We can think about the world as it is (was/will be), as it can be, or as it should be. If, and insofar as, our factual thought is merely a matter of observation or empirical experience, it is descriptive. Such 'descriptive' thought, however, may also concern modal conditions rather than factual ones, especially when it is stated that something is possible. In the case of thought about modal conditions it would be better to use the term speculative, or some such term, to denote that the process of thinking is not grounded in mere observation or actual sense experience and that it is inconclusive in the factual sphere. Of course, one can also 'speculate' about facts and norms but the meaning of to speculate is then simply that of to think. Finally, normative thought unequivocally designates thought about norms, or about the world as it should be.

The belief about what is possible or probable is a form of speculative (modal) thought, and the belief about what is good or superior a form of normative thought. Now, modal conditions --we have assumed-- are entirely independent of normative conditions, and yet this does not mean that the belief in what can be is not determined by the belief in what should be. Especially the belief in what cannot be, or is highly improbable, is but too often a mere expression of the lack of belief in what should be (and, similarly, the belief in what can be a mere expression of faith in what should be). But these facts are not facts of the same level as the modal and normative conditions the belief is about; they are facts of speculative and of normative, propositional attitudes themselves. Obviously there are different levels on which facts, modes and norms are operative.

Let us use the word ground to refer to the zero-level of the propositional hierarchy. Nonpropositional reality is, then, the ground-level on which we live ourselves, at least as biological beings. Factual, modal and normative conditions on this level are 'ground-facts', 'ground-modes' and 'ground-norms' or 'factual', 'modal' and 'normative ground-conditions'. Thus, it is descriptive thought about the nonpropositional world in which we live which yields the ground-facts (if the propositions are true). In such thought the ground-world is described as it actually is. Speculative (and statistical) theories about the ground-world which show that states of affairs are impossible, improbable, neither improbable nor probable, probable or necessary yield the ground-modes (if true). And normative theories about the ground-world, if true or correct, supply us with the ground-norm or -norms of this world.

On the first propositional level, descriptive (factual), speculative (modal) and normative theories are themselves objects of descriptive, speculative and normative thought on the second propositional level. A descriptive theory is, then, thus and so, can be thus and so, or should be thus and so. This applies equally to speculative and normative theories. That a descriptive theory about the ground-world is thus and so is, then, a first-order fact, whereas the proposition that it is thus and so is a second-order proposition. Similarly, it is a first-order fact that a normative theory has a certain characteristic, whereas the proposition that it has this characteristic is of the second order.

The first-order facts of descriptive, speculative (or statistical) and normative theories about the ground-world are first-order facts of thought or 'first-order propositional facts'. Their first-order modes are, similarly, first-order modes of thought, and their first-order norms, first-order norms of thought. But the object of second-order theories is not only first-order theories. It is also the relationship between the ground-world and these first-order theories. If, and when, such a relationship exists, we call it "correspondence" (between the ground-world and a theory about the ground-world). The fact pertaining to this relationship is neither a ground-fact nor a first-order fact of thought as defined above. We shall call it "a first-order fact of correspondence". In the same way there are one or more first-order modes and norms of correspondence.

The combination of propositional hierarchy and the division of reality into a factual, a modal and a normative sphere leads to quite a complicated, but systematic, conceptual structure. It leaves us with interesting questions we cannot treat here. One is whether all norms of descriptive, speculative and normative thought are the same, and another whether the first-order norms of thought and of correspondence are the same as the second- and higher-order norms of thought and of correspondence. If so, we need only speak of "the norms of thought and of correspondence". (One may also speak of "principles".) Yet, these questions do not concern our ultimate conceptual framework but rather the content of norms or principles. At this stage we will not yet argue for any particular substantive norm or principle, let alone for the universal scope of such a norm or principle. Nevertheless, we cannot refrain from taking a look at the normative principles which remain implicit in thought which is purportedly purely factual, empirical or descriptive.