From 1921 to 1933, Günther studied sinology and philosophy at the universities of Heidelberg and Berlin, and wrote his doctor's thesis on Hegel in 1933 under the guidance of Eduard Spranger.
From 1935 to 1937, he worked at the institute of Arnold Gehlen at the University of Leipzig, publishing Christliche Metaphysik und das Schicksal des modernen Bewusstseins (Christian metaphysics and the fate of modern consciousness, together with Helmut Schelsky in 1937).
In the same year, following his wife, the Jewish psychologist Dr. Marie Günther-Hendel, he emigrated from Germany first to Italy, afterwards to Stellenbosch University in South Africa and, in 1940, to the United States.
His great study Die philosophische Idee einer nicht-Aristotelischen Logik (“The philosophical concept of a non-Aristotelian logic”) went to print in 1957 (Hamburg, Meiner).
As a research professor, he joined the department of electrical engineering at the University of Illinois at Urbana-Champaign in 1960, working together with Warren Sturgis McCulloch, Heinz von Foerster, Humberto Maturana and others.