In a previous thread, I proposed the use of a set of logical functions to indicate the kind of speech-act being made, especially distinguishing the direction-of-fit aspect of it, so that that part of an expression can be separated from the propositional content of the speech-act, the idea that the speech-act is about. This is primarily because all of the rest of logic is about the relationships between those ideas alone, independent of whatever we might be communicating about some attitudes toward those ideas.

A classic example of a formal logical inference is that from the propositions "all men are mortal" and "Socrates is a man" we can logically infer the proposition "Socrates is mortal". But, I hold, we could equally well infer from the propositions "all men ought to be mortal" and "Socrates ought to be a man" that "Socrates ought to be mortal". I say that it is really just the ideas of "all men being mortal" and "Socrates being a man" that entail the idea of "Socrates being mortal", and whether we hold descriptive, mind-to-fit-world attitudes about those ideas, or prescriptive, world-to-fit-mind attitudes about them, whether we're impressing or expressing those attitudes, even whether we're making statements or asking questions about them, does not affect the logical relations between the ideas at all.

So I propose that rather than treating a statement like "All men are mortal" as one proposition and a statement like "All men ought to be mortal" as another, completely unrelated proposition, we instead take the idea that they have in common, "all men being mortal", and wrap that in a function that conveys what we wish to communicate about some attitude toward that idea. For example we might write there-is(all men being mortal) to mean "all men are mortal", and be-there(all men being mortal) to mean "all men ought to be mortal"; and generally, write there-is(S) and be-there(S) for the equivalent descriptive and prescriptive statements about the idea of some state of affairs S, whatever S is. We might wish to use shorter names for the functions, like simply is() and be(), or some other names entirely; I am merely using the indicative and imperative moods of the copula verb "to be" to capture the descriptive and prescriptive natures of the respective functions.



The use of these mood functions also facilitates something superficially resembling the motivations for non-classical types of logic such as paraconsistent logics and intuitionist logics, without actually abandoning the principle that differentiates classical logic from them: the principle of bivalence. The principle of bivalence is the principle that every statement must be assigned exactly one of two truth values, "true" or "false", no more and no less. Intuitionist logics allow for statements to be assigned neither of those truth values, while paraconsistent logics allow for statements to be assigned both of them at the same time.

With these mood functions, similar things can be constructed without actually violating the principle of bivalance, because there is nothing strictly logically prohibiting it being the case that neither is(P) nor is(not-P), if for example P were some kind of descriptively meaningless statement; it is merely necessary, to preserve bivalance, that either is(P) or not(is(P)), but not(is(P)) doesn't have to entail that is(not-P). Similarly, there is nothing strictly prohibiting it being the case that be(P) and be(not-P), if for example there were some morally intractable situation where both P and not-P were required, and so any outcome was unacceptable; it is merely necessary, to preserve bivalence, that either be(P) or not(be(P)), but not(be(P)) doesn't have to entail be(not-P).

Fleshing out the philosophical implications of things like descriptively meaningless claims and morally intractable situations is a topic for further discussion. But in any case a logic of this form is in principle capable of discussing things that are, in a loose sense, "both true and false" or "neither true nor false", without technically violating the principle of bivalence.