We ordinarily assume that we have reliable knowledge of our immediate surroundings, so much so that almost all the time we entrust our lives to the truth of what we take ourselves to know, without a moment’s thought. But if, as Karl Popper and others have maintained, all our knowledge is conjectural, then this habitual assumption that our common sense knowledge of our environment is secure and trustworthy would seem to be an illusion. Popper’s philosophy of science, in particular, fails (...) to do justice to the distinction we ordinarily draw between secure knowledge and mere conjecture. But Popper’s philosophy of science, in particular his attempted solution to the problem of induction, is defective. It fails to take into account that physics, in only accepting unified theories, even though endlessly empirically more successful disunified rivals are always available, makes the persistent metaphysical assumption that all disunified theories are false. Once this point is acknowledged, it becomes clear that a new conception of scientific method is required which sees science as making a hierarchy of metaphysical assumptions concerning the comprehensibility and knowability of the universe. This provides a framework of relatively unproblematic assumptions and associated methods of science within which much more problematic assumptions and associated methods can be critically assessed and improved. This hierarchical view seems at first to intensify the problem of distinguishing certainty from conjecture, in that it emphasizes that scientific knowledge, and even humble common sense knowledge, contain usually unacknowledged cosmological conjectures. But actually it explicates the basis we have for drawing the distinction between trustworthy knowledge and mere conjecture, and even goes some way towards providing a rationale for this distinction, in so far as one exists. (shrink)

Recent developments in cosmology and particle physics have led to speculation that our universe is merely one of a multitude of universes. While this notion, the multiverse hypothesis, is highly contested as legitimate science, it has nonetheless struck many physicists as a necessary consequence of the effort to construct a final, unified theory. In Process and Reality (1929), his magnum opus, Alfred North Whitehead advanced a cosmology as part of his general metaphysics of process. Part of this project involved a (...) theory of cosmic epochs which bears a remarkable affinity to current cosmological speculation. This paper demonstrates how the basic framework of a multiverse theory is already present in Whitehead’s cosmology and defends the necessity of speculation in the quest for an explanatory description. (shrink)

Kant’s early essay, Universal Natural History and Theory of the Heavens, is commonly regarded as an original contribution to the development of Newtonian cosmological ideas, and as a step in the evolution of Kant’s own thought. In this paper I try to show, firstly, that despite the recognised debt to Newton’s Principia, the young German thinker makes a personal philosophical synthesis of several ancient and modern sources of cosmological thought; secondly, that besides the novelty of the exposed (...) class='Hi'>conjectures about the mechanical production and systematic constitution of the Universe as a whole, and beyond the boldness of the proposed perspectives on the origins and continuous formation or creation of the Cosmos, this essay is also an interesting example of the manner how the young Kant works in such matters as cosmology and cosmogony. There, we can perceive and identify the epistemic presuppositions he puts in action, which are founded in the principle of analogy, used largely as a heuristic principle when the direct observation of phenomena is not possible or the propositions of natural philosophy cannot reach the mathematical precision and geometrical rigour. (shrink)

In recent years, observational techniques at cosmological distances have been sufficiently improved that cosmology has become an empirical science, rather than a field for unchecked speculation. There remains the fact that its object, the whole universe, exists only once; hence, we are unable to separate “general” features from particular aspects of “our” universe. This might not be a serious drawback if we were justified in the belief that presently accepted laws of nature remain valid on the cosmological scale. (...) In the author's opinion, however, there are grounds for doubting that belief. The three arguments presented are (1) the possibility that apparent constants of nature may, during cosmological times, turn out to vary (Dirac conjecture); (2) the effective breakdown of the principle of relativity caused by the effects of the cosmological environment on local experiments; and (3) the fact that present theory leads to field singularities at the early stages of the expanding universe, which might be a signal that currently accepted theoretical concepts are inadequate for an understanding of highly condensed matter. (shrink)

Elaborating on an old conjecture by Blackett, we formulate a new conjecture about the neutrality of matter according to which any physical system possesses an active electric charge proportional to its mass. We discuss limits on the conjecture coming from existing laboratory experiments on the neutrality of matter and from the observation of the global surface electric field of the Earth. In a cosmological setting, we show that a cosmic rotation of the Universe is inevitable if our conjecture is (...) true and if the magnetic fields observed today in large-scale gravitationally bounded objects and cosmic voids have a primordial origin. Finally, we discuss the possibility that the angular momentum of spiral galaxies could be a signature of a rotating Universe. (shrink)

During the last three decades, there has been a growing realization among physicists and cosmologists that the relation between particle physics and cosmology may constitute yet another successful example of the unity of science. However, there are important conceptual problems in the unification of the two disciplines, e.g. in connection with the cosmological constant and the conjecture of inflation. The present article will outline some of these problems, and argue that the victory for the unity of science in the (...) context of cosmology and particle physics is still far from obvious. (shrink)

Cosmological questions (e.g., how far the world extends and how it all began) have occupied humans for ages and given rise to numerous conjectures, both within and outside philosophy. To put to rest fruitless speculation, Kant argued that these questions move beyond the limits of human knowledge. This article begins with Kant’s doubts about cosmology and shows that his arguments presuppose unreasonably high standards on knowledge and unwarranted assumptions about space-time. As an analysis of the foundations of twentieth-century (...) cosmology reveals, other worries about the discipline can be avoided too if the universe is modeled using Einstein’s general theory of relativity. There is now strong observational support for one particular model. However, due to underdetermination problems, the big cosmological questions cannot be fully answered using this model either. This opens the space for more speculative proposals again (e.g., that the universe is only part of a huge multiverse). (shrink)

Six "divine conjectures" frame the place of Theóne (The One to Whom we pray) in the creation of our universe and for its continuing development in five subsequent stages into a loving universe. The first stage, the cosmological universe, establishes the laws of nature, understood by scientists as the "standard model". The second stage introduces life and death into the universe by a process we are only now beginning to understand. Stage 3 requires certain life forms to become (...) conscious with a subset of those life-forms acquiring language that results in that subset becoming self-conscious. The next stage, Conjecture 4, identifies certain persons who become addicted to learning in their unrelenting effort to learn as much of what can be known as possible. The fifth conjecture requires individual persons to act as agents of Theóne in achieving Conjecture 6—a universe that is both loving and lawful. During the course of the exposition subsidiary discussions of the concepts of conjecture and hypothesis explicate the function of each in the advancement of knowledge and understanding. There are brief discussions of prayer and purpose in relation to the Divine. (shrink)

This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

Cosmological speculation about the ultimate nature of the universe, being necessary for science to be possible at all, must be regarded as a part of scientific knowledge itself, however epistemologically unsound it may be in other respects. The best such speculation available is that the universe is comprehensible in some way or other and, more specifically, in the light of the immense apparent success of modern natural science, that it is physically comprehensible. But both these speculations may be false; (...) in order to take this possibility into account, we need to adopt an hierarchy of increasingly contentless cosmological conjectures until we arrive at the conjecture that the universe is such that it is possible for us to acquire some knowledge of something, a conjecture which we are justified in accepting as knowledge since doing so cannot harm the pursuit of knowledge in any circumstances whatsoever. As a result of adopting such an hierarchy of increasingly contentless cosmological conjectures in this way, we maximize our chances of adopting conjectures that promote the growth of knowledge, and minimize our chances of taking some cosmological assumption for granted that is false and impedes the growth of knowledge. The hope is that as we increase our knowledge about the world we improve (lower level) cosmological assumptions implicit in our methods, and thus in turn improve our methods. As a result of improving our knowledge we improve our knowledge about how to improve knowledge. Science adapts its own nature to what it learns about the nature of the universe, thus increasing its capacity to make progress in knowledge about the world. This aim-oriented empiricist conception of science solves outstanding problems in the philosophy of science such as the problems of induction, simplicity and verisimilitude. (shrink)

We develop and apply a multi-dimensional account of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that establishes initial conditions fine-tuning as a dimension of explanatory depth relevant to debates in contemporary cosmology. We propose dynamical fine-tuning and autonomy as two further dimensions of depth in the context of problems with instability and trans-Planckian modes that afflict bouncing and inflationary approaches respectively. In (...) the context of the latter issue, we argue that the recently formulated trans-Planckian censorship conjecture leads to a trade-off for inflationary models between dynamical fine-tuning and autonomy. We conclude with the suggestion that explanatory preference with regard to the different dimensions of depth is best understood in terms of differing attitudes towards heuristics for future model building. (shrink)

We develop and apply a multi-dimensional conception of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that establishes initial condition fine-tuning as a dimension of explanatory depth relevant to debates in contemporary cosmology. We propose dynamical fine-tuning and autonomy as two further dimensions of depth in the context of problems with instability and trans-Planckian modes that afflict bouncing and inflationary approaches respectively. In (...) the context of the latter issue, we argue that the recently formulated trans-Planckian censorship conjecture leads to a trade-off for inflationary models between dynamical fine-tuning and autonomy. We conclude with the suggestion that explanatory preference with regard to the different dimensions of depth is best understood in terms of differing attitudes towards heuristics for future model building. (shrink)

I provide some philosophical groundwork for the recently proposed ‘trans-Planckian censorship’ conjecture in theoretical physics. In particular, I argue that structure formation in early universe cosmology is, at least as we typically understand it, autonomous with regards to quantum gravity, the high energy physics that governs the Planck regime in our universe. Trans-Planckian censorship is then seen as a means of rendering this autonomy an empirical constraint within ongoing quantum gravity research.

I provide some philosophical groundwork for the recently proposed ‘trans-Planckian censorship’ conjecture in theoretical physics. In particular, I argue that structure formation in early universe cosmology is, at least as we typically understand it, autonomous with regards to quantum gravity, the high energy physics that governs the Planck regime in our universe. Trans-Planckian censorship is then seen as a means of rendering this autonomy an empirical constraint within ongoing quantum gravity research.

In the absence of a fundamental theory that precisely predicts values for observable parameters, anthropic reasoning attempts to constrain probability distributions over those parameters in order to facilitate the extraction of testable predictions. The utility of this approach has been vigorously debated of late, particularly in light of theories that claim we live in a multiverse, where parameters may take differing values in regions lying outside our observable horizon. Within this cosmological framework, we investigate the efficacy of top-down anthropic (...) reasoning based on the weak anthropic principle. We argue contrary to recent claims that it is not clear one can either dispense with notions of typicality altogether or presume typicality, in comparing resulting probability distributions with observations. We show in a concrete, top-down setting related to dark matter, that assumptions about typicality can dramatically affect predictions, thereby providing a guide to how errors in reasoning regarding typicality translate to errors in the assessment of predictive power. We conjecture that this dependence on typicality is an integral feature of anthropic reasoning in broader cosmological contexts, and argue in favour of the explicit inclusion of measures of typicality in schemes invoking anthropic reasoning, with a view to extracting predictions from multiverse scenarios. (shrink)

In theories of gravity with a positive cosmological constant, we consider product solutions with flux, of the form (A)dS p ×S q . Most solutions are shown to be perturbatively unstable, including all uncharged dS p ×S q spacetimes. For dimensions greater than four, the stable class includes universes whose entropy exceeds that of de Sitter space, in violation of the conjectured “N-bound.” Hence, if quantum gravity theories with finite-dimensional Hilbert space exist, the specification of a positive cosmological (...) constant will not suffice to characterize the class of spacetimes they describe. (shrink)

This essay focuses on the concept of consciousness in C. S. Peirce’s work, revealing how its ways of being are associated with the three Peircean phenomenological categories. In this article, I intend to reflect on the heuristic power of the mind, namely, its ability to bring about new ideas, which, within Peirce’s logic of inquiry, is called by the well-known term of abduction. The abductive logical step promotes a synthesis of signs that constitutes a logical structure capable of proposing a (...) new mediation or representation of a new phenomenon. I make use of a metaphorical passage from Peirce not only to give the title to this essay, but also to highlight the importance of the first category as a sort of synechistic envelopment of an unprecedented logical structure of signs that composes a new synthesis. Two continua intertwine themselves, namely, those of the first and third categories, to account for what appears as a fact of the world in the theater of secondness. The essay also seeks to bring to light the core realism of Peirce’s philosophy, the genetic aspect of this bottomless lake, through its cosmology, where the generalization of forms and the acquisition of habits of reality are the proper ground of his Objective Idealism. One of the heuristic aspect of the lake metaphor is a sort of invitation to extend the concept of synthesis from the realm of logical structures to that one of arts, which in this essay will remain as a suggestion for a further reflection. (shrink)

The Big Bang singularity in standard model cosmology suggests a program of study in ‘early universe’ quantum gravity phenomenology. Inflation is usually thought to undermine this program’s prospects by means of a dynamical diluting argument, but such a view has recently been disputed within inflationary cosmology, in the form of a ‘trans-Planckian censorship’ conjecture. Meanwhile, trans-Planckian censorship has been used outside of inflationary cosmology to motivate alternative early universe scenarios that are tightly linked to ongoing theorizing in quantum gravity. Against (...) the resulting trend toward early universe quantum gravity phenomenology within and without inflation, Ijjas and Steindhardt suggest a further alternative: a ‘generalized cosmic censorship’ principle. I contrast the generalized cosmic censorship principle with the logic of its namesake, the cosmic censorship conjectures. I also remark on foundational concerns in the effective field theory approach to cosmology beyond the standard model, which would be based on that principle. (shrink)

A methodology of science must satisfy two requirements: (i) It must be ampliative: the theories which it generates must make statements that go far beyond any data or observations that may have motivated those theories in the first place. (ii) It must be epistemically probative: it must somehow provide a warrant for believing that the theories so produced are correct, or at least partially correct, even if they can never be fully confirmed. These two requirements pull in opposite directions, and (...) attempts to specify the “scientific method” often focus on one to the exclusion of the other. On a few points there now exists something approaching a consensus. (i) Scientific hypotheses — including, particularly, statements about unobserved or unobservable entities or mechanisms — remain conjectural, no matter how frequently predictions based on those hypotheses are found to coincide with data. (ii) A good (best?) indicator of a theory’s verisimilitude is its ability to successfully predict phenomena which it was not specifically designed to predict. I discuss these ideas with particular reference to cosmological theories. (shrink)

Around 3 decades ago, Jayant Narlikar & Halton Arp argued on possible variable mass hypothesis cosmology (VMH). In the meantime, the Earth expansion problem has attracted great interest, and recent study gives geodetic evidence that the Earth has been expanding, at least over the recent several decades. Therefore, in the present article discusses some interesting effects related to varying G, but here we argue that instead of varying G we can think of varying mass (M). Among other things we discuss (...) receding planets from the Sun, calculation of Pioneer spacecraft anomaly as proposed by B.G. Sidharth, and also possible slight change of LAGEOS Satellite. Further observation to verify or refute this conjecture is recommended, especially based on geological evidence of expanding earth. (shrink)

Recent models in quantum cosmology make use of the concept of imaginary time. These models all conjecture a join between regions of imaginary time and regions of real time. We examine the model of James Hartle and Stephen Hawking to argue that the various no-boundary attempts to interpret the transition from imaginary to real time in a logically consistent and physically significant way all fail. We believe this conclusion also applies to quantum tunneling models, such as that proposed by Alexander (...) Vilenkin. We conclude, therefore, that the notion of emerging from imaginary time is incoherent. A consequence of this conclusion seems to be that the whole class of cosmological models appealing to imaginary time is thereby refuted. (shrink)

The basic theme of Popper's philosophy--that something can come from nothing--is related to the present situation in physical theory. Popper carries his investigation right to the center of current debate in quantum physics. He proposes an interpretation of physics--and indeed an entire cosmology--which is realist, conjectural, deductivist and objectivist, anti-positivist, and anti-instrumentalist. He stresses understanding, reminding us that our ignorance grows faster than our conjectural knowledge.

Here, we briefly review the notion of observational indistinguishability within the context of classical general relativity. We settle a conjecture given by Malament (1977) concerning the subject and then strengthen the result considerably. The upshot is this: There seems to be a robust sense in which the global structure of every cosmological model is underdetermined.

This work investigates how ancient philosophers understood productive knowledge or technê and used it to explain ethics, rhetoric, politics and cosmology. In eleven chapters leading scholars set out the ancient debates about technê from the Presocratic and Hippocratic writers, through Plato and Aristotle and the Hellenistic age, ending in the Neoplatonism of Plotinus and Proclus. Amongst the many themes that come into focus are: the model status of ancient medicine in defining the political art, the similarities between the Platonic and (...) Aristotelian conceptions of technê, the use of technê as a paradigm for virtue and practical rationality, technê´s determining role in Platonic conceptions of cosmology, technê´s relationship to experience and theoretical knowledge, virtue as an 'art of living', the adaptability of the criteria of technê to suit different skills, including philosophy itself, the use in productive knowledge of models, deliberation, conjecture and imagination. (shrink)

Joel Feinberg : In Memoriam. Preface. Part I: INTRODUCTION TO THE NATURE AND VALUE OF PHILOSOPHY. 1. Joel Feinberg: A Logic Lesson. 2. Plato: "Apology." 3. Bertrand Russell: The Value of Philosophy. PART II: REASON AND RELIGIOUS BELIEF. 1. The Existence and Nature of God. 1.1 Anselm of Canterbury: The Ontological Argument, from Proslogion. 1.2 Gaunilo of Marmoutiers: On Behalf of the Fool. 1.3 L. Rowe: The Ontological Argument. 1.4 Saint Thomas Aquinas: The Five Ways, from Summa Theologica. 1.5 Samuel (...) Clarke: A Modern Formulation of the Cosmological Argument. 1.6 William L. Rowe: The Cosmological Argument. 1.7 William Paley: The Argument from Design. 1.8 Michael Ruse: The Design Argument. 1.9 David Hume: Dialogues Concerning Natural Religion. 2. The Problem of Evil. 2.1 Fyodor Dostoyevsky: Rebellion. 2.2 J. L. Mackie: Evil and Omnipotence. 2.3 Peter van Inwagen: The Argument from Evil. 2.4 Michael Murray and Michael Rea: The Argument from Evil. 2.5 B. C. Johnson: God and the Problem of Evil. 3. Reason and Faith. 3.1 W. K. Clifford: The Ethics of Belief. 3.2 William James: The Will to Believe. 3.3 Kelly James Clark: Without Evidence or Argument. 3.4 Blaise Pascal: The Wager. 3.5 Lawrence Shapiro: Miracles and Justification. 3.6 Simon Blackburn: Infini-Rien. Part III. HUMAN KNOWLEDGE: ITS GROUNDS AND LIMITS. 1. Skepticism. 1.1 John Pollock: A Brain in a Vat. 1.2 Michael Huemer: Three Skeptical Arguments. 1.3 Robert Audi: Skepticism. 2. The Nature and Value of Knowledge. 2.1 Plato: Knowledge as Justified True Belief. 2.2 Edmund Gettier: Is Justified True Belief Knowledge? 2.3 James Cornman, Keith Lehrer, and George Pappas: An Analysis of Knowledge. 2.4 Gilbert Ryle: Knowing How and Knowing That. 2.5 Plato: "Meno". 2.6 Linda Zagzebski, Epistemic Good and The Good Life. 3. Our Knowledge of the External World. 3.1 Bertrand Russell: Appearance and Reality and the Existence of Matter. 3.2 René Descartes: Meditations on First Philosophy. 3.3 John Locke: The Causal Theory of Perception. 3.4 George Berkeley: Of the Principles of Human Knowledge. 3.5 G. E. Moore: Proof of an External World. 4. The Methods of Science. 4.1 David Hume: An Inquiry Concerning Human Understanding. 4.2 Wesley C. Salmon: An Encounter with David Hume. 4.3 Karl Popper: Science: Conjectures and Refutations. 4.4 Philip Kitcher: Believing Where We Cannot Prove. Part IV: MIND AND ITS PLACE IN NATURE. 1. The Mind-Body Problem. 1.1 Brie Gertler: In Defense of Mind--Body Dualism. 1.2 Frank Jackson: The Qualia Problem. 1.3 David Papineau: The Case for Materialism. 1.4 Paul Churchland: Functionalism and Eliminative Materialism. 2. Can Non-Humans Think? 2.1 Alan Turing: Computing Machinery and Intelligence. 2.2 John R. Searle: Minds, Brains, and Programs. 2.3 William G. Lycan: Robots and Minds. 3. Personal Identity and the Survival of Death. 3.1 John Locke: The Prince and the Cobbler. 3.2 Thomas Reid: Of Mr. Locke’s Account of Our Personal Identity. 3.3 David Hume: The Self. 3.4 Derek Parfit: Divided Minds and the Nature of Persons. 3.5 Shelly Kagan: What Matters. 3.6 John Perry: A Dialogue on Personal Identity and Immortality. Part V: DETERMINISM, FREE WILL, AND RESPONSIBILITY. 1. Libertarianism: The Case for Free Will and Its Incompatibility with Determinism. 1.1 Roderick M. Chisholm: Human Freedom and the Self. 1.2 Robert Kane: Free Will: Ancient Dispute, New Themes. 2. Hard Determinism: The Case for Determinism and its Incompatibility with Its Incompatibility with Any Important Sense of Free Will. 2.1 James Rachels: The case against Free Will. 2.2 Derk Pereboom: Why We Have No Free Will and Can Live Without It. 3. Compatibilism: The Case for Determinism and Its Compatibility with the Most Important Sense of Free Will. 3.1 David Hume: Of Liberty and Necessity. 3.2 Helen Beebee: Compatibilism and the Ability to do Otherwise. 4. Freedom and Moral Responsibility. 4.1 Galen Strawson: Luck Swallows Everything. 4.2 Harry Frankfurt: Alternate Possibilities and Moral Responsibility. 4.3 Thomas Nagel: Moral Luck. 4.4 Susan Wolf: Sanity and the Metaphysics of Responsibility. Part VI: MORALITY AND ITS CRITICS. 1. Changes to Morality. 1.1 Joel Feinberg: Psychological Egoism. 1.2 Plato: The Immoralist’s Challenge. 1.3 Friedrich Nietzche: Master and Slave Morality. 1.4 Richard Joyce: The Evolutionary Debunking of Morality. 2. Proposed Standards and Right of Conduct. 2.1 Russ Shafer-Landau: Ethical Subjectivism. 2.2 Mary Midgley: Trying Out One’s New Sword. 2.3 Aristotle: Virtue and the Good Life. 2.4 Thomas Hobbes: Leviathan. 2.5 Plato: Euthyphro. 2.6 Immanuel Kant: The Good Will and the Categorical Imperative. 2.7 J.S. Mill: Utilitarianism, Chapters 2 and 4. 2.8 W. D. Ross: What Makes Right Acts Right? 2.9 Hilde Lindemann: What Is Feminist Ethics? 3. Ethical Problems. 3.1 Kwame Anthony Appiah: What Will Future Generations Condemn Us For? 3.2 Peter Singer: Famine, Affluence and Morality. 3.3 John Harris: The Survival Lottery. 3.4 James Rachels: Active and Passive Euthanasia. 3.5 Mary Anne Warren: The Moral and Legal Status of Abortion. 3.6 Don Marquis: Why Abortion Is Immoral. 4. The Meaning of Life. 4.1 Epicurus: Letter to Menoeceus. 4.2 Richard Taylor: The Meaning of Life. 4.3 Richard Kraut: Desire and the Human Good. 4.4 Leo Tolstoy: My Confession. 4.5 Susan Wolf: Happiness and Meaning. 4.6 Thomas Nagel: The Absurd. (shrink)

I critically discuss a controversial ‘trans-Planckian censorship’ conjecture, which has recently been introduced to researchers working at the intersection of fundamental physics and cosmology. My focus explicitly avoids any appeals to contingent research within string theory or regarding the more general gravitational ‘swampland’. Rather, I concern myself with the conjecture’s foundations in our current, well-trodden physics of quantized fields, spacetime, and gravity. In doing so, I locate what exactly within trans-Planckian censorship amounts to a departure from current physics—identifying what is, (...) ultimately, so conjectural about the conjecture. (shrink)

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In (...) this essay, I will honour Istvan's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and D\'avid might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis. (shrink)

String theory is often depicted as the best chance for natural science to find a Theory of Everything. Whiteheadians may object that only a philosophical cosmology such as Whitehead presents in PR can “frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted” (PR 3). But then they have to show that Whitehead’s scheme and string theory fit together nicely, with each helping to resolve residual problem areas in the (...) other. The present article conjectures that the tiny vibrating strings postulated by string theory and the superjects of individual actual entities might correspond to the “final, real things of which the world is made up” (PR 18). Likewise, the extra spatial dimensions required by the mathematics of string theory might be more intelligible in terms of the interaction of different levels of subsocieties within a Whiteheadian structured society. (shrink)

David Hume (1711-1776) is widely recognized as one of the most influential and significant critics of religion in the history of philosophy. There remains, nevertheless, considerable disagreement about the exact nature of his views. According to some, he was a skeptic who regarded all conjectures relating to religious hypotheses to be beyond the scope of human understanding – he neither affirmed nor denied these conjectures. Others read him as embracing a highly refined form of “true religion” of some (...) kind. On the other side of this spectrum, it is claimed that Hume was committed to atheism, although due to social conditions at the time, this had to be (thinly) concealed or masked. The aim of this article is to provide an overview of Hume’s core concerns and arguments on this subject and to provide the reader with a framework for interpreting and assessing his various contributions. (shrink)

The idea that the mass m of an elementary particle is explained in the semi-classical approximation by quantum-mechanical zero-point vacuum fluctuations has been applied previously to spin-1/2 fermions to yield a real and positive constant value for m, expressed through the spinorial connection Γ i in the curved-space Dirac equation for the wave function ψ due to Fock. This conjecture is extended here to bosonic particles of spin 0 and spin 1, starting from the basic assumption that all fundamental fields (...) must be conformally invariant. As a result, in curved space-time there is an effective scalar mass-squared term $m_{0}^{2}=-R/6=2\varLambda_{\mathrm{b}}/3$ , where R is the Ricci scalar and Λ b is the cosmological constant, corresponding to the bosonic zero-point energy-density, which is positive, implying a real and positive constant value for m 0, through the positive-energy theorem. The Maxwell Lagrangian density $\mathcal{L} =- \sqrt{-g}F_{ij}F^{ij}/4$ for the Abelian vector field F ij ≡A j,i −A i,j is conformally invariant without modification, however, and the equation of motion for the four-vector potential A i contains no mass-like term in curved space. Therefore, according to our hypothesis, the free photon field A i must be massless, in agreement with both terrestrial experiment and the notion of gauge invariance. (shrink)

Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z 2 and correlated (...) by conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:On Dante, Hyperspheres, and the Curvature of the Medieval CosmosWilliam EggintonIn the course of his lectures on medieval literature at Oxford University in the 1950s C. S. Lewis would ask students to walk alone at night, gaze at the star-filled sky, and try to imagine how it might look to a walker in the Middle Ages. It would not likely have occurred to him that some forty years later (...) several astrophysicists would ask that their readers perform the same activity, at least figuratively—not, however, with the intention of experiencing medieval conceptions of the cosmos but rather in order to begin to imagine the shape of our own. One of the astrophysicists in question is Stanford Professor Emeritus Robert Osserman, whose 1995 book The Poetry of the Universe is an attempt to acquaint lay readers with what the most recent research suggests is the shape of the universe by leading them through a brief history of the mathematical and technological developments that made such boundary-breaking thought possible. Paradoxically, when it comes to trying to imagine that all-encompassing form which is derived from a four-dimensional mathematical model called a hypersphere, he turns not to ultra-modern computer-generated images nor to dry but technically accurate exegeses of mathematical formulae but rather to the verses of a fourteenth-century Italian poet, Dante Alighieri. His claim is that in the third canticle of the Divine Comedy, which details his ascent through the heavens, Dante describes the cosmos with astonishing precision as a hypersphere, exactly as modern physics has determined it to be.If the cosmology of the present makes use of Dante heuristically, however, it never asks the most obvious question: Why? Why does one need to go back to the fourteenth century for a poetic description of how the universe appears to modern science? Osserman assumes it to be a mere coincidence, and why should he not? What possible access would a thinker—a poet even—of the European Middle Ages have to the highest achievements of almost six centuries of subsequent thought? In answering this question, I am not proposing to naively interpret the past in our own image, claiming Dante to be a mathematical genius [End Page 195] before his time. I am, however, suggesting that there is an excellent explanation for why one must look to the fourteenth century for models of expression adequate to the challenges posed by nineteenth and twentieth-century advances in mathematics: namely, that in the course of the Scientific Revolution, wherein were laid the epistemological foundations for the discoveries of modern science, certain possibilities of thought and imagination were discarded, forgotten, and certain abilities were, if only temporarily, lost. The Middle Ages has long been painted as a period whose culture was hostile to free thought and new knowledge; perhaps it is now time to recognize that it was also a time in which phenomena could sustain mutually exclusive and contradictory explanations, when the battle between faith and science had not yet been conclusively won by either side, and when the efforts to bridge the stories they told could produce conceptual edifices whose mere possibility would be unthinkable only 200 years later. This essay is about one such conceptual edifice and how openness to its perspective allowed a poet to put into words what could not be imagined by his descendants, and what eludes us even today.The Shape of the Modern UniverseImagine that you are a completely flat creature, living happily in your two-dimensional world.1 As observers we are outside this world, and we can see you milling about with your flat friends, blissfully unaware of the uncharted regions one dimension away on either side of you. Now imagine that this plane is not flat—in the sense of rectilineal—as you might have created it in your mind, but rather is curved; in fact it is a sphere. Assuming that this sphere is large enough, there is no reason that you, an inhabitant of this surface, should be aware of its curvature. Even we, the three-dimensional observers, if close enough to the surface, would not recognize its curvature. One could conjecture, however... (shrink)

ONE OBSERVATION FORCES ITSELF UPON US AT THE OUTSET. It is just as hard to think about the problem of life today as it was a hundred or a thousand years ago. If we observe the state of the sciences, we are led to the conviction that an important issue still remains open: to develop a philosophy of life and the organism that is adequate to the level of biological discoveries. Our most urgent need in the dialogue among science, philosophy, (...) and theology does not arise, as it has happened for centuries, from physics and cosmology but from the life sciences, notably biology and genetics. This is a necessity on which thinkers of different schools, such as Hans Jonas and John Polkinghorne, are agreed. Physics is no longer the guiding science, or the sole guiding science: its place has been taken by biology, and it is high time that philosophy and theology turned to address the issues it raises, without entrusting the realm of nature and life solely to the sciences. While there is still a rich crop of studies about the Big Bang theory and scientific cosmology in general, little has been written on philosophical biology, where the presence of the theologians has been exiguous. One may wonder why this should be so: perhaps because the Big Bang theory seems allusively to evoke the truth of the creation, though a more careful consideration of this scientific theory, rather controversial and highly speculative, shows that it has nothing to do with the theme of creation, as it deals only with the cosmic becoming: as such it is unable to formulate statements on what transcends becoming and on creation understood as the total position in being of all things. But one may also conjecture that this insufficient interest in biology stems from the difficult problem of teleology and, more generally, from the reductionist attitude frequently displayed by scientists when they pass beyond their own field of research and formulate hypotheses and theories with universal implications, as they are prompted by an unbridled enthusiasm which has proved ill-advised on other occasions in the past. (shrink)

If modern natural science were to be our guide, the truth of cosmology ought to be fully expressible in the abstruse but concise language of mathematics. As an account of the genesis of the universe as a whole and in its every part, however, a truly completed cosmology would culminate in an understanding of its own coming to be, and thereby provide both a recapitulation of the many past attempts human beings have made to understand themselves and their place, and (...) an explanation of the genesis of that which is true and false in each such attempt. For this and for other reasons one might well doubt whether a genuinely comprehensive cosmogenesis is possible for us, to say nothing of one set forth in exclusively mathematical terms. It seems fair to say, in any case, that that part of a conjectural history of the universe devoted to “the history of the human experience of the universe” would easily dwarf all of its other parts in size, and not only in size. (shrink)

_Conjectures and Refutations_ is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

_Conjectures and Refutations_ is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

This classic remains one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history.

Clayton and Stevens argue that political liberals should engage with the religiously unreasonable by offering religious responses and showing that their religious views are mistaken, instead of refusing to engage with them. Yet they recognize that political liberals will face a dilemma due to such religious responses: either their responses will alienate certain reasonable citizens, or their engagements will appear disingenuous. Thus, there should be a division of justificatory labour. The duty of engagement should be delegated to religious citizens. In (...) this comment, I will argue that the division of justificatory labour is indefensible. This dilemma can be avoided if politicians and political philosophers correctly use conjecture, a form of discourse that involves non-public reason. As a conditional response, conjecture avoids alienating any reasonable citizens. Also, if conjecture is given in a sincere and open-minded manner, then the problem of disingenuousness can be overcome. My comment concludes that while the engagement of politicians and political philosophers does not necessarily jeopardize overlapping consensus, they should be permitted, or perhaps even required, to engage with the religiously unreasonable due to the natural duty of justice. (shrink)

The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism: that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable'. Criticism of our conjectures is of decisive importance: by bringing out our mistakes (...) it makes us understand the difficulties of the problems which we try to solve. This is how we become better acquainted with our problem, and able to propose more mature solutions: the very refutation of a theory - that is, of a tentative solution to our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows, even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason here for despair of reason. And since we can never know for certain, the can be no authority here for any claim to authority, for conceit over our knowledge, or for smugness. The essays and lectures of which this book is composed apply this thesis to many topics, ranging from problems of the philosophy and history of the physical and social sciences to historical and political problems. (shrink)

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

. This paper outlines some major ideas concerning cosmogony and cosmogony and cosmology that pervade the Hindu conceptual world. The basic source for this discussion is the philosophical literature of some of the principal schools of Hindu thought, such as VaiVaiśika, Sānkhya, and Advaita Vedānta, focusing on the themes of cosmology, time, and soteriology. The core of Hindu philosophical thinking regarding these issues is traced back to the Rk Vedic cosmogonical speculations, analyzed, and contrasted with the “views of the opponent.” (...) The relevance of the Hindu worldview for overcoming the conflict between science and religion is pointed out. (shrink)

In this paper I argue that, in at least two cases - his discussions of the temporal precedence o f polytheism over monotheism and of the origins of civil society - we see Hume consigning to historical development certain aspects of reason which, as a comparison with Locke will show, have sometimes been held to be uniform. In the first of these cases Hume has recourse to claims about the general historical development of human thought. In the second case, the (...) origin of the civil institution of justice and government is not linked directly to external circumstances and the principles of human nature, as it is in contractarian theories, but makes a detour through the historical acquisition of certain concepts. Because Hume's position does not conform in any simple sense to Dugald Stewart's 'incontrovertible logical maxim' that the capacities of the human mind have been the same in all ages, Stewart's account of the method of conjectural history is, in any simple sense, inadequate as a description of Hume's practice. (shrink)

Ever since Copernicus, scientists have continually adjusted their view of human nature, moving it further and further from its ancient position at the center of Creation. But in recent years, a startling new concept has evolved that places it more firmly than ever in a special position. Known as the Anthropic Cosmological Principle, this collection of ideas holds that the existence of intelligent observers determines the fundamental structure of the Universe. In its most radical version, the Anthropic Principle asserts (...) that "intelligent information-processing must come into existence in the Universe, and once it comes into existence, it will never die out." This wide-ranging and detailed book explores the many ramifications of the Anthropic Cosmological Principle, covering the whole spectrum of human inquiry from Aristotle to Z bosons. Bringing a unique combination of skills and knowledge to the subject, John D. Barrow and Frank J. Tipler--two of the world's leading cosmologists--cover the definition and nature of life, the search for extraterrestrial intelligence, and the interpretation of the quantum theory in relation to the existence of observers. The book will be of vital interest to philosophers, theologians, mathematicians, scientists, and historians, as well as to anyone concerned with the connection between the vastness of the universe of stars and galaxies and the existence of life within it on a small planet out in the suburbs of the Milky Way. (shrink)