William Thomas is best known for the Thomas Theorem, which is a sociological theory about what is and is not real. Thomas’s theorem holds that situations can have real consequences whenever people define them as real. His theorem helps to explain why some things happen even when they objectively should not happen.
For example, let us look at the fears among many conservative Americans that the government will take away all of their firearms. This fear is, by most objective standards, unreasonable. However, they still believe in it and act on it in real ways, because they believe that it is true. These people have believed for some time that President Obama is not a true American and wants to erode their freedoms. They now believe that one way he wants to do that is by depriving them of their guns. Because they believe these things, they take actions such as buying more guns and stridently (verbally) attacking the government.
The Thomas Theorem helps to explain such things. It says that people will act on situations that they think are real. When this happens, things that are objectively false can have consequences that are as real as they would be if they were true.