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A Primer of Probability Logic

Center for the Study of Language and Inf (1996)

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  1. Acceptance and Certainty, Doxastic Modals, and Indicative Conditionals.Kurt Norlin - 2022 - Journal of Philosophical Logic 51 (5):951-971.
    I give a semantics for a logic with two pairs of doxastic modals and an indicative conditional connective that all nest without restriction. Sentences are evaluated as accepted, rejected, or neither. Certainty is the necessity-like modality of acceptance. Inferences may proceed from premises that are certain, or merely accepted, or a mix of both. This semantic setup yields some striking results. Notably, the existence of inferences that preserve certainty but not acceptance very directly implies both failure of modus ponens for (...)
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  • Probabilistic Justification Logic.Joseph Lurie - 2018 - Philosophies 3 (1):2-0.
    Justification logics are constructive analogues of modal logics. They are often used as epistemic logics, particularly as models of evidentialist justification. However, in this role, justification logics are defective insofar as they represent justification with a necessity-like operator, whereas actual evidentialist justification is usually probabilistic. This paper first examines and rejects extant candidates for solving this problem: Milnikel’s Logic of Uncertain Justifications, Ghari’s Hájek–Pavelka-Style Justification Logics and a version of probabilistic justification logic developed by Kokkinis et al. It then proposes (...)
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  • A graph model for probabilities of nested conditionals.Anna Wójtowicz & Krzysztof Wójtowicz - 2022 - Linguistics and Philosophy 45 (3):511-558.
    We define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz. The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning logical and metalogical (...)
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  • The Oxford Handbook of Causal Reasoning.Michael Waldmann (ed.) - 2017 - Oxford, England: Oxford University Press.
    Causal reasoning is one of our most central cognitive competencies, enabling us to adapt to our world. Causal knowledge allows us to predict future events, or diagnose the causes of observed facts. We plan actions and solve problems using knowledge about cause-effect relations. Without our ability to discover and empirically test causal theories, we would not have made progress in various empirical sciences. In the past decades, the important role of causal knowledge has been discovered in many areas of cognitive (...)
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  • Bernoulli Semantics and Ordinal Semantics for Conditionals.Stefan Kaufmann - forthcoming - Journal of Philosophical Logic:1-22.
    Conditionals with conditional constituents pose challenges for the Thesis, the idea that the probability of a conditional is the corresponding conditional probability. This note is concerned with two proposals for overcoming those challenges, both inspired by early work of van Fraassen: the Bernoulli Semantics associated with Stalnaker and Jeffrey, and augmented with a mechanism for obtaining “local probabilities” by Kaufmann; and a proposal by Bacon which I dub Ordinal Semantics. Despite differences in mathematical details and emphasis of presentation, both proposals (...)
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  • Bayes' Theorem.James Joyce - 2008 - Stanford Encyclopedia of Philosophy.
    Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...)
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  • Internalism, Externalism, and Epistemic Source Circularity.Ian David MacMillan - unknown
    The dissertation examines the nature and epistemic implications of epistemic source circularity. An argument exhibits this type of circularity when at least one of the premises is produced by a belief source the conclusion says is legitimate, e.g. a track record argument for the legitimacy of sense perception that uses premises produced by sense perception. In chapter one I examine this and several other types of circularity, identifying relevant similarities and differences between them. In chapter two I discuss the differences (...)
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  • The Probability of Iterated Conditionals.Janneke Wijnbergen‐Huitink, Shira Elqayam & David E. Over - 2015 - Cognitive Science 39 (4):788-803.
    Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth-table task, (...)
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  • Logical Questions Behind the Lottery and Preface Paradoxes: Lossy Rules for Uncertain Inference.David Makinson - 2012 - Synthese 186 (2):511-529.
    We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the (...)
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  • Reasoning with Conditionals.Guy Politzer - 2007 - Topoi 26 (1):79-95.
    This paper reviews the psychological investigation of reasoning with conditionals, putting an emphasis on recent work. In the first part, a few methodological remarks are presented. In the second part, the main theories of deductive reasoning (mental rules, mental models, and the probabilistic approach) are considered in turn; their content is summarised and the semantics they assume for if and the way they explain formal conditional reasoning are discussed, in particular in the light of experimental work on the probability of (...)
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  • Understanding Conditionals in the East: A Replication Study of Politzer Et Al. With Easterners.Hiroko Nakamura, Jing Shao, Jean Baratgin, David E. Over, Tatsuji Takahashi & Hiroshi Yama - 2018 - Frontiers in Psychology 9.
  • New Normative Standards of Conditional Reasoning and the Dual-Source Model.Henrik Singmann, Karl Christoph Klauer & David Over - 2014 - Frontiers in Psychology 5.
  • Bayesian Reasoning with Ifs and Ands and Ors.Nicole Cruz, Jean Baratgin, Mike Oaksford & David E. Over - 2015 - Frontiers in Psychology 6.
  • Conditionals, Context, and the Suppression Effect.Fabrizio Cariani & Lance J. Rips - 2017 - Cognitive Science 41 (3):540-589.
    Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B. Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional (...)
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  • Uncertain Deduction and Conditional Reasoning.Jonathan St B. T. Evans, Valerie A. Thompson & David E. Over - 2015 - Frontiers in Psychology 6.
  • What Should I Believe About What Would Have Been the Case?Franz Huber - 2015 - Journal of Philosophical Logic 44 (1):81-110.
    The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...)
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  • New Psychological Paradigm for Conditionals and General de Finetti Tables.J. Baratgin, D. Over & G. Politzer - 2014 - Mind and Language 29 (1):73-84.
    The new Bayesian paradigm in the psychology of reasoning aims to integrate the study of human reasoning, decision making, and rationality. It is supported by two findings. One, most people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test. Two, they judge if A then B to be void when A is false. Their three-valued response table used to be called ‘defective’, but should be termed the (...)
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  • The Evidential Support Theory of Conditionals.Igor Douven - 2008 - Synthese 164 (1):19-44.
    According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.
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  • Message Framing, Normative Advocacy and Persuasive Success.Adam Corner & Ulrike Hahn - 2010 - Argumentation 24 (2):153-163.
    In a recent article in Argumentation, O’Keefe (Argumentation 21:151–163, 2007) observed that the well-known ‘framing effects’ in the social psychological literature on persuasion are akin to traditional fallacies of argumentation and reasoning and could be exploited for persuasive success in a way that conflicts with principles of responsible advocacy. Positively framed messages (“if you take aspirin, your heart will be more healthy”) differ in persuasive effect from negative frames (“if you do not take aspirin, your heart will be less healthy”), (...)
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  • Nonfallacious Rhetorical Strategies: Lyndon Johnson’s Daisy Ad. [REVIEW]Scott Jacobs - 2006 - Argumentation 20 (4):421-442.
    The traditional concepts of rhetorical strategy and argumentative fallacy cannot be readily reconciled. Doing so requires escaping the following argument: All argumentation involves rhetorical strategies. All rhetorical strategies are violations of logical or dialectical ideals. All violations of logical or dialectical ideals are fallacies. Normative pragmatics provides a perspective in which rhetorical strategies can be seen to have the potential for constructive contributions to argumentation and in which fallacies are not simply violations of ideals. One kind of constructive contribution, framing (...)
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  • Wondering What Might Be.Moritz Schulz - 2010 - Philosophical Studies 149 (3):367 - 386.
    This paper explores the possibility of supplementing the suppositional view of indicative conditionals with a corresponding view of epistemic modals. The most striking feature of the suppositional view consists in its claim that indicative conditionals are to be evaluated by conditional probabilities. On the basis of a natural link between indicative conditionals and epistemic modals, a corresponding thesis about the probabilities of statements governed by epistemic modals can be derived. The paper proceeds by deriving further consequences of this thesis, in (...)
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  • Conditional Predictions.Stefan Kaufmann - 2005 - Linguistics and Philosophy 28 (2):181 - 231.
    The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...)
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  • Why Undermining Evolutionary Debunkers is Not Enough.Andrew del Rio - 2021 - Synthese 199 (3-4):7437-7452.
    Denying the conclusion of a valid argument is not generally permissible if one suspends on one premise of the argument and believes the other premise. This can happen when one’s only critique of an argument is to undermine one premise. There is incoherence there. Here I examine how this is relevant to the debate on evolutionary debunking of our moral knowledge. I argue that one significant line of response to the debunker is unsuccessful: merely undermining the debunker’s empirical claim. It (...)
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  • Counterfactuals and Probability. [REVIEW]Justin Khoo - 2020 - Philosophical Review 129 (3):489-495.
  • A Causal Semantics of IS Generics.Robert van Rooij & Katrin Schulz - 2020 - Journal of Semantics 37 (2):269-295.
    The felicity, or acceptability, of IS generics, i.e. generic sentences with indefinite singulars, is considerably more restricted compared to BP generics, generics with bare plurals. The goal of this paper is to account for the limited felicity of IS generics compared to BP generics, on the one hand, while preserving the close similarity between the two types of generics, on the other. We do so by proposing a causal analysis of IS generics, and show that this corresponds closely with a (...)
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  • Putting Inferentialism and the Suppositional Theory of Conditionals to the Test.Niels Skovgaard-Olsen - 2017 - Dissertation, University of Freiburg
    This dissertation is devoted to empirically contrasting the Suppositional Theory of conditionals, which holds that indicative conditionals serve the purpose of engaging in hypothetical thought, and Inferentialism, which holds that indicative conditionals express reason relations. Throughout a series of experiments, probabilistic and truth-conditional variants of Inferentialism are investigated using new stimulus materials, which manipulate previously overlooked relevance conditions. These studies are some of the first published studies to directly investigate the central claims of Inferentialism empirically. In contrast, the Suppositional Theory (...)
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  • Credence for Epistemic Discourse.Paolo Santorio - manuscript
    Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...)
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  • Is the Basic Conditional Probabilistic?Geoffrey P. Goodwin - 2014 - Journal of Experimental Psychology: General 143 (3):1214-1241.
  • Imaging Deductive Reasoning and the New Paradigm.Mike Oaksford - 2015 - Frontiers in Human Neuroscience 9.
  • Deductive Reasoning Under Uncertainty: A Water Tank Analogy.Guy Politzer - 2016 - Erkenntnis 81 (3):479-506.
    This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...)
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  • Knowledge and Conditionals of (Dis)Connection.Danilo Šuster - 2015 - Croatian Journal of Philosophy 15 (3):267-294.
    The gist of modal epistemology is expressed in the idea that you fail to know if you do believe truly but it is seriously possible for you to believe falsely. According to subjunctivism, this idea is captured by certain subjunctive conditionals. One formulation invokes a safety condition—“If S had believed P, then P would have been the case,” while the other invokes a sensitivity condition—“If P had been false, S would not have believed that P.” According to simple subjunctivism, such (...)
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  • Against Philo’s Interpretation of Conditional. The Case of Aristotle´s Thesis.Miguel López-Astorga - 2016 - Agora 35 (2).
    There is an Aristotelian thesis that can be considered controversial. That is the thesis related to a denied conditional with only one propositional variable and in which, in addition, one of its clauses is also denied. While the thesis is not a tautology, people tend to accept it as true. Pfeifer’s approach can account for this fact. However, I try to show that this problem can also be explained from other alternative frameworks, in particular, from that of the mental models (...)
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  • Triviality Results and the Relationship Between Logical and Natural Languages.Justin Khoo & Matthew Mandelkern - 2019 - Mind 128 (510):485-526.
    Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...)
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  • The Dialectics of Infinitism and Coherentism: Inferential Justification Versus Holism and Coherence.Frederik Herzberg - 2014 - Synthese 191 (4):701-723.
    This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification (...)
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  • The Fall of “Adams' Thesis”?Alan Hájek - 2012 - Journal of Logic, Language and Information 21 (2):145-161.
    The so-called ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically: $${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$ The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is . I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new (...)
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  • Conditioning Against the Grain.Stefan Kaufmann - 2004 - Journal of Philosophical Logic 33 (6):583-606.
    This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between (...)
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  • Uncertainty and the Suppression of Inferences.Guy Politzer - 2005 - Thinking and Reasoning 11 (1):5 – 33.
    The explanation of the suppression of Modus Ponens inferences within the framework of linguistic pragmatics and of plausible reasoning (i.e., deduction from uncertain premises) is defended. First, this approach is expounded, and then it is shown that the results of the first experiment of Byrne, Espino, and Santamar a (1999) support the uncertainty explanation but fail to support their counterexample explanation. Second, two experiments are presented. In the first one, aimed to refute one objection regarding the conclusions observed, the additional (...)
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  • An Exact Measure of Paradox.A. C. Paseau - 2013 - Analysis 73 (1):17-26.
    We take seriously the idea that paradoxes come in quantifiable degree by offering an exact measure of paradox. We consider three factors relevant to the degree of paradox, which are a function of the degree of belief in each of the individual propositions in the paradox set and the degree of belief in the set as a whole. We illustrate the proposal with a particular measure, and conclude the discussion with some critical remarks.
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  • Conditionals, Predicates and Probability.Brian Weatherson - manuscript
    Ernest Adams has claimed that a probabilistic account of validity gives the best account of our intuitive judgements about the validity of arguments. In particular, he claims, it has the best hope of accounting for our judgements about many arguments involving conditionals. Most of the examples in the literature on this topic have been arguments framed in the language of propositional logic. I show that once we consider arguments involving predicates and involving identity, Adams’s strategy is less successful.
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  • The Theory of the Formal Discipline and the Possible Interpretation of Conditionals: Material Versus Defective Conditionals.Miguel López Astorga - 2014 - Abstracta 8 (1):31-39.
    Attridge and Inglis try to check whether or not the ‘Theory of Formal Discipline’ is correct. This theory states that learning mathematics improves logical reasoning, and Attridge and Inglis review it by means of an experiment. Their conclusion is that, indeed, learning mathematics improves conditional inferences causing that conditionals are interpreted as defective. In this paper, I analyze Attridge and Inglis´s experiment and hold that it has a methodological problem and that hence does not really prove that learning mathematics lead (...)
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  • Models in Systems Medicine.Jon Williamson - unknown
    Systems medicine is a promising new paradigm for discovering associations, causal relationships and mechanisms in medicine. But it faces some tough challenges that arise from the use of big data: in particular, the problem of how to integrate evidence and the problem of how to structure the development of models. I argue that objective Bayesian models offer one way of tackling the evidence integration problem. I also offer a general methodology for structuring the development of models, within which the objective (...)
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  • Realizing What Might Be.Malte Willer - 2011 - Philosophical Studies 153 (3):365 - 375.
    Schulz has shown that the suppositional view of indicative conditionals leads to a corresponding view of epistemic modals. But his case backfires: the resulting theory of epistemic modals gets the facts wrong, and so we end up with a good argument against the suppositional view. I show how and why a dynamic view of indicative conditionals leads to a better theory of epistemic modals.
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  • Indicative Conditionals: Probabilities and Relevance.Franz Berto & Aybüke Özgün - 2021 - Philosophical Studies.
    We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) (...)
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  • The Logic of the Future in Quantum Theory.Anthony Sudbery - 2017 - Synthese 194 (11):4429-4453.
    According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice (...)
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  • The Impact Factor Fallacy.Frieder M. Paulus, Nicole Cruz & Sören Krach - 2018 - Frontiers in Psychology 9.
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  • Imaging Uncertainty.Benjamin Eva & Stephan Hartmann - unknown
    The technique of imaging was first introduced by Lewis, in order to provide a novel account of the probability of conditional propositions. In the intervening years, imaging has been the object of significant interest in both AI and philosophy, and has come to be seen as a philosophically important approach to probabilistic updating and belief revision. In this paper, we consider the possibility of generalising imaging to deal with uncertain evidence and partial belief revision. In particular, we introduce a new (...)
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  • Skeptical Theism, Abductive Atheology, and Theory Versioning.Timothy Perrine & Stephen J. Wykstra - 2014 - In Trent Dougherty & Justin McBrayer (eds.), Skeptical Theism: New Essays. Oxford University Press..
    What we call “the evidential argument from evil” is not one argument but a family of them, originating (perhaps) in the 1979 formulation of William Rowe. Wykstra’s early versions of skeptical theism emerged in response to Rowe’s evidential arguments. But what sufficed as a response to Rowe may not suffice against later more sophisticated versions of the problem of evil—in particular, those along the lines pioneered by Paul Draper. Our chief aim here is to make an earlier version of skeptical (...)
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  • Probabilistic Logic of Quantum Observations.A. Sernadas, J. Rasga, C. Sernadas, L. Alcácer & A. B. Henriques - 2019 - Logic Journal of the IGPL 27 (3):328-370.
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  • Hypothetical Revision and Matter-of-Fact Supposition.Horacio Arló Costa - 2001 - Journal of Applied Non-Classical Logics 11 (1-2):203-229.
    The recent literature offers several models of the notion of matter of fact supposition1 revealed in the acceptance of the so-called indicative conditionals. Some of those models are qualitative [Collins 90], [Levi 96], [Stalnaker 84]. Other probabilistic models appeal either to infinitesimal probability or two place probability functions. Recent work has made possible to understand which is the exact qualitative counterpart of the latter probabilistic models. In this article we show that the qualitative notion of change that thus arises is (...)
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