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.
It is argued that ordinary enumerative induction can achieve everywhere convergence, whereas meta-induction fails even to achieve almost everywhere convergence, and no inference method whatsoever achieves almost everywhere convergence.
Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayesians and frequentists; moreover, it is unclear when and why acting on them actually leads to desirable outcomes. Here, we argue that every probability is the output of a...
The book presents a novel, abductivist theory of knowledge and argues for it over its two main rivals: safety theory and causal explanationism. According to abductivism, a belief constitutes knowledge when, given the way it is formed or maintained, the best explanation of its being true rather than false lies in the...
In this article I revisit the frequency interpretation of probability of von Mises, and argue that it contains the key elements of any coherent interpretation of scientific probability - notwithstanding the heavy criticisms von Mises collected from mathematicians and philosophers alike. I propose a modified definition...
In this paper, we introduce the study of probability functions based on the 6-valued paradefinite (i.e., paraconsistent and paracomplete) logic LETK+. This logic is a powerful and versatile Logic of Evidence and Truth (LET) which is a conservative expansion of both classical logic and FDE. The framework introduced here...
Verónica Borja Macías, M. Coniglio, Alejandro Hernández-Tello· 0 citations
