How Bayesian Confirmation Theory Handles the Paradox of the Ravens

Fitelson, Branden; Hawthorne, James

doi:10.1007/978-90-481-3615-5_11

Cited by 41 publications

(35 citation statements)

References 30 publications

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“…Remember Hempel's diagnosis that tacitly introduced or deliberately suppressed background information is the source of the paradox. While perfectly agreeing with Hempel on this point, Fitelson and Hawthorne (2009) point out that Hempel is unable to make that difference in his own theory of confirmation. The reason is that his account is in general monotone with regard to the background knowledge: As long as the domain of the evidence is not extended (i.e.…”

mentioning

confidence: 62%

“…But comparative results can at least substantiate some of our intuitions about the paradox. The most recent and ambitious result in the area is due to Fitelson and Hawthorne (2009). They have argued that with the help of two apparently innocent assumptions, the raven paradox can be solved:…”

Section: The Comparative Paradoxmentioning

confidence: 99%

“…(The proof can be found in Fitelson and Hawthorne 2009.) The theorem asserts that the degree of support which Ba.Ra lends to H, as measured by the log-likelihood ratio l, exceeds the degree of support ¬Ba.¬Ra lends to H (see (3)).…”

Section: The Comparative Paradoxmentioning

confidence: 99%

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Hempel and the Paradoxes of Confirmation

Sprenger¹

2011

Handbook of the History of Logic

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mentioning

confidence: 62%

Section: The Comparative Paradoxmentioning

confidence: 99%

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Hempel and the Paradoxes of Confirmation

Sprenger¹

2011

Handbook of the History of Logic

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“…However, Hempel's own account of confirmation is inconsistent with this analysis (Fitelson and Hawthorne 2010): relative to the background knowledge…”

Section: Classical Problems For Qualitative Accountsmentioning

confidence: 95%

A Synthesis of Hempelian and Hypothetico-Deductive Confirmation

Sprenger

2013

Erkenn

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This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypotheticodeductive traditions in confirmation theory. Our merger of these two approaches solves classical problems such as the tacking paradoxes and the raven paradox and is subsequently extended to the piecemeal confirmation of entire theories. We compare our proposal to rivalling suggestions and discuss its merits and drawbacks, especially vis-à-vis Bayesianism.

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“…They quantify the degree to which the evidence in the rule's premise E provides support for or against the hypothesised piece of evidence in the rule's conclusion H (Fitelson, 2001). More formally, for a rule E → H, an interestingness measure c(H, E) has the property of Bayesian confirmation (i.e., it is a confirmation measure) when it satisfies the following conditions (1):…”

Section: Application Of the Visualization Techniquesmentioning

confidence: 99%

Can interestingness measures be usefully visualized?

Susmaga

Szczźch

2015

International Journal of Applied Mathematics and Computer Science

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The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional data may be effectively represented in three dimensions using a tetrahedron-based barycentric coordinate system. At the same time, an additional, scalar function of the data (referred to as the operational function, e.g., any interestingness measure) may be rendered using colour. Throughout the paper a particular group of interestingness measures, known as confirmation measures, is used to demonstrate the capabilities of the visualization techniques. They cover a wide spectrum of possibilities, ranging from the determination of specific values (extremes, zeros, etc.) of a single measure, to the localization of pre-defined regions of interest, e.g., such domain areas for which two or more measures do not differ at all or differ the most.

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How Bayesian Confirmation Theory Handles the Paradox of the Ravens

Cited by 41 publications

References 30 publications

Hempel and the Paradoxes of Confirmation

Hempel and the Paradoxes of Confirmation

A Synthesis of Hempelian and Hypothetico-Deductive Confirmation

Can interestingness measures be usefully visualized?

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