Induction and the rule of succession through a possibilistic inferential model lens
Abstract
Induction is the process by which empirical evidence is transformed to knowledge. Hume famously argued---and Popper and others agree---that there can be no logical justification for induction. A weaker form of induction, due to Bayes, expresses the aforementioned knowledge in terms of probabilities, and we review some well-known and not-so-well-known criticisms of the Bayesian solution. We then investigate the relatively new possibilistic inferential model (IM) framework, showing that, in addition to the IM's strong, statistical reliability guarantees that it uniquely enjoys, it is safe from those criticisms that damage the Bayesian foundations. For illustration, we reconsider the classical sunrise problem and compare our proposed solution with Laplace's famous rule of succession.
Related
- An Efficient Monte Carlo Method for Valid Prior-Free Possibilistic Statistical Inference
- Possibilistic Logic over a Logic of Formal Inconsistency
- Open-ended Scientific Discovery with Possibilistic Reasoning
- Probing automorphic induction through zero correlations and secondary arithmetic terms
- Possibilistic Radial Transport for Approximate IM Inference
BibTeX
@misc{martin2026induction,
title = {{Induction and the rule of succession through a possibilistic inferential model lens}},
author = {Ryan Martin and Shih-Ni Prim and Max Raner and Jonathan P. Williams},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.11935},
eprint = {2608.11935},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11935},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Induction and the rule of succession through a possibilistic inferential model lens
AU - Ryan Martin
AU - Shih-Ni Prim
AU - Max Raner
AU - Jonathan P. Williams
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.11935
UR - https://arxiv.org/abs/2608.11935
AB - Induction is the process by which empirical evidence is transformed to knowledge. Hume famously argued---and Popper and others agree---that there can be no logical justification for induction. A weaker form of induction, due to Bayes, expresses the aforementioned knowledge in terms of probabilities, and we review some well-known and not-so-well-known criticisms of the Bayesian solution. We then investigate the relatively new possibilistic inferential model (IM) framework, showing that, in addition to the IM's strong, statistical reliability guarantees that it uniquely enjoys, it is safe from those criticisms that damage the Bayesian foundations. For illustration, we reconsider the classical sunrise problem and compare our proposed solution with Laplace's famous rule of succession.
ER -