Results for 'confirmation'

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  1. Bruno de finetti.A. Short Confirmation of My Standpoint - 1979 - In Maurice Allais & Ole Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. D. Reidel. pp. 161.
  2. USC Football Notebook: Robey, McDonald Secondary Stalwarts.White House Confirms Cyber Attack - forthcoming - Hermes.
     
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    Comments akd criticism 383.A. Query On Confirmation - 1996 - In Sahotra Sarkar (ed.), Logic, Probability, and Epistemology: The Power of Semantics. Garland Pub. Co.. pp. 227.
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  4. Jaakko Hintikka.Paradoxes Of Confirmation - 1969 - In Nicholas Rescher (ed.), Essays in Honor of Carl G. Hempel. Reidel. pp. 24.
  5. Seeking confirmation: A puzzle for norms of inquiry.Jared Millson - 2020 - Analysis 80 (4):683-693.
    Like other epistemic activities, inquiry seems to be governed by norms. Some have argued that one such norm forbids us from believing the answer to a question and inquiring into it at the same time. But another, hither-to neglected norm seems to permit just this sort of cognitive arrangement when we seek to confirm what we currently believe. In this paper, I suggest that both norms are plausible and that the conflict between them constitutes a puzzle. Drawing on the felicity (...)
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  6. Inquiry and Confirmation.Arianna Falbo - 2021 - Analysis 81 (4):622–631.
    A puzzle arises when combining two individually plausible, yet jointly incompatible, norms of inquiry. On the one hand, it seems that one shouldn’t inquire into a question while believing an answer to that question. But, on the other hand, it seems rational to inquire into a question while believing its answer, if one is seeking confirmation. Millson (2021), who has recently identified this puzzle, suggests a possible solution, though he notes that it comes with significant costs. I offer an (...)
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  7.  52
    Comparative Confirmation and the Problem of Evil.Richard Otte - 2012 - In Jake Chandler & Victoria S. Harrison (eds.), Probability in the Philosophy of Religion. Oxford University Press. pp. 127.
    In this chapter probability and confirmation theory are used to investigate the problem of evil, concentrating on whether a theist should consider our ignorance of a good reason for God to permit evil to support a non-religious alternative over a typical theist's beliefs. It is argued that according to Likelihoodism, our ignorance of a good reason does not favor a competing hypothesis over the religious view that there is an incomprehensible good reason for God to permit evil. Bayesian accounts (...)
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  8.  29
    Confirmation Bias.David Kyle Johnson - 2018-05-09 - In Robert Arp, Steven Barbone & Michael Bruce (eds.), Bad Arguments. Wiley. pp. 317–320.
    This chapter focuses on one of the common fallacies in Western philosophy, “confirmation bias”. Confirmation bias is the human tendency only to look for evidence that confirms what one wants to believe or what one already thinks is true. Usually people are not too keen to look for evidence against what they want to believe is true. The human propensity for self‐delusion is strong. When one is confronted with sufficient evidence against some belief that one holds, what one (...)
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  9. 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, (...)
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    6. Confirmation and Verisimilitude.Stephen Yablo - 2014 - In Aboutness. Oxford: Princeton University Press. pp. 95-111.
  11. Confirmation, heuristics, and explanatory reasoning.Timothy McGrew - 2003 - British Journal for the Philosophy of Science 54 (4):553-567.
    Recent work on inference to the best explanation has come to an impasse regarding the proper way to coordinate the theoretical virtues in explanatory inference with probabilistic confirmation theory, and in particular with aspects of Bayes's Theorem. I argue that the theoretical virtues are best conceived heuristically and that such a conception gives us the resources to explicate the virtues in terms of ceteris paribus theorems. Contrary to some Bayesians, this is not equivalent to identifying the virtues with likelihoods (...)
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    Confirmability and meaningfulness.D. H. M. Brooks - 1980 - Philosophical Papers 9 (1):41-44.
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    Confirmation, transitivity, and Moore: the Screening-Off Approach.William Roche & Tomoji Shogenji - 2014 - Philosophical Studies 168 (3):797-817.
    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, (...)
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  14. Confirmation via Analogue Simulation: What Dumb Holes Could Tell Us about Gravity.Radin Dardashti, Karim P. Y. Thébault & Eric Winsberg - 2017 - British Journal for the Philosophy of Science 68 (1).
    In this article we argue for the existence of ‘analogue simulation’ as a novel form of scientific inference with the potential to be confirmatory. This notion is distinct from the modes of analogical reasoning detailed in the literature, and draws inspiration from fluid dynamical ‘dumb hole’ analogues to gravitational black holes. For that case, which is considered in detail, we defend the claim that the phenomena of gravitational Hawking radiation could be confirmed in the case that its counterpart is detected (...)
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  15. Confirmation of ecological and evolutionary models.Elisabeth A. Lloyd - 1987 - Biology and Philosophy 2 (3):277-293.
    In this paper I distinguish various ways in which empirical claims about evolutionary and ecological models can be supported by data. I describe three basic factors bearing on confirmation of empirical claims: fit of the model to data; independent testing of various aspects of the model, and variety of evident. A brief description of the kinds of confirmation is followed by examples of each kind, drawn from a range of evolutionary and ecological theories. I conclude that the greater (...)
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  16. Confirmation, increase in probability, and partial discrimination: A reply to Zalabardo.William Roche - 2016 - European Journal for Philosophy of Science 6 (1):1-7.
    There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and (...)
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  17. Measuring confirmation.David Christensen - 1999 - Journal of Philosophy 96 (9):437-461.
    The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this measure nevertheless reveals (...)
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  18. Positive confirmation bias in the acquisition of information.Martin Jones & Robert Sugden - 2001 - Theory and Decision 50 (1):59-99.
    An experiment is reported which tests for positive confirmation bias in a setting in which individuals choose what information to buy, prior to making a decision. The design – an adaptation of Wason's selection task – reveals the use that subjects make of information after buying it. Strong evidence of positive confirmation bias, in both information acquisition and information use, is found; and this bias is found to be robust to experience. It is suggested that the bias results (...)
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  19.  58
    Allocating confirmation with derivational robustness.Aki Lehtinen - 2016 - Philosophical Studies 173 (9):2487-2509.
    Robustness may increase the degree to which the robust result is indirectly confirmed if it is shown to depend on confirmed rather than disconfirmed assumptions. Although increasing the weight with which existing evidence indirectly confirms it in such a case, robustness may also be irrelevant for confirmation, or may even disconfirm. Whether or not it confirms depends on the available data and on what other results have already been established.
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  20. What is relative confirmation?David Christensen - 1997 - Noûs 31 (3):370-384.
    It is commonly acknowledged that, in order to test a theoretical hypothesis, one must, in Duhem' s phrase, rely on a "theoretical scaffolding" to connect the hypothesis with something measurable. Hypothesis-confirmation, on this view, becomes a three-place relation: evidence E will confirm hypothesis H only relative to some such scaffolding B. Thus the two leading logical approaches to qualitative confirmation--the hypothetico-deductive (H-D) account and Clark Glymour' s bootstrap account--analyze confirmation in relative terms. But this raises questions about (...)
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  21. Confirmation and justification. A commentary on Shogenji’s measure.David Atkinson - 2012 - Synthese 184 (1):49-61.
    So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; (...)
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  22. Seeking Confirmation Is Rational for Deterministic Hypotheses.Joseph L. Austerweil & Thomas L. Griffiths - 2011 - Cognitive Science 35 (3):499-526.
    The tendency to test outcomes that are predicted by our current theory (the confirmation bias) is one of the best-known biases of human decision making. We prove that the confirmation bias is an optimal strategy for testing hypotheses when those hypotheses are deterministic, each making a single prediction about the next event in a sequence. Our proof applies for two normative standards commonly used for evaluating hypothesis testing: maximizing expected information gain and maximizing the probability of falsifying the (...)
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  23. Confirmation bias without rhyme or reason.Matthias Michel & Megan A. K. Peters - 2020 - Synthese 199 (1-2):2757-2772.
    Having a confirmation bias sometimes leads us to hold inaccurate beliefs. So, the puzzle goes: why do we have it? According to the influential argumentative theory of reasoning, confirmation bias emerges because the primary function of reason is not to form accurate beliefs, but to convince others that we’re right. A crucial prediction of the theory, then, is that confirmation bias should be found only in the reasoning domain. In this article, we argue that there is evidence (...)
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  24. Confirmation and explaining how possible.Patrick Forber - 2010 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 41 (1):32-40.
    Confirmation in evolutionary biology depends on what biologists take to be the genuine rivals. Investigating what constrains the scope of biological possibility provides part of the story: explaining how possible helps determine what counts as a genuine rival and thus informs confirmation. To clarify the criteria for genuine rivalry I distinguish between global and local constraints on biological possibility, and offer an account of how-possibly explanation. To sharpen the connection between confirmation and explaining how possible I discuss (...)
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  25. Confirmation and law-likeness.Elliott Sober - 1988 - Philosophical Review 97 (1):93-98.
    Nelson Goodman suggests that a generalization of the form “all A’s are B” is confirmable by an observed instance only if the generalization is law-like. Jackson and Pargetter deny this and give examples of how accidental generalizations can be confirmed. A possible response from Goodman appears to make these accidental generalizations look law-like, but I show it’s defective. And Jackson and Pargetter's substitute nomological condition fares no better than Goodman’s. Because of the multiplicity of possible background assumptions, I doubt that (...)
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  26.  37
    Confirmation by analogy.Francesco Nappo - 2022 - Synthese 200 (1):1-26.
    This paper proposes a framework for representing in Bayesian terms the idea that analogical arguments of various degrees of strength may provide inductive support to yet untested scientific hypotheses. On this account, contextual information plays a crucial role in determining whether, and to what extent, a given similarity or dissimilarity between source and target may confirm an empirical hypothesis over a rival one. In addition to showing confirmation by analogy compatible with the adoption of a Bayesian standpoint, the proposal (...)
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  27. Confirmation, Coherence and the Strength of Arguments.Stephan Hartmann & Borut Trpin - 2023 - Proceedings of the Annual Meeting of the Cognitive Science Society 45:1473-1479.
    Alongside science and law, argumentation is also of central importance in everyday life. But what characterizes a good argument? This question has occupied philosophers and psychologists for centuries. The theory of Bayesian argumentation is particularly suitable for clarifying it, because it allows us to take into account in a natural way the role of uncertainty, which is central to much argumentation. Moreover, it offers the possibility of measuring the strength of an argument in probabilistic terms. One way to do this, (...)
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    Confirmation and explaining how possible.Patrick Forber - 2008 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 41 (1):32-40.
    Confirmation in evolutionary biology depends on what biologists take to be the genuine rivals. Investigating what constrains the scope of biological possibility provides part of the story: explaining how possible helps determine what counts as a genuine rival and thus informs confirmation. To clarify the criteria for genuine rivalry I distinguish between global and local constraints on biological possibility, and offer an account of how-possibly explanation. To sharpen the connection between confirmation and explaining how possible I discuss (...)
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  29. Confirmation versus Falsificationism.Ray Scott Percival - 2015 - In Robin L. Cautin & Scott O. Lilienfeld (eds.), The Encyclopedia of Clinical Psychology. Wiley-Blackwell.
    Confirmation and falsification are different strategies for testing theories and characterizing the outcomes of those tests. Roughly speaking, confirmation is the act of using evidence or reason to verify or certify that a statement is true, definite, or approximately true, whereas falsification is the act of classifying a statement as false in the light of observation reports. After expounding the intellectual history behind confirmation and falsificationism, reaching back to Plato and Aristotle, I survey some of the main (...)
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    Confirmation based on analogical inference: Bayes meets Jeffrey.Christian J. Feldbacher-Escamilla & Alexander Gebharter - 2020 - Canadian Journal of Philosophy 50 (2):174-194.
    Certain hypotheses cannot be directly confirmed for theoretical, practical, or moral reasons. For some of these hypotheses, however, there might be a workaround: confirmation based on analogical reasoning. In this paper we take up Dardashti, Hartmann, Thébault, and Winsberg’s (in press) idea of analyzing confirmation based on analogical inference Baysian style. We identify three types of confirmation by analogy and show that Dardashti et al.’s approach can cover two of them. We then highlight possible problems with their (...)
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  31. Probability, confirmation, and the conjunction fallacy.Vincenzo Crupi, Branden Fitelson & Katya Tentori - 2007 - Thinking and Reasoning 14 (2):182 – 199.
    The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main (...)
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  32. Confirmation.Alan Hájek & James M. Joyce - 2008 - In S. Psillos & M. Curd (eds.), The Routledge Companion to the Philosophy of Science. Routledge.
    Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.
     
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  33. Confirmation and Reduction: a Bayesian Account.Foad Dizadji-Bahmani, Roman Frigg & Stephan Hartmann - 2011 - Synthese 179 (2):321-338.
    Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. (...)
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  34. Confirmational holism and bayesian epistemology.David Christensen - 1992 - Philosophy of Science 59 (4):540-557.
    Much contemporary epistemology is informed by a kind of confirmational holism, and a consequent rejection of the assumption that all confirmation rests on experiential certainties. Another prominent theme is that belief comes in degrees, and that rationality requires apportioning one's degrees of belief reasonably. Bayesian confirmation models based on Jeffrey Conditionalization attempt to bring together these two appealing strands. I argue, however, that these models cannot account for a certain aspect of confirmation that would be accounted for (...)
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  35. Bayesian Confirmation: A Means with No End.Peter Brössel & Franz Huber - 2015 - British Journal for the Philosophy of Science 66 (4):737-749.
    Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry? In this article, we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be making a claim about how worthy of belief various hypotheses are. Then we consider a different use to which Bayesian confirmation might be put, namely, determining the epistemic value of experimental outcomes, (...)
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  36.  61
    Confirmational holism and its mathematical (w)holes.Anthony Peressini - 2008 - Studies in History and Philosophy of Science Part A 39 (1):102-111.
    I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science.
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    Confirmational Response Bias Among Social Work Journals.William M. Epstein - 1990 - Science, Technology and Human Values 15 (1):9-38.
    This article reports the results of a study of confirmational response bias among social work journals. A contrived research paper with positive findings and its negative mirror image were submitted to two different groups of social work journals and to two comparison groups of journals outside social work. The quantitative results, suggesting bias, are tentative; but the qualitative findings based upon an analysis of the referee comments are clear and consistent. Few referees from prestigious or nonprestcgrous social work journals prepared (...)
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  38.  37
    Confirmation, disconfirmation, and information in hypothesis testing.Joshua Klayman & Young-won Ha - 1987 - Psychological Review 94 (2):211-228.
  39. Confirmation, explanation, and logical strength.David E. Nelson - 1996 - British Journal for the Philosophy of Science 47 (3):399-413.
    Van Fraassen argues that explanatory power cannot be a conformational virtue. In this paper I will show that informational features of scientific theories can be positively relevant to their levels of conformation. Thus, in the cases where the explanatory power of a theory is tied to an informational feature of the theory, it can still be the case that the explanatory power of the theory is positively relevant to its level of confirmation.
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  40. Confirmation, Increase in Probability, and the Likelihood Ratio Measure: a Reply to Glass and McCartney.William Roche - 2017 - Acta Analytica 32 (4):491-513.
    Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any (...)
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  41. Dwindling Confirmation.William Roche & Tomoji Shogenji - 2014 - Philosophy of Science 81 (1):114-137.
    We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to (...)
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  42. Coherence & Confirmation: The Epistemic Limitations of the Impossibility Theorems.Ted Poston - 2022 - Kriterion - Journal of Philosophy 36 (1):83-111.
    It is a widespread intuition that the coherence of independent reports provides a powerful reason to believe that the reports are true. Formal results by Huemer, M. 1997. “Probability and Coherence Justification.” Southern Journal of Philosophy 35: 463–72, Olsson, E. 2002. “What is the Problem of Coherence and Truth?” Journal of Philosophy XCIX : 246–72, Olsson, E. 2005. Against Coherence: Truth, Probability, and Justification. Oxford University Press., Bovens, L., and S. Hartmann. 2003. Bayesian Epistemology. Oxford University Press, prove that, under (...)
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  43. Confirmation theory.James Hawthorne - 2011 - In Prasanta S. Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier.
    Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed, or even refuted by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses should largely depend on their empirical content – on what they say the evidentially accessible parts of the world are like, and on the extent to which they turn out to be right about that. Thus, all theories (...)
     
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  44. Confirmation theory and indispensability.Mark Colyvan - 1999 - Philosophical Studies 96 (1):1-19.
    In this paper I examine Quine''s indispensability argument, with particular emphasis on what is meant by ''indispensable''. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine''s argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.
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  45. Why Confirm Laws?Barry Ward - forthcoming - The British Journal for the Philosophy of Science.
    We argue that a particular approach to satisfying the broad predictive ambitions of the sciences demands law confirmation. On this approach we confirm non-nomic generalizations by confirming there are no actually realized ways of causing disconfirming cases. This gives causal generalizations a crucial role in prediction. We then show how rational judgements of relevant causal similarity can be used to confirm that causal generalizations themselves have no actual disconfirmers, providing a distinctive and clearly viable methodology for inductively confirming them. (...)
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  46. Confirming mathematical theories: An ontologically agnostic stance.Anthony Peressini - 1999 - Synthese 118 (2):257-277.
    The Quine/Putnam indispensability approach to the confirmation of mathematical theories in recent times has been the subject of significant criticism. In this paper I explore an alternative to the Quine/Putnam indispensability approach. I begin with a van Fraassen-like distinction between accepting the adequacy of a mathematical theory and believing in the truth of a mathematical theory. Finally, I consider the problem of moving from the adequacy of a mathematical theory to its truth. I argue that the prospects for justifying (...)
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  47.  57
    Confirmation by Robustness Analysis: A Bayesian Account.Lorenzo Casini & Jürgen Landes - forthcoming - Erkenntnis:1-43.
    Some authors claim that minimal models have limited epistemic value (Fumagalli, 2016; Grüne-Yanoff, 2009a). Others defend the epistemic benefits of modelling by invoking the role of robustness analysis for hypothesis confirmation (see, e.g., Levins, 1966; Kuorikoski et al., 2010) but such arguments find much resistance (see, e.g., Odenbaugh & Alexandrova, 2011). In this paper, we offer a Bayesian rationalization and defence of the view that robustness analysis can play a confirmatory role, and thereby shed light on the potential of (...)
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  48.  11
    Confirming (climate) change: a dynamical account of model evaluation.Suzanne Kawamleh - 2022 - Synthese 200 (2):1-26.
    Philosophers of science have offered various accounts of climate model evaluation which have largely centered on model-fit assessment. However, despite the wide-spread prevalence of process-based evaluation in climate science practice, this sort of model evaluation has been undertheorized by philosophers of science. In this paper, I aim to expand this narrow philosophical view of climate model evaluation by providing a philosophical account of process evaluation that is rooted in a close examination of scientific practice. I propose dynamical adequacy as a (...)
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  49. Illegitimate Values, Confirmation Bias, and Mandevillian Cognition in Science.Uwe Peters - 2021 - British Journal for the Philosophy of Science 72 (4):1061-1081.
    In the philosophy of science, it is a common proposal that values are illegitimate in science and should be counteracted whenever they drive inquiry to the confirmation of predetermined conclusions. Drawing on recent cognitive scientific research on human reasoning and confirmation bias, I argue that this view should be rejected. Advocates of it have overlooked that values that drive inquiry to the confirmation of predetermined conclusions can contribute to the reliability of scientific inquiry at the group level (...)
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  50.  46
    Confirmation theory, order, and periodicity.Peter Achinstein - 1963 - Philosophy of Science 30 (1):17-35.
    This paper examines problems of order and periodicity which arise when the attempt is made to define a confirmation function for a language containing elementary number theory as applied to a universe in which the individuals are considered to be arranged in some fixed order. Certain plausible conditions of adequacy are stated for such a confirmation function. By the construction of certain types of predicates, it is proved, however, that these conditions of adequacy are violated by any (...) function defined for the type of language in question. Various possible solutions to these difficulties are explored and found to be inadequate. In particular, a proposal which stems from the suggestion to restrict a fundamental principle of confirmation to hypotheses containing only non-positional predicates is cited. This proposal, however, is shown to prevent confirmation functions from taking periodicities into account, and so is deemed unsatisfactory. A general theorem is proved to the effect that if non-positional predicates are taken to satisfy the conditions of adequacy which have been formulated, then no periodicity predicates whatsoever (i.e., predicates used in formulating hypotheses which foretell periodicities) can be subject to these conditions, on pain of contradiction. Yet it seems that periodicity predicates must be subject to these conditions of adequacy if a confirmation function is to recognize periodic occurrences. Thus, an impasse seems to be reached. In the final sections we consider the beginnings of one possible solution to these difficulties. Our proposal involves treating sets of individuals, rather than individuals themselves, as instances of an hypothesis which predicts a periodicity. On this basis we formulate new conditions of adequacy which are free from the previous difficulties and which will permit a confirmation function that satisfies them to take periodicities into account. (shrink)
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