The four kinds of proposition are:
1) Analytic: "All triangles have three sides."
2) Internal: "I have a headache."
3) External, or Empirical: "I see a table here before me."
4) Categorical: which can be expressed as a moral proposition, "Human beings should not kill other human beings"; as a political proposition, "The Crimean vote to succeed from Ukraine is illegal according to international law"; or as an aesthetic proposition, "Fellini's films are beautiful even when they are grotesque."
As far as my understanding takes me, there is only one type of proposition that can be proven true or false; that is, the Analytic proposition. The others are rather statements of a different order. Internal propositions do not describe anything that can be logically proven: moreover, whether they are true or false has no bearing upon our philosophical understanding or the description of actual reality. Rather such statements guide (or do not guide) our behavior. External propositions can be no more than descriptive. They are not logically true, but rather they are descriptive; that is, they are useful. If descriptive statements are false then they are simply nonsense; they don't inform us about anything, except perhaps that a person who vocalizes them is careless, is ignorant, is misinformed, is a joker, or is a liar. Categorical propositions--or rather expressions of moral, political, or aesthetic belief--are neither true nor false, they are simply statements about belief. The question is, are they persuasive?
The key point I am turning upon here is what can be proven with logic. The philosophical material that informs the various subjects addressed by philosophers (or by social-scientists, scientists, and poets) is itself very thin. That is, their theories, hypotheses and mythological constructions are enchanting, intriguing, or somehow appealing to our understanding; nevertheless, they remain matters that cannot be proven with logic, and so we must remain circumspect about the truth claims of the many voices that seek to sway our opinions, or which seek to enlist us in their projects. As for science, that can still proceed, for our science really does not seek what is true, but merely what seems to work at any given point in time, or in some context, or when given a certain set of circumstances or conditions. Nor do I want a science that seeks to do more.