Concepts are the elementary units of reason and linguistic meaning. They are conventional and relatively stable. As such, they must somehow be the result of neural activity in the brain. The questions are: Where? and How? A common philosophical position is that all concepts—even concepts about action and perception—are symbolic and abstract, and therefore must be implemented outside the brain's sensory-motor system. We will argue against this position using (1) neuroscientific evidence; (2) results from neural computation; and (3) results about the nature of concepts from cognitive linguistics. We will propose that the sensory-motor system has the right kind of structure to characterise both sensory-motor and more abstract concepts. Central to this picture are the neural theory of language and the theory of cogs, according to which, brain structures in the sensory-motor regions are exploited to characterise the so-called “abstract” concepts that constitute the meanings of grammatical constructions and general inference patterns.

The automatic translation of folk psychology into newly formed brain modules specifically dedicated to mind-reading and other social cognitive abilities should be carefully scrutinized. Searching for the brain location of intentions, beliefs and desires— as such —might not be the best epistemic strategy to disclose what social cognition really is. The results of neurocognitive research suggest that in the brain of primates, mirror neurons, and more generally the premotor system, play a major role in several aspects of social cognition, from action and intention understanding to language processing. This evidence is presented and discussed within the theoretical frame of an embodied simulation account of social cognition. Embodied simulation and the mirror neuron system underpinning it provide the means to share communicative intentions, meaning and reference, thus granting the parity requirements of social communication.

It has been proposed that the capacity to code the ‘like me’ analogy between self and others constitutes a basic prerequisite and a starting point for social cognition. It is by means of this self/other equivalence that meaningful social bonds can be established, that we can recognize others as similar to us, and that imitation can take place. In this article I discuss recent neurophysiological and brain imaging data on monkeys and humans, showing that the ‘like me’ analogy may rest upon a series of ‘mirror–matching’ mechanisms. A new conceptual tool able to capture the richness of the experiences we share with others is introduced: the shared manifold of intersubjectivity. I propose that all kinds of interpersonal relations (imitation, empathy and the attribution of intentions) depend, at a basic level, on the constitution of a shared manifold space. This shared space is functionally characterized by automatic, unconscious embodied simulation routines.