Natural Science

This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work. The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations. Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level. Contents:Mathematical Concepts and Physical ObjectsIncompleteness and Indetermination in Mathematics and PhysicsSpace and Time from Physics to BiologyInvariances, Symmetries, and Symmetry BreakingsCauses and Symmetries: The Continuum and the Discrete in Mathematical ModelingExtended Criticality: The Physical Singularity of Life PhenomenaRandomness and Determination in the Interplay between the Continuum and the DiscreteConclusion: Unification and Separation of Theories, or the Importance of Negative Results Readership: Graduate students and professionals in the fields of natural sciences, biology, computer science, mathematics, and physics. Keywords:Foundations of Mathematics and of Physics;Epistemology;Theoretical BiologyKey Features:This book is an epistemological reflection carried out by two working scientists, a physicist and a mathematician, who focus on biology. They first address a comparative analysis of the founding principles of their own disciplines. On the grounds of a three-fold blend, they then introduce a unique proposal, which does not passively transfer the paradigms of the first two theoretically well-established disciplines, to suggest a novel theoretical framework for the third discipline

"Translated by Frederick Amrine and Konrad Oberhuber from shorthand reports unrevised by the lecturer, from the 4th edition (1969) of the German text published under the title Grenzen der Naturerkenntnis (Vol. 322 in the Bibliographic survey)"--Copyright page.

A comparison of the cognitive foundations of religion and science and an argument that religion is cognitively natural and that science is cognitively unnatural.

5 public lectures and an evening discussion, various cities, June 17, 1920 - May 11, 1922 (CW 75) This previously untranslated volume in The Collected Works of Rudolf Steiner showcases Rudolf Steiner presenting the key concepts and methods of spiritual science to more or less skeptical academic audiences in the early 1920s. Step by step, he presented to his listeners the fundamentals of the anthroposophic path of knowledge. Steiner was less concerned with presenting results from his spiritual-scientific research than with leading his academic audience to an objective understanding of spiritual science in a propaedeutic, conceptually transparent way. The central questions of his approach were: What are the tools and instruments required to orient oneself in the world of the soul and the spirit? How can we know that the spiritual world is an objective world and not merely a psychic projection? What authorizes the spiritual researcher to acknowledge what he has experienced "on the other side" as a reality that is independent of him? Rudolf Steiner addresses these and other questions in such a structured and readily comprehensible way that the volume as a whole is well suited, both as an introductory text and as a means for anyone to deepen their understanding of how anthroposophy relates to and builds upon the natural sciences. At the time these presentations were given, serious voices had been raised denying Steiner's scientific credibility and denouncing his methods as unsound. Partly in response to such criticisms, Steiner here describes a means by which human beings can gain, through methodical and rigorous training, a direct experience of the spiritual dimension of life. He lays out the methodology of spiritual science, which is rooted in the scientific approach, outlining the three stages of higher knowledge --imagination, inspiration, and intuition --and describing the inner processes that lead from intellectual thinking to these higher modes of cognition. Ultimately, what Steiner proposes is not a deviation from the natural sciences but their expansion and development beyond unnecessary boundaries --that is, the establishment of anthroposophical spiritual science as a recognized method and practice of scientific research. This book is a translation from German of Das Verhältnis der Anthroposophie zur Naturwissenschaft, 1st edition (GA 75, Rudolf Steiner Verlag, Dornach, Switzerland, 2010).

New essays on Kant's complex work, considering its place in his oeuvre and in the history of science.

A concise introduction to scientific history and ideas, with a special emphasis on physics and astronomy. Physicist Stephen M. Barr’s lucid Student’s Guide to Natural Science aims to give students an understanding, in broad outline, of the nature, history, and great ideas of natural science from ancient times to the present, with a primary focus on physics. Barr begins with the contributions of the ancient Greeks, in particular the two great ideas that reality can be understood by the systematic use of reason and that phenomena have natural explanations. He goes on to discuss, among other things, the medieval roots of the scientific revolution of the seventeenth century, the role played by religion in fostering the idea of a lawful natural order, and the major breakthroughs of modern physics, including how many newer “revolutionary” theories are in fact related to much older ones. Throughout this thoughtful guide, Barr draws his readers’ attention to the larger themes and trends of scientific history, including the increasing unification and “mathematization” of our view of the physical world that has resulted in the laws of nature appearing more and more as forming a single harmonious mathematical edifice.