This talk explores the thesis that probability is best understood as a theoretical-linguistic model (TLM), rather than as a subjective, ontological, or frequentist theory. Gillies 2006 discusses five main interpretations of probability and defends three: subjective theory (ST), where probability is an individual degree of belief (DB); propensity theory (PT), where probability is a tendency in repeatable conditions; and inter subjective theory (IST), where probability reflects social consensus. Hacking 2 distinguishes ”frequency-type” and ”belief-type” probabilities. However, these perspectives fail to explain probability from a historical and philosophical standpoint. The proposal of probability as a TLM is supported by our interpretation from Schurz’ 2015 work, which bridges ”statistical” and ST perspectives using principles like the ”Nearest Reference Class Principle”. Following Schurz, I prefer ‘statistical’ over ‘frequentist’ because the model concerns limits of frequencies, not actual frequencies. When analyzing sample frequency, we focus on the distribution of characteristics (e.g., mean or proportion) within a sample, while limiting distribution describes statistical behavior as the sample size approaches infinity, aligning with the Central Limit Theorem. A theoretical model based on limiting distributions serves as a tool for statistical decision making, rather than relying on sample frequencies. This distinction makes the model ”statistical” rather than ”frequentist.” Schurz unifies probability theory for both objective statistics and degrees of belief, which can be interpreted as a TLM. While Schurz sees a dualistic theory, we propose a linguistic model with two applications: beliefs and decisions. We argue that probability is a TLM because it relies on idealized abstractions, such as perfect dice and symmetric distributions. Schurz’s bridging principles enable practical applications in DB reasoning and statistical inference, but these applications do not define probability itself. What defines probability is how it is historically constructed.
Marcos Sousa (Wed,) studied this question.