Peter Geach spent his earliest years in Cardiff.. He received instruction in logic and philosophy from his father who, as a member of the Indian Educational Service, had been Professor of Philosophy at Lahore and later Principal of a teacher training college in Peshawar.
Geach spent a year (1938-39) as a Gladstone Research Student, based at St Deiniol’s Library, Hawarden. Following the end of World War II in 1945, he undertook further research at Cambridge.
In 1951, Geach was appointed to his first substantive academic post, as Assistant Lecturer at the University of Birmingham, going on to become Reader in Logic. In 1966 he was appointed Professor of Logic in the Department of Philosophy at the University of Leeds. Geach retired from his chair in 1981 with the title Emeritus Professor of Logic. He also held Visiting Professorships at the universities of Cornell, Chicago, Michigan, Pennsylvania and Warsaw.