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.

"This book is an attempt at a not too technical scientists' philosophy of science" - Preface.

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.

String theory currently is the only viable candidate for a unified description of all known natural forces. This article tries to demonstrate that the fundamental structural and methodological differences that set string theory apart from other physical theories have important philosophical consequences. Focussing on implications for the realism debate in philosophy of science, it is argued that both poles of that debate face new problems in the context of string theory. On the one hand, the claim of underdetermination of scientific (...) theory by the available empirical data, which is a pivotal element of empiricism, loses much of its plausibility. On the other hand, the dissolution of any meaningful notion of an external ontological object destroys the basis for conventional versions of scientific realism. String theory seems to suggest an intermediate position akin to Structural Realism that is based on a newly emerging principle, to be called the principle of theoretical uniqueness. (shrink)

Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...) issues in the philosophy of mathematics; in particular it may help platonists respond to a recent challenge by Joseph Melia concerning the force of the Indispensability Argument. (shrink)

Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.

“What did the President know and when did he know it?”Senator Howard Baker, Watergate hearings, 1973Why do scientists accept or reject theories? More specifically: why do they change from one theory to another? What is the role of empirical tests in the evaluation of theories?This paper focuses on a narrowly-defined question: in judging theories, do scientists give greater weight (other things being equal) to successfulnovel predictionsthan to successful deductions of previously-known facts? The affirmative answer is called the “predictivist thesis” (Maher (...) 1988).It is primarily philosophers who are interested in this question, and they have treated it mostly as a normative or logical problem. Can the writings of historians of science tell us how scientists have treated novel predictions in the past? Until recently historians have rarely addressed this point. (shrink)

I will give arguments for why the enormous progress made during the last century on understanding elementary particles and their fundamental interactions suggests strings as the truly elementary constituents of Nature. I will then address the issue of whether the string paradigm can in principle be falsified or whether it should be considered as mere metaphysics.

"This book is an attempt at a not too technical scientists' philosophy of science" - Preface.

In The Origin of Species (1859) Darwin challenged many of the most deeply-held beliefs of the Western world. Arguing for a material, not divine, origin of species, he showed that new species are achieved by "natural selection." The Origin communicates the enthusiasm of original thinking in an open, descriptive style, and Darwin's emphasis on the value of diversity speaks more strongly now than ever. As well as a stimulating introduction and detailed notes, this edition offers a register of the many (...) writers referred to by Darwin in the text. (shrink)

Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just described (...) were the only ones possible, there could be no objection to this melding of numbers with genes and quarks. However, the position I call contrastive empiricism (Sober 1990a) stands opposed to both realism and to Van Fraassen's em- piricism. As it turns out, contrastive empiricism entails that coalesc- ing mathematics with empirical science is highly problematic. I believe that there is an important kernel of truth in abductive ar- guments for genes and quarks. But no counterpart argument exists for the case of numbers. Of course, the existence of this third way would be uninteresting, if contrastive empiricism were wholly implausible. However, I will argue that contrastive empiricism captures what makes sense in standard versions of realism and empiricism, while avoiding the excesses of each. This third way is a middle way; it cannot be dismissed out of hand. (shrink)

String theory is at the moment the only advanced approach to a unification of all interactions, including gravity. But, in spite of the more than 30 years of its existence, it does not make any empirically testable predictions, and it is completely unknown which physically interpretable principles could form the basis of string theory. At the moment, “string theory” is no theory at all, but rather a labyrinthic structure of mathematical procedures and intuitions. The only motivations for string theory consist (...) in the mutual incompatibility of the standard model of quantum field theory and of general relativity as well as in the metaphysics of the unification program of physics, aimed at a final unified theory of all interactions, including gravity. The article gives a perspective on the problems leading to and resulting from this situation. (shrink)

According to a standard view, predictions of new phenomena provide stronger evidence for a theory than explanations of old ones. More guardedly, a theory that predicts phenomena that did not prompt the initial formulation of that theory is better supported by those phenomena than is a theory by known phenomena that generated the theory in the first place. So say various philosophers of science, including William Whewell (1847) in the 19th century and Karl Popper (1959) in the 20th, to mention (...) just two.Stephen Brush takes issue with this on historical grounds. In a series of fascinating papers he argues that generally speaking scientists do not regard the fact that a theory predicts new phenomena, even ones of a kind totally different from those that prompted the theory in the first place, as providing better evidential support for that theory than is provided by already known facts explained by the theory. (shrink)

The theoretical physicist Paul Dirac rejected, explicitly on aesthetic grounds, a successful theory known as quantum electrodynamics (QED), which is the prototype for the family of theories known as quantum field theories (QFTs). Remarkably, the theoretical physicist Steven Weinberg, also largely on aesthetic grounds, supports QED and other QFTs. In order to evaluate these opposing aesthetic views a short introduction to the physical properties of QFTs is presented together with a detailed analysis of the aesthetic claims of Dirac and Weinberg. (...) It turns out that Dirac rejected QED, without regard to its success, because this theory fails to yield to what he perceived as beautiful mathematics, whereas Weinberg's support of QFTs is founded primarily on the physical concepts of the theories. In particular, he relies on symmetries that are the basis for the construction of the extremely successful current fundamental theories of particles physics. This success was decisive in leading to Weinberg's conviction of the beauty of QFTs. As a result of the evaluation of these approaches, the factors causing scientists to perceive a theory as being a fundamentally beautiful theory are discussed in detail. (shrink)

The thesis that scientists give greater weight to novel predictions than to explanations of known facts is tested against historical cases in physical science. Several theories were accepted after successful novel predictions but there is little evidence that extra credit was given for novelty. Other theories were rejected despite, or accepted without, making successful novel predictions. No examples were found of theories that were accepted primarily because of successful novel predictions and would not have been accepted if those facts had (...) been previously known. (shrink)

THE PHILOSOPHY OF THe INDUCTIVE SCIENCES. PART II. OF KNOWLEDGE. ' . VOL. II. ...