Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the (...) understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole. (shrink)

WHAT do we mean by saying that a being, God for example, is omniscient? One way of answering this question is to translate ‘God is omniscient’ into some slightly more formalised language than colloquial English, e.g. one with variables of a number of different types, including variables replaceable by statements, and quantifiers binding thes.

This paper deals with the historical and philosophical background of the introduction of the notion of branching time in philosophical logic as it is revealed in the hitherto unpublished mail-correspondence between Saul Kripke and A.N. Prior in the late 1950s. The paper reveals that the idea was first suggested by Saul Kripke in a letter to A.N. Prior, dated September 3, 1958, and it is shown how the elaboration of the idea in the course of the correspondence was intimately intervowen (...) with considerations of how to represent indeterminism and of the adequacy of tensed logic in light of special relativity. The correspondence underpins the point that Prior's later development of branching time may be understood as a crucial part of his attempt at the formulating a conceptual framework integrating basic human notions of time and free choice. (shrink)

There seems to be a minimal core that every theory wishing to accommodate the intuition that the future is open must contain: a denial of physical determinism (i.e. the thesis that what future states the universe will be in is implied by what states it has been in), and a denial of strong fatalism (i.e. the thesis that, at every time, what will subsequently be the case is metaphysically necessary).1 Those two requirements are often associated with the idea of an (...) objective temporal flow and the non-reality of the future. However, at least certain ways to frame the “openness” intuition do not rely on any of these. Branching Time Theory (BTT) is one such: it is compatible with the denial that time flow is objective and it is couched in a language with a (prima facie) commitment to an eternalist ontology. BTT, though, urges us to resist certain intuitions about the determinacy of future claims, which arguably do not lead either to physical determinism or to fatalism. Against BTT, supporters of the Thin Red Line Theory (TRL) argue that their position avoids determinism and fatalism, while also representing the fact that there is a future which is “special” because it is the one that will be the case. But starting with Belnap and Green 1994, some have objected to the tenability of TRL, mainly on metaphysical grounds. In particular, those argue that “positing a thin red line amounts to giving up objective indeterminism,”2 and that “has unacceptable consequences, ranging from a mistreatment of actuality to an inability to talk coherently about what would have happened had what is going to happen not taken place.”3 In this paper, we wish to reframe the.. (shrink)

Logic and Reality is a collection of essays by philosophers, logicians, mathematicians, and computer scientists, celebrating the work of the late distinguished philosopher Arthur Prior on the eightieth anniversary of his birth. Topics range from philosophical discussions of the nature of time and of the nature of logic itself, to descriptions of computer systems that can reason and take account of the fact that they exist in a temporal world.

It is commonly presumed that the earliest recoverable writing of the New Zealand born Philosopher Arthur N. Prior is that published in the Australasian Journal of Philosophy and Psychology in 1937. Yet Prior was an extremely active writer as both an undergraduate and as a recent graduate, in a variety of publications. This paper recovers the unknown early Prior and discusses the importance of neo–orthodox Christian theology upon the life and thought of the early Arthur Prior. During the 1930s Prior (...) was primarily a theologian–philosopher and in these early writings there can be discerned important influences upon his thinking. This paper traces Prior’s writings from an early unpublished manuscript through his theological writings and the development of his neo–orthodox thinking to a point where preparatory work for his influential 1942 article ‘Can Religion be Discussed?’ occurs. It ends where Prior bibliographies begin, with a theologian–philosopher remaking himself as a philosopher theologian. Yet to understand the later Prior we need to understand his early life, thought and writing. This paper is an attempt to recover Prior’s early life and note his influences and talent in areas apart from tense logic. (shrink)

The man who is isolated over against God is as such rejected by God. But to be this man can only be the choice of the Godless man himself. The witness of the Community of God to every individual man points in this direction: that this choice of the Godless is null and void, that he belongs to Jesus Christ from eternity and thus is not rejected, but rather chosen by God in Jesus Christ, that the reprobation which he deserves (...) on the basis of his wrong choice is borne and removed by Jesus Christ; that on the basis of the true, the Divine choice he is chosen for eternal life with God. The promise of his election will determine him as a member of the Church to become himself a carrier of its witness to the whole world. And the revelation of his rejection can determine him only to believe in Jesus Christ as Him by whom it is borne and removed. (Fourth of Karl Barth's "main theses" on God's Election of Grace in his Dogmatic II/2). (shrink)

In his paper, The logic of obligation and the obligations of the logician, A.N. Prior considers Hintikka's theorem, according to which a statement cannot be both impossible and permissible. This theorem has been seen as problematic for the very idea of a logic of obligation. However, Prior rejects the view that the logic of obligation cannot be formalised. He sees this resistance against such a view as an important part of what could be called the obligation of the logician. Prior (...) argues that Hintikka's theorem should not be seen as something paradoxical. On the contrary, it should be seen as a fully acceptable consequence of a basic and reasonable assumption in deontic logic, namely Hintikka's rule. (shrink)

The paper re-evaluates Prior's tenets about indeterminism and relativity from the point of view of the current state of the debate. We first discuss Prior's claims about indeterministic tense logic and about relativity separately and confront them with new technical developments. Then we combine the two topics in a discussion of indeterministic approaches to space-time logics. Finally we show why Prior would not have to "dig his heels in" when it comes to relativity: We point out a way of combining (...) the existential import of the distinction between past, present, and future with a frame-relative notion of the present. (shrink)

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. (shrink)