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  1. 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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  2. A Comprehensive Theory of Induction and Abstraction, Part I.Cael L. Hasse - manuscript
    I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...)
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  3. Absolutely No Free Lunches!Gordon Belot - forthcoming - Theoretical Computer Science.
    This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that (...)
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  4. "Objective Purport, Relational Confirmation, and the Presumption of Moral Objectivism: A Probabilistic Argument From Moral Experience".Tanner Hammond - forthcoming - Southwest Philosophy Review.
    All else being equal, can granting the objective purport of moral experience support a presumption in favor of some form of moral objectivism? Don Loeb (2007) has argued that even if we grant that moral experience appears to present us with a realm of objective moral fact—something he denies we have reason to do in the first place—the objective purport of moral experience cannot by itself provide even prima facie support for moral objectivism. In this paper, I contend against Loeb (...)
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  5. Speed-Optimal Induction and Dynamic Coherence.Michael Nielsen & Eric Wofsey - forthcoming - British Journal for the Philosophy of Science:axz030.
    A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.
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  6. Naturalness as a Constraint on Priors.Darren Bradley - 2020 - Mind 129 (513):179-203.
    Many epistemological problems can be solved by the objective Bayesian view that there are rationality constraints on priors, that is, inductive probabilities. But attempts to work out these constraints have run into such serious problems that many have rejected objective Bayesianism altogether. I argue that the epistemologist should borrow the metaphysician’s concept of naturalness and assign higher priors to more natural hypotheses.
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  7. The Power of Logic, 6th Edition.Daniel Howard-Snyder, Frances Howard-Snyder & Ryan Wasserman - 2020 - New York: McGraw-Hill.
    This is a basic logic text for first-time logic students. Custom-made texts from the chapters is an option as well. And there is a website to go with text too.
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  8. Completeness Theorems for Σ–Additive Probabilistic Semantics.Nebojša Ikodinović, Zoran Ognjanović, Aleksandar Perović & Miodrag Rašković - 2020 - Annals of Pure and Applied Logic 171 (4):102755.
  9. Channels’ Confirmation and Predictions’ Confirmation: From the Medical Test to the Raven Paradox.Chenguang Lu - 2020 - Entropy 22 (4):384.
    After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple proposed the Raven Paradox. Then, Carnap used the increment of logical probability as the confirmation measure. So far, many confirmation measures have been proposed. Measure F proposed by Kemeny and Oppenheim among them possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the (...)
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  10. Comparative Infinite Lottery Logic.Matthew W. Parker - 2020 - Studies in History and Philosophy of Science Part A 84:28-36.
    As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models based (...)
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  11. Inductive Logic From the Viewpoint of Quantum Information.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (13):1-2.
    The resolving of the main problem of quantum mechanics about how a quantum leap and a smooth motion can be uniformly described resolves also the problem of how a distribution of reliable data and a sequence of deductive conclusions can be uniformly described by means of a relevant wave function “Ψdata”.
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  12. David Hume’un Nedensellik Eleştirisi Bağlamında Tümevarımsal Akıl Yürütmeye Yönelik Argümanlarının Yeniden Yapılandırılması.Alper Bilgehan Yardımcı - 2020 - Ankara, Türkiye: Gece Kitaplığı.
    Gözlemlenenlerden gözlemlen(e)meyenlere diğer bir deyişle genel yasalara ulaşma imkânı veren çıkarım yöntemi olarak tümevarımsal ya da endüktif akıl yürütmenin rasyonel olarak temellendirilmesinin imkanına yönelik soruşturma tarih içerisinde tümevarım sorunu ya da endüksiyon problemi olarak tezahür etmiştir. Bu sorunun temel argümanı tarihsel okumalara baktığımızda İskoç ampirist filozof David Hume tarafından öne sürülmüştür. Hume, tümevarımsal çıkarımlar temelinde, gözlenmeyen meseleler hakkındaki inançlarımıza hangi gerekçelerle ulaştığımızı soruşturmaktadır. Hume soruşturmasının sonucunda gözlemlenenden gözlemlen(e)meyen durumlara ilişkin yapılan olgu meseleleri ile ilgili bütün tümevarımsal akıl yürütmelerin dolaylı ya (...)
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  13. Reason Better: An Interdisciplinary Guide to Critical Thinking.David Manley - 2019 - Toronto, ON, Canada: Tophat Monocle.
    This book is the result of rethinking the standard playbook for critical thinking courses, to include only the most useful skills from the toolkits of philosophy, cognitive psychology, and behavioral economics. -/- The text focuses on: -/- - a mindset that avoids systematic error, more than the ability to persuade others - the logic of probability and decisions, more than than the logic of deductive arguments - a unified treatment of evidence, covering statistical, causal, and best-explanation inferences -/- The unified (...)
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  14. A Logic for Best Explanations.Jared Millson & Christian Straßer - 2019 - Journal of Applied Non-Classical Logics 29 (2):184-231.
    Efforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanations exhibit, such as contradiction-intolerance and irreflexivity. This paper aims to surmount these challenges by utilising a new, more precise theory that treats explanations as expressions that codify defeasible inferences. To formalise this account, we provide a sequent calculus in which IBE serves as an elimination rule for a connective that exhibits many of (...)
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  15. An Introduction to Critical Thinking and Symbolic Logic Volume 2: Informal Reasoning Assignments.Rebeka Ferreira & Anthony Ferrucci - 2018 - Open Educational Resource: OpenStax-CNX and Canvas Commons.
    This textbook is not a textbook in the traditional sense. Here, what we have attempted is compile a set of assignments and exercise that may be used in critical thinking courses. To that end, we have tried to make these assignments as diverse as possible while leaving flexibility in their application within the classroom. Of course these assignments and exercises could certainly be used in other classes as well. Our view is that critical thinking courses work best when they are (...)
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  16. Inductive Logic.Avi Sion - 2018 - Geneva, Switzerland: CreateSpace & Kindle; Lulu..
    Inductive Logic is a ‘thematic compilation’ by Avi Sion. It collects in one volume many (though not all) of the essays, that he has written on this subject over a period of some 23 years, which all demonstrate the possibility and conditions of validity of human knowledge, the utility and reliability of human cognitive means when properly used, contrary to the skeptical assumptions that are nowadays fashionable.
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  17. Mill on Logic.David Godden - 2017 - In Dale E. Miller & Christopher Macleod (eds.), A companion to Mill. Hoboken, NJ: John Wiley & Sons. pp. 175-191.
    Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides an introduction to Mill’s logical theory by reviewing his position on the relationship between induction and deduction, and the role of general premises and principles in reasoning. Locating induction, understood as a kind of analogical reasoning from particulars to particulars, as the basic form of inference that is (...)
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  18. Bridging Ranking Theory and the Stability Theory of Belief.Eric Raidl & Niels Skovgaard-Olsen - 2017 - Journal of Philosophical Logic 46 (6):577-609.
    In this paper we compare Leitgeb’s stability theory of belief and Spohn’s ranking-theoretic account of belief. We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking functions and probability functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of Leitgeb’s theory correspond to certain models (...)
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  19. Grounding Reichenbach’s Pragmatic Vindication of Induction.Michael J. Shaffer - 2017 - Polish Journal of Philosophy 11 (1):43-55.
    This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...)
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  20. The Principle of Indifference and Inductive Scepticism.Robert Smithson - 2017 - British Journal for the Philosophy of Science 68 (1):253-272.
    Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that the opposite (...)
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  21. Lectures on Inductive Logic.Jon Williamson - 2017 - Oxford University Press.
    Inductive logic is a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as to scientific problems.
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  22. Argument and Inference: An Introduction to Inductive Logic.Johnson Gregory - 2016 - MIT Press.
  23. 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.
  24. 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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  25. What Conceptual Spaces Can Do for Carnap's Late Inductive Logic.Marta Sznajder - 2016 - Studies in History and Philosophy of Science Part A 56:62-71.
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  26. Qualitative Probabilistic Inference Under Varied Entropy Levels.Paul D. Thorn & Gerhard Schurz - 2016 - Journal of Applied Logic 19 (2):87-101.
    In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield (...)
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  27. The Bayesian Who Knew Too Much.Yann Benétreau-Dupin - 2015 - Synthese 192 (5):1527-1542.
    In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid (...)
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  28. Explicating Formal Epistemology: Carnap's Legacy as Jeffrey's Radical Probabilism.Christopher F. French - 2015 - Studies in History and Philosophy of Science Part A 53:33–42.
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  29. Rudolf Carnap: Philosophy of Science as Engineering Explications.Christopher F. French - 2015 - In Uskali Mäki, Stephanie Ruphy, Gerhard Schurz & Ioannis Votsis (eds.), Recent Developments in the Philosophy of Science: EPSA13 Helsinki. Springer. pp. 293-303.
    One way of explaining Rudolf Carnap’s mature philosophical view is by drawing an analogy between his technical projects—like his work on inductive logic—with a certain kind of conceptual engineering. After all, there are many mathematical similarities between Carnap’s work in inductive logic and a number of results from contemporary confirmation theory, statistics and mathematical probability theory. However, in stressing these similarities, the conceptual dependence of Carnap’s inductive logic on his work on semantics is downplayed. Yet it is precisely the conceptual (...)
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  30. The Theory of Spectrum Exchangeability.E. Howarth & J. B. Paris - 2015 - Review of Symbolic Logic 8 (1):108-130.
  31. The Inheritance of Defaults in the Case of Exceptional Subclasses.Paul D. Thorn - 2015 - The Reasoner 9 (11):93.
  32. The Twin Continua of Inductive Methods.Alena Vencovská & Jeff B. Paris - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 355-366.
  33. 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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  34. What is the Permissibility Solution a Solution Of? -- A Question for Kroedel.Franz Huber - 2014 - Logos and Episteme 5 (3):333-342.
    Kroedel has proposed a new solution, the permissibility solution, to the lottery paradox. The lottery paradox results from the Lockean thesis according to which one ought to believe a proposition just in case one’s degree of belief in it is sufficiently high. The permissibility solution replaces the Lockean thesis by the permissibility thesis according to which one is permitted to believe a proposition if one’s degree of belief in it is sufficiently high. This note shows that the epistemology of belief (...)
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  35. Second Order Inductive Logic and Wilmers' Principle.M. S. Kließ & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
  36. 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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  37. 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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  38. 7. Is There an Inductive Logic?Nicholas Rescher - 2014 - In Logical Inquiries: Basic Issues in Philosophical Logic. De Gruyter. pp. 78-106.
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  39. Empiricism, Probability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Journal of Applied Logic 12 (3):319–348.
    The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy (...)
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  40. Upping the Stakes and the Preface Paradox.Jonny Blamey - 2013 - In Frank Zenker (ed.), Bayesian Argumentation. Springer. pp. 195-210.
    Abstract The Preface Paradox, first introduced by David Makinson (1961), presents a plausible scenario where an agent is evidentially certain of each of a set of propositions without being evidentially certain of the conjunction of the set of propositions. Given reasonable assumptions about the nature of evidential certainty, this appears to be a straightforward contradiction. We solve the paradox by appeal to stake size sensitivity, which is the claim that evidential probability is sensitive to stake size. The argument is that (...)
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  41. Machines and Scientific Method.Piotr Giza - 2013 - Filozofia Nauki 21 (2):75 - +.
  42. 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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  43. Non-Zero Probabilities for Universal Generalizations.Ruurik Holm - 2013 - Synthese 190 (18):4001-4007.
    This article discusses the classical problem of zero probability of universal generalizations in Rudolf Carnap’s inductive logic. A correction rule for updating the inductive method on the basis of evidence will be presented. It will be shown that this rule has the effect that infinite streams of uniform evidence assume a non-zero limit probability. Since Carnap’s inductive logic is based on finite domains of individuals, the probability of the corresponding universal quantification changes accordingly. This implies that universal generalizations can receive (...)
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  44. Note on Induction.Ted Parent - 2013 - Think 12 (33):37-39.
    ExtractSome logic textbooks say, as if it were the received wisdom, that inductive arguments are partly defined by the thinker's intentions. The claim is that an inductive argument is one where the premises are intended to make the conclusion likely. This contrasts with a deductive argument, where the premises are intended to entail the conclusion. However, since entailing is one way of making more likely, a further way to distinguish induction is needed. The addition offered is that the premises are (...)
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  45. 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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  46. Ampliative Inference Under Varied Entropy Levels.Paul D. Thorn & Gerhard Schurz - 2013 - In Christoph Beierle & Gabriele Kern-Isberner (eds.), Proceedings of the 4th Workshop on Dynamics of Knowledge and Belief (DKB-2013). Fakultät für Mathematik und Informatik, FernUniversität in Hagen. pp. 77-88.
  47. From Bayesian Epistemology to Inductive Logic.Jon Williamson - 2013 - Journal of Applied Logic 11 (4):468-486.
    Inductive logic admits a variety of semantics (Haenni et al., 2011, Part 1). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010, Chapter 7). §1 introduces the semantics and then, in §2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008). §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) (...)
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  48. Scientific Method in Brief.Hugh G. Gauch - 2012 - Cambridge University Press.
  49. A Formal Explication Of The Search For Explanations: The Adaptive Logics Approach To Abductive Reasoning.Hans Lycke - 2012 - Logic Journal of the IGPL 20 (2):497-516.
    Most logic–based approaches characterize abduction as a kind of backwards deduction plus additional conditions, which means that a number of conditions is specified that enable one to decide whether or not a particular abductive inference is sound . Despite the fact that these approaches succeed in specifying which formulas count as valid consequences of abductive inference steps, they do not explicate the way people actually reason by means of abductive inferences. This is most clearly shown by the absence of a (...)
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  50. 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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