. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.

Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and models (...) are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one?

We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity "validity!", and in Section 2 we contrast it with the standard notion, which we call "validity2". Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics. (shrink)

The Reduction of the Possible to the Real. Modern philosophy cannot avoid dealing with possible worlds - neither in the field of intensional logic nor in other fields not directly connected with logical investigations. This paper attempts to develop a method to substitute possible worlds by the real world, referring to the works of Stig Kanger and Nino B. Cocchiarella. This is done by investigating the metaphorical and dynamical functions of natural languages. It is proved that this new technique is (...) adequate for use in the semantics of intensional languages. As an example a language is constructed, which is based on the aristotelian view of universal concepts. (shrink)

The paper intends to show, that W. N. Hohfeld's theory of fundamental jural relations is relevant to economic theory, and that Hohfeld's system can be reconstructed by the concepts of 'liberty space' and 'ability space', understood as an agent's Spielraum for action. The first half of the paper is devoted to an exposition of Hohfeld's system and to the question of its relation to the economic analysis of property rights. The second half concerns Spielraum theory and the reformulation of Hohfeldian (...) distinctions in terms of liberty spaces and ability spaces. It is argued that the reformulation is useful, inter alia, for describing exchange of property rights by contract. El artículo intenta mostrar: que la teoría de las relaciones jurídicas fundamentales de W. N. Hohfeld es relevante para la teoría económica y que el sistema de Hohfeld puede ser reconstruido mediante los conceptos de "espacio de libertad" y "espacio de capacidad", entendidos como el Spielraum para la acción del agente. La primera mitad del artículo está dedicada a la exposición del sistema de Hohfeld y al problema de su relación con el análisis económico de los derechos reales. La segunda mitad se refiere a la teoría del Spielraum y a la reformulación de las distinciones hohfeldianas en términos de espacio de libertad y espacio de capacidad. Se argumenta que esta reformulación es útil, inter alia, para describir el cambio de los derechos reales mediante contratos. (shrink)

This collection of essays is the definitive version of a widely discussed debate over the origins of the New Theory of Reference. In new articles, written especially for this volume, Quentin Smith and Scott Soames, the original participants in the debate, elaborate their positions on who was responsible for the ideas that Saul Kripke presented in his Naming and Necessity. They are joined by John Burgess, who weighs in on the side of Soames, while Smith adds a further dimension in (...) discussing the contributions of philosophers such as Follesdal, Geach, Hintikka, and Plantinga. Also included are lengthy excerpts from Follesdal's 1961 Harvard dissertation and a careful examination by Sten Lindstrom of the respective contributions of Kripke and Stig Kanger to the development of modal semantics. The collection will be essential reading for anyone acquainted with these influential ideas. (shrink)

This paper describes and compares the first step in modern semantic theory for deontic logic which appeared in works of Stig Kanger, Jaakko Hintikka, Richard Montague and Saul Kripke in late 50s and early 60s. Moreover, some further developments as well as systematizations are also noted.

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms.

This paper is a reply to some of Scott Soames ' comments on my colloquium paper Marcus, Kripke, and the Origin of the New Theory of Reference. Except for the indicated parts added in May, 1995, this paper was written on December 16th–25th, 1994 as my reply to Soames for the APA colloquium in Boston, December 28, 1994. In this paper, I argue that Soames ' contention that Marcus is not one of the primary founders of contemporary nondescriptivist theories of (...) reference is false. Soames presents numerous arguments for his thesis that Marcus did not originate ideas later elaborated upon by Kripke, but his arguments are unsound; they are based in part on a misunderstanding of Marcus' theory and in part on an inadequate grasp of some of the key notions of the New Theory of Reference, such as the notion of a posteriori necessities and the notion of reference-fixing descriptions. (shrink)

This paper argues that several leading theories of subjunctive conditionals are incompatible with ordinary intuitions about what credences we ought to have in subjunctive conditionals. In short, our theory of subjunctives should intuitively display semantic humility, i.e. our semantic theory should deliver the truth conditions of sentences without pronouncing on whether those conditions actually obtain. In addition to describing intuitions about subjunctive conditionals, I argue that we can derive these ordinary intuitions from justified premises, and I answer a possible worry (...) for my derivation by refuting a subjunctive triviality result modeled on (Lewis 1976). I conclude that the debate over the correct theory of subjunctive conditionals requires settling meta-philosophical questions about the relative value of various virtues of first-order theories of subjunctive conditionals. (shrink)

Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural two-sorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result (...) is established between the category of sober algebras and the category of general Kripke structures. A simple enrichment of the proposed sequent calculi is proved to be complete over standard Kripke structures. The calculi are shown to be analytic in a useful sense. (shrink)

In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but (...) with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form. (shrink)

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink)

In the early days of the semantics for modal logic the `possible worlds' were thought of as models or interpretations. This was particularly so when the interpretation was of emph{logical} necessity or possibility, where this was understood in terms of validity. Arnould Bayart in 1958 may have been the first modal logician to argue explicitly against the identification of necessity and validity. This note contrasts his semantics with that provided by Rudolf Carnap in 1946, and examines Bayart's proof that if (...) you identify necessity with validity then certain theorems of S5 are not valid. The proof is then examined using Carnap's semantics. (shrink)

The essays presented in this collection were written over a long period. The first two : "On the Classification of Verbs and Actions" and "On von Wright's Theory of Action" constitute steps in my preparation for the book Events, Actions, and Ordinary Language, Lund 1977. Much of the contents of the former paper was carried over to the book, whereas the analyses in the latter paper were more or less completely left out. These papers have not been published before. "On (...) Various Forms of Interaction" is a development of soroe ideas in Events, Actions, and Ordinary Language. This paper was previously published in Swedish in Henschen-Dahlqvist A-M ed. Filosofiska smulor, Festskrift tillägnad Kon rad Marc- Wogau på hans 75-årsdag, Uppsala 1977. "Action- Explanations Reconsidered" was wri t ten in 1981 and has not been previously published. It is a short presentation of a basic idea in my dissertation Explanation of Human Actions, Uppsala 1974, as well as a commentary on sorne criticisrns that could be directed against it. "On Not Being Able To Act", finally, is a slightly modified version of a paper previously published in Pauli T. ed, Philosophical essays dedicated to Lennart Åqvist on his fiftieth birthday, Uppsala 1982. The analysis sketched in this paper has been more fully developed in my Disabilities and Their Classification, Linköping 1983. (shrink)

Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

The goal of this paper is to consider how the notion of analyticity can be dealt with in model-theoretical terms. The standard approach to possible-world semantics allows us to define logical truth and necessity, but analyticity is considerably more difficult to account for.

When I talk about the objects of belief I do not mean, e.g., the sun to which my thought that the sun will rise tomorrow refers; I do not mean the objects we think about. I take objects rather in a general philosophical sense; they simply are the bearers of properties and the relata of relations. I am thus concerned with the objects that are related by the belief relation „_a_ believes that _p_“. In this scheme „ _a _“ represents (...) a person or an epistemic subject; but I am not going to discuss what a person is. „ _p _“ or „that _p _“ represents an object, namely the object of belief; and I am going to discuss what this is. In other words, I am interested in belief contents – to use a less neutral, narrower and equally unclear term. (shrink)

The goal of this paper is to consider how the notion of analyticity can be dealt with in model-theoretical terms. The standard approach to possible-world semantics allows us to define logical truth and necessity, but analyticity is considerably more difficult to account for.