Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...) short presentation of Carnap''s theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti''s theorem Carnap''s inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald''s decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments. (shrink)

In this paper it is argued that there are relevant similarities of Aristotle's account of definition and Carnap's account of explication. To show this, first, Aristotle's conditions of adequacy for definitions are provided and an outline of the main critique put forward against Aristotle's account of definition is given. Subsequently, Carnap's conditions of adequacy for explications are presented and discussed. It is shown that Aristotle's conditions of extensional correctness can be interpreted against the backdrop of Carnap's condition of similarity once (...) one skips Aristotelian essentialism and takes in a Carnapian and more pragmatic stance. Finally, it is argued that, in general, a complementary rational reconstruction of both approaches allows for resolving problems of interpretational underdetermination. (shrink)

Um den Begriff des Originals gibt es heftige Debatten. Können Fälschungen ebenso gut sein wie Originale? Wann sind Kopien vielleicht sogar besser? Und ist die Zeit des Originals nicht überhaupt vorbei? Dabei tritt die Frage, was ein Original eigentlich sei, oft in den Hintergrund. Doris Reisinger stellt die These auf: Der Begriff des Originals ist nicht nur nicht obsolet, er hat auch nicht notwendig mit Neuheit, Urheberschaft oder ästhetischem Wert zu tun - das Problem des Originalbegriffs besteht schlicht darin, dass (...) seine komplexe Struktur verkannt wird. Vor diesem Ausgangspunkt erarbeitet sie einen Explikationsvorschlag, der die Beantwortung einer ganzen Reihe von Fragen dieser klassischen philosophischen Debatte erlaubt. (shrink)

According to a popular interpretation, Carnap’s interpretation of probability had evolved from a logical towards a subjective conception. However Carnap himself insisted that his basic philosophical view of probability was always the same. I address this apparent clash between Carnap's self-identification and the subsequent interpretations of his work. Following its original intentions, I reconstruct inductive logic as an explication. The emerging picture is of a versatile linguistic framework, whose main function is not the discovery of objective logical relations in the (...) object language, but the stipulation of conceptual possibilities. Within this representation, I map out the changes that the project went through. Seen from such an explication-based perspective, inductive logic becomes quite hard to categorize using the standard labels. (shrink)

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.

In 1959 Carnap published a probability model that was meant to allow forreasoning by analogy involving two independent properties. Maher (2000)derived a generalized version of this model axiomatically and defended themodel''s adequacy. It is thus natural to now consider how the model mightbe extended to the case of more than two properties. A simple extension waspublished by Hess (1964); this paper argues that it is inadequate. Amore sophisticated one was developed jointly by Carnap and Kemeny in theearly 1950s but never (...) published; this paper gives the first published descriptionof Carnap and Kemeny''s model and argues that it too is inadequate. Since noother way of extending the two-property model is currently known, the conclusionof this paper is that a satisfactory extension to multiple properties requires somenew approach. (shrink)

We consider the desirability, or otherwise, of various forms of induction in the light of certain principles and inductive methods within predicate uncertain reasoning. Our general conclusion is that there remain conflicts within the area whose resolution will require a deeper understanding of the fundamental relationship between individuals and properties.

This paper documents the pragmatic turn in the later philosophy of C. G. Hempel.

We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.

Summary In the last decade analytical philosophy of science has been considered by many people as a descriptive activity. In part I of this paper we show that philosophy of science has been designed as normative logical analysis by Reichenbach and Carnap before world war II. Thus the identification analytical = descriptive is historically unjustified. In part II we discuss three tasks of analytical philosophy of science, the logical reconstruction of concepts, theories, and methods. While the first is mainly descriptive, (...) the third mainly normative, the second may be both, depending on the intended goal. (shrink)

This paper concerns exchangeable analogical predictions based on similarity relations between predicates, and deals with a restricted class of such relations. It describes a system of Carnapian λγ rules on underlying predicate families to model the analogical predictions for this restricted class. Instead of the usual axiomatic definition, the system is characterized with a Bayesian model that employs certain statistical hypotheses. Finally the paper argues that the Bayesian model can be generalized to cover cases outside the restricted class of similarity (...) relations. (shrink)

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...) individually. (shrink)

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.

The article deals with problems of incommensurability and meaning change in thecontext of scientific dynamics. Its main topic is a proposal made by Putnam basedon his version of the principle of charity. It is shown that this proposal does not workas a general principle for the understanding of theory change, for it leads in some cases to an unconvincing interpretation of now discarded theories and is even uncharitable. So it could be polemically described as a kind of defamation ('üle Nachrede') (...) of these theories. This will be demonstrated in two case studies. The first one sketches the development of economic value theory, while the second deals with the development of the concept of probability. (shrink)

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).

The formulae advanced by Popper to calculate the degree of corroboration C of a scientific hypothesis are unsatisfactory in that the probability values required in the computation are often not available. An attempt is made to define a quantitative measure B* in the place of C in which only countable empirical values would be used. This condition is fulfilled in two basic formulae and eq. ), which could be applied to calculate the degree of corroboration. When m successful falsifications of (...) the hypothesis h appear after a sequence of n unsuccessful ones, the pragmatic degree of corroboration B* results from the difference between B and the analogue value of the falsification F* and eq. ). In the event that the hypothesis can be "rescued" through a correction, increased experimental effort must be made with the revision. This would be taken into account through the correction equation ). When the hypothesis cannot be corrected, however, it can no longer exceed the value of 1-F*, even after numerous verification experiments. In the process of deciding whether a hypothesis is "adequately" verified or falsified, a lower threshold ${\rm B}_{{\rm u}}$ und Bₒ must be selected. These values have to be chosen on an intuitive subjective basis. The same applies to the strength of unsuccessful falsifications . This evaluation is expressed by a multiplicative constant a̱ ) or an additive constant kₐ in eq. . Despite the subjectivity of the values a̱, kₐ necessary for the calculation of B*, and of the values ${\rm B}_{{\rm u}}$ , Bₒ for the decision to discontiue the examination of the hypothesis, I feel that amongst the scientists within a particular field of research, a consensus for these values should be possible. Through a quantitative determination of B* the procedure for testing a hypothesis, considered to be a closed loop process, becomes clearer. To estimate the values of B* could not only have an influence upon the decisions of the respective researchers or research groups examining a hypothesis, but also be of assistance in decisions regarding research grants when financial resources are limited. (shrink)

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.