Leon Horsten

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics

This article discusses Peter Galison's views on the structure and evolution of experimental and instrumental cultures in 20th century particle physics, which are unfolded in his recent book Image and Logic. A Material Culture of Microphysics. First a description is given of the uncomfortable predicament in which the Kuhnian tradition finds itself in the past two decades. It is then explained how Galison distinguishes a layered structure in the practice of modern particle physics. Physics as a practice consists of three relatively autonomous levels: the experimental level, the instrumental level and the theoretical level. This paper focuses mainly (but not exclusively) on the instrumental level in particle physics. Subsequently an analysis is given of Galison's metaphor of the wall, which Galison offers as an alternative to the Kuhnian image of paradigms and scientific revolutions. Galison's model is also compared with Laudan's reticulational model of the evolution of scientific research traditions. To conclude, an analysis is made of Galison's attempt to solve the incommensurability problem