The Founder of Modern Temporal Logic

A Brief Story of Arthur N. Prior

Prior went to Otago University at Dunedin in 1932. He set out to study medicine, but after a short time he instead went into philosophy and psychology. In 1934 he attended Findlay's courses on ethics and logic. Through Findlay Prior became interested in the history of logic and was introduced to Prantl's textbooks. His M.A. thesis was devoted to this subject. In 1949 Prior wrote about Findlay: "I owe to his teaching, directly or indirectly, all that I know of either Logic or Ethics".

Prior was brought up as a Methodist, but while he was a student he came to consider Methodistic theology too unsystematic, and he became a Presbyterian. He also became a very active member of the Student Christian Movement (SCM). In the years about 1940 he found himself in a crisis of belief. During these years he wrote the article 'Can religion be discussed?'(1942), in which he advocated an almost atheistic position. This view, however, does not seem to have lasted very long. He continued to treasure his theological library and to join the work of the SCM. Later in his life, however, he became an agnostic.

In 1943 he married Mary. From 1946 to 1958 he taught philosophy at Canterbury University College in New Zealand. In 1953 he became a professor of philosophy. In 1949 his book Logic and the Basis of Ethics had been published. After that time he became even more interested in logical problems. During 1950 and 1951 he wrote a manuscript for a book with the working title The Craft of Logic. This book was, however, never published as a whole, but in 1976 P. T. Geach and A. J. P. Kenny edited parts of it. In the first chapter of the book, Propositions and Sentences, the author among other things analysed Aristotle's view on some of the problems concerning time and tense. Prior found that according to the ancient as well as the medieval view a proposition may be true at one time and false at another.

In the following years Prior worked mainly on questions in the history of logic. From 1952 to 1955 he had seven articles on the history of logic published. Four of these were concerned with Medieval logic and one with Diodorean logic. His interest in the history of logic is also evident in his Formal Logic, published in 1955. According to Mary Prior his resurging interest in the history of logic was very much due to the fact that the university library bought Bochenski's Précis de Logique Mathématique (1948).

It seems that a short article by Benson Mates in 1949 made Prior even more aware of the interesting relation between time and logic. The paper was concerned with Diodorean logic, primarily Diodorus' definition of implication. Prior seemed to realise that it might be possible to relate Diodorus' ideas to contemporary works on modality by developing a calculus which included temporal operators analogous to the operators of modal logic. Mary Prior has described the first occurrence of this idea: "I remember his waking me one night, coming and sitting on my bed, and reading a footnote from John Findlay's article on Time, and saying he thought one could make a formalised tense logic." This must have been some time in 1953.

Findlay's considerations on the relation between time and logic in this footnote were not very elaborated, but it gave Prior the idea of developing a formal calculus which would capture this relation in detail. For this reason Prior called Findlay "the founding father of modern tense logic". But there are, in our opinion, certainly not sufficient reasons for viewing Findlay as the founder of tense logic. The honour of being the founder must without doubt be attributed to Prior himself. With his many articles and books on questions in tense logic he presented a very extensive and thorough corpus, which still forms the basis of tense logic as a discipline. Findlay's major merit in tense logic is to have had the luck of inspiring Prior to initiate the development of formal tense logic.

A. N. Prior must be said to have laid the foundation for modern tense-logic. He revived the medieval attempt at formulating a temporal logic for natural language. Therefore his work also established a paradigm applicable to the exact study of the logic of natural language. Prior held that logic should be related as closely as possible to intuitions embodied in everyday discourse, and his tense logic can indeed account for a large number of linguistic inferences. In the 1950's and 1960's he laid out the foundation of tense-logic and showed that this important discipline was intimately connected with modal logic. Prior also argued that temporal logic is fundamental for understanding and describing the world in which we live. He regarded tense and modal logic as particularly relevant to a number of important theological problems. Using his temporal logic Prior analysed the fundamental question of determinism versus freedom of choice.

As a teacher Prior was very inspiring. He was always able to find nice and understandable illustrations of the logical systems he wanted to introduce. It seems clear that he very much liked teaching and lecturing. He was not 'the Oxford type', but it appears that he almost immediately build up a reputation as one of the best lecturers in Oxford.

Prior died on October 6th., 1969, whilst on a lecture tour in Scandinavia. On the day of his death he was visiting Trondheim in Norway. Prior had by then accomplished an impressive production. The bibliographical overview of Prior's philosophical works comprises more than 150 titles. In this overview one can follow how Prior's interests developed in the course of his work. Summarising the main trends it can be said that his work until the middle of the 1950's was characterised by a preoccupation with ethics and the history of logic. From the mid-fifties and onwards he devoted himself mainly to the study of the relation between time, modality, and logic. That should be seen as a natural consequence of his endeavour to develop the formal calculus of tense logic, a task which he took up around 1953 (at the time of being inspired by Findlay's footnote).