Studia Semiotyczne (Dec 2023)
The Subjective Probability of Conditionals and Its Formalizations
Abstract
DOI: https://doi.org/10.26333/sts.xxxvii1.04 The aim of the paper is to discuss the problem of the assignment of the degree of belief to conditional sentences by a rational agent. After presenting the general methodological framework, we analyze two possible approaches. In both cases we assume that we have a non-conditional probabilistic system of beliefs expressed in a language L0, and modeled in some initial probability space S, which allows us to assign probabilities to sentences from L0. Our aim is to extend this system of beliefs to a given class of sentences Φ containing conditionals. The first approach is what we call the “credence-like” approach: for a given class Φ, we define credence as a function defined directly on linguistic objects. The second approach consists in assuming the existence of a standard probability space, in which the sentences from the set Φ are interpreted as events. In this case, the degree of belief of α is defined as the probability of the corresponding event in the probability space SΦ. We present both of these approaches, indicating what their advantages and disadvantages are. The thesis of the article is that the probabilistic approach to the analysis of degrees of belief of sentences containing the conditional connective is by far the more universal one and preferable method, particularly in the context of more complex conditionals.
