Imagine you walk into a barbershop and the barber asks how he can help you. You tell him that you’d like him to give you a haircut. But then add that you don’t want him to cut your hair. If you tell the barber this, he will likely think that you are crazy and refuse to provide any services at all. But what if the barber only wanted to cut your hair? In this case, the barber’s statement that he won’t cut your hair could have seemed completely rational. Since it has nothing to do with cutting your hair!
A paradox (plural paradoxes or paradoxes) is a statement that, despite apparently sound reasoning from true premises, leads to an absurd or contradictory conclusion. A paradox involves contradictory yet interrelated elements that exist simultaneously and persists over time. While they are unresolvable in principle, they may be resolvable in practice. Logical paradoxes involve propositions that are seemingly contradictory and make no sense. Semantic paradoxes involve words or phrases which seem to defy common sense, but can still be given some meaning, and epistemic paradoxes arise when we fail to know what we thought we knew about something.
Define the barber paradox
The barber paradox is used in philosophy to describe a situation where someone makes an irrational decision or no decision at all. Essentially, it describes how people can make faulty assumptions about what others believe or don’t believe, based on limited information about that person. It’s not hard to see how this extends to many aspects of life. Politicians, for example, are notorious for taking stances on issues they themselves don’t believe in; they do so because they think their constituents want them to do so. Even though you may know better than most people what you truly want and need out of life. Everyone makes assumptions about other people’s beliefs that don’t hold up under scrutiny.
Example of barber paradox
Suppose that everyone goes to only one barber, who claims that he will shave everyone who does not shave themselves. Does everyone have to shave themselves? Yes and no. No one has to shave themselves because if they don’t they will be shaved by the barber whether or not they go to him. And yet every man must go to him (and thus be shaved). Because if he didn’t he would be shaving himself, which would mean that he doesn’t (and hence does) go to him. But since it was stated in his ad that if anyone shaves himself then he needn’t come. It follows that anyone who shaves himself must go to him, and therefore will get shaved.
History of the barber paradox
This paradox is often incorrectly attributed to Bertrand Russell. The version described here was given in 1851 by William James (although not published until 1895). Russell gave another version in 1903. A different paradox with a similar name sometimes called the barber’s chairs, appears in Russell’s 1912 book The Problems of Philosophy. This form is posed as follows. Consider a small town with 1000 men and 1000 women. Assume that every man shaves himself, but only every other woman shaves herself. Finally, assume that no man ever shaved himself but always got shaved by someone else. Let N be the number of people who have shaved themselves at some time during their lives.
The Ultimate Answer to the Barber’s Paradox
First, let’s discuss why we can even say that there will be someone in town who has never been shaved. We know that there must be at least one person in town who hasn’t been shaved. Because if there wasn’t, then all of the men would have to shave themselves, which contradicts our initial assumption that at least one man shaves himself. So there must be at least one man in town who hasn’t been shaved yet. But how many men are actually in town without having ever been shaved? Well, of course, it depends on how many men have already had their first shave and how many more people might move into town between now and when all of these additional people get their first shave.
Next Steps After Solving the Barber’s Paradox
This paradox serves as an excellent springboard to discuss logical fallacies, which are errors in logic that cause our reasoning to fail. If you can identify a logical fallacy, you’ll be better equipped at arguing intelligently. Thus providing sound support for your own claims. More importantly, if someone else attempts to engage you in a fallacious argument (something they will no doubt do!), you’ll be able to help them improve their thinking. A single paradox like the barber’s shows why it’s important not only to reason carefully but also to make sure your reasoning avoids these errors!
The question then remains, who shaves the barber?
The idea here is that if you need to shave, then someone must do it. If it’s not you, and not anyone else, then who shaves the barber? This makes no sense. In order for there to be a barber (or some other person) who shaves himself, there has to be someone else around who does not shave himself. But if that’s true then he can’t also be shaving himself. It doesn’t make any sense! If he can cut his own hair or shave his own face, then by definition he isn’t someone else – by definition he is himself.
What is the proof of the barbers paradox?
In many towns, only one barber shaves all of its citizens who do not shave themselves. And for every man in town who does not shave himself there exists someday, when he goes to get shaved at the barbershop, that he will encounter a situation in which his barber doesn’t shave himself. Thus there are men (non-shavers) who encounter their own barbers and thus get shaved by someone other than themselves. Therefore they couldn’t have gone to get shaved at their own barbershop, yet they did end up getting shaved by someone else! This clearly shows that self-shaving is impossible. If it were possible then we wouldn’t have as many paradoxes.
What is the barber paradox predicate logic?
The barber paradox in predicate logic states that you cannot prove, using predicate logic alone, that a man who shaves all men who do not shave themselves must shave himself. The barber paradox was formalized by logician Bertrand Russell and his student Alfred North Whitehead in Principia Mathematica (1910). This three-volume work proposed to treat mathematics as an axiomatic system that could derive its truths from basic principles of symbolic logic. Bertrand Russell’s work aimed to establish foundations for mathematical certainty.
As soon as you have finished reading what follows, forget it. This paradox illustrates an idea from cognitive science called context-dependent memory. The paradox revolves around a hypothetical village where everyone’s haircutting needs are taken care of by one barber who, for reasons not important here, has never shaved himself. The puzzle is posed as follows: In a village, there lives one barber who shaves all and only those inhabitants who do not shave themselves. Does such a man exist? If so, how would he shave himself? If not, why not? Most people find that they cannot answer these questions. They know what they mean when they first hear them but somehow can’t get back to that meaning later on.
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