A paradox is a premise that contradicts itself. It’s a situation that seems to defy logic by producing an inconsistency that goes against common sense. Most logical paradoxes are known to be invalid arguments. However, they are still valuable for promoting critical thinking and sometimes proving a point by contradiction. Teasing your mind and question everything you think you know makes for great intellectual activity. Indeed, the closer you examine things, the more you’ll start to discover paradoxes all around you.
Here are some of the most fascinating paradoxes you should know about. These will boggle your mind every time you read or think about them. Enjoy!
1. Likely to exist means likely to be found, but where is everybody?
A mind-blowing paradox comes from the apparent contradiction that exists between the high probability of extraterrestrial civilizations being out there somewhere, and our lack of alien contact or evidence.
In a universe of infinite space, the odds of life existing on a planet other than Earth are pretty high. However, no confirmed signs of intelligence have been spotted outside Earth, either in our galaxy or in the more than 80 billion other galaxies of the observable universe.
Hence physicists Enrico Fermi’s famous question: “Where is everybody?”
2. Does an object that has all its components replaced remain the same object?
This is a classic paradox drawn from the ancient Greeks’ original Ship of Theseus Paradox. It was famously described by Plutarch to get at the contradictions of identity. It goes like this:
You have an old wooden ship. You remove a plank from the ship one at a time and replace it with a new plank. You do this with every piece until the old ship is completely replaced. Is it still the same ship? If you construct a new ship out of the old pieces you took off the first ship, which one is the original ship?
A newer version of this paradox that drives the contradictions of identity closer to home replaces the “ship” with the “brain”. If you somehow quickly replaced parts of your brain material with identical clones and made a separate brain with the old brain material, would that be you too? Would you still be you?
3. Time travel (if possible) would result in some extremely strange situations.
Consider the following version of the popular science fiction themed Bootstrap Paradox, involving time travel and bringing an object or information back in time:
A stranger appears out of nowhere and hands you a strange device. The stranger then runs away and you never see them again. You discover the device handed to you is a time machine. After holding it for a while, you get bored. Instead of getting rid of it, you figure: “Hey, why not give it to myself?” So you go back in time and give yourself the device hence starting the whole cycle again.
Where did the device come from?
4. Can you travel back in time and prevent yourself from being born?
Another famous example of a time travel paradox is the Grandfather Paradox. In this mind blowing scenario, someone travels back in time and kills their own grandfather to prevent their own birth.
Think about this: A girl goes back in time and kills her grandfather before he has a chance to meet her grandmother and sire her father. Since her grandfather is dead, the girl was never born.
If she were never born, how could she kill her grandfather?
5. Can an omnipotent being defy the laws of logic and be both omnipotent and not omnipotent?
This version of the Omnipotent Being Paradox arises from the simple but strange exclamation: “Let God Almighty create a stone, which he himself is not capable of lifting!”
Can God be omnipotent and not at the same time? How does free will even exist if God is omniscient?
These are just some of the many paradoxes that arise when you try to apply logic to definitions of God or an almighty being.
6. If destiny designed a master plan which defines everything that is to happen, isn’t it useless to go to a doctor, for example?
According to this Lazy-bones Paradox, if you are ill and it is your destiny to regain health, then you will regain your health whether you visit a doctor or not.
If it is your destiny not to regain health, then seeing a doctor can’t help you. This is a paradox that might arise if you reject the notion of an omnipotent God or a supreme being who’s in charge.
How would you question this premise or supposition?
7. A heterological word is a word that does not describe itself. Does “heterological” describe itself?
For example, “verb” is a heterological word since it is not a verb (as opposed to “noun,” which is itself a noun). Similarly, “long” is a heterological word since it is not a long word (as opposed to “short,” which is actually a short word). So then, is “heterological” a heterological word?
This is one of many self-referential paradoxes that have kept mathematicians and logicians up at night.
If “heterological” were a word that didn’t describe itself, then it would describe itself. However, if it did describe itself, then it would not be a word that described itself.
8. If someone says “I always lie,” are they telling the truth? Or are they lying?
The great stoical logician Chrysippos came up with a paradox popularly known as the Liar Paradox. It tells of a Cretan who sails to Greece. Upon arriving, he is greeted by Greek men on the shore and says, “All Cretans are liars.” Did he speak the truth, or did he lie? A week later, the Cretan sails to Greece again and says, “All Cretans are liars and all I say is the truth.”
The Greeks were truly puzzled. None were more confused than the grammarian and critic Philetus of Cos, who is said to have died of exhaustion while attempting to resolve the paradox.
Maybe we should just let this one go unsolved then? No?
9. A barber shaves everyone who does not shave himself, but no one else. Who shaves the barber?
This paradox is similar to the Liar Paradox. It was formulated by English logician, mathematician, and philosopher Bertrand Russell to emphasize the importance of establishing careful rules when creating sets. His Set Theoretic Paradox would lay the groundwork for 20th-century mathematics.
It goes like this: There is only one barber in town. The barber (who is a man) shaves only those men who do not shave themselves, but no one else.
Who shaves the barber? Does he shave himself?
10. What happens when an unstoppable object faces an immovable object?
An ancient story is told of a man who was walking through a market when he came across a merchant. The merchant advertised two of his wares boldly: “This spear can pierce any shield!” and “This shield can block any spear!”
The man contemplates these opposing statements for a moment. He then walks up to the merchant and asks, “What happens when you pierce the shield with the spear?” The merchant had no answer to this question.
A more recent account of an unstoppable object facing an immovable object involves a bullet and armor. Imagine there is a bullet which can shoot through any barrier. There is also some absolutely bullet-proof armor which no object can penetrate.
What will happen if such a bullet hits such an armor?