This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a (...) large extent, the story of philosophy of mathematics. (shrink)

Feminist science critics, in particular Sandra Harding, Carolyn Merchant, and Evelyn Fox Keller, claim that misogynous sexual metaphors played an important role in the rise of modern science. The writings of Francis Bacon have been singled out as an especially egregious instance of the use of misogynous metaphors in scientific philosophy. This paper offers a defense of Bacon.

Human beings have the unique ability to view the world in a detached way: We can think about the world in terms that transcend our own experience or interest, and consider the world from a vantage point that is, in Nagel's words, "nowhere in particular". At the same time, each of us is a particular person in a particular place, each with his own "personal" view of the world, a view that we can recognize as just one aspect of the (...) whole. How do we reconcile these two standpoints--intellectually, morally, and practically? To what extent are they irreconcilable and to what extent can they be integrated? Thomas Nagel's ambitious and lively book tackles this fundamental issue, arguing that our divided nature is the root of a whole range of philosophical problems, touching, as it does, every aspect of human life. He deals with its manifestations in such fields of philosophy as: the mind-body problem, personal identity, knowledge and skepticism, thought and reality, free will, ethics, the relation between moral and other values, the meaning of life, and death. Excessive objectification has been a malady of recent analytic philosophy, claims Nagel, it has led to implausible forms of reductionism in the philosophy of mind and elsewhere. The solution is not to inhibit the objectifying impulse, but to insist that it learn to live alongside the internal perspectives that cannot be either discarded or objectified. Reconciliation between the two standpoints, in the end, is not always possible. (shrink)

Published research findings are sometimes refuted by subsequent evidence, says Ioannidis, with ensuing confusion and disappointment.

The terms ``objectivity'''' and ``objective'''' are among the mostused yet ill-defined terms in the philosophy of science and epistemology. Common to all thevarious usages is the rhetorical force of ``I endorse this and you should too'''', orto put it more mildly, that one should trust the outcome of the objectivity-producing process.The persuasive endorsement and call to trust provide some conceptual coherenceto objectivity, but the reference to objectivity is hopefully not merely an attemptat persuasive endorsement. What, in addition to epistemological endorsement,does (...) objectivity carry with it? Drawing on recent historical and philosophical work,I articulate eight operationally accessible and distinct senses of objectivity.While there are links among these senses, providing cohesion to the concept, I argue thatnone of the eight senses is strictly reducible to the others, giving objectivity itsirreducible complexity. (shrink)

Ecology's reputation as a holistic science is partly due to widespread misconceptions of its nature as well as shortcomings in its methodology. This article argues that the pursuit of empirical laws of ecology can foster the emergence of a more unified and predictive science based on complementary modes of explanation. Numerical analyses of population dynamics have a distinguished pedigree, spatial analyses generate predictive laws of macroecology, and physical analyses are typically pursued by the ecosystem paradigm. The most characteristically ecological laws, (...) however, are found in biotic analyses in the functional trait paradigm. Holistic credentials for ecology may thus be restored on two bases: its accommodating complementary modes of analysis and explanation, and its having some laws within the least reductionistic mode consistent with its subject matter. These claims, grounded in the aspectual theory of Herman Dooyeweerd, lead to some suggestions for enhancing the versatility and usefulness of ecology—and other sciences—by balancing different research paradigms under a holistic vision. (shrink)

Objectivity has a history, and it is full of surprises. In Objectivity, Lorraine Daston and Peter Galison chart the emergence of objectivity in the mid-nineteenth-century sciences--and show how the concept differs from its alternatives, truth-to-nature and trained judgment. This is a story of lofty epistemic ideals fused with workaday practices in the making of scientific images. From the eighteenth through the early twenty-first centuries, the images that reveal the deepest commitments of the empirical sciences--from anatomy to crystallography--are those featured in (...) scientific atlases, the compendia that teach practitioners what is worth looking at and how to look at it. Galison and Daston use atlas images to uncover a hidden history of scientific objectivity and its rivals. Whether an atlas maker idealizes an image to capture the essentials in the name of truth-to-nature or refuses to erase even the most incidental detail in the name of objectivity or highlights patterns in the name of trained judgment is a decision enforced by an ethos as well as by an epistemology. As Daston and Galison argue, atlases shape the subjects as well as the objects of science. To pursue objectivity--or truth-to-nature or trained judgment--is simultaneously to cultivate a distinctive scientific self wherein knowing and knower converge. Moreover, the very point at which they visibly converge is in the very act of seeing not as a separate individual but as a member of a particular scientific community. Embedded in the atlas image, therefore, are the traces of consequential choices about knowledge, persona, and collective sight. Objectivity is a book addressed to anyone interested in the elusive and crucial notion of objectivity-- and in what it means to peer into the world scientifically. Lorraine Daston is Director at the Max Planck Institute for the History of Science in Berlin, Germany. She is the coauthor of Wonders and the Order of Nature, 1150-1750 and the editor of Things That Talk: Object Lessons from Art and Science. Peter Galison is Pellegrino University Professor of the History of Science and of Physics at Harvard University. He is the author of Einstein's Clocks, Poincaré's Maps: Empires of Time, How Experiments End, and Image and Logic: A Material Culture of Microphysics, and other books, and coeditor of The Architecture of Science. (shrink)

Background: Randomised controlled trials (RCTs) are commonly viewed as the best research method to inform public health and social policy. Usually they are thought of as providing the most rigorous evidence of a treatment’s effectiveness without strong assumptions, biases and limitations. Objective: This is the first study to examine that hypothesis by assessing the 10 most cited RCT studies worldwide. Data sources: These 10 RCT studies with the highest number of citations in any journal were identified by searching Scopus (the (...) largest database of peer-reviewed journals). Results: This study shows that these world-leading RCTs that have influenced policy produce biased results by illustrating that participants’ background traits that affect outcomes are often poorly distributed between trial groups, that the trials often neglect alternative factors contributing to their main reported outcome and, among many other issues, that the trials are often only partially blinded or unblinded. The study here also identifies a number of novel and important assumptions, biases and limitations not yet thoroughly discussed in existing studies that arise when designing, implementing and analysing trials. Conclusions: Researchers and policymakers need to become better aware of the broader set of assumptions, biases and limitations in trials. Journals need to also begin requiring researchers to outline them in their studies. We need to furthermore better use RCTs together with other research methods. (shrink)