Propositions cannot exist

What a proposition is, or is supposed to be, can be grasped through abstraction principles. An abstraction principle is something of the form:

\[\forall \alpha \forall \beta (\Sigma(\alpha) = \Sigma(\beta) \leftrightarrow \alpha \sim \beta \]

Where \(\Sigma \) is an appropriate term-forming operator and \(\sim \) an equivalence relation. In the case of propositions, the abstraction principle will be something like:

The proposition expressed by u₁ = the proposition expressed by u₂ if and only if the content of u₁ is the same as the content of u₂

where u_i are appropriate tokenings such as utterances or inscriptions. A proposition is what is expressed by a sentence, written or spoken, and, furthermore, propositions are taken to be truth-bearers: they are the sorts of things that can be true or false. All this tells us that propositions are intentional entities: they are about or of the world; they pertain to things, and so on. The problem for propositions arises when one starts to consider what intentionality consists in, or what it is for something to be about, to be of, or to pertain to the world. It’s often (rightly) said that whatever aboutness propositions or sentence tokens have must be derivative from the fundamental intentionality associated with intentional agents. But something stronger can be said. Being about something essentially requires being responsible to that thing—not, it is worth emphasising, be responsive to a thing: lumps of wax are responsive to heat but are not about heat, thoughts about things outside our light cone are not responsive to those things but are about them; something different is required. If I think about the Empty Quarter I make my thinking responsible to the Empty Quarter itself. If I think of the Empty Quarter that it is the largest expanse of sand in the world then my thinking goes wrong—is subject to negative normative assessment—if it is not the largest expanse of sand in the world, and my thinking goes right—is subject to positive normative assessment—if it is the largest expanse of sand in the world. This isn’t an accidental feature of intentionality, it’s an essential one. So the only entities that can be about things are those that can be responsible to those things. Only persons are responsible in this way, abstract objects like propositions can’t be. But propositions are defined as things which are about the world; the result being that propositions would have to possess an essential property they cannot possibly have. Propositions then, cannot exist.