Originally given the Hebrew name "Peretz," Weiss says in his autobiography that the name "Paul" was his "registered name" and "part of his mother's attempt to move upward in the American world.
At the College of the City of New York, he studied with Morris R. Cohen, who awakened in him an interest in the American pragmatist and logician Charles Sanders Peirce.
from the City College of New York, Weiss immediately enrolled at Harvard, where he studied philosophy under Étienne Gilson, William Ernest Hocking, C. I. Lewis, Ralph Barton Perry, and Alfred North Whitehead.
C. I. Lewis, who was at the time the department chair of philosophy at Harvard, eventually approved Weiss to work alongside Hartshorne for the remainder of the project.
As Weiss explains, Bryn Mawr was at the time "the self-chosen destination of the most intellectual, intelligent, determined, and well-prepared young women in America.
Weiss and his son Jonathan, a lawyer and director of Legal Services for the Elderly in New York, challenged the Catholic University of America's decision.
The Equal Employment Opportunity Commission investigated the case and eventually ruled in Weiss's favor.
He even published eleven volumes under the title Philosophy in Process, detailing his continuing and sometimes daily reflections over the years 1955–1987.
A recurring point in Weiss's philosophy is the claim that Being consists of a plurality of individuals that are unified by universality, which gives a structure to all there is, but that it is also irreducible in four distinct ways.
Weiss was opposed to various philosophies that were popular at the time, including that of the analytics, that of the logical positivists, and that of the Marxists.
After his death, his remaining papers and his extensive library (and also the legal papers, French and Russian translations, novels, and other non-fiction books of his son) were bequeathed to the Institute for American Thought housed at Indiana University–Purdue University Indianapolis (IUPUI) and the IUPUI University Library.
The exchange was featured in Raoul Peck's documentary I Am Not Your Negro, and described by media reviewer A. O. Scott: the "initial spectacle of mediocrity condescending to genius is painful, but the subsequent triumph of [Baldwin's] self-taught brilliance over credentialed ignorance is thrilling to witness".