Top 10 Completely Mind-Bending Paradoxes — TopTenzNet

Top 10 Completely Mind-Bending Paradoxes

Paradoxes are a fascinating part of reality and there are paradoxes in many different fields like math, physics, logic, psychology, and language. When it comes to trying to understand them, paradoxes can make the brain feel like it’s doing somersaults, but they can also expand your mind and make you look at the world in a whole new way.

10. Hilbert’s Paradox of the Grand Hotel
Imagine if you will, there is a hotel with an infinite number of rooms and each room is booked with an infinite number of guests. If that were the case, then every single room would be booked, right? Because an infinite amount of guests would fill an infinite amount of rooms. But the hotel has a weird paradox where there are always vacancies and they are always booked. This can be seen when a new guest shows up. To find him a room, David Hilbert, who thought of the paradox, suggested that everyone move to the next room. For example, one moves into two, two moves into three and so on.

But what happens if more than one person shows up, say another infinite amount of people? Hilbert says that the people in the rooms could just go to the room number that is double their current number and then there will be room for everyone.

This paradox speaks to the nature of infinity and has fascinated mathematicians for decades. It also probably has given more than a few hotel employees terrible nightmares.

9. The Raven’s Paradox
Logician Carl Gustav Hempel first proposed his “raven paradox” in the 1940s and it questions our belief in confirmation. We make confirmations in both science and everyday life based on observations. For example, let’s say a detective was trying to solve a crime. He would find evidence and the evidence would back up his theory, disprove his theory, or the evidence could be neutral. The evidence could also be strong or weak. What Hempel asks is what does it take for a piece of evidence to confirm the hypothesis, rather than disprove it or be neutral about it?

To demonstrate the paradox, Hempel talked about ravens. He said that after observing a few ravens and noticing they were all black, someone may infer that all ravens everywhere are black. But that is impossible to check, because there have been so many ravens throughout history and there will be more in the future and just one non-black raven would disprove the theory that all ravens are black.

Also, there is the contrapositive, which is another theory that is the opposite of the hypothesis but it is still true. For example, the contrapositive for “all ravens are black” is that “all non-black things are non-ravens.” That means that every single thing that is non-black and non-raven, like a blue shirt or a yellow tennis ball, proves that ravens are black. Of course, there are way too many non-black non-raven things in the universe and so that type of information really does not contribute to the hypothesis that all ravens are black.

The raven paradox is meant to be a warning against generalization and that there needs to be a limited scope if a scientist wants to prove something beyond a doubt.

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Coming up:

10. Hilbert’s Paradox of the Grand Hotel
9. The Raven’s Paradox
8. The Friendship Paradox
7. The Barber Paradox
6. Buridan’s Bridge
5. The Liar’s Paradox
4. The Sorites Paradox and The Ship of Theseus
3. The Birthday Paradox
2. The Bootstrap Paradox
1. Specious Present

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