  Can new cosmic physics be uncovered through tensions amongst datasets?
Tensions in parameter determinations amongst different types of cosmological
observation, especially the `Hubble tension' between probes of the expansion
rate, have been invoked as possible indicators of new physics, requiring
extension of the $\Lambda$CDM paradigm to resolve. Within a fully Bayesian
framework, we show that the standard tension metric gives only part of the
updating of model probabilities, supplying a data co-dependence term that must
be combined with the Bayes factors of individual datasets. This shows that, on
its own, a reduction of dataset tension under an extension to $\Lambda$CDM is
insufficient to demonstrate that the extended model is favoured. Any analysis
that claims evidence for new physics {\it solely} on the basis of alleviating
dataset tensions should be considered incomplete and suspect. We describe the
implications of our results for the interpretation of the Hubble tension.
