How do you find only properties that have both a getter and setter?

C#, .NET 3.5

I am trying to get all of the properties of an object that have BOTH a getter and a setter for the instance. The code I thought should work is

PropertyInfo[] infos = source.GetType().GetProperties(BindingFlags.Instance | BindingFlags.Public | BindingFlags.SetProperty | BindingFlags.GetProperty);

However, the results include a property that does not have a setter. To give you a simple idea of my inheritance structure that might be affecting this (though I don't know how):

public interface IModel
{
    string Name { get; }
}

public class BaseModel<TType> : IModel
{
    public virtual string Name { get { return "Foo"; } }

    public void ReflectionCopyTo(TType target)
    {
        PropertyInfo[] infos = this.GetType().GetProperties(BindingFlags.Instance | BindingFlags.Public | BindingFlags.SetProperty | BindingFlags.GetProperty);
        foreach (PropertyInfo info in infos)
            info.SetValue(target, info.GetValue(this, null), null);
    }
}

public class Child : BaseModel<Child>
{
    // I do nothing to override the Name property here
}

I end up with the following error when working with Name:

System.ArgumentException: Property set method not found.

EDIT: I would like to know why this does not work, as well as what I should be doing to not get the error.