7 mind-twisting paradoxes of all time

This paradox is also known as the grandfather's axe paradox. Suppose you have a ship made of 100 pieces of wood. Every now and then you replace an old piece of wood with a new piece and you keep the old pieces in a shed. Over the course of many years, you replace all of the old pieces with new pieces of wood, but that’s still the same original ship to you, right?

Well, the paradox occurs when you consider what happens when you take all of the old pieces of wood and reassemble them. The question then becomes: Which is the original ship?

This paradox asks: Could an omnipotent being limit its own power? Another way to word it: Could God create a stone so heavy that even he couldn’t lift it? This is paradoxical because if God does have unlimited power and can do anything, then, of course, he could create a stone that he couldn’t lift. If that’s true and he couldn’t lift it then that’s something he can’t do, hence the paradox.

A judge tells a prisoner that he’s sentenced to be hanged at noon one week day in the coming week, but that it’ll be a surprise and he won’t know until his executioner knocks on his door on the chosen day. The prisoner reflects a bit on his new sentence and concludes that since it’s to be a surprise hanging it can’t happen on Friday, because if it hasn’t happened by Thursday, there would be only one day left, thus it isn’t a surprise. He then continues to reason that the hanging can’t be Thursday either because Friday’s eliminated and if it hasn’t happened by Wednesday, Thursday would not be a surprise.

He continues this line of reasoning and concludes that the hanging cannot happen on Wednesday, Tuesday, or Monday, and finally decides that the hanging will not happen at all. This is of course until the executioner knocks on his door on Wednesday at noon and everything the judge said came true. The paradoxical nature of this situation is primarily due to the language used.

This is one of the most famous paradoxes ever created. Suppose a time traveler goes back in time before his grandfather meets his grandmother. If the time traveler kills his grandfather that would mean he was never born, but if he was never born, he wouldn’t be able to go back and kill his grandfather in the first place.

Suppose that there’s a town with just one male barber. Now, in this town, there’s a rule that every man must keep himself clean-shaven, either by shaving himself or going to the barber and having the barber shave him. Using that rule, logic follows that the barber shaves only those men who do not shave themselves. The paradox is: If the barber does not shave himself, he must abide by the rule and shave himself, but if he does that, according to the rule, he will not shave himself.

Also known as the Liar Paradox, this is another example of an infinite regression that can be phrased in many ways, but most simply as follows: “This statement is false”. Now, if the statement that I just said was, in fact, false, then, of course, it would be true, but if it were true, then that would make it false, which of course would again make it true…

Created by logician Carl Gustav Hempel, this paradox is based off the following three statements:

• All ravens are black.
  
• Everything that is not black is not a raven.
• This green thing is an apple and thus not a raven.

Now, here’s what’s interesting. By saying those three sentences in that order, it logically follows that the sight of a green apple is somehow evidence supporting the notion that all ravens are black. This of course a paradox, because it implies that information has been gained about ravens by simply looking at an apple, which of course makes no sense.