Time in Philosophical Logic • Peter Øhrstrøm Aalborg University Aalborg Denmark • Per F. V. Hasle Aalborg University Aalborg Denmark

The aim of the study of time in philosophical logic is to provide a conceptual framework for an interdisciplinary study of the nature of time and to formalize and study various conceptions and systems of time. In addition, the introduction of time into logic has led to the development of formal systems, which are particularly well suited to represent and study temporal phenomena such as program execution, temporal databases, and argumentation in natural language.

Historical Background

The philosophy of time is based on a long tradition, going back to ancient thought. It is an accepted wisdom within the field that no attempt to clarify the concept of time can be more than an accentuation of some aspects of time at the expense of others. Plato's statement that time is the "moving image of eternity" and Aristotle's suggestion that "time is the number of motion with respect to earlier and later" are no exceptions (see [17]). According to St. Augustine (354-430) time cannot be satisfactorily described using just one single definition or explanation: "What, then, is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not." [5, p. 40] Time is not definable in terms of other concepts. On the other hand, according to the Augustinian insight, all human beings have a tacit knowledge of what time is. In a sense, the endeavor of the logic of time is to study important manifestations and structures of this tacit knowledge.

There were many interesting contributions to the study of time in Scholastic philosophy, e.g., the analysis of the notions of beginning and ending, the duration of the present, temporal ampliation, the logic of "while," future contingency, and the logic of tenses.Anselm of Canterbury (ca. 1033-1109), William of Sherwood (ca. 1200-1270), William of Ockham (ca. 1285-1349), John Buridan (ca. 1295-1358), and Paul of Venice (ca. 1369-1429) all contributed significantly to the development of the philosophical and logical analysis of time. With the Renaissance, however, the logical approach to the study of timefell into disrepute, although it never disappeared completely from philosophy.

However, the twentieth century has seen a very important revival of the philosophical study of time. The most important contribution to the modern philosophy of time was made in the 1950s and 1960s by A. N. Prior (1914-1969). In his endeavors, A. N. Prior took great inspiration from ancient and medieval thinkers and especially their work on time and logic.

The Aristotelian idea of time as the number of motion with respect to earlier and later actually unites two different pictures of time, the dynamic and the static view. On the one hand, time is linked to motion, i.e., changes in the world (the flow of time), and on the other hand time can be conceived as a stationary order of events represented by numbers. In his works, A. N. Prior logically analyzed the tension between the dynamic and the static approach to time, and developed four possible positions in regard to this tension. In particular, A. N. Prior used the idea of branching time to demonstrate that there is a model of time which is logically consistent with his ideas of free choice and indeterminism. (See [8, 189 ff.].)

After A. N. Prior's development of formalised temporal logic, a number of important concepts have been studied within this framework. In relation to temporal databases the studies of the topology of time and discussions regarding time in narratives are particularly interesting.