Sten Lindström

Ddl Unlimited: Dynamic Doxastic Logic for Introspective Agents

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical language: a dynamic modal logic.1 Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL).2 This framework may be seen as an extension of standard Hintikka-style doxastic logic (Hintikka 1962) with dynamic operators representing various kinds of transformations of the agents doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about

A Note on Quantification and Modalities

In this short note I shall make a few comments on the interpretation of quantification in modal logic. My points of departure are the formal language L of the lower predicate logic with modalities, and an interpretation of L. The interpretation I have in mind has the form of the valuation given in my paper The Morning Star Paradox (Theoria 23 (1957), 1-11), except that the valuation shall apply to the formulas of L and not only to the statements.

Situations, Truth and Knowability: A Situation-Theoretic Analysis of A Paradox By Fitch

According to a non-realist conception, the notion of truth is epistemically constrained: the anti-realist accepts one version or another of the Knowability Principle (‘Any true proposition is knowable’). There is, however, a well-known argument, first published by Frederic Fitch (1963), which seems to threaten the anti-realist position. Starting out from seemingly innocuous assumptions, Fitch claims to prove: if there is some true proposition which nobody knows to be true, then there is a true proposition which nobody can know to be true.

An Exposition and Development of Kanger’s Early Semantics for Modal Logic

Stig Kanger — born of Swedish parents in China in 1924 — was professor of Theoretical Philosophy at Uppsala University from 1968 until his death in 1988. He received his Ph. D. from Stockholm University in 1957 under the supervision of Anders Wedberg. Kanger’s dissertation, Provability in Logic, was remarkably short, only 47 pages, but also very rich in new ideas and results. By combining Gentzen-style techniques with a model theory a la Tarski, Kanger obtained new and simplified proofs of central metalogical results of classical predicate logic: Godel’s completeness theorem, Lowenheim-Skolem’s theorem and Gentzen’s Hauptsatz. The part that had the greatest impact, however, was the 15 pages devoted to modal logic. There Kanger developed a new semantic interpretation for quantified modal logic which had a close family resemblance to semantic theories that were developed around the same time by Jaakko Hintikka, Richard Montague and Saul Kripke (independently of each other and independently of Kanger).

Conditionals and the Ramsey Test

Frank Plumpton Ramsey (1903–1930)—the brilliant Cambridge philosopher whose short but very intensive career started when he was still a teenager only to be interrupted by his untimely death about a decade later—made important contributions to logic and even more fundamental contributions to decision theory. As is well known, he and de Finetti—independently of each other—were the founders of the so-called subjectivist (or ‘personalist’) approach to probability. It should be mentioned that the first comprehensive monograph on the different aspects of Ramsey’s work has only recently been published [Sahlin, 1990].

Epistemology versus Ontology

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the ...

Epistemology versus ontology : essays on the philosophy and foundations of mathematics in honour of Per Martin-Löf

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the ...

How to Model Relational Belief Revision

Some years ago, we proposed a generalization of the well-known approach to belief revision due to Peter Gardenfors (cf. Gardenfors 1988). According to him, for each theory G (i.e., each set of propositions closed under logical consequence) and each proposition A, there is a unique theory, G*A, which would be the result of revising G with A as new piece of information. There is a unique theory which would constitute the revision of G with A. Thus, belief revision is seen as a function. Our proposal was to view belief revision as a relation rather than as a function on theories. The idea was to allow for there being several equally reasonable revisions of a theory with a given proposition. If G and H are theories, and A is a proposition, then GRAH is to be read as: H is an admissible revision of G with A. (Cf. Lind-strom and Rabinowicz, 1989 and 1990.)

21 Modal logic and philosophy

Publisher Summary Modal logic was born in philosophy, and has travelled widely; it retains important links with the discipline. This chapter discusses the historical heartland of philosophical modal logic—namely, the scope and limitations of modal logic as an account of necessity and possibility. It also examines modal logic and the logic of belief change, and modal logic as logic of action. The relationship between the logical and metaphysical interpretation of the alethic modalities is discussed. The epistemic logic and deontic logic are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. Modal logic is brought to bear on an area that has already reached a degree of maturity and that is formulated with little or no regard to modal logic. There is a strong connection between the theory of belief change and the logic of conditionals.

Horwich's minimalist conception of truth: some logical difficulties

Aristotle’s words in the Metaphysics: “to say of what is that it is, or of what is not that it is not, is true” are often understood as indicating a correspondence view of truth: a statement is true if it corresponds to something in the world that makes it true. Aristotle’s words can also be interpreted in a deflationary, i.e., metaphysically less loaded, way. According to the latter view, the concept of truth is contained in platitudes like: ‘It is true that snow is white iff snow is white’, ‘It is true that neutrinos have mass iff neutrinos have mass’, etc. Our understanding of the concept of truth is exhausted by these and similar equivalences. This is all there is to truth.