Rysiek Sliwinski

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.

Choice Based on Preference

In this paper, I shall develop an axiomatic theory for binary choice functions C defined for subsets of a grand domain U of alternatives. When V,X ⫃ U, I intend to interpret C(V,X) as the set of those alternatives of (V∩X) which, compared with alternatives of V, are regarded as not being worse than any alternative of (V∩X). In other words: x ∈ C(V,X) iff x ∈ (V∩X) & (y)(yPvx →y∈ (V-X)) where Pv is a preference relation included in VxV. (Read yPvx as: y is better than x in V.)

New Foundations for Ethical Theory

There are philosophers who believe they really tell us how we ought to behave, and there are philosophers who believe they ought to tell us how we really behave. There are also philosophers of a more convenient sort, who only wish to tell us something about ethical theories. The doctrines advocated by these three kinds of philosophers all belong to the wide domain of ethics, and they are easily confused. However, we shall try not to confuse them here, and for that purpose, we may put them under three distinct headings: 1. ethical theory proper 2. the psychology and sociology of morals 3. moral philosophy.

The Paradox of the Unexpected Hanging, Regained Again

The Judge, who sentenced the prisoner to be hanged by the neck provided he, the condemned — before he is actually brought to the gallows — is not convinced that he should hang.

Provability in Logic

Most of the investigations contained in this essay were made for a course in logic, which I gave during the spring term of 1955 at the University of Stockholm. My intention at that time was to present a technique of logical proof that would be easier to master than those usually encountered in textbooks on logic. Thus, the essay may be regarded as having a kind of pedagogical aim. It is hoped that this aim is not overshadowed by the technical character of my exposition.

The Morning Star Paradox

Modal logic got its modern revival with Lewis [1] and a further development through works such as Carnap [2], [3], and Church [3]. The progress is, however, marred by some puzzling difficulties, to which Quine, in particular, has drawn attention.1 Consider for instance the following puzzle, called the Morning Star paradox.

Rights and Parliamentarism

It is almost a truism that the idea of having a right is vague and ambiguous, and that it can be approached from many angles. It is also clear that good explications of this idea are needed in many fields, but one can hardly say that the attempts to provide them have been very successful. The best attempts, so far, at an explication or analysis of the notion of a right are found in jurisprudence. Hohfeld’s contribution should especially be mentioned in this connection. The object of the first part of this essay is to give an analysis of the concept of a right which, in certain respects, is a further development of Hohfeld’s distinctions.1

A Simplified Proof Method for Elementary Logic

It is a well-known fact that there are complete effective proof methods for elementary logic. In other words, there are effective methods M such that whenever a formula F in the language of elementary logic happens to be a logical consequence of a sequence Γ of such formulas, this fact may be demonstrated by means of the method M. And since M is effective, we may — in principle at least — program a computer to carry out the demonstrations. Thus there is a possibility to use a computer to prove theorems in any elementary axiomatic theory. In order to prove a theorem F in a theory with the axioms Γ, we have the computer show that F is a logical consequence of Γ.

Decision by Democratic Procedure

Is it possible to arrive at a parliamentary decision method, for example, in the form of a voting procedure, that is democratically satisfactory? This is one of the more interesting problems in theoretical political science and political philosophy, and it is worth more consideration than it has received. Roughly speaking, the work that has been done to deal with the problem can be divided in the area into two groups: works with a positive orientation, which aim at finding a satisfactory voting system, and works with a negative orientation, which aim at showing that a satisfactory parliamentary decision process is impossible. The most important piece of work with a negative orientation is Kenneth J. Arrow’s Social Choice and Individual Values (New York, 1951). A good source for survey and information within this area of research is Luce & Raiffa’s Games and Decisions (New York, 1957), chap. 14.

Some Aspects on the Concept of Influence

In the essay “Rattighetsbegreppet” (The Concept of Rights) (1963), I conceived of rights as relations between pairs of parties with respect to states of affairs. In a similar vein, we can conceive of influence as a relation between two parties with respect to a state of affairs. And just as there are several different rights-types, there are also different influence-types.