- Lecturer in Mathematics, University of Leeds (England, UK), 1951-1955
- Lecturer in History and Philosophy of Science, University of London, University College (England, UK), 1955-1959
- Lecturer in Philosophy of Science, University of Cambridge (England, UK), 1960-1968
Member of the Council of Senate, 1962-1966
Visiting Professor at Yale University (US), 1962-63
Visiting Professor at the 'Minnesota Center for the Philosophy of Science', University of Minnesota (US), 1966
- University Reader in Philosophy of Science, University of Cambridge (England, UK), 1968-1975
Visiting Professor at the University of Chicago (US), 1968
Visiting Professor at the University of Notre Dame (US), 1972
- Professor of Philosophy of Science, University of Cambridge (England, UK), 1975-1985
Stanton Lecturer, University of Cambridge (England, UK), 1978-80
Gifford Lecturer (joint), University of Edinburgh (Scotland, UK), 1983
Doctor of Science honoris causa, University of Hull (England, UK), 1984
- Professor Emerita of the Philosophy of Science, University of Cambridge (England, UK), 1986-present
Doctor of Science honoris causa, University of Guelph (Ontario, Canada), 1987
Doctor of Science honoris causa, University of Cambridge (England, UK), 2002