Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

As past president of both the History of Science Society and the American Society of Church History, Ronald L. Numbers is uniquely qualified to assess the historical relations between science and Christianity. In this collection of his most recent essays, he moves beyond the clichés of conflict and harmony to explore the tangled web of historical interactions involving scientific and religious beliefs. In his lead essay he offers an unprecedented overview of the history of science and (...) Christianity from the perspective of the ordinary people who filled the pews of churchesor loitered around outside. Unlike the elite scientists and theologians on whom most historians have focused, these vulgar Christians cared little about the discoveries of Copernicus, Newton, and Einstein. Instead, they worried about the causes of the diseases and disasters that directly affected their lives and about scientists preposterous attempts to trace human ancestry back to apes. Far from dismissing opinion-makers in the pulpit, Numbers closely looks at two the most influential Protestant theologians in nineteenth-century America: Charles Hodge and William Henry Green. Hodge, after decades of struggling to harmonize Gods two revelationsin nature and in the Biblein the end famously described Darwinism as atheism. Green, on the basis of his careful biblical studies, concluded that Ussher's chronology was unreliable, thus opening the door for Christian anthropologists to accommodate the subsequent discovery of human antiquity. In Science without God Numbers traces the millennia-long history of so-called methodological naturalism, the commitment to explaining the natural world without appeals to the supernatural. By the early nineteenth century this practice was becoming the defining characteristic of science; in the late twentieth century it became the central point of attack in the audacious attempt of intelligent designers to redefine science. Numbers ends his reassessment by arguing that although science has markedly changed the world we live in, it has contributed less to secularizing it than many have claimed. Taken together, these accessible and authoritative essays form a perfect introduction to Christian attitudes towards science since the 17th century. (shrink)

Focuses on Hartry Field's Instrumentalism. The ‘Conservation Theorems’, upon which Field bases so much of his form of Instrumentalism, are examined in detail, as is Field's attempt to ‘nominalize’ physics. Doubts are raised about the adequacy of Field's views of mathematics and physics, and a detailed comparison with the Constructibility Theory is presented.

FieldHartry. Science Without Numbers: A Defense of Nominalism 2nd ed.Oxford University Press, 2016. ISBN 978-0-19-877792-2. Pp. vi + 56 + vi + 111.

A collection of original essays offering a comprehensive history of the emergence of scientific naturalism. Beginning with the naturalists of ancient Greece, and proceeding through the middle ages, the scientific revolution, and into the nineteenth century, the contributors examine past ideas about 'nature' and 'the supernatural'. Ranging over different scientific disciplines and historical periods, they show how past thinkers often relied upon theological ideas and presuppositions in their systematic investigations of the world. In addition to providing material that contributes to (...) a history of 'nature' and naturalism, this collection challenges a number of widely held misconceptions about the history of scientific naturalism. (shrink)

In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some (...) advantages over existing nominalistic accounts of applied mathematics. It also provides a nominalistic account of pure mathematics. (shrink)

Numbers without Science opposes the Quine-Putnam indispensability argument, seeking to undermine the argument and reduce its profound influence. Philosophers rely on indispensability to justify mathematical knowledge using only empiricist epistemology. I argue that we need an independent account of our knowledge of mathematics. The indispensability argument, in broad form, consists of two premises. The major premise alleges that we are committed to mathematical objects if science requires them. The minor premise alleges that science in fact (...) requires mathematical objects. The most common rejection of the argument denies its minor premise by introducing scientific theories which do not refer to mathematical objects. Hartry Field has shown how we can reformulate some physical theories without mathematical commitments. I argue that Field’s preference for intrinsic explanation, which underlies his reformulation, is ill-motivated, and that his resultant fictionalism suffers unacceptable consequences. I attack the major premise instead. I argue that Quine provides a mistaken criterion for ontic commitment. Our uses of mathematics in scientific theory are instrumental and do not commit us to mathematical objects. Furthermore, even if we accept Quine’s criterion for ontic commitment, the indispensability argument justifies only an anemic version of mathematics, and does not yield traditional mathematical objects. The first two chapters of the dissertation develop these results for Quine’s indispensability argument. In the third chapter, I apply my findings to other contemporary indispensabilists, specifically the structuralists Michael Resnik and Stewart Shapiro. In the fourth chapter, I show that indispensability arguments which do not rely on Quine’s holism, like that of Putnam, are even less successful. Also in Chapter 4, I show how Putnam’s work in the philosophy of mathematics is unified around the indispensability argument. In the last chapter of the dissertation, I conclude that we need an account of mathematical knowledge which does not appeal to empirical science and which does not succumb to mysticism and speculation. Briefly, my strategy is to argue that any defensible solution to the demarcation problem of separating good scientific theories from bad ones will find mathematics to be good, if not empirical, science. (shrink)

The conceptual building blocks suggested by developmental psychologists may yet play a role in how the human learner arrives at an understanding of natural number. The proposal of Rips et al. faces a challenge, yet to be met, faced by all developmental proposals: to describe the logical space in which learners ever acquire new concepts.

This book, in language accessible to the general reader, investigates twelve of the most notorious, most interesting, and most instructive episodes involving the interaction between science and Christianity, aiming to tell each story in its historical specificity and local particularity. Among the events treated in When Science and Christianity Meet are the Galileo affair, the seventeenth-century clockwork universe, Noah's ark and flood in the development of natural history, struggles over Darwinian evolution, debates about the origin of the human (...) species, and the Scopes trial. Readers will be introduced to St. Augustine, Roger Bacon, Pope Urban VIII, Isaac Newton, Pierre-Simon de Laplace, Carl Linnaeus, Charles Darwin, T. H. Huxley, Sigmund Freud, and many other participants in the historical drama of science and Christianity. (shrink)

Like other English-speaking peoples around the world, New Zealanders began debating Darwinism in the early 1860s, shortly after the publication of Charles Darwin's Origin of Species. Despite the opposition of some religious and political leaders – and even the odd scientist – biological evolution made deep inroads in a culture that increasingly identified itself as secular. The introduction of pro-evolution curricula and radio broadcasts provoked occasional antievolution outbursts, but creationism remained more an object of ridicule than a threat until the (...) last decades of the twentieth century, when first American and then Australian creationists began fomenting antievolutionism among New Zealanders. Although Stephen Jay Gould assured them in 1986 that they had little to fear from so-called scientific creationism, because it was a ‘peculiarly American’ phenomenon, scientific creationism by the mid-1990s had captured the allegiance of an estimated five per cent of the country and proved especially attractive to Maori and Pacific Islanders. In 1992 New Zealand creationists formed their own antievolution society, Creation Science. (shrink)

Originally published in 1995, The Selected Works of George McCready Price is the seventh volume in the series, Creationism in Twentieth Century America, reissued in 2019. The volume brings together the original writings and pamphlets of George McCready Price, a leading creationist of the early antievolution crusade of the 1920s. McCready Price labelled himself the 'principal scientific authority of the Fundamentalists' and as a self-taught scientist he enjoyed more scientific repute amongst fundamentalists of the time. This interesting and unique collection (...) of original source material includes five of his writings between 1906 and 1924, challenging the new Darwinian theory of evolution and natural selection through his writings on the natural sciences. His literature covers the topics of evolution and biology and critiques biological arguments for evolution. He also wrote widely on geology offering his own alternative argument of 'flood geography' in opposition to the Darwinian theory concerning palaeontology and geology. This volume will be of interest to historians of natural history and the creationism movement, as well as scholars of religion and American history. (shrink)

Models of memory in cognitive science and philosophy have traditionally explained human remembering in terms of storage and retrieval. This tendency has been entrenched by reliance on computationalist explanations over the course of the twentieth century; even research programs that eschew computationalism in name, or attempt the revision of traditional models, demonstrate tacit commitment to computationalist assumptions. It is assumed that memory must be stored by means of an isomorphic trace, that memory processes must divide into conceptually distinct systems (...) and phases, and that human remembering consists in inner, cognitive processes that are implemented by distinct neural processes. This dissertation draws on recent empirical work, and on philosophical arguments from Ludwig Wittgenstein and others, to demonstrate that this latent computationalism in the study of memory is problematic, and that it can and should be eliminated. Cognitive psychologists studying memory have encountered numerous data in recent decades that belie archival models. In cognitive neuroscience, establishing the neural basis of storage and retrieval processes has proven elusive. A number of revised models on offer in memory science, that have taken these issues into account, fail to sufficiently extricate the archival framework. Several impasses in memory science are products of these underlying computationalist assumptions. Wittgenstein and other philosophers offer a number of arguments against the need for, and the efficacy of, the storage and retrieval of traces in human remembering. A study of these arguments clarifies the ways that these computationalist assumptions are presently impeding the science of memory, and provides ways forward in removing them. We can and should characterize and model human memory without invoking the storage and retrieval of traces. A range of work in connectionism, dynamical systems theory, and recent philosophical accounts of memory demonstrate how the science of memory can proceed without these assumptions, toward non-archival models of remembering. (shrink)

This chapter presents a historical analysis of pseudoscience, tracking down the coinage and currency of the term and explaining its shifting meaning in tandem with the emerging historical identity of science. The discussions cover the invention of pseudoscience; science and pseudoscience in the late nineteenth century; pseudoscience in the new century; and pseudoscience and its critics in the late twentieth century.