  Mathematical approaches to modeling the mind since the 1950s are reviewed.
Difficulties faced by these approaches are related to the fundamental
incompleteness of logic discovered by K. G\"odel. A recent mathematical
advancement, dynamic logic (DL) overcame these past difficulties. DL is
described conceptually and related to neuroscience, psychology, cognitive
science, and philosophy. DL models higher cognitive functions: concepts,
emotions, instincts, understanding, imagination, intuition, consciousness. DL
is related to the knowledge instinct that drives our understanding of the world
and serves as a foundation for higher cognitive functions. Aesthetic emotions
and perception of beauty are related to 'everyday' functioning of the mind. The
article reviews mechanisms of human symbolic ability, language and cognition,
joint evolution of the mind, consciousness, and cultures. It touches on a
manifold of aesthetic emotions in music, their cognitive function, origin, and
evolution. The article concentrates on elucidating the first principles and
reviews aspects of the theory proven in laboratory research.
