Hierarchical Propositions

The notion of a proposition plays a central role in the philosophy of mind (through the notion of a propositional attitude) and the philosophy of language (through the theory of speech acts). However, as we have known for a long time, it is subject to paradoxes. A natural response is to stratify propositions into some sort of hierarchy; and, ever since Russell proposed his ‘ramified theory of types’ in 1908, this has been the strategy of choice here. But there is a problem that any such response must overcome, if it is to be adequate. Unfortunately, this problem does not seem to have been recognized before, let alone overcome. The upshot would seem to be that we are not in possession of an adequate hierarchical response after all. The aim of this paper, however, is to remedy this situation, by providing a hierarchical account that does overcome the problem in question. The structure of the paper is as follows. In §1, I will introduce some paradoxes for propositions, and explain how the appeal to some sort of hierarchy would seem to be a natural and effective response to these. But in §2 I will explain the problem that this strategy faces, and how existing accounts, including Russell’s, fall foul of this problem. In §§3 and 4 I will then explain how one can give a hierarchical account of propositions that overcomes the problem: §3 gives the basic idea, while §4 gives the account in full. In the appendix I give a model of the account in standard set theory. There is something that I should make clear at the outset. This paper is about hierarchical accounts of propositions, but I do not assume that these are necessarily superior to non-hierarchical accounts. Rather, I suspect that the situation with propositions is similar to that with sets (for example). Thus, in that case, the simplest, and in many ways the most natural, response to the paradoxes is a hierarchical theory: Zermelo-Fraenkel set theory (ZF), which is hierarchical in the sense that every set belongs to a ‘level’, and can only contain as members things at lower levels. Despite its virtues, however, this hierarchical theory has certain