This book offers a philosophy for error-prone humans trying to understand messy systems in the real world.

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, (...) linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability. (shrink)

Despite the promises made by molecular evolutionists since the early 1960s that phylogenies would be readily reconstructed using molecular data, the construction of molecular phylogenies has both retained many methodological problems of the past and brought up new ones of considerable epistemic relevance. The field is driven not only by changes in knowledge about the processes of molecular evolution, but also by an ever-present methodological anxiety manifested in the constant search for an increased objectivity—or in its converse, the avoidance of (...) subjectivity.This paper offers an exhaustive account of the methodological and conceptual difficulties embedded in each of the steps required to elaborate molecular phytogenies. The authors adopt a historical perspective on the field in order to follow the development of practices that seek to increase the objectivity of their methods and representations. These include the adoption and development of explicit criteria for evaluation of evidence, and of procedures associated with methods of statistical inference, quantification and automation. All these are linked to an increasing use of computers in research since the mid 1960s. We will show that the practices of objectivity described are highly dependent on the problems and tools of molecular phylogenetics. (shrink)

"Legend is overdue for replacement, and an adequate replacement must attend to the process of science as carefully as Hull has done. I share his vision of a serious account of the social and intellectual dynamics of science that will avoid both the rosy blur of Legend and the facile charms of relativism.... Because of [Hull's] deep concern with the ways in which research is actually done, Science as a Process begins an important project in the study of science. It (...) is one of a distinguished series of books, which Hull himself edits."—Philip Kitcher, Nature "In Science as a Process, [David Hull] argues that the tension between cooperation and competition is exactly what makes science so successful.... Hull takes an unusual approach to his subject. He applies the rules of evolution in nature to the evolution of science, arguing that the same kinds of forces responsible for shaping the rise and demise of species also act on the development of scientific ideas."—Natalie Angier, New York Times Book Review "By far the most professional and thorough case in favour of an evolutionary philosophy of science ever to have been made. It contains excellent short histories of evolutionary biology and of systematics (the science of classifying living things); an important and original account of modern systematic controversy; a counter-attack against the philosophical critics of evolutionary philosophy; social-psychological evidence, collected by Hull himself, to show that science does have the character demanded by his philosophy; and a philosophical analysis of evolution which is general enough to apply to both biological and historical change."—Mark Ridley, Times Literary Supplement "Hull is primarily interested in how social interactions within the scientific community can help or hinder the process by which new theories and techniques get accepted.... The claim that science is a process for selecting out the best new ideas is not a new one, but Hull tells us exactly how scientists go about it, and he is prepared to accept that at least to some extent, the social activities of the scientists promoting a new idea can affect its chances of being accepted."—Peter J. Bowler, Archives of Natural History "I have been doing philosophy of science now for twenty-five years, and whilst I would never have claimed that I knew everything, I felt that I had a really good handle on the nature of science, Again and again, Hull was able to show me just how incomplete my understanding was.... Moreover, [Science as a Process] is one of the most compulsively readable books that I have ever encountered."—Michael Ruse, Biology and Philosophy. (shrink)

This paper is based on my M.Sc. dissertation: ‘The Origins of Numerical Taxonomy’ 1985, submitted to the University of Leicester during the tenure of a D.E.S. State Studentship. For this work I drew extensively on interviews with Professors A. J. Cain, G. A. Harrison, R. R. Sokal and P. H. A. Sneath. I am very grateful to them for their time, interest and encouragement. Without the indefatigable assistance of Jon Harwood, this paper would never have been finished.

Exact sciences are described as sciences whose theories are formalized. These are contrasted to inexact sciences, whose theories are not formalized. Formalization is described as a broader category than mathematization, involving any form/content distinction allowing forms, e.g., as represented in theoretical models, to be studied independently of the empirical content of a subject-matter domain. Exactness is a practice depending on the use of theories to control subject-matter domains and to align theoretical with empirical models and not merely a state of (...) a science. Inexact biological sciences tolerate a degree of “mismatch” between theoretical and empirical models and concepts. Three illustrations from biological sciences are discussed in which formalization is achieved by various means: Mendelism, Weismannism, and Darwinism. Frege’s idea of a “conceptual notation” is used to further characterize the notion of a form/content distinction. (shrink)

Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by (...) Mark Steiner), according to which a genuine MES incorporates an explanatory proof of the mathematical result being used. The central case study involves an explanation for why bees build the cells of their honeycombs in the shape of hexagons. I make a distinction between two kinds of MES, mathematics-driven explanation in science and science-driven mathematical explanation, and argue that it is the second category which is both scientifically and philosophical more central. I conclude that the explanatory relation involved in MES is genuinely scientific and hence that the phenomenon of MES poses a challenge to general accounts of scientific explanation. (shrink)

The twentieth century witnessed a dramatic increase in the use of statistics by biologists, including systematists. The modern synthesis and new systematics stimulated this development, particularly after World War II. The rise of "the statistical frame of mind " resulted in a rethinking of the relationship between biological and mathematical points of view, the roles of objectivity and subjectivity in systematic research, the implications of new computing technologies, and the place of systematics among the biological disciplines.

"--Joel Cracraft, American Museum of Natural History "This is not the potted history that one usually finds in texts and review articles.

One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. (...) Not only does mathematics help with empirical predictions, it allows elegant and economical statement of many theories. Indeed, so important is the language of mathematics to science, that it is hard to imagine how theories such as quantum mechanics and general relativity could even be stated without employing a substantial amount of mathematics. (shrink)

WE HAVE LEARNED in the preceding chapter that a revolutionary change of the species concept is in the making, a change which not only affects taxonomic procedure, but which also contributes considerably toward a better understanding of ...

This paper explores the work of Nicolas Rashevsky, a Russian émigré theoretical physicist who developed a program in "mathematical biophysics" at the University of Chicago during the 1930s. Stressing the complexity of many biological phenomena, Rashevsky argued that the methods of theoretical physics -- namely mathematics -- were needed to "simplify" complex biological processes such as cell division and nerve conduction. A maverick of sorts, Rashevsky was a conspicuous figure in the biological community during the 1930s and early 1940s: he (...) participated in several Cold Spring Harbor symposia and received several years of funding from the Rockefeller Foundation. However, in contrast to many other physicists who moved into biology, Rashevsky's work was almost entirely theoretical, and he eventually faced resistance to his mathematical methods. Through an examination of the conceptual, institutional, and scientific context of Rashevsky's work, this paper seeks to understand some of the reasons behind this resistance. (shrink)