The aim of this paper is not only to deal with the concept of infinity, but also to develop some considerations about the epistemological status of cosmology. These problems are connected because from an epistemological point of view, cosmology, meant as the study of the universe as a whole, is not merely a physical (or empirical) science. On the contrary it has an unavoidable metaphysical character which can be found in questions like “why is there this universe (or a universe (...) at all)?”. As a consequence, questions concerning the infinity of the universe in space and time can correctly arise only taking into account this metaphysical character of cosmology. Accordingly, in the following paper it will be shown that two different concepts of physical infinity of the universe (the relativistic one and the inflationary one) rely on two different ways of solution of a metaphysical problem. The difference between these concepts cannot be analysed using the classical distinctions between actual/potential infinity or numerable/continuum infinity, but the introduction of a new “modal” distinction will be necessary. Finally, it will be illustrated the role of a philosophical concept of infinity of the universe. (shrink)

If cosmology is to obtain knowledge about the whole universe, it faces an underdetermination problem: Alternative space-time models are compatible with our evidence. The problem can be avoided though, if there are good reasons to adopt the Cosmological Principle (CP), because, assuming the principle, one can confine oneself to the small class of homogeneous and isotropic space-time models. The aim of this paper is to ask whether there are good reasons to adopt the Cosmological Principle in order to avoid underdetermination (...) in cosmology. Various strategies to justify the CP are examined. For instance, arguments to the effect that the truth of the CP follows generically from a large set of initial conditions; an inference to the best explanation; and an inductive strategy are assessed. I conclude that a convincing justification of the CP has not yet been established, but this claim is contingent on a number of results that may have to be revised in the future. (shrink)

When the ancient Greeks looked up into the heavens, they saw not just sun and moon, stars and planets, but a complete, coherent universe, a model of the Good that could serve as a guide to a better life. How this view of the world came to be, and how we lost it (or turned away from it) on the way to becoming modern, make for a fascinating story, told in a highly accessible manner by Remi Brague in this wide-ranging (...) cultural history. Before the Greeks, people thought human action was required to maintain the order of the universe and so conducted rituals and sacrifices to renew and restore it. But beginning with the Hellenic Age, the universe came to be seen as existing quite apart from human action and possessing, therefore, a kind of wisdom that humanity did not. Wearing his remarkable erudition lightly, Brague traces the many ways this universal wisdom has been interpreted over the centuries, from the time of ancient Egypt to the modern era. Socratic and Muslim philosophers, Christian theologians and Jewish Kabbalists all believed that questions about the workings of the world and the meaning of life were closely intertwined and that an understanding of cosmology was crucial to making sense of human ethics. Exploring the fate of this concept in the modern day, Brague shows how modernity stripped the universe of its sacred and philosophical wisdom, transforming it into an ethically indifferent entity that no longer serves as a model for human morality. Encyclopedic and yet intimate, The Wisdom of the World offers the best sort of history: broad, learned, and completely compelling. Brague opens a window onto systems of thought radically different from our own. (shrink)

This essay explores a simple argument for a Ground of Being, objections to it, and limitations on it. It is nonsensical to refer to Nothing in the sense of utter absence, hence nothing can be claimed to come from Nothing. If, as it seems, the universe, or any physical ensemble containing it, is past-finite, it must be caused by an uncaused Ground. Speculative many-worlds, pocket universes and multiverses do not affect this argument, but the quantum cosmologies of Alex Vilenkin, and (...) J. B. Hartle and Stephen Hawking, which claim that the universe came from literally nothing, would. I argue that their novel project cannot work for reasons both physical (their "nothing" is actually a vacuum state governed by eternal physical laws) and methodological (physical theory cannot explain the emergence of the physical per se). Thus my argument stands. However, as David Hume showed, a posteriori arguments like mine infer a creation, and Creator, of a certain character, namely, a stochastic concept of creation and a panentheistic, partly physical Creator lacking omniscience and omnipotence. Rather than undermining the cosmological argument, as Hume intended, these limitations liberate the concept of the Ground from unnecessary problems, as Hartshorne suggested. (shrink)

Interpretations, or generalizations, of quantum theory that are applicable to cosmology are of interest because they must display and resolve the "paradoxes" directly. The Everett interpretation is reexamined and compared with two alternatives. Its "metaphysical" connotations can be removed, after which it is found to be more acceptable than a theory which incorporates collapse, while retaining some unsatisfactory features.

Contemporary science presents us with the remarkable theory that the universe began to exist about fifteen billion years ago with a cataclysmic explosion called "the Big Bang." The question of whether Big Bang cosmology supports theism or atheism has long been a matter of discussion among the general public and in popular science books, but has received scant attention from philosophers. This book sets out to fill this gap by means of a sustained debate between two philosophers, William Lane Craig (...) and Quentin Smith, who defend opposing positions. Craig argues that the Big Bang that began the universe was created by God, while Smith argues that the Big Bang has no cause. Alternating chapters by the two philosophers criticize and attempt to refute preceding arguments. Their arguments are based on Einstein's theory of relativity and include a discussion of the new quantum cosmology recently developed by Stephen Hawking and popularized in A Brief History of Time. (shrink)

Examines the formation, structure and collapse of the bourgeois world view, exploring the concepts of fun, happiness, pleasure, and excitement.

Furley's study presents a clear picture of the opposing views of the natural world and its contents as seen by philosophers and scientists in classical antiquity. On one side were the materialists whose world was mechanistic, evolutionary, and unbounded, lacking the focus of a natural center. The other side included teleologists, whose world was purposive, non-evolutionary, finite, and centrifocal. This volume takes the reader up to the criticisms of Plato and Aristotle. The second volume will examine Plato and Aristotle's own (...) cosmology and follow the debate to the sixth century. Professor Furley has produced a history of the early views of the physical world whose scope makes this book of major importance. (shrink)

Mathematics equivalent to Bell's derivation of the inequalities, also allows a local hidden variables explanation for the correlation between distant measurements.

We discuss a number of fundamental aspects of modern cosmological concepts, from the phenomenological, observational, theoretical and epistemic points of view. We argue that the modern cosmology, despite a great advent, in particular in the observational sector, is yet to solve important problems, posed already by the classical times. In particular the stress is put on discerning the scientific features of modern cosmological paradigms from the more speculative ones, with the latter immersed in some aspects deeply into mythological world (...) picture. We finally discuss the principal paradigms, which are present in the modern cosmological studies and evaluate their epistemic merits. (shrink)

Physical cosmology purports to establish precise and testable claims about the origin of the universe. Thus, cosmology bears directly on traditional metaphysical claims -- in particular, claims about whether the universe has a creator (i.e. God). What is the upshot of cosmology for the claims of theism? Does big-bang cosmology support theism? Do recent developments in quantum and string cosmology undermine theism? We discuss the relations between physical cosmology to theism from both historical and systematic points of view.

It is shown that, for certain classes of cosmological model which either postulate or give rise to infinitely many universes, only a measure zero subset of the set of possible universes above a given size can in fact be physically realized. It follows that claims to explain the fine tuning of our universe on the basis of such models by appeal to the existence of all possible universes fail.

John Norton has recently argued that Newtonian gravitation theory (at least as applied to cosmological contexts where one envisions the possibility of a homogeneous mass distribution throughout all of space) is inconsistent. I am not convinced. Traditional formulations of the theory may seem to break down in cases of the sort Norton considers. But the difficulties they face are only apparent. They are artifacts of the formulations themselves, and disappear if one passes to the so-called "geometrized" formulation of the theory.

Review of Michael Heller, Ultimate Explanations of the Cosmos, Springer, 2009.

In this paper I argue that we can solve the interpretation problem of quantum mechanics and the question of ontology of Quantum Field Theory on the basis of simple metaphysical position: The connection of the phase space with the ancient Theory of Logi of Beings, which is, by giving ontological meaning to the entities which "live" at the phase space, the Hamiltonian or Lagrangian formalism. There is a physical subject of such functions and it is the logos of a being. (...) Therefore we can refer to the logical space as the total sum of logi of being. The result of this position is that we can attribute to the wave function a physical meaning, a special case of logos of a being and also give an ontological meaning at a quantum field. The developed metaphysical scheme can interpret the quantum paradoxes, by using the commonly accepted mathematical formalism. It can also interpret certain issues of Quantum Field Theory, although further study of this topic is necessary. (shrink)

In this paper, a survey is made of some of the contributionsto the interpretation of Hartle and Hawking's theory of thewave function of the universe and its beginning. It is arguedthat there are considerable difficulties with the interpretationof the theory, but that there is at least one interpretationhitherto not found in the literature which survives existingphilosophical objections.

The claims of some authors to have introduced a new type of explanation in cosmology, based on the anthropic principle, are examined and found wanting. The weak anthropic principle is neither anthropic nor a principle. Either in its direct or in its Bayesian form, it is a mere tautology lacking explanatory force and unable to yield any prediction of previously unknown results. It is a pattern of inference, not of explanation. The strong anthropic principle is a gratuitous speculation with no (...) other support than previous religious commitment or the assumption of an actual infinity of universes, for which there is no the slightest empirical hint. But even assuming so much, it does not work. In particular, the assumption of an infinity of different universes is no guarantee of finding among them one like this one. The loose anthropic way of reasoning does not stand up to the usual methodological standards of empirical science. And it does not signal any anthropocentric turn in contemporary science. (shrink)

The paper is inspired by the arguments raised recently by Grunbaum criticizing the current approaches of many cosmologists to the problem of spacetime singularity, matter creation and the origin of the universe. While agreeing with him that the currently favored cosmological ideas do not indicate the biblical notion of divine creation ex nihilo, I present my viewpoint on the same issues, which differs considerably from Grunbaum's. First I show that the symmetry principle which leads to the conservation law of energy (...) is violated when the time axis is terminated at t = 0. Next I discuss why this epoch (t = 0) is more a mathematical artifact whose supposed significance may disappear when one goes beyond the classical relativistic cosmology. This is illustrated by the example of quantum cosmology. (shrink)

In [3], Quentin Smith claims that `the Hartle Hawking cosmology' is inconsistent with classical theism in a way which redounds to the discredit of classical theism; and, moreover, that the truth of `the Hartle Hawking cosmology' would undermine reasonsed belief in any other varieties of theism which hold that the universe is created.

In [3], Quentin Smith claims that `the Hartle-Hawking cosmology' is inconsistent with classical theism in a way which redounds to the discredit of classical theism; and, moreover, that the truth of `the Hartle- Hawking cosmology' would undermine reasonsed belief in any other varieties of theism which hold that the universe is created.

We analyse aspects of the Big Bang program in modern cosmology, with special focus on the strategies employed by its adherents both in defending the theory against anomalous data and in dismissing rival accounts. We illustrate this by critically examining four aspects of Big Bang cosmology: the interpretation of the cosmic red-shift, the explanation of the cosmic background radiation, the inflation hypothesis and the search for dark matter. We conclude that the Big Bang's dominance of contemporary cosmology (...) is not justified by the degree of experimental support it receives relative to rival theories. (shrink)

I analyse two different methods for the retrieval of a classical notion of spacetime from the theory of quantum cosmology in terms of the different means they employ to bring about the necessary loss of coherence. One method employs a direct coarse graining of the appropriate phase space, whereas the other method is based on decohering the system by the interaction with an environment. Although these methods are equivalent on a phenomenological level, I argue that conceptually the decoherence approach is (...) superior. The coarse graining approach construes the necessary loss of coherence in epistemic terms, whereas the method based on decohering the system by interaction with an environment provides a dynamical explanation for the emergence of classical notions of spacetime. On the latter account the emergence of classical behaviour is an objective property of the physical system under consideration, in contradistinction with the subjective coarse graining account of the retrieval of a classical spacetime in terms of measurements made by an observer. (shrink)

The creation-of-matter hypothesis of the Bondi-Gold-Hoyle steady-state cosmology requires that in an infinite time to which the first transfinite number may be assigned the number of atoms of matter produced would be equal to the cardinal number of the set of mathematical points in the continuum. The existence of a set of finite atoms with that cardinal number is physically unacceptable. The argument for the production of a non-denumerable set of atoms, in infinite time, is given in terms of a (...) model which is shown to be isomorphic with the original Cantor "diagonal" proof for the existence of a non-denumerable infinity. An alternative model which meets the requirements of the steady-state theory is presented; in this model, the number of atoms is explicitly no greater than countably infinite, and remains countably infinite as long as the past time of the universe is restricted to the unlimited set of finite unit-time intervals. If the origin of the steady-state universe is taken as being within that infinite set, expressed by the negative natural numbers, the contradiction of an atom at every mathematical point does not arise. The contradiction does arise if the origin is not within the set of finite numbers, and accordingly there is a restriction as to which concept of infinite past may properly be maintained in the steady-state theory. (shrink)

A discussion of European understanding of the physical world from the 9th century to the 15th, ranging from astronomy to zoology and refuting the more recent ...

So tight was his perception of reality he could find no room in it for empty space; a position which led him to deny the reality of motion. ...

In this note a recently developed quantum oscillating finite space cosmological model is described. The principle novelty of the model is that there is a quantum blurring of the classical singularity between cycles, instead of a singularity free bounce. Recently, Quentin Smith (1988) has argued that present theoretical and observational evidence justifies the belief that the past history of the universe is finite. The relevance of this cosmological model to Smith's arguments is discussed.

'In principle, one can predict everything in the universe solely from physical laws. Thus, the long standing 'first cause' problem intrinsic in cosmology has finally been dispelled.' Fang and Wu, (1986):3).

There is sufficient evidence at present to justify the belief that the universe began to exist without being caused to do so. This evidence includes the Hawking-Penrose singularity theorems that are based on Einstein's General Theory of Relativity, and the recently introduced Quantum Cosmological Models of the early universe. The singularity theorems lead to an explication of the beginning of the universe that involves the notion of a Big Bang singularity, and the Quantum Cosmological Models represent the beginning largely in (...) terms of the notion of a vacuum fluctuation. Theories that represent the universe as infinitely old or as caused to begin are shown to be at odds with or at least unsupported by these and other current cosmological notions. (shrink)

Richard Tarnas’s The Passion of the Western Mind —acclaimed by leading voices in philosophy, religion, psychology, and history—sets the stage for this major work, thirty years in the making, that dramatically reframes our understanding of the universe in the light of extraordinary new evidence. Cosmos and Psyche is the first book by a widely respected scholar to demonstrate the existence of a consistent correspondence between planetary movements and the unfolding drama of human history. A vast and impressive body of evidence (...) illuminates patterns of meaning and precise correlations between the universe and the world of human endeavor. With meticulous detail, Richard Tarnas takes us on a journey that begins with the ancient Greeks and culminates in our own era and its transformative potential, putting into perspective these chaotic, tumultuous times—from the sixties to September 11, 2001—and pointing the way towards the future. In terms of planetary cycles, our present moment in history is most comparable to the period five hundred years ago—that era of “extraordinary turbulence and creativity,” the High Renaissance. Not since Copernicus conceived the heliocentric theory has the human community faced such a profound realignment of the way we think. Readers of every persuasion will be impressed by the vast canvas here, the wealth of research and analysis, and the profound conclusions that may be drawn—conclusions that reunite religion and science, and restore a transcendent dimension to the universe. (shrink)

This paper follows up a debate as to the consistency of Newtonian cosmology. Whereas Malament (1995) has shown that Newtonian cosmology *is* not inconsistent, to date there has been no analysis of Norton’s claim (1995) that Newtonian cosmology *was* inconsistent prior to certain advances in the 1930s, and in particular prior to Seeliger’s seminal paper of 1895. In this paper I agree that there are assumptions, Newtonian and cosmological in character, and relevant to the real history of science, which are (...) inconsistent. But there are some important corrections to make to Norton’s account. Here I display for the first time the inconsistencies—four in total—in all their detail. Although this extra detail shows there to be several different inconsistencies, it also goes some way towards explaining why they went unnoticed for two hundred years. (shrink)

Jan Greben criticized fine-tuning by taking seriously the idea that nature is quantum mechanical . I argue that this quantum view is limited, and that fine-tuning is real, in the sense that our current physical models require fine-tuning. Second, I examine and clarify many difficult and fundamental issues raised by Rüdiger Vaas’ comments on Cosmological Artificial Selection.

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself increases in (...) entropy, and that (iii) the Second Law of thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse. (shrink)

Two and a half thousand years ago Greek philosophers "looked up at the sky and formed a theory of everything." Though their solutions are little credited today, the questions remain fresh. Early Greek thinkers struggled to come to terms with and explain the totality of their surroundings, to identitify an original substance from which the universe was compounded, and to reconcile the presence of balance and proportion with the apparent disorder of the cosmos. M. R. Wright examines cosmological theories of (...) the "natural philosophers" from Thales, Anaximander and Anaximenes to Plato, the Stoics and the NeoPlatonists. The importance of Babylonian and Egyptian forerunners is also emphasized. Cosmology in Antiquity is a comprehensive introduction to the cosmological thought in ancient times. (shrink)