There is a village in which a barber is to shave all and only those men that don’t shave themselves. Does the barber shave himself?

when we try to make sense of things i.e. whether something is correct, we reason our way to a conclusion. We may look out into the world to find truths or assess things internally in ourselves but how can we know we're actually reasoning right? To check if our reasoning is sound, we can abstract the logic of our premises and conclusions. That is to say, we are checking if the statements we are making that lead to our conclusion, are logically sound.

Examples

Valid logic, true values:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal

Can an argument be logically valid but not true? YES:

Dogs are cats
Cats are birds
Therefore dogs are birds

Can you have false premises but have a true conclusion? YES:

Cats are birds
Birds are mammals
Therefore cats are mammals

Can true premises and true conclusion guarantee a valid argument? NO:

Cats are mammals
Tigers are mammals
Therefore Tigers are cats

OR

All roses are flowers
This bouquet contains flowers
Therefore, this bouquet contains roses

A judge sentences a condemned prisoner to death by hanging.

The judge informs the prisoner that the execution will take place at noon on a weekday within the next seven days, but the exact day will be a surprise to the prisoner.

The prisoner reasons that he cannot be hanged on Friday, because if he is still alive on Thursday afternoon, he would know that Friday is the day of his execution, which contradicts the judge's statement that the execution will be a surprise.

He takes this reasoning further and applies to Thursday as Friday is now ruled out. He cannot be hanged on a Thursday as he will know by Wednesday if he is to be hanged on a Thursday, meaning Thursday cannot be a surprise. This reasoning is applied to all weekdays and therefore the prisoner thinks he cannot be hanged because it won’t meet the condition of a surprised hanging.

Smiling, the prisoner considers himself a free man. However the guard summons him on a Wednesday and to the prisoner’s surprise, he is hanged.

Ockham's Razor is the principle that we should favour the simpler ideas over the more complicated ones. This is not to say, go for the simple idea but instead opt for the simplest idea possible, considering the circumstances. Ockham believed academic philosophical theories became unnecessarily complex, especially when talking about imaginary entities. We should instead seek to shave away unnecessary assumptions when trying to come up with a theory: we should not " multiply entities beyond necessity," or to re-phrase,“It is useless to do with more what can be done with less”.