Why the tuple theory of structured propositions isn't a theory of structured propositions

Abstract

Much is at stake. The notion of structured propositions – in particular structured singular propositions – is a cornerstone of the theory of direct reference, yet if the intuitive notion of structured proposition cannot possibly translate into ordered ntuples, as direct reference theory does, then that theory finds itself without a semantics in one of its key areas. This would prove an embarrassment, considering that its founding father, David Kaplan, first put forward the notion a quarter of a century ago. If the objections go through, however, it’s not only direct reference theory that will be seen to have left a central notion dangling. E.g., also Max J. Cresswell’s brand of categorial grammar relies on tuples as propositional structures (see Cresswell, 1985). It’s important to stress that the attack on tuples as propositional structures isn’t an attack on the notions of either singular or structured proposition. Indeed, both have much to be said for them, albeit they would deserve to be developed within a different framework. An historical parallel might be in place. Since Frege never came around to developing a formal theory of Sinne, it at some point became tempting to construe them as intensions a la possible worlds semantics, i.e., as functions (mappings) defined on a set of possible worlds. It’s well-known today that, and why, the construal was an aberration. Similarly, since Russell never got a firm grip on his propositions, it has become tempting to construe them as tuples. This essay tries to show why they shouldn’t be. In setting out why, we’ll see, among other, that the old problem of propositional unity afflicting Russell’s propositions rears its head again (see Jacquette 1992/93, Griffin 1993). But tuples-as-structures are open to an even more fundamental objection (Section IV).