Hermann Vetter

The usual axioms and inference rules of deontic logic employ as a new primitive term an operator for ‘obligatory’ or for ‘permitted’. These axioms and inference rules are here derived from a language which instead of the operator contains a predicate ‘admissible’ defined on the set of state descriptions of an assertoric language. This approach eliminates the problem of constructing a deontic formalism of its own. The predicate version requires fewer and weaker decisions and is closer to intuitive notions than the operator version. The solutions of some open problems of deontic logic flow automatically from the well-known rules of the assertoric predicate calculus. Special attention is given to the relations between deontic and assertoric statements.The proposed formulation of deontic logic suggests a natural generalization by proceeding from two to any number of degrees of admissibility. When there is a continuum of degrees of desirability, deontic logic becomes identical with the calculus of utilities.

SummaryPopper's verisimilitude is the excess of truth content over falsity content. It is shown that hismeasures of truth and falsity content are at variance with his respectiveconcepts. It is further shown that both his actual measure of verisimilitude and measures based on measures of truth and falsity content consistent with his definition of the concepts, have undesirable properties. Moreover, any measure of verisimilitude based solely on content and truth value does not capture the notion of closeness to truth. A new concept of verisimilitude is proposed, based on a metric in the space of state descriptions.