A Relational Formulation of the Theory of Types

This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language

Normativity all the way down: from normative realism to pannormism

In this paper, I provide an argument for pannormism, the view according to which there are normative properties all the way down. In particular, I argue for what I call the trickling down principle, which says that if there is a metaphysically basic normative property, then, if whatever instantiates it has a ground, that ground instantiates it as well

A categorical semantics for causal structure

We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within categorical quantum mechanics, the objects of this theory encode fine-grained causal relationships between subsystems and give a new method for expressing and deriving consequences for a broad class of causal structures. We show that this framework enables one to define families of processes which are consistent with arbitrary acyclic causal orderings. In particular, one can define one-way signalling (a.k.a. semi-causal) processes, non-signalling processes, and quantum $n$-combs. Furthermore, our framework is general enough to accommodate recently-proposed generalisations of classical and quantum theory where processes only need to have a fixed causal ordering locally, but globally allow indefinite causal ordering. To illustrate this point, we show that certain processes of this kind, such as the quantum switch, the process matrices of Oreshkov, Costa, and Brukner, and a classical three-party example due to Baumeler, Feix, and Wolf are all instances of a certain family of processes we refer to as $\textrm{SOC}_n$ in the appropriate category of higher-order causal processes. After defining these families of causal structures within our framework, we give derivations of their operational behaviour using simple, diagrammatic axioms.Comment: Extended version of a LICS 2017 paper with the same titl

Information structure and the accessibility of clausally introduced referents

This paper will examine the role of various factors in affecting the salience, and hence the accessibility to pronominal reference, of entities introduced into a discourse by a full clause. We begin with the premise that the possibility of pronominal reference with it versus that depends on the cognitive status of the referent, in the sense of Gundel, Hedberg and Zacharski (1993). This formulation of the problem provides grounds for an explanation of the data presented above, and provides a framework within which we examine the role of various other factors in promoting the salience of a clausally introduced entity, including the information structure of the utterance in which the entity is introduced. For entities introduced by clausal complements to bridge verbs, we show that the information structure of the utterance introducing the entity has a partial, or one-sided, effect on the salience of the entity. When the complement clause is focal, the salience of the entity depends only on its referential givenness-newness (in the sense of Gundel 1988, 1999b), as we would expect. But when the complement clause is ground material, the salience of an entity introduced by the clause is enhanced. Other factors, including the presuppositionality of factive and interrogative complements, also serve to enhance the salience of entities introduced by complement clauses

Scrambling and reference in german

Although the linear order of arguments (and adverbials) in German is relatively free, it underlies certain restrictions; these don’t apply to the so-called unmarked order for arguments (Lenerz 1977) and adverbials (Frey/Pittner 1998). It is a common assumption to take the unmarked order as basic and derive all other orders from it by scrambling, whatever its specific characteristics may be (cf., amongst others, Haider/Rosengren 1998). The observable restrictions obtaining for some linear ordering may then be considered as constraints on a movement operation (scrambling). [...] In the following, I will try to present the outlines of a possible explanation for the restriction, based on a proposal governing the proper referential interpretation of indefinite NPs

Tense and the Logic of Change

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic

Against the iterative conception of set

According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty set and raises serious epistemological concerns; but the leading realist interpretations---ontological and modal interpretations of priority---are deeply problematic as well. I conclude that the purported explanatory virtues of the iterative conception are, at present, unfounded