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The paradigm of embodied cognition provides a perspective for rethinking the nature of experience, intersubjectivity, and the interaction of the human animal with its physical and sociocultural environments. Embodied cognitive science can be a productive framework for the study of aesthetic experience and visual communication, enabling us to transcend the cognitivist paradigm of the twentieth century, understood here as the view that cognition is the rule-based manipulation of symbolic representations in a disembodied and decontextualized mind. Summaries of key concepts of embodied cognition are provided, with suggestions for their use in the exploration of aesthetics and visual language.

A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.