The Sciences

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

During the 19th century, much of the modern scientific enterprise took shape: scientific disciplines were formed, institutions and communities were founded and unprecedented applications to and interactions with other aspects of society and culture occurred. taught us about this exciting time and identify issues that remain unexamined or require reconsideration. They treat scientific disciplines - biology, physics, chemistry, the earth sciences, mathematics and the social sciences - in their specific intellectual and sociocultural contexts as well as the broader topics of science and medicine; science and religion; scientific institutions and communities; and science, technology and industry. From Natural Philosophy to the Sciences should be valuable for historians of science, but also of great interest to scholars of all aspects of 19th-century life and culture.

The Sciences of the Artificialreveals the design of an intellectual structure aimed at accommodating those empirical phenomena that are "artificial" rather than "natural." The goal is to show how empirical sciences of artificial systems are possible, even in the face of the contingent and teleological character of the phenomena, their attributes of choice and purpose. Developing in some detail two specific examples—human psychology and engineering design—Professor Simon describes the shape of these sciences as they are emerging from developments of the past 25 years. "Artificial" is used here in a very specific sense: to denote systems that have a given form and behavior only because they adapt (or are adapted), in reference to goals or purposes, to their environment. Thus, both man-made artifacts and man himself, in terms of his behavior, are artificial. Simon characterizes an artificial system as an interface between two environments—inner and outer. These environments lie in the province of "natural science," but the interface, linking them, is the realm of "artificial science." When an artificial system adapts successfully, its behavior shows mostly the shape of the outer environment and reveals little of the structure or mechanisms of the inner. The inner environment becomes significant for behavior only when a system reaches the limits of its rationality and adaptability, and contingency degenerates into necessity.

This book, published in 2000, examines the intersection between science and books from early medieval times to the nineteenth century.

To the scientists and philosophers of our time, Hegel has been either a ne glected or a provocative thinker, a source of irrelevant dark metaphysics or of complex but insightful analysis. His influence upon the work of natural scientists has seemed minimal, in the main; and his stimulus to the nascent sciences of society and to psychology has seemed to be as often an obstacle as an encouragement. Nevertheless his philosophical analysis of knowledge and the knowing process, of concepts and their evolutionary formation, of rationality in its forms and histories, of the stages of empirical awareness and human practice, all set within his endless inquiries into cultural formations from the entire sweep of human experience, must, we believe, be confronted by anyone who wants to understand the scientific consciousness. Indeed, we may wish to situate the changing theories of nature, and of humankind in nature, within a philosophical account of men and women as social practi tioners and as sensing, thinking, feeling centers of privacy; and then we will see the work of Hegel as a major effort to mediate between the purest of epistemological investigations and the most practical of the political and the religious. This book, long delayed to our deep regret, derives from a Symposium on Hegel and the Sciences which was sponsored jointly by the Hegel Society of America and the Boston University Center for Philosophy and History of Science a decade ago.

This book explores the work of Thomas Seebohm (1934-2014), a leading phenomenologist and hermeneuticist. It features papers that offer a critical and constructive dialogue about Seebohm’s analyses and their implications for the sciences. The net result is an in-depth study and a helpful overview of Seebohm’s general approach and his specific views on various areas of modern science. The contributors focus especially upon his final text, History as a Science and the System of the Sciences. They view this as the culmination and summary of his historical and phenomenological investigations into the foundations, nature, and limits of modern sciences. This includes not just history but the Geisteswissenschaften more generally, along with the social and natural sciences as well. The essays in this volume reflect that range. This volume presents insightful discussions about the nature and legitimacy of the human sciences as sciences and the unique character of the social sciences. It will be of interest not just as a matter of historical scholarship, but also and above all as an important contribution to phenomenology and to the philosophy of science and the sciences as such. It deserves attention by scholars from any philosophical tradition interested in thinking about the foundations of their disciplines and a philosophy of science that includes, but is not limited to, the natural sciences.

of him in like measure within myself, that is my highest wish. This noble individual was not conscious of the fact that at that very moment the divine within him and the divine of the universe were most intimately united. So, for Goethe, the resonance with a natural rationality seems part of the genius of modern science. Einstein's 'cosmic religion', which reflects Spinoza, also echoes Goethe's remark (Ibid. , Item 575 from 1829): Man must cling to the belief that the incomprehensible is comprehensible. Else he would give up investigating. But how far will Goethe share the devotion of these cosmic rationalists to the beautiful harmonies of mathematics, so distant from any pure and 'direct observation'? Kepler, Spinoza, Einstein need not, and would not, rest with discovery of a pattern within, behind, as a source of, the phenomenal world, and they would not let even the most profound of descriptive generalities satisfy scientific curiosity. For his part, Goethe sought fundamental archetypes, as in his intuition of a Urpjlanze, basic to all plants, infinitely plastic. When such would be found, Goethe would be content, for (as he said to Eckermann, Feb. 18, 1829): . . . to seek something behind (the Urphaenomenon) is futile. Here is the limit. But as a rule men are not satisfied to behold an Urphaenomenon. They think there must be something beyond. They are like children who, having looked into a mirror, turn it around to see what is on the other side.

This book is an intellectual journey into epistemology, pedagogy, physics, architecture, medicine and metallurgy. The focus is on various dimensions of African Indigenous Knowledge (AIK) with an emphasis on the sciences, an area that has been neglected in AIK discourse. The authors provide diverse views and perspectives on African indigenous scientific and technological knowledge that can benefit a wide spectrum of academics, scholars, students, development agents, and policy makers, in both governmental and non-governmental organizations, and enable critical and alternative analyses and possibilities for understanding science and technology in an African historical and contemporary context.