Pap entered the Juilliard School of Music where he spent a term before starting his studies at Columbia in the fall of 1941.
Ernst Cassirer, who was guest professor at Yale from 1941 to 1944, became his supervisor and provided the original stimulus for Pap's work on hypothetical necessity and the functional a priori.
In 1944 Pap went back to Columbia where he completed his PhD thesis under the supervision of Ernest Nagel, who first rejected the manuscript.
Pap started teaching at various universities and had the opportunity to meet some leading philosophers, notably Rudolf Carnap, with whom he developed a lasting friendship.
Returning from Europe, Pap stayed briefly at Lehigh University, then took succession from Carl Hempel as analytic philosopher of science at Yale.