In our paper we discuss the Berlin Gestalt theory, its relation to modelling with artificial neural networks and ask if Gestalt theory may serve as a paradigm for future research on music perception in the realm of (computational) auditory perceptual organization. To answer this question, we made a logical analysis of important Gestaltist concepts from the point of view of philosophy of science, discuss a particular model of brain functioning and perception which is often assumed to be a modified follow up of Gestalt theory, and study Gestalt theory in relation to modelling perceptual organization with artificial neural networks using some well known facts from automata theory. The paper is divided into three parts: (i) Gestalt theoretical concepts such as "Gestaltqualität", functional whole ("Wirkungszusammenhang") and emergence are studied in discussing prior logical interpretations of Gestalt theory, (ii) K. Pribram's holographic brain metaphor is discussed in relation to W. Köhler's concept of a functional whole and related to artificial neural network research, (iii) the relevance of Gestalt theory — especially the principle of "Prägnanz" and the concept of a functional whole — in connection to artificial neural networks for research on perceptual organization is analysed. The idea of emergent computations is discussed with regard to concepts from automata theory. In our conclusion we present an answer to our main question and give some hints for future research.