the statement S. But if the statement S were true, then it would entail the existence of a pasta monster;
- but this is exactly what is stated in the statement S, thus S is true;
- hence the pasta monster exists!