The inverse square law is about gravity, the triangle inequality is about triangles, "the grass is green" is about grass. They sure are. But what makes them being about? A brick wall has bricks in it, but it is not about bricks, or anything. What distinguishes the three examples above from the brick wall is that they are not objects but propositions. Well, what are propositions? They are a kind of thoughts, a.k.a. intentional acts, expressed by declarative sentences. And this is the secret of it: this use of "about" isn't jarring only because it implicitly relates to a more familiar one, the "intentionality" of it is derivative from the "primary" intentionality. In another sense, the triangle inequality is not about triangles, or anything at all, it is a brick wall, a formula, a cipher, only our intention makes it about triangles.
We can try to evade this by reinterpreting what propositions and laws are. One route is to house them in a Platonic heaven as pure forms. But pure forms are like brick walls, and we face the classical problem of relating them to their "matter", which they are supposed to be about, at all, let alone intentionally. The traditional metaphysics (Plotinus, Avicenna) helpfully embedded Plato's forms into a cosmic mind, where they are placed into such a relation by being its thoughts. But then we did not escape consciousness after all. And on the nominalist/conceptualist route the forms only manifest through particulars, from which they are abstracted by a subject's mind. So there is nothing in the ontology that is about something else, again until we encounter a consciousness.
My point is that attempting to model intentionality on "x means y" misses the target because it is in essence a ternary relation: "x means y to z". A berry can be about eating to a bear, and about a beautiful shade of color to an artist, intentionality is only "intrinsic" by ellipsis. Now, z has been traditionally assumed to be (something like) a conscious subject. The question is if that is necessary. Well, whatever else "means" means z has to be able to relate y to x, and reproducibly so. So it has to be an actor capable of developing "habits", then in the most primitive cases x is a piece of a habit which, if put into action, reaches y (I am skipping a volume here, in particular the role of society and language). That is more or less what Peirce, Ryle, Merleau-Ponty, Dreyfus and other pragmatist advocates of embodied cognition assert. The habit part requires discrimination between "success" and "failure", which could be accomplished through some sort of "tension" qualia, that is Merleau-Ponty's route. But if we admit both habits and qualia we are already pretty close to awareness. I do not think that the qualia are necessary though: the discriminator for habit formation can function causally, "blindly", like a motion sensor connected to a circuit breaker. If so, what we get is a philosophical zombie capable of acting and learning, hence of forming x-s and connecting them to y-s.
I am afraid that Searle will object that the zombie's "intentionality" is parasitic on our own: we say that x "means" y to the zombie because we project ourselves onto it, along with that precious "true" intentionality of ours. But the zombie only "learns" to repeat it mindlessly, it really is just a brick wall that moves. In contrast, the empiricist school (Sellars, Davidson, Dennett) argues that our intentionality is a zombie intentionality, and the strategy is to give a plausible account of how we come to believe, historically and developmentally, that it is more. Sellars's Myth of Jones is an influential hypothetical reconstruction of that.