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113 found
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  1. Probability and Inductive Logic.Antony Eagle - manuscript
    Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...)
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  2. A comprehensive theory of induction and abstraction, part II.Cael Hasse - manuscript
    This is part II in a series of papers outlining Abstraction Theory, a theory that I propose provides a solution to the characterisation or epistemological problem of induction. Logic is built from first principles severed from language such that there is one universal logic independent of specific logical languages. A theory of (non-linguistic) meaning is developed which provides the basis for the dissolution of the `grue' problem and problems of the non-uniqueness of probabilities in inductive logics. The problem of counterfactual (...)
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  3. The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - manuscript
    Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that (...)
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  4. Formal Qualitative Probability.Daniel Kian Mc Kiernan - manuscript
    Choices rarely deal with certainties; and, where assertoric logic and modal logic are insufficient, those seeking to be reasonable turn to one or more things called “probability.” These things typically have a shared mathematical form, which is an arithmetic construct. The construct is often felt to be unsatisfactory for various reasons. A more general construct is that of a preordering, which may even be incomplete, allowing for cases in which there is no known probability relation between two propositions or between (...)
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  5. Scientific Metaphysics and Information.Bruce Long - forthcoming - Springer.
    This book investigates the interplay between two new and influential subdisciplines in the philosophy of science and philosophy: contemporary scientific metaphysics and the philosophy of information. Scientific metaphysics embodies various scientific realisms and has a partial intellectual heritage in some forms of neo-positivism, but is far more attuned than the latter to statistical science, theory defeasibility, scale variability, and pluralist ontological and explanatory commitments, and is averse to a-priori conceptual analysis. The philosophy of information is the combination of what has (...)
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  6. Epistemic Probabilities are Degrees of Support, not Degrees of (Rational) Belief.Nevin Climenhaga - 2024 - Philosophy and Phenomenological Research 108 (1):153-176.
    I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had B as (...)
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  7. Probability and Statistics in the Tinbergen-Keynes Debates.William Peden - 2022 - Erasmus Journal for Philosophy and Economics 15 (2):aa–aa.
    As part of a book symposium on Erwin Dekker's Jan Tinbergen (1903–1994) and the Rise of Economic Expertise (2021), William Peden reflects on shared views on the objectivity and nature of statistics between Tinbergen and Keynes underlying the Tinbergen-Keynes debates.
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  8. Carnap’s Logical Probability and Free Will Dilemma.Paweł Pruski - 2022 - Open Journal of Philosophy 12 (1):133-145.
    Pondering the question of free will in the context of probability allows us to take a fresh look at a number of old problems. We are able to avoid deterministic entrapments and attempt to look at free will as an outcome of the entire decision-making system. In my paper, I will argue that free will should be considered in the context of a complex system of decisions, not individual cases. The proposed system will be probabilistic in character, so it will (...)
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  9. An approach to stochastic processes via non-classical logic.Antonio Di Nola, Anatolij Dvurečenskij & Serafina Lapenta - 2021 - Annals of Pure and Applied Logic 172 (9):103012.
  10. David Stove (1927-1994), Sydney philosopher and master of argument: life and work.James Franklin - 2021 - Sydney Realist 43:1-8.
    David Stove was a philosopher strong on argument and polemic. His work on the logical intepretation of probability led to a defence of induction in The Rationality of Induction (1986). It resulted too in his denunciation of Popper, Kuhn, Lakatos and Feyeraband as irrationalists because of their "deductivism" (the thesis that the only logic is deductive logic). Stove also defended controversial views on the intelligence of women and on Darwinism. The article surveys his life and work.
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  11. Recurrence and the existence of invariant measures.Manuel J. Inselmann & Benjamin D. Miller - 2021 - Journal of Symbolic Logic 86 (1):60-76.
    We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locally compact Polish group on a standard Borel space satisfies such a condition but does not have an orbit supporting an invariant Borel probability measure, then there is an invariant Borel set on which the action satisfies the condition but does not have an invariant Borel probability measure.
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  12. Probability and arguments: Keynes’s legacy.William Peden - 2021 - Cambridge Journal of Economics 45 (5):933–950.
    John Maynard Keynes’s A Treatise on Probability is the seminal text for the logical interpretation of probability. According to his analysis, probabilities are evidential relations between a hypothesis and some evidence, just like the relations of deductive logic. While some philosophers had suggested similar ideas prior to Keynes, it was not until his Treatise that the logical interpretation of probability was advocated in a clear, systematic and rigorous way. I trace Keynes’s influence in the philosophy of probability through a heterogeneous (...)
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  13. Epistemic theories of objective chance.Richard Johns - 2020 - Synthese 197 (2):703-730.
    Epistemic theories of objective chance hold that chances are idealised epistemic probabilities of some sort. After giving a brief history of this approach to objective chance, I argue for a particular version of this view, that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. The main argument for this view is the demonstration that it entails all of the commonly-accepted properties of chance. For example, this analysis entails that chances (...)
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  14. Sure-wins under coherence: a geometrical perspective.Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi - 2019 - In Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science.
    In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...)
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  15. Imprecise Probability and the Measurement of Keynes's "Weight of Arguments".William Peden - 2018 - IfCoLog Journal of Logics and Their Applications 5 (4):677-708.
    Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the usefulness (...)
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  16. No Interpretation of Probability.Wolfgang Schwarz - 2018 - Erkenntnis 83 (6):1195-1212.
    I argue that none of the usual interpretations of probability provide an adequate interpretation of probabilistic theories in science. Assuming that the aim of such theories is to capture noisy relationships in the world, I suggest that we do not have to give them classical truth-conditional content at all: their probabilities can remain uninterpreted. Indirectly, this account turns out to explain what is right about the frequency interpretation, the best-systems interpretation, and the epistemic interpretation.
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  17. Carnap’s Relevance Measure as a Probabilistic Measure of Coherence.Jakob Koscholke - 2017 - Erkenntnis 82 (2):339-350.
    Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to investigate Carnap’s measure (...)
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  18. Ancient Indian Logic and Analogy.J. B. Paris & A. Vencovska - 2017 - In S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119. Springer. pp. 198-210.
    B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.
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  19. The Principal Principle does not imply the Principle of Indifference.Richard Pettigrew - 2017 - British Journal for the Philosophy of Science:axx060.
    In a recent paper in this journal, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson argue that the principal principle entails the principle of indifference. In this paper, I argue that it does not. Lewis’s version of the principal principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW base their argument on certain intuitions concerning when one proposition is admissible for another: Conditions 1 and 2. There are two ways of reading their (...)
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  20. Случайности. Историческа типология.Vassil Vidinsky - 2017 - Sofia: Sofia University Press.
    В настоящата книга се изследва идеята за случайността през нейното историческо и концептуално развитие и са отделени пет основни и типични понятия. Анализът тръгва от класическите примери – Платон, Аристотел, Кант и Хегел – и стига до съвременния контекст на случайността, който е представен през теорията на вероятностите и теорията на сложността. Някои от изведените понятия са формализирани и имат по-логически, математически или пък информационен характер, а други са по-скоро физически или субектни, но всички те са представени в една обща (...)
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  21. An examination of the SEP candidate analogical inference rule within pure inductive logic.E. Howarth, J. B. Paris & A. Vencovská - 2016 - Journal of Applied Logic 14:22-45.
  22. Combining Analogical Support in Pure Inductive Logic.J. B. Paris & A. Vencovská - 2016 - Erkenntnis (2):01-19.
    We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...)
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  23. The theory of spectrum exchangeability.E. Howarth & J. B. Paris - 2015 - Review of Symbolic Logic 8 (1):108-130.
    Spectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural extension of Atom Exchangeability to polyadic languages. It has been shown1that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed languageLis the set of sentences ofLwhich must be assigned probability 1 by every probability function satisfying Sx, by examining separately the (...)
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  24. The Twin Continua of Inductive Methods.Alena Vencovská & Jeff B. Paris - 2015 - In Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. Boston: De Gruyter. pp. 355-366.
  25. Principles of Remembering and Forgetting.E. Howarth & J. B. Paris - 2014 - Logique Et Analyse 57 (228):489-511.
    We propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A partial classification is given of the probability functions which satisfy these principles.
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  26. Second order inductive logic and Wilmers' principle.M. S. Kließ & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
  27. Second Order Inductive Logic and Wilmers' Principle.M. S. Kliess & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
    We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.
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  28. Predicate Exchangeability and Language Invariance in Pure Inductive Logic.M. S. Kliess & J. B. Paris - 2014 - Logique Et Analyse 57 (228):513-540.
    In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.
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  29. The principle of maximum entropy and a problem in probability kinematics.Stefan Lukits - 2014 - Synthese 191 (7):1-23.
    Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. This (...)
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  30. The Only Probability Is Verbal Probability.George Masterton - 2014 - Metaphysica 15 (1).
    In 1977 van Fraassen showed convincingly, and in detail, how one can give a dissentive answer to the question `[a]re there necessities in nature?'. In this paper I follow his lead and show in a similar fashion and detail, how it is possible to give a dissentive answer to: Are there probabilities in nature? This is achieved by giving a partial analysis—with the aid of Kaplanian pragmatics—of objective chance in terms of that credence that is reasonable where prevailing laws and (...)
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  31. Remarks on the idealist and empiricist interpretation of frequentism: Robert Leslie Ellis versus John Venn.Lukas M. Verburgt - 2014 - BSHM Bulletin: Journal of the British Society for the History of Mathematics 29 (3):184-195.
    The goal of this paper is to correct a widespread misconception about the work of Robert Leslie Ellis and John Venn, namely that it can be considered as the ‘British empiricist’ reaction against the traditional theory of probability. It is argued, instead, that there was no unified ‘British school’ of frequentism during the nineteenth century. Where Ellis arrived at frequentism from a metaphysical idealist transformation of probability theory’s mathematical calculations, Venn did so on the basis of an empiricist critique of (...)
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  32. Introduction: Chance and temporal asymmetry.Alastair Wilson - 2014 - In Chance and Temporal Asymmetry. Oxford University Press.
    This volume is a collection of cutting-edge research papers in scientifically informed metaphysics, tackling a range of philosophical puzzles which have emerged from recent work on chance and temporal asymmetry. How do the probabilities found in fundamental physics and the probabilities of the special sciences relate to one another? How can we account for the normative significance of chance? Can constraints on the initial conditions of the universe underwrite the second law of thermodynamics, and potentially also all other lawlike regularities? (...)
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  33. Non-deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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  34. An Analogy Principle in Inductive Logic.A. Hill & J. B. Paris - 2013 - Annals of Pure and Applied Logic 164 (12):1293-1321.
    We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrmsʼ ‘Wheel of Fortune’.
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  35. In Defense of Bertrand: The Non-Restrictiveness of Reasoning by Example.D. Klyve - 2013 - Philosophia Mathematica 21 (3):365-370.
    This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica, which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités. Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, (...)
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  36. An observation on Carnapʼs Continuum and stochastic independencies.J. B. Paris - 2013 - Journal of Applied Logic 11 (4):421-429.
    We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.
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  37. Bertrand's Paradox Revisited: Why Bertrand's 'Solutions' Are All Inapplicable.Darrell Patrick Rowbottom - 2013 - Philosophia Mathematica 21 (1):110-114.
    This paper shows that Bertrand's proposed 'solutions' to his own question, which generates his chord paradox, are inapplicable. It uses a simple analogy with cake cutting. The problem is that none of Bertrand's solutions considers all possible cuts. This is no solace for the defenders of the principle of indifference, however, because it emerges that the paradox is harder to solve than previously anticipated.
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  38. Popper’s Measure of Corroboration and P.Darrell Patrick Rowbottom - 2013 - British Journal for the Philosophy of Science 64 (4):axs029.
    This article shows that Popper’s measure of corroboration is inapplicable if, as Popper argued, the logical probability of synthetic universal statements is zero relative to any evidence that we might possess. It goes on to show that Popper’s definition of degree of testability, in terms of degree of logical content, suffers from a similar problem. 1 The Corroboration Function and P(h|b) 2 Degrees of Testability and P(h|b).
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  39. Symmetry in Polyadic Inductive Logic.J. B. Paris & A. Vencovská - 2012 - Journal of Logic, Language and Information 21 (2):189-216.
    A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.
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  40. Varieties of Conditional Probability.Kenny Easwaran - 2011 - In Prasanta Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. North Holland.
    I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.
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  41. The objective Bayesian conceptualisation of proof and reference class problems.James Franklin - 2011 - Sydney Law Review 33 (3):545-561.
    The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...)
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  42. The Modern Epistemic Interpretations of Probability: Logicism and Subjectivism.Maria Carla Galavotti - 2011 - In Dov M. Gabby & John Woods (eds.), Handbook of the History of Logic: Inductive Logic. North Holland: Amsterdam. pp. 153--203.
  43. Reasoning by analogy in inductive logic.Alexandra Hill & J. B. Paris - 2011 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications. pp. 63--76.
  44. A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic.J. Landes, J. B. Paris & A. Vencovská - 2011 - Synthese 181 (S1):19 - 47.
    We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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  45. A Note on Irrelevance in Inductive Logic.Jeff B. Paris & Alena Vencovská - 2011 - Journal of Philosophical Logic 40 (3):357 - 370.
    We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson's Sufficientness Principle, JSP, which is classically important because it leads to Carnap's influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix-Paris Continuum. We argue that the derivation of two very disparate families of inductive methods from alternative perceptions of (...)
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  46. Pure Inductive Logic.Jeffrey Paris & Alena Vencovská - 2011 - Cambridge, UK: Cambridge University Press. Edited by Alena Vencovská.
    Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.
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  47. Evidential Probability and Objective Bayesian Epistemology.Gregory Wheeler & Jon Williamson - 2011 - In Prasanta S. Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier.
    In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.
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  48. Wittgenstein on Prior Probabilities.Michael E. Cuffaro - 2010 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 23:85-98.
    Wittgenstein did not write very much on the topic of probability. The little we have comes from a few short pages of the Tractatus, some 'remarks' from the 1930s, and the informal conversations which went on during that decade with the Vienna Circle. Nevertheless, Wittgenstein's views were highly influential in the later development of the logical theory of probability. This paper will attempt to clarify and defend Wittgenstein's conception of probability against some oft-cited criticisms that stem from a misunderstanding of (...)
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  49. Probabilistic Logics and Probabilistic Networks.Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson - 2010 - Dordrecht, Netherland: Synthese Library. Edited by Gregory Wheeler, Rolf Haenni, Jan-Willem Romeijn & and Jon Williamson.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
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  50. Probability logic, logical probability, and inductive support.Isaac Levi - 2010 - Synthese 172 (1):97-118.
    This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...)
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