Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and philosophy of science, (...) the volume is a valuable reference for students and researchers. (shrink)

Steiner defines naturalism in opposition to anthropocentrism, the doctrine that the human mind holds a privileged place in the universe. He assumes the anthropocentric nature of mathematics and argues that physicists' employment of mathematically guided strategies in the discovery of quantum mechanics challenges scientists' naturalism. In this paper I show that Steiner's assumption about the anthropocentric character of mathematics is questionable. I draw attention to mathematicians' rejection of what Maddy calls ‘definabilism’, a methodological maxim governing the development of mathematics. I (...) contend that because definabilism is anthropocentric, its rejection casts doubts on Steiner's assumption. (shrink)

In this paper, I motivate the view that quantitative parsimony is a theoretical virtue: that is, we should be concerned not only to minimize the number of kinds of entities postulated by our theories (i. e. maximize qualitative parsimony), but we should also minimize the number of entities postulated which fall under those kinds. In order to motivate this view, I consider two cases from the history of science: the postulation of the neutrino and the proposal of Avogadro's hypothesis. I (...) also consider two issues concerning how a principle of quantitative parsimony should be framed. (shrink)

Hermann Weyl succeeded in presenting a consistent overarching analysis that accounts for symmetry in material artifacts, natural phenomena, and physical theories. Weyl showed that group theory is the underlying mathematical structure for symmetry in all three domains. But in this study Weyl did not include appeals to symmetry arguments which, for example, Einstein expressed as “for reasons of symmetry”. An argument typically takes the form of a set of premises and rules of inference that lead to a conclusion. Symmetry may (...) enter an argument both in the premises and the rules of inference, and the resulting conclusion may also exhibit symmetrical properties. Taking our cue from Pierre Curie, we distinguish two categories of symmetry arguments, axiomatic and heuristic; they will be defined and then illustrated by historical cases. (shrink)

A draft version of Chapter 11 of the edited volume 'Interpreting Bodies. Classical and Quantum Objects in Modern Physics',. The Chapter is devoted to illustrating the group-theoretic approach to the issue of physical objects. In particular, the Chapter discusses the group-theoretic constitution of classical and quantum particles in the nonrelativistic case.

The debate about the relative epistemic weights carried in favour of a theory by predictions of new phenomena as opposed to accommodations of already known phenomena has a long history. We readdress the issue through a detailed re-examination of a particular historical case that has often been discussed in connection with it—that of Mendeleev and the prediction by his periodic law of the three ‘new’ elements, gallium, scandium and germanium. We find little support for the standard story that these predictive (...) successes were outstandingly important in the success of Mendeleev's scheme. Accommodations played an equal role—notably that of argon, the first of the ‘noble gases’ to be discovered; and the methodological situation in this chemical example turns out to be in interesting ways different from that in other cases—invariably from physics—that have been discussed in this connection. The historical episode when accurately analysed provides support for a different account of the relative weight of prediction and accommodation—one that is further articulated here. (shrink)

Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.