PhilSci Archive

Resolution of the Miller-Popper paradox

Eyre, John (2023) Resolution of the Miller-Popper paradox. [Preprint]

miller-popper paradox resolution deanon revised 231104.pdf

Download (219kB) | Preview


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.

Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Eyre, JohnjohnReyre@btinternet.com0000-0002-9877-392X
Additional Information: Accepted for publication in Synthese
Keywords: scientific theory, predictions, comparison with observations, closeness
Subjects: General Issues > Theory/Observation
Depositing User: Dr John Eyre
Date Deposited: 03 Dec 2023 02:05
Last Modified: 03 Dec 2023 02:05
Item ID: 22806
DOI or Unique Handle: SYNT-D-23-00181R2
Subjects: General Issues > Theory/Observation
Date: 7 November 2023

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item