The most pressing question about cognitive brains is how they support the compositionality that enables combinatorial manipulations of images, thoughts, and actions. When addressing this problem with synthetic modeling, the conventional idea prevalent in artificial intelligence and cognitive science, generally, is to assume hybrid systems and corresponding neural network models, where higher order cognition is realized by means of symbolic representation and lower sensory-motor processes by analog processing. However, the crucial problem with such approaches is that the symbols represented at higher order cognitive levels cannot be grounded naturally in sensory-motor reality. The former are defined in a discrete space without any metric, and the latter are defined in a continuous space with a physical metric. These, therefore, cannot directly interact with each other, regardless of the interface that is assigned between them. The proposal in the current paper is to reconstruct higher order cognition by means of continuous neurodynamic systems that can elaborate delicate interactions with the sensory-motor level while sharing the same metric space. Our neurorobotics experiments-including language-action associations and the learning of goal-directed actions-show that the compositionality necessary for higher order cognitive tasks can be acquired by means of self-organizing dynamic structures, via interactive learning between the top-down intentional process of acting on the physical world and the bottom-up recognition of perceptual reality. Using robotic simulations, the current paper demonstrates that nonlinear dynamic phenomena, such as bifurcations and the chaotic dynamics induced by unstable fixed points, could play essential roles in realizing higher order functions.