This paper inquires into the nature of intertheoretic relations between psychology and neuroscience. This relationship has been characterized by some as one in which psychological explanations eventually will fall away as otiose, overthrown completely by neurobiological ones. Against this view it will be argued that it squares poorly with scientific practices and empirical developments in the cognitive neurosciences. We analyse a case from research on visual perception, which suggests a much more subtle and complex interplay between psychology and neuroscience than (...) a complete take-over of the former by the latter. In the case of vision, cross-theory influences between psychology and neuroscience go back and forth, resulting in refinement in both disciplines.We interpret this case study as showing that:(1) Mutual co-evolution of psychological and neurobiological theories, exemplifying persisting top-down influences from psychology, is a more empirically adequate way to describe psychoneural theory relations than a view on co-evolution, favoured by reductionists, which regards the cross-theory contributions from psychology as merely heuristically useful with no enduring influence on neurobiological theorizing;(2) In research on vision, discovering (or hypothesizing) the neural basis of functions vindicates psychological approaches, it does not eliminate them;(3) Current work on vision shows that many perceptual phenomena must be understood in terms of dynamical interactions between an observer and his/her environment. Therefore, we argue that internalist characterizations of the visual system must be supplemented with externalist accounts that address these reciprocal observer-environment interactions involved in vision. Such processes seem quite different from (internal) cellular and molecular ones, and as such seem to lie outside the scope of neuroscientific inquiry. We conclude that psychoneural reduction or elimination is implausible as a meta-theoretical prediction of theory choice in empirical work. Instead, this case study of vision shows that both psychology and neuroscience contribute to, and complement one another in the study of visual perception. 1. Psychoneural reductionism1.1Introduction1.2New Wave Reductionism1.3NWR and psychology: three characteristics of psychoneural reductionism1.4NWR and the problem of mutual feedback1.4.1The ‘Mere Heuristics’ claim1.4.2The disappearance of psychology as an irrelevant historical accident1.5Summary: three claims of NWR on psychoneural reduction2. Vision: a case study2.1Introduction2.1.1Three opposing claims2.1.2Psychology and neuroscience of vision: the orthodoxy2.2Testing claim 1: vanishing heuristics or persisting influences?2.2.1From what and where to perception and action2.2.2Real co-evolution: more than vanishing heuristics2.2.3First moral2.3Testing claim 2: replacement or vindication?2.3.1Perception and action revisited: mapping approaches on systems2.3.2Vindicating psychological approaches2.3.3Second moral2.4Testing claim 3: equipotent image or explanatory loss?2.4.1Perception and action extended: including the environment2.4.2Distinguishing levels, widening explanations2.4.3Third moral3. Conclusion: three morals. (shrink)