A FORMAL CONSTRUCTION OF THE SPACETIME MANIFOLD

The spacetime manifold, the stage on which physics is played, is constructed ab initio in a formal program that resembles the logicist reconstruction of mathematics. Zermelo’s set theory extended by urelemente serves as a framework, to which physically interpretable proper axioms are added. From this basis, a topology and subsequently a Hausdorff manifold are readily constructed which bear the properties of the known spacetime manifold. The present approach takes worldlines rather than spacetime points to be primitive, having them represented by urelemente. Thereby it is demonstrated that an important part of physics is formally reducible to set theory.     

Modal Logics of Succession for 2-Dimensional Integral Spacetime

We consider the problem of axiomatizing various natural successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the standard modal language (i.e. the language containing and ) is not finitely axiomatizable.     

THE VARIETY OF PANENTHEISMS

Abstract. In this article I review the efforts of eighteen scientists and theologians, recorded in this book, to describe the relation of God to the universe during a conference sponsored by the John Templeton Foundation at Windsor Castle in 2001. Theologians from several branches of Christian faith articulate their understanding of panentheism, revealing a considerable diversity. I deal with each author in relation to six issues: the way God acts, how God's intimate relation to the world is to be described, the relation of God to spacetime, whether God is dependent upon the world, what type of language is used, and the problem of dipolar panentheism. I identify significant differences between these authors, suggest where fruitful dialogue is possible, and distinguish between intelligibility and plausibility in comparing dipolar panentheism with other types.     

SIMONE WEIL'S SPIRITUAL CRITIQUE OF MODERN SCIENCE: AN HISTORICAL‐CRITICAL ASSESSMENT

Simone Weil is widely recognized today as one of the profound religious thinkers of the twentieth century. Yet while her interpretation of natural science is critical to Weil's overall understanding of religious faith, her writings on science have received little attention compared with her more overtly theological writings. The present essay, which builds on Vance Morgan's Weaving the World: Simone Weil on Science, Necessity, and Love (2005), critically examines Weil's interpretation of the history of science. Weil believed that mathematical science, for the ancient Pythagoreans a mystical expression of the love of God, had in the modern period degenerated into a kind of reification of method that confuses the means of representing nature with nature itself. Beginning with classical (Newtonian) science's representation of nature as a machine, and even more so with the subsequent assimilation of symbolic algebra as the principal language of mathematical physics, modern science according to Weil trades genuine insight into the order of the world for symbolic manipulation yielding mere predictive success and technological domination of nature. I show that Weil's expressed desire to revive a Pythagorean scientific approach, inspired by the “mysterious complicity” in nature between brute necessity and love, must be recast in view of the intrinsically symbolic character of modern mathematical science. I argue further that a genuinely mystical attitude toward nature is nascent within symbolic mathematical science itself.     

ETERNITY,TIME, AND SPACE

Abstract. The concepts of space and time are important in physics and geometry, but their definition is not the exclusive prerogative of those sciences. Space and time are important for ordinary human experience, as well as for philosophy and theology. Samuel Clarke, Gottfried Wilhelm Leibniz, Isaac Newton, Immanuel Kant, and Albert Einstein are important figures in shaping our understandings of space, time, and eternity. The author subjects their arguments to critical examination. Space is neither an infinite and empty receptacle (Newton) nor a system of relations in the mind (Leibniz). Infinite space and time can be interpreted as expressing God's eternity and omnipresence in relating to the creation (Clarke), but such an interpretation is enhanced by Kant's thinking, to clarify that even though time and space are differentiated in individual events, the whole is at the same time present. Even human experience recognizes this wholeness, and for God eternity is the simultaneous presence and possession of the wholeness. The temporal existence of finite entities is also related to a future participation in God's eternal life. Concepts of contingency are brought into the discussion as well.     

Categorical Ontology of Levels and Emergent Complexity: An Introduction

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered.     

The Relevance of Tillich for the Theology and Science Dialogue

This paper explores the relevance of the theology of Paul Tillich for the contemporary dialogue with the natural sciences. The focus is on his Systematic Theology , volume I. First I discuss the general relevance of Tillich's methodology (namely, the method of correlation) for that dialogue, stressing that a genuine dialogue requires cognitive input from both sides and that both sides find "value added" according to their own criteria (or what I call the method of "mutual creative interaction"). Then I move specifically to a Tillichian theological analysis of twentieth-century theoretical science and its empirical discoveries, including Big Bang, inflationary, and quantum cosmologies, quantum physics, thermodynamics, chaos and complexity, and molecular and evolutionary biology, suggesting how they relate to such Tillichian themes as finitude and the categories of being and knowing (time, space, causality, and substance) and to Tillich's understanding of such symbols as God, freedom and destiny, creation, and estrangement. In doing so, my intention is to provide a point of departure for further extended analyses of Tillich's theology in relation to contemporary natural science.     

Do the laws of physics forbid the operation of time machines?

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer.