Our brains make up a series of signs and are engaged in making or manifesting or reacting to a series of signs: through this semiotic activity they are at the same time engaged in being minds and so in thinking intelligently. An important effect of this semiotic activity of brains is a continuous process of externalization of the mind that exhibits a new cognitive perspective on the mechanisms underlying the emergence of abductive processes of meaning formation. To illustrate this process I have taken advantage of the analysis of some aspects of the cognitive interplay between internal and external representations. I consider this interplay critical in analyzing the relation between meaningful semiotic internal resources and devices and their dynamical interactions with the externalized semiotic materiality suitably stocked in the environment. Hence, minds are material, extended and artificial in themselves. I have recently provided concrete examples relating my philosophical points to neuroanatomy and neuropsychology taking advantage of an analysis of some aspects of animal cognition and of the concept of direct and indirect affordance.