Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. Pincock tackles this perennial question by asking how mathematics contributes to the success of our best scientific representations.
This Element answers four questions. Can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? If traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain? What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not?
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.
This Element answers four questions. Can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? If traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain? What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not?
Fundamental Causation addresses issues in the metaphysics of deterministic singular causation, the metaphysics of events, property instances, facts, preventions, and omissions, as well as the debate between causal reductionists and causal anti-reductionists. The book also pays special attention to causation and causal structure in physics. Weaver argues that causation is a multigrade obtaining relation that is transitive, irreflexive, and asymmetric. When causation is singular, deterministic and such that it relates purely contingent events, the relation is also universal, intrinsic, and well-founded. He shows that proper causal relata are events understood as states of substances at ontological indices. He then proves that causation cannot be reduced to some non-causal base, and that the best account of that relation should be unashamedly primitivist about the dependence relation that underwrites its very nature. The book demonstrates a distinctive realist and anti-reductionist account of causation by detailing precisely how the account outperforms reductionist and competing anti-reductionist accounts in that it handles all of the difficult cases while overcoming all of the general objections to anti-reductionism upon which other anti-reductionist accounts falter. This book offers an original and interesting view of causation and will appeal to scholars and advanced students in the areas of metaphysics, philosophy of science, and philosophy of physics.
This book focuses on how to improve equal and public participation in a range of innovative citizen forums that could revitalize democracy around the world.
From the moment we wake until the time we go to sleep, we are bombarded by the benefits of science in the practical elements of everyday life. Electricity, lights, hot showers, breakfast cereals, clothing, cars, cell phones, roads, security systems, computers, communications, traffic lights, climate control, and entertainment are just a sampling of the many benefits of science. In addition to technological advances, medicine and agriculture progress with science as well. Even educational, political, and marketing strategists invoke science to substantiate their claims. Science dominates the collective Western mindset, and we regard it with the utmost respect. Yet society remains generally religious, even though science and religion are frequently thought of as being at odds with one another. How do we reconcile the two? Christians are taught to believe that God is in control of everything, including the natural elements. But how does God relate to physical laws? Is God in control of the world, or laws of nature? Could both views be correct? This book examines the Christian doctrine of divine providence and its implications for the laws of nature and the problem of induction before contrasting secular and Islamic approaches to these same topics.
While many interpreters hold that Hegel avoided the traditional problem of free will, Yeomans argues both that the problem is unavoidable, and that the two versions of the Logic fruitfully engage the tensions between explicability and both the control and alternate possibilities constitutive of free agency.
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