Brian Hepburn

1. Overview and organizing themes 2. Historical Review: Aristotle to Mill 3. Logic of method and critical responses 3.1 Logical constructionism and Operationalism 3.2. H-D as a logic of confirmation 3.3. Popper and falsificationism 3.4 Meta-methodology and the end of method 4. Statistical methods for hypothesis testing 5. Method in Practice 5.1 Creative and exploratory practices 5.2 Computer methods and the ‘third way’ of doing science 6. Discourse on scientific method 6.1 “The scientific method” in science education and as seen by scientists 6.2 Privileged methods and ‘gold standards’ 6.3 Scientific method in the court room 6.4 Deviating practices 7. Conclusion Bibliography Academic Tools Other Internet Resources Related Entries

This article explores the relation between the concept of symmetry and its formalisms. The standard view among philosophers and physicists is that symmetry is completely formalized by mathematical groups. For some mathematicians however, the groupoid is a competing and more general formalism. An analysis of symmetry that justifies this extension has not been adequately spelled out. After a brief explication of how groups, equivalence, and symmetries classes are related, we show that, while it’s true in some instances that groups are too restrictive, there are other instances for which the standard extension to groupoids is too un restrictive. The connection between groups and equivalence classes, when generalized to groupoids, suggests a middle ground between the two. *Received July 2007. †To contact the authors, please write to: Alexandre Guay, UFR Sciences et Techniques, Université de Bourgogne, 9 Avenue Alain Savary, 21078 Dijon Cedex, France; e‐mail: [email protected] ; or to Brian Hepburn, Department of Philosophy, University of British Columbia, 1866 Main Mall E370, Vancouver, BC, Canada V6T 1Z1; e‐mail: [email protected].

Euler’s ‘On the force of percussion and its true measure’, published in 1746, shows that not only had the issue of vis viva not been settled, but that the concepts of inertia and even force were still very much up for grabs. This paper details Euler’s treatment of the vis viva problem. Within those details we find differences between his physics and that of Newton, in particular the rejection of empty space and reduction of all forces to the operation of inertia through contact. One can further see how Euler’s philosophy of science embraced explanation through mechanisms and equilibrium conditions.Keywords: Leonhard Euler; Vis viva; Equlibrium; Mechanics; Eighteenth century.

I criticize Shimony's argument from the Transient Now (Shimony 1993) that the B-series view of time is inadequate but offer a reading of that argument that is more charitable than one offered and rejected by Eilstein (1996). Shimony's argument turns on putative phenomenological features of the Now (singularity and numerical identity) but transience only arises as a logical implication of those features. Transience is thus a second order phenomenon. If these two features are accurate then the B-series cannot provide a complete account of the Now and Eilstein misses the role of Shimony's Phenomenological Principle (PP) in this regard. Holding a B-theoretic view then demands giving up the numerical identity of person-slices across time.

Here is a phrase never uttered before: ”Euler’s philosophy of science.” Known as an extraordinary mathematician first, a mathematical physicist Known as an extraordinary mathematician first, a mathematical physicist second, but never really a physicist — not enough empirical cred — no one has considered whether Euler had a philosophy of science. Even his famed “Letters to a Princess” is described as a somewhat naive parroting of New- ton. But Euler is no Newtonian. His philosophy of science borrows from Leibniz, a little from Descartes, but is best seen as continuous with the tradition of a Galilean interpre- tation of the world as consisting of interacting mechanisms, and the practice of letting the requirements of sound mechanical description and problem solving dictate metaphysics.

An intuitive and appealing way to characterize problem solving is as the application of constraints which reduce the problem-solution space. Any advantage offered by interdisciplinary problem solving would then plausi- bly derive from the integration of constraints from the fields involved. We propose an account of interdisciplinary problem solving which treats the integration of constraints as an iterative process. Appealing to a general- ization of entity-activity dualism from mechanical explanation, we extend the accounts of Bechtel and of Craver to non-hierarchical, non-life-science, interdisciplinary problem-solving. Integration of disciplines occurs at the level of fields and their explanatory frameworks.

A key theme in the historiographical work of Machamer has been the ways that motion is made intelligible through explanatory means of natural motion and models of the simple machines such as the lever and pendulum. One way of spelling out the explanatory value of these strategies is through the concept of equilibrium. Natural motion and simple machines allow the simplification of complex problems in terms of self-evident, intelligible equilibrium conditions. This chapter connects the theme of equilibrium and natural motion across Machamer’s work on mechanisms and mechanical explanation, on Aristotle, Galileo, Descartes and Newton, and on the pendulum and mental models. Just as equilibrium can be found within science, it also becomes a model of intelligibility for doing history and philosophy of science: a normative but objective representation of the important properties of science.