Although there are many debates about the distribution of consciousness (or subjective experiencing), there is a general agreement among biologists that the only consciousness that we are currently aware of is the consciousness of living beings. I present a view of biological consciousness developed by Simona Ginsburg and myself, which conceptualizes consciousness as a biological mode of being and investigates it using an evolutionary approach. We adopt a methodology suggested by the Hungarian system- chemist Tibor Gánti for the study of minimal life to the study of minimal consciousness. We start by listing the set of capacities that are deemed necessary for minimal consciousness by biology- oriented scholars, and follow it by identifying a single capacity, an evolutionary transition marker, which, when present, entails the complete set of the consciousness-characterizing capacities and points to the completion of the evolutionary transition to a new sustainable mode of being (minimal consciousness in our case). The evolutionary transition marker that we suggest is a form of domain- general, open-ended associative learning, which we call unlimited associative learning (UAL). We argue that the organizational dynamics of UAL constitute the dynamics of minimal consciousness and put forward a toy model of UAL. We suggest that the neural implementation of UAL evolved over time and that a comparative study of UAL in different animal groups can resolve some of the current debates about the necessary and sufficient conditions for consciousness and inform us about the different forms it takes. I end with some theoretical generalizations and predictions stemming from the UAL model.