Theoretical objections to hypothesis testing 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.
 A: This paper characterizes the publication/scientific practice in psychology as being a ritual of finding p<.05. They argue against hypothesis testing without solid theoretical basis. Note, though, that it is--if at all--more philosophical than anything else. But maybe it helps.
A: Well, try virtually any book about Bayesian statistics. I haven't find one that doesn't have at least a few paragraphs debunking practice of significance testing. Really. And Gelman's books are good example of that. I used to remember relevant titles (I still remember my first one: E.T. Jaynes "Probability theory - the logic of science". Jaynes definitely wrote with passion, and the controversy over significance testing is something, that really made me do statistics professionally ;-) ), but soon I got overwhelmed by the abundance of literature on this topic. 
Try also the phrase +bayesian significance testing fisher in Google Scholar and I guarantee you will find at least dozen good references (and some interesting info too).
A: I'm reading an article right now called "Principles of Inference and Their Consequences" by D.G. Mayo and M. Kruse. It's a good article so far about how hypothesis testing can violate principles like the likelihood principle(LP). They go through a concrete example of coin-tossing and show how the concept of statistical significance violates the LP. 
