We've all seen how $p$-values can be misinterpreted to draw false inferences. However, I'm interested in learning more about theoretical/mathematical/philosophical objections to the hypothesis-testing-paradigm, ie. I'd like to learn why someone would prefer (say) a likelihood ratio over a hypothesis test.
I've read some articles by Andrew Gelman on this topic, but I'm trying to find more literature. Any help would be greatly appreciated.