The issues I explore in this paper are best introduced by the table with which it begins. The left-hand entry in each row gives expression to a kind objectivity; the right-hand entry affirms the existence of a special kind of object. When philosophers believe in any of the entities on the right, it is typically because they think them necessary to ground the facts on the left. By the same token, when philosophers deny any of the facts on the left, (...) it is often because they cannot bring themselves to believe in the associated kind of object on the right. My project is to explore the extent to which it is possible to have the objectivity without the objects—for example, absolute motion without substantival space, objective predication without universals, objective synonymy without propositions, and objective modality without possible worlds. Each of these combinations would have been congenial to A.N. Prior. (shrink)

Although ‘glue semantics’ is the most extensively developed theory of semantic composition for LFG, it is not very well integrated into the LFG projection architecture, due to the absence of a simple and well-explained correspondence between glue-proofs and f-structures. In this paper I will show that we can improve this situation with two steps: (1) Replace the current quantificational formulations of glue (either Girard’s system F, or first order linear logic) with strictly propositional linear logic (the quantifier, unit and exponential (...) free version of either MILL or ILL, depending on whether or not tensors are used). (2) Reverse the direction of the standard σ-projection from f-structure to meaning, giving one going from the (atomic nodes of) the glue-proof to the f-structure, rather than from the f-structure to a ‘semantic projection’ which is itself somehow related to the glue-proof. As a side effect, the standard semantic projection of LFG glue semantics can be dispensed with. A result is that LFG sentence structures acquire a level composed of strictly binary trees, constructed out of nodes representing function application and lambda abstraction, with a significant resemblance to external and internal merge in the Minimalist Program. This increased resemblance between frameworks might assist in making useful comparisons. (shrink)