Online research in philosophy

ABSTRACT. In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the well-known public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using so-called reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand.

.  On a structuralist account of logic, the logical operators, as well as modal operators are defined by the specific ways that they interact with respect to implication. As a consequence, the same logical operator (conjunction, negation etc.) can appear to be very different with a variation in the implication relation of a structure. We illustrate this idea by showing that certain operators that are usually regarded as extra-logical concepts (Tarskian algebraic operations on theories, mereological sum, products and negates of individuals, intuitionistic operations on mathematical problems, epistemic operations on certain belief states) are simply the logical operators that are deployed in different implication structures. That makes certain logical notions more omnipresent than one would think.

This paper discusses some recent responses to Kripke’s modal objections to descriptivism about names. One response, due to Gluer-Pagin and Pagin, involves employing "actually" operators in a new way. Another, developed mainly by Chalmers, involves distinguishing the dimension of meaning modal operators affect from the dimension other operators, especially epistemic ones, affect. I argue that both these moves run into problems with "mixed" contexts involving factive verbs such as "know", "establish", "prove", etc. In mixed contexts there are both modal and epistemic operators, and it seems that some contradictory examples, such as "possibly (Hesperus has a moon and someone establishes that Hesperus has no moon)", are classified as true according to these views.

In this article we explore multiple change operators, i.e., operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, where both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of postulates and we present different constructions: kernel changes and partial meet changes.

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

A proof is presented that a form of incompleteness in Quantum Mechanics follows directly from the use of unbounded operators. It is then shown that the problems that arise for such operators are not connected to the non- commutativity of many pairs of operators in Quantum Mechanics and hence are an additional source of incompleteness to that which allegedly flows from the..