Gerhard Tintner: Written Reply on Foundations of Probability and Statistical Inference (1949)

Gerhard Tintner’s written reply within a journal discussion clarifies and defends aspects of Carnap’s inductive logic. Its central concern is how a logical degree of confirmation can respond to experience despite depending on an initially chosen assignment of measures. The reply proceeds from acknowledgments of intellectual precedents to predictive inference, then considers the language and evidence required by Carnap’s system. It offers a qualified defense: the construction has desirable properties, but its linguistic assumptions and extension to continuous variables remain matters for scrutiny.

Tintner welcomes the discussants’ connections with d’Alembert, Ramsey, Jeffreys, and Whitworth, while referring historical questions to Carnap’s forthcoming book. He then addresses the assignment of equal measures to structures. He concedes that this choice rests on procedural simplicity, but contrasts it with assigning equal measures to state descriptions, which produces an unacceptable consequence:

If the second method is adopted the probability$_{1}$ is independent of all previous experience. This is evidently not a desirable property for the degree of confirmation.

The objection identifies responsiveness to evidence as a criterion for evaluating a formal construction. A measure of confirmation must allow observations to affect its results; mathematical simplicity alone cannot make an experience-insensitive procedure adequate.

Predictive inference supplies a further defense. Tintner presents Carnap’s rule, corresponding to Laplace’s rule of succession, as $c = (s_1 + w_1)/(s + k)$. Here the prediction concerns whether an item outside the sample possesses property $M$. The resulting confirmation lies between the relative logical width and the observed relative frequency of that property. This makes the relation between the logical starting point and accumulated observations explicit:

It tends for large samples towards the second quantity. Hence the particular way of assigning the fundamental measures is irrelevant in large samples.

In context, “the second quantity” is the sample’s relative frequency. Tintner’s claim is therefore specifically about large-sample predictive inference: the initial assignment loses its influence as observations accumulate. It does not establish that all possible foundational choices are equivalent.

The reply next marks limits and prerequisites. Tintner expects invariance properties to matter for continuous variables but postpones their discussion until a suitable theory exists. He lists Carnap’s requirements for the underlying language: logically independent atomic sentences, distinct and separate individuals, independent attributes, and a complete set of simple primitive predicates. He explicitly acknowledges difficulty in the concept of simplicity, understood here as resistance to analysis into more elementary components.

The concluding emphasis is on evidential completeness:

In computing the degree of confirmation the total evidence available should be taken into account. The only evidence which can be neglected is irrelevant evidence, i.e. evidence which does not change the degree of confirmation.

Irrelevance is thus defined by an item’s effect on confirmation. Tintner closes with Carnap’s proposed incorporation of order, including temporal relations, as a possible route to treating random temporal sequences. The reply’s significance lies in connecting formal choices to empirical learning while identifying the conditions and unfinished extensions on which the theory’s broader application depends.