Inductive logic After having considered problems in semantics, i.e. the theory of the concepts of meaning and truth (Foundations of Logic and Mathematics, 1939; Introduction to Semantics, 1942; Formalization of Logic, 1943), Carnap turned his attention to the subject of probability and inductive logic. His views on that subject are for the most part exposed in Logical foundations of probability (1950) where Carnap aims to give a sound logical interpretation of probability. Carnap thought that according to certain conditions, the concept of probability had to be interpreted as a purely logical concept. In this view, probability is a basic concept anchored in all inductive inferences, whereby the conclusion of every inference that holds without deductive necessity is said be more or less likely to be the case. In fact, Carnap claims that the problem of induction is a matter of finding a precise explanation of the logical relation that holds between a hypothesis and the evidence that supports it. An inductive logic is thus based on the idea that probability is a logical relation between two types of statements: the hypothesis (conclusion) and the premises (evidence). Accordingly, a theory of induction should explain how, by pure logical analysis, we can ascertain that certain evidence establishes a degree of confirmation strong enough to confirm a given hypothesis.
Inductive logic After having considered problems in semantics ie the theory of the concepts of meaning and truth (Foundations of Logic and Mathematics 1939; Introduction to Semantics 1942; Formalization of Logic 1943) Carnap turned his attention to the subject of probability and inductive logic His views on that subject are for the most part exposed in Logical foundations of probability (1950) where Carnap aims to give a sound logical interpretation of probability Carnap thought that according to certain conditions the concept of probability had to be interpreted as a purely logical concept In this view probability is a basic concept anchored in all inductive inferences whereby the conclusion of every inference that holds without deductive necessity is said be more or less likely to be the case In fact Carnap claims that the problem of induction is a matter of finding a precise explanation of the logical relation that holds between a hypothesis and the evidence that supports it An inductive logic is thus based on the idea that probability is a logical relation between two types of statements the hypothesis (conclusion) and the premises (evidence) Accordingly a theory of induction should explain how by pure logical analysis we can ascertain that certain evidence establishes a degree of confirmation strong enough to confirm a given hypothesis