Resolution of the Miller-Popper paradox.
A longstanding paradox was first reported by David Miller in 1975 and highlighted by Karl Popper in 1979. Miller showed that the ranking of predictions from two theories, in terms of closeness to observation, appears to be reversed when the problem is transformed into a different mathematical space....
| Published in: | Synthese Vol. 203; no. 1; pp. 1 - 14 |
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| Format: | Article |
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Springer Nature
Jan2024
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=174268032&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 174268032 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jan2024 vid: 203 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 174268032 10.1007/s11229-023-04425-7 ppf: 1 ppct: 13 formats: fmt: – @attributes: type: T – @attributes: type: P size: 312KB tig: atl: Resolution of the Miller-Popper paradox. aug: au: Eyre, John affil: Retired, Formerly Met Office, Exeter, UK su: Popper, Karl Raimund, Sir, 1902-1994 Paradox Gaussian measures Probability theory Gaussian distribution sug: subj: Popper, Karl Raimund, Sir, 1902-1994 Paradox Gaussian measures Probability theory Gaussian distribution keyword: Closeness Comparison with observations Predictions Scientific theory ab: A longstanding paradox was first reported by David Miller in 1975 and highlighted by Karl Popper in 1979. Miller showed that the ranking of predictions from two theories, in terms of closeness to observation, appears to be reversed when the problem is transformed into a different mathematical space. He concluded that "... no false theory can ... be closer to the truth than is another theory". This flies in the face of normal scientific practice and is thus paradoxical; it is named here the "Miller-Popper paradox". This paper proposes a resolution of the paradox, through consideration of the inevitable errors and uncertainties in both observations and predictions. It is proved that, for linear transformations and Gaussian error distributions, the transformation between spaces creates no change in quantitative measures of "closeness-to-observation" when these measures are based in probability theory. The extension of this result to nonlinear transformations and to non-Gaussian error distributions is also discussed. These results demonstrate that concepts used in comparison of predictions with observations—concepts of "closeness", "consistency", "agreement", "falsification", etc.—all imply some knowledge of the uncertainty characteristics of both predictions and observations. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2024. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
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