Per Hasle

Determinism and the Origins of Temporal Logic

The founder of symbolic temporal logic, A. N. Prior was to a great extent motivated by philosophical concerns. The philosophical problem with which he was most concerned was determinism versus free will. The aim of this paper is to point out some crucial interrelations between this philosophical problem and temporal logic. First, we sketch how Prior’s personal reasons for studying the problems related to determinism were philosophical — initially, indeed theological. Second, we discuss his reconstruction of the classical Master Argument, which has since Antiquity been considered a strong argument for determinism. Furthermore, the treatment of determinism in two of Prior’s proposed temporal systems, namely the Ockhamistic and the Peircean systems, is investigated. Third, we illustrate the fundamental role of the very same issue in more recent discussions of some tempo-modal systems: The ‚Leibniz-system‘ based on ideas of Nishimura (1979) as well as Belnap and Green’s argument (! 1994), to which we add some necessary revisions.

The persuasive expansion: rhetoric, information architecture, and conceptual structure

Conceptual structures are, as a rule, approached from logical perspectives in a broad sense. However, since Antiquity there has been another approach to conceptual structures in thought and language, namely the rhetorical tradition. The relationship between these two grand traditions of Western Thought, Logic and Rhetoric, is complicated and sometimes uneasy – and yet, both are indispensable, as it would seem. Certainly, a (supposedly) practical field such as Information Architecture bears witness to the fact that for those who actually strive to work out IT systems conceptually congenial to human users, rhetorical and logical considerations intertwine in an almost inextricable manner.

Ockhamistic logics and true futures of counterfactual moments

Various Ockhamistic logics are compared, with the aim of making clear the role of true futures of counterfactual moments, i.e. true futures of moments outside the true chronicle. First, we give an account of A.N. Priors (1967) original Ockhamistic semantics, where the truth of a formula is relative to a moment and a chronicle. We prove that this is equivalent to a semantics put forward by Thomason and Gupta (1980), where truth is relative to a moment and a so-called chronicle function which assigns a chronicle to each moment. This is the case because true futures of counterfactual moments do not matter in Thomson and Guptas semantics. Later, we discuss how two options considered by Belnap and Green (1994) might be formalised. They come about by associating either a chronicle or a chronicle function to be given once and for all. The first of the two options is unable to give an account of certain statements from natural language, and the second option invalidates an intuitively valid formula. We propose a new Ockhamistic semantics where the formula in question is valid, and furthermore, where true features of counterfactual moments are taken into account. Finally, we discuss possible applications within artificial intelligence.

The problem of predestination: as a prelude to A. N. Prior’s tense logic

Arthur Norman Prior’s early theological writings have been relatively neglected for many years. Moreover, to the extent that they have been discussed at all they have been treated mainly as youthful work quite separate from Prior’s later work as a philosopher and logician. However, as interest in Prior’s achievements has been growing significantly in recent years it has become more important to investigate the development with his overall work. In fact, Prior’s putatively “youthful” theological work overlapped his work as a philosopher and logician for many years, as is richly documented by examples discussed in this paper. A particularly important theme is the problem of predestination. This paper presents comprehensive evidence that this theme, which was Prior’s most important single preoccupation as a theological writer, was a most important source of inspiration for his development of tense logic. Via questions regarding divine foreknowledge and human free will, predestination was to motivate Prior as a logician to focus on time and tense. Whilst investigating this development, the paper also traces Prior’s parallel development from Calvinist Christian believer to a more agnostic position.

Prior’s paradigm for the study of time and its methodological motivation

A. N. Prior’s writings should obviously be studied already for historical reasons. His inventions of modern temporal logic and hybrid logic are clearly important events in the history of logic. But the enduring importance of studying his works also rests on his methodological approach, which remains highly relevant also for systematical reasons. In this paper we argue that Prior’s formulation in the 1950s of a tense-logical paradigm for the study of time should be understood in the light of at least three other principles or perspectives which were manifest already in his studies during the 1940s and further developed in the 1950s: (1) his emphasis on the value of interdisciplinary studies, (2) his reflections on formalisation and (3) his view of the role of symbolic logic in conceptual studies and in the philosophy of science. Our investigation into Prior’s basic tenets and principles makes extensive use of Prior’s Nachlass. It is thereby also exemplified how his correspondence and unpublished papers contain important information for a deeper understanding of Prior’s paradigm for the study of time.

Linguistic and Tense-Logical Considerations on the Generality of a Three-Point Structure of Tenses

This paper is concerned with a specific proposal of a formalism for studying tenses, namely Hans Reichenbach’s ‘three-point structure’ [14]. That proposal explicitly claims to be based on Jespersen’s ideas on time and tense in [10]. The main goal is to examine the relationship between this logic and its underlying linguistic assumptions, with a particular view to A. N. Prior’s tense logic. We bring forth a historical as well as a systematical result. The historical result consists in revealing certain prevalent misunderstandings concerning Reichenbach’s linguistic background in Jespersen’s work. The systematical result consists in determining a specific relation between some well-established linguistic temporal categories and tense logic. Thus the following study may serve to show how a careful examination of underlying linguistic assumptions may bear on the development of logic, and conversely, how logical observations can be fruitfully employed in the study of language.

From a logical angle

On January 21, 1955 the young New Zealander Jonathan Bennett wrote a letter to A.N. Prior. He had received a copy of Prior’s “The Logic of Obligation and the Obligations of the Logician”. “I have finished, and thoroughly enjoyed, your piece on Obligation”, Bennett wrote, and in addition he suggested that Prior should publish a book on logic of which this paper should be an essential part. In Bennett’s view Prior should also include some other papers “preferably sharing with the Obligation piece the characteristic of at once doing logic, applying logic, and showing what kind of thing the doing of logic is”. Bennett added that if Prior would follow this idea, he would “have a bloody useful book.” Bennett also suggested that calling this new book ‘From a logical angle’ could be a good idea. In fact, during the early 1950s Prior had been considering several book ideas. In a notebook1 from this period he had even written the following short introduction to a textbook on logic: