7 Paradoxes That Will Drive You Crazy

It’s all about contradiction

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 surrounding us; nevertheless, they are precious for the development of critical thinking.

We find new ways to explain various mysterious phenomena, moving further towards knowledge about 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 it in the comments.

1— Omnipotence paradox

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?”

Meanwhile, Richard Dawkins notes that God's omnipotence and omniscience also conflict with each other: either God knows what he will do tomorrow or has the freedom (ability) to do whatever.

2— Ship of Theseus paradox

Briefly described, it sounds like this: an object, all the components of which have been replaced, can remain the same object?

Plutarch retold this classic paradox. 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 was 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— Epimenides paradox

A common paradox that has several subspecies. It was not without the Greeks, as the greatest lovers, to ask questions to which there is no single answer. For example, here is the theme of Epimenides, an ancient Greek priest, and seer. The paradox, by the way, can be read in the New Testament of the Apostle Paul. It goes 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.

4— Grandfather paradox

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 to do it. 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 because one of your parents was never born, which means 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 born, 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.

5 — The Barber’s Paradox

In fact, it 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 in this article, but we will reveal the essence of the paradox through the situation that Russell himself proposed.

Imagine that one village council 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 be referred to those who shave themselves, 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 Aristotle formulated in his treatise Metaphysics. Actually, that is why many people perceive the paradox of the barber as a pseudo-paradox.

6 — Fermi paradox

Apparently, physicist Enrico Fermi 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 instills hope in ufologists, logically justifying the high chances of meeting 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 our understanding of nature or our observations is incomplete and erroneous.

7— Curry’s paradox

You heard about him, as it seems to us. It’s as simple as a bacon sandwich: “If this sentence 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 A is true”;

We do not know if the statement S is true. But if the statement S were true, then it would entail the existence of a B;

But this is exactly what is stated in the statement S; thus, S is true;

Hence A is true!

If you still did not understand here is a natural language example

If this sentence is true, then the pasta monster exist.

Even though we know that the pasta monster does not exist, the example sentence certainly is a natural-language sentence, and so the truth of that sentence can be analyzed. The paradox follows from this analysis. The analysis consists of two steps.

First, common natural-language proof techniques can be used to prove that the example sentence is true.

Second, the truth of the example sentence can be used to prove that the pasta monster exist. Because the pasta monster does not exist, this suggests that there has been an error in one of the proofs.

Even though the above paradoxes look weird and very simple, other than the 5th one, all of these paradoxes can be proven using mathematical logic. If you feel like the answer is obvious, most of the time, you take some laws for granted. It is like believing 1+1 =2. Yes, it is obvious. But have you ever thought about why 1+1 =2? If you have learned Real Analysis, you know why 1+1=2 for real numbers. These paradoxes are also like that. They are simple until you apply principles of mathematical logic.

Thank you!