In addition to the assumptions, we also have no definition of “positive.” Is there universal agreement on what is positive? There is not.
To quote Dr. Christopher Small:
Gödel suggested that a property could be said to be positive in a moral-aesthetic sense or in a sense of pure attribution. While many of us would differ over the details, a moral-aesthetic interpretation of Pos(F) is reasonably clear. The interpretation of Pos(F) as signifying "pure attribution" is far from obvious. Gödel interpreted the negation of "pure attribution" as "privation", i.e., a lacking in certain elements of being. For example, if F is the property of being present at the Eiffel tower on May 17 at 9:35 a.m. then we might be willing to accept that Pos(F) is true. This is not to say that being somewhere else at the same time is also not a form of pure attribution. If to be present at one location means to be absent from another location, then the participation in an aspect of being could not be said to be pure. So God could be said to be present at the Eiffel tower in the sense of pure attribution. Are there many other types of pure attribution? Probably, both sublime and ridiculous. One might argue that F="knows the capitals of all the states of the United States" is a form of pure attribution. Certainly, the property ~F seems to indicate a type of educational privation that most people possess, myself included. I would expect that God would get full marks in a quiz on this topic. Pure attribution may also require that a property has "fullness of being," although this idea is itself unclear to me.
Is there any relationship between positivity as a moral-aesthetic concept and positivity as pure attribution? I would like to think that the answer is yes. That which is moral or aesthetic typically enhances or deepens being. Alternatively, one could say that those things which are moral or aesthetic are things which affirm the creative over the destructive. A resolution of this issue is, fortunately, unnecessary to the argument which follows.
The only other indication that Gödel gave for his intentions here is to say that positivity is "independent of the accidental structure of the world".