Synthese (2012) 188:325–330 DOI 10.1007/s11229-011-9941-5

From a logical angle Some studies in A.N. Prior’s ideas on time, discourse and metaphysics Peter Øhrstrøm · Per F. V. Hasle

Received: 13 April 2011 / Accepted: 13 April 2011 / Published online: 7 June 2011 © Springer Science+Business Media B.V. 2011

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: Logic is the study of conditions of valid inference, and formal logic the study of formally valid inference, i.e. of the conditions under which an inference is valid in virtue of its form alone. What is meant by “form” of an inference is one of the most difficult questions in logic; but the notion of “valid inference” is one with which everyone is familiar, though not necessarily under that name. We perform an inference whenever we move from one belief or statement (or set of beliefs

1 The notebook is in Mary Prior’s possession and it has kindly been lent to the editors of this volume.

P. Øhrstrøm (B) Department of Communication and Psychology, Aalborg University, Aalborg, Denmark e-mail: [email protected] P. F. V. Hasle Royal School of Library and Information Science, Copenhagen, Denmark e-mail: [email protected]

123

326

Synthese (2012) 188:325–330

or statement), technically called the premise (or premises) of the inference, to a belief or statement (the conclusion of the inference) which is taken to “follow from” that (or those) from which we start. If the conclusion really follows from the premises, the inference is a “valid” one; if not, it is “invalid”. Thus if a man says “That is a sheep, for it is an animal & all sheep are animals”, he performs an invalid inference, for a little reflection will make it evident to most people that “That is a sheep” does not really follow from “That is an animal & all sheep are animals”; though it would follow from “That is an animal & all animals are sheep” (so that “All animals are sheep, & that is an animal, therefore that is a sheep” is not an invalid but a valid inference; though one of its premises is false). It should be plain now that logic might equally well have been defined as the study of the conditions under which one statement or belief “follows from” another or others. This introduction to the nature of logic seems to have written for beginners in the field. However, it is also a clear exposition of Prior’s view of logic. In his opinion logic is about reality. It is not merely a human invention. Even though logic is not an empirical science, the logician can in fact by use of human rationality find out about important features of the world. Moreover, logic is supposed to describe what will be “evident to most people” after some reflection. There is a longer version of the above introduction, which Prior for some reason has abandoned, preferring the shorter version above. In the longer version he wrote: As far as Europe is concerned, the study of logic seems to have begun with the ancient Greeks. That is not, of course, to say that the Greeks were the first Europeans to perform inferences. Men have performed inferences, i.e. they have reasoned, ever since they have been men. “God has not been so sparing to men as to make them barely two-legged creatures, and left it to Aristotle to make them rational”. But it is one thing to think logically, and another to study logic (though of course we may do both—i.e. we may think logically about the subject-matter of Logic). For to study logic is not merely to reason, validly or invalidly, but to reflect upon the conditions under which reasoning is valid. It seems that Prior accepted Locke’s view that the ability to reason and in fact also to study and use logic is given to man as part of his nature. The view seems to be that mankind has had this ability as a divine gift right from the beginning of the history of man. In the passage from Locke’s An Essay concerning Human Understanding from which Prior quotes this is stated in the following way: But God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational, i.e. those few of them that he could get so to examine the grounds of syllogisms, as to see that, in above three score ways that three propositions may be laid together, there are but about fourteen wherein one may be sure that the conclusion is right; and upon what grounds it is, that, in these few, the conclusion is certain, and in the other not. God has been more bountiful to mankind than so. He has given them a mind that can reason, without being instructed in methods of syllogizing: the

123

Synthese (2012) 188:325–330

327

understanding is not taught to reason by these rules; it has a native faculty to perceive the coherence or incoherence of its ideas, and can range them right, without any such perplexing repetitions. (John Locke, An Essay concerning Human Understanding, IV. xvii.4) In his logical approach to the world, Prior wanted to include as many aspects of reality as possible. Indeed, it seems that he would be unwilling beforehand to exclude any part or aspect of reality from being studied from a logical angle. Prior however also recognised that “some domains do have more structure than others” (Øhrstrøm and Hasle 1993, p. 41) and hence, that some domains might be difficult or impossible to describe fully by formal logic. For instance, he very much doubted that a satisfactory formalization of biology could be developed (ibid., p. 42). This restriction notwithstanding, his conviction seems to have been that we should at least try to look for a logic of every part or aspect of reality. As it appears from this volume it is obvious that he believed in a logic of time and in a logic of ethics, but that it was more debatable to him whether there is also a logic of religious and theological questions. However, Prior is likely to have held that in as far as there is a spiritual part or aspect of reality, then we should also look for a logic of this part or aspect of reality. Prior never followed Bennett’s idea of a book with the title “From a Logical Angle”. Instead he concentrated on the publication of other books as well as on a number of papers. So, Prior’s paper “The Logic of Obligation and the Obligations of the Logician” has remained unpublished until now. In the present volume, however, it is published together with three other hitherto unpublished Prior papers: “The Fable of the Four Preachers”, “Faith, Unbelief and Evil”, and “The Paradox of the Prisoner in Logical Form”. These four Prior papers are discussed and put into a wider perspective in separate papers. Finally, this volume also includes some recent studies in the philosophy of A.N. Prior. The four papers by Prior may seem somewhat diverse at first glance, but in fact there are important links between them. These links are established partly by some interesting anticipations of tense logic, especially in “The Fable of the Four Preachers” and “The Paradox of the Prisoner in Logical Form”, and partly by an abiding concern with the question whether ethical and theological questions can be investigated and discussed rationally, and more specifically, by and with formal logic. We shall come back to these questions, albeit briefly, after having introduced the contributions to the volume. Prior’s paper “The Logic of Obligation and the Obligations of the Logician” has been edited by Anne Katrine Christensen, Jörg Zeller and Peter Øhrstrøm. In addition this rather substantial paper has been analysed and discussed in a joint paper by Jörg Zeller, Ulrik Sandborg-Petersen, and Peter Øhrstrøm. Prior’s paper on obligation clearly presents an interesting formalism and a number of nice proofs, but the essential message in the paper is that it is possible to deal with ethical and other metaphysical problems in terms of logic. But how far can this view be taken? For instance, can religious questions be discussed in terms of logic and rational discourse? This was the theme in Prior’s “Can religion be discussed?” (1942) and also in the hitherto unpublished paper “Faith, Unbelief and Evil”, which

123

328

Synthese (2012) 188:325–330

is included in the volume. In the format of a dialogue Prior analyses the possibilities of carrying out rational argumentation within the realm of religious and ethical matters. This volume also includes a paper by David Jakobsen, in which Prior’s view on the topic has been analysed and discussed in the light of “Faith, Unbelief and Evil”. Prior’s hitherto unpublished paper, “The Fable of the Four Preachers”, is an entertaining presentation of some basic problems regarding time and identity. The text has been edited by Julie Jespersen and Peter Øhrstrøm, and the philosophical problems and challenges to which the fable gives rise have been carefully discussed in a paper by Márta Ujvári, “Prior’s Fable and the Limits of de re Possibility”. “The Fable of the Four Preachers” should be seen as one of Prior’s early contributions to the discussion of logical problems of time. The same can be said about Prior’s paper “The Paradox of the Prisoner in Logical Form”. In his analysis of the paradox Prior presents a basic framework that can easily be seen as a forerunner of his later temporal logic. Prior’s text has been edited and discussed in this volume by Lasse Burri Gram-Hansen, Ulrik Sandborg-Petersen, and Peter Øhrstrøm. Prior held that the relation between time and logic should be studied and clarified through tense logic. In this context, Prior insisted on the logical possibility of indeterminism and free choice; and in addition to this, he himself stated his belief in the reality of those. He also maintained that the present, the Now, should be seen as essential for the understanding of reality. These views gave rise to a certain tension between the notions of tense logic (in particular the importance of the Now), and the consequences of the special theory of relativity according to which it is impossible to uphold the view of absolute simultaneity, at any rate as long as simultaneity is defined in the traditional manner. In their paper in this volume, Thomas Müller and Niko Strobach present an overview of the discussion of this problem since the death of Prior, and they argue that it is in fact possible to combine the basic tense logical view with a frame-relative notion of the present. Prior’s logical approach to discourse and language should be seen in a historical perspective. In particular, he was interested in ancient and medieval logic. One of the key questions is the proper understanding of the logical meaning of natural language statements, i.e., the study of the formal aspects of semantics. In the present volume, Sara L. Uckelman has discussed this interest based on material in the Prior archive in Bodleian Library, Oxford University. Drawing on this material, she presents an interesting overview of Prior’s work on ancient and medieval logic. In another paper in this volume Sara L. Uckelman demonstrates how Prior’s analysis of an insolubilium of Jean Buridan may have provided an conceptual inspiration for Prior’s later development of hybrid logic. This volume is a result of the increasing interest in Prior’s work since the early 1990s. Within the same period, there has been an increasing awareness of the importance of his early work. That interest is partly historical, reflecting Prior’s importance within modern logic and philosophy, and partly based on the value of Prior’s early works in their own right. For instance, Grimshaw (2002) has “dug out” early work by Prior partly out of biographical and partly out of theological interest. But there are other and in our opinion more important aspects to be learned from a more comprehensive study of all of Prior’s work. It has become increasingly clear that Prior’s

123

Synthese (2012) 188:325–330

329

theological and concomitant ethical concerns were a considerable inspiration in general to his mature work within logic and ethics, and in particular to his development of tense logic. This background is not to be written off simply as the young Prior’s accidental work before he found his real theme, but was rather, as Jakobsen writes in his paper in this volume: …the seedbed of much of the thinking he was to occupy himself with later. Research into the theological thinking of Prior will not only teach us something about the prior Prior, but it will equally help us understand the Priors of logic, tense and ethics. This realisation, which is corroborated significantly by the papers in this volume, in reality marks a breach with the view that seems to have been prevalent from Prior’s death till the second half of the 1990s. To the best of our knowledge, the first paper to emphasise the continuity and development of Prior’s work in its entirety was Hasle (1997) with the telling title “The Problem of Predestination—a Prelude to A. N. Prior’s Logic of Time”. It ought to be noted here that already Kenny (1970) observed a unity (as well as a diversity) in Prior’s work: Prior’s greatest scholarly achievement was undoubtedly the creation and development of tense-logic. But his research and reflection on this topic led him to elaborate, piece by piece, a whole metaphysical system of an individual and characteristic stamp. He had many different interests at different periods of his life, but from different angles he constantly returned to the same central and unchanging themes. Throughout his life, for instance, he worked away at the knot of problems surrounding determinism: first as a predestinarian theologian, then as a moral philosopher, finally as a metaphysician and logician. (Kenny 1970, p. 348) But in any event, before 1997 no papers tried to investigate the possible cohesion within Prior’s overall work. We have included an elaborated version of Hasle (1997) in this volume, partly because it was first published in a rather inaccessible and littleknown source, and partly because it may serve to connect the other contributions to this volume. So, the perception and interpretation of Prior’s work in its entirety has changed by now. Indeed, in our view a picture of an overall architecture within Prior’s work is emerging, where theology, ethics, and logic mark the three points within which tense logic develops. On a personal level, Prior’s views changed from being a practising Presbyterian to being agnostic and two years before he died he described himself in an autobiographical note for his entry in Who’s Who as having “no religious beliefs” (Kenny 1970, p. 321). And clearly his work also developed in an increasingly abstract and logical direction. But even Past, Present and Future bears testimony to the importance he kept on attributing to theological questions. It seems clear that his interest in the question of whether (and how) religion and ethics can be debated rationally remained throughout his entire work. To our mind, the question is answered affirmatively, if not directly by Prior himself, then by his work.

123

330

Synthese (2012) 188:325–330

References Grimshaw, M. (2002). The prior Prior: Neglected early writings of Arthur N. Prior. Heythrop journal, 43, 480–495. Hasle, P. (1997). The problem of predestination – as a prelude to A. N. Prior’s tense logic. Department of Communication, Aalborg University. Later published in M. Wegener (Ed.) (1999). Time, creation and world-order (pp. 139–159). Aarhus University Press. Kenny, A. (1970). Arthur Normann Prior (1914–1969). Proceedings of the British Academy, LVI, 321–349. Øhrstrøm, P., & Hasle, P. (1993). A.N. Prior’s rediscovery of tense logic. Erkenntnis, 39, 23–50. Prior, A. (1942). Can religion be discussed? Australasian Journal of Psychology and Philosophy, 15, 141–151. Reprinted in A. Flew & A. MacIntyre (Eds.) (1955). New essays in philosophical theology (pp. 1–11). London: S. C. M. Press.

123