Eyre, John
(2024)
Corroboration and uncertainty.
[Preprint]
Abstract
In science, uncertainty is always with us, both in observations and in predictions from theory. This paper investigates the important role played by uncertainty in two related problems in philosophy of science: corroboration and the language-dependence of closeness to truth. When predictions from theory are confronted with observations, the theories can be falsified or corroborated. This is an iterative process, since new observations may falsify a previously corroborated theory. Quantification of uncertainty is crucial in determining whether a prediction is consistent with an observation or not. Moreover, quantitative measures of corroboration must be time-dependent, because they rely on estimates of uncertainty, which are always open to reassessment. We also discuss some consequences of these ideas on corroboration for theories of verisimilitude.
In response to Karl Popper’s original concept of verisimilitude, Pavel Tichý offered an alternative method for ranking theories in terms of closeness to truth. David Miller raised objections, showing that rankings within Tichý’s system did not survive transformation into a different mathematical space. This problem is named here the “Miller-Tichý paradox”, and it has implications for the language-dependence of closeness to truth. We show how this paradox can be resolved by taking account of the inevitable uncertainties in observations and in predictions from theory.
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