He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore, and his protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians.With A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics. His philosophical essay "On Denoting" has been considered a 'paradigm of philosophy'. His work has had a considerable influence on logic, mathematics, set theory, linguistics, artificial intelligence, cognitive science, and philosophy, especially the philosophy of language, epistemology, and metaphysics.

Watts and peers including foreword authors Timothy Leary and Richard Alpert (then Harvard professors) anticipated physicists’ recognizing the individual’s “inseparability from the rest of the world,” the work of New Age thinkers who combine scientific findings and spiritual experiences, and federally funded clinical trials utilizing psilocybin to treat a variety of conditions. More than an artifact, The Joyous Cosmology is both a riveting memoir of Watts’s personal experiments and a profound meditation on our perennial questions about the nature of existence and the existence of the sacred.

It’s actually had quite a fundamental [impact] on my life because these are his little snippets of wisdom on almost any imaginable topic, and all of them are brilliant. There are things like, ‘The company of women is schooling in good manners,’ or ‘Boldness has genius, power, and magic.’ Ones you don’t remember in their precise form, but which nonetheless act as little micro filters for interpreting reality.” (Cooke's Notes, Tribe of Mentors)

The patterning of the raindrops on the roofs, the pavement, the lampposts, and the buildings, gives you—because of the echo—a sense of 3-D space, where most of the time your 3-D space only goes a couple of yards in front of you, and otherwise is just the void.” (Cooke’s Notes, Tribe of Mentors)