Carnap Rudolf (1891–1970), German-born American philosopher, one of the leaders of the Vienna Circle, a movement loosely called logical positivism or logical empiricism. He made fundamental contributions to semantics and the philosophy of science, as well as to the foundations of probability and inductive logic. He was a staunch advocate of, and active in, the unity of science movement.
Carnap received his Ph.D. in philosophy from the University of Jena in 1921. His first major work was Die Logische Aufbau der Welt (1928), in which he sought to apply the new logic recently developed by Frege and by Russell and Whitehead to problems in the philosophy of science. Although influential, it was not translated until 1967, when it appeared as The Logical Structure of the World. It was important as one of the first clear and unambiguous statements that the important work of philosophy concerned logical structure: that language and its logic were to be the focus of attention. In 1935 Carnap left his native Germany for the United States, where he taught at the University of Chicago and then at UCLA. Die Logiche Syntax der Sprach (1934) was rapidly translated into English, appearing as The Logical Syntax of Language (1937). This was followed in 1941 by Introduction to Semantics, and in 1942 by The Formalization of Logic. In 1947 Meaning and Necessity appeared; it provided the groundwork for a modal logic that would mirror the meticulous semantic development of first-order logic in the first two volumes. One of the most important concepts introduced in these volumes was that of a state description. A state description is the linguistic counterpart of a possible world: in a given language, the most complete description of the world that can be given. Carnap then turned to one of the most pervasive and important problems to arise in both the philosophy of science and the theory of meaning. To say that the meaning of a sentence is given by the conditions under which it would be verified (as the early positivists did) or that a scientific theory is verified by predictions that turn out to be true, is clearly to speak loosely. Absolute verification does not occur. To carry out the program of scientific philosophy in a realistic way, we must be able to speak of the support given by inconclusive evidence, either in providing epistemological justification for scientific knowledge, or in characterizing the meanings of many of the terms of our scientific language. This calls for an understanding of probability, or as Carnap preferred to call it, degree of confirmation. We must distinguish between two senses of probability: what he called probability1, corresponding to credibility, and probability2, corresponding to the frequency or empirical conception of probability defended by Reichenbach and von Mises. ‘Degree of confirmation’ was to be the formal concept corresponding to credibility. The first book on this subject, written from the same point of view as the works on semantics, was The Logical Foundations of Probability (1950). The goal was a logical definition of ‘c(h,e)’: the degree of confirmation of a hypothesis h, relative to a body of evidence e, or the degree of rational belief that one whose total evidence was e should commit to h. Of course we must first settle on a formal language in which to express the hypothesis and the evidence; for this Carnap chooses a first-order language based on a finite number of one-place predicates, and a countable number of individual constants. Against this background, we perform the following reductions: ‘c(h,e)’ represents a conditional probability; thus it can be represented as the ratio of the absolute probability of h & e to the absolute probability of e. Absolute probabilities are represented by the value of a measure function m, defined for sentences of the language. The problem is to define m. But every sentence in Carnap’s languages is equivalent to a disjunction of state descriptions; the measure to be assigned to it must, according to the probability calculus, be the sum of the measures assigned to its constituent state descriptions. Now the problem is to define m for state descriptions. (Recall that state descriptions were part of the machinery Carnap developed earlier.) The function c† is a confirmation function based on the assignment of equal measures to each state description. It is inadequate, because if h is not entailed by e, c†(h,e) % m†(h), the a priori measure assigned to h. We cannot ‘learn from experience.’ A measure that does not have that drawback is m*, which is based on the assignment of equal measures to each structure description. A structure description is a set of state descriptions; two state descriptions belong to the same structure description just in case one can be obtained from the other by a permutation of individual constants. Within the structure description, equal values are assigned to each state description.
In the next book, The Continuum of Inductive Methods, Carnap takes the rate at which we learn from experience to be a fundamental parameter of his assignments of probability. Like measures on state descriptions, the values of the probability of the singular predictive inference determine all other probabilities. The ‘singular predictive inference’ is the inference from the observation that individual 1 has one set of properties, individual 2 has another set of properties, etc., to the conclusion: individual j will have property k.
Finally, in the last works (Studies in Inductive Logic and Probability, vols. I [1971] and II [1980], edited with Richard Jeffrey) Carnap offered two long articles constituting his Basic System of Inductive Logic. This system is built around a language having families of attributes (e.g., color or sound) that can be captured by predicates. The basic structure is still monadic, and the logic still lacks identity, but there are more parameters. There is a parameter l that reflects the ‘rate of learning from experience’; a parameter h that reflects an inductive relation between values of attributes belonging to families. With the introduction of arbitrary parameters, Carnap was edging toward a subjective or personalistic view of probability. How far he was willing to go down the subjectivist garden path is open to question; that he discovered more to be relevant to inductive logic than the ‘language’ of science seems clear. Carnap’s work on probability measures on formal languages is destined to live for a long time. So too is his work on formal semantics. He was a staunch advocate of the fruitfulness of formal studies in philosophy, of being clear and explicit, and of offering concrete examples. Beyond the particular philosophical doctrines he advocated, these commitments characterize his contribution to philosophy. See also CONFIRMATION, PHILOSOPHY OF SCIENCE , PROBABILITY, VIENNA CIRCL. H.E.K.