Why do automatic properties require both getters AND setters?

Question

In C#, if I declare an auto-implemented property, why do I have to declare BOTH the get and set part?

i.e.

public string ThisWorks { get; set; }

public string ThisDoesnt { get; }

Isn't this just syntactic sugar - i.e. the compiler inserts a private field for the property? So why the problem?

Curious.

Answer 1

If you didn't have a setter - then how would you ever set the property?

Incidentally, you can specify the accessibility, eg:

public string Foo
{
  get;
  private set;
}