On the evolution of the concept of probability as a mirror of the evolution of reason

• URL: http://arxiv.org/abs/2606.00102v1
• Date: Tue, 26 May 2026 08:58:53 GMT
• Title: On the evolution of the concept of probability as a mirror of the evolution of reason
• Abstract summary: Article interprets that evolution not merely as a mathematical history, but as a transformation of rationality itself.<n>Probability theory has grown from the calculus of games of chance into a central framework for reasoning under uncertainty.<n> Fuzzy logic is presented as a rigorous language for graded meaning and qualitative judgment, while deep learning is analyzed as a powerful mode of prediction.
• Score: 31.458406135473805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Over the centuries, probability theory has grown from the calculus of games of chance into a central framework for reasoning under uncertainty. This article interprets that evolution not merely as a mathematical history, but as a transformation of rationality itself. From Pascal and Fermat's combinatorial symmetry to the inductive logic of Bayes and Laplace, from Poisson's statistics of events to Kolmogorov's axiomatic formalization, probability progressively incorporated uncertainty, time, and coherence into scientific judgment. This trajectory reaches a mature epistemological form in modern Bayesian inference, especially in Tarantola's view of probability as a logic of information, where prior knowledge and data are combined coherently. Yet this framework also exposes a limit: probability quantifies uncertainty about well-defined propositions, but does not by itself formalize the vagueness of the concepts used to describe them. The article therefore examines how rationality extends beyond probability. Fuzzy logic is presented as a rigorous language for graded meaning and qualitative judgment, while deep learning is analyzed as a distinct, powerful mode of prediction based on geometric interpolation and optimization rather than explicit inference. By situating probability, fuzzy logic, and deep learning in a common historical and epistemological perspective, the article clarifies their roles and limits. It argues that contemporary scientific rationality cannot be reduced to data-driven performance alone, but requires the explicit articulation of uncertainty, vagueness, and inference.

Related papers

• Maxitive Donsker-Varadhan Formulation for Possibilistic Variational Inference [5.621958475334369]
  We develop a principled formulation of possibilistic variational inference.<n>Applying it to a special class of exponential-family functions, we highlight parallels with their probabilistic counterparts.
  arXiv  Detail & Related papers  (2025-11-26T09:53:28Z)
• On the Fundamental Impossibility of Hallucination Control in Large Language Models [0.0]
  Impossibility Theorem: no LLM performing non-trivial knowledge aggregation can simultaneously achieve truthful knowledge representation, semantic information conservation, and revelation of relevant knowledge.<n>We prove this by modeling inference as an auction of ideas, where distributed components compete to influence responses using encoded knowledge.<n>We show that hallucination and imagination are mathematically identical, and both violate at least one of the four essential properties.
  arXiv  Detail & Related papers  (2025-06-04T23:28:39Z)
• FactReasoner: A Probabilistic Approach to Long-Form Factuality Assessment for Large Language Models [59.171510592986735]
  We propose FactReasoner, a new factuality assessor that relies on probabilistic reasoning to assess the factuality of a long-form generated response.<n>Our experiments on labeled and unlabeled benchmark datasets demonstrate clearly that FactReasoner improves considerably over state-of-the-art prompt-based approaches.
  arXiv  Detail & Related papers  (2025-02-25T19:01:48Z)
• Isopignistic Canonical Decomposition via Belief Evolution Network [12.459136964317942]
  We propose an isopignistic transformation based on the belief evolution network. This decomposition offers a reverse path between the possibility distribution and its isopignistic mass functions. This paper establishes a theoretical basis for building general models of artificial intelligence based on probability theory, Dempster-Shafer theory, and possibility theory.
  arXiv  Detail & Related papers  (2024-05-04T12:39:15Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• A Simple Generative Model of Logical Reasoning and Statistical Learning [0.6853165736531939]
  Statistical learning and logical reasoning are two major fields of AI expected to be unified for human-like machine intelligence. We here propose a simple Bayesian model of logical reasoning and statistical learning. We simply model how data causes symbolic knowledge in terms of its satisfiability in formal logic.
  arXiv  Detail & Related papers  (2023-05-18T16:34:51Z)
• The Unreasonable Effectiveness of Deep Evidential Regression [72.30888739450343]
  A new approach with uncertainty-aware regression-based neural networks (NNs) shows promise over traditional deterministic methods and typical Bayesian NNs. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a quantification rather than an exact uncertainty.
  arXiv  Detail & Related papers  (2022-05-20T10:10:32Z)
• The intersection probability: betting with probability intervals [7.655239948659381]
  We propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty. We outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.
  arXiv  Detail & Related papers  (2022-01-05T17:35:06Z)
• Logical Credal Networks [87.25387518070411]
  This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. We investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud.
  arXiv  Detail & Related papers  (2021-09-25T00:00:47Z)
• Logical Neural Networks [51.46602187496816]
  We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning) Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omni rather than focused on predefined target variables, and corresponds to logical reasoning.
  arXiv  Detail & Related papers  (2020-06-23T16:55:45Z)
• Logic, Probability and Action: A Situation Calculus Perspective [12.47276164048813]
  The unification of logic and probability is a long-standing concern in AI. We explore recent results pertaining to the integration of logic, probability and actions in the situation calculus. Results are motivated in the context of cognitive robotics.
  arXiv  Detail & Related papers  (2020-06-17T13:49:53Z)
• Invariant Rationalization [84.1861516092232]
  A typical rationalization criterion, i.e. maximum mutual information (MMI), finds the rationale that maximizes the prediction performance based only on the rationale. We introduce a game-theoretic invariant rationalization criterion where the rationales are constrained to enable the same predictor to be optimal across different environments. We show both theoretically and empirically that the proposed rationales can rule out spurious correlations, generalize better to different test scenarios, and align better with human judgments.
  arXiv  Detail & Related papers  (2020-03-22T00:50:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.