This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics ...

This chapter discusses various senses in which mathematics is applied to the material world. It distinguishes between canonical and noncanonical applications of mathematics, the former being those for which the mathematics was developed to deal with in the first place. It also distinguishes between empirical and nonempirical applications, thus yielding four different kinds of applications. Examples of each are provided, and philosophical problems connected with each are treated.

The first part of the essay describes how mathematics, in particular mathematical concepts, are applicable to nature. mathematical constructs have turned out to correspond to physical reality. this correlation between the world and mathematical concepts, it is argued, is a true phenomenon. the second part of this essay argues that the applicability of mathematics to nature is mysterious, in that not only is there no known explanation for the correlation between mathematics and physical reality, but there is a good reason (...) to except no such correlation. it is argued that there is a subjective element in the decision as to what constitutes a mathematical concept. a number of purported solutions to the mystery of the applicability of mathematics to nature are discarded, until we are left with eugene wigner's thesis that we are here confronted with a "miracle that we neither understand nor deserve.". (shrink)

Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the contributions of Hartry Field and Eugene Wigner. Finally, I argue (...) that there are epistemological problems concerning the applicability of mathematics that nobody in the philosophical community has yet confronted, though the problems are well known to physicists. (shrink)

During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e. , that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assigns to empirical regularities had profound implications for all (...) of his later philosophy; some of these implications (particularly to rule following) are addressed in the essay. (shrink)

A fundamental aspect of biological systems is their spatial organization. In development, regeneration and repair, directional signals are necessary for the proper placement of the components of the organism. Likewise, pathogens that invade other organisms rely on directional signals to target vulnerable areas. It is widely understood that chemical gradients are important directional signals in living systems. Less well recognized are electrical fields, which can also provide directional information. Small, steady electrical fields can directly guide cell movement and growth and (...) can generate chemical gradients of charged macromolecules against the leveling action of diffusion. At the site of a lesion in an ion‐transporting epithelium, for example, a substantial electrical field is instantly generated and may extend over many cell diameters. There are numerous other situations in which relatively long‐range electrical fields have been shown to exist naturally. Recently, there has been substantial progress in identifying specific processes that are controlled, to some extent, by these endogenous electrical fields. This review highlights these recent data and discusses possible mechanisms by which the fields might affect biological processes. BioEssays 25:759–766, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

Remarks on the Foundations of Mathematics, Wittgenstein, despite his official 'mathematical nonrevisionism', slips into attempting to refute Gödel's theorem. Actually, Wittgenstein could have used Gödel's theorem to good effect, to support his view that proof, and even truth, are 'family resemblance' concepts. The reason that Wittgenstein did not see all this is that Gödel's theorem had become an icon of mathematical realism, and he was blinded by his own ideology. The essay is a reply to Juliet Floyd's work on Gödel: (...) what she says Wittgenstein said, I say he should have said, but didn't (couldn't). (shrink)

Quine has expressed the view that the reduction of one mathematical theory to another is merely the "modeling" of the one in the other. i argue that, just as in the physical sciences, some reductions "explain" the phenomena they reduce in addition to "modeling" them; and that, conversely, "modeling" one theory in another may actually destroy the explanatory value of the former.

In recent years evolutionary theorists have been engaged in a protracted and bitter disagreement concerning how natural selection affects units such as genes, individuals, kin groups, and groups. Central to this debate has been whether selective pressures affecting group success can trump the selective pressures that confer advantage at the individual level. In short, there has been a debate about the utility of group selection, with noted theorist Steven Pinker calling the concept useless for the social sciences. We surveyed 175 (...) evolutionary anthropologists to ascertain where they stood in the debate. We found that most were receptive to group selection, especially in the case of cultural group selection. The survey also revealed that liberals and conservatives, and males and females, all displayed significant differences of opinion concerning which selective forces were important in humanity’s prehistory. We conclude by interpreting these findings in the context of recent research in political psychology. (shrink)

This chapter considers individual differences associated with alcohol effects. There is wide variability in subjective and other responses to alcohol. The sources of this variability include allelic variation in enzymes responsible for the metabolism of alcoholism, sensitivity, temperament, neurocognitive functioning, and social learning. These sources of heterogeneity in alcohol response appear to be very important not only in understanding the acute effects of alcohol on the individual but also in understanding risk processes underlying the development of alcohol use disorders.

Responding to volatile criticisms frequently leveled at Leo Strauss and those he influenced, the prominent contributors to this volume demonstrate the profound influence that Strauss and his students have exerted on American liberal democracy and contemporary political thought. By stressing the enduring vitality of classic books and by articulating the theoretical and practical flaws of relativism and historicism, the contributors argue that Strauss and the Straussians have identified fundamental crises of modernity and liberal democracy.