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Logical Foundations of Probability

Mind 62 (245):86-99 (1953)

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  1. Les fonctions de probabilité: la question de leur définissabilité récursive.Hugues Leblanc & Peter Roeper - 1992 - Dialogue 31 (4):643-.
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  • Two Dogmas of Strong Objective Bayesianism.Prasanta S. Bandyopadhyay & Gordon Brittan - 2010 - International Studies in the Philosophy of Science 24 (1):45 – 65.
    We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...)
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  • Semantic Intuitions, Conceptual Analysis, and Cross-Cultural Variation.Henry Jackman - 2009 - Philosophical Studies 146 (2):159 - 177.
    While philosophers of language have traditionally relied upon their intuitions about cases when developing theories of reference, this methodology has recently been attacked on the grounds that intuitions about reference, far from being universal, show significant cultural variation, thus undermining their relevance for semantic theory. I’ll attempt to demonstrate that (1) such criticisms do not, in fact, undermine the traditional philosophical methodology, and (2) our underlying intuitions about the nature of reference may be more universal than the authors suppose.
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  • Axioms in Mathematical Practice.D. Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
    On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...)
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  • Evolution, Dysfunction, and Disease: A Reappraisal: Table 1.Paul E. Griffiths & John Matthewson - 2016 - British Journal for the Philosophy of Science:axw021.
  • Two Impossibility Results for Measures of Corroboration.Jan Sprenger - 2015 - British Journal for the Philosophy of Science:axw016.
    According to influential accounts of scientific method, such as critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in statistical inference and science in general, their philosophical foundations remain shaky. In particular, the interpretation of non-significant results—those that do not reject the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis, or provide a reason to accept it? Popper sought for measures of corroboration that could (...)
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  • Progress in Defining Disease: Improved Approaches and Increased Impact.H. Schwartz Peter - 2017 - Journal of Medicine and Philosophy 42 (4):485-502.
    In a series of recent papers, I have made three arguments about how to define “disease” and evaluate and apply possible definitions. First, I have argued that definitions should not be seen as traditional conceptual analyses, but instead as proposals about how to define and use the term “disease” in the future. Second, I have pointed out and attempted to address a challenge for dysfunction-requiring accounts of disease that I call the “line-drawing” problem: distinguishing between low-normal functioning and dysfunctioning. Finally, (...)
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  • In Search of the Philosopher's Stone: Remarks on Humphreys and Freedman's Critique of Causal Discovery.Kevin B. Korb & Chris S. Wallace - 1997 - British Journal for the Philosophy of Science 48 (4):543-553.
  • On a Straw Man in the Philosophy of Science - A Defense of the Received View.Sebastian Lutz - 2012 - Hopos: The Journal of the International Society for the History of Philosophy of Science 2 (1):77–120.
    I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to (...)
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  • Notes on Bayesian Confirmation Theory.Michael Strevens - manuscript
    Bayesian confirmation theory—abbreviated to in these notes—is the predominant approach to confirmation in late twentieth century philosophy of science. It has many critics, but no rival theory can claim anything like the same following. The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where (...)
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  • Epistemic Disjunctivism and the Evidential Problem.José Zalabardo - 2015 - Analysis 75 (4):615-627.
    I argue that Epistemic Disjunctivism doesn’t sustain a successful anti-sceptical strategy. I contend, in particular, that the treatment of scepticism that Duncan Pritchard puts forward on behalf of Epistemic Disjunctivism is unsatisfactory.
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  • Dimensions of Objectual Understanding.Christoph Baumberger & Georg Brun - 2017 - In Stephen Grimm Christoph Baumberger & Sabine Ammon (eds.), Explaining Understanding: New Perspectives from Epistemology and Philosophy of Science. Routledge. pp. 165-189.
    In science and philosophy, a relatively demanding notion of understanding is of central interest: an epistemic subject understands a subject matter by means of a theory. This notion can be explicated in a way which resembles JTB analyses of knowledge. The explication requires that the theory answers to the facts, that the subject grasps the theory, that she is committed to the theory and that the theory is justified for her. In this paper, we focus on the justification condition and (...)
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  • Error and Inference: An Outsider Stand on a Frequentist Philosophy.Christian P. Robert - 2013 - Theory and Decision 74 (3):447-461.
  • A Simulation Approach to Veritistic Social Epistemology.Erik J. Olsson - 2011 - Episteme 8 (2):127-143.
    In a seminal book, Alvin I. Goldman outlines a theory for how to evaluate social practices with respect to their , i.e., their tendency to promote the acquisition of true beliefs (and impede the acquisition of false beliefs) in society. In the same work, Goldman raises a number of serious worries for his account. Two of them concern the possibility of determining the veritistic value of a practice in a concrete case because (1) we often don't know what beliefs are (...)
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  • Putnam’s Diagonal Argument and the Impossibility of a Universal Learning Machine.Tom F. Sterkenburg - 2019 - Erkenntnis 84 (3):633-656.
    Putnam construed the aim of Carnap’s program of inductive logic as the specification of a “universal learning machine,” and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff and Levin lead to a mathematical foundation of precisely those aspects of Carnap’s program that Putnam took issue with, and in particular, resurrect the notion of a universal mechanical rule for induction. In this paper, I take up the question whether the Solomonoff–Levin proposal is (...)
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  • Human Rationality Challenges Universal Logic.Brian R. Gaines - 2010 - Logica Universalis 4 (2):163-205.
    Tarski’s conceptual analysis of the notion of logical consequence is one of the pinnacles of the process of defining the metamathematical foundations of mathematics in the tradition of his predecessors Euclid, Frege, Russell and Hilbert, and his contemporaries Carnap, Gödel, Gentzen and Turing. However, he also notes that in defining the concept of consequence “efforts were made to adhere to the common usage of the language of every day life.” This paper addresses the issue of what relationship Tarski’s analysis, and (...)
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  • Confirmation, Transitivity, and Moore: The Screening-Off Approach.William Roche & Tomoji Shogenji - 2013 - Philosophical Studies (3):1-21.
    It is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2. In this paper we distinguish four senses of confirmation and examine additional conditions under which confirmation in different senses becomes transitive. We conduct this examination both in the general case where H1 confirms H2 and in the special case where H1 also logically entails H2. Based on these analyses, we argue that (...)
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  • A Simulation Approach to Veritistic Social Epistemology.Erik J. Olsson - 2011 - Episteme 8 (2):127-143.
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  • Prichard's Heresy.Sandy Berkovski - 2011 - Philosophy 86 (4):503-524.
    H. A. Prichard ascribed to Aristotle a form of closeted hedonism. Aristotle allegedly misunderstood his own task: while his avowed goal in Nicomachean Ethics is to give an account of the nature of happiness, his real goal must be to offer an account of the factors most efficiently generating happiness. The reason is that the nature of happiness is enjoyment, and this fact is supposed to have been recognised by Aristotle and his audience. While later writers judged Prichard's view obviously (...)
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  • Reward Versus Risk in Uncertain Inference: Theorems and Simulations.Gerhard Schurz & Paul D. Thorn - 2012 - Review of Symbolic Logic 5 (4):574-612.
    Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...)
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  • A Synthesis of Hempelian and Hypothetico-Deductive Confirmation.Jan Sprenger - 2013 - Erkenntnis 78 (4):727-738.
    This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypothetico-deductive traditions in confirmation theory. The merger of these two approaches is subsequently extended to the piecemeal confirmation of entire theories. It is then argued that this synthetic account makes a useful contribution from both a historical and a systematic perspective.
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  • Hempel’s Logic of Confirmation.Franz Huber - 2008 - Philosophical Studies 139 (2):181-189.
    This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another (...)
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  • Carnap on Empirical Significance.Sebastian Lutz - 2017 - Synthese 194 (1):217-252.
    Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...)
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  • Evidential Support and Instrumental Rationality.Peter Broessel, Anna-Maria A. Eder & Franz Huber - 2013 - Philosophy and Phenomenological Research 87 (2):279-300.
  • Belief and Degrees of Belief.Franz Huber - 2009 - In F. Huber & C. Schmidt-Petri (eds.), Degrees of Belief. Springer.
    Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...)
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  • Coherence as a Heuristic.Staffan Angere - 2008 - Mind 117 (465):1-26.
    The impossibility results of Bovens and Hartmann (2003) and Olsson (2005) call into question the strength of the connection between coherence and truth. As part of the inquiry into this alleged link, I define a notion of degree of truth-conduciveness, relevant for measuring the usefulness of coherence measures as rules-of-thumb for assigning probabilities in situations of partial knowledge. I use the concept to compare the viability of some of the measures of coherence that have been suggested so far under different (...)
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  • Inductive Logic as Explication: The Evolution of Carnap’s Notion of Logical Probability.Marta Sznajder - 2018 - The Monist 101 (4):417-440.
    According to a popular interpretation, Carnap’s interpretation of probability had evolved from a logical towards a subjective conception. However Carnap himself insisted that his basic philosophical view of probability was always the same. I address this apparent clash between Carnap's self-identification and the subsequent interpretations of his work. Following its original intentions, I reconstruct inductive logic as an explication. The emerging picture is of a versatile linguistic framework, whose main function is not the discovery of objective logical relations in the (...)
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  • Merging of Opinions and Probability Kinematics.Simon M. Huttegger - 2015 - Review of Symbolic Logic 8 (4):611-648.
  • Evidential Support, Transitivity, and Screening-Off.William Roche - 2015 - Review of Symbolic Logic 8 (4):785-806.
    Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...)
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  • Jaakko Hintikka 1929–2015.Jouko Väänänen - 2015 - Bulletin of Symbolic Logic 21 (4):431-436.
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  • What is Fake News?Nikil Mukerji - 2018 - Ergo: An Open Access Journal of Philosophy 5:923-946.
    An important way in which philosophy can contribute to public discourse is by clarifying concepts that are central to it. This paper is a philosophical contribution in that spirit. It offers an account of fake news—a notion that has entered public debate following the 2016 US presidential election. On the view I defend, fake news is Frankfurtian bullshit that is asserted in the form of a news publication. According to Frankfurt’s famous account, bullshit has two characteristics. There is, firstly, an (...)
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  • Carnap, the Necessary a Priori, and Metaphysical Anti-Realism.Stephen Biggs & Jessica M. Wilson - 2016 - In Stephen Blatti & Sandra Lapointe (eds.), Ontology after Carnap. Oxford: pp. 81-104.
    In Meaning and Necessity (1947/1950), Carnap advances an intensional semantic framework on which modal claims are true in virtue of semantical rules alone, and so are a priori. In 'Empiricism, Semantics, and Ontology' (1950), Carnap advances an epistemic-ontological framework on which metaphysical claims are either trivial or meaningless, since lacking any means of substantive confirmation. Carnap carried out these projects two decades before Kripke influentially argued, in Naming and Necessity (1972/1980), that some modal claims are true a posteriori. How should (...)
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  • Foundations of a Probabilistic Theory of Causal Strength.Jan Sprenger - 2018 - Philosophical Review 127 (3):371-398.
    This paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of plausible (...)
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  • Proceedings of Sinn Und Bedeutung 9.Emar Maier, Corien Bary & Janneke Huitink (eds.) - 2005 - Nijmegen Centre for Semantics.
  • Probability and Chance.Michael Strevens - 2006 - In D. M. Borchert (ed.), Encyclopedia of Philosophy, second edition. Macmillan.
    The weather report says that the chance of a hurricane arriving later today is 90%. Forewarned is forearmed: expecting a hurricane, before leaving home you pack your hurricane lantern.
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  • Universality, Invariance, and the Foundations of Computational Complexity in the Light of the Quantum Computer.Michael Cuffaro - 2018 - In Sven Hansson (ed.), Technology and Mathematics: Philosophical and Historical Investigations. Springer. pp. 253-282.
    Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For model-independence (...)
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  • The Constituents of an Explication.Moritz Cordes - forthcoming - Synthese.
    The method of explication has been somewhat of a hot topic in the last ten years. Despite the multifaceted research that has been directed at the issue, one may perceive a lack of step-by-step procedural or structural accounts of explication. This paper aims at providing a structural account of the method of explication in continuation of the works of Geo Siegwart. It is enhanced with a detailed terminology for the assessment and comparison of explications. The aim is to provide means (...)
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  • On the Justification of Deduction and Induction.Franz Huber - 2017 - European Journal for Philosophy of Science 7 (3):507-534.
    The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...)
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  • A Partial Consequence Account of Truthlikeness.Gustavo Cevolani & Roberto Festa - 2018 - Synthese:1-20.
    Popper’s original definition of truthlikeness relied on a central insight: that truthlikeness combines truth and information, in the sense that a proposition is closer to the truth the more true consequences and the less false consequences it entails. As intuitively compelling as this definition may be, it is untenable, as proved long ago; still, one can arguably rely on Popper’s intuition to provide an adequate account of truthlikeness. To this aim, we mobilize some classical work on partial entailment in defining (...)
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  • Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew W. Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.
    A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...)
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  • Sleeping Beauty Goes to the Lab: The Psychology of Self-Locating Evidence.Matteo Colombo, Jun Lai & Vincenzo Crupi - unknown - Review of Philosophy and Psychology 10 (1):173-185.
    Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” and those endorsing the “1/3 view”. The disagreement concerns the evidential relevance of self-locating information. Unlike halfers, thirders regard self-locating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations of the Sleeping Beauty Problem do not fit (...)
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  • Empirical Significance, Predictive Power, and Explication.Surovell Jonathan/R. - forthcoming - Synthese.
    Criteria of empirical significance are supposed to state conditions under which reference to an unobservable object or property is “empirically meaningful.” The intended kind of empirical meaningfulness should be necessary for admissibility into the selective contexts of scientific inquiry. I defend Justus’s recent argument that the reasons generally given for rejecting the project of defining a significance criterion are unpersuasive. However, as I show, this project remains wedded to an overly narrow conception of its subject matter. Even the most cutting (...)
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  • String Theory, Non-Empirical Theory Assessment, and the Context of Pursuit.Frank Cabrera - 2018 - Synthese:1-29.
    In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...)
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  • Bayesian Statistical Inference and Approximate Truth.Olav B. Vassend - unknown
    Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is supposed to represent the probability that the hypothesis is true. I investigate whether Bayesianism can accommodate the idea that false hypotheses are sometimes approximately true or that some hypotheses or models can be closer to the truth than others. I argue that the idea that some hypotheses are approximately true in an absolute sense is (...)
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  • Beyond Logical Empiricism.William R. Shea - 1971 - Dialogue 10 (2):223-242.
  • A Note on Two-Place Predicates and Fitting Sequences of Measure Functions.Herman Rubin & Patrick Suppes - 1955 - Journal of Symbolic Logic 20 (2):121-122.
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  • Explication of Inductive Probability.Patrick Maher - 2010 - Journal of Philosophical Logic 39 (6):593 - 616.
    Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.
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  • Conditional Probability in the Light of Qualitative Belief Change.David C. Makinson - 2011 - Journal of Philosophical Logic 40 (2):121 - 153.
    We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on (...)
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  • Comparison of Confirmation Measures.Katya Tentori, Vincenzo Crupi, Nicolao Bonini & Daniel Osherson - 2007 - Cognition 103 (1):107-119.
  • Dialectics, Evaluation, and Argument.Maurice A. Finocchiaro - 2003 - Informal Logic 23 (1).
    A critical examination of the dialectical approach, focusing on a comparison ofthe illative and the dialectical definitions of argument. I distinguish a moderate, a strong and a hyper dialectical conception of argument. I critique Goldman's argument for the moderate conception and Johnson's argument for the strong conception, and argue that the moderate conception is correct.
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