It is shown that the basic postulate of utilitarianism does not work when we must decide whether a person should be brought into existence. Utilitarianism must be supplemented by further axioms. Those proposed lead to the consequence that as far as the potential child's utility is concerned, it is morally preferable not to produce children at all. This consequence is accepted. It is still recommended when parents? utility is taken into account.

In this paper I want to discuss some basic problems of inductive logic, i.e. of the attempt to solve the problem of induction by means of a calculus of logical probability. I shall try to throw some light upon these problems by contrasting inductive logic, based on logical probability, and working with undefined samples of observations, with mathematical statistics, based on statistical probability, and working with representative random samples.

Inductivism is understood as the explication of the degree of confirmation as conditional logical probability. Inductivism is not recommendable in the form of Carnap's λ-system, but tenable in the form of Bayesianism. Objections directed at it are either irrelevant or can be taken account of within Bayesianism.