Are cosmological theories compatible with all possible evidence: A missing methodological link

Abstract
This paper argues that our current best cosmological theories, according to which cosmos is very big are compatible with all possible evidence. The problem is unrelated to the Quine-Duhem underdetermination thesis. The compatibility to which this paper draws attention is much more radical: it appears as if all of our best cosmological theories are perfectly probabilistically compatible with all possible evidence and that no empirical discovery could give us any reason whatever to favor one such theory over another. This consequence is absurd. In order to create an evidential link between cosmological theory and observation, a new methodological principle is needed. A candidate for such a principle is proposed, using a Bayesian framework that takes account of observation selection effects. Various applications in other scientific fields are considered.
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