Logic and the Basis of Theology: an Investigation into the Help Logic Can Give to the Understanding of Different Theologies, Following the Contributions to Both Disciplines of Arthur Prior, 1914-1969

<p>My thesis is that modem symbolic mathematical logics have an important contribution to make to theologies. I demonstrate this firstly in a 'theoretical section' (i) by showing what logics are and why they can be trusted; (ii) by showing how all theologies may be correctly treated as axiomatic systems; (iii) by outlining some modern logics which can assist theological thinking, including a logic I construct for this purpose called the Theologic. I demonstrate this, secondly, in an 'applied logic' section, by looking at (iv) the theology of one current branch of Christianity in detail, outlining its logical problems and the consequences of trying to avoid them; (v) 'post-modern' Christian theologies, firstly those that suggest that the word 'God' is a symbol rather than a name, and secondly at three feminist theologies two of which are logically quite radical; (vi) pantheism, in particular at Spinoza's ideas and Lovelock's Gaia; (vii) two religions, Buddhism and Confucianism, which, in their basic religious thinking, can be said to have no gods. I find that all religions I have studied - and they are representative of religions actual, proposed and imagined - have serious logical flaws, some known of old, others brought to light by the modern logics. The consequences of making the religions more logically sound are generally unacceptable to the members of the faiths. The suggestion that the gods use a different sort of logic to us is generally logically unacceptable. This does not leave abandoning religion as the only other possibility: the work of theologians in future, assisted by mathematical logic, may be (a) to bring about changes in basic beliefs, and (b) to assist in the birth of new, logically sound, religions. These investigations are carried out in the spirit of A N Prior, who came to logic through a Christian upbringing which gave him an interest in theology, a desire to make that theology more consistent, and as Professor of Philosophy at Canterbury College (as it then was) taught me. My upbringing was similar. We both, in the end, found conventional Christianity too illogical to believe. Time having past, I have been able to examine the logic of other, and newer, theologies.</p>

Logic and the Basis of Theology: an Investigation into the Help Logic Can Give to the Understanding of Different Theologies, Following the Contributions to Both Disciplines of Arthur Prior, 1914-1969

<p>My thesis is that modem symbolic mathematical logics have an important contribution to make to theologies. I demonstrate this firstly in a 'theoretical section' (i) by showing what logics are and why they can be trusted; (ii) by showing how all theologies may be correctly treated as axiomatic systems; (iii) by outlining some modern logics which can assist theological thinking, including a logic I construct for this purpose called the Theologic. I demonstrate this, secondly, in an 'applied logic' section, by looking at (iv) the theology of one current branch of Christianity in detail, outlining its logical problems and the consequences of trying to avoid them; (v) 'post-modern' Christian theologies, firstly those that suggest that the word 'God' is a symbol rather than a name, and secondly at three feminist theologies two of which are logically quite radical; (vi) pantheism, in particular at Spinoza's ideas and Lovelock's Gaia; (vii) two religions, Buddhism and Confucianism, which, in their basic religious thinking, can be said to have no gods. I find that all religions I have studied - and they are representative of religions actual, proposed and imagined - have serious logical flaws, some known of old, others brought to light by the modern logics. The consequences of making the religions more logically sound are generally unacceptable to the members of the faiths. The suggestion that the gods use a different sort of logic to us is generally logically unacceptable. This does not leave abandoning religion as the only other possibility: the work of theologians in future, assisted by mathematical logic, may be (a) to bring about changes in basic beliefs, and (b) to assist in the birth of new, logically sound, religions. These investigations are carried out in the spirit of A N Prior, who came to logic through a Christian upbringing which gave him an interest in theology, a desire to make that theology more consistent, and as Professor of Philosophy at Canterbury College (as it then was) taught me. My upbringing was similar. We both, in the end, found conventional Christianity too illogical to believe. Time having past, I have been able to examine the logic of other, and newer, theologies.</p>

Necessary, Transcendental, and Universal Truth

A simple puzzle leads Fine to conclude that we should distinguish between worldly sentences like “Socrates exists,” whose truth values depend on circumstances and unworldly ones like “Socrates is human,” which are true or false independently of circumstances. The former, if true in every circumstance, express necessary propositions. The latter, if true, express transcendental propositions, which, for theoretical convenience, we regard as necessary in an extended sense. Here it is argued that this understanding is backwards. Transcendental truths and sentences true in every circumstance (here labeled universal truths) are both species of necessary truth. The revised understanding is clarified by a simple formal system with distinct operators for necessary, transcendental, and universal truth. The system is axiomatized. Its universal-truth fragment coincides with something that Arthur Prior once proposed as System A. The ideas of necessary, transcendental truth are further clarified by considering their interaction with actual truth. Adding an operator for actually true to the formal system produces a system closely related to one of Crossley and Humberstone.

That's Outrageous

I show how non-presentists ought to respond to a popular objection originally due to Arthur Prior and lately updated by Dean Zimmerman. Prior and Zimmerman say that non-presentism cannot account for the fittingness of certain emotional responses to things past. But presentism gains no advantage here, because it is equally incapable of accounting for the fittingness of certain other emotional responses to things past, in particular moral outrage.

Arthur Prior A ‘Young Progressive’ Letters to Ursula Bethell and to Hugh Teague 1936-1941.

Arthur Prior is scarcely a household name in New Zealand, but in some respects his story repeats a narrative we like to think of as quintessentially Kiwi—that of the small town boy who ‘makes it’ on the world stage. Born and raised in the rural township of Masterton in 1914, Prior became a leading philosopher of the 20th century, feted for his invention of tense logic (or temporal logic as it is now called), invited by no less a figure than Gilbert Ryle to deliver the prestigious John Locke lectures in Oxford in 1956, offered a Chair in Philosophy at Manchester in 1958, then a Fellowship at Balliol College, Oxford, in 1966. Tragically, he died at the relatively young age of 54, but he remains one of the central figures in the development of logic in the 20th century.

Hybrid Logic as extension of Modal and Temporal Logic

La lógica temporal fue creada por Arthur Prior para representar información temporal en un sistema lógico mediante operadores modales-temporales como P, F, H o G. Intuitivamente tales operadores pueden entenderse respectivamente como “fue alguna vez en el pasado...”, “será alguna vez en el futuro...”, “ha sido siempre en el pasado...” y “será siempre en el futuro...”. La evaluación de las fórmulas construidas a partir de ellos se lleva a cabo en semánticas kripkeanas y, de este modo, la lógica modal y la temporal están relacionadas. Sin embargo, aunque sus mecanismos permiten formalizar la información modal-temporal con cierta precisión, ambas lógicas adolecen de un problema de expresividad que la lógica híbrida es capaz de solventar. En efecto, uno de los problemas de la lógica modal reside en su incapacidad para nombrar puntos concretos dentro de un modelo. La lógica temporal, al basarse en ella, tampoco puede hacerlo. Pero la lógica de primer orden sí es capaz gracias a las constantes y a la relación de identidad. La lógica híbrida, que resulta de combinar la lógica modal con la lógica de primer orden, sería una solución a este problema. El principal objetivo de este artículo consiste en explicar el origen de la lógica híbrida a partir de la modal-temporal para mostrar qué añade a ambos sistemas en la representación de información, porqué es más expresiva que ellos y qué relación guarda con el lenguaje de correspondencia de la lógica de primer orden.

Information professionals meet Arthur Prior

The paper investigates the supporting role of information professionals in interdisciplinary digital research projects. It identifies three encounter scenarios in which information professionals meet domain researchers (as research librarian, as information specialist, and as iHumanist) and links them to the domain researchers ‘modes of orientation’. We examine these theoretical distinctions by discussing three cases from our own practical engagement in the Prior project. Our discussion shows that the scenarios help to understand information professionals’ supporting work, explain the conflicts that emerge, and explicate information professionals’ shifting conceptions of what they are doing in terms of the shifting encounter scenarios. In short, the paper presents methodological and theoretical insights that can be useful in understanding encounters between information professionals and domain researchers.

New Zealand, philosophy in

Philosophy as an academic discipline in New Zealand came into its own during the late 1930s under the influence of J.N. Findlay and Karl Popper. Arthur Prior was the first New Zealand philosopher to gain prominence and to inaugurate original research into logic and its application to philosophy. This tradition was continued by local philosophers such as Max Cresswell and Richard Sylvan (formerly Routley) and those from overseas who found the developing analytical ethos congenial, such as George Hughes, Krister Segerberg and Pavel Tichý. New Zealand philosophy found its footing within analytic philosophy, not so much on the side of philosophy of language, but in logic used both as an analytic tool and as a subject in its own right. Philosophers also explored what would have then been regarded by many elsewhere as ‘fringe’ logics, such as modal and tense logics; these however have now become mainstream within both logic and metaphysics. The current philosophical scene is one that allows as much diversity as might be possible in a small country with a small number of academic philosophers. Their preoccupations are very much those that one would find in many universities elsewhere. But whereas earlier philosophical interests were based on philosophical connections with the UK, now these have become quite minor compared with the very strong connections with philosophy in Australia and the USA. Although philosophy has found a firm and energetic place in New Zealand, it remains to consider whether there is a distinctive New Zealand philosophy, and to ask what that might even be. Earlier philosophers were much more willing to take on unconventional and unfashionable points of view and turn them into viable philosophical positions; even though that is still the case, there is much more of a seamless connection with philosophy elsewhere. However, there are applications of philosophy to local matters that often have to do with relations with the indigenous Maori, the nature of the New Zealand state, which sees itself as both a bi-cultural and a multi-cultural society, the nature of New Zealand’s social and cultural identity, and local ethical issues that arise in respect to, for example, medicine, biotechnology and the environment. Most of these, of course, are concerns elsewhere also; but the local context calls for work by local philosophers in a way for which others cannot substitute.

Hegel’s Treatment of Predication Considered in the Light of a Logic for the Actual World

One prominent feature of analytic metaphysics in the second half of the twentieth century was the revival of metaphysical debate over modality, and in this paper I suggest that a particular position that emerged within this debate, ‘modal actualism’, bears a striking resemblance to the way that Hegel discusses modal notions in the final chapter of Book 2 of the Science of Logic, ‘Wirklichkeit’ or ‘Actuality’. Modal actualists opposed David Lewis’s counter-intuitive claims about the existence of alternate possible worlds, and aimed to reconcile the reality of alternate possibilities with the common-sense idea of the actual world as all there is. Like Hegel in the chapter ‘Actuality’, they thus argue that possible alternatives to the actual world must, somehow, exist within the actual world. Here I approach these issues via the ideas of John N. Findlay who, in the 1950s, had attempted to reintroduce Hegel into an Anglophone philosophical culture, but who also influenced the later development of modal actualism via his influence on the modal logician, Arthur Prior. Like certain actualists, Findlay distinguished between two modes of predication in order to distinguish, but relate, judgements about the actual from those about the possible. This predicative dualism is strikingly similar to the way Hegel distinguishes two types of predication in his treatment of judgement in Book 3 of the Science of Logic. Reading Hegel’s dualistic account of judgement structure against this background enables us to see how it was meant to provide a logical framework for the ‘actualist’ metaphysics he earlier sketched in the chapter, ‘Actuality’.

Examining Polarimetric Radar Observations of Bulk Microphysical Structures and Their Relation to Vortex Kinematics in Hurricane Arthur (2014)

Dual-polarization radar observations were taken of Hurricane Arthur prior to and during landfall, providing needed insight into the microphysics of tropical cyclone precipitation. A total of 30 h of data were composited and analyzed by annuli capturing storm features (eyewall, inner rainbands, and outer rainbands) and by azimuth relative to the deep-layer environmental wind shear vector. Polarimetric radar variables displayed distinct signatures indicating a transition from convective to stratiform precipitation in the downshear-right to downshear-left quadrants, which is an organization consistent with the expected kinematic asymmetry of a sheared tropical cyclone. In the downshear-right quadrant, vertical profiles of differential reflectivity ZDR and copolar correlation coefficient ρHV were more vertically stretched within and above the melting layer at all annuli, which is attributed to convective processes. An analysis of specific differential phase KDP indicated that nonspherical ice particles had an increased presence in two layers: just above the melting level and near 8-km altitude. Here, convective updrafts generated ice particles in the lower layer, which were likely columnar crystals, and increased the available moisture in the upper layer, leading to increased planar crystal growth. A sharp transition in hydrometeor population occurred downwind in the downshear-left quadrant where ZDR and ρHV profiles were more peaked within the melting layer. Above the melting layer, these signatures indicated reduced ice column counts and shape diversity owing to aggregation in a predominantly stratiform regime. The rainband quadrants exhibited a sharper transition compared to the eyewall quadrants owing to weaker winds and longer distances that decreased azimuthal mixing of ice hydrometeors.