The conflict between the positivsts and the Quartet looks a battle beteen the sexes. The sexist males frown on the cognitive relevance of emotions, while the females champion emotions because, as the stereotype would have it, they're more in touch with their emotions or the men are more repressed.
Would the positivists really deny the causal power of emotions, though? Wasn't the dispute about the cognitive relevance of emotions to reason? Emotions have meaning as natural indicators of their cause, but there's no logic to the emotions, no emergent order there that's susceptible to an epistemic analysis.
In any case, positivism or hyper-empiricism collapsed in philosophy. Psychologists have largely taken over, and they often argue that emotions act as evolved quasi-algorithms, or as intuitive, heuristic ways of solving problems and of coming to a decision. The question for rationalists, then, is whether logic and science are more anomalous and independent of that practical grounding.