On confirmation

Hosiasson-Lindenbaum, Janina

doi:10.2307/2268173

Cited by 115 publications

(19 citation statements)

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“…Which of these two correct predictions would leave you more convinced that the forecaster can accurately predict the weather and is not merely guessing? The more informative of the two observations is the correct prediction of rain, the rare event, at least according to Bayesian statistics (Horwich, 1982;Howson & Urbach, 1989; see also Alexander, 1958;Good, 1960;Hosiasson-Lindenbaum, 1940;Mackie, 1963). Qualitatively, the reason for this is that it would not be surprising to correctly predict a sunny day by chance in the desert because almost every day is sunny.…”

Section: Adaptive Behaviormentioning

confidence: 99%

Judgment and Decision Making

McKenzie¹

2005

Handbook of Cognition

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Section: Adaptive Behaviormentioning

confidence: 99%

Judgment and Decision Making

McKenzie¹

2005

Handbook of Cognition

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“…It is easy to show that both (2) and (3) do hold for Carnap's r (proofs omitted).10 An early quantitative resolution of the Ravens Paradox was given byHosiasson- Lindenbaum (1940). Hosiasson-Lindenbaum was not working within a relevance framework.…”

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confidence: 99%

The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity

1999

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Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity.

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“…Because nonblack things and nonravens are both common, observing a nonblack nonraven would not be unusual and would therefore confirm the hypothesis only negligibly. In contrast, because few things are black and few things are ravens, observing a black raven would be surprising and would constitute stronger confirmation (Alexander, 1958;Good, 1960;Horwich, 1982;Hosiasson-Lindenbaum, 1940; Howson & Urbach, 1989,pp. 88-91;Mackie, 1963).1 The paradox appears to stem from our inability to distinguish intuitively between nonconfirmatory and minutely confirmatory evidence: The nonblack nonraven appears completely uninformative but, in fact, provides very weak confirmation.…”

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The psychological side of Hempel’s paradox of confirmation

McKenzie

Mikkelsen

2000

Psychonomic Bulletin & Review

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People often test hypotheses about two variables (X and Y), each with two levels (e.g., Xl and X2). When testing "IfXl, then YI,~observing the conjunction ofXl and Y1 is overwhelmingly perceived as more supportive than observing the conjunction ofX2 and Y2, although both observations support the hypothesis. Normatively, the X2&Y2 observation provides stronger support than the XI&YI observation if the former is rarer. Because participants in laboratory settings typically test hypotheses they are unfamiliar with, previous research has not examined whether participants are sensitive to the rarity of observations. The experiment reported here showed that participants were sensitive to rarity, even judging a rare X2&Y2 observation more supportive than a common XI&YI observation under certain conditions. Furthermore, participants' default strategy ofjudgingXI&YI observations more informative might be generally adaptive because hypotheses usually regard rare events.A fundamental issue in the study of human inference is what, psychologically speaking, constitutes confirmatory evidence for a hypothesis. In 1945, philosopher Carl Hempel noted the following paradox regarding confirmatory evidence. Assume that the hypothesis of interest is "All ravens are black." This statement can be rewritten as "If something is a raven, then it is black," or RavenB lack. Clearly, observing a black raven would count as confirming evidence. Similarly, if the hypothesis were "If something is not black, then it is not a raven," or -Black~-Raven, observing a nonblack nonraven (e.g., a white shoe or a yellow pencil) would clearly be confirming evidence. Because these two hypotheses are logically equivalent (one is the contrapositive ofthe other), any evidence that confirms one must confirm the other. It follows, then, that observing a nonblack nonraven confirms Raven~Black. Thus, one could apparently confirm the hypothesis about the color of ravens by sitting in one's office and never even observing a raven. Most people find this highly counterintuitive; hence, the paradox.Other philosophers have pointed out that the paradox can be resolved if one conceives of confirmation as a matter of degree rather than all-or-none. Although black ravens and nonblack nonravens both confirm RavenB lack, they do not do so equally strongly. From a Bayesian perspective, confirming evidence supports a hypothesis to the extent that it is rare, or surprising. Because nonblack things and nonravens are both common, observing a nonblack nonraven would not be unusual and would therefore confirm the hypothesis only negligibly. In contrast, because few things are black and few things are ravens, observing a black raven would be surprising and would constitute stronger confirmation (Alexander, 1958;Good, 1960;Horwich, 1982;Hosiasson-Lindenbaum, 1940; Howson & Urbach, 1989,pp. 88-91;Mackie, 1963).1 The paradox appears to stem from our inability to distinguish intuitively between nonconfirmatory and minutely confirmatory evidence: The nonblack nonraven appears completely u...

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On confirmation

Cited by 115 publications

References 1 publication

Judgment and Decision Making

Judgment and Decision Making

The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity

The psychological side of Hempel’s paradox of confirmation

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