Foundations of Mathematics

Axiomatic System

When is a paradox not a paradox?

There are many proposed paradoxes that are not really one—even though they sound like it. One just-for-fun, simple example of a non-paradox can be called a “friends” paradox. Brought out in a study on friendships by sociologists Scott L. Feld, it demonstrates the seeming paradox of why your friends seem to have more friends than you do. Follow us here: There are 12 people who have a friend who has 12 friends, but there is only one person who has a friend who has only one friend. There is also no one who has a friend who doesn’t have any friends. There is only one friend who has 12 friends. Thus, the number 12 gets counted only once when you compute the average number of friends that people have, but it gets counted 12 times when you calculate the average number of friends that their friends have. Thus, it seems like a paradox that your friends have more friends than you do, when in reality, it’s merely that you’re more likely to be friends with someone who has more friends than with someone who has fewer friends. If you’re totally confused, don’t worry. That’s the nature of logic and the paradox.


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