Stegmüller can be credited with essential contributions to the dissemination of ideas of analytical philosophy and philosophy of science in the German-speaking world. In his inaugural lecture at the University of Innsbruck, he outlined the four problems in epistemology, which he focussed on in his later work:
In his books Das Wahrheitsproblem und die Idee der Semantik, and Unvollständigkeit und Unentscheidbarkeit Stegmüller disseminated the ideas of Alfred Tarski and Rudolf Carnap on semantics and logics as well as those of Kurt Gödel on mathematical logic. Later similar works are on Die Antinomien und ihre Behandlung as well as Strukturtypen der Logik.
Epistemology
One of the most influential books of Stegmüller is "Metaphysik, Skepsis, Wissenschaft". In this work, he discusses the epistemological foundations of metaphysics, scepticism, and science. He demonstrates that any search for epistemological fundamentals will necessarily lead to the problem of the evidence — which Stegmüller does not regard as solvable. He also refuses the potential solution that universal skepticism is self-refuting. Even if it were self-refuting, universal skepticism can be stated if the skeptic does not try to justify it. In consequence, explicit conditions are necessary in metaphysics as well as in science. This means that neither can be fundamentally justified but do presuppose a decision. A further focus of Stegmüller's work was phenomenalism. In "Der Phänomenalismus und seine Schwierigkeiten", he describes the extreme problems, which hinder a stringent implementation of the phenomentalist program.
Philosophy of science
Stegmüller is regarded as one of the leading philosophers of science of the second half of the 20th century. Deeply influenced by Thomas S. Kuhn and Joseph D. Sneed, he and several co-workers expanded upon the ideas of Sneed in order to overcome the prevalent rationality crisis of the science that was often regarded as a consequence of Kuhn's works. Furthermore, this led him to a new answer to the problems of theoretical concepts. This line of investigations is today known as the ""structural theory of the empirical sciences".
Selected publications
Das Wahrheitsproblem und die Idee der Semantik, 1957
Unvollständigkeit und Unentscheidbarkeit, 1959
Einheit und Problematik der wissenschaftlichen Welterkenntnis, 1967
Metaphysik-Skepsis-Wissenschaft, 1969
Probleme und Resultate der Wissenschafttheorie und Analytischen Philosophie
*Band I, Erklärung-Begründung-Kausalität, 1983
*Band II, Theorie und Erfahrung, 1974
**1. Teilband: Theorie und Erfahrung, 1974
**2. Teilband: Theorienstrukturen und Theoriendynamik, 1985
**3. Teilband: Die Entwicklung des neuen Strukturalismus seit 1973, 1986
*Band III, Strukturtypen der Logik, 1984
*Band IV, Personelle und statistische Wahrscheinlichkeit, 1973
**1. Halbband: Personelle Wahrscheinlichkeit und rationale Entscheidung, 1973